A Tale of Planet Formation: From Dust to Planets
RResearch in Astron. Astrophys.
Vol. No. , XX(9pp) doi:10.1088/1674-4527/20/10/XX R esearch in A stronomy and A strophysics A Tale of Planet Formation: From Dust to Planets
Beibei Liu , and Jianghui Ji , Zhejiang Institute of Modern Physics, Department of Physics & Zhejiang University-PurpleMountain Observatory Joint Research Center for Astronomy, Zhejiang University, 38 Zheda Road,Hangzhou 310027, China Department of Astronomy and Theoretical Physics, Lund Observatory, Box 43, SE–22100, Sweden CAS Key Laboratory of Planetary Sciences, Purple Mountain Observatory, Chinese Academy ofSciences, Nanjing 210008, China CAS Center for Excellence in Comparative Planetology, Hefei 230026, Chinaemail: [email protected], [email protected]
Received 2020 August 1; accepted 2020 September 4
Abstract
The characterization of exoplanets and their birth protoplanetary disks has enor-mously advanced in the last decade. Benefitting from that, our global understanding of theplanet formation processes has been substantially improved. In this review, we first sum-marize the cutting-edge states of the exoplanet and disk observations. We further presenta comprehensive panoptic view of modern core accretion planet formation scenarios, in-cluding dust growth and radial drift, planetesimal formation by the streaming instability,core growth by planetesimal accretion and pebble accretion. We discuss the key conceptsand physical processes in each growth stage and elaborate on the connections betweentheoretical studies and observational revelations. Finally, we point out the critical ques-tions and future directions of planet formation studies.
Key words: planets and satellites: general – planets and satellites: formation – planetsand satellites: dynamical evolution and stability – protoplanetary disks
In this article, we review modern planet formation scenarios in the context of the core accretionparadigm. Since observation and theory are two closely-related aspects, we first recap the detectionand characterization of exoplanets in Sect. 1.1 and protoplanetary disks in Sect. 1.2. The outline of gen-eral planet formation processes are given in Sect. 1.3, classified by the characteristic sizes of growingplanetary bodies. Finally, we introduce the relevant topics that will be covered in the subsequent sectionsof the paper.
Half of the
Nobel Prize in Physics was awarded to Michel Mayor and Didier Queloz, as an ac-knowledgement for their milestone discovery of the first exoplanet orbiting a main-sequence star. Thisis one of the most influential scientific breakthroughs in astronomy of the past decades. Already in 1995,the above two astronomers detected the exoplanet Pegasi b around a nearby, Sun-like star in the con-stellation of Pegasus (Mayor & Queloz 1995). Such a discovery was extraordinary and unexpected atthat time. It opened an entirely new era in astronomical observations. After that, the detection of planets a r X i v : . [ a s t r o - ph . E P ] N ov B. Liu & J. H. Ji : From Dust to Planets beyond our Solar System has been enormously developed and grown into a rapidly evolving branch inastronomy.One major exoplanet detection method is called radial velocity (RV, or Doppler spectroscopy). Astar and its accompanying planet co-orbit their center of mass. Observers can see the periodic movementof the star induced by the planet. Due to the Doppler effect, the observed stellar spectral lines areblueshifted when the star approaches us and are red shifted when the star recedes from us. Therefore,the radial velocity of the star can be acquired by measuring the displacement of stellar spectral lines.Through this technique, the minimum mass of the planet can be obtained. Since we do not really observethe planet but infer it from the wobble of the central star, this is an indirect way to acquire informationabout the planet. The first exoplanet, Pegasi b, was discovered by this method. Also, the radialvelocity method was involved in most of the exoplanet discoveries in the early planet-hunting epochbefore the launch of the Kepler satellite.Another leading exoplanet detection method is called transit, which monitors the time variationof a star’s brightness to probe the existence of planet(s). When a planet transits in front of its parentstar, the surface of the star is partially blocked by the planet and hence the observed stellar flux dropsaccordingly. This periodic decrement in the stellar flux reflects the size ratio between the planet andthe star. Therefore, this method can uniquely determine the radius of the planet. Compared to RV thatrequires high resolution spectroscopic measurements, transit is a photometric method, and is thus moreefficient in detecting planets. Combining the above two methods together, we can know both the massesand radii, and therefore deduce the bulk densities and chemical compositions of the planets.The Kepler satellite is recognized as the most successful planet hunting mission to date, whichutilized transit in space to maximize the detection ability and efficiency (Borucki et al. 2010). Thekey to the success of the Kepler telescope is that it has both a large field of view and extremely highphotometric precisions. More than confirmed exoplanets and planet candidates were detectedby Kepler during its nine year operational lifetime ( - ). Thanks to the vastly increased numberof exoplanets detected by Kepler, the analysis of planet properties from a statistical perspective hasbecome feasible for the first time (Lissauer et al. 2011; Batalha et al. 2013; Burke et al. 2014).The observed planets are incredibly diverse in terms of masses, sizes, compositions and orbitalproperties. As illustrated in Figure 1, the confirmed exoplanets span several orders of magnitude intheir masses and orbital periods . Based on the above two properties, exoplanets can be classifiedinto the following types: hot Jupiters (Mayor et al. 1997), cold Jupiters (Zhu & Wu 2018), warm (hot)Neptunes (Dong et al. 2018), super-Earths (Borucki et al. 2011) and low-mass rocky planets. Figure 1also marks one particular type of planets with orbital periods less than day, which are called ultra-short period (USP) planets (Sanchis-Ojeda et al. 2014; Winn et al. 2018). Super-Earths strictly referto the planets with . Nobel Prize in Physics was awarded to Michel Mayor and Didier Queloz, as an ac-knowledgement for their milestone discovery of the first exoplanet orbiting a main-sequence star. Thisis one of the most influential scientific breakthroughs in astronomy of the past decades. Already in 1995,the above two astronomers detected the exoplanet Pegasi b around a nearby, Sun-like star in the con-stellation of Pegasus (Mayor & Queloz 1995). Such a discovery was extraordinary and unexpected atthat time. It opened an entirely new era in astronomical observations. After that, the detection of planets a r X i v : . [ a s t r o - ph . E P ] N ov B. Liu & J. H. Ji : From Dust to Planets beyond our Solar System has been enormously developed and grown into a rapidly evolving branch inastronomy.One major exoplanet detection method is called radial velocity (RV, or Doppler spectroscopy). Astar and its accompanying planet co-orbit their center of mass. Observers can see the periodic movementof the star induced by the planet. Due to the Doppler effect, the observed stellar spectral lines areblueshifted when the star approaches us and are red shifted when the star recedes from us. Therefore,the radial velocity of the star can be acquired by measuring the displacement of stellar spectral lines.Through this technique, the minimum mass of the planet can be obtained. Since we do not really observethe planet but infer it from the wobble of the central star, this is an indirect way to acquire informationabout the planet. The first exoplanet, Pegasi b, was discovered by this method. Also, the radialvelocity method was involved in most of the exoplanet discoveries in the early planet-hunting epochbefore the launch of the Kepler satellite.Another leading exoplanet detection method is called transit, which monitors the time variationof a star’s brightness to probe the existence of planet(s). When a planet transits in front of its parentstar, the surface of the star is partially blocked by the planet and hence the observed stellar flux dropsaccordingly. This periodic decrement in the stellar flux reflects the size ratio between the planet andthe star. Therefore, this method can uniquely determine the radius of the planet. Compared to RV thatrequires high resolution spectroscopic measurements, transit is a photometric method, and is thus moreefficient in detecting planets. Combining the above two methods together, we can know both the massesand radii, and therefore deduce the bulk densities and chemical compositions of the planets.The Kepler satellite is recognized as the most successful planet hunting mission to date, whichutilized transit in space to maximize the detection ability and efficiency (Borucki et al. 2010). Thekey to the success of the Kepler telescope is that it has both a large field of view and extremely highphotometric precisions. More than confirmed exoplanets and planet candidates were detectedby Kepler during its nine year operational lifetime ( - ). Thanks to the vastly increased numberof exoplanets detected by Kepler, the analysis of planet properties from a statistical perspective hasbecome feasible for the first time (Lissauer et al. 2011; Batalha et al. 2013; Burke et al. 2014).The observed planets are incredibly diverse in terms of masses, sizes, compositions and orbitalproperties. As illustrated in Figure 1, the confirmed exoplanets span several orders of magnitude intheir masses and orbital periods . Based on the above two properties, exoplanets can be classifiedinto the following types: hot Jupiters (Mayor et al. 1997), cold Jupiters (Zhu & Wu 2018), warm (hot)Neptunes (Dong et al. 2018), super-Earths (Borucki et al. 2011) and low-mass rocky planets. Figure 1also marks one particular type of planets with orbital periods less than day, which are called ultra-short period (USP) planets (Sanchis-Ojeda et al. 2014; Winn et al. 2018). Super-Earths strictly referto the planets with . Orbital period /d Warm-NeptunesHot-Jupiters USP planets Cold-Jupiters Super-Earths P l a n e t a r y m a ss M p / M Rocky planets ⊕ Fig. 1: Orbital period and mass distribution of exoplanet populations, including hot Jupiters, coldJupiters, warm-Neptunes, super-Earths and rocky-dominated terrestrial planets. A special type of planetwith orbital period less than day is called an ultra-short period (USP) planet. Figure adopted from Ji& Huang (2020). – The occurrence rate of giant planets exhibits strong dependences on both stellar mass (Johnsonet al. 2007, 2010; Jones et al. 2016) and metallicity (Santos et al. 2004; Fischer & Valenti 2005;Sousa et al. 2011). The occurrence rate of super-Earth seems to be much more weakly dependent onstellar metallicity (Sousa et al. 2008; Buchhave et al. 2012, 2014; Wang & Fischer 2015; Schlaufman2015; Zhu et al. 2016; Zhu 2019). Nevertheless, super-Earths are even more abundant around M-dwarfs compared to those around Sun-like stars (Howard et al. 2012; Bonfils et al. 2013; Dressing& Charbonneau 2015; Mulders et al. 2015; Yang et al. 2020). – Hot Jupiters are nearly circular while the mean eccentricity of cold Jupiters is ∼ . (Marcy et al.2005). Obliquity defines the angle between the spin axis of the host star and the orbital angular mo-mentum axis of the planet, which can be measured through the Rossiter-McLaughlin effect (Winn2010). Many hot Jupiters manifest high obliquities, sometimes even polar or retrograde (Triaud et al.2010; Albrecht et al. 2012). Theoretically, hot Jupiters were proposed to grow at further out disklocations and then migrate inward to the present-day orbits (Lin et al. 1996). Planet-disk interactionwill lead the giant planets on circular and coplanar orbits (Lin & Papaloizou 1993; Artymowicz1993; Ward 1997; Nelson et al. 2000), while the high eccentricities and inclinations of giant planetscan originate from a Kozai-Lidov cycle (Kozai 1962; Lidov 1962) induced by a distant compan-ion (Wu & Murray 2003; Fabrycky & Tremaine 2007; Naoz et al. 2011, 2013; Dong et al. 2014;Anderson et al. 2016) or planet-planet scatterings (Rasio & Ford 1996; Chatterjee et al. 2008; Juri´c& Tremaine 2008; Ford & Rasio 2008; Dawson & Murray-Clay 2013). The latter two planetary dy-namical processes could result in the observed high obliquities. On the other hand, such misalign-ments could also arise from re-orientation of the host star’s spin through internal waves (Rogers B. Liu & J. H. Ji : From Dust to Planets et al. 2012; Lai 2012) or tilted protoplanetary disks through binary-disk interactions (Lai 2014;Matsakos & K¨onigl 2017; Zanazzi & Lai 2018). – Based on Kepler data, multi-transit systems have relatively low eccentricities and inclinations whilesingle-transit systems exhibit much higher eccentricities and inclinations (Tremaine & Dong 2012;Johansen et al. 2012; Fabrycky et al. 2014; Xie et al. 2016; Zhu et al. 2018). One hypothesis is thatthese single-transit planets come from multiple systems. Their orbits are further excited/disruptedby long-term planet-planet interactions or by outer companions, causing them to appear as “singles”in transit surveys (Pu & Wu 2015; Lai & Pu 2017; Mustill et al. 2017). – Hot Jupiters/Neptunes seldom have nearby companions up to a few AUs (Steffen et al. 2012; Donget al. 2018), consistent with the Kozai-Lidov cycle and planet-planet scattering scenarios (Mustillet al. 2015). On the contrary, nearly half of warm Jupiters co-exist with low-mass planets (Huanget al. 2016). Cold Jupiters also seem to be commonly accompanied by close-in, super-Earths (Zhu& Wu 2018; Bryan et al. 2019). Besides, − of the systems with a cold Jupiter are found tohost additional giant planets (Wright et al. 2009; Wittenmyer et al. 2020). – The period ratios of adjacent planet pairs neither show strong pile-ups at mean motion resonances(MMRs) nor uniform distribution in Kepler data. These planets exhibit an asymmetric distributionaround major resonances, such as : and : MMRs (Figure 6 of Winn & Fabrycky 2015). Differentscenarios are proposed to explain the above features, including tidal damping (Lithwick & Wu 2012;Batygin & Morbidelli 2013; Lee et al. 2013; Delisle & Laskar 2014; Xie 2014), retreat of the innermagnetospheric cavity (Liu et al. 2017; Liu & Ormel 2017), resonant overstability (Goldreich &Schlichting 2014), interaction with planetesimals (Chatterjee & Ford 2015), stochastic migration inhighly turbulent disks (Rein 2012; Batygin & Adams 2017) or in shock-generated inviscid disks(McNally et al. 2019; Yu et al. 2010), mass growth of a planet (Petrovich et al. 2013; Wang &Ji 2017), and dynamical instability of tightly packed planetary chains (Izidoro et al. 2017, 2019;Ogihara et al. 2015, 2018). – The occurrence rate of close-in super-Earths has a bimodal radius distribution, with a factor of twodrop at R p ∼ . − R ⊕ (Fulton et al. 2017; Fulton & Petigura 2018; Van Eylen et al. 2018). Thisso-called planetary radius valley implies a composition transition from rocky planets without H / He gaseous envelopes to planets with envelopes of a few percent in mass (Lopez & Fortney 2013; Owen& Wu 2013). The above radius gap can be explained by the gas mass loss due to stellar photoevap-oration (Owen & Wu 2017; Jin & Mordasini 2018) or core-powered heating (Ginzburg et al. 2018;Gupta & Schlichting 2019). Besides, giant impacts may also contribute to this compositional diver-sity by striping the planetary primordial atmospheres through disruptive collisions (Liu et al. 2015;Inamdar & Schlichting 2016). Based on the photoevaporation model, (Owen & Wu 2017) deducedthat the composition of these super-Earths are rocky dominated, ruling out low-density, water-worldplanets. Although this interpretation should be taken with caution, the water-deficit outcome may becaused by the fact that short-lived radionuclides dehydrate planetesimals during their early accretionphase (Lichtenberg et al. 2019), thermal effects take place in planetary interiors during long-termevolution phase (Vazan et al. 2018), or the planets experience a runaway greenhouse effect and losesubstantial surface water through photo-dissociation (Luger & Barnes 2015; Tian & Ida 2015).The above results are summarized based on the current demographic and orbital properties of ex-oplanets For knowledge of exoplanet atmospheres, we recommend a recent review by Zhang (2020).Figure 2 exhibits the launched and future planned space missions for exoplanet detection and charac-terization from the National Aeronautics and Space Administration (NASA), European Space Agency(ESA) and China National Space Administration/Chinese Academy of Sciences (CNSA/CAS). For in-stance, the successor of the Kepler mission, Transiting Exoplanet Survey Satellite (TESS) which waslaunched in , aims at discovering short period planets around nearby stars (Ricker et al. 2015;Huang et al. 2018a). Compared to Kepler, the advantage of TESS is that the target stars are easier forground-based and space-based follow-up characterization observations.On the other hand, three Chinese space missions have been initiated and approved for detection ofexoplanets in the coming decades. The Chinese Space Station Telescope (CSST), scheduled for launch . Liu & J. H. Ji. Liu & J. H. Ji Super-Earths P l a n e t a r y m a ss M p / M Rocky planets ⊕ Fig. 1: Orbital period and mass distribution of exoplanet populations, including hot Jupiters, coldJupiters, warm-Neptunes, super-Earths and rocky-dominated terrestrial planets. A special type of planetwith orbital period less than day is called an ultra-short period (USP) planet. Figure adopted from Ji& Huang (2020). – The occurrence rate of giant planets exhibits strong dependences on both stellar mass (Johnsonet al. 2007, 2010; Jones et al. 2016) and metallicity (Santos et al. 2004; Fischer & Valenti 2005;Sousa et al. 2011). The occurrence rate of super-Earth seems to be much more weakly dependent onstellar metallicity (Sousa et al. 2008; Buchhave et al. 2012, 2014; Wang & Fischer 2015; Schlaufman2015; Zhu et al. 2016; Zhu 2019). Nevertheless, super-Earths are even more abundant around M-dwarfs compared to those around Sun-like stars (Howard et al. 2012; Bonfils et al. 2013; Dressing& Charbonneau 2015; Mulders et al. 2015; Yang et al. 2020). – Hot Jupiters are nearly circular while the mean eccentricity of cold Jupiters is ∼ . (Marcy et al.2005). Obliquity defines the angle between the spin axis of the host star and the orbital angular mo-mentum axis of the planet, which can be measured through the Rossiter-McLaughlin effect (Winn2010). Many hot Jupiters manifest high obliquities, sometimes even polar or retrograde (Triaud et al.2010; Albrecht et al. 2012). Theoretically, hot Jupiters were proposed to grow at further out disklocations and then migrate inward to the present-day orbits (Lin et al. 1996). Planet-disk interactionwill lead the giant planets on circular and coplanar orbits (Lin & Papaloizou 1993; Artymowicz1993; Ward 1997; Nelson et al. 2000), while the high eccentricities and inclinations of giant planetscan originate from a Kozai-Lidov cycle (Kozai 1962; Lidov 1962) induced by a distant compan-ion (Wu & Murray 2003; Fabrycky & Tremaine 2007; Naoz et al. 2011, 2013; Dong et al. 2014;Anderson et al. 2016) or planet-planet scatterings (Rasio & Ford 1996; Chatterjee et al. 2008; Juri´c& Tremaine 2008; Ford & Rasio 2008; Dawson & Murray-Clay 2013). The latter two planetary dy-namical processes could result in the observed high obliquities. On the other hand, such misalign-ments could also arise from re-orientation of the host star’s spin through internal waves (Rogers B. Liu & J. H. Ji : From Dust to Planets et al. 2012; Lai 2012) or tilted protoplanetary disks through binary-disk interactions (Lai 2014;Matsakos & K¨onigl 2017; Zanazzi & Lai 2018). – Based on Kepler data, multi-transit systems have relatively low eccentricities and inclinations whilesingle-transit systems exhibit much higher eccentricities and inclinations (Tremaine & Dong 2012;Johansen et al. 2012; Fabrycky et al. 2014; Xie et al. 2016; Zhu et al. 2018). One hypothesis is thatthese single-transit planets come from multiple systems. Their orbits are further excited/disruptedby long-term planet-planet interactions or by outer companions, causing them to appear as “singles”in transit surveys (Pu & Wu 2015; Lai & Pu 2017; Mustill et al. 2017). – Hot Jupiters/Neptunes seldom have nearby companions up to a few AUs (Steffen et al. 2012; Donget al. 2018), consistent with the Kozai-Lidov cycle and planet-planet scattering scenarios (Mustillet al. 2015). On the contrary, nearly half of warm Jupiters co-exist with low-mass planets (Huanget al. 2016). Cold Jupiters also seem to be commonly accompanied by close-in, super-Earths (Zhu& Wu 2018; Bryan et al. 2019). Besides, − of the systems with a cold Jupiter are found tohost additional giant planets (Wright et al. 2009; Wittenmyer et al. 2020). – The period ratios of adjacent planet pairs neither show strong pile-ups at mean motion resonances(MMRs) nor uniform distribution in Kepler data. These planets exhibit an asymmetric distributionaround major resonances, such as : and : MMRs (Figure 6 of Winn & Fabrycky 2015). Differentscenarios are proposed to explain the above features, including tidal damping (Lithwick & Wu 2012;Batygin & Morbidelli 2013; Lee et al. 2013; Delisle & Laskar 2014; Xie 2014), retreat of the innermagnetospheric cavity (Liu et al. 2017; Liu & Ormel 2017), resonant overstability (Goldreich &Schlichting 2014), interaction with planetesimals (Chatterjee & Ford 2015), stochastic migration inhighly turbulent disks (Rein 2012; Batygin & Adams 2017) or in shock-generated inviscid disks(McNally et al. 2019; Yu et al. 2010), mass growth of a planet (Petrovich et al. 2013; Wang &Ji 2017), and dynamical instability of tightly packed planetary chains (Izidoro et al. 2017, 2019;Ogihara et al. 2015, 2018). – The occurrence rate of close-in super-Earths has a bimodal radius distribution, with a factor of twodrop at R p ∼ . − R ⊕ (Fulton et al. 2017; Fulton & Petigura 2018; Van Eylen et al. 2018). Thisso-called planetary radius valley implies a composition transition from rocky planets without H / He gaseous envelopes to planets with envelopes of a few percent in mass (Lopez & Fortney 2013; Owen& Wu 2013). The above radius gap can be explained by the gas mass loss due to stellar photoevap-oration (Owen & Wu 2017; Jin & Mordasini 2018) or core-powered heating (Ginzburg et al. 2018;Gupta & Schlichting 2019). Besides, giant impacts may also contribute to this compositional diver-sity by striping the planetary primordial atmospheres through disruptive collisions (Liu et al. 2015;Inamdar & Schlichting 2016). Based on the photoevaporation model, (Owen & Wu 2017) deducedthat the composition of these super-Earths are rocky dominated, ruling out low-density, water-worldplanets. Although this interpretation should be taken with caution, the water-deficit outcome may becaused by the fact that short-lived radionuclides dehydrate planetesimals during their early accretionphase (Lichtenberg et al. 2019), thermal effects take place in planetary interiors during long-termevolution phase (Vazan et al. 2018), or the planets experience a runaway greenhouse effect and losesubstantial surface water through photo-dissociation (Luger & Barnes 2015; Tian & Ida 2015).The above results are summarized based on the current demographic and orbital properties of ex-oplanets For knowledge of exoplanet atmospheres, we recommend a recent review by Zhang (2020).Figure 2 exhibits the launched and future planned space missions for exoplanet detection and charac-terization from the National Aeronautics and Space Administration (NASA), European Space Agency(ESA) and China National Space Administration/Chinese Academy of Sciences (CNSA/CAS). For in-stance, the successor of the Kepler mission, Transiting Exoplanet Survey Satellite (TESS) which waslaunched in , aims at discovering short period planets around nearby stars (Ricker et al. 2015;Huang et al. 2018a). Compared to Kepler, the advantage of TESS is that the target stars are easier forground-based and space-based follow-up characterization observations.On the other hand, three Chinese space missions have been initiated and approved for detection ofexoplanets in the coming decades. The Chinese Space Station Telescope (CSST), scheduled for launch . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 5 Kepler/K2SpitzerHubble TESS JWST Gaia CHEOPS ( a ) (b) (c) (d) (e) CoRot (f ) (g) (h) PLATO (i) ARIEL (j) MiYin NASAESACNSA/CAS (a)NASA/ESA Partnership(e)NASA/ESA/CSA Partnership(f)CNES/ESA Partnership China Space Station Telescope(CSST) Close-by Habitable Exoplanets Survey(CHES) Fig. 2: Launched and future-designed exoplanets exploration missions from NASA, ESA andCNSA/CAS. Credit: (a–e) NASA; (f-j) ESA. Figure adopted from Ji & Huang (2020).in , will survey mature Jupiter-like planets, Neptunes and super-Earths around solar-type stars us-ing a high-contrast imaging technique, which expects to discover tens of exoplanetary candidates andbrown dwarfs. The Closeby Habitable Exoplanet Survey (CHES) mission aims at searching for terres-trial planets in habitable zones around solar-type stars within pc by using astrometry in space. CHESwill observe the target stars with high astrometric precisions of microarcsecond at the Sun-Earth L point. The mission expects to discover at least Earth-like planets or super-Earths around FGKstars with well-determined masses and orbital parameters. Miyin, on the other hand, is designed for de-tecting habitable exoplanets around nearby stars with interferometry. To achieve direct imaging of theseexoplanets and assess their habitability, the mission will launch spacecrafts with groups of telescopesworking in the mid-infrared wavelengths, which ensures an extremely-high spatial resolution of . arcsecond. Planets form in protoplanetary disks surrounding their infant stars. Since the birth and growth of planetsare tightly related with their forming environment, studying the physical and chemical conditions ofprotoplantary disks becomes essential to understanding the planet formation processes. A large numberof young protoplanetary disks have been observed and extensively studied in literature. Here we brieflyintroduce the up-to-date observations of disk substructures and provide several hints for the existence ofemerging planets. Discussions on the disk solid masses and dust sizes will be presented in Sect. 2.2.Thanks to the unprecedentedly high sensitivity and angular resolution of the Atacama LargeMillimeter/submillimeter Array (ALMA), we now have the capability to reveal the disk structures ata spectacular level of detail. The spatial resolution of the resolved disks in nearby star forming regionsis approximately − AU. Axisymmetric rings, gaps, inner cavities and spirals are commonly observedamong these disks over a wide range of ages and masses of stellar hosts (Andrews et al. 2018; Huanget al. 2018b; Long et al. 2018). These disk substructures are in disagreement with the traditional pictureof a smooth disk profile. For instance, Figure 3(a) shows the disk of HL Tau with a series of concentricbright rings separated by faint gaps from the dust continuum emission (ALMA Partnership et al. 2015). B. Liu & J. H. Ji : From Dust to Planets There are different explanations for the formation of the above ring-like substructures. These fea-tures can be explained by grain growth (Zhang et al. 2015) or dust sintering (Okuzumi et al. 2016) atthe condensation fronts of major volatile species, zonal flows in magnetized disks (Flock et al. 2015), acombined effect of the above mechanisms (Hu et al. 2019) or secular gravitational instability (Takahashi& Inutsuka 2014). Apart from those interpretations, the most widely accepted scenario is that these sub-structures are induced by gap-opening planets (Pinilla et al. 2012b; Dipierro et al. 2015; Dong et al.2015c; Jin et al. 2016; Fedele et al. 2017; Liu et al. 2018; Zhang et al. 2018; Liu et al. 2019d; Erikssonet al. 2020). One important note is that, if these ring-like features are indeed the planet origin, the youngage of HL Tau ( t< Myr) implies that planet formation may be faster than previously thought. In ad-dition, this early formation hypothesis may also be supported by Harsono et al. (2018), who analyzedthe radial distributions of disk dust and gas around TMC1A and suggested that millimeter-sized grainshave already formed around such a young Class I object at an age of ∼ yr.In addition to the disk dust-component, the properties of gas, such as gas velocities, can also beobtained from molecular line emissions of CO isotopes. The kinematic deviations of gas velocitiesfrom Keplerian flows, together with the detected dust gaps at the same disk locations, strongly supportthe existence of embedded planets associated with gap-opening (Teague et al. 2018; Pinte et al. 2018,2020).The revealed spiral structures in disks from the scattered light images have been proposed to featuredifferent origins as well (Muto et al. 2012; Grady et al. 2012; Stolker et al. 2016; Benisty et al. 2016;Muro-Arena et al. 2020). For instance, these patterns can be explained by density waves excited by theplanets (Zhu et al. 2015; Dong et al. 2015b; Fung & Dong 2015; Bae & Zhu 2018). In the early phasewhen the disk is massive and self-gravitating, the gravitational instability can also induce large-scalespiral arms (Lodato & Rice 2005; Dong et al. 2015a). In addition, it might also be caused by the shadowfrom the warped disk (Montesinos et al. 2016), or a Rossby wave instability triggered vortex (Li et al.2000; Huang et al. 2019).Due to diverse explanations, previously mentioned disk kinematics could be treated as indirectindications of the planets. More straightforward evidence of young planets and ongoing planet formationis demonstrated as follows. The first clue comes from the RV measurements of young stars, where hotJupiter candidates are reported around CI Tau (Johns-Krull et al. 2016) and V Tau (Donati et al.2016). Furthermore, Plavchan et al. (2020) discovered a Neptune-sized planet co-existing with a debrisdisk around the nearby M dwarf star AU Mic by transit surveys. All above stars are in their pre-main-sequences with an age of approximately Myr. In addition, two embedded planets have been detectedin PDS ’s protoplanetary disk by using the high-contrast imager Spectro-Polarimetric High-contrastExoplanet REsearch (SPHERE) on European Southern Observatory’s Very Large Telescope (ESO’sVLT, Keppler et al. 2018; M¨uller et al. 2018). Figure 3(b) displays a synthetic image of the PDS system, where two planets reside inside the gap of their protoplanetary disk. This is the first time thatyoung planets have been directly imaged in their birth environment. Further analyses with submillimetercontinuum and resolved H α line emissions indicated the presence of a circumplanetary disk (Isella et al.2019) as well as the proceeding gas accretion onto planet (Haffert et al. 2019). All these findings,together with the previous results from the disk morphologies/kinematics, provide valuable constraintson how, when and where planets can form. The study of planet formation is a highly multi-scale and multi-physics subject. The size increment ofa planetary body varies by more than orders of magnitude, from (sub)micron-sized (dust grain) to > km (super-Earth/gas giant planet). It results in different physical mechanisms operating at differ-ent length scales and in different growth stages. We categorize the planetary bodies into four charac-teristic size objects: µ m-sized dust grains, millimeter/centimeter (mm/cm)-sized pebbles, -km-sized Donati et al. (2020) pointed out that the RV modulations of CI Tau may also be attributed to the stellar activity. . Liu & J. H. Ji. Liu & J. H. Ji AU Mic by transit surveys. All above stars are in their pre-main-sequences with an age of approximately Myr. In addition, two embedded planets have been detectedin PDS ’s protoplanetary disk by using the high-contrast imager Spectro-Polarimetric High-contrastExoplanet REsearch (SPHERE) on European Southern Observatory’s Very Large Telescope (ESO’sVLT, Keppler et al. 2018; M¨uller et al. 2018). Figure 3(b) displays a synthetic image of the PDS system, where two planets reside inside the gap of their protoplanetary disk. This is the first time thatyoung planets have been directly imaged in their birth environment. Further analyses with submillimetercontinuum and resolved H α line emissions indicated the presence of a circumplanetary disk (Isella et al.2019) as well as the proceeding gas accretion onto planet (Haffert et al. 2019). All these findings,together with the previous results from the disk morphologies/kinematics, provide valuable constraintson how, when and where planets can form. The study of planet formation is a highly multi-scale and multi-physics subject. The size increment ofa planetary body varies by more than orders of magnitude, from (sub)micron-sized (dust grain) to > km (super-Earth/gas giant planet). It results in different physical mechanisms operating at differ-ent length scales and in different growth stages. We categorize the planetary bodies into four charac-teristic size objects: µ m-sized dust grains, millimeter/centimeter (mm/cm)-sized pebbles, -km-sized Donati et al. (2020) pointed out that the RV modulations of CI Tau may also be attributed to the stellar activity. . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 7 Fig. 3: Left (a): protoplanetary disk of HL Tauri with multiple rings and gaps from ALMA dust con-tinuum emission. Credit: ALMA (ESO/NAOJ/NRAO). Right (b): synthetic image of two young planetsinside the gap of the disk around PDS . The data are adopted from ALMA, and SPHERE and MUSE(The Multi Unit Spectroscopic Explorer) instruments on ESO’s Very Large Telescope. Credit: ALMA(ESO/NAOJ/NRAO) A. Isella; ESO. We note that the above two images are not on the same spatialscale.planetesimals, and larger than -km-sized protoplanets /planets. The final planets are either rocky-dominated terrestrial planets/super-Earths, or gas-dominated giant planets. Chronologically, the planetformation can be classified into the following three stages: from dust to pebbles (Section 2), from peb-bles to planetesimals (Section 3), and from planetesimals to protoplanets/planets (Section 4, 5 and 6).Figure 4 is a sketch of planet formation with characteristic size bodies and dominant physical pro-cesses. Small dust grains coagulate into larger particles in the beginning. Direct sticking is neverthelessstalled for pebbles of roughly mm/cm size (G¨uttler et al. 2010). Other mechanisms are needed to makethe growth of larger bodies proceed. One leading mechanism is the streaming instability (Youdin &Goodman 2005), which clusters pebbles and directly collapses into planetesimals by the collective effectof self-gravity. The subsequent growth of planetesimals can proceed by accreting surrounding planetes-imals and/or pebbles that drift inward from the outer part of the disk. When the core mass reaches acritical value ( ∼ M ⊕ , Pollack et al. 1996) and there is still ample disk gas left, the protoplanets canaccrete surrounding gas rapidly to form massive gas giant planets with a timescale much shorter than thedisk lifetime. Otherwise, protoplanets only modestly accrete gas and form low-mass terrestrial planetsor super-Earths.Besides the mass growth, planetary bodies also interact and transfer angular momentum with diskgas, which induce orbital migration. For instance, solid particles and small planetesimals mainly feelaerodynamic gas drag, and their orbital decay is termed radial drift (Adachi et al. 1976; Weidenschilling1977). Meanwhile, large planetesimals/planets exert gravitational forces with disk gas, and the corre-sponding movement is called planet migration (Goldreich & Tremaine 1979, 1980; Lin & Papaloizou1986).We discuss how planetary bodies grow at each stage in the following sections. Our focus is howstate-of-the-art planet formation models fit into frontier observational studies. Due to the length of thepaper, we do not go deep into the topics of planet migration and gas accretion in the gas-rich disk phase, Protoplanets are sometimes also termed protoplanetary embryos in literature studies. We do not conceptually distinguishthese two words and refer to them as the same planetary object. B. Liu & J. H. Ji : From Dust to Planets dust m direct coagulation pebble mm / cm streaming instability planetesimal 10 100 km planetesimal/pebbleaccretion protoplanet/embryo > 1000 km terrestrial planet/super Earth M gas giant > 50 100 M M c M With gasW/O gas gas accretionradial drift aerodynamic gas drag planet migration gravitational torque Planet Formation Fig. 4: Planet formation flow chart with characteristic planet bodies including µ m sized dust grains,mm/cm sized pebbles, km sized planetesimals, > km sized protoplanets and final planets (ei-ther gas-deficit terrestrial planets, super-Earth planets or gas-rich giant planets). The physical processesare marked in red text, where the orbital migration is shown in the left while the mass growth is exhibitedin the right.and the long-term dynamical evolution of planetary systems in the gas-free phase. The key relevantquestions that will be discussed in this paper are listed as follows: – What challenges are involved in dust coagulation? What is the characteristic size of the particlesthat µ m-sized dust grains can directly grow into (Section 2)? – How can planetesimals form by the streaming instability? When and where are planetesimals likelyto form (Section 3)? – What are the differences and features between planetesimal accretion (Section 4) and pebbleaccretion (Section 5)? – Which is the dominant accretion channel for planetesimal/protoplanet growth (Section 6)? . Liu & J. H. Ji. Liu & J. H. Ji Fig. 4: Planet formation flow chart with characteristic planet bodies including µ m sized dust grains,mm/cm sized pebbles, km sized planetesimals, > km sized protoplanets and final planets (ei-ther gas-deficit terrestrial planets, super-Earth planets or gas-rich giant planets). The physical processesare marked in red text, where the orbital migration is shown in the left while the mass growth is exhibitedin the right.and the long-term dynamical evolution of planetary systems in the gas-free phase. The key relevantquestions that will be discussed in this paper are listed as follows: – What challenges are involved in dust coagulation? What is the characteristic size of the particlesthat µ m-sized dust grains can directly grow into (Section 2)? – How can planetesimals form by the streaming instability? When and where are planetesimals likelyto form (Section 3)? – What are the differences and features between planetesimal accretion (Section 4) and pebbleaccretion (Section 5)? – Which is the dominant accretion channel for planetesimal/protoplanet growth (Section 6)? . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 9 In this section we visit the first stage of planet formation: the growth and radial drift of dust grains. Wefocus on the comparison between state-of-the-art theoretical and laboratory studies and the latest diskobservations. Since the gas in protoplanetary disks is pressure-supported, it rotates around the central star at a velocity v φ, g = (1 − η ) v K , where φ refers to the azimuthal direction in cylindrical coordinates, v K ≡ (cid:112) GM (cid:63) /r isthe Keplerian velocity at the radial disk distance r , G is the gravitational constant and M (cid:63) is the mass ofthe central star. The headwind prefactor that measures the disk pressure gradient is given by (Nakagawaet al. 1986) η = − c v ∂ ln P g ∂ ln r = 1 . − . k T − k Σ (cid:18) H g r (cid:19) , (1)where c s is the gas sound speed, P g is the gas pressure, H g is the gas disk scale height, h g = H g /r is thedisk aspect ratio, and k Σ and k T are the gradients of gas surface density and temperature, respectively.The relative velocity between v φ, g and v K is often referred to as the headwind velocity ηv K . In mostregions of the protoplantary disk, the pressure gradient is negative, and gas orbits at a sub-Keplerianvelocity. All notations utilized in this paper are listed in Table 1.There are various disk models used for studying young protoplanetary disks, of which the MinimumMass Solar Nebula (MMSN) model is most commonly adopted. The MMSN model represents the min-imum amount of solids necessary to build the Solar System planets (Hayashi 1981), which is givenby Σ g = 1700 (cid:16) r (cid:17) − / g cm − , T g = 280 (cid:16) r (cid:17) − / K , h g = 3 . × − (cid:16) r (cid:17) / . (2)Therefore, at a AU orbital distance η =1 . × − and the headwind velocity ηv K (cid:39) 50 m s − . Here wechoose the MMSN as a canonical disk model. Other disk models of surface densities include the mini-mum mass extrasolar nebula (MMEN) model based on mass extrapolation from short period exoplanets(Chiang & Laughlin 2013), obtained from the emission of dust disks at (sub)millimeter wavelengths(Andrews et al. 2009) or inferred from the disk accretion rate and viscous theory (Lynden-Bell & Pringle1974; Hartmann et al. 1998). The disk heating source and dust opacity determine the gas temperatureprofile. The dominant heating mechanisms include viscous dissipation (Ruden & Lin 1986; Garaud &Lin 2007) and stellar irradiation (Chiang & Goldreich 1997; Bell et al. 1997; Dullemond et al. 2001;Dullemond & Dominik 2004).Unlike gas, a solid particle does not feel the pressure gradient force and tends to move at theKeplerian velocity. The solid particle experiences a hydrodynamic gas drag when its velocity deviatesfrom that of the gas (Whipple 1972; Weidenschilling 1977) (cid:126)F drag = − π ρ g R v th (cid:126) ∆ v [Epstein drag law] , − π C D R ρ g ∆ v (cid:126) ∆ v [Stokes drag law] , (3)where R is the radius of a spherical particle, ρ g is the gas density, v th = (cid:112) /πc s is the mean thermalvelocity of the gas, (cid:126) ∆ v = (cid:126)v − (cid:126)v g is the relative velocity between the particle and gas, and C D is given by C D = R − R e < , R − . ≤ R e ≤ , . R e > . (4) B. Liu & J. H. Ji : From Dust to Planets The drag coefficient C D depends on the particle’s Reynolds number R e =2 R ∆ v/ν mol , where ν mol = λ mfp v th / is the kinematic molecular viscosity, λ mfp = m mol /σ mol ρ g is the gas mean free path, m mol = µm H and σ mol =2 × − cm − are the mass and collisional cross section of the gas moleculerespectively, and µ =2 . and m H =1 . × − g are the gas mean molecular weight and the hydrogenatom mass respectively.The gas drag acceleration can also be written as (cid:126)a drag = − ( (cid:126)v − (cid:126)v g ) /t stop , where t stop is the stoppingtime of the particle, which quantifies how fast the particle adjusts its velocity toward the surroundinggas. The stopping time of the particles varies in different regimes. For instance, t stop = Rρ • v th ρ g when R < / λ mfp [Epstein regime] , R λ mfp Rρ • v th ρ g when R ≥ / λ mfp [Stokes regime] . (5)We note that the above expression in the Stokes regime holds when R e (cid:46) . As a particle’s size increases, F drag eventually becomes quadratic in ∆ v , and the stopping time is inversely proportional to ∆ v .The stopping time is also widely expressed in a dimensionless form τ s = t stop Ω K , where τ s is termedthe Stokes number, and Ω K = v K /r is the Keplerian angular frequency. Generally, pebbles are consideredas mm/cm sized small rocks. However, from a hydrodynamical perspective, pebbles are specificallyreferred to as solid particles with a range of Stokes number approximately from − to . As will bedemonstrated in Sect. 5, particles with such Stokes numbers are marginally coupled to the disk gas, andcan be efficiently accreted by larger protoplanetary bodies, such as planetesimals/planets.The radial and azimuthal velocity of the solid particle with respect to the Keplerian motion is givenby Nakagawa et al. (1986), v r = − τ s τ ηv K + 11 + τ v r , g v φ = − 11 + τ ηv K + τ s τ ) v r , g , (6)where v r , g in the second term on the right side of the equation is the gas radial velocity due to diskaccretion, much lower than the headwind velocity ηv K in the first term.From Eq. 6, the radial velocity of the solid particle peaks at τ s =1 . For the MMSN, such particlesare roughly meter-sized at AU and cm-sized at AU. They are strongly affected by the gas and drifttoward the central star within a timescale of approximately orbits. For pebble-sized particles of τ s ≈ − − and in the protoplanetary disk regions of r (cid:46) AU, the radial drift timescale is shorter thanthe gas disk lifetime ( ∼ Myr, Haisch et al. 2001). Therefore, due to the rapid inward drift, the survivalof these high Stokes number particles in protoplanetary disks is a long-standing conundrum in planetformation (Adachi et al. 1976; Weidenschilling 1977). The primordial solids in protoplanetary disks are dust grains that originate from the interstellar medium(ISM). These solid particles follow a size distribution n ( R ) ∝ R − . , in a range between nanometer and(sub)micron (Mathis et al. 1977). The microphysics of grain growth is not controlled by gravity, butrelies on electromagnetic interaction, like the Van der Waals force. Such inter-particle attractive forcesbring small dust grains together to form large aggregates through pairwise collisions.The collision outcome depends on the impact velocity between dust particles. In the early phase oflow-velocity gentle collision, (sub)micron-sized dust stick together to form large aggregates with porousstructures. This is referred to as the “hit-and-stick” regime. As the growth proceeds, their collisionvelocity increases with the size of the particle. In this intermediate velocity regime, the aggregates resultin restructuring through compactification (Dominik & Tielens 1997; Blum & Wurm 2000). The above . Liu & J. H. Ji. Liu & J. H. Ji The primordial solids in protoplanetary disks are dust grains that originate from the interstellar medium(ISM). These solid particles follow a size distribution n ( R ) ∝ R − . , in a range between nanometer and(sub)micron (Mathis et al. 1977). The microphysics of grain growth is not controlled by gravity, butrelies on electromagnetic interaction, like the Van der Waals force. Such inter-particle attractive forcesbring small dust grains together to form large aggregates through pairwise collisions.The collision outcome depends on the impact velocity between dust particles. In the early phase oflow-velocity gentle collision, (sub)micron-sized dust stick together to form large aggregates with porousstructures. This is referred to as the “hit-and-stick” regime. As the growth proceeds, their collisionvelocity increases with the size of the particle. In this intermediate velocity regime, the aggregates resultin restructuring through compactification (Dominik & Tielens 1997; Blum & Wurm 2000). The above . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 11 process increases the mass-to-area ratio and thus the Stokes number of the particles, resulting in moreenergetic collisions. The further mass growth is terminated by either bouncing or fragmentation dueto high velocity, catastrophic impacts (G¨uttler et al. 2010). This results in particles only growing upto millimeter to centimeter sized pebbles in nominal protoplanetary disk conditions (Zsom et al. 2010;Birnstiel et al. 2012).The sticking and growth patterns of the dust aggregates depend on their material properties. Inthe inner protoplanetary disk regions of less than a few AUs, silicates are the main constituent of dustgrains. During collisions, these silicate aggregates bounce off or even fragment completely at a thresholdvelocity of approximately − (Blum & Wurm 2008). Meanwhile, for the regions outside the water-ice line, dust grains are dominated by water-ice. The icy or ice-coated aggregates are more porous thansilicate aggregates, and thus the bouncing is less evident for them (Wada et al. 2011). In addition, thesticking still occurs at a collision of 10 ms − for the icy aggregates. Due to a higher surface energy anda lower elastic modulus, these icy aggregates are more sticky compared to silicates (Gundlach & Blum2015). Nevertheless, based on the recent laboratory experiments, Musiolik & Wurm (2019) found thatthe surface energy of icy aggregates is comparable to that of silicates when the disk temperature is lowerthan K. If this is true, it implies that the actual difference in the growth pattern of the above twotypes of aggregates might be less pronounced than anticipated in the literature (also see Gundlach et al.2018 and Steinpilz et al. 2019).Theoretical studies of the global dust coagulation and radial transport have shown that (sub)micron-sized dust grains succeed in growing to mm/cm-sized pebbles (Ormel et al. 2007; Brauer et al. 2008;Zsom et al. 2010; Birnstiel et al. 2010, 2012; Krijt et al. 2016; Estrada et al. 2016). The size of peb-bles is either regulated by the radial drift in the outer disk region of r (cid:38) AU, or limited by bounc-ing/fragmentation in the inner disk region of r< AU (e.g., Fig. 3 of Testi et al. (2014)). Nevertheless,further mass increase by incremental growth becomes problematic, due to the above mentioned bounc-ing and fragmentation barriers. The most straightforward evidence for radial drift of dust comes from the size comparison between thedust and gas components of the disks. The sizes of dust and gas disks can be separately inferred frommillimeter dust continuum emission and the molecular line emission of CO isotopes (Dutrey et al. 1998;Hughes et al. 2008). By these comparisons, gas disks are generally found to be much smaller than dustdisks, indicating the radial drift of millimeter dust particles has already taken place at the correspondingages of the systems (Andrews et al. 2012; Ansdell et al. 2018; Jin et al. 2019; Trapman et al. 2020).The other evidence is from the commonly observed substructures in protoplanetary disks, such ascavities, rings and gaps. These features resolve the drift timescale problem; otherwise, pebbles shouldbe depleted in the disk regions of r (cid:46) AU within a few Myr (Sect. 2.1.1). The difference in spatialdistributions of grains with different sizes is usually used to test the presence of pressure bumps and astrong indicator of the mobility of dust grains. The disks with large inner cavities/holes of a few tens ofAUs are called ‘transitional disks’ (Calvet et al. 2005; Espaillat et al. 2014; Owen 2016). In these disks,different spatial distributions are observed from the emissions of the millimeter continuum, infraredscattering light and/or molecular lines (Dong et al. 2012; van der Marel et al. 2013, 2015). One shouldnote that the former emission probes the mm-sized pebbles, while the latter two trace µ m grains and gas,respectively. The above phenomena can be explained by the dust filtration effect (Rice et al. 2006; Zhuet al. 2012; Pinilla et al. 2012a), where small grains are tightly coupled to gas flow, while large pebblesdrift toward and halt at local pressure maxima, resulting in mm-sized dust cavities larger than gas/smallgrain cavities. Similarly, such variation in the gas and dust components is also resolved in ring-shapedsubstructures (Isella et al. 2016).Furthermore, the drift of pebbles also leads to a radial variation of chemical compositions in diskgas. For instance, in the protoplanetary disk the CO molecule condenses into solids outside of the CO - B. Liu & J. H. Ji : From Dust to Planets ice line while it sublimates into vapor inside. Since some fraction of C is in refractory materials, thedisk gas interior to the CO -ice line is expected to have a C / H lower than the stellar value when pebblesare assumed to be static. However, when these pebbles continuously drift inwardly and cross the CO -ice line, a substantial amount of C is loading interior to the ice line and sublimates into vapor, whichnaturally increases C / H interior to the CO -ice line (Krijt et al. 2018). When comparing the C / H in thestellar photosphere and in the disk gas, Zhang et al. (2020) first reported an elevated C / H interior tothe CO -ice line in the disk of HD , which is − times higher than the stellar value. This C / H enrichment is in line with the large-scale radial drift of icy dust particles. Opacity index Let us first look at what we can know from the dust continuum emission of young protoplanetarydisks at (sub)millimeter and radio wavelengths. The observed intensity is I ν = I ν [1 − exp( − τ ν )] , wherethe subscript refers to the value at the disk midplane, τ ν = κ ν Σ d is the optical depth from the diskmidplane to the surface layer, κ ν is the disk opacity at the corresponding frequency, and Σ d and T d are the dust mass and temperature, respectively. When the disk is optically thin ( τ (cid:28) ) at the observedwavelengths, I ν ≈ τ I ν ≈ κ ν Σ d I ν . Consequently, the observed integrated flux F ν ∝ κ ν M d B ν ( T d ) and M d is the dust mass. At millimeter wavelengths, the Plank function B ν is expected to approximatelyfollow the Rayleigh-Jeans law, B ν ≈ k B T d ν /c , where k B is the Boltzmann constant and c is thelight speed. Therefore, F ν ∝ κ ν ν M d T d . This means that, if κ ν and T d are known, the dust mass canbe estimated from the observed flux.In addition, the spectral index of dust opacity can be obtained from disk observations. Assumingthat the opacity has a power-law dependence on frequency κ ν ∝ ν β and F ν ∝ ν α , we have F ν ∝ k ν ν ∝ ν β . Since the spectral index α is measured from the spectral energy distribution, the dustopacity index can be calculated accordingly through β = α − .The commonly accepted evidence for grain growth is based on the spectral index measurements atmillimeter wavelengths (Draine 2006). The interpretation is given as follows. Based on the Mie theorycalculation, the maximum grain size matters for the dust opacity. When the maximum grain size issmaller than the observed wavelength (Rayleigh regime), κ ν is independent of grain sizes and β remainshigh. When the maximum grain size is larger than the observed wavelength (geometric regime), κ ν decreases with the grain size and β drops to a lower value close to − (Fig. 3 of Ricci et al. 2010).As a result, grains with a maximum size (cid:38) mm naturally result in a less than unity spectral index atmillimeter wavelengths. In other words, the value of β can principally reveal the size of the largest grainin disks. In a realistic situation, β is also affected by the size distribution, composition and porosity of thedust aggregates. Nonetheless, these dependence-induced uncertainties are generally smaller comparedto that due to the maximum grain size (Figure 4 of Testi et al. 2014).It is worth mentioning that the opacity spectral index observed in ISM gives β ISM ∼ . , whilethe inferred spectral index of most protoplanetary disks is β disk (cid:46) , much smaller than the typicalISM value. Studies that combines multi-wavelength observations with detailed modelings suggestedthe ubiquitous presence of grain growth in disks with a variety of ages and around stars with differentmasses (Natta et al. 2004; Ricci et al. 2010, 2014; Miotello et al. 2014; Pinilla et al. 2017). Furthermore,the maximum grain size also correlates with the disk radial distance, where generally centimeter sizedparticles reside in the inner disk regions and millimeter sized grains are present further out (P´erez et al.2012; Tazzari et al. 2016). Noticeably, for disks with substructures, the spectral index also varies acrossthe rings and gaps, with lowest values in the rings and highest values in the gaps, indicating further graingrowth in the high density centric ring regions (Huang et al. 2018b; Li et al. 2019c; Long et al. 2020)..The above spectral index interpretation is based on two underlying assumptions: the dust emissionis optically thin, and the opacity is dominated by absorption rather than scattering at the observed wave-lengths. These two assumptions may also be intrinsically correlated. For instance, if the scattering is themain source of opacity instead of absorption, the observed intensity would be I ν ≈√ − w ν τ ν I ν (Zhu . Liu & J. H. Ji. Liu & J. H. Ji Let us first look at what we can know from the dust continuum emission of young protoplanetarydisks at (sub)millimeter and radio wavelengths. The observed intensity is I ν = I ν [1 − exp( − τ ν )] , wherethe subscript refers to the value at the disk midplane, τ ν = κ ν Σ d is the optical depth from the diskmidplane to the surface layer, κ ν is the disk opacity at the corresponding frequency, and Σ d and T d are the dust mass and temperature, respectively. When the disk is optically thin ( τ (cid:28) ) at the observedwavelengths, I ν ≈ τ I ν ≈ κ ν Σ d I ν . Consequently, the observed integrated flux F ν ∝ κ ν M d B ν ( T d ) and M d is the dust mass. At millimeter wavelengths, the Plank function B ν is expected to approximatelyfollow the Rayleigh-Jeans law, B ν ≈ k B T d ν /c , where k B is the Boltzmann constant and c is thelight speed. Therefore, F ν ∝ κ ν ν M d T d . This means that, if κ ν and T d are known, the dust mass canbe estimated from the observed flux.In addition, the spectral index of dust opacity can be obtained from disk observations. Assumingthat the opacity has a power-law dependence on frequency κ ν ∝ ν β and F ν ∝ ν α , we have F ν ∝ k ν ν ∝ ν β . Since the spectral index α is measured from the spectral energy distribution, the dustopacity index can be calculated accordingly through β = α − .The commonly accepted evidence for grain growth is based on the spectral index measurements atmillimeter wavelengths (Draine 2006). The interpretation is given as follows. Based on the Mie theorycalculation, the maximum grain size matters for the dust opacity. When the maximum grain size issmaller than the observed wavelength (Rayleigh regime), κ ν is independent of grain sizes and β remainshigh. When the maximum grain size is larger than the observed wavelength (geometric regime), κ ν decreases with the grain size and β drops to a lower value close to − (Fig. 3 of Ricci et al. 2010).As a result, grains with a maximum size (cid:38) mm naturally result in a less than unity spectral index atmillimeter wavelengths. In other words, the value of β can principally reveal the size of the largest grainin disks. In a realistic situation, β is also affected by the size distribution, composition and porosity of thedust aggregates. Nonetheless, these dependence-induced uncertainties are generally smaller comparedto that due to the maximum grain size (Figure 4 of Testi et al. 2014).It is worth mentioning that the opacity spectral index observed in ISM gives β ISM ∼ . , whilethe inferred spectral index of most protoplanetary disks is β disk (cid:46) , much smaller than the typicalISM value. Studies that combines multi-wavelength observations with detailed modelings suggestedthe ubiquitous presence of grain growth in disks with a variety of ages and around stars with differentmasses (Natta et al. 2004; Ricci et al. 2010, 2014; Miotello et al. 2014; Pinilla et al. 2017). Furthermore,the maximum grain size also correlates with the disk radial distance, where generally centimeter sizedparticles reside in the inner disk regions and millimeter sized grains are present further out (P´erez et al.2012; Tazzari et al. 2016). Noticeably, for disks with substructures, the spectral index also varies acrossthe rings and gaps, with lowest values in the rings and highest values in the gaps, indicating further graingrowth in the high density centric ring regions (Huang et al. 2018b; Li et al. 2019c; Long et al. 2020)..The above spectral index interpretation is based on two underlying assumptions: the dust emissionis optically thin, and the opacity is dominated by absorption rather than scattering at the observed wave-lengths. These two assumptions may also be intrinsically correlated. For instance, if the scattering is themain source of opacity instead of absorption, the observed intensity would be I ν ≈√ − w ν τ ν I ν (Zhu . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 13 et al. 2019), where w ν is the single-scattering albedo. The above formula reduces to the previously men-tioned I ν ≈ τ I ν where the scattering is negligible compared to the absorption ( w ν → ). This meansthat the scattering causes disks to look cooler than they actually are (e.g., Figure 9 of Birnstiel et al.2018). In this respect, the disk mass and optical depth are likely to be underestimated when the scat-tering is ignored in literature studies (Zhu et al. 2019; Liu 2019; Ballering & Eisner 2019). If the disksare indeed very massive and optically thick even in millimeter wavelengths, then the above approachfor the grain size estimation is not valid anymore. Recently, Carrasco-Gonz´alez et al. (2019) consideredboth scattering and absorption in dust opacity and neglected any underlying assumption on the opti-cal depth for the study of the HL Tau disk. They still found that the grains have grown to millimetersize. Importantly, similar treatments with careful assumptions should be applied to other disks for morerealistic estimates of the grain size as well. Polarization Several studies attempted to explain the disk polarized emission by dust scattering (Kataoka et al.2016; Yang et al. 2016), although other interpretations such as grain alignment with the disk magneticfield could still be relevant. If the dust scattering is indeed the dominant mechanism, the maximum grainsizes can also be constrained by the observed polarization degree. For the same system, the HL Tau disk,Kataoka et al. (2017) reported a maximum grain size of µ m , one order of magnitude smaller thanthe size estimated from Carrasco-Gonz´alez et al. (2019). Despite these polarimetric measurements beingonly applied to a small number of disks, the inferred size is considerably lower than that obtained fromopacity index measurements (Hull et al. 2018; Bacciotti et al. 2018; Ohashi et al. 2020).The above polarization analysis overall supports grain growth. Nevertheless, it is still unclearwhether the discrepancy in grain size estimation between these two interpretations is because of theexistence of multi-specie dust grains, or due to the limitations and degeneracies in methodologies them-selves. Future studies are warranted to make further claims. Meteorites in the Solar System There is evidence of grain growth in our Solar System. For instance, the calcium-aluminium-rich in-clusions (CAIs) are sub-mm to cm-sized grains identified in the most primitive meteorites. These re-fractory inclusions are thought to be the earliest solids condensed from the young nebula that form theSolar System. In cosmochemistry, the Pb – Pb isotopic dating shows that CAIs formed . Gyr ago(Amelin et al. 2010; Connelly et al. 2012). The size of CAIs supports the hypothesis of coagulation-driven growth of condensates. In addition, chondrules are igneous-textured spherules dominating inchondrites. The typical size of chondrules is . to mm (Friedrich et al. 2015; Ebel et al. 2016; Simonet al. 2018). Although there are still discrepancies between Pb - Pb ages and Al - Mg ages (see Kruijeret al. 2020), chronological studies indicated that a small fraction of chondrules might be formed as earlyas the CAIs, while the majority formed − Myr after the formation of CAIs (Amelin et al. 2002; Kleineet al. 2009; Villeneuve et al. 2009; Connelly et al. 2012; Pape et al. 2019). The presence of chondrulesand CAIs in meteorites supports grain growth in the Solar System.In summary, the current disk observations, in line with theoretical/laboratory studies, togetherdemonstrate that the first step of planet formation, from dust to pebbles, is robust and ubiquitous duringthe protoplanetary disk evolutionary stage. As stated in Sect. 2, the direct coagulation fails to produce aggregates much larger than pebble-sized. Inthis section, we emphasize one powerful planetesimal formation mechanism termed the streaming in-stability, which overcomes the above growth barrier by clustering and collapsing dense pebble filamentsinto planetesimals. The concept of the streaming instability mechanism and the operating disk condi-tions are presented in Sect. 3.1 and Sect. 3.2, respectively. The observational evidence that supports theplanetesimal formation by streaming instability is discussed in Sect. 3.3.We also note that there are other alternative scenarios to form planetesimals (see Johansen et al.2014 for a review). For instance, incremental growth may still proceed when aggregates have very highporous structures without significant compactifications (Suyama et al. 2008). Such fluffy particles have B. Liu & J. H. Ji : From Dust to Planets gas becomes very turbulent near the midplane due to interactions with particles A Local Shearing-box Simulation of Particle-Gas System a) dust filaments form via the streaming instabilityparticles settle and evolve in the midplaneb) filaments collapse to planetesimals under self-gravity Fig. 5: Illustration of D local shearing-box simulation of the streaming instability for the gas-particlesystem. Left: the box shows the simulation domain, with each side a fraction of gas scale height. Colormaps the vertical gas momentum, which exhibits high turbulence near the midplane due to interactionsbetween gas and sedimented solid particles. Right: solid particles (color refers to the surface density) inthe midplane (a) form dense filaments due to the streaming instability, and (b) collapse into planetesimalsthrough the collective effect of self-gravity once the solid density exceeds the Roche density. Courtesyof Rixin Li.a higher area-to-mass ratio compared to the compact grains, resulting in a higher collisional rate and alower Stokes number. These highly porous aggregates could still overcome the above growth and radialdrift barriers and form planetesimals under certain circumstances (Okuzumi et al. 2012; Kataoka et al.2013; Homma et al. 2019). Besides, turbulent clustering is another mechanism that directly concentratessmall dust grains into planetesimals. (Cuzzi et al. 2008; Hartlep & Cuzzi 2020). Different than thestreaming instability, this mechanism requires a prior condition of underlying turbulence. The optimalsize of operating particles is crucially related to the energy cascade models (Cuzzi et al. 2010; Pan et al.2011; Hartlep et al. 2017; Hartlep & Cuzzi 2020). The streaming instability is applicable for a wide size range of solid particles but most efficiently forthe particles of τ s (cid:39) . − . We conventionally use the word ‘pebbles’ hereafter to refer to the solid par-ticles incorporated in the streaming instability mechanism. Basically speaking, the streaming instabilityincludes two processes, namely the concentration of pebbles into dense clumping filaments, and grav-itational collapse of pebble filaments into planetesimals. The snapshots of the above processes and thespatial distribution of solids in a streaming instability simulation are illustrated in Figure 5. . Liu & J. H. Ji. Liu & J. H. Ji The streaming instability is applicable for a wide size range of solid particles but most efficiently forthe particles of τ s (cid:39) . − . We conventionally use the word ‘pebbles’ hereafter to refer to the solid par-ticles incorporated in the streaming instability mechanism. Basically speaking, the streaming instabilityincludes two processes, namely the concentration of pebbles into dense clumping filaments, and grav-itational collapse of pebble filaments into planetesimals. The snapshots of the above processes and thespatial distribution of solids in a streaming instability simulation are illustrated in Figure 5. . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 15 We give a qualitative explanation here. Firstly, inward drifting pebbles get concentrated radially dueto the solid-to-gas back reaction (Youdin & Goodman 2005). This is because pebbles feel the gas dragforce and lose angular momentum. Similarly, the surrounding gas gains angular momentum from peb-bles due to the solid-to-gas back reaction, and thus the gas velocity gets accelerated. The strength of thisreaction force is determined by the volume density ratio between pebbles and gas ( ρ peb /ρ g ). We usuallyneglect this back reaction since the pebble density is much lower than the gas density in the nominalprotoplanetary disk condition. However, when the pebble density is comparable to the gas density, theback reaction force is non-trivial. In this situation, the pebble density perturbation grows and concen-trates pebbles effectively. Since the gas is accelerated towards the Keplerian velocity, and the relativevelocity between gas and pebbles becomes smaller, these pebbles feel weaker gas drag and drift inwardmore slowly. Hence, the fast drifting pebbles from the outer part of the disk thereby catch these slowerdrifting pebbles and form denser filaments. Because this is a positive feedback, once an initial, radialconcentration of solids is achieved ( ρ peb (cid:39) ρ g ), the further clumping is self-amplified, and eventually thepebble density grows rapidly in a non-linear manner. Youdin & Goodman (2005) proposed the conceptof the streaming instability and provided the analytical linear instability solution. The robustness of thepebble clumping was later confirmed in numerical simulations (Youdin & Johansen 2007; Johansen &Youdin 2007).Secondly, the effect of self-gravity becomes dominant when the pebble density exceeds the Rochedensity ( ρ R =9Ω / πG ). In this circumstance, gravitational force overcomes tidal shear, and the pebblefilaments gravitationally collapse into -km-sized planetesimals . The primordial idea of the gravita-tional instability was proposed by Goldreich & Ward (1973). At that time these authors only consideredthat dust sediment into a super thin midplane layer to exceed the Roche density. However, such a ver-tical solid concentration generates the Kelvin-Helmholtz instability and develops the vertical velocitystirring, which prevents the subsequent solid enrichment (Weidenschilling 1980; Cuzzi et al. 1993). Onthe contrary, the streaming instability induces a radial concentration of solid particles. The gravitationalcollapse of dense particle filaments by the above streaming effect was numerically verified by Johansenet al. (2007, 2009).We remark a few things here. Strictly speaking, only the first step is relevant to the concept of theinstability – the streaming motion between solids and gas. Unlike other concentration mechanisms, (e.g.,Cuzzi et al. 2008), one feature of the streaming effect does not require any underlying disk turbulence.The second step does not inherently depend on any initiated mechanisms that cluster pebbles. It broadlyrepresents a pebble collapsing process that forms planetesimals aided by the self-gravity. These two stepshave been commonly investigated together in literature studies and have been frequently recognized asa unified mechanism termed the streaming instability.We also point out that this pebble clumping effect also triggers turbulence, even if the flow of thebackground gas was originally laminar. As numerically investigated by Li et al. (2018), the densityfluctuation induced by the streaming instability is not sufficient to halt and concentrate pebbles. Thereason for pebble clumping still arises from the previously mentioned streaming motion between pebblesand gas.It is noteworthy that most of these streaming instability simulations are conducted in a cubic boxcentered on a local, co-rotating coordinate frame with fixed Keplerian frequency and radial orbital dis-tance (also called shearing-box simulations, see Figure 5). The length scale of the box is much smallerthan the orbital distance, and therefore, the motion of particles in that box is linearized with the Keplerianshear. For most streaming instability simulations, gas fluid is based on a Eulerian grid, and solid par-ticles are treated as Lagrangian superparticles, each representing a swarm of actual pebbles. Such aparticle-fluid hybrid approach substantially reduces the computational cost for investigating the non-linear pebble clumping and planetesimal formation processes.The mass of planetesimals formed by streaming instability simulations follows a top-heavy massdistribution, which can be roughly fitted by a power-law plus exponential decay for the intermediate and Gerbig et al. (2020) further suggested that the collapse criterion requires gravitational force to overcome turbulent diffusionon small scales, which also regulates the sizes of forming planetesimals. B. Liu & J. H. Ji : From Dust to Planets high mass branch (Johansen et al. 2015; Sch¨afer et al. 2017; Abod et al. 2019). A turnover mass mayexist in the lower mass branch (Li et al. 2019b). The planetesimals have a characteristic size of ∼ km when they form at the asteroid belt region (Johansen et al. 2015). The characteristic mass/size in-creases with disk metallicity, the mass of the central star and radial distance (Johansen et al. 2012, 2015;Simon et al. 2016), modestly increases with gas pressure gradient (Abod et al. 2019), and appears to beindependent of Stokes number (Simon et al. 2017). Based on the extrapolation of literature streaminginstability simulations, Liu et al. (2020) derived the characteristic mass of planetesimals as M pl = 5 × − (cid:18) Z . (cid:19) / (cid:16) γπ − (cid:17) / (cid:18) h g . (cid:19) (cid:18) M (cid:63) M (cid:12) (cid:19) M ⊕ , (7)where Z is the local disk metallicity and γ =4 πGρ g / Ω is a self-gravity parameter , related withgas density, stellar mass and radial distance. Adopting the MMSN model, we obtain γ =0 . and theresultant planetesimal is − M ⊕ in mass ( km in radius) at r =2 . AU around a solar-mass star.Based on Eq. 7, we expect that smaller planetesimals form at shorter orbital distances and around lower-mass stars.Most of the streaming instability studies simply considered a laminar background gas, despite thatthe protoplanetary disk should be turbulent in nature (Lyra et al. 2019). How the streaming instabilityoperates in a realistic turbulent condition has not been fully understood. First of all, disk turbulence in-duces stochastic motion and density fluctuation of the gas. Overdense pressure bumps can be producedat the region in which particles of τ s ∼ are efficiently trapped. This type of solid concentration thatfacilitates planetesimal formation is obtained in disks where the source of turbulence is either the mag-netorotational instability (MRI, Johansen et al. 2007), or the vertical shear instability (VSI, Sch¨afer et al.2020), by which angular velocity depends on the disk vertical distance (Nelson et al. 2013; Stoll & Kley2014; Lin & Youdin 2015; Flock et al. 2017). When considering the non-ideal magnetohydrodynamical(MHD) effects, Yang et al. (2018) found that dust diffusion is weak in the radial direction and strongclumping can still occur in the dead zone region where the MRI is inactive because of low ionizationfraction (Gammie 1996). On the other hand, the turbulent diffusivity acts to suppress sedimentation andconcentration of particles, and therefore, the birth rate of planetesimals can be slower or even quenchedwhen the disk turbulence increases (Gole et al. 2020). These numerical studies have only been exploredin a very narrow range of parameter spaces ( τ s and α t ) with various disk turbulence mechanisms.In order to quantify the role of turbulence, Umurhan et al. (2020) and Chen & Lin (2020) have con-ducted linear stability analyses for the motion equations of gas and solid particles by including additionalviscous forcing terms. They also found that the growth rate gets reduced even when the disk is mod-erately turbulent. Nevertheless, the adopted simplified isotropic, α prescription cannot fully mimic therealistic non-linear pattern of the disk turbulence. For instance, the aforementioned turbulent-inducedzonal flows and pressure bumps seem to promote dust concentration and subsequent planetesimal for-mation (Johansen et al. 2007; Sch¨afer et al. 2020), which is not captured in these theoretical analyses.On the whole, it is still premature to reach definitive conclusions yet, and future studies are required forbuilding a unified and consistent picture of this topic. In order to trigger the streaming instability, the volume density of solids needs to be enhanced com-parable to that of gas, ρ peb (cid:39) ρ g (Youdin & Goodman 2005). The onset criterion can also be expressedin terms of the surface density ratio, i.e., the metallicity Z =Σ peb / Σ g . The dust to gas mass ratio ismeasured to be . in the ISM (Bohlin et al. 1978), while the canonical value of the solar metallicityis . (Asplund et al. 2009). Numerical studies reported that a super-solar metallicity ( (cid:38) − ) isrequired for triggering the streaming instability (Johansen et al. 2009; Carrera et al. 2015; Yang et al.2017). Such a threshold metallicity also depends on the disk and pebble properties. The streaming insta-bility is easier to be triggered when the disk metallicity is higher (Johansen et al. 2009), the strength of We note that γ can be related with the Toomre Q T parameter by Q T = (cid:112) /π/γ . Thus, γ =0 . is equivalent to Q T =47 . . Liu & J. H. Ji. Liu & J. H. Ji The streaming instability is applicable for a wide size range of solid particles but most efficiently forthe particles of τ s (cid:39) . − . We conventionally use the word ‘pebbles’ hereafter to refer to the solid par-ticles incorporated in the streaming instability mechanism. Basically speaking, the streaming instabilityincludes two processes, namely the concentration of pebbles into dense clumping filaments, and grav-itational collapse of pebble filaments into planetesimals. The snapshots of the above processes and thespatial distribution of solids in a streaming instability simulation are illustrated in Figure 5. . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 15 We give a qualitative explanation here. Firstly, inward drifting pebbles get concentrated radially dueto the solid-to-gas back reaction (Youdin & Goodman 2005). This is because pebbles feel the gas dragforce and lose angular momentum. Similarly, the surrounding gas gains angular momentum from peb-bles due to the solid-to-gas back reaction, and thus the gas velocity gets accelerated. The strength of thisreaction force is determined by the volume density ratio between pebbles and gas ( ρ peb /ρ g ). We usuallyneglect this back reaction since the pebble density is much lower than the gas density in the nominalprotoplanetary disk condition. However, when the pebble density is comparable to the gas density, theback reaction force is non-trivial. In this situation, the pebble density perturbation grows and concen-trates pebbles effectively. Since the gas is accelerated towards the Keplerian velocity, and the relativevelocity between gas and pebbles becomes smaller, these pebbles feel weaker gas drag and drift inwardmore slowly. Hence, the fast drifting pebbles from the outer part of the disk thereby catch these slowerdrifting pebbles and form denser filaments. Because this is a positive feedback, once an initial, radialconcentration of solids is achieved ( ρ peb (cid:39) ρ g ), the further clumping is self-amplified, and eventually thepebble density grows rapidly in a non-linear manner. Youdin & Goodman (2005) proposed the conceptof the streaming instability and provided the analytical linear instability solution. The robustness of thepebble clumping was later confirmed in numerical simulations (Youdin & Johansen 2007; Johansen &Youdin 2007).Secondly, the effect of self-gravity becomes dominant when the pebble density exceeds the Rochedensity ( ρ R =9Ω / πG ). In this circumstance, gravitational force overcomes tidal shear, and the pebblefilaments gravitationally collapse into -km-sized planetesimals . The primordial idea of the gravita-tional instability was proposed by Goldreich & Ward (1973). At that time these authors only consideredthat dust sediment into a super thin midplane layer to exceed the Roche density. However, such a ver-tical solid concentration generates the Kelvin-Helmholtz instability and develops the vertical velocitystirring, which prevents the subsequent solid enrichment (Weidenschilling 1980; Cuzzi et al. 1993). Onthe contrary, the streaming instability induces a radial concentration of solid particles. The gravitationalcollapse of dense particle filaments by the above streaming effect was numerically verified by Johansenet al. (2007, 2009).We remark a few things here. Strictly speaking, only the first step is relevant to the concept of theinstability – the streaming motion between solids and gas. Unlike other concentration mechanisms, (e.g.,Cuzzi et al. 2008), one feature of the streaming effect does not require any underlying disk turbulence.The second step does not inherently depend on any initiated mechanisms that cluster pebbles. It broadlyrepresents a pebble collapsing process that forms planetesimals aided by the self-gravity. These two stepshave been commonly investigated together in literature studies and have been frequently recognized asa unified mechanism termed the streaming instability.We also point out that this pebble clumping effect also triggers turbulence, even if the flow of thebackground gas was originally laminar. As numerically investigated by Li et al. (2018), the densityfluctuation induced by the streaming instability is not sufficient to halt and concentrate pebbles. Thereason for pebble clumping still arises from the previously mentioned streaming motion between pebblesand gas.It is noteworthy that most of these streaming instability simulations are conducted in a cubic boxcentered on a local, co-rotating coordinate frame with fixed Keplerian frequency and radial orbital dis-tance (also called shearing-box simulations, see Figure 5). The length scale of the box is much smallerthan the orbital distance, and therefore, the motion of particles in that box is linearized with the Keplerianshear. For most streaming instability simulations, gas fluid is based on a Eulerian grid, and solid par-ticles are treated as Lagrangian superparticles, each representing a swarm of actual pebbles. Such aparticle-fluid hybrid approach substantially reduces the computational cost for investigating the non-linear pebble clumping and planetesimal formation processes.The mass of planetesimals formed by streaming instability simulations follows a top-heavy massdistribution, which can be roughly fitted by a power-law plus exponential decay for the intermediate and Gerbig et al. (2020) further suggested that the collapse criterion requires gravitational force to overcome turbulent diffusionon small scales, which also regulates the sizes of forming planetesimals. B. Liu & J. H. Ji : From Dust to Planets high mass branch (Johansen et al. 2015; Sch¨afer et al. 2017; Abod et al. 2019). A turnover mass mayexist in the lower mass branch (Li et al. 2019b). The planetesimals have a characteristic size of ∼ km when they form at the asteroid belt region (Johansen et al. 2015). The characteristic mass/size in-creases with disk metallicity, the mass of the central star and radial distance (Johansen et al. 2012, 2015;Simon et al. 2016), modestly increases with gas pressure gradient (Abod et al. 2019), and appears to beindependent of Stokes number (Simon et al. 2017). Based on the extrapolation of literature streaminginstability simulations, Liu et al. (2020) derived the characteristic mass of planetesimals as M pl = 5 × − (cid:18) Z . (cid:19) / (cid:16) γπ − (cid:17) / (cid:18) h g . (cid:19) (cid:18) M (cid:63) M (cid:12) (cid:19) M ⊕ , (7)where Z is the local disk metallicity and γ =4 πGρ g / Ω is a self-gravity parameter , related withgas density, stellar mass and radial distance. Adopting the MMSN model, we obtain γ =0 . and theresultant planetesimal is − M ⊕ in mass ( km in radius) at r =2 . AU around a solar-mass star.Based on Eq. 7, we expect that smaller planetesimals form at shorter orbital distances and around lower-mass stars.Most of the streaming instability studies simply considered a laminar background gas, despite thatthe protoplanetary disk should be turbulent in nature (Lyra et al. 2019). How the streaming instabilityoperates in a realistic turbulent condition has not been fully understood. First of all, disk turbulence in-duces stochastic motion and density fluctuation of the gas. Overdense pressure bumps can be producedat the region in which particles of τ s ∼ are efficiently trapped. This type of solid concentration thatfacilitates planetesimal formation is obtained in disks where the source of turbulence is either the mag-netorotational instability (MRI, Johansen et al. 2007), or the vertical shear instability (VSI, Sch¨afer et al.2020), by which angular velocity depends on the disk vertical distance (Nelson et al. 2013; Stoll & Kley2014; Lin & Youdin 2015; Flock et al. 2017). When considering the non-ideal magnetohydrodynamical(MHD) effects, Yang et al. (2018) found that dust diffusion is weak in the radial direction and strongclumping can still occur in the dead zone region where the MRI is inactive because of low ionizationfraction (Gammie 1996). On the other hand, the turbulent diffusivity acts to suppress sedimentation andconcentration of particles, and therefore, the birth rate of planetesimals can be slower or even quenchedwhen the disk turbulence increases (Gole et al. 2020). These numerical studies have only been exploredin a very narrow range of parameter spaces ( τ s and α t ) with various disk turbulence mechanisms.In order to quantify the role of turbulence, Umurhan et al. (2020) and Chen & Lin (2020) have con-ducted linear stability analyses for the motion equations of gas and solid particles by including additionalviscous forcing terms. They also found that the growth rate gets reduced even when the disk is mod-erately turbulent. Nevertheless, the adopted simplified isotropic, α prescription cannot fully mimic therealistic non-linear pattern of the disk turbulence. For instance, the aforementioned turbulent-inducedzonal flows and pressure bumps seem to promote dust concentration and subsequent planetesimal for-mation (Johansen et al. 2007; Sch¨afer et al. 2020), which is not captured in these theoretical analyses.On the whole, it is still premature to reach definitive conclusions yet, and future studies are required forbuilding a unified and consistent picture of this topic. In order to trigger the streaming instability, the volume density of solids needs to be enhanced com-parable to that of gas, ρ peb (cid:39) ρ g (Youdin & Goodman 2005). The onset criterion can also be expressedin terms of the surface density ratio, i.e., the metallicity Z =Σ peb / Σ g . The dust to gas mass ratio ismeasured to be . in the ISM (Bohlin et al. 1978), while the canonical value of the solar metallicityis . (Asplund et al. 2009). Numerical studies reported that a super-solar metallicity ( (cid:38) − ) isrequired for triggering the streaming instability (Johansen et al. 2009; Carrera et al. 2015; Yang et al.2017). Such a threshold metallicity also depends on the disk and pebble properties. The streaming insta-bility is easier to be triggered when the disk metallicity is higher (Johansen et al. 2009), the strength of We note that γ can be related with the Toomre Q T parameter by Q T = (cid:112) /π/γ . Thus, γ =0 . is equivalent to Q T =47 . . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 17 the disk pressure gradient is lower (Bai & Stone 2010), and/or the Stokes number of pebbles is highertowards unity (Carrera et al. 2015).Nonetheless, unless some other mechanisms can operate in the first place to enhance the pebbledensity, the disk with solar metallicity can hardly form planetesimals by the streaming instability. Thenthe question is how the solid density can be enriched to satisfy this condition?We list several scenarios that propose pebble enrichment at peculiar disk locations. For instance, theformation site can be the water-ice line (Ros & Johansen 2013; Ida & Guillot 2016; Schoonenberg &Ormel 2017; Dra¸ ˙zkowska & Alibert 2017; Hyodo et al. 2019). This is because the water-ice in pebblessublimates into vapor when these pebbles drift inwardly across the water-ice line ( T g (cid:39) K). First,pebbles are locally piled-up by a “traffic jam” effect since the outer fast drifting icy pebbles catch upwith the inner slow drifting silicate grains. Second, the released water vapor diffuses back to the outsideof the ice line and condenses onto the continuously inwardly drifting icy pebbles. This diffusion and re-condensation process also enhances the local solid density (Stevenson & Lunine 1988; Cuzzi & Zahnle2004). The former mechanism generates “dry” planetesimals slighter interior to the ice line while thelatter one produces “wet” planetesimals with a substantial water fraction slightly exterior to the iceline. Similar processes could also be expected at the ice lines of other volatile-rich species, such as CO and NH . Besides these ice lines, other possible pebble trapping sites can be the edge of the deadzone (Dra¸ ˙zkowska et al. 2013; Chatterjee & Tan 2014; Hu et al. 2016; Miranda et al. 2017), the vortexgenerated by hydrodynamical instabilities (Surville et al. 2016; Huang et al. 2018c), and the spiral armsin self-gravitating disks (Gibbons et al. 2012).Apart from the above mentioned mechanisms that relate with local disk properties, there are otherways of increasing the disk metallicity. For instance, Dra¸ ˙zkowska et al. (2016) showed that this enrich-ment can occur in the inner sub-AU disk region as a result of the global dust growth and radial drift.In addition, pebble trapping is thought to be a natural consequence of giant planet formation. The mas-sive planet opens a gap (Lin & Papaloizou 1986) and produces a local pressure maximum in its vicinity(Lambrechts et al. 2014). Pebbles drift more and more slowly and get concentrated on their way towardsthis local pressure maximum. When these pebbles reach the threshold metallicity at or close to the gapedge, the streaming instability is triggered to form planetesimals (Eriksson et al. 2020). Moreover, thesolid enrichment can be fulfilled in the late disk dispersal phase when stellar photoevaporation domi-nates. In this case, pebbles have already decoupled from gas and sedimented to the disk midplane. Thephotoevaporating wind blows gas away from the disk surface. Therefore, the solid-to-gas ratio increasesglobally (Carrera et al. 2017).To summarize, the planetesimal formation can either occur locally at peculiar disk locations such asice lines and pressure bumps, or in a wide range of disk regions when stellar photoevaporation globallydepletes the disk gas. Where and when the planetesimals form crucially depend on the detailed diskconditions and pebble concentration mechanisms. For instance, the formation location can broadly rangefrom the most inner sub-AU disk region (dead zone edge) to the outer part of the disk extending to a fewtens/hundreds of AUs (spiral arms in self-gravitating disks). The formation time is even more difficultto quantify, which might occur at an early phase when the disk is still self-gravitating ( t (cid:46) . − Myr),or at a late phase when gas is significantly dispersed ( t> Myr). The other time constraint is from themeteorite chronology in our Solar System (see Kruijer et al. 2020 for a review). What we learn is thatthese parent bodies of meteorites are apparently not all formed at once. They are more likely to formsuccessively or undergo multiple formation phases over the entire disk lifetime. For instance, the parentbodies of iron meteorites formed within the first Myr (Kruijer et al. 2014), whereas those of chondriticmeteorites formed slightly later, ∼ − Myr after CAI formation (Villeneuve et al. 2009; Sugiura &Fujiya 2014; Doyle et al. 2015). One tentative argument that supports the streaming instability mechanism arises from the optical depthmeasurements of the rings in young protoplanetary disks from the DSHARP survey. All these dustyrings shown in various systems have similar optical depths of the order of unity (Dullemond et al. B. Liu & J. H. Ji : From Dust to Planets ρ peb >ρ g , while it is quenched when ρ peb <ρ g . Thus, such a regulated processremoves the excess pebbles into planetesimals, maintaining the midplane dust-to-gas ratio to be of orderunity. Since the optical depth correlates with the dust-to-gas ratio, this interpretation naturally explainsthe peculiar optical depths in the observed rings. Evidence of the streaming instability can also be found from the minor bodies in our Solar System.Morbidelli et al. (2009) conducted collisional coagulation simulations and found that in order to repro-duce the current size distribution of main-belt asteroids, the primordial planetesimals should be (cid:38) km in size. Rather than incremental growth, this characteristic size and the slopes of size distributionsof main-belt asteroids and Kupiter belt objects are more consistent with planetesimals obtained fromstreaming instability simulations (Johansen et al. 2015; Simon et al. 2016).The most appealing evidence is from the Kuiper belt objects. Recently, a contact binary namedArrokoth (previously known as Ultima Thule or ) was imaged by the New Horizons space-craft during its flyby. Arrokoth, resembling other cold classical Kuiper belt objects, is thought to be wellpreserved in terms of the pristine properties since its formation. It consists of two equal-sized, compo-sitionally homogeneous lobes with a narrow contact neck (Stern et al. 2019; Grundy et al. 2020; Zhao2020). Such a peculiar shape with little distortion, and the good alignment of the two lobes stronglyindicate that this type of object originated from gentle, low-speed mergers of planetesimals within agravitationally collapsing clump of pebbles (McKinnon et al. 2020).The prevalence of equal-sized binaries found in the Kuiper belt supports that they form by the grav-itational collapsing mechanism (Nesvorn´y et al. 2010; Robinson et al. 2020). Most of these binaries arein the cold classical Kuiper belt which have low heliocentric orbital inclinations and eccentricities andthus remain primordial compared to other populations. Furthermore, these binaries are observed to havesimilar colors even though the color distribution of the binary population has a large intrinsic scatter(Benecchi et al. 2009; Marsset et al. 2020). This is also expected from the gravitational collapsing, sincethey form from the same reservoir of solids in the pebble clumps. In addition, based on the obliquitymeasurements of trans-Neptunian binaries, Grundy et al. (2019) found that the prograde binaries aremore common than the retrograde ones among tight binaries ( / ). Such a binary orientation distri-bution is consistent with the predictions of the streaming instability simulations (Nesvorn´y et al. 2019).In contrast, the above properties are difficult to fulfill when the binaries form by sequential coagulationand capture (Goldreich et al. 2002).To conclude, the streaming instability seems to be the widely-accepted and leading mechanism ofplanetesimal formation. The success of the streaming instability is not only because the robustness ofthe mechanism itself is verified by numerous theoretical/numerical work, but also many key features ofthe planetesimal populations generated by the streaming instability are consistent with current observa-tions, both within and beyond the Solar System. The streaming instability succeeds in bridging the gapbetween the pebbles and planetesimals. The growth of planetesimals after formation will be discussedin subsequent sections. We review the planet formation process from planetesimals to planets from Sect. 4 to Sect. 6. In thissection we focus on planetesimal accretion. The accretion cross section and accretion rates in differentregimes are described in Sects. 4.1 and 4.2 respectively. We further discuss the underlying physicalprocesses in Sect. 4.3 and summarize the key features and applications in Sects. 4.4 and 4.5 respectively. The large-scale dust clumping at the edges of the rings are also resolved from hydrodynamic simulations (Huang et al. 2020). . Liu & J. H. Ji. Liu & J. H. Ji One tentative argument that supports the streaming instability mechanism arises from the optical depthmeasurements of the rings in young protoplanetary disks from the DSHARP survey. All these dustyrings shown in various systems have similar optical depths of the order of unity (Dullemond et al. B. Liu & J. H. Ji : From Dust to Planets ρ peb >ρ g , while it is quenched when ρ peb <ρ g . Thus, such a regulated processremoves the excess pebbles into planetesimals, maintaining the midplane dust-to-gas ratio to be of orderunity. Since the optical depth correlates with the dust-to-gas ratio, this interpretation naturally explainsthe peculiar optical depths in the observed rings. Evidence of the streaming instability can also be found from the minor bodies in our Solar System.Morbidelli et al. (2009) conducted collisional coagulation simulations and found that in order to repro-duce the current size distribution of main-belt asteroids, the primordial planetesimals should be (cid:38) km in size. Rather than incremental growth, this characteristic size and the slopes of size distributionsof main-belt asteroids and Kupiter belt objects are more consistent with planetesimals obtained fromstreaming instability simulations (Johansen et al. 2015; Simon et al. 2016).The most appealing evidence is from the Kuiper belt objects. Recently, a contact binary namedArrokoth (previously known as Ultima Thule or ) was imaged by the New Horizons space-craft during its flyby. Arrokoth, resembling other cold classical Kuiper belt objects, is thought to be wellpreserved in terms of the pristine properties since its formation. It consists of two equal-sized, compo-sitionally homogeneous lobes with a narrow contact neck (Stern et al. 2019; Grundy et al. 2020; Zhao2020). Such a peculiar shape with little distortion, and the good alignment of the two lobes stronglyindicate that this type of object originated from gentle, low-speed mergers of planetesimals within agravitationally collapsing clump of pebbles (McKinnon et al. 2020).The prevalence of equal-sized binaries found in the Kuiper belt supports that they form by the grav-itational collapsing mechanism (Nesvorn´y et al. 2010; Robinson et al. 2020). Most of these binaries arein the cold classical Kuiper belt which have low heliocentric orbital inclinations and eccentricities andthus remain primordial compared to other populations. Furthermore, these binaries are observed to havesimilar colors even though the color distribution of the binary population has a large intrinsic scatter(Benecchi et al. 2009; Marsset et al. 2020). This is also expected from the gravitational collapsing, sincethey form from the same reservoir of solids in the pebble clumps. In addition, based on the obliquitymeasurements of trans-Neptunian binaries, Grundy et al. (2019) found that the prograde binaries aremore common than the retrograde ones among tight binaries ( / ). Such a binary orientation distri-bution is consistent with the predictions of the streaming instability simulations (Nesvorn´y et al. 2019).In contrast, the above properties are difficult to fulfill when the binaries form by sequential coagulationand capture (Goldreich et al. 2002).To conclude, the streaming instability seems to be the widely-accepted and leading mechanism ofplanetesimal formation. The success of the streaming instability is not only because the robustness ofthe mechanism itself is verified by numerous theoretical/numerical work, but also many key features ofthe planetesimal populations generated by the streaming instability are consistent with current observa-tions, both within and beyond the Solar System. The streaming instability succeeds in bridging the gapbetween the pebbles and planetesimals. The growth of planetesimals after formation will be discussedin subsequent sections. We review the planet formation process from planetesimals to planets from Sect. 4 to Sect. 6. In thissection we focus on planetesimal accretion. The accretion cross section and accretion rates in differentregimes are described in Sects. 4.1 and 4.2 respectively. We further discuss the underlying physicalprocesses in Sect. 4.3 and summarize the key features and applications in Sects. 4.4 and 4.5 respectively. The large-scale dust clumping at the edges of the rings are also resolved from hydrodynamic simulations (Huang et al. 2020). . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 19 The Hill radius of a planetary body orbiting a central star is defined as R H = (cid:18) M p M (cid:63) (cid:19) / a, (8)where M p and a are the mass and semimajor axis of the body respectively. The Hill velocity is v H = R H Ω K . Within the Hill sphere, the planetary body’s gravitational force is more important thanthat of the star.We consider planetesimal accretion in the case of a few massive protoplanetary embryos embeddedin a swarm of less massive planetesimals. Hereafter we call these two populations the large and smallbodies, and their masses are expressed as M and m , respectively. Only the gravitational force operatesduring their encounters. The collisional (accretion) cross section of the large body can be expressed as σ = πR (cid:18) v δv (cid:19) = πR (cid:18) GMR M δv (cid:19) , (9)where R M is the physical radius of the large body, and v esc = (cid:112) GM/R M and δv are the escape velocityof the large body and the relative velocity between the large and small bodies respectively. The collisionis in the gravitational focusing regime when δv The Hill radius of a planetary body orbiting a central star is defined as R H = (cid:18) M p M (cid:63) (cid:19) / a, (8)where M p and a are the mass and semimajor axis of the body respectively. The Hill velocity is v H = R H Ω K . Within the Hill sphere, the planetary body’s gravitational force is more important thanthat of the star.We consider planetesimal accretion in the case of a few massive protoplanetary embryos embeddedin a swarm of less massive planetesimals. Hereafter we call these two populations the large and smallbodies, and their masses are expressed as M and m , respectively. Only the gravitational force operatesduring their encounters. The collisional (accretion) cross section of the large body can be expressed as σ = πR (cid:18) v δv (cid:19) = πR (cid:18) GMR M δv (cid:19) , (9)where R M is the physical radius of the large body, and v esc = (cid:112) GM/R M and δv are the escape velocityof the large body and the relative velocity between the large and small bodies respectively. The collisionis in the gravitational focusing regime when δv The formation timescales of terrestrial planets can be measured by using radioactive decay of short-lived isotopes, among which the hafnium-tungsten ( Hf − W ) isotope is widely adopted for radiometricdating. This is not only due to its applicable radioactive decay half-life time of Myr, but is also relatedto the chemical properties of these two elements: Hf is lithophile (“rock loving”) and W is siderophile(“iron loving”). W preferentially settles into the metal core and Hf remains in the silicate mantle beforethe protoplanet becomes massive enough to segregate. For instance, if the core forms early (early mantle-core segregation), the measured W abundance in the mantle would be high. On the other hand, if thecore forms late, W would be high in the core, leaving the W -deficient mantle. Therefore, measuring the Hf / W ratio in the current Earth mantle can be utilized to constrain its core formation and differentiation.Such isotope analyses indicate that core formation of Earth occurred − Myr after formation ofthe Solar System (Kleine et al. 2002; Yin et al. 2002; Jacobsen 2005; Touboul et al. 2007; Kleine et al.2009; Rudge et al. 2010). Similarly, based on Martian meteorites, the formation time of Mars is inferredto be within a few Myr (Kleine et al. 2004; Foley et al. 2005; Dauphas & Pourmand 2011), comparableto the lifetime of the proto-solar nebula.The final accretion stage of Solar System terrestrial planets, or called late giant-impact stage, istypically modeled by a numerical N-body approach (see Izidoro & Raymond (2018) for a summary ofnumerical methods). Before this stage, protoplanetary embryos of lunar to Martian masses were alreadyformed in the terrestrial planet forming region by accreting planetesimals (see Sect. 4.2). The random ve-locities of the embryos will be stirred without efficient damping, and planet-planet collisions frequentlyoccur after dispersal of the disk gas. On the other hand, giant planets have already grown to their currentmasses. The influence of gas giants (in particular Jupiter and Saturn) is crucial for sculpting the architec-ture and water delivery of the asteroid belt and the inner terrestrial planets (Raymond & Izidoro 2017;Zheng et al. 2017). Numerous numerical simulations have attempted to reproduce the terrestrial plan-ets, both in terms of the dynamical properties and geochemical accretion timescale (Chambers 2001;Raymond et al. 2004, 2006, 2009; O’Brien et al. 2006; Thommes et al. 2008; Morishima et al. 2010;Jacobson et al. 2014). The above models are either assumed to have giant planets on their current po-sitions with nearly circular or slightly eccentric orbits. However, these models still have shortcomings.For instance, the planets emerging out of the Mars forming region have masses comparable to Earth andVenus. In other words, the Mars analogs are difficult to produce in the above numerical simulations,known as the “small Mars problem”. Hansen (2009) first proposed that the proper Mars-size objectscan be yielded when the planetesimal disk is truncated at around AU. As a further step, Walsh et al.(2011) proposed that such a truncation can be physically caused by the inward-then-outward migrationof Jupiter and Saturn through planet-disk interactions, which is known as the Grand Tack model. Thekey ingredient of this model, the migration of two giant planets, is consistent with our current under-standing of the disk migration theory (Kley & Nelson 2012; Baruteau et al. 2014) and has been validatedby hydrodynamic simulations (Masset & Snellgrove 2001; Morbidelli & Crida 2007; Pierens & Nelson2008a; Zhang & Zhou 2010). The appealing point of the Grand Tack model is that it satisfactorily re-produces key observational features of the inner Solar System, such as the orbital and mass distributionsof the terrestrial planets, mass depletion and the chemical compositions of planetesimals in the asteroidbelt, and water content of Earth (O’Brien et al. 2014). On the other hand, Clement et al. (2018) pro-posed that Mars’ growth can also be stunted if the giant planet instability occurs relatively early duringthe terrestrial planet formation (e.g., (cid:46) Myr after the gas disk dispersal).It is also worth mentioning that most of the current N-body simulations only consider perfect merg-ers when two bodies collide with each other. However, the random velocities of planetesimals wouldbe excited when the masses of the protoplanets increase. The collisional outcome sensitively relatesto the masses and velocities of the colliding bodies, which could be catastrophic disruption, grindingor fragmentation (Leinhardt & Stewart 2012; Agnor & Asphaug 2004; Genda et al. 2012; Liu et al.2015). Dedicated N-body simulations including realistic collision recipes showed that the final massesand numbers of surviving planets are comparable to the case when only perfect mergers are considered, . Liu & J. H. Ji. Liu & J. H. Ji The formation timescales of terrestrial planets can be measured by using radioactive decay of short-lived isotopes, among which the hafnium-tungsten ( Hf − W ) isotope is widely adopted for radiometricdating. This is not only due to its applicable radioactive decay half-life time of Myr, but is also relatedto the chemical properties of these two elements: Hf is lithophile (“rock loving”) and W is siderophile(“iron loving”). W preferentially settles into the metal core and Hf remains in the silicate mantle beforethe protoplanet becomes massive enough to segregate. For instance, if the core forms early (early mantle-core segregation), the measured W abundance in the mantle would be high. On the other hand, if thecore forms late, W would be high in the core, leaving the W -deficient mantle. Therefore, measuring the Hf / W ratio in the current Earth mantle can be utilized to constrain its core formation and differentiation.Such isotope analyses indicate that core formation of Earth occurred − Myr after formation ofthe Solar System (Kleine et al. 2002; Yin et al. 2002; Jacobsen 2005; Touboul et al. 2007; Kleine et al.2009; Rudge et al. 2010). Similarly, based on Martian meteorites, the formation time of Mars is inferredto be within a few Myr (Kleine et al. 2004; Foley et al. 2005; Dauphas & Pourmand 2011), comparableto the lifetime of the proto-solar nebula.The final accretion stage of Solar System terrestrial planets, or called late giant-impact stage, istypically modeled by a numerical N-body approach (see Izidoro & Raymond (2018) for a summary ofnumerical methods). Before this stage, protoplanetary embryos of lunar to Martian masses were alreadyformed in the terrestrial planet forming region by accreting planetesimals (see Sect. 4.2). The random ve-locities of the embryos will be stirred without efficient damping, and planet-planet collisions frequentlyoccur after dispersal of the disk gas. On the other hand, giant planets have already grown to their currentmasses. The influence of gas giants (in particular Jupiter and Saturn) is crucial for sculpting the architec-ture and water delivery of the asteroid belt and the inner terrestrial planets (Raymond & Izidoro 2017;Zheng et al. 2017). Numerous numerical simulations have attempted to reproduce the terrestrial plan-ets, both in terms of the dynamical properties and geochemical accretion timescale (Chambers 2001;Raymond et al. 2004, 2006, 2009; O’Brien et al. 2006; Thommes et al. 2008; Morishima et al. 2010;Jacobson et al. 2014). The above models are either assumed to have giant planets on their current po-sitions with nearly circular or slightly eccentric orbits. However, these models still have shortcomings.For instance, the planets emerging out of the Mars forming region have masses comparable to Earth andVenus. In other words, the Mars analogs are difficult to produce in the above numerical simulations,known as the “small Mars problem”. Hansen (2009) first proposed that the proper Mars-size objectscan be yielded when the planetesimal disk is truncated at around AU. As a further step, Walsh et al.(2011) proposed that such a truncation can be physically caused by the inward-then-outward migrationof Jupiter and Saturn through planet-disk interactions, which is known as the Grand Tack model. Thekey ingredient of this model, the migration of two giant planets, is consistent with our current under-standing of the disk migration theory (Kley & Nelson 2012; Baruteau et al. 2014) and has been validatedby hydrodynamic simulations (Masset & Snellgrove 2001; Morbidelli & Crida 2007; Pierens & Nelson2008a; Zhang & Zhou 2010). The appealing point of the Grand Tack model is that it satisfactorily re-produces key observational features of the inner Solar System, such as the orbital and mass distributionsof the terrestrial planets, mass depletion and the chemical compositions of planetesimals in the asteroidbelt, and water content of Earth (O’Brien et al. 2014). On the other hand, Clement et al. (2018) pro-posed that Mars’ growth can also be stunted if the giant planet instability occurs relatively early duringthe terrestrial planet formation (e.g., (cid:46) Myr after the gas disk dispersal).It is also worth mentioning that most of the current N-body simulations only consider perfect merg-ers when two bodies collide with each other. However, the random velocities of planetesimals wouldbe excited when the masses of the protoplanets increase. The collisional outcome sensitively relatesto the masses and velocities of the colliding bodies, which could be catastrophic disruption, grindingor fragmentation (Leinhardt & Stewart 2012; Agnor & Asphaug 2004; Genda et al. 2012; Liu et al.2015). Dedicated N-body simulations including realistic collision recipes showed that the final massesand numbers of surviving planets are comparable to the case when only perfect mergers are considered, . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 23 but differences still exist in planet spins, eccentricities, core mass fractions and formation timescales(Kokubo & Genda 2010; Chambers 2013; Carter et al. 2015; Clement et al. 2019). Exoplanetary systems The observed exoplanets are more diverse than Solar System planets. One important question is howto form different planet populations, such as gas giants and super-Earths. The growth of giant planetsfirst requires the assembly of massive cores ( ∼ M ⊕ ) that can initiate rapid gas accretion (Pollack et al.1996; Ikoma et al. 2000; Hubickyj et al. 2005; Movshovitz et al. 2010) before the dispersal of the diskgas. For a nominal disk model, the planetesimal isolation mass at a distance of a few AU (the formationzone of Jupiter and Saturn) is generally lower than this critical mass (Ida & Lin 2004a). Therefore, giantplanet formation was thought to be challenging, unless the disks are extremely massive.Protoplanets approaching such isolation masses can undergo substantial orbital migration . Theseprotoplanets migrate towards and get trapped into MMRs at some zero-torque locations (or called trap-ping locations, Lyra et al. 2010; Horn et al. 2012; Kretke & Lin 2012). Depending on the number ofplanets and the gas disk mass, the resonant configurations can be disrupted with rapid migration, result-ing in frequent planet-planet collisions even in the gas-rich disk phase (Hellary & Nelson 2012; Pierenset al. 2013; Zhang et al. 2014; Liu et al. 2015). In this circumstance, massive cores can be attained earlyenough and subsequently grow into gas giants. This interpretation prefers that the cores of gas giantsonly form early when the disk is massive, e.g., the disk accretion rate is higher than ∼ − M (cid:12) yr − .Comparing that with the typical observed disk accretion rates and the ˙ M g − M (cid:63) dependence (Hartmannet al. 1998; Natta et al. 2006; Manara et al. 2016), it explains why only a minor fraction of stars harborgas giant planets (Liu et al. 2015) and why gas giant fraction increases with the mass of the central star(Liu et al. 2016). On the other hand, if planet-planet collisions do not occur early enough, planets re-main low-mass and they evolve into super-Earth systems with compact, (near) resonant configurations(Terquem & Papaloizou 2007; Ogihara & Ida 2009; Cossou et al. 2014; Ogihara et al. 2015; Izidoroet al. 2017). Numerous works also explored the detailed resonant trapping and stability of multiplesuper-Earth systems both numerically (Wang et al. 2012; Wang & Ji 2014; Sun et al. 2017; Pan et al.2020) and analytically (Quillen 2011; Hadden & Lithwick 2018; Petit et al. 2020).When examining the giant planets in the Solar System and based on the results of the Juno mission,the core of Jupiter is inferred to be diluted with an extended layer of heavy elements (Wahl et al. 2017;Helled & Stevenson 2017). The growth of proto-Jupiter has a strong influence on nearby planetesimalsand protoplanets (Zhou & Lin 2007; Ida et al. 2013). Such a diluted internal structure is likely to resultfrom the giant impacts among protoplanets during their assembling phase (Liu et al. 2019c) .The other possible explanation of super-Earths is that they only form late and in-situ when disk gasdissipates significantly. In that case, gas damping is weak and the super-Earth cores can grow quicklythrough the mergers of protoplanets (Lee & Chiang 2016). This could also explain why observed mas-sive super-Earths ( ∼ M ⊕ ) do not undergo runaway gas accretion to become gas giants (Lee et al.2014). The exact compositions and orbital properties of the formed super-Earths are determined by acombined effects of gas damping and solid accretion (Dawson et al. 2016), and potential further outgiant planets (Ji et al. 2011; Jin & Ji 2011). On the other hand, recent hydrodynamic studies found thatbecause the gas recycles efficiently between the planetary envelopes and surrounding disk, the rapidgas accretion onto super-Earths can be actually protracted (Ormel et al. 2015; Cimerman et al. 2017;Lambrechts & Lega 2017; Kuwahara et al. 2019). This also provides an interpretation for the ubiquitouspresence of super-Earths but not gas giant planets.The population synthesis model is an ideal tool to explore the influence of key physical processeson planet formation and evolution. In this approach, different physical processes are simplified into spe-cialized recipes and combined into a unified deterministic model. By Monte Carlo sampling the initialconditions over appropriate distributions, the synthetic planetary populations can be generated and thuscompared to the observed exoplanet sample in a statistical manner (see Benz et al. (2014) for a review). It worth pointing out that although the migration theory was first proposed in the late s (Lin & Papaloizou 1979;Goldreich & Tremaine 1979, 1980), it was not considered in the classical formation models of the Solar System planets (Lissauer1993). The disk migration theory attracted attention until close-in exoplanets were subsequently discovered (Lin et al. 1996). B. Liu & J. H. Ji : From Dust to Planets Ida & Lin (2004a) first applied such a calculation to investigate planet formation around Sun-like stars,and further extended their study to systems around stars of various masses and metallicities (Ida &Lin 2004b, 2005). The predicted correlation between gas giant planets and their stellar hosts exhibitedgood agreements with RV measurements (Fischer & Valenti 2005; Johnson et al. 2007). Sophisticatedpopulation synthesis models based on planetesimal accretion are further developed to make testableobservational comparisons and to study how forming planets are related to the initial disk and stellarproperties (Mordasini et al. 2009, 2012a,b; Ida et al. 2013; Jin et al. 2014; Coleman & Nelson 2014,2016; Alibert & Benz 2017; Mulders et al. 2019; Miguel et al. 2020). Stellar Binary System The previously mentioned studies focus on planet formation around single stars. However, nearlyhalf of Sun-like stars are in binaries (Duquennoy & Mayor 1991; Raghavan et al. 2010), and this frac-tion is even higher for higher-mass stars (Kouwenhoven et al. 2007). Thus, studying how planets form instellar binary systems is of crucial importance. Up to now, more than exoplanets have been discov-ered in stellar binary systems, including both S-type (satellite-like orbits around one of the single stars)and P-type (planet-like orbits around binary stars). P-type planets are also referred to as circumbinaryplanets.Planets are less common in binary systems compared to single hosts (Wang et al. 2014a,b). TheS-type planets have not yet been found in binaries with a period less than days. Close binary com-panions play a destructive role in forming S-type planets (Thebault & Haghighipour 2015). First, theprotoplanetary disk would be tidally truncated by the secondary companion, reducing the disk mass andlifetime (Artymowicz & Lubow 1994; Miranda & Lai 2015). Second, secular perturbations induced bythe companion excites high relative velocities among planetesimals, leading to catastrophic collisions(Heppenheimer 1978; Th´ebault et al. 2006, but also see Xie et al. 2010b). Third, hydrodynamic sim-ulations showed that the dynamics of disk gas in the binary system is much more complicated thantypical assumed static, axisymmetric configurations in theoretical analyses (Paardekooper et al. 2008;Kley et al. 2008; Marzari et al. 2009; M¨uller & Kley 2012). All above effects are detrimental for thegrowth of planetesimals. A noteworthy point is that, disruptive collisions among planetesimals wouldproduce a reservoir of dust debris. The sweeping of the dust debris can nevertheless boost further massgrowth of surviving, leftover planetesimals (Paardekooper & Leinhardt 2010; Xie et al. 2010a).Although in-situ formation of S-type planets in close binaries seems to be very challenging, it iscomparatively easy to form P-type planets. Disk-driven migration needs to be considered when theplanets grow massive (Pierens & Nelson 2008b; Kley & Haghighipour 2015). The subsequent evolutionof planetary systems includes the MMR capture, excitation of eccentricities along with the gas disk dis-sipation and planet–planet scattering. Gong & Ji (2018) suggested that S-type planets can form throughplanet-planet scattering from P-type planets and then tidally capture in various binary configurations. Asmaller eccentricity or a lower mass ratio of the binary leads to a higher capture probability up to and produces S-type planets with retrograde orbits, consistent with the result of the two unequal-massplanet ejection model (Gong & Ji 2017).Another important topic is the orbital configuration of circumbinary planets (P-type orbits). Morethan circumbinary planets have been detected so far (Schwarz et al. 2016). For those discovered bythe Kepler mission, the planets are inferred to be inclined by less than a few degrees relative to thebinary plane (Kostov et al. 2014). However, the above coplanarity might be caused by the observationalbias: planets orbiting in the binary plane are easier to detect. On the other hand, circumbinary diskswith high inclinations have been subsequently discovered (Kennedy et al. 2012; Brinch et al. 2016;Czekala et al. 2019), even on polar orbits (Kennedy et al. 2019). Such misaligned disks may stronglyindicate the existence of high-inclination circumbinary planets. In addition, since most stars originatefrom star clusters and stellar associations (Lada & Lada 2003), the planetary orbits can be influencedby perturbations from stellar fly-bys. This idea has been explored mainly for planetary systems aroundSun-like single stellar hosts, and the corresponding studies generally found that close encounters fromthe passing-by stars are prone to be destructive for planetary systems, reducing their multiplicities withsurviving planets on more eccentric and inclined orbits. (Spurzem et al. 2009; Malmberg et al. 2011;Pfalzner 2013; Liu et al. 2013; Hao et al. 2013; Li & Adams 2015; Zheng et al. 2015; Cai et al. 2017; . Liu & J. H. Ji. Liu & J. H. Ji The previously mentioned studies focus on planet formation around single stars. However, nearlyhalf of Sun-like stars are in binaries (Duquennoy & Mayor 1991; Raghavan et al. 2010), and this frac-tion is even higher for higher-mass stars (Kouwenhoven et al. 2007). Thus, studying how planets form instellar binary systems is of crucial importance. Up to now, more than exoplanets have been discov-ered in stellar binary systems, including both S-type (satellite-like orbits around one of the single stars)and P-type (planet-like orbits around binary stars). P-type planets are also referred to as circumbinaryplanets.Planets are less common in binary systems compared to single hosts (Wang et al. 2014a,b). TheS-type planets have not yet been found in binaries with a period less than days. Close binary com-panions play a destructive role in forming S-type planets (Thebault & Haghighipour 2015). First, theprotoplanetary disk would be tidally truncated by the secondary companion, reducing the disk mass andlifetime (Artymowicz & Lubow 1994; Miranda & Lai 2015). Second, secular perturbations induced bythe companion excites high relative velocities among planetesimals, leading to catastrophic collisions(Heppenheimer 1978; Th´ebault et al. 2006, but also see Xie et al. 2010b). Third, hydrodynamic sim-ulations showed that the dynamics of disk gas in the binary system is much more complicated thantypical assumed static, axisymmetric configurations in theoretical analyses (Paardekooper et al. 2008;Kley et al. 2008; Marzari et al. 2009; M¨uller & Kley 2012). All above effects are detrimental for thegrowth of planetesimals. A noteworthy point is that, disruptive collisions among planetesimals wouldproduce a reservoir of dust debris. The sweeping of the dust debris can nevertheless boost further massgrowth of surviving, leftover planetesimals (Paardekooper & Leinhardt 2010; Xie et al. 2010a).Although in-situ formation of S-type planets in close binaries seems to be very challenging, it iscomparatively easy to form P-type planets. Disk-driven migration needs to be considered when theplanets grow massive (Pierens & Nelson 2008b; Kley & Haghighipour 2015). The subsequent evolutionof planetary systems includes the MMR capture, excitation of eccentricities along with the gas disk dis-sipation and planet–planet scattering. Gong & Ji (2018) suggested that S-type planets can form throughplanet-planet scattering from P-type planets and then tidally capture in various binary configurations. Asmaller eccentricity or a lower mass ratio of the binary leads to a higher capture probability up to and produces S-type planets with retrograde orbits, consistent with the result of the two unequal-massplanet ejection model (Gong & Ji 2017).Another important topic is the orbital configuration of circumbinary planets (P-type orbits). Morethan circumbinary planets have been detected so far (Schwarz et al. 2016). For those discovered bythe Kepler mission, the planets are inferred to be inclined by less than a few degrees relative to thebinary plane (Kostov et al. 2014). However, the above coplanarity might be caused by the observationalbias: planets orbiting in the binary plane are easier to detect. On the other hand, circumbinary diskswith high inclinations have been subsequently discovered (Kennedy et al. 2012; Brinch et al. 2016;Czekala et al. 2019), even on polar orbits (Kennedy et al. 2019). Such misaligned disks may stronglyindicate the existence of high-inclination circumbinary planets. In addition, since most stars originatefrom star clusters and stellar associations (Lada & Lada 2003), the planetary orbits can be influencedby perturbations from stellar fly-bys. This idea has been explored mainly for planetary systems aroundSun-like single stellar hosts, and the corresponding studies generally found that close encounters fromthe passing-by stars are prone to be destructive for planetary systems, reducing their multiplicities withsurviving planets on more eccentric and inclined orbits. (Spurzem et al. 2009; Malmberg et al. 2011;Pfalzner 2013; Liu et al. 2013; Hao et al. 2013; Li & Adams 2015; Zheng et al. 2015; Cai et al. 2017; . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 25 Li et al. 2019a). Similarly, the cluster environment can also significantly impact the planets in binarysystems. Ma et al. (2020) showed that these stellar fly-bys can affect the inclination distribution ofcircumbinary planets. For instance, for close binary systems originating in open clusters with a spacingof > AU, a few repeated fly-bys can already induce their highly-inclined orbits. In this section, we recapitulate pebble accretion, including the physical mechanism (Sect. 5.1), the ac-cretion rates and efficiencies in different regimes (Sect. 5.2), the properties (Sect. 5.3) and applications(Sect. 5.4). In contrast to planetesimal accretion, pebble accretion refers to pebble-sized ( ∼ mm-cm) solid particlesthat get accreted by planetary bodies (Ormel & Klahr 2010; Lambrechts & Johansen 2012). Since thesesmall pebbles are strongly influenced by the surrounding disk gas, both gas drag and gravitational forceplay decisive roles during the pebble-planet encounter (also see reviews of Johansen & Lambrechts2017 and Ormel 2017). Here we provide a physical picture of pebble accretion based on the order-of-magnitude timescale analysis. How and in which condition pebble accretion commences are discussedas follows.During a pebble-planet encounter, the operation of pebble accretion needs to satisfy the followingtwo conditions:1. The time a pebble settled onto the planet t set is shorter than the pebble-planet encounter time t enc ;otherwise, the pebble cannot be accreted onto the planet.2. The stopping time of the pebble t stop is shorter than the pebble-planet encounter time t enc , whichmeans that gas drag matters during pebble-planet interaction; otherwise, the pebble-planet interac-tion is similar to the planetesimal-planet interaction, where only gravitational force plays a role.An illustration of the pebble-planet encounter is displayed in Figure 6. When the pebble closelyinteracts with the planet, the gas drag acceleration a drag =( v peb − v g ) /t stop is adjusted quasi-staticallyto balance the gravitational acceleration a g = GM p /b , where b is the impact parameter during the en-counter and t stop is the stopping time of the pebble, which quantifies how fast the orbit of the pebble isadapted to the gas due to the gas friction force. The pebble reaches a terminal velocity to sediment ontothe planet such that v set (cid:39) GM p t stop /b . The settling time and encounter time are given by t set = b/v set and t enc = b/ ∆ v respectively (see Figure 6), where ∆ v is the unperturbed relative velocity between theplanet and pebble. When the above two terms are equal, it gives the largest pebble accretion radius inthe settling regime (Ormel & Klahr 2010; Lambrechts & Johansen 2012; Ida et al. 2016) b set (cid:39) (cid:114) GM p t stop ∆ v . (17)As can be seen from the above equation, b set is smaller as t stop becomes shorter. Physically, this isbecause smaller pebbles with a shorter t stop are more tightly coupled to gas. The trajectories of thesepebbles become strongly affected by the planet only when they sediment deeply enough to the planet.The accretion radius is therefore smaller.Equivalently, criterion (1) can also be derived from the concept of gravitational deflection(Lambrechts & Johansen 2012). Pebble accretion occurs when the gravitational deflation time t g =∆ v/a g = ∆ v/ ( GM p /b ) is shorter than the pebble stopping time t stop . Equation 17 can be ob-tained by equating t g with t stop .Criterion (2) breaks down when the unperturbed encounter velocity ∆ v is so high that t stop ≥ t enc . Inthis limit, gas drag is too weak to influence the orbit of the pebble during this short timespan. By equatingthe above two timescales, we obtain a threshold velocity v ∗ = (cid:112) M p /M (cid:63) τ s v K . When ∆ v (cid:28) v ∗ , pebble B. Liu & J. H. Ji : From Dust to Planets planet e r e v set b b v pebble Fig. 6: Sketch of the pebble-planet encounter, viewed in a co-moving frame with a central planet. Theapproach velocity is given by the unperturbed relative velocity between these two bodies ( ∆ v ). Theperturbed and unperturbed trajectories are represented in the blue solid and dashed lines respectivelywith an impact distance parameter b . The important timescales are: the stopping time of the pebble t stop , the pebble-planet encounter time t enc = b/ ∆ v , and the settling time t set = b/v set , where v set isthe sedimentation velocity when the planet’s gravity equals the gas drag. Figure adopted from Liu &Ormel (2018).accretion is in the settling regime (Ormel & Klahr 2010) (equivalent to the strongly-coupled regimein Lambrechts & Johansen 2012). When ∆ v (cid:38) v ∗ , the accretion enters the inefficient ballistic regime(weakly-coupled regime), where gas drag is unimportant. An exponential decay function is applied tofit such a transition (Ormel & Klahr 2010; Liu & Ormel 2018), f set = exp (cid:34) − . (cid:18) ∆ vv ∗ (cid:19) (cid:35) , (18)and the accretion radius is expressed as b PA = b set f set .In order to distinguish from planetesimal accretion, conventionally, pebble accretion refers to thesettling regime when the growth is efficiently assisted by the gas drag ( f set ∼ = 1 ). However, when themass of the planet/planetesimal is low or τ s is high, the settling condition is not always satisfied and theaccretion can be inefficient. We can obtain the critical mass for the onset of efficient pebble accretion( f set ∼ = 1 ) by equating v ∗ with ∆ v (adopted to be the headwind velocity ηv K , see Sect. 5.2), which gives M onset = τ s η M (cid:63) = 2 . × − (cid:16) τ s . (cid:17) (cid:18) η × − (cid:19) (cid:18) M (cid:63) M (cid:12) (cid:19) M ⊕ , (19)corresponding to a km radius planetesimal . Since the typical planetary bodies we consider aremuch more massive than M onset , for simplicity, the referred pebble accretion hereafter only correspondsto the accretion in the settling regime ( b PA = b set ). The above expression is consistent with Eq. 25 of Visser & Ormel (2016). . Liu & J. H. Ji. Liu & J. H. Ji In contrast to planetesimal accretion, pebble accretion refers to pebble-sized ( ∼ mm-cm) solid particlesthat get accreted by planetary bodies (Ormel & Klahr 2010; Lambrechts & Johansen 2012). Since thesesmall pebbles are strongly influenced by the surrounding disk gas, both gas drag and gravitational forceplay decisive roles during the pebble-planet encounter (also see reviews of Johansen & Lambrechts2017 and Ormel 2017). Here we provide a physical picture of pebble accretion based on the order-of-magnitude timescale analysis. How and in which condition pebble accretion commences are discussedas follows.During a pebble-planet encounter, the operation of pebble accretion needs to satisfy the followingtwo conditions:1. The time a pebble settled onto the planet t set is shorter than the pebble-planet encounter time t enc ;otherwise, the pebble cannot be accreted onto the planet.2. The stopping time of the pebble t stop is shorter than the pebble-planet encounter time t enc , whichmeans that gas drag matters during pebble-planet interaction; otherwise, the pebble-planet interac-tion is similar to the planetesimal-planet interaction, where only gravitational force plays a role.An illustration of the pebble-planet encounter is displayed in Figure 6. When the pebble closelyinteracts with the planet, the gas drag acceleration a drag =( v peb − v g ) /t stop is adjusted quasi-staticallyto balance the gravitational acceleration a g = GM p /b , where b is the impact parameter during the en-counter and t stop is the stopping time of the pebble, which quantifies how fast the orbit of the pebble isadapted to the gas due to the gas friction force. The pebble reaches a terminal velocity to sediment ontothe planet such that v set (cid:39) GM p t stop /b . The settling time and encounter time are given by t set = b/v set and t enc = b/ ∆ v respectively (see Figure 6), where ∆ v is the unperturbed relative velocity between theplanet and pebble. When the above two terms are equal, it gives the largest pebble accretion radius inthe settling regime (Ormel & Klahr 2010; Lambrechts & Johansen 2012; Ida et al. 2016) b set (cid:39) (cid:114) GM p t stop ∆ v . (17)As can be seen from the above equation, b set is smaller as t stop becomes shorter. Physically, this isbecause smaller pebbles with a shorter t stop are more tightly coupled to gas. The trajectories of thesepebbles become strongly affected by the planet only when they sediment deeply enough to the planet.The accretion radius is therefore smaller.Equivalently, criterion (1) can also be derived from the concept of gravitational deflection(Lambrechts & Johansen 2012). Pebble accretion occurs when the gravitational deflation time t g =∆ v/a g = ∆ v/ ( GM p /b ) is shorter than the pebble stopping time t stop . Equation 17 can be ob-tained by equating t g with t stop .Criterion (2) breaks down when the unperturbed encounter velocity ∆ v is so high that t stop ≥ t enc . Inthis limit, gas drag is too weak to influence the orbit of the pebble during this short timespan. By equatingthe above two timescales, we obtain a threshold velocity v ∗ = (cid:112) M p /M (cid:63) τ s v K . When ∆ v (cid:28) v ∗ , pebble B. Liu & J. H. Ji : From Dust to Planets planet e r e v set b b v pebble Fig. 6: Sketch of the pebble-planet encounter, viewed in a co-moving frame with a central planet. Theapproach velocity is given by the unperturbed relative velocity between these two bodies ( ∆ v ). Theperturbed and unperturbed trajectories are represented in the blue solid and dashed lines respectivelywith an impact distance parameter b . The important timescales are: the stopping time of the pebble t stop , the pebble-planet encounter time t enc = b/ ∆ v , and the settling time t set = b/v set , where v set isthe sedimentation velocity when the planet’s gravity equals the gas drag. Figure adopted from Liu &Ormel (2018).accretion is in the settling regime (Ormel & Klahr 2010) (equivalent to the strongly-coupled regimein Lambrechts & Johansen 2012). When ∆ v (cid:38) v ∗ , the accretion enters the inefficient ballistic regime(weakly-coupled regime), where gas drag is unimportant. An exponential decay function is applied tofit such a transition (Ormel & Klahr 2010; Liu & Ormel 2018), f set = exp (cid:34) − . (cid:18) ∆ vv ∗ (cid:19) (cid:35) , (18)and the accretion radius is expressed as b PA = b set f set .In order to distinguish from planetesimal accretion, conventionally, pebble accretion refers to thesettling regime when the growth is efficiently assisted by the gas drag ( f set ∼ = 1 ). However, when themass of the planet/planetesimal is low or τ s is high, the settling condition is not always satisfied and theaccretion can be inefficient. We can obtain the critical mass for the onset of efficient pebble accretion( f set ∼ = 1 ) by equating v ∗ with ∆ v (adopted to be the headwind velocity ηv K , see Sect. 5.2), which gives M onset = τ s η M (cid:63) = 2 . × − (cid:16) τ s . (cid:17) (cid:18) η × − (cid:19) (cid:18) M (cid:63) M (cid:12) (cid:19) M ⊕ , (19)corresponding to a km radius planetesimal . Since the typical planetary bodies we consider aremuch more massive than M onset , for simplicity, the referred pebble accretion hereafter only correspondsto the accretion in the settling regime ( b PA = b set ). The above expression is consistent with Eq. 25 of Visser & Ormel (2016). . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 27 The above analysis holds when the planet feedback onto the disk gas is negligible. However, theplanet perturbation increases with its growing mass. When the planet is massive enough to open a gapand reverse the local gas pressure gradient, the inward drifting pebbles stop at the local pressure max-imum. In this case, pebble accretion cannot proceed, quenching the core mass growth. Such a processleads to a ‘pebble isolation’ from the planet, and the onset mass of the planet is called pebble isolationmass (Lambrechts et al. 2014; Bitsch et al. 2018; Ataiee et al. 2018). For instance, Bitsch et al. (2018)obtained a fitting formula for the pebble isolation mass from hydrodynamical simulations, which reads M iso =25 (cid:18) h g . (cid:19) (cid:18) M (cid:63) M (cid:12) (cid:19) (cid:34) . (cid:18) − α t (cid:19) + 0 . (cid:35)(cid:20) − ∂ ln P g /∂ ln r + 2 . (cid:21) M ⊕ , (20)where α t is the efficiency factor of the turbulent viscosity where ν t = α t c s H g (Shakura & Sunyaev 1973).The termination of pebble accretion corresponds to − M ⊕ super-Earth planets around solar-massstars and Earth-mass planets around . M (cid:12) late M-dwarf stars. As shown in Eq. 17, the accretion radius depends on the relative velocity between the pebble and planet ∆ v . For a planet on a circular orbit, ∆ v is a sum of the headwind velocity ηv K and the Keplerian shearvelocity Ω K b set . The accretion is in the headwind regime (Bondi regime) when ∆ v is dominated by ηv K , while it is in the shear regime (Hill regime) when ∆ v is dominated by the Keplerian shear. Thetransition planet mass between the headwind and shear regimes can be calculated by equating the abovetwo velocities, M hw / sh = η M (cid:63) /τ s (cid:39) . (cid:18) η × − (cid:19) (cid:16) τ s . (cid:17) − (cid:18) M (cid:63) M (cid:12) (cid:19) M ⊕ . (21)When a planet is on an eccentric and inclined orbit, ∆ v is additionally contributed by the epicyclicmotion ( ev K and iv K ) of the planet relative to its Keplerian velocity (Johansen et al. 2015; Liu & Ormel2018; Ormel & Liu 2018).The pebble mass accretion rate can be expressed as (Lambrechts & Johansen 2014; Morbidelli et al.2015) ˙ M PA = b set ∆ v Σ peb (cid:39) (cid:112) GM p t stop ∆ v Σ peb [2D] ,b ∆ vρ peb (cid:39) GM p t stop Σ peb √ πH peb [3D] , (22)where Σ peb = √ πH peb ρ peb . The scale height of the pebble disk is given by Youdin & Lithwick (2007), H peb = (cid:114) δ d δ d + τ s H g , (23)where δ d represents the coefficient of the gas diffusivity, which approximates to the efficiency factorof the turbulent viscosity α t when the disk turbulence is driven by the MRI (Johansen & Klahr 2005;Zhu et al. 2015) . In order to distinguish the dominant accretion regime, one can numerically compare ˙ M PA , / to see which one is higher for given disk and planet parameters. From a physical perspective,whether the accretion is in D/ D is determined by the ratio between the pebble accretion radius b set It is worth noting that the non-ideal MHD effects, such as ambipolar diffusion and Hall Effect, also play important roles indistributing angular momentum of disk gas. The above processes crucially depend on the disk chemistry and the geometry andstrength of the magnetic field (Bai & Stone 2013; Bai 2015, 2016; Gressel et al. 2015). B. Liu & J. H. Ji : From Dust to Planets and the pebble scale height H peb (Morbidelli et al. 2015). When the pebble accretion radius is largerthan the pebble scale height, it is in the D accretion regime; otherwise, it is in the D accretion regime.The disk pebble flux that bypasses the orbit of the planet is ˙ M peb = 2 πr Σ peb v r . The pebble ac-cretion efficiency is defined as the probability of pebbles accreted by the planet, ε PA = ˙ M PA / ˙ M peb (Guillot et al. 2014; Lambrechts & Johansen 2014). When the radial velocity of the gas is neglected in v r (Eq. 6), the efficiency can be written as ε PA = × − (cid:18) M p . M ⊕ (cid:19) / (cid:16) τ s . (cid:17) − / (cid:18) η . × − (cid:19) − / (cid:18) M (cid:63) M (cid:12) (cid:19) − / [2D headwind] , × − (cid:18) M p . M ⊕ (cid:19) / (cid:16) τ s . (cid:17) − / (cid:18) η . × − (cid:19) − (cid:18) M (cid:63) M (cid:12) (cid:19) − / [2D shear] , × − (cid:18) M p . M ⊕ (cid:19) (cid:18) h peb . × − (cid:19) − (cid:18) η . × − (cid:19) − (cid:18) M (cid:63) M (cid:12) (cid:19) − [3D] , (24)where h peb = H peb /r is the pebble disk aspect ratio. The full expression of ε PA including the eccentricityand inclination dependences can be found in Liu & Ormel (2018) and Ormel & Liu (2018). The pebbleaccretion efficiency is a crucial quantity in planet formation, since it corresponds to how efficiently thedisk pebble mass can be converted into planet mass.The pebble accretion timescale is therefore given by t PA = M p ˙ M peb ε PA (cid:39) × (cid:18) M p . M ⊕ (cid:19) / (cid:16) τ s . (cid:17) / (cid:18) η . × − (cid:19) / (cid:32) ˙ M peb − M ⊕ yr (cid:33) − (cid:18) M (cid:63) M (cid:12) (cid:19) / yr [2D headwind] , × (cid:18) M p . M ⊕ (cid:19) / (cid:16) τ s . (cid:17) / (cid:18) η . × − (cid:19)(cid:32) ˙ M peb − M ⊕ yr (cid:33) − (cid:18) M (cid:63) M (cid:12) (cid:19) / yr [2D shear] , × (cid:18) h peb . × − (cid:19) (cid:18) η . × − (cid:19) (cid:32) ˙ M peb − M ⊕ yr (cid:33) − (cid:18) M (cid:63) M (cid:12) (cid:19) yr [3D] , (25)We can see that t PA is proportional to M / or M / in the D headwind or shear accretion regime,while τ PA is independent of the planet mass in the D regime. The first important feature is that pebble accretion is not a runaway process. From Eq. 22 we can seethat ( dM/dt ) /M ∝ M in the D regime, and ( dM/dt ) /M ∝ M − / or M − / in the D headwindor shear regime. This means that the mass ratios among the growing bodies would approach the orderof unity as the accretion proceeds. This is the feature of the orderly growth. Nevertheless, even not in arunaway mode, pebble accretion can still be very fast due to a large accretion cross section and a highflux of continuous feeding pebbles from the outer part of the disk (see discussions in Sect. 6).The efficiency of pebble accretion is determined by the Stokes number of the pebbles. When pebbleaccretion is in the D regime, the efficiency increases with the Stokes number. This is because higher . Liu & J. H. Ji. Liu & J. H. Ji The first important feature is that pebble accretion is not a runaway process. From Eq. 22 we can seethat ( dM/dt ) /M ∝ M in the D regime, and ( dM/dt ) /M ∝ M − / or M − / in the D headwindor shear regime. This means that the mass ratios among the growing bodies would approach the orderof unity as the accretion proceeds. This is the feature of the orderly growth. Nevertheless, even not in arunaway mode, pebble accretion can still be very fast due to a large accretion cross section and a highflux of continuous feeding pebbles from the outer part of the disk (see discussions in Sect. 6).The efficiency of pebble accretion is determined by the Stokes number of the pebbles. When pebbleaccretion is in the D regime, the efficiency increases with the Stokes number. This is because higher . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 29 Stokes number pebbles sediment into a thinner vertical layer, increasing the number density of pebblesfor being accreted. When the accretion is in the D regime, the efficiency decreases with τ s . In this case,higher Stokes number pebbles drift faster and have a lower probability to be accreted by the planet (seeFig.4 of Ormel & Liu (2018)). The above dependences hold when pebbles are marginally coupled to thedisk gas ( − (cid:46) τ s (cid:46) ). When τ s is much larger than the order of unity, gas drag is negligible andpebbles are more aerodynamic like planetesimals. In that circumstance, the actual accretion rate dropssubstantially (Ormel & Klahr 2010). Conversely, when τ s (cid:46) − , the pebbles are tightly coupled tothe gas flow. Accretion rate is also very low in this geometric regime (Guillot et al. 2014). Therefore,the preferred Stokes number for pebble accretion ranges from − to , corresponding to . mm to cm size particles at AU in the MMSN model.Pebble accretion is suppressed when the disk is highly turbulent (Morbidelli et al. 2015; Ormel &Liu 2018; Rosenthal et al. 2018). There are two reasons. First, pebbles are stirred up vertically due tothe turbulent diffusion. In a strongly turbulent case, a vertically extended distribution of pebbles leadsto less amount of them being accreted, and the corresponding efficiency is lower. This is similar to theeffect of the smaller pebbles in the D regime discussed above. Second, the pebble’s random velocityalso correlates with disk turbulence as √ α t τ s c s (Ormel & Cuzzi 2007). The impact velocity between thepebble and planet is additionally contributed by this turbulent-induced motion. The settling conditionfails when the turbulent velocity is very high (Sect. 5.1), and therefore, the accretion is also significantlysuppressed. Ormel & Liu (2018) obtained a pebble accretion efficiency formula by accounting for thestochastic turbulent velocity into the equation of motion for the pebble. Their results are in agreementwith the pebble accretion measured from more realistic MHD simulations of Xu et al. (2017) as well asthe VSI hydrodynamic simulations of Picogna et al. (2018).We note that the trajectories of pebbles and accretion features could deviate from the above de-scribed paradigm that only steady-state shear gas flow is considered (Sect. 5.1). There are two additionaleffects. First, when pebbles are sedimented and accreted onto the planet, the potential energy of pebblesis transferred into frictional heat, which raises the temperature of surrounding gas. The deep gas layerclose to the planet is more dynamically convective caused by this accretion-driven heating, which mayaffect the pebble accretion. Taking into account both adiabatic and convective models of pebble accre-tion in hydrodynamic simulations, Popovas et al. (2018) found that even though an active mass mixingamong different layers is indeed observed due to the vigorous gas motion, the net pebble accretion isnot strongly affected, except for the smallest particles that are tightly coupled to the gas.Second, when the pebbles fall into the region close to the planet with a temperature exceedingtheir evaporation temperature, these pebbles get vaporized, resulting in an enrichment of the planetaryenvelope rather than direct accretion onto the core (Alibert 2017; Brouwers et al. 2018; Valletta &Helled 2019). This enrichment increases the gas mean molecular weight of the envelope, resulting in athinner, opaque envelope (Venturini et al. 2016). Meanwhile, hydrodynamic simulations indicated thatthe envelopes of gas for low-mass protoplanets are not in a steady-state but rather get replenished by thesurrounding disk gas (Ormel et al. 2015; Fung & Dong 2015; Cimerman et al. 2017). It is unclear howlargely the envelope enrichment process would be affected by the above gas recycling. The ablation ofaccreting pebbles with realistic radiative transfer plus gas replenishment models, and how these affectthe core mass growth and gas accretion are an active research topics for future investigations. The pebble accretion scenario has been used to explain the formation of the Solar System. Based on thefact that icy pebbles drift across the water-ice line and sublimate into small silicate pebbles, Morbidelliet al. (2015) inferred that the growth of protoplanets is in a slow D accretion interior to the ice line anda fast D accretion exterior to the ice line. This results in low-mass progenitors of terrestrial planets inthe inner disk regions and massive cores of giant planets in the outer disk regions, in agreement withthe architecture of the Solar System. Levison et al. (2015) found that before efficient pebble accretioncommences, an early phase of velocity stirring of protoplanets is required. Protoplanets then evolve B. Liu & J. H. Ji : From Dust to Planets into a bimodal mass distribution. Due to dynamical friction, the massive protoplanets have low veloc-ity dispersions. After this phase, only these massive protoplanets can undergo rapid pebble accretionand grow to giant planet cores. The above self-excitation process is essential to explain why only afew giant planet cores formed in the Solar System. If there were no such pre-stirring phase, hundredsof Earth-mass objects would form instead (Kretke & Levison 2014). Johansen et al. (2015) proposedthe formation of asteroids and Kuiper belt objects by accreting chondrules, which are millimeter-sizedspherules commonly found in primitive meteorites. Furthermore, formation of the Galilean satellites hasalso been recently proposed to be aided by pebble accretion (Shibaike et al. 2019; Ronnet & Johansen2020). Exoplanetary Systems The pebble accretion scenario is also widely adopted to explain the formation of super-Earths and gasgaints in exoplanetary systems. Lambrechts & Johansen (2014) constructed a dust growth and pebbledrift model to investigate the formation of giant planet cores by pebble accretion. Bitsch et al. (2015)studied the influence of disk radial distance and evolutional phase on the growth and migration of asingle protoplanet, and Johansen et al. (2019) focused on conditions under which growth can overcomemigration. Numerous recent studies have incorporated the pebble accretion model into an N-body codeto investigate the impact of pebble accretion on final planetary architectures (Matsumura et al. 2017;Lambrechts et al. 2019; Bitsch et al. 2019; Izidoro et al. 2019; Liu et al. 2019b; Schoonenberg et al.2019; Coleman et al. 2019; Wimarsson et al. 2020; Ogihara et al. 2020). For instance, Lambrechtset al. (2019) demonstrated that the final type of planetary system (terrestrial planets or super-Earths)is crucially determined by the pebble flux, or equivalently, the total mass of the pebble reservoir in aprotoplanetary disk. Systems around Low-mass Stars Studies of pebble accretion are not only limited to the systems around solar-mass stars, but also are gen-eralized to stellar hosts of different masses. Ormel (2017) proposed a formation scenario for TRAPPIST- (Gillon et al. 2016, 2017) and other compact systems around very low-mass M-dwarf stars. In theirscenario, protoplanets form by the streaming instability at the water-ice line. These protoplanets subse-quently undergo inward migration and accrete pebbles to reach their final masses. Ormel (2017) sug-gested that all TRAPPIST- planets of roughly Earth-mass could be an indication of the planet mass reg-ulated by pebble isolation. The follow-up numerical simulations by Schoonenberg et al. (2019) verifiedthat these forming planets have ≈ water mass fractions, consistent with bulk density measurementsand interior modeling of the TRAPPIST- planets (Grimm et al. 2018; Unterborn et al. 2017; Dorn et al.2018).Liu et al. (2019a) investigated pebble-driven planet formation around stars of masses from . M (cid:12) to M (cid:12) . Figure 7 illustrates the planet populations from observations and the population synthesismodel of Liu et al. (2019a). It should be noted that the observed sample is adopted from different surveysand uncorrected for any selectional bias. The figure nevertheless illustrates important features. First, apaucity of giant planets but not super-Earths is found around stars with masses below (cid:39) . − . M (cid:12) (Figure 7a). Since larger planets are easier to detect than smaller planets for the same mass stellar hosts,the above planet desert is physical. Second, there seems to be a linear mass trend between the low-massrocky-dominated planets (reflecting their core masses) and their stellar hosts for systems around starsless massive than . M (cid:12) . Again, the observational bias would not be the cause of this pattern, whichleads to the opposite trend, due to the fact that more massive planets are easier to detect around smallerstars. For systems around stars more massive than . M (cid:12) , we cannot directly infer the core masses,since the observed sample is outnumbered by gas-rich giant planets. On the other hand, the above linear M c − M (cid:63) correlation exhibited in late-M dwarf systems is in good agreement with the inter-systemuniformity reported from the super-Earth planets detected by the Kepler mission around more massiveearly M-dwarfs and FGK stars (Pascucci et al. 2018; Wu 2019). The validity of this positive correlationalso needs to be unbiased and complementarily tested by current and future RV programs for a widermass range of stellar hosts, such as High Accuracy Radial Velocity Planet Searcher, (HARPS, Mayoret al. 2003, 2011; Udry et al. 2019), Echelle Spectrograph for Rocky Exoplanet and Stable SpectroscopicObservations (ESPRESSO, Pepe et al. 2010), Planet Finder Spectrograph, (PFS,Crane et al. 2010; Feng . Liu & J. H. Ji. Liu & J. H. Ji Studies of pebble accretion are not only limited to the systems around solar-mass stars, but also are gen-eralized to stellar hosts of different masses. Ormel (2017) proposed a formation scenario for TRAPPIST- (Gillon et al. 2016, 2017) and other compact systems around very low-mass M-dwarf stars. In theirscenario, protoplanets form by the streaming instability at the water-ice line. These protoplanets subse-quently undergo inward migration and accrete pebbles to reach their final masses. Ormel (2017) sug-gested that all TRAPPIST- planets of roughly Earth-mass could be an indication of the planet mass reg-ulated by pebble isolation. The follow-up numerical simulations by Schoonenberg et al. (2019) verifiedthat these forming planets have ≈ water mass fractions, consistent with bulk density measurementsand interior modeling of the TRAPPIST- planets (Grimm et al. 2018; Unterborn et al. 2017; Dorn et al.2018).Liu et al. (2019a) investigated pebble-driven planet formation around stars of masses from . M (cid:12) to M (cid:12) . Figure 7 illustrates the planet populations from observations and the population synthesismodel of Liu et al. (2019a). It should be noted that the observed sample is adopted from different surveysand uncorrected for any selectional bias. The figure nevertheless illustrates important features. First, apaucity of giant planets but not super-Earths is found around stars with masses below (cid:39) . − . M (cid:12) (Figure 7a). Since larger planets are easier to detect than smaller planets for the same mass stellar hosts,the above planet desert is physical. Second, there seems to be a linear mass trend between the low-massrocky-dominated planets (reflecting their core masses) and their stellar hosts for systems around starsless massive than . M (cid:12) . Again, the observational bias would not be the cause of this pattern, whichleads to the opposite trend, due to the fact that more massive planets are easier to detect around smallerstars. For systems around stars more massive than . M (cid:12) , we cannot directly infer the core masses,since the observed sample is outnumbered by gas-rich giant planets. On the other hand, the above linear M c − M (cid:63) correlation exhibited in late-M dwarf systems is in good agreement with the inter-systemuniformity reported from the super-Earth planets detected by the Kepler mission around more massiveearly M-dwarfs and FGK stars (Pascucci et al. 2018; Wu 2019). The validity of this positive correlationalso needs to be unbiased and complementarily tested by current and future RV programs for a widermass range of stellar hosts, such as High Accuracy Radial Velocity Planet Searcher, (HARPS, Mayoret al. 2003, 2011; Udry et al. 2019), Echelle Spectrograph for Rocky Exoplanet and Stable SpectroscopicObservations (ESPRESSO, Pepe et al. 2010), Planet Finder Spectrograph, (PFS,Crane et al. 2010; Feng . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 31 P l a n e t m a ss [ M ] (a) observed exoplanets Msini from RV mass from RV + transit or TTV P l a n e t m a ss [ M ] (b) simulated planet population Fig. 7: Planet mass vs. stellar mass for the observed exoplanets (top) and simulated planet populations(bottom). Top panel: the blue dots are the planets only detected by RV surveys with a low mass limit,and the red dots are the planets with true masses either from combined RV and transit surveys, or fromtransit timing variation measurements. The selected planets also have relatively precise stellar massmeasurements ( ∆ (cid:15) =∆ M (cid:63) /M (cid:63) ≤ ). The data are adopted from the NASA exoplanet archive, whichis not corrected for observational bias. Bottom panel: Monte Carlo sampling plot of the resultant planets,where the initial protoplanetary seeds are assumed to form at the water-ice line with masses of . M ⊕ .The solid line represents the characteristic mass of super-Earths, set by the pebble isolation mass fromEq. 26, whereas the dashed lines indicate a factor of two mass variation. The figure is reproduced basedon Liu et al. (2019a). B. Liu & J. H. Ji : From Dust to Planets et al. 2019), and Calar Alto high-Resolution search for M dwarfs with Exoearths with Near-infrared andoptical Echelle Spectrographs (CARMENES, Quirrenbach et al. 2016).Importantly, Liu et al. (2019a) proposed that the characteristic mass (core mass) of super-Earths isset by the pebble isolation mass, which increases linearly with the mass of the stellar host. The pebbleisolation mass can be written as (Liu et al. 2019a) M iso = 25 (cid:18) M (cid:63) M (cid:12) (cid:19) (cid:18) h g . (cid:19) M ⊕ = 25 (cid:18) M (cid:63) M (cid:12) (cid:19) / (cid:32) ˙ M g (cid:12) × − M (cid:12) yr − (cid:33) / . (26)In the above equation, we neglect α t and η dependencies on M iso , ˙ M g (cid:12) is the fiducial disk accretion ratearound the solar-mass star, and h g is derived from the viscously heated disk model by assuming that thedisk accretion rate scales with the stellar mass squared. Figure 7(b) shows the resultant planets generatedfrom the population synthesis model, and the solid line refers to the pebble isolation mass (Eq. 26). Weclearly see that the super-Earths reaching M iso increase with their stellar masses, approximately Earth-mass terrestrial planets around stars of . M (cid:12) and − M ⊕ around solar-mass stars. We also notethat M iso decreases when the disk evolves and h g as well as ˙ M g decline. For instance, planets aroundsolar-mass stars reach M iso of M ⊕ when ˙ M g (cid:12) =10 − M (cid:12) yr − . Since M iso is so low around lateM-dwarfs, massive gas giants are unlikely to form in such systems through the pebble accretion planetformation channel. Liu et al. (2020) further applied this approach for even lower-mass central hosts andfound the above linear mass scaling holds for planets around brown dwarfs. We compare the efficiency of pebble accretion and planetesimal accretion in Sect. 6.1. The stellar massand radial distance dependence are discussed in Sect. 6.2. We highlight the importance of incorporatingthese two accretion mechanisms for planet formation in Sect. 6.3. Pebble accretion has gained attention since it is a more efficient growth process compared to planetesi-mal accretion. This comparison can be demonstrated from the following two aspects: the accretion crosssection and total mass of feeding materials.For planetesimal accretion, the gravitational focusing factor reaches its maximum value when δv = v H (see Sect. 4.1). Therefore, the ratio between accretion radius and physical radius is expressed as b PlA /R = (cid:115) (cid:18) v esc R H Ω K (cid:19) (cid:39) (cid:18) M p M (cid:63) (cid:19) / (cid:18) aR (cid:19) / (cid:39) (cid:16) a (cid:17) / (cid:18) ρ • − (cid:19) / (cid:18) M (cid:63) M (cid:12) (cid:19) − / . (27)In the shear-dominated pebble accretion regime ( ∆ v (cid:39) b peb Ω K ), from Eq. 17 the accretion radiusreads b PA (cid:39) (cid:114) GM p t stop ∆ v (cid:39) τ / R H . (28)The pebble accretion radius can maximally approach the planet Hill radius when τ s reaches the order ofunity. The enhanced factor is given by b PA /R (cid:39) τ / (cid:18) R H R (cid:19) ∼ τ / (cid:16) a (cid:17) (cid:18) ρ • − (cid:19) / (cid:18) M (cid:63) M (cid:12) (cid:19) − / , (29) . Liu & J. H. Ji. Liu & J. H. Ji Pebble accretion has gained attention since it is a more efficient growth process compared to planetesi-mal accretion. This comparison can be demonstrated from the following two aspects: the accretion crosssection and total mass of feeding materials.For planetesimal accretion, the gravitational focusing factor reaches its maximum value when δv = v H (see Sect. 4.1). Therefore, the ratio between accretion radius and physical radius is expressed as b PlA /R = (cid:115) (cid:18) v esc R H Ω K (cid:19) (cid:39) (cid:18) M p M (cid:63) (cid:19) / (cid:18) aR (cid:19) / (cid:39) (cid:16) a (cid:17) / (cid:18) ρ • − (cid:19) / (cid:18) M (cid:63) M (cid:12) (cid:19) − / . (27)In the shear-dominated pebble accretion regime ( ∆ v (cid:39) b peb Ω K ), from Eq. 17 the accretion radiusreads b PA (cid:39) (cid:114) GM p t stop ∆ v (cid:39) τ / R H . (28)The pebble accretion radius can maximally approach the planet Hill radius when τ s reaches the order ofunity. The enhanced factor is given by b PA /R (cid:39) τ / (cid:18) R H R (cid:19) ∼ τ / (cid:16) a (cid:17) (cid:18) ρ • − (cid:19) / (cid:18) M (cid:63) M (cid:12) (cid:19) − / , (29) . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 33 x [ R H ]10.500.51 y [ R H ] gravitional force planetesimal accretion 1 0.5 0 0.5 1 x [ R H ]10.500.51 gravitional force+ gas drag planet gravitygas drag pebble accretion Fig. 8: Illustration of planetesimal-planet (left) and pebble-planet (right) encounters, viewed in a co-moving frame with a central planet. The filled circle signifies an Earth-mass planet and the dashed circleindicates the planet Hill sphere. Two blue lines represent the trajectories of planetesimals or pebblesfrom the two different impact distances. In the above illustration, planetesimals are deflected (left) whilepebbles get accreted (right). We note that the central filled circle is not scaled with the physical size ofthe planet. We set a zero-drag force for the planetesimal-planet interaction and pebbles of τ s =1 for thepebble-planet interaction, corresponding to ≈ cm size at AU in the MMSN model. The black dotsrepresent the snapshots of planetesimals or pebbles, whereas the green and orange arrows correspond tothe planet gravitational force and gas drag respectively. The direction and length of the arrow representthe direction and magnitude of the force respectively. Aided by gas drag, pebbles can be more efficientlyaccreted by the planet compared to planetesimals.From Eqs. 27 and 29, we can see that generally the pebble accretion has a larger accretion cross sectioncompared to the planetesimal accretion. This feature can be seen in Figure 8, which illustrates the tra-jectories of planetesimals (left) and pebbles (right) during their interactions with an Earth-mass planet.Pebbles lose angular momentum more efficiently and sediment towards to the planet by a combinationof gas drag and gravitational force. The above difference is more pronounced when the Stokes numberof the pebbles is closer to the order of unity, and the planet is further out and/or around less massivestellar hosts.In addition, since planetesimals ( ∼ km) are weakly affected by gas, the orbits of the planetes-imals are relatively fixed. The planetary bodies only accrete their local planetesimals. The maximummass that the planet can reach (planetesimal isolation mass) is written as M pl , iso =2 πa ∆ a Σ pl where thewidth of the feeding zone ∆ a ∼ R H . For the MMSN, the planet grows maximumly to Mars mass in theinner terrestrial planet region and a few Earth masses beyond the water ice line (e.g., Ida & Lin 2004a).On the contrary, pebble accretion is not limited to the local pebble density. The majority of thedust reside in the outer part of the disk. Pebbles, which grow from dust grains, drift inwardly from theouter region of the disk. Due to the mobility of pebbles, there is no concept of feeding zone for pebbleaccretion. The feeding materials correspond to all pebbles that are able to bypass the orbit of the planet.The planets stop their core growth only when they reach the pebble isolation mass, which has a similarscaling as the gap opening mass (Eq. 20). Therefore, in contrast to planetesimal accretion, the final coremass of the planet by pebble accretion mainly depends on the mass of the central star and the aspectratio of the disk, but not the local density of solids. B. Liu & J. H. Ji : From Dust to Planets Here we qualitatively discuss how these two accretion scenarios depend on the mass of the stellar hostand the orbital distance.First, we focus on the stellar mass dependence. Based on Eq. 15, the growth timescale for plan-etesimal accretion is given by t PlA ∝ Σ − M − / (cid:63) . We have t PA ∝ ˙ M − M / (cid:63) in the D headwindregime from Eq. 25. Since observations indicate lower-mass disks around less massive massive stars(Natta et al. 2006; Andrews et al. 2013; Pascucci et al. 2016), the planetesimal surface density and peb-ble flux are expected to decrease with the mass of the stellar host. As a result, both pebble accretion andplanetesimal accretion tend to be slower as M (cid:63) decreases. Furthermore, assuming that the planetesimalsurface density and pebble flux have the same stellar mass dependence, we find that the ratio of thesetwo timescales ( τ PA /τ PlA ) increases with M (cid:63) . This in turn indicates that the decreasing rate of planetes-imal accretion is faster than that of pebble accretion as M (cid:63) decreases. In other words, pebble accretionis even more pronounced compared to planetesimal accretion for the planet growth around lower massstars than higher mass stars. The above conclusion holds as well when adopting t PA for the D shearregime (Eq. 25) or t PlA corresponding to the oligarchic growth (Eq. 14).The radial distance dependence is explained as follows. Based on Eq. 15, the planetesimal accretiontimescale is written as t PlA ∝ Σ − r / . Since the disk surface density additionally decreases with r , t PlA is expected to be a strongly increasing function of r . Planetesimals spend a much longer timegrowing their masses at further out disk locations. Moreover, as discussed in Sect. 4.4, planet-planetencounters result in scatterings/ejections instead of collisions at large orbital distances. Therefore, thegrowth by planetesimal accretion is strongly suppressed or even quenched at large orbital distances. Onthe other hand, for pebble accretion, t PA ∝ η in the D shear regime. Although the growth by pebbleaccretion also turns out to be slower at further out disk locations, the radial distance dependence isweaker than planetesimal accretion. Therefore, pebble accretion is more appealing for the formation ofdistant massive planets.To summarize, when comparing these two accretion scenarios, we find that pebble accretion be-comes more attractive than planetesimal accretion when the stellar host is less massive and/or the accre-tion occurs at a larger orbital distance. Despite the above distinctive differences, we want to raise the point that pebble accretion and planetesi-mal accretion are not two isolated, mutually exclusive growth channels. They are nevertheless likely tobe connected and complementary for planet growth.On the one hand, the above two mechanisms can operate concurrently and jointly contribute to themass increase. On the other hand, they also compete at certain levels since both pebbles and planetesi-mals are basic components of solids in protoplanetary disks (Schoonenberg et al. 2019). For instance, thestreaming instability converts pebbles into planetesimals once the triggering condition is satisfied. Afterthat, these forming planetesimals accrete surrounding planetesimals as well as pebbles that continuouslydrift from the outer region of the disk. The following mass growth is a combination of accreting pebblesand planetesimals (Liu et al. 2019b; Schoonenberg et al. 2019). We can consider two types of extremesituations. In one circumstance, the streaming instability is extensively triggered and the majority of thesolids are in the form of planetesimals. The following growth is naturally led by planetesimal accre-tion. In the other circumstance, when the streaming instability is modestly triggered, the dominant solidmasses are still in pebbles. Therefore, pebble accretion is the central mechanism for the growth of thecores. As can be expected, a more general pattern is that pebble and planetesimal accretions co-operatetogether to feed the planet growth.In addition, the above two mechanisms may occur at different evolutionary stages (Alibert et al.2018; Venturini & Helled 2020) and/or in different disk regions (Ormel et al. 2017). For example,when a planet reaches the pebble isolation mass, the inwardly drifting pebble flux is truncated. Pebbleaccretion and planetesimal accretion occur for planets whose orbits are beyond the gap-opening planet. . Liu & J. H. Ji. Liu & J. H. Ji Despite the above distinctive differences, we want to raise the point that pebble accretion and planetesi-mal accretion are not two isolated, mutually exclusive growth channels. They are nevertheless likely tobe connected and complementary for planet growth.On the one hand, the above two mechanisms can operate concurrently and jointly contribute to themass increase. On the other hand, they also compete at certain levels since both pebbles and planetesi-mals are basic components of solids in protoplanetary disks (Schoonenberg et al. 2019). For instance, thestreaming instability converts pebbles into planetesimals once the triggering condition is satisfied. Afterthat, these forming planetesimals accrete surrounding planetesimals as well as pebbles that continuouslydrift from the outer region of the disk. The following mass growth is a combination of accreting pebblesand planetesimals (Liu et al. 2019b; Schoonenberg et al. 2019). We can consider two types of extremesituations. In one circumstance, the streaming instability is extensively triggered and the majority of thesolids are in the form of planetesimals. The following growth is naturally led by planetesimal accre-tion. In the other circumstance, when the streaming instability is modestly triggered, the dominant solidmasses are still in pebbles. Therefore, pebble accretion is the central mechanism for the growth of thecores. As can be expected, a more general pattern is that pebble and planetesimal accretions co-operatetogether to feed the planet growth.In addition, the above two mechanisms may occur at different evolutionary stages (Alibert et al.2018; Venturini & Helled 2020) and/or in different disk regions (Ormel et al. 2017). For example,when a planet reaches the pebble isolation mass, the inwardly drifting pebble flux is truncated. Pebbleaccretion and planetesimal accretion occur for planets whose orbits are beyond the gap-opening planet. . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 35 Interior to this massive planet, collisions between planetesimals and protoplanets are the only pathwayfor core mass growth. This might provide an explanation for the mass dichotomy between the innerlow-mass terrestrial planets and outer massive giant planets in the Solar System (Ormel et al. 2017). Allin all, the detailed exploration based on the concept of hybrid planetesimal and pebble accretion is anactive research area and requires future studies. In this review, we have recapitulated the current states of exoplanet demographics and disk observations(Section 1). The planet formation theories have been overviewed chronologically, including dust co-agulation and radial drift (Section 2), planetesimal formation (Section 3), and subsequent planetesimalgrowth by planetesimal accretion (Section 4) and pebble accretion (Section 5). Importantly, we havediscussed how different planet formation models fit into observations in each growth stage.Lastly, we propose some open questions in this field, which are existing topics with disputed inter-pretations and unsolved puzzles that require future studies. These questions are summarized as follows: – What is the characteristic size of solid particles in protoplanetary disks? Are these particlesmm-cm size as suggested by spectral index observations, or µ m as inferred from polarizationmeasurements? On the one hand, the answer itself is valuable, since it needs to test the validity ofdifferent model interpretations and the built-in assumptions. On the other hand, the answer is alsorelated to the subsequent planet formation processes such as the streaming instability and pebbleaccretion, which essentially depend on the size of solid particles. – Current streaming instability and pebble acceretion studies are limited to the systems aroundsingle stars. Since the gas streamline in protoplantary disks around binaries significantly deviatesfrom static, axisymmetric cases around single stellar hosts, it still remains to be seen how thesegas-assisted formation mechanisms operate in this highly-perturbed binary environment. – How can we distinguish planetesimal accretion and pebble accretion mechanisms from an ob-servational perspective? Namely, what would be the key observational signatures that result fromdifferent formation channels (see e.g., Br¨ugger et al. 2020)? Can we really claim which types ofsystems can be uniquely produced by pebble accretion, or vice versa? – Recent impact models found that the accreting pebbles as well as small planetesimals may getvaporized on their way to the planet interior due to the increased thermal ablation and friction (seeSect. 5.3). The materials enrich the planetary atmospheres rather than directly impact the solidcores. The resultant core mass is substantially lower than the traditional critical mass that a planetrequires for initiating rapid gas accretion (Brouwers & Ormel 2020). How this mass depositionprocess affects the compositional and thermal structures of envelopes, and further influences the gasaccretion are not well understood. In addition, small bodies in protoplanetary disks feel head windfrom the disk gas and suffer the surface shear stress (Paraskov et al. 2006; Schaffer et al. 2020).The influence of wind erosion during the above two accretion processes is also poorly investigated. – How early can planets form? There seems to be evidence of large grains existing in the earlyClass I disk phase (Harsono et al. 2018). Based on the isotope measurements of meteorites, thecore of Jupiter with ∼ M ⊕ is suggested to form early within . − Myr (Kruijer et al. 2017).Furthermore, if the rings and gaps in the HL Tau disk are induced by planets, it then indicates thatplanets of sub-Jupiter masses might already form at large orbital separations within Myr in such ayoung system. Putting all clues together, can we speculate that planet formation is more rapid thanwhat we thought before? – We have already learned much about of the planet-related properties from exoplanet demographics:occurrence rate, mass, radius and corresponding dependencies on the mass and metallicity of the B. Liu & J. H. Ji : From Dust to Planets stellar host. The next step is to understand the planetary-system-related properties, i.e., the architec-tures. Can different populations of planets co-exist with each other under certain conditions, or theformation of one type of planets inhibit the growth of the others? What would be the architectureof these systems? Some of these questions have already been pointed out by Zhu & Wu (2018) andMasuda et al. (2020). In order to further address these questions, both follow-up observations anddedicated numerical modelings are needed. – As raised by Murchikova & Tremaine (2020), is planet formation really an independent andgeneralized process such that planets do not know each other and the environment where theyreside? Or is planet formation universally set by a few key physical processes related to disk andhost properties (Liu et al. 2019a), and therefore, the imprinted planetary systems may contain somedegrees of intra-system/inter-system similarity (Millholland et al. 2017; Wang 2017; Weiss et al.2018; Wu 2019)?With a rapidly increasing number of characterized exoplanets and protoplanetary disks, we havegreatly improved the statistics of planet formation, in the context of both initial conditions and finalproducts. The theoretical study of planet formation has been advanced enormously in the last decade.The validity of modern planet formation scenarios needs to match various observational constraints.Future work is also required to account for the consistency with findings from ongoing/upcoming spaceand ground-based facilities, such as TESS and ALMA. Acknowledgements We thank editor Wing-Huen Ip and the anonymous referee for useful commentsand suggestions. We also thank Anders Johansen, Michiel Lambrechts, Joanna Dra¸ ˙zkowska, ChrisOrmel, Rixin Li, Jiwei Xie, Shangfei Liu, Wei Zhu and Feng Long for proofreading the manuscriptand providing helpful suggestions. B.L. greatly appreciates the valuable discussions with Gijs Mulders,Daniel Harsono, Joanna Dra¸ ˙zkowska and Chris Ormel as a PPVII chapter proposal team.In addition, B.L. wishes to express the deepest gratefulness to Adam Showman (1968-2020) for hisinspiration and guidance in B.L.’s early academic career. Adam is an amazing scientist and a tremen-dous mentor. His scientific contribution as well as great personality will keep influencing and beingremembered by the community. Lastly, B.L. feels especially grateful to his girlfriend, Jing Yang, for herspiritual support during the writing period. In these tough COVID-19 pandemic times, many things thatformerly seemed extraordinary have now become ordinary. The work would not be done successfullywithout her dedicated encouragements.B.L. is supported by the European Research Council (ERC Consolidator Grant 724687-PLANETESYS), the Swedish Walter Gyllenberg Foundation, and start-up grant of Bairen program fromZhejiang University. J.J. is supported by the B-type Strategic Priority Program of the Chinese Academyof Sciences (Grant No. XDB41000000), the National Natural Science Foundation of China (Grant Nos.12033010 and 11773081), CAS Interdisciplinary Innovation Team and Foundation of Minor Planets ofthe Purple Mountain Observatory. References Abod, C. P., Simon, J. B., Li, R., et al. 2019, ApJ, 883, 192Adachi, I., Hayashi, C., & Nakazawa, K. 1976, Progress of Theoretical Physics, 56, 1756Agnor, C., & Asphaug, E. 2004, ApJ, 613, L157Agnor, C. B., Canup, R. M., & Levison, H. F. 1999, Icarus, 142, 219Albrecht, S., Winn, J. N., Johnson, J. A., et al. 2012, ApJ, 757, 18Alibert, Y., & Benz, W. 2017, A&A, 598, L5Alibert, Y. 2017, A&A, 606, A69Alibert, Y., Venturini, J., Helled, R., et al. 2018, Nature Astronomy, 2, 873 . Liu & J. H. Ji. Liu & J. H. Ji Abod, C. P., Simon, J. B., Li, R., et al. 2019, ApJ, 883, 192Adachi, I., Hayashi, C., & Nakazawa, K. 1976, Progress of Theoretical Physics, 56, 1756Agnor, C., & Asphaug, E. 2004, ApJ, 613, L157Agnor, C. B., Canup, R. M., & Levison, H. F. 1999, Icarus, 142, 219Albrecht, S., Winn, J. N., Johnson, J. A., et al. 2012, ApJ, 757, 18Alibert, Y., & Benz, W. 2017, A&A, 598, L5Alibert, Y. 2017, A&A, 606, A69Alibert, Y., Venturini, J., Helled, R., et al. 2018, Nature Astronomy, 2, 873 . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 37 Table 1: List of Notations Symbol Description v g ( v φ, g , v r , g ) gas velocity with azimuthal and radial components v ( v φ , v r ) particle’s velocity with azimuthal and radial components v peb pebble velocity v K Keplerian velocity v th gas mean thermal velocity c s gas sound speed v ∗ threshold velocity between settling and ballistic pebble accretion regimes v set settling velocity of pebble onto planet v esc planet escape velocity ∆ v relative velocity between gas and particle δv relative velocity between large and small planetesimals Ω K Keplerian angular frequency η gas headwind prefactor P g gas pressure T g gas temperature T d dust temperature H g gas disk scale height H peb pebble disk scale height H vertical height of small planetesimals h g gas disk aspect ratio h peb pebble disk aspect ratio Σ g gas surface density Σ d dust surface density Σ peb pebble surface density ρ g gas volume density ρ peb pebble volume density Z disk metallicity Q T Toomre parameter γ self-gravity parameter G gravitational constant F drag hydrodynamic gas drag force a drag hydrodynamic gas drag acceleration C D coefficient of gas drag force R e particle’s Reynolds number ν mol kinematic molecular viscosity ν t turbulent viscosity σ mol collisional cross section of gas molecule λ mfp gas mean free path m mol mass of gas molecule m H mass of hydrogen atom µ gas mean molecular weight ρ • internal density of solid body r disk radial distance R radius of solid body R H Hill radius a semimajor axis t stop stopping time τ s Stokes number or dimensionless stopping time τ ν optical depth (at the corresponding frequency ν ) I ν disk emission intensity F ν observed flux κ ν disk opacity B ν Plank function w ν single-scattering albedo c light speed δ d coefficient of gas diffusivity α t efficiency factor of turbulent viscosity α spectral energy index β dust opacity index β ISM opacity index of ISM dust β disk opacity index of protoplanetary dust k B Boltzmann constant k Σ gradient of disk surface density k T gradient of disk temperature M (cid:63) stellar mass M pl characteristic mass of planetesimal M p planet mass M , m mass of large and small planetesimals R M , R m radius of large and small planetesimals σ collisional cross section of large planetesimal B. Liu & J. H. Ji : From Dust to Planets Table 1: Continued. Symbol Description n m , n M number density of small and large planetesimals Σ m , Σ M surface density of small and large planetesimals t set settling timescale of pebble onto planet t enc pebble-planet encounter timescale t PA pebble accretion timescale t PlA planetesimal accretion timescale t grow mass growth timescale t vs viscous stirring timescale t e , gas gas eccentricity damping timescale t og oligarchic growth timescale t rg runaway growth timescale C rg numerical prefactor of runaway growth Φ ratio between planetary escape velocity and Keplerian velocity ln Λ Coulomb factor b impact parameter during pebble-planet encounter b set pebble accretion radius in the settling regime b PA pebble accretion radius b PlA planetesimal accretion radius f set fitting function between settling and ballistic regimes f gf gravitational focusing factor M onset planet mass for onset of efficient pebble accretion M iso planet mass for termination of pebble accretion M hw / sh planet mass between headwind and shear-dominated pebble accretion regimes ˙ M g gas disk accretion rate ˙ M g (cid:12) gas disk accretion rate around solar-mass star ˙ M peb disk pebble flux ˙ M PA pebble accretion rate ε PA pebble accretion efficiency ALMA Partnership, Brogan, C. L., P´erez, L. M., et al. 2015, ApJ, 808, L3Amelin, Y., Kaltenbach, A., Iizuka, T., et al. 2010, Earth and Planetary Science Letters, 300, 343Amelin, Y., Krot, A. N., Hutcheon, I. D., & Ulyanov, A. A. 2002, Science, 297, 1678Anderson, K. R., Storch, N. I., & Lai, D. 2016, MNRAS, 456, 3671Andrews, S. M., Rosenfeld, K. A., Kraus, A. L., & Wilner, D. J. 2013, ApJ, 771, 129Andrews, S. M., Wilner, D. J., Hughes, A. M., Qi, C., & Dullemond, C. P. 2009, ApJ, 700, 1502Andrews, S. M., Wilner, D. J., Hughes, A. M., et al. 2012, ApJ, 744, 162Andrews, S. M., Huang, J., P´erez, L. M., et al. 2018, ApJ, 869, L41Ansdell, M., Williams, J. P., Trapman, L., et al. 2018, ApJ, 859, 21Artymowicz, P. 1993, ApJ, 419, 166Artymowicz, P., & Lubow, S. H. 1994, ApJ, 421, 651Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481Ataiee, S., Baruteau, C., Alibert, Y., & Benz, W. 2018, A&A, 615, A110Bacciotti, F., Girart, J. M., Padovani, M., et al. 2018, ApJ, 865, L12Bae, J., & Zhu, Z. 2018, ApJ, 859, 119Bai, X.-N. 2015, ApJ, 798, 84Bai, X.-N. 2016, ApJ, 821, 80Bai, X.-N., & Stone, J. M. 2010, ApJ, 722, 1437Bai, X.-N., & Stone, J. M. 2013, ApJ, 769, 76Ballering, N. P., & Eisner, J. A. 2019, AJ, 157, 144Baruteau, C., Crida, A., Paardekooper, S. J., et al. 2014, in Protostars and Planets VI, ed. H. Beuther, R. S. Klessen,C. P. Dullemond, & T. Henning, 667Batalha, N. M., Rowe, J. F., Bryson, S. T., et al. 2013, ApJS, 204, 24Batygin, K., & Adams, F. C. 2017, AJ, 153, 120 . Liu & J. H. Ji. Liu & J. H. Ji Symbol Description n m , n M number density of small and large planetesimals Σ m , Σ M surface density of small and large planetesimals t set settling timescale of pebble onto planet t enc pebble-planet encounter timescale t PA pebble accretion timescale t PlA planetesimal accretion timescale t grow mass growth timescale t vs viscous stirring timescale t e , gas gas eccentricity damping timescale t og oligarchic growth timescale t rg runaway growth timescale C rg numerical prefactor of runaway growth Φ ratio between planetary escape velocity and Keplerian velocity ln Λ Coulomb factor b impact parameter during pebble-planet encounter b set pebble accretion radius in the settling regime b PA pebble accretion radius b PlA planetesimal accretion radius f set fitting function between settling and ballistic regimes f gf gravitational focusing factor M onset planet mass for onset of efficient pebble accretion M iso planet mass for termination of pebble accretion M hw / sh planet mass between headwind and shear-dominated pebble accretion regimes ˙ M g gas disk accretion rate ˙ M g (cid:12) gas disk accretion rate around solar-mass star ˙ M peb disk pebble flux ˙ M PA pebble accretion rate ε PA pebble accretion efficiency ALMA Partnership, Brogan, C. L., P´erez, L. M., et al. 2015, ApJ, 808, L3Amelin, Y., Kaltenbach, A., Iizuka, T., et al. 2010, Earth and Planetary Science Letters, 300, 343Amelin, Y., Krot, A. N., Hutcheon, I. D., & Ulyanov, A. A. 2002, Science, 297, 1678Anderson, K. R., Storch, N. I., & Lai, D. 2016, MNRAS, 456, 3671Andrews, S. M., Rosenfeld, K. A., Kraus, A. L., & Wilner, D. J. 2013, ApJ, 771, 129Andrews, S. M., Wilner, D. J., Hughes, A. M., Qi, C., & Dullemond, C. P. 2009, ApJ, 700, 1502Andrews, S. M., Wilner, D. J., Hughes, A. M., et al. 2012, ApJ, 744, 162Andrews, S. M., Huang, J., P´erez, L. M., et al. 2018, ApJ, 869, L41Ansdell, M., Williams, J. P., Trapman, L., et al. 2018, ApJ, 859, 21Artymowicz, P. 1993, ApJ, 419, 166Artymowicz, P., & Lubow, S. H. 1994, ApJ, 421, 651Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481Ataiee, S., Baruteau, C., Alibert, Y., & Benz, W. 2018, A&A, 615, A110Bacciotti, F., Girart, J. M., Padovani, M., et al. 2018, ApJ, 865, L12Bae, J., & Zhu, Z. 2018, ApJ, 859, 119Bai, X.-N. 2015, ApJ, 798, 84Bai, X.-N. 2016, ApJ, 821, 80Bai, X.-N., & Stone, J. M. 2010, ApJ, 722, 1437Bai, X.-N., & Stone, J. M. 2013, ApJ, 769, 76Ballering, N. P., & Eisner, J. A. 2019, AJ, 157, 144Baruteau, C., Crida, A., Paardekooper, S. J., et al. 2014, in Protostars and Planets VI, ed. H. Beuther, R. S. Klessen,C. P. Dullemond, & T. Henning, 667Batalha, N. M., Rowe, J. F., Bryson, S. T., et al. 2013, ApJS, 204, 24Batygin, K., & Adams, F. C. 2017, AJ, 153, 120 . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 39Batygin, K., & Morbidelli, A. 2013, AJ, 145, 1Bell, K. R., Cassen, P. M., Klahr, H. H., & Henning, T. 1997, ApJ, 486, 372Benecchi, S. D., Noll, K. S., Grundy, W. M., et al. 2009, Icarus, 200, 292Benisty, M., Stolker, T., Pohl, A., et al. 2016, A&A, 597, A42Benz, W., Ida, S., Alibert, Y., Lin, D., & Mordasini, C. 2014, in Protostars and Planets VI, ed. H. Beuther, R. S.Klessen, C. P. Dullemond, & T. Henning, 691Birnstiel, T., Dullemond, C. P., & Brauer, F. 2010, A&A, 513, A79Birnstiel, T., Klahr, H., & Ercolano, B. 2012, A&A, 539, A148Birnstiel, T., Dullemond, C. P., Zhu, Z., et al. 2018, ApJ, 869, L45Bitsch, B., Izidoro, A., Johansen, A., et al. 2019, A&A, 623, A88Bitsch, B., Johansen, A., Lambrechts, M., & Morbidelli, A. 2015, A&A, 575, A28Bitsch, B., Morbidelli, A., Johansen, A., et al. 2018, A&A, 612, A30Blum, J., & Wurm, G. 2000, Icarus, 143, 138Blum, J., & Wurm, G. 2008, ARA&A, 46, 21Bohlin, R. C., Savage, B. D., & Drake, J. F. 1978, ApJ, 224, 132Bonfils, X., Delfosse, X., Udry, S., et al. 2013, A&A, 549, A109Borucki, W. J., Koch, D., Basri, G., et al. 2010, Science, 327, 977Borucki, W. J., Koch, D. G., Basri, G., et al. 2011, ApJ, 736, 19Brauer, F., Dullemond, C. P., & Henning, T. 2008, A&A, 480, 859Brinch, C., Jørgensen, J. K., Hogerheijde, M. R., Nelson, R. P., & Gressel, O. 2016, ApJ, 830, L16Brouwers, M. G., & Ormel, C. W. 2020, A&A, 634, A15Brouwers, M. G., Vazan, A., & Ormel, C. W. 2018, A&A, 611, A65Br¨ugger, N., Burn, R., Coleman, G., Alibert, Y., & Benz, W. 2020, A&A, 640, A21Bryan, M. L., Knutson, H. A., Lee, E. J., et al. 2019, AJ, 157, 52Buchhave, L. A., Latham, D. W., Johansen, A., et al. 2012, Nature, 486, 375Buchhave, L. A., Bizzarro, M., Latham, D. W., et al. 2014, Nature, 509, 593Burke, C. J., Bryson, S. T., Mullally, F., et al. 2014, ApJS, 210, 19Cai, M. X., Kouwenhoven, M. B. N., Portegies Zwart, S. F., & Spurzem, R. 2017, MNRAS, 470, 4337Calvet, N., D’Alessio, P., Watson, D. M., et al. 2005, ApJ, 630, L185Carrasco-Gonz´alez, C., Sierra, A., Flock, M., et al. 2019, ApJ, 883, 71Carrera, D., Gorti, U., Johansen, A., & Davies, M. B. 2017, ApJ, 839, 16Carrera, D., Johansen, A., & Davies, M. B. 2015, A&A, 579, A43Carter, P. J., Leinhardt, Z. M., Elliott, T., Walter, M. J., & Stewart, S. T. 2015, ApJ, 813, 72Chambers, J. E. 2001, Icarus, 152, 205Chambers, J. E. 2013, Icarus, 224, 43Chambers, J. E., & Wetherill, G. W. 1998, Icarus, 136, 304Chatterjee, S., & Ford, E. B. 2015, ApJ, 803, 33Chatterjee, S., Ford, E. B., Matsumura, S., & Rasio, F. A. 2008, ApJ, 686, 580Chatterjee, S., & Tan, J. C. 2014, ApJ, 780, 53Chen, K., & Lin, M.-K. 2020, ApJ, 891, 132Chiang, E. I., & Goldreich, P. 1997, ApJ, 490, 368Chiang, E., & Laughlin, G. 2013, MNRAS, 431, 3444Cimerman, N. P., Kuiper, R., & Ormel, C. W. 2017, MNRAS, 471, 4662Clement, M. S., Kaib, N. A., Raymond, S. N., Chambers, J. E., & Walsh, K. J. 2019, Icarus, 321, 778Clement, M. S., Kaib, N. A., Raymond, S. N., & Walsh, K. J. 2018, Icarus, 311, 340Coleman, G. A. L., Leleu, A., Alibert, Y., & Benz, W. 2019, A&A, 631, A7Coleman, G. A. L., & Nelson, R. P. 2014, MNRAS, 445, 479Coleman, G. A. L., & Nelson, R. P. 2016, MNRAS, 457, 2480Connelly, J. N., Bizzarro, M., Krot, A. N., et al. 2012, Science, 338, 651Cossou, C., Raymond, S. N., Hersant, F., & Pierens, A. 2014, A&A, 569, A560 B. Liu & J. H. Ji : From Dust to PlanetsCrane, J. D., Shectman, S. A., Butler, R. P., et al. 2010, in Society of Photo-Optical Instrumentation Engineers(SPIE) Conference Series, Vol. 7735, Ground-based and Airborne Instrumentation for Astronomy III, 773553Cumming, A., Butler, R. P., Marcy, G. W., et al. 2008, PASP, 120, 531Cuzzi, J. N., Dobrovolskis, A. R., & Champney, J. M. 1993, Icarus, 106, 102Cuzzi, J. N., Hogan, R. C., & Bottke, W. F. 2010, Icarus, 208, 518Cuzzi, J. N., Hogan, R. C., & Shariff, K. 2008, ApJ, 687, 1432Cuzzi, J. N., & Zahnle, K. J. 2004, ApJ, 614, 490Czekala, I., Chiang, E., Andrews, S. M., et al. 2019, ApJ, 883, 22Dauphas, N., & Pourmand, A. 2011, Nature, 473, 489Dawson, R. I., Lee, E. J., & Chiang, E. 2016, ApJ, 822, 54Dawson, R. I., & Murray-Clay, R. A. 2013, ApJ, 767, L24Delisle, J. B., & Laskar, J. 2014, A&A, 570, L7Dipierro, G., Price, D., Laibe, G., et al. 2015, MNRAS, 453, L73Dominik, C., & Tielens, A. G. G. M. 1997, ApJ, 480, 647Donati, J. F., Moutou, C., Malo, L., et al. 2016, Nature, 534, 662Donati, J. F., Bouvier, J., Alencar, S. H., et al. 2020, MNRAS, 491, 5660Dong, R., Hall, C., Rice, K., & Chiang, E. 2015a, ApJ, 812, L32Dong, R., Zhu, Z., Rafikov, R. R., & Stone, J. M. 2015b, ApJ, 809, L5Dong, R., Zhu, Z., & Whitney, B. 2015c, ApJ, 809, 93Dong, R., Rafikov, R., Zhu, Z., et al. 2012, ApJ, 750, 161Dong, S., Katz, B., & Socrates, A. 2014, ApJ, 781, L5Dong, S., Xie, J.-W., Zhou, J.-L., Zheng, Z., & Luo, A. 2018, Proceedings of the National Academy of Science,115, 266Dong, S., & Zhu, Z. 2013, ApJ, 778, 53Dorn, C., Mosegaard, K., Grimm, S. L., & Alibert, Y. 2018, ApJ, 865, 20Doyle, P., Jogo, K., Nagashima, K., et al. 2015, Nat Commun, 6, 7444Draine, B. T. 2006, ApJ, 636, 1114Dra¸˙zkowska, J., & Alibert, Y. 2017, A&A, 608, A92Dra¸˙zkowska, J., Alibert, Y., & Moore, B. 2016, A&A, 594, A105Dra¸˙zkowska, J., Windmark, F., & Dullemond, C. P. 2013, A&A, 556, A37Dressing, C. D., & Charbonneau, D. 2015, ApJ, 807, 45Dullemond, C. P., & Dominik, C. 2004, A&A, 417, 159Dullemond, C. P., Dominik, C., & Natta, A. 2001, ApJ, 560, 957Dullemond, C. P., Birnstiel, T., Huang, J., et al. 2018, ApJ, 869, L46Duquennoy, A., & Mayor, M. 1991, A&A, 500, 337Dutrey, A., Guilloteau, S., Prato, L., et al. 1998, A&A, 338, L63Ebel, D. S., Brunner, C., Konrad, K., et al. 2016, Geochim. Cosmochim. Acta, 172, 322Eriksson, L. E. J., Johansen, A., & Liu, B. 2020, A&A, 635, A110Espaillat, C., Muzerolle, J., Najita, J., et al. 2014, in Protostars and Planets VI, ed. H. Beuther, R. S. Klessen, C. P.Dullemond, & T. Henning, 497Estrada, P. R., Cuzzi, J. N., & Morgan, D. A. 2016, ApJ, 818, 200Fabrycky, D. C., Lissauer, J. J., Ragozzine, D., et al. 2014, ApJ, 790, 146Fabrycky, D., & Tremaine, S. 2007, ApJ, 669, 1298Fedele, D., Carney, M., Hogerheijde, M. R., et al. 2017, A&A, 600, A72Feng, F., Crane, J. D., Xuesong Wang, S., et al. 2019, ApJS, 242, 25Fernandes, R. B., Mulders, G. D., Pascucci, I., Mordasini, C., & Emsenhuber, A. 2019, ApJ, 874, 81Fischer, D. A., & Valenti, J. 2005, ApJ, 622, 1102Flock, M., Nelson, R. P., Turner, N. J., et al. 2017, ApJ, 850, 131Flock, M., Ruge, J. P., Dzyurkevich, N., et al. 2015, A&A, 574, A68 . Liu & J. H. Ji. Liu & J. H. Ji B. Liu & J. H. Ji : From Dust to PlanetsCrane, J. D., Shectman, S. A., Butler, R. P., et al. 2010, in Society of Photo-Optical Instrumentation Engineers(SPIE) Conference Series, Vol. 7735, Ground-based and Airborne Instrumentation for Astronomy III, 773553Cumming, A., Butler, R. P., Marcy, G. W., et al. 2008, PASP, 120, 531Cuzzi, J. N., Dobrovolskis, A. R., & Champney, J. M. 1993, Icarus, 106, 102Cuzzi, J. N., Hogan, R. C., & Bottke, W. F. 2010, Icarus, 208, 518Cuzzi, J. N., Hogan, R. C., & Shariff, K. 2008, ApJ, 687, 1432Cuzzi, J. N., & Zahnle, K. J. 2004, ApJ, 614, 490Czekala, I., Chiang, E., Andrews, S. M., et al. 2019, ApJ, 883, 22Dauphas, N., & Pourmand, A. 2011, Nature, 473, 489Dawson, R. I., Lee, E. J., & Chiang, E. 2016, ApJ, 822, 54Dawson, R. I., & Murray-Clay, R. A. 2013, ApJ, 767, L24Delisle, J. B., & Laskar, J. 2014, A&A, 570, L7Dipierro, G., Price, D., Laibe, G., et al. 2015, MNRAS, 453, L73Dominik, C., & Tielens, A. G. G. M. 1997, ApJ, 480, 647Donati, J. F., Moutou, C., Malo, L., et al. 2016, Nature, 534, 662Donati, J. F., Bouvier, J., Alencar, S. H., et al. 2020, MNRAS, 491, 5660Dong, R., Hall, C., Rice, K., & Chiang, E. 2015a, ApJ, 812, L32Dong, R., Zhu, Z., Rafikov, R. R., & Stone, J. M. 2015b, ApJ, 809, L5Dong, R., Zhu, Z., & Whitney, B. 2015c, ApJ, 809, 93Dong, R., Rafikov, R., Zhu, Z., et al. 2012, ApJ, 750, 161Dong, S., Katz, B., & Socrates, A. 2014, ApJ, 781, L5Dong, S., Xie, J.-W., Zhou, J.-L., Zheng, Z., & Luo, A. 2018, Proceedings of the National Academy of Science,115, 266Dong, S., & Zhu, Z. 2013, ApJ, 778, 53Dorn, C., Mosegaard, K., Grimm, S. L., & Alibert, Y. 2018, ApJ, 865, 20Doyle, P., Jogo, K., Nagashima, K., et al. 2015, Nat Commun, 6, 7444Draine, B. T. 2006, ApJ, 636, 1114Dra¸˙zkowska, J., & Alibert, Y. 2017, A&A, 608, A92Dra¸˙zkowska, J., Alibert, Y., & Moore, B. 2016, A&A, 594, A105Dra¸˙zkowska, J., Windmark, F., & Dullemond, C. P. 2013, A&A, 556, A37Dressing, C. D., & Charbonneau, D. 2015, ApJ, 807, 45Dullemond, C. P., & Dominik, C. 2004, A&A, 417, 159Dullemond, C. P., Dominik, C., & Natta, A. 2001, ApJ, 560, 957Dullemond, C. P., Birnstiel, T., Huang, J., et al. 2018, ApJ, 869, L46Duquennoy, A., & Mayor, M. 1991, A&A, 500, 337Dutrey, A., Guilloteau, S., Prato, L., et al. 1998, A&A, 338, L63Ebel, D. S., Brunner, C., Konrad, K., et al. 2016, Geochim. Cosmochim. Acta, 172, 322Eriksson, L. E. J., Johansen, A., & Liu, B. 2020, A&A, 635, A110Espaillat, C., Muzerolle, J., Najita, J., et al. 2014, in Protostars and Planets VI, ed. H. Beuther, R. S. Klessen, C. P.Dullemond, & T. Henning, 497Estrada, P. R., Cuzzi, J. N., & Morgan, D. A. 2016, ApJ, 818, 200Fabrycky, D. C., Lissauer, J. J., Ragozzine, D., et al. 2014, ApJ, 790, 146Fabrycky, D., & Tremaine, S. 2007, ApJ, 669, 1298Fedele, D., Carney, M., Hogerheijde, M. R., et al. 2017, A&A, 600, A72Feng, F., Crane, J. D., Xuesong Wang, S., et al. 2019, ApJS, 242, 25Fernandes, R. B., Mulders, G. D., Pascucci, I., Mordasini, C., & Emsenhuber, A. 2019, ApJ, 874, 81Fischer, D. A., & Valenti, J. 2005, ApJ, 622, 1102Flock, M., Nelson, R. P., Turner, N. J., et al. 2017, ApJ, 850, 131Flock, M., Ruge, J. P., Dzyurkevich, N., et al. 2015, A&A, 574, A68 . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 41Foley, C. N., Wadhwa, M., Borg, L. E., et al. 2005, Geochim. Cosmochim. Acta, 69, 4557Ford, E. B., & Rasio, F. A. 2008, ApJ, 686, 621Friedrich, J. M., Weisberg, M. K., Ebel, D. S., et al. 2015, Chemie der Erde / Geochemistry, 75, 419Fulton, B. J., & Petigura, E. A. 2018, ApJ, 156, 264Fulton, B. J., Petigura, E. A., Howard, A. W., et al. 2017, AJ, 154, 109Fung, J., & Dong, R. 2015, ApJ, 815, L21Gammie, C. F. 1996, ApJ, 457, 355Garaud, P., & Lin, D. N. C. 2007, ApJ, 654, 606Genda, H., Kokubo, E., & Ida, S. 2012, ApJ, 744, 137Gerbig, K., Murray-Clay, R. A., Klahr, H., & Baehr, H. 2020, ApJ, 895, 91Gibbons, P. G., Rice, W. K. M., & Mamatsashvili, G. R. 2012, MNRAS, 426, 1444Gillon, M., Jehin, E., Lederer, S. M., et al. 2016, Nature, 533, 221Gillon, M., Triaud, A. H. M. J., Demory, B.-O., et al. 2017, Nature, 542, 456Ginzburg, S., Schlichting, H. E., & Sari, R. 2018, MNRAS, 476, 759Goldreich, P., Lithwick, Y., & Sari, R. 2002, Nature, 420, 643Goldreich, P., Lithwick, Y., & Sari, R. 2004, ARA&A, 42, 549Goldreich, P., & Schlichting, H. E. 2014, AJ, 147, 32Goldreich, P., & Tremaine, S. 1979, ApJ, 233, 857Goldreich, P., & Tremaine, S. 1980, ApJ, 241, 425Goldreich, P., & Ward, W. R. 1973, ApJ, 183, 1051Gole, D. A., Simon, J. B., Li, R., Youdin, A. N., & Armitage, P. J. 2020, arXiv e-prints, arXiv:2001.10000Gong, Y.-X., & Ji, J. 2017, AJ, 154, 179Gong, Y.-X., & Ji, J. 2018, MNRAS, 478, 4565Grady, C. A., Muto, T., Hashimoto, J., et al. 2012, ApJ, 762, 48Greenberg, R., Wacker, J. F., Hartmann, W. K., & Chapman, C. R. 1978, Icarus, 35, 1Gressel, O., Turner, N. J., Nelson, R. P., & McNally, C. P. 2015, ApJ, 801, 84Grimm, S. L., Demory, B.-O., Gillon, M., et al. 2018, A&A, 613, A68Grundy, W. M., Noll, K. S., Roe, H. G., et al. 2019, Icarus, 334, 62Grundy, W. M., Bird, M. K., Britt, D. T., et al. 2020, Science, 367, aay3705Guillot, T., Ida, S., & Ormel, C. W. 2014, A&A, 572, A72Gundlach, B., & Blum, J. 2015, ApJ, 798, 34Gundlach, B., Schmidt, K. P., Kreuzig, C., et al. 2018, MNRAS, 479, 1273Gupta, A., & Schlichting, H. E. 2019, MNRAS, 1166G¨uttler, C., Blum, J., Zsom, A., Ormel, C. W., & Dullemond, C. P. 2010, A&A, 513, A56Hadden, S., & Lithwick, Y. 2018, AJ, 156, 95Haffert, S. Y., Bohn, A. J., de Boer, J., et al. 2019, Nature Astronomy, 3, 749Haisch, Jr., K. E., Lada, E. A., & Lada, C. J. 2001, ApJ, 553, L153Hansen, B. M. S. 2009, ApJ, 703, 1131Hao, W., Kouwenhoven, M. B. N., & Spurzem, R. 2013, MNRAS, 433, 867Harsono, D., Bjerkeli, P., van der Wiel, M. H. D., et al. 2018, Nature Astronomy, 2, 646Hartlep, T., & Cuzzi, J. N. 2020, ApJ, 892, 120Hartlep, T., Cuzzi, J. N., & Weston, B. 2017, Phys. Rev. E, 95, 033115Hartmann, L., Calvet, N., Gullbring, E., & D’Alessio, P. 1998, ApJ, 495, 385Hayashi, C. 1981, Progress of Theoretical Physics Supplement, 70, 35Hellary, P., & Nelson, R. P. 2011, MNRAS, 419, 2737Helled, R., & Stevenson, D. 2017, ApJ, 840, L4Heppenheimer, T. A. 1978, A&A, 65, 421Homma, K. A., Okuzumi, S., Nakamoto, T., & Ueda, Y. 2019, ApJ, 877, 128Horn, B., Lyra, W., Mac Low, M.-M., & S´andor, Z. 2012, ApJ, 750, 34Howard, A. W., Marcy, G. W., Johnson, J. A., et al. 2010, Science, 330, 6532 B. Liu & J. H. Ji : From Dust to PlanetsHoward, A. W., Marcy, G. W., Bryson, S. T., et al. 2012, ApJS, 201, 15Hu, X., Zhu, Z., Okuzumi, S., et al. 2019, ApJ, 885, 36Hu, X., Zhu, Z., Tan, J. C., & Chatterjee, S. 2016, ApJ, 816, 19Huang, C., Wu, Y., & Triaud, A. H. M. J. 2016, ApJ, 825, 98Huang, C. X., Shporer, A., Dragomir, D., et al. 2018a, arXiv e-prints, arXiv:1807.11129Huang, J., Andrews, S. M., Cleeves, L. I., et al. 2018b, ApJ, 852, 122Huang, P., Dong, R., Li, H., Li, S., & Ji, J. 2019, ApJ, 883, L39Huang, P., Isella, A., Li, H., Li, S., & Ji, J. 2018c, ApJ, 867, 3Huang, P., Li, H., Isella, A., et al. 2020, ApJ, 893, 89Hubickyj, O., Bodenheimer, P., & Lissauer, J. J. 2005, Icarus, 179, 415Hughes, A. M., Wilner, D. J., Qi, C., & Hogerheijde, M. R. 2008, ApJ, 678, 1119Hull, C. L. H., Yang, H., Li, Z.-Y., et al. 2018, ApJ, 860, 82Hyodo, R., Ida, S., & Charnoz, S. 2019, A&A, 629, A90Ida, S., & Guillot, T. 2016, A&A, 596, L3Ida, S., Guillot, T., & Morbidelli, A. 2016, A&A, 591, A72Ida, S., & Lin, D. N. C. 2004a, ApJ, 604, 388Ida, S., & Lin, D. N. C. 2004b, ApJ, 616, 567Ida, S., & Lin, D. N. C. 2005, ApJ, 626, 1045Ida, S., Lin, D. N. C., & Nagasawa, M. 2013, ApJ, 775, 42Ida, S., & Makino, J. 1993, Icarus, 106, 210Ida, S., & Nakazawa, K. 1989, A&A, 224, 303Ikoma, M., Nakazawa, K., & Emori, H. 2000, ApJ, 537, 1013Inamdar, N. K., & Schlichting, H. E. 2016, ApJ, 817, L13Isella, A., Benisty, M., Teague, R., et al. 2019, ApJ, 879, L25Isella, A., Guidi, G., Testi, L., et al. 2016, Phys. Rev. Lett., 117, 251101Izidoro, A., Bitsch, B., Raymond, S. N., et al. 2019, arXiv e-prints, arXiv:1902.08772Izidoro, A., Ogihara, M., Raymond, S. N., et al. 2017, MNRAS, 470, 1750Izidoro, A., & Raymond, S. N. 2018, Handbook of Exoplanets, 2365–2423Jacobsen, S. B. 2005, Annual Review of Earth and Planetary Sciences, 33, 531Jacobson, S. A., Morbidelli, A., Raymond, S. N., et al. 2014, Nature, 508, 84Ji, J. H., & Huang, X. M. 2020, Chinese Science Bulletin, in pressJi, J., Jin, S., & Tinney, C. G. 2011, ApJ, 727, L5Jin, S., Isella, A., Huang, P., et al. 2019, ApJ, 881, 108Jin, S., & Ji, J. 2011, MNRAS, 418, 1335Jin, S., Li, S., Isella, A., Li, H., & Ji, J. 2016, ApJ, 818, 76Jin, S., & Mordasini, C. 2018, ApJ, 853, 163Jin, S., Mordasini, C., Parmentier, V., et al. 2014, ApJ, 795, 65Johansen, A., Blum, J., Tanaka, H., et al. 2014, Protostars and Planets VI, 547Johansen, A., Ida, S., & Brasser, R. 2019, A&A, 622, A202Johansen, A., & Klahr, H. 2005, ApJ, 634, 1353Johansen, A., & Lambrechts, M. 2017, Annual Review of Earth and Planetary Sciences, 45, 359Johansen, A., Mac Low, M.-M., Lacerda, P., & Bizzarro, M. 2015, Science Advances, 1, 1500109Johansen, A., Oishi, J. S., Mac Low, M.-M., et al. 2007, Nature, 448, 1022Johansen, A., & Youdin, A. 2007, ApJ, 662, 627Johansen, A., Youdin, A., & Mac Low, M.-M. 2009, ApJ, 704, L75Johansen, A., Youdin, A. N., & Lithwick, Y. 2012, A&A, 537, A125Johns-Krull, C. M., McLane, J. N., Prato, L., et al. 2016, ApJ, 826, 206Johnson, J. A., Aller, K. M., Howard, A. W., & Crepp, J. R. 2010, PASP, 122, 905Johnson, J. A., Butler, R. P., Marcy, G. W., et al. 2007, ApJ, 670, 833Jones, M. I., Jenkins, J. S., Brahm, R., et al. 2016, A&A, 590, A38 . Liu & J. H. Ji. Liu & J. H. Ji B. Liu & J. H. Ji : From Dust to PlanetsHoward, A. W., Marcy, G. W., Bryson, S. T., et al. 2012, ApJS, 201, 15Hu, X., Zhu, Z., Okuzumi, S., et al. 2019, ApJ, 885, 36Hu, X., Zhu, Z., Tan, J. C., & Chatterjee, S. 2016, ApJ, 816, 19Huang, C., Wu, Y., & Triaud, A. H. M. J. 2016, ApJ, 825, 98Huang, C. X., Shporer, A., Dragomir, D., et al. 2018a, arXiv e-prints, arXiv:1807.11129Huang, J., Andrews, S. M., Cleeves, L. I., et al. 2018b, ApJ, 852, 122Huang, P., Dong, R., Li, H., Li, S., & Ji, J. 2019, ApJ, 883, L39Huang, P., Isella, A., Li, H., Li, S., & Ji, J. 2018c, ApJ, 867, 3Huang, P., Li, H., Isella, A., et al. 2020, ApJ, 893, 89Hubickyj, O., Bodenheimer, P., & Lissauer, J. J. 2005, Icarus, 179, 415Hughes, A. M., Wilner, D. J., Qi, C., & Hogerheijde, M. R. 2008, ApJ, 678, 1119Hull, C. L. H., Yang, H., Li, Z.-Y., et al. 2018, ApJ, 860, 82Hyodo, R., Ida, S., & Charnoz, S. 2019, A&A, 629, A90Ida, S., & Guillot, T. 2016, A&A, 596, L3Ida, S., Guillot, T., & Morbidelli, A. 2016, A&A, 591, A72Ida, S., & Lin, D. N. C. 2004a, ApJ, 604, 388Ida, S., & Lin, D. N. C. 2004b, ApJ, 616, 567Ida, S., & Lin, D. N. C. 2005, ApJ, 626, 1045Ida, S., Lin, D. N. C., & Nagasawa, M. 2013, ApJ, 775, 42Ida, S., & Makino, J. 1993, Icarus, 106, 210Ida, S., & Nakazawa, K. 1989, A&A, 224, 303Ikoma, M., Nakazawa, K., & Emori, H. 2000, ApJ, 537, 1013Inamdar, N. K., & Schlichting, H. E. 2016, ApJ, 817, L13Isella, A., Benisty, M., Teague, R., et al. 2019, ApJ, 879, L25Isella, A., Guidi, G., Testi, L., et al. 2016, Phys. Rev. Lett., 117, 251101Izidoro, A., Bitsch, B., Raymond, S. N., et al. 2019, arXiv e-prints, arXiv:1902.08772Izidoro, A., Ogihara, M., Raymond, S. N., et al. 2017, MNRAS, 470, 1750Izidoro, A., & Raymond, S. N. 2018, Handbook of Exoplanets, 2365–2423Jacobsen, S. B. 2005, Annual Review of Earth and Planetary Sciences, 33, 531Jacobson, S. A., Morbidelli, A., Raymond, S. N., et al. 2014, Nature, 508, 84Ji, J. H., & Huang, X. M. 2020, Chinese Science Bulletin, in pressJi, J., Jin, S., & Tinney, C. G. 2011, ApJ, 727, L5Jin, S., Isella, A., Huang, P., et al. 2019, ApJ, 881, 108Jin, S., & Ji, J. 2011, MNRAS, 418, 1335Jin, S., Li, S., Isella, A., Li, H., & Ji, J. 2016, ApJ, 818, 76Jin, S., & Mordasini, C. 2018, ApJ, 853, 163Jin, S., Mordasini, C., Parmentier, V., et al. 2014, ApJ, 795, 65Johansen, A., Blum, J., Tanaka, H., et al. 2014, Protostars and Planets VI, 547Johansen, A., Ida, S., & Brasser, R. 2019, A&A, 622, A202Johansen, A., & Klahr, H. 2005, ApJ, 634, 1353Johansen, A., & Lambrechts, M. 2017, Annual Review of Earth and Planetary Sciences, 45, 359Johansen, A., Mac Low, M.-M., Lacerda, P., & Bizzarro, M. 2015, Science Advances, 1, 1500109Johansen, A., Oishi, J. S., Mac Low, M.-M., et al. 2007, Nature, 448, 1022Johansen, A., & Youdin, A. 2007, ApJ, 662, 627Johansen, A., Youdin, A., & Mac Low, M.-M. 2009, ApJ, 704, L75Johansen, A., Youdin, A. N., & Lithwick, Y. 2012, A&A, 537, A125Johns-Krull, C. M., McLane, J. N., Prato, L., et al. 2016, ApJ, 826, 206Johnson, J. A., Aller, K. M., Howard, A. W., & Crepp, J. R. 2010, PASP, 122, 905Johnson, J. A., Butler, R. P., Marcy, G. W., et al. 2007, ApJ, 670, 833Jones, M. I., Jenkins, J. S., Brahm, R., et al. 2016, A&A, 590, A38 . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 43Juri´c, M., & Tremaine, S. 2008, ApJ, 686, 603Kataoka, A., Tanaka, H., Okuzumi, S., & Wada, K. 2013, A&A, 557, L4Kataoka, A., Tsukagoshi, T., Pohl, A., et al. 2017, ApJ, 844, L5Kataoka, A., Tsukagoshi, T., Momose, M., et al. 2016, ApJ, 831, L12Kennedy, G. M., Wyatt, M. C., Sibthorpe, B., et al. 2012, MNRAS, 421, 2264Kennedy, G. M., Matr`a, L., Facchini, S., et al. 2019, Nature Astronomy, 3, 230Kenyon, S. J., & Bromley, B. C. 2006, AJ, 131, 1837Keppler, M., Benisty, M., M¨uller, A., et al. 2018, A&A, 617, A44Kleine, T., Mezger, K., M¨unker, C., Palme, H., & Bischoff, A. 2004, Geochim. Cosmochim. Acta, 68, 2935Kleine, T., M¨unker, C., Mezger, K., & Palme, H. 2002, Nature, 418, 952Kleine, T., Touboul, M., Bourdon, B., et al. 2009, Geochim. Cosmochim. Acta, 73, 5150Kley, W., & Haghighipour, N. 2015, A&A, 581, A20Kley, W., & Nelson, R. P. 2012, ARA&A, 50, 211Kley, W., Papaloizou, J. C. B., & Ogilvie, G. I. 2008, A&A, 487, 671Kokubo, E., & Genda, H. 2010, ApJ, 714, L21Kokubo, E., & Ida, S. 1996, Icarus, 123, 180Kokubo, E., & Ida, S. 1998, Icarus, 131, 171Kokubo, E., & Ida, S. 2000, Icarus, 143, 15Kostov, V. B., McCullough, P. R., Carter, J. A., et al. 2014, ApJ, 784, 14Kouwenhoven, M. B. N., Brown, A. G. A., Portegies Zwart, S. F., & Kaper, L. 2007, A&A, 474, 77Kozai, Y. 1962, AJ, 67, 591Kretke, K. A., & Levison, H. F. 2014, AJ, 148, 109Kretke, K. A., & Lin, D. N. C. 2012, ApJ, 755, 74Krijt, S., Ormel, C. W., Dominik, C., & Tielens, A. G. G. M. 2016, A&A, 586, A20Krijt, S., Schwarz, K. R., Bergin, E. A., & Ciesla, F. J. 2018, ApJ, 864, 78Kruijer, T. S., Burkhardt, C., Budde, G., & Kleine, T. 2017, Proceedings of the National Academy of Science, 114,6712Kruijer, T. S., Kleine, T., & Borg, L. E. 2020, Nature Astronomy, 4, 32Kruijer, T. S., Touboul, M., Fischer-G¨odde, M., et al. 2014, Science, 344, 1150Kuwahara, A., Kurokawa, H., & Ida, S. 2019, A&A, 623, A179Lada, C. J., & Lada, E. A. 2003, ARA&A, 41, 57Lai, D. 2012, MNRAS, 423, 486Lai, D. 2014, MNRAS, 440, 3532Lai, D., & Pu, B. 2017, AJ, 153, 42Lambrechts, M., & Johansen, A. 2012, A&A, 544, A32Lambrechts, M., & Johansen, A. 2014, A&A, 572, A107Lambrechts, M., Johansen, A., & Morbidelli, A. 2014, A&A, 572, A35Lambrechts, M., & Lega, E. 2017, A&A, 606, A146Lambrechts, M., Morbidelli, A., Jacobson, S. A., et al. 2019, A&A, 627, A83Lee, E. J., & Chiang, E. 2016, ApJ, 817, 90Lee, E. J., Chiang, E., & Ormel, C. W. 2014, ApJ, 797, 95Lee, M. H., Fabrycky, D., & Lin, D. N. C. 2013, ApJ, 774, 52Leinhardt, Z. M., & Stewart, S. T. 2012, ApJ, 745, 79Levison, H. F., Kretke, K. A., & Duncan, M. J. 2015, Nature, 524, 322Li, D., Mustill, A. J., & Davies, M. B. 2019a, MNRAS, 488, 1366Li, G., & Adams, F. C. 2015, MNRAS, 448, 344Li, H., Finn, J. M., Lovelace, R. V. E., & Colgate, S. A. 2000, ApJ, 533, 1023–1034Li, R., Youdin, A. N., & Simon, J. B. 2018, ApJ, 862, 14Li, R., Youdin, A. N., & Simon, J. B. 2019b, ApJ, 885, 69Li, Y.-P., Li, H., Ricci, L., et al. 2019c, ApJ, 878, 394 B. Liu & J. H. Ji : From Dust to PlanetsLichtenberg, T., Golabek, G. J., Burn, R., et al. 2019, Nature Astronomy, 3, 307Lidov, M. L. 1962, Planet. Space Sci., 9, 719Lin, D. N. C., Bodenheimer, P., & Richardson, D. C. 1996, Nature, 380, 606Lin, D. N. C., & Papaloizou, J. 1979, MNRAS, 186, 799Lin, D. N. C., & Papaloizou, J. 1986, ApJ, 309, 846Lin, D. N. C., & Papaloizou, J. C. B. 1993, in Protostars and Planets III, ed. E. H. Levy & J. I. Lunine, 749Lin, M.-K., & Youdin, A. N. 2015, ApJ, 811, 17Lissauer, J. J. 1993, ARA&A, 31, 129Lissauer, J. J., Ragozzine, D., Fabrycky, D. C., et al. 2011, ApJS, 197, 8Lithwick, Y., & Wu, Y. 2012, ApJ, 756, L11Liu, B., Lambrechts, M., Johansen, A., & Liu, F. 2019a, A&A, 632, A7Liu, B., Lambrechts, M., Johansen, A., Pascucci, I., & Henning, T. 2020, A&A, 638, A88Liu, B., & Ormel, C. W. 2017, A&A, 606, A66Liu, B., & Ormel, C. W. 2018, A&A, 615, A138Liu, B., Ormel, C. W., & Johansen, A. 2019b, A&A, 624, A114Liu, B., Ormel, C. W., & Lin, D. N. C. 2017, A&A, 601, A15Liu, B., Zhang, X., & Lin, D. N. C. 2016, ApJ, 823, 162Liu, B., Zhang, X., Lin, D. N. C., & Aarseth, S. J. 2015, ApJ, 798, 62Liu, H. B. 2019, ApJ, 877, L22Liu, H.-G., Zhang, H., & Zhou, J.-L. 2013, ApJ, 772, 142Liu, S.-F., Hori, Y., Lin, D. N. C., & Asphaug, E. 2015, ApJ, 812, 164Liu, S.-F., Hori, Y., M¨uller, S., et al. 2019c, Nature, 572, 355Liu, S.-F., Jin, S., Li, S., Isella, A., & Li, H. 2018, ApJ, 857, 87Liu, Y., Dipierro, G., Ragusa, E., et al. 2019d, A&A, 622, A75Lodato, G., & Rice, W. K. M. 2005, MNRAS, 358, 1489–1500Long, F., Pinilla, P., Herczeg, G. J., et al. 2018, ApJ, 869, 17Long, F., Pinilla, P., Herczeg, G. J., et al. 2020, ApJ, 898,36LLopez, E. D., & Fortney, J. J. 2013, ApJ, 776, 2Luger, R., & Barnes, R. 2015, Astrobiology, 15, 119Lynden-Bell, D., & Pringle, J. E. 1974, MNRAS, 168, 603Lyra, W., Paardekooper, S.-J., & Mac Low, M.-M. 2010, ApJ, 715, L68Lyra, W., & Umurhan, O. 2019, PASP, 131, 2001LMa, C.-T., Gong, Y.-X., Wu, X.-M., & Ji, J. 2020, MNRAS, 493, 1907Malmberg, D., Davies, M. B., & Heggie, D. C. 2011, MNRAS, 411, 859Manara, C. F., Rosotti, G., Testi, L., et al. 2016, A&A, 591, L3Marcy, G., Butler, R. P., Fischer, D., et al. 2005, Progress of Theoretical Physics Supplement, 158, 24–42Marsset, M., Fraser, W. C., Bannister, M. T., et al. 2020, The Planetary Science Journal, 1, 16Marzari, F., Scholl, H., Th´ebault, P., & Baruteau, C. 2009, A&A, 508, 1493Masset, F., & Snellgrove, M. 2001, MNRAS, 320, L55Masuda, K., Winn, J. N., & Kawahara, H. 2020, AJ, 159, 38Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425Matsakos, T., & K¨onigl, A. 2017, AJ, 153, 60Matsumura, S., Brasser, R., & Ida, S. 2017, A&A, 607, A67Mayor, M., & Queloz, D. 1995, Nature, 378, 355Mayor, M., Queloz, D., Udry, S., & Halbwachs, J.-L. 1997, in IAU Colloq. 161: Astronomical and BiochemicalOrigins and the Search for Life in the Universe, ed. C. Batalli Cosmovici, S. Bowyer, & D. Werthimer, 313Mayor, M., Pepe, F., Queloz, D., et al. 2003, The Messenger, 114, 20Mayor, M., Marmier, M., Lovis, C., et al. 2011, arXiv:1109.2497McKinnon, W. B., Richardson, D. C., Marohnic, J. C., et al. 2020, Science, 367, aay6620McNally, C. P., Nelson, R. P., & Paardekooper, S.-J. 2019, MNRAS, 489, L17 . Liu & J. H. Ji. Liu & J. H. Ji B. Liu & J. H. Ji : From Dust to PlanetsLichtenberg, T., Golabek, G. J., Burn, R., et al. 2019, Nature Astronomy, 3, 307Lidov, M. L. 1962, Planet. Space Sci., 9, 719Lin, D. N. C., Bodenheimer, P., & Richardson, D. C. 1996, Nature, 380, 606Lin, D. N. C., & Papaloizou, J. 1979, MNRAS, 186, 799Lin, D. N. C., & Papaloizou, J. 1986, ApJ, 309, 846Lin, D. N. C., & Papaloizou, J. C. B. 1993, in Protostars and Planets III, ed. E. H. Levy & J. I. Lunine, 749Lin, M.-K., & Youdin, A. N. 2015, ApJ, 811, 17Lissauer, J. J. 1993, ARA&A, 31, 129Lissauer, J. J., Ragozzine, D., Fabrycky, D. C., et al. 2011, ApJS, 197, 8Lithwick, Y., & Wu, Y. 2012, ApJ, 756, L11Liu, B., Lambrechts, M., Johansen, A., & Liu, F. 2019a, A&A, 632, A7Liu, B., Lambrechts, M., Johansen, A., Pascucci, I., & Henning, T. 2020, A&A, 638, A88Liu, B., & Ormel, C. W. 2017, A&A, 606, A66Liu, B., & Ormel, C. W. 2018, A&A, 615, A138Liu, B., Ormel, C. W., & Johansen, A. 2019b, A&A, 624, A114Liu, B., Ormel, C. W., & Lin, D. N. C. 2017, A&A, 601, A15Liu, B., Zhang, X., & Lin, D. N. C. 2016, ApJ, 823, 162Liu, B., Zhang, X., Lin, D. N. C., & Aarseth, S. J. 2015, ApJ, 798, 62Liu, H. B. 2019, ApJ, 877, L22Liu, H.-G., Zhang, H., & Zhou, J.-L. 2013, ApJ, 772, 142Liu, S.-F., Hori, Y., Lin, D. N. C., & Asphaug, E. 2015, ApJ, 812, 164Liu, S.-F., Hori, Y., M¨uller, S., et al. 2019c, Nature, 572, 355Liu, S.-F., Jin, S., Li, S., Isella, A., & Li, H. 2018, ApJ, 857, 87Liu, Y., Dipierro, G., Ragusa, E., et al. 2019d, A&A, 622, A75Lodato, G., & Rice, W. K. M. 2005, MNRAS, 358, 1489–1500Long, F., Pinilla, P., Herczeg, G. J., et al. 2018, ApJ, 869, 17Long, F., Pinilla, P., Herczeg, G. J., et al. 2020, ApJ, 898,36LLopez, E. D., & Fortney, J. J. 2013, ApJ, 776, 2Luger, R., & Barnes, R. 2015, Astrobiology, 15, 119Lynden-Bell, D., & Pringle, J. E. 1974, MNRAS, 168, 603Lyra, W., Paardekooper, S.-J., & Mac Low, M.-M. 2010, ApJ, 715, L68Lyra, W., & Umurhan, O. 2019, PASP, 131, 2001LMa, C.-T., Gong, Y.-X., Wu, X.-M., & Ji, J. 2020, MNRAS, 493, 1907Malmberg, D., Davies, M. B., & Heggie, D. C. 2011, MNRAS, 411, 859Manara, C. F., Rosotti, G., Testi, L., et al. 2016, A&A, 591, L3Marcy, G., Butler, R. P., Fischer, D., et al. 2005, Progress of Theoretical Physics Supplement, 158, 24–42Marsset, M., Fraser, W. C., Bannister, M. T., et al. 2020, The Planetary Science Journal, 1, 16Marzari, F., Scholl, H., Th´ebault, P., & Baruteau, C. 2009, A&A, 508, 1493Masset, F., & Snellgrove, M. 2001, MNRAS, 320, L55Masuda, K., Winn, J. N., & Kawahara, H. 2020, AJ, 159, 38Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425Matsakos, T., & K¨onigl, A. 2017, AJ, 153, 60Matsumura, S., Brasser, R., & Ida, S. 2017, A&A, 607, A67Mayor, M., & Queloz, D. 1995, Nature, 378, 355Mayor, M., Queloz, D., Udry, S., & Halbwachs, J.-L. 1997, in IAU Colloq. 161: Astronomical and BiochemicalOrigins and the Search for Life in the Universe, ed. C. Batalli Cosmovici, S. Bowyer, & D. Werthimer, 313Mayor, M., Pepe, F., Queloz, D., et al. 2003, The Messenger, 114, 20Mayor, M., Marmier, M., Lovis, C., et al. 2011, arXiv:1109.2497McKinnon, W. B., Richardson, D. C., Marohnic, J. C., et al. 2020, Science, 367, aay6620McNally, C. P., Nelson, R. P., & Paardekooper, S.-J. 2019, MNRAS, 489, L17 . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 45Miguel, Y., Cridland, A., Ormel, C. W., Fortney, J. J., & Ida, S. 2020, MNRAS, 491, 1998Millholland, S., Wang, S., & Laughlin, G. 2017, ApJ, 849, L33Miotello, A., Testi, L., Lodato, G., et al. 2014, A&A, 567, A32Miranda, R., & Lai, D. 2015, MNRAS, 452, 2396Miranda, R., Li, H., Li, S., & Jin, S. 2017, ApJ, 835, 118Montesinos, M., Perez, S., Casassus, S., et al. 2016, ApJ, 823, L8Morbidelli, A., Bottke, W. F., Nesvorn´y, D., & Levison, H. F. 2009, Icarus, 204, 558Morbidelli, A., & Crida, A. 2007, Icarus, 191, 158Morbidelli, A., Lambrechts, M., Jacobson, S., & Bitsch, B. 2015, Icarus, 258, 418Mordasini, C., Alibert, Y., & Benz, W. 2009, A&A, 501, 1139Mordasini, C., Alibert, Y., Benz, W., Klahr, H., & Henning, T. 2012a, A&A, 541, A97Mordasini, C., Alibert, Y., Georgy, C., et al. 2012b, A&A, 547, A112Morishima, R., Stadel, J., & Moore, B. 2010, Icarus, 207, 517Movshovitz, N., Bodenheimer, P., Podolak, M., & Lissauer, J. J. 2010, Icarus, 209, 616Mulders, G. D., Mordasini, C., Pascucci, I., et al. 2019, ApJ, 887, 157Mulders, G. D., Pascucci, I., & Apai, D. 2015, ApJ, 798, 112Mulders, G. D., Pascucci, I., Apai, D., & Ciesla, F. J. 2018, AJ, 156, 24M¨uller, A., Keppler, M., Henning, T., et al. 2018, A&A, 617, L2M¨uller, T. W. A., & Kley, W. 2012, A&A, 539, A18Murchikova, L., & Tremaine, S. 2020, AJ, 160, 160MMuro-Arena, G. A., Ginski, C., Dominik, C., et al. 2020, A&A, 636, L4Musiolik, G., & Wurm, G. 2019, ApJ, 873, 58Mustill, A. J., Davies, M. B., & Johansen, A. 2015, ApJ, 808, 14Mustill, A. J., Davies, M. B., & Johansen, A. 2017, MNRAS, 468, 3000Muto, T., Grady, C. A., Hashimoto, J., et al. 2012, ApJ, 748, L22Nakagawa, Y., Sekiya, M., & Hayashi, C. 1986, Icarus, 67, 375Naoz, S., Farr, W. M., Lithwick, Y., Rasio, F. A., & Teyssandier, J. 2011, Nature, 473, 187Naoz, S., Farr, W. M., Lithwick, Y., Rasio, F. A., & Teyssandier, J. 2013, MNRAS, 431, 2155Natta, A., Testi, L., Neri, R., Shepherd, D. S., & Wilner, D. J. 2004, A&A, 416, 179Natta, A., Testi, L., & Randich, S. 2006, A&A, 452, 245Nelson, R. P., Gressel, O., & Umurhan, O. M. 2013, MNRAS, 435, 2610Nelson, R. P., Papaloizou, J. C. B., Masset, F., & Kley, W. 2000, MNRAS, 318, 18Nesvorn´y, D., Li, R., Youdin, A. N., Simon, J. B., & Grundy, W. M. 2019, Nature Astronomy, 3, 808Nesvorn´y, D., Youdin, A. N., & Richardson, D. C. 2010, AJ, 140, 785O’Brien, D. P., Morbidelli, A., & Levison, H. F. 2006, Icarus, 184, 39O’Brien, D. P., Walsh, K. J., Morbidelli, A., Raymond, S. N., & Mandell, A. M. 2014, Icarus, 239, 74Ogihara, M., & Ida, S. 2009, ApJ, 699, 824Ogihara, M., Kokubo, E., Suzuki, T. K., & Morbidelli, A. 2018, A&A, 615, A63Ogihara, M., Kunitomo, M., & Hori, Y. 2020, ApJ, 899, 91Ogihara, M., Morbidelli, A., & Guillot, T. 2015, A&A, 578, A36Ohashi, S., Kataoka, A., Van der Marel, N., et al. 2020, arXiv e-prints, arXiv:2007.15014Okuzumi, S., Momose, M., Sirono, S.-i., Kobayashi, H., & Tanaka, H. 2016, ApJ, 821, 82Okuzumi, S., Tanaka, H., Kobayashi, H., & Wada, K. 2012, ApJ, 752, 106Ormel, C. W. 2017, Astrophysics and Space Science Library, Vol. 445, The Emerging Paradigm of PebbleAccretion, ed. M. Pessah & O. Gressel, Astrophysics and Space Science Library, Vol. 445, Astrophysics andSpace Science Library, ed. M. Pessah & O. Gressel, 197Ormel, C. W., & Cuzzi, J. N. 2007, A&A, 466, 413Ormel, C. W., Dullemond, C. P., & Spaans, M. 2010, ApJ, 714, L103Ormel, C. W., & Klahr, H. H. 2010, A&A, 520, A436 B. Liu & J. H. Ji : From Dust to PlanetsOrmel, C. W., & Liu, B. 2018, A&A, 615, A178Ormel, C. W., Liu, B., & Schoonenberg, D. 2017, A&A, 604, A1Ormel, C. W., Shi, J.-M., & Kuiper, R. 2015, MNRAS, 447, 3512Ormel, C. W., Spaans, M., & Tielens, A. G. G. M. 2007, A&A, 461, 215Owen, J. E. 2016, PASA, 33, e005Owen, J. E., & Wu, Y. 2013, ApJ, 775, 105Owen, J. E., & Wu, Y. 2017, ApJ, 847, 29Paardekooper, S. J., & Leinhardt, Z. M. 2010, MNRAS, 403, L64Paardekooper, S. J., Th´ebault, P., & Mellema, G. 2008, MNRAS, 386, 973Pan, L., Padoan, P., Scalo, J., Kritsuk, A. G., & Norman, M. L. 2011, ApJ, 740, 6Pan, M., Wang, S., & Ji, J. 2020, MNRAS, 496, 4688Pape, J., Mezger, K., Bouvier, A. S., & Baumgartner, L. P. 2019, Geochim. Cosmochim. Acta, 244, 416Paraskov, G. B., Wurm, G., & Krauss, O. 2006, ApJ, 648, 1219Pascucci, I., Mulders, G. D., Gould, A., & Fernandes, R. 2018, ApJ, 856, L28Pascucci, I., Testi, L., Herczeg, G. J., et al. 2016, ApJ, 831, 125Pepe, F. A., Cristiani, S., Rebolo Lopez, R., et al. 2010, in Society of Photo-Optical Instrumentation Engineers(SPIE) Conference Series, Vol. 7735, Ground-based and Airborne Instrumentation for Astronomy III, 77350FP´erez, L. M., Carpenter, J. M., Chand ler, C. J., et al. 2012, ApJ, 760, L17Petigura, E. A., Howard, A. W., & Marcy, G. W. 2013, Proceedings of the National Academy of Science, 110,19273Petit, A. C., Pichierri, G., Davies, M. B., & Johansen, A. 2020, arXiv e-prints, arXiv:2006.14903Petrovich, C., Malhotra, R., & Tremaine, S. 2013, ApJ, 770, 24Pfalzner, S. 2013, A&A, 549, A82Picogna, G., Stoll, M. H. R., & Kley, W. 2018, A&A, 616, A116Pierens, A., Cossou, C., & Raymond, S. N. 2013, A&A, 558, A105Pierens, A., & Nelson, R. P. 2008a, A&A, 482, 333Pierens, A., & Nelson, R. P. 2008b, A&A, 483, 633Pinilla, P., Benisty, M., & Birnstiel, T. 2012a, A&A, 545, A81Pinilla, P., Birnstiel, T., Ricci, L., et al. 2012b, A&A, 538, A114Pinilla, P., Quiroga-Nu˜nez, L. H., Benisty, M., et al. 2017, ApJ, 846, 70Pinte, C., Price, D. J., M´enard, F., et al. 2018, ApJ, 860, L13Pinte, C., Price, D. J., M´enard, F., et al. 2020, ApJ, 890, L9Plavchan, P., Barclay, T., Gagn´e, J., et al. 2020, Nature, 582, 497Pollack, J. B., Hubickyj, O., Bodenheimer, P., et al. 1996, Icarus, 124, 62Popovas, A., Nordlund, ˚A., Ramsey, J. P., & Ormel, C. W. 2018, MNRAS, 479, 5136Pu, B., & Wu, Y. 2015, ApJ, 807, 44Quillen, A. C. 2011, MNRAS, 418, 1043Quirrenbach, A., Amado, P. J., Caballero, J. A., et al. 2016, in Society of Photo-Optical Instrumentation Engineers(SPIE) Conference Series, Vol. 9908, Ground-based and Airborne Instrumentation for Astronomy VI, 990812Rafikov, R. R. 2003, AJ, 125, 942Raghavan, D., McAlister, H. A., Henry, T. J., et al. 2010, ApJS, 190, 1Rasio, F. A., & Ford, E. B. 1996, Science, 274, 954Raymond, S. N., & Izidoro, A. 2017, Icarus, 297, 134Raymond, S. N., O’Brien, D. P., Morbidelli, A., & Kaib, N. A. 2009, Icarus, 203, 644Raymond, S. N., Quinn, T., & Lunine, J. I. 2004, Icarus, 168, 1Raymond, S. N., Quinn, T., & Lunine, J. I. 2006, Icarus, 183, 265Rein, H. 2012, MNRAS, 427, L21Ricci, L., Testi, L., Natta, A., et al. 2010, A&A, 512, A15Ricci, L., Testi, L., Natta, A., et al. 2014, ApJ, 791, 20 . Liu & J. H. Ji. Liu & J. H. Ji B. Liu & J. H. Ji : From Dust to PlanetsOrmel, C. W., & Liu, B. 2018, A&A, 615, A178Ormel, C. W., Liu, B., & Schoonenberg, D. 2017, A&A, 604, A1Ormel, C. W., Shi, J.-M., & Kuiper, R. 2015, MNRAS, 447, 3512Ormel, C. W., Spaans, M., & Tielens, A. G. G. M. 2007, A&A, 461, 215Owen, J. E. 2016, PASA, 33, e005Owen, J. E., & Wu, Y. 2013, ApJ, 775, 105Owen, J. E., & Wu, Y. 2017, ApJ, 847, 29Paardekooper, S. J., & Leinhardt, Z. M. 2010, MNRAS, 403, L64Paardekooper, S. J., Th´ebault, P., & Mellema, G. 2008, MNRAS, 386, 973Pan, L., Padoan, P., Scalo, J., Kritsuk, A. G., & Norman, M. L. 2011, ApJ, 740, 6Pan, M., Wang, S., & Ji, J. 2020, MNRAS, 496, 4688Pape, J., Mezger, K., Bouvier, A. S., & Baumgartner, L. P. 2019, Geochim. Cosmochim. Acta, 244, 416Paraskov, G. B., Wurm, G., & Krauss, O. 2006, ApJ, 648, 1219Pascucci, I., Mulders, G. D., Gould, A., & Fernandes, R. 2018, ApJ, 856, L28Pascucci, I., Testi, L., Herczeg, G. J., et al. 2016, ApJ, 831, 125Pepe, F. A., Cristiani, S., Rebolo Lopez, R., et al. 2010, in Society of Photo-Optical Instrumentation Engineers(SPIE) Conference Series, Vol. 7735, Ground-based and Airborne Instrumentation for Astronomy III, 77350FP´erez, L. M., Carpenter, J. M., Chand ler, C. J., et al. 2012, ApJ, 760, L17Petigura, E. A., Howard, A. W., & Marcy, G. W. 2013, Proceedings of the National Academy of Science, 110,19273Petit, A. C., Pichierri, G., Davies, M. B., & Johansen, A. 2020, arXiv e-prints, arXiv:2006.14903Petrovich, C., Malhotra, R., & Tremaine, S. 2013, ApJ, 770, 24Pfalzner, S. 2013, A&A, 549, A82Picogna, G., Stoll, M. H. R., & Kley, W. 2018, A&A, 616, A116Pierens, A., Cossou, C., & Raymond, S. N. 2013, A&A, 558, A105Pierens, A., & Nelson, R. P. 2008a, A&A, 482, 333Pierens, A., & Nelson, R. P. 2008b, A&A, 483, 633Pinilla, P., Benisty, M., & Birnstiel, T. 2012a, A&A, 545, A81Pinilla, P., Birnstiel, T., Ricci, L., et al. 2012b, A&A, 538, A114Pinilla, P., Quiroga-Nu˜nez, L. H., Benisty, M., et al. 2017, ApJ, 846, 70Pinte, C., Price, D. J., M´enard, F., et al. 2018, ApJ, 860, L13Pinte, C., Price, D. J., M´enard, F., et al. 2020, ApJ, 890, L9Plavchan, P., Barclay, T., Gagn´e, J., et al. 2020, Nature, 582, 497Pollack, J. B., Hubickyj, O., Bodenheimer, P., et al. 1996, Icarus, 124, 62Popovas, A., Nordlund, ˚A., Ramsey, J. P., & Ormel, C. W. 2018, MNRAS, 479, 5136Pu, B., & Wu, Y. 2015, ApJ, 807, 44Quillen, A. C. 2011, MNRAS, 418, 1043Quirrenbach, A., Amado, P. J., Caballero, J. A., et al. 2016, in Society of Photo-Optical Instrumentation Engineers(SPIE) Conference Series, Vol. 9908, Ground-based and Airborne Instrumentation for Astronomy VI, 990812Rafikov, R. R. 2003, AJ, 125, 942Raghavan, D., McAlister, H. A., Henry, T. J., et al. 2010, ApJS, 190, 1Rasio, F. A., & Ford, E. B. 1996, Science, 274, 954Raymond, S. N., & Izidoro, A. 2017, Icarus, 297, 134Raymond, S. N., O’Brien, D. P., Morbidelli, A., & Kaib, N. A. 2009, Icarus, 203, 644Raymond, S. N., Quinn, T., & Lunine, J. I. 2004, Icarus, 168, 1Raymond, S. N., Quinn, T., & Lunine, J. I. 2006, Icarus, 183, 265Rein, H. 2012, MNRAS, 427, L21Ricci, L., Testi, L., Natta, A., et al. 2010, A&A, 512, A15Ricci, L., Testi, L., Natta, A., et al. 2014, ApJ, 791, 20 . Liu & J. H. Ji. Liu & J. H. Ji : From Dust to Planets 47Rice, W. K. M., Armitage, P. J., Wood, K., & Lodato, G. 2006, MNRAS, 373, 1619Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015, Journal of Astronomical Telescopes, Instruments, andSystems, 1, 014003Robinson, J. E., Fraser, W. C., Fitzsimmons, A., & Lacerda, P. 2020, arXiv e-prints, arXiv:2008.04207Rogers, T. M., Lin, D. N. C., & Lau, H. H. B. 2012, ApJ, 758, L6Ronnet, T., & Johansen, A. 2020, A&A, 633, A93Ros, K., & Johansen, A. 2013, A&A, 552, A137Rosenthal, M. M., Murray-Clay, R. A., Perets, H. B., & Wolansky, N. 2018, ApJ, 861, 74Ruden, S. P., & Lin, D. N. C. 1986, ApJ, 308, 883Rudge, J. F., Kleine, T., & Bourdon, B. 2010, Nature Geoscience, 3, 439Safronov, V. S. 1972, Evolution of the protoplanetary cloud and formation of the earth and planets.Sanchis-Ojeda, R., Rappaport, S., Winn, J. N., et al. 2014, ApJ, 787, 47Santos, N. C., Israelian, G., & Mayor, M. 2004, A&A, 415, 1153Sch¨afer, U., Johansen, A., & Banerjee, R. 2020, A&A, 635, A190Sch¨afer, U., Yang, C.-C., & Johansen, A. 2017, A&A, 597, A69Schaffer, N., Johansen, A., Cedenblad, L., Mehling, B., & Mitra, D. 2020, A&A, 639, A39Schlaufman, K. C. 2015, ApJ, 799, L26Schoonenberg, D., Liu, B., Ormel, C. W., & Dorn, C. 2019, A&A, 627, A149Schoonenberg, D., & Ormel, C. W. 2017, A&A, 602, A21Schwarz, R., Funk, B., Zechner, R., & Bazs´o, ´A. 2016, MNRAS, 460, 3598Seager, S., Kuchner, M., Hier-Majumder, C. A., & Militzer, B. 2007, ApJ, 669, 1279Shakura, N. I., & Sunyaev, R. A. 1973, A&A, 24, 337Shibaike, Y., Ormel, C. W., Ida, S., Okuzumi, S., & Sasaki, T. 2019, ApJ, 885, 79Simon, J. B., Armitage, P. J., Li, R., & Youdin, A. N. 2016, ApJ, 822, 55Simon, J. B., Armitage, P. J., Youdin, A. N., & Li, R. 2017, ApJ, 847, L12Simon, J. I., Cuzzi, J. N., McCain, K. A., et al. 2018, Earth and Planetary Science Letters, 494, 69Sousa, S. G., Santos, N. C., Israelian, G., Mayor, M., & Udry, S. 2011, A&A, 533, A141Sousa, S. G., Santos, N. C., Mayor, M., et al. 2008, A&A, 487, 373Spurzem, R., Giersz, M., Heggie, D. C., & Lin, D. N. C. 2009, ApJ, 697, 458Stammler, S. M., Dra¸˙zkowska, J., Birnstiel, T., et al. 2019, ApJ, 884, L5Steffen, J. H., Ragozzine, D., Fabrycky, D. C., et al. 2012, Proceedings of the National Academy of Science, 109,7982Steinpilz, T., Teiser, J., & Wurm, G. 2019, ApJ, 874, 60Stern, S. A., Weaver, H. A., Spencer, J. R., et al. 2019, Science, 364, aaw9771Stevenson, D. J., & Lunine, J. I. 1988, Icarus, 75, 146Stolker, T., Dominik, C., Avenhaus, H., et al. 2016, A&A, 595, A113Stoll, M. H. R., & Kley, W. 2014, A&A, 572, A77Sugiura, N., & Fujiya, W. 2014, Meteoritics and Planetary Science, 49, 772Sun, Z., Ji, J., Wang, S., & Jin, S. 2017, MNRAS, 467, 619Surville, C., Mayer, L., & Lin, D. N. C. 2016, ApJ, 831, 82Suyama, T., Wada, K., & Tanaka, H. 2008, ApJ, 684, 1310Takahashi, S. Z., & Inutsuka, S.-i. 2014, ApJ, 794, 55Tazzari, M., Testi, L., Ercolano, B., et al. 2016, A&A, 588, A53Teague, R., Bae, J., Bergin, E. A., Birnstiel, T., & Foreman-Mackey, D. 2018, ApJ, 860, L12Terquem, C., & Papaloizou, J. C. B. 2007, ApJ, 654, 1110Testi, L., Birnstiel, T., Ricci, L., et al. 2014, in Protostars and Planets VI, ed. H. Beuther, R. S. Klessen, C. P.Dullemond, & T. Henning, 339Thebault, P., & Haghighipour, N. 2015, Planet Formation in Binaries, Planetary Exploration and Science: RecentResults and Advances, 3098 B. Liu & J. H. Ji : From Dust to PlanetsTh´ebault, P., Marzari, F., & Scholl, H. 2006, Icarus, 183, 193Thommes, E., Nagasawa, M., & Lin, D. N. C. 2008, ApJ, 676, 728Thommes, E. W., Duncan, M. J., & Levison, H. F. 2003, Icarus, 161, 431Tian, F., & Ida, S. 2015, Nature Geoscience, 8, 177Touboul, M., Kleine, T., Bourdon, B., Palme, H., & Wieler, R. 2007, Nature, 450, 1206Trapman, L., Ansdell, M., Hogerheijde, M. R., et al. 2020, A&A, 638, A38Tremaine, S., & Dong, S. 2012, AJ, 143, 94Triaud, A. H. M. J., Collier Cameron, A., Queloz, D., et al. 2010, A&A, 524, A25Udry, S., Dumusque, X., Lovis, C., et al. 2019, A&A, 622, A37Umurhan, O. M., Estrada, P. R., & Cuzzi, J. N. 2020, ApJ, 895, 4Unterborn, C. T., Desch, S. J., Hinkel, N. R., & Jr, A. L. 2017, arXiv:1706.02689Valencia, D., Sasselov, D. D., & O’Connell, R. J. 2007, ApJ, 665, 1413Valletta, C., & Helled, R. 2019, ApJ, 871, 127van der Marel, N., van Dishoeck, E. F., Bruderer, S., P´erez, L., & Isella, A. 2015, A&A, 579, A106van der Marel, N., van Dishoeck, E. F., Bruderer, S., et al. 2013, Science, 340, 1199Van Eylen, V., Agentoft, C., Lundkvist, M. S., et al. 2018, MNRAS, 479, 4786–4795Vazan, A., Ormel, C. W., Noack, L., & Dominik, C. 2018, ApJ, 869, 163Venturini, J., Alibert, Y., & Benz, W. 2016, A&A, 596, A90Venturini, J., & Helled, R. 2020, A&A, 634, A31Villeneuve, J., Chaussidon, M., & Libourel, G. 2009, Science, 325, 985Visser, R. G., & Ormel, C. W. 2016, A&A, 586, A66Wada, K., Tanaka, H., Suyama, T., Kimura, H., & Yamamoto, T. 2011, ApJ, 737, 36Wahl, S. M., Hubbard, W. B., Militzer, B., et al. 2017, Geophys. Res. Lett., 44, 4649Walsh, K. J., Morbidelli, A., Raymond, S. N., O’Brien, D. P., & Mandell, A. M. 2011, Nature, 475, 206Wang, J., & Fischer, D. A. 2015, AJ, 149, 14Wang, J., Fischer, D. A., Xie, J.-W., & Ciardi, D. R. 2014a, ApJ, 791, 111Wang, J., Xie, J.-W., Barclay, T., & Fischer, D. A. 2014b, ApJ, 783, 4Wang, S. 2017, Research Notes of the American Astronomical Society, 1, 26Wang, S., & Ji, J. 2014, ApJ, 795, 85Wang, S., & Ji, J. 2017, AJ, 154, 236Wang, S., Ji, J., & Zhou, J.-L. 2012, ApJ, 753, 170Ward, W. R. 1997, Icarus, 126, 261Weidenschilling, S. J. 1977, MNRAS, 180, 57Weidenschilling, S. J. 1980, Icarus, 44, 172Weiss, L. M., Marcy, G. W., Petigura, E. A., et al. 2018, AJ, 155, 48Wetherill, G. W., & Stewart, G. R. 1989, Icarus, 77, 330Whipple, F. L. 1972, in From Plasma to Planet, ed. A. Elvius, 211Wimarsson, J., Liu, B., & Ogihara, M. 2020, MNRAS, 496, 3314Winn, J. N. 2010, arXiv e-prints, arXiv:1001.2010Winn, J. N., & Fabrycky, D. C. 2015, ARA&A, 53, 409Winn, J. N., Sanchis-Ojeda, R., & Rappaport, S. 2018, New Astron. Rev., 83, 37Wittenmyer, R. A., Wang, S., Horner, J., et al. 2020, MNRAS, 492, 377Wright, J. T., Marcy, G. W., Howard, A. W., et al. 2012, ApJ, 753, 160Wright, J. T., Upadhyay, S., Marcy, G. W., et al. 2009, ApJ, 693, 1084Wu, Y. 2019, ApJ, 874, 91Wu, Y., & Murray, N. 2003, ApJ, 589, 605Xie, J.-W. 2014, ApJ, 786, 153Xie, J.-W., Payne, M. J., Th´ebault, P., Zhou, J.-L., & Ge, J. 2010a, ApJ, 724, 1153Xie, J.-W., Zhou, J.-L., & Ge, J. 2010b, ApJ, 708, 1566Xie, J.-W., Dong, S., Zhu, Z., et al. 2016, Proceedings of the National Academy of Science, 113, 41 . Liu & J. H. Ji. Liu & J. H. Ji