The Formation and Dynamics of Super-Earth Planets
aa r X i v : . [ a s t r o - ph . E P ] J un Annu. Rev. Earth Planet. Sci. 2013, Vol 41:469-95
The Formation and Dynamics ofSuper-Earth Planets
Nader Haghighipour
Institute for Astronomy and NASA Astrobiology Institute, University ofHawaii, Honolulu, HI 96822, USA, Email:[email protected]
Key Words planetary system: formation, planetary system: dynamics
Abstract
Super-Earths, objects slightly larger than Earth and slightly smaller than Uranus,have found a special place in exoplanetary science. As a new class of planetary bodies, theseobjects have challenged models of planet formation at both ends of the spectrum and havetriggered a great deal of research on the composition and interior dynamics of rocky planetsin connection to their masses and radii. Being relatively easier to detect than an Earth-sizedplanet at 1 AU around a G star, super-Earths have become the focus of worldwide observationalcampaigns to search for habitable planets. With a range of masses that allows these objects toretain moderate atmospheres and perhaps even plate tectonics, super-Earths may be habitableif they maintain long-term orbits in the habitable zones of their host stars. Given that in thepast two years a few such potentially habitable super-Earths have in fact been discovered, it isnecessary to develop a deep understanding of the formation and dynamical evolution of theseobjects. This article reviews the current state of research on the formation of super-Earths anddiscusses different models of their formation and dynamical evolution.
CONTENTS
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Formation of Super-Earths Around Low-Mass Stars . . . . . . . . . . . . . . . . . . . . The Core-Accretion Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of stellar evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of planet migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Disk-Instability Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nader Haghighipour
The discovery of planets around other stars has undoubtedly revolutionized ourunderstanding of the formation and dynamical evolution of planetary systems.The diverse and surprising characteristics of these objects, both in orbital con-figuration and physical properties, have confronted astronomers with many newchallenges and have reinvigorated the fields of planet formation and dynamics.One surprising characteristic of the currently known extrasolar planets is therange of their masses. Unlike in the Solar System, where planets belong to twodistinct categories of terrestrial (with masses equal to that of Earth or slightlysmaller) and giant [ ∼
14 Earth masses ( M ⊕ ) and larger], many extrasolar planetshave masses in an intermediate range, from slightly larger than Earth to 10 M ⊕ .Dubbed super-Earths, these objects present a new class of planetary bodies withphysical and dynamical properties that for the past few years have been the focusof research among many planetary scientists.The first super-Earth around a main sequence star was discovered by Rivera etal. (2005) using the radial velocity technique. [Note that in 1992, Wolszczan &Frail (1992) discovered at least two terrestrial-class planets around the pulsar PSR1257+12.] Thanks to ground-based observational projects such as the HARPSSearch for Southern Extrasolar Planets , the California Planet Survey (CPS) ,the Lick-Carnegie Exoplanet Survey (LCE), M2K (Clubb et al. 2009), and theMEarth Project (Nutzman & Charbonneau 2008; Irwin et al. 2009a,b) , and theongoing success of the CoRoT and Kepler space telescopes, to date, the numberof these objects has exceeded 90. Tables 1 and 2 show the masses and orbitalelements of the currently known super-Earths. As shown, the vast majority ofthese objects have orbital periods smaller than 50 days. A survey of the parentstars of these bodies indicates that more than half of these stars are hosts tomultiple planets. This implies that super-Earths may be more likely to formin short-period orbits and in systems with multiple bodies - two characteristicsthat play important roles in developing models of their formation and dynamicalevolution.Among the currently known super-Earths, a few have gained special attention.CoRoT-7 b, the seventh planet discovered by the CoRoT space telescope (L´egeret al. 2009; Queloz et al. 2009; Hatzes et al. 2010, 2011), and GJ 1214 b, the firstsuper-Earth discovered by transit photometry around an M star (Charbonneauet al. 2009), are the first super-Earths for which the values of mass and radiushave been measured [CoRoT-7 b: 2.38 M ⊕ , 1.65 Earth radii ( R ⊕ ); GJ 1214 b:5.69 M ⊕ , 2.7 R ⊕ ]. This major achievement has enabled theoreticians to developmodels for the evolution of super-Earths interiors (e.g., Valencia et al. 2006,2007a,b,c, 2009, 2010; ONeill & Lenardic 2007; Sotin & Schubert 2009; Tackley& van Heck 2009) and their possible atmospheric properties (e.g., Miller-Ricciet al. 2009; Seager & Deming 2009; Bean et al. 2010; Miller-Ricci & Fortney2010; Rogers & Seager 2010a,b; Bean et al. 2011; D´esert et al. 2011; Heng &Vogt 2011; Berta et al. 2012; Menou 2012; Fraine et al. 2013). The three super-Earth-class bodies GL 581 d (Mayor et al. 2009, Forveille et al. 2011), GL 581 http://smsc.cnes.fr/COROT/index.htm http://kepler.nasa.gov/ uper-Earths
3g (Vogt et al. 2010, 2012), and GJ 667C c (Anglada-Escud´e et al. 2011) havealso made headlines. These planets are the first terrestrial-class objects that havebeen discovered in their respective habitable zones.For the past few years, the formation and characteristics of super-Earths havebeen the subject of extensive research.This is primarily because being slightlylarger than a typical terrestrial planet, these objects have the capability of devel-oping moderate atmospheres and may have dynamic interiors with plate tectonics- two conditions that would render a super-Earth potentially habitable if its orbitwere in the habitable zone of its host star (see Haghighipour 2011 for a completereview). Also, unlike Earth-sized planets, super-Earths are relatively easy todetect. Current observations of super-Earths have indicated that these objectsseem to be more common around cool and low-mass stars (see, e.g., Dressing &Charbonneau 2013, Swift et al. 2013), where the habitable zone is in closer orbit.Two prime examples of such systems are GL 581, an M3V star with one or twopotentially habitable super-Earths (Mayor et al. 2009; Vogt et al. 2010, 2012;Forveille et al. 2011), and the M1.5 star GJ 667C, with a 4.5 M ⊕ planet in itshabitable zone (Anglada-Escud´e et al. 2011).Given the success of observational techniques in detecting potentially habitablesuper-Earths, and that during the past two years the number of these objectsincreased twofold, it would be natural to expect that many more habitable super-Earths will be detected in the near future. It is, therefore, imperative to developa thorough understanding of the formation and dynamical evolution of thesebodies, particularly in connection with their habitability. This article presents areview of the current state of research on this topic.Since there are no super-Earths in the Solar System, it is important to knowwhether the formation of these objects requires developing new models of planetformation or whether one can use the models of the formation of planets inthe Solar System to explain the formation of super- Earths. In the latter case,these models will require major revisions. For instance, one characteristic ofsuper-Earths that presents a challenge to the theories of planet formation is theirclose-in orbits. While some models suggest that super-Earths were formed atlarge distances and migrated to their present locations, other models present thepossibility of their in-place formation. Fortunately, the physical characteristicsof super-Earths, namely their densities,when considered within the context ofdifferent planet formation scenarios, present a potential pathway for differentiat-ing between these models. In that respect, the study of super-Earths plays animportant role in identifying the most viable planet formation mechanism. Therest of this article presents a review of the current state of research on this topic.I begin in Section 2 by briefly reviewing the models of planet formation in theSolar System. In Section 3, I discuss in detail the application of these models tothe formation of super-Earths, and I conclude in Section 4. Explaining the formation of planets is one of the most outstanding problemsin planetary astronomy. Despite centuries of efforts to explain the formationof the planets of the Solar System, this problem is still unresolved, and planetformation is still an open question. The discovery of extrasolar planets has addedeven more to these complexities. As explained in Section 1, many of these objects
Nader Haghighipour have physical and orbital properties that are unlike those of the planets in theSolar System and are not well explained by the current models of Solar Systemformation and dynamics.Although the diversity of extrasolar planets has been a continuous challenge tothe models of planet formation, a common practice in explaining the formation ofthese objects has been to modify, revise, and/or complement the models of planetformation in the Solar System in such a way that they would be applicable to otherplanetary bodies. This suggests that to understand the formation of extrasolarplanets (such as super-Earths), it is necessary to develop a deep understandingof the models of giant and terrestrial planet formation in the Solar System. Thissection is devoted to this task. I begin by explaining the growth of dust particlesto larger bodies, then discuss different phases of planet growth until a full giantor terrestrial planet is formed.It is widely accepted that planet formation begins in a circumstellar disk of gasand dust known as a nebula by the growth of dust particles to larger objects. Thisprocess, highly dependent on the mass and dynamical properties of the nebula,proceeds in four stages: • coagulation of dust particles through gentle hitting and sticking, whichresults in the formation of centimeter- and decimeter-sized objects; • growth of centimeter- and decimeter-sized bodies to kilometer-sized plan-etesimals; • collision and accretion of planetesimals to planetary embryos (moon- toMars-sized objects) in the inner part of the Solar System and to the cores of giantplanets in the outer parts; and • the accretion of gas and formation of giant planets followed by the collisionalgrowth of planetary embryos to terrestrial-class bodies.The first stage of this process is well understood. Dust grains at this stage undergodifferent types of random and systematic motions (Weidenschilling 1977) andfrequently collide with one another. Particles smaller than 100 µ m are mainlysubject to Brownian motion and collide with relative velocities smaller than 1mm s1. Larger objects, although slightly faster, are still strongly coupled to thegas, and their dynamics is governed by the gravitational attraction of the centralstar, nongravitational forces such as radiation pressure, and their interaction withthe nebula through gas drag. Gas molecules, however, are subject to pressuregradient (which is necessary for maintaining the gas at hydrostatic equilibrium),and as a result, their velocities are slightly smaller than Keplerian. The slightvelocity differences between dust particles and gas molecules cause dust grainsto drift inward and approach one another with small relative velocities (Safronov1969; Weidenschilling 1980; Nakagawa et al. 1981, 1986; Supulver & Lin 2000;Dullemond & Dominik 2005). Turbulence also causes dust grains to collide andis more effective among same-sized particles. As the collisions of dust particlesare gentle, van der Waals forces act between their surfaces and stick the dustparticles to one another. As shown by laboratory experiments and computationalsimulations, such gentle collisions result in the fractal growth of dust grains tolarger aggregates (Figure 1) (Smoluchowski 1916; Dominik & Tielens 1997; Blumet al. 1998; Wurm & Blum 1998; Blum & Wurm 2000; Krause & Blum 2004;Blum 2006, 2010; Wada et al. 2007).While the process of the growth of micrometer-sized dust grains to millimeter- uper-Earths Nader Haghighipour
In a gaseous disk, the turbulent eddies created by magnetorotational instabilityare examples of such high-pressure regions. As Johansen et al. (2006, 2007, 2008)have shown, the formation of these turbulent eddies causes small centimeter- anddecimeter-sized objects to accumulate in their vicinities and increases the localdensity of solid material. As the accumulation of solid objects continues, theirlocal spatial density increases until their region becomes gravitationally unstableand the accumulated bodies fragment into several 1001,000-km-sized planetesi-mals. This mechanism, known as streaming instability, has been presented as ascenario for planetesimal formation. [See Chiang & Youdin (2010) for a reviewand Cuzzi et al. (2008) and Weidenschilling (2010) for alternative viewpoints.]It is important to note that as shown by Shariff & Cuzzi (2011), the local en-hancement of solid to gas surface density necessary for the onset of instability isachievable only when the turbulence is extremely weak. These authors indicatethat when the effect of turbulent mass diffusivity is taken into account, stream-ing instability becomes inefficient, and the growth rate of planetesimals reducessignificantly.Other mechanisms of the formation of planetesimals include trapping dust par-ticles in vortices (Barge & Sommeria 1995, Klahr & Henning 1997, Lyra et al.2009a), trapping particles in pressure enhanced regions created by the evapora-tion front of water in the protoplanetary disk (Kretke & Lin 2007; Brauer etal. 2008a,b; Lyra et al. 2009b), turbulent concentration of solids (Chambers2010), turbulent clustering of protoplanetary bodies (Pan et al. 2011), concen-tration of solid objects at the snowline (the region beyond which water is in thepermanent state of ice) as a result of the sublimation of drifting ice aggregates(Aumatell & Wurm 2011), trapping of solid objects in dead zones (Gressel etal. 2012) and at the boundary between steady super/sub-Keplerian flow createdby inhomogeneous growth of magnetorotational instabilities (Kato et al. 2012),rapid coagulation of porous dust aggregates outside the snowline (Okuzumi et al.2012), and planetesimal formation in self-gravitating disks (Gibbons et al. 2012,Shi & Chiang 2013).The four stages of planet formation outlined above share one interesting feature:The underlying physics of each stage is almost distinct from that of the otherphases. This makes it possible to study each phase separately. Once the dustgrains have grown and kilometer-sized planetesimals are formed, although thecircumstellar disk still contains gas and dust, its dynamics is now mainly drivenby the interaction of planetesimals with one another. These interactions areprimarily gravitational, although gas drag also plays a role. At this stage, becausethe planetesimals are the main components populating the disk, collisions amongthese objects are frequent, which results in low eccentricities and low inclinationsfor these bodies. Because the relative velocity between two bodies is an increasingfunction of their orbital eccentricities, lowering the eccentricity of planetesimalsdue to their mutual collisions and dynamical friction, combined with their almostcoplanar orbits, reduces their relative velocities. The latter facilitates the mergingof these objects and enhances the rate of their accretion to larger bodies.As a planetesimal grows, the influence zone of its gravitational field expandsand as a result, it attracts more material from its surroundings. In other words,more material will be available for the planetesimal to accrete, and the rate of itsgrowth increases. Known as runaway growth, this process results in the growthof kilometer-sized planetesimals to larger bodies in a short time (Safronov 1969;Greenberg et al. 1978; Wetherill & Stewart 1989, 1993; Ida & Makino 1993; uper-Earths > Nader Haghighipour submitted; Izidoro et al. submitted). The planet formation models as explainedabove, although capable of explaining many features of the Solar System, faceseveral complicated challenges. The core-accretion model, for instance, requiresthe nebular gas to be available for ∼
10 Ma while the core of Jupiter grows andaccretes gas from its surroundings (Pollack et al. 1996). However, the observa-tional estimates of the lifetimes of disks around young stars suggest a lifetimeof 0.110 Ma, with 3 Ma being the age at which half the stars show evidence ofdisks (Strom et al. 1993, Haisch et al. 2001, Chen & Kamp 2004, Maercker etal. 2006). These simulations also suggest a solid core for Jupiter with a mass of ∼ M ⊕ . Computational modeling of the interiors of Jupiter and Saturn, how-ever, has indicated different possible values for the cores of these objects, rangingfrom 0 to as large as 14 M ⊕ (Guillot 2005, Militzer et al. 2008). It is unclearwhat the actual masses of the cores of our gas-giant planets are, and if smallerthan 10 M ⊕ , how they accumulated their thick envelopes in a short time. I referthe reader to a review by Guillot (2005) for more details.To overcome these difficulties, the core-accretion model has undergone severalimprovements. Hubickyj et al. (2005) and Lissauer et al. (2009) have shownthat increasing the surface density of the nebula to higher than that suggestedby Pollack et al. (1996) significantly reduces the time of the giant planet for-mation. An improved treatment of grain physics as given by Podolak (2003),Movshovitz & Podolak (2008), and Movshovitz et al. (2010) has also indicatedthat the value of the grain opacity in the envelope of the growing Jupiter inthe original core-accretion model (Pollack et al. 1996) is too high, and a lowervalue has to be adopted. This lower opacity has led to a revised version of thecore-accretion model in which the time of giant planet formation is considerablysmaller (Hubickyj et al. 2005, Movshovitz et al. 2010). Most recently, Bromley& Kenyon (2011) have developed a new hybrid N-body-coagulation code that hasenabled the authors to form Saturn- and Jupiter-sized planets in ∼ ∼ ,
000 years. Although thismechanism presents a fast track to the formation of a gas-giant planet, it suffersfrom the lack of an efficient cooling process necessary to take energy away froma planet-forming clump in a sufficiently short time before it disperses.
The extent to which current planet formation scenarios can be used to explainthe formation of super-Earths varies with the mass and orbital architecture ofthese objects. Since the dynamics and characteristics of planet-forming nebulaeare different for stars with different spectral types, the parent stars of super-Earths also play an important role. The range of masses for the currently knownsuper-Earths, when considered within the context of giant and terrestrial planet uper-Earths
The discovery of planets of different sizes, from Jovian-type [e.g., GJ 876 b, c,and e (Rivera et al. 2010); HIP 57050 b (Haghighipour et al. 2010); GL 581 b(Bonfils et al. 2005); KOI-254 b (Johnson et al. 2012); Kepler-32 d (Swift et al.2013)] to small super-Earths [e.g., GL 581 c, d, e, and g (Udry et al. 2007, Mayoret al. 2009, Vogt et al. 2010); GJ 667C c (Anglada-Escud´e et al. 2011); Kepler-32 b and c (Swift et al. 2013)] around M dwarfs indicates that both giant andterrestrial planet formation can proceed efficiently around low-mass stars. Thisimplies that the circumstellar disks around these stars can accommodate theformation of super-Earths both as a failed core of a giant planet through the gas-giant planet formation process, and also as small terrestrial-class objects throughdirect collisional growth of protoplanetary bodies and planetary embryos. Thesemechanisms have to also account for the short periods of super-Earths, whetherthrough planet migration, planet-planet scattering, or a combination of both.I begin this section by considering the core-accretion model as the mechanismfor the formation of super-Earths. As mentioned above, the discovery of super-Earths can be taken as strong evidence in support of this model. However, asis explained at the end of the next section, this mechanism alone cannot explainthe formation and orbital architecture of all the currently known super- Earths.Other effects such as the evolution of the central star and planet migration haveto be taken into consideration as well. I discuss these effects in the next sectionand conclude this article by reviewing the formation of super-Earths through thedisk-instability model.0
Nader Haghighipour
As mentioned in Section 2, the efficiency of the core-accretion model and the rateof the growth of the cores of giant planets increase with the disk surface den-sity. Around low-mass stars, where the surface density of the disk is smaller thanaround the Sun, the solid material (i.e., the planetesimals) is more spatially scat-tered, and as a result, the collisions among planetesimals and planetary embryosare less frequent. This smaller rate of collision prolongs the growth of planetes-imals to larger sizes, and causes the time of the core growth around low-massstars to be several times longer than the time of the formation of Jupiter aroundthe Sun. As shown by Laughlin et al. (2004), in disks around stars with massessmaller than 0.5 solar masses ( M ⊙ ), the core-accretion mechanism can produceplanets ranging from terrestrial-class to Neptune sizes. However, the time forthe formation of these objects is much longer than the time for the formation ofJupiter in the Solar System through the core-accretion model. During this time,around M stars, for instance, the gaseous component of the circumstellar diskdisperses, leaving the slowly growing core with much less gas to accrete.The short lifetime of the gas in circumstellar disks around M stars can beattributed to two important factors: • the high internal radiation of young M stars (at this stage, these stars arealmost as bright as Sun-like stars), and • external perturbations from other close-by stars.The latter is primarily due to the fact that most stars are formed in clusters(Lada & Lada 2003), and as such, their circumstellar disks are strongly affectedby the gravitational perturbations and the radiations of other stars (Adams et al.2004). For M stars, this causes the circumstellar disk to receive a high amount ofradiation from both the central star and external sources. This high amount ofradiation combined with the low masses of M stars, which points to their smallgravitational fields, increases the effectiveness of the photoevaporation of thegaseous component of the circumstellar disk by up to two orders of magnitude.As a result, the majority of the gas leaves the disk at the early stages of giantplanet formation, leaving a still-forming core with not much gas to accrete. Although the growth of giant planets cores through collision and accretion ofplanetesimals is similar in disks around solar-type and low-mass stars, the factthat around smaller stars this process takes longer introduces a fundamental dif-ference in the formation of giant planets in these two environments. As opposedto young Sun-like stars whose luminosities stay almost constant during the for-mation of giant and terrestrial planets (e.g., 10-100 Ma), the luminosity of apremain sequence, low-mass star (e.g., 0 . M ⊙ ) fades by a factor of 10 to 100during this process (Hayashi 1981). This causes the internal temperature of thecircumstellar disk to decrease, which subsequently causes the disks snowline tomove toward the central star and to close distances. The forward migration of thesnowline results in an increase in the population of icy materials (kilometer-sizedand larger planetesimals) in the outer regions of the disk, which in turn increasesthe efficiency of the collisional growth of these objects to protoplanetary bod-ies (as mentioned in Section 2, sticking is more efficient among icy bodies). Asshown by Kennedy et al. (2006), around a 0.25- M ⊙ star, the moving snowline uper-Earths As mentioned above, one of the major developments in the field of planetarydynamics that was a direct consequence of the detection of extrasolar planets isthe concept of planet migration. Although previously post-formation migrationhad been proposed as a mechanism to explain the orbital architecture of smallbodies in the Solar System (e.g., moons of giant planets and Kuiper belt ob-jects), the migration of planets during their formation had not been incorporatedinto the models of planetary formation. In other words, the planet formationscenarios mentioned above were developed assuming that planets form in place.The discovery of extrasolar planets, almost from the beginning, challenged thisassumption. The detection of the first hot Jupiter in a 4-day orbit around thestar 51 Pegasi (Mayor & Queloz 1995) revealed that planet migration is an in-separable part of the evolution of a planetary system and prompted astronomersto revisit this concept and to incorporate it into their models of planet forma-tion. Today, planet migration is well developed and widely accepted as part of acomprehensive planet formation scenario.Planetary and satellite migration has long been recognized as a major con-tributor to the formation and orbital architecture of planets, their moons, andother minor bodies in the Solar System. As shown by Greenberg et al. (1972)and Greenberg (1973), mean-motion resonances (i.e., commensurable orbital pe-riods ) among the natural satellites of giant planets (e.g., Titan and Hyperion,satellites of Saturn) may have been the result of the radial migration of theseobjects due to their tidal interactions with their parent planets (Goldreich 1965).The dynamical architecture of Galilean satellites, with their three-body, Laplaceresonance, has also been attributed to the migration of these objects. It is ac-cepted that these satellites migrated inward during their formation as a resultof interacting with the circumplanetary disk of satellitesimals around Jupiter(Canup & Ward 2002), and subsequently by tidal forces after their formation(Peale & Lee 2002). The lack of irregular satellites between Callisto, the outer-most Galilean satellite, and Themisto, the innermost irregular satellite of Jupiter,also can be explained by a dynamical clearing process that occurred during theformation and migration of Galilean satellites (Haghighipour & Jewitt 2008).Among the planets of our Solar System, the post-formation, planetesimal-drivenmigration of giant planets has been proposed as a mechanism to explain the cur-rent state of the asteroid belt (Tsiganis et al. 2005; Minton & Malhotra 2009,2011; see also Gomes 1997), late heavy bombardment (Gomes et al. 2005), theorigin of Jupiter Trojan asteroids (Morbidelli et al. 2005), the effects of secularresonances on terrestrial planet formation (Agnor & Lin 2012), and the smallmass and size of Mars (Walsh et al. 2011). I refer the reader to Morbidelli et al.(2012) for a review on these topics.The idea of the migration of planetary bodies was first proposed by Fernandez Orbital commensurability is necessary for two planets to be in a mean-motion resonance;however, it is not sufficient. Other constraints have to exist between the angular elements oftheir orbits as well. For more details, the reader is referred to Roy (1982), Danby (1992), andMurray & Dermott (1999). Nader Haghighipour & Ip (1984). These authors suggested that after the dispersal of the nebulargas, fully formed giant planets may drift from their original orbits due to theexchange of angular momentum with the disk of planetesimals. As a result ofthis post-formation migration, small bodies either are scattered out of the SolarSystem or may reach other regions where they may reside in long-term stableorbits. As shown by Malhotra (1993, 1995), this mechanism can explain thepeculiar orbit of Pluto (highly eccentric, inclined, and long-term chaotic), and asshown by Malhotra (1996) and Hahn & Malhotra (2005), it can also explain thedynamical structure of Kuiper belt objects.The past two decades have witnessed major developments in the theories ofplanet migration. Simulations of the formation of planetary bodies and theirinteractions with circumstellar disks have shown that planet migration does nothave to occur necessarily after the planets are fully formed. In fact, planets canmigrate while they are forming as a result of exchanging angular momentumwith their surrounding environment. This naturally suggests that the physicaland dynamical characteristics of a planet and its circumstellar disk will playan important role in this process. For instance, the planet may undergo typeI migration, in which case it does not accrete nebular material as it migrates(Figure 3a). Conversely, the planet may be large and accrete nebular material,in which case it may create a gap in the disk as it migrates (Figure 3b). Thistype of migration is known as type II migration. Planet migration may occur inother forms as well. The contribution of planet migration to the formation of close-in super-Earthsmay appear in different forms. The most common scenario involves the inwardmigration of a fully formed giant planet in a disk of planetesimals and planetaryembryos. The giant planet in this scenario affects the dynamics of protoplanetarybodies interior to its orbit by either increasing their orbital eccentricities andscattering them to larger distances or causing them to migrate to closer orbits.The migrating protoplanets may be shepherded by the giant planet into smallclose-in regions, where they are captured in mean-motion resonances. As Zhouet al. (2005), Fogg & Nelson (2005, 2006, 2007a,b, 2009), and Raymond et al.(2008) have shown, around Sun-like stars, the shepherded protoplanets may alsocollide and grow to terrestrial-class and super-Earth objects (see, e.g., Figure 6b).Studies of the back-scattered objects in the simulations of disks around massivestars have shown that these bodies may also collide and grow to planetary sizes(Mandell & Sigurdsson 2003, Raymond et al. 2006a, Mandell et al. 2007).While around Sun-like stars, despite the out-scattering of protoplanetary bod-ies during the migration of a giant planet, the formation of super-Earths throughthe collision and growth of planetesimals and planetary embryos proceeds effi-ciently, around low-mass stars this scenario is not always the case. Simulations ofthe dynamics of protoplanetary bodies at distances smaller than 0.2 AU arounda 0.3 M ⊙ star have shown that during the inward migration of one or several gi-ant planets (the latter involves migrating planets in mean-motion resonances), themajority of the protoplanets leave the system and do not contribute to the forma- I do not discuss these mechanisms here, as they may not be entirely relevant to the formationand dynamical evolution of super-Earths. Instead, I refer the reader to numerous articles thathave been published on these subjects. Unfortunately, the richness of the literature does notallow me to cite all these articles here, but among them, one can refer to Nelson et al. (2001),Mass´et & Snellgrove (2001), Papaloizou & Terquem (2006), Chambers (2009), Armitage (2010),and a recent review by Baruteau & Mass´et (2013). uper-Earths M ⊕ , Terquem &Papaloizou (2007) have shown that a few close-in super-Earths may form in thisway with masses up to 12 M ⊕ . The results of these simulations suggest that insystems in which merging of migrating cores results in the formation of super-Earths and Neptune-like planets, such planets will always be accompanied bygiant bodies and most likely will be in mean-motion resonances. Similar resultshave also been reported by Haghighipour & Rastegar (2011).Interestingly, several planetary systems have been discovered in which centralstars host only small Neptune-sized objects and super-Earths (e.g., HD 69830,GL 581). The planets in these systems do not have a Jupiter-like companionthat could have migrated to facilitate their formation. Such systems seem toimply that a different mechanism may be responsible for the formation of theirsuper-Earth bodies. Kennedy & Kenyon (2008a) and Kenyon & Bromley (2009)have suggested that the migration of protoplanetary embryos may be the key infacilitating the close-in accretion of these objects. These authors considered acircumstellar disk with a density enhancement at the region of its snowline andsimulated the dynamics and growth of its planetary embryos. They showed thatwhile interacting with one another (colliding and accreting), many of these objectsmay migrate toward the central star. Around a solar-type star, the time of suchmigrations for an Earth-sized planet at 1 AU is ∼ − years - much smallerthan the time for the chaotic growth of a typical moon- or Mars-sized embryo (10 years) (Goldreich et al. 2004). This implies that most of the migration occursprior to the onset of the final growth. Depending on their relative velocities, theinteractions among the migrating embryos may result in their growth, scattering,and/or shepherding, as in the case of a migrating giant planet. Simulations byKennedy & Kenyon (2008b) and Kenyon & Bromley (2009) have shown thatsuper-Earth objects with masses up to 8 M ⊕ may form in this way around starsranging from 0.25 to 2 M ⊙ (Figure 6). The formation of super-Earths through the mechanisms explained above, partic-ularly when those mechanisms are used to explain the formation of these objectsat the higher end of their mass range, naturally favors the core-accretion modelof giant planet formation. However, the fact that Jovian-type planets have beendiscovered around low-mass stars (e.g., GJ 876, with three planets ranging from4
Nader Haghighipour ∼ ∼ M ⊙ star at a distance of ∼ As evident from this review, it is generally accepted that super-Earths are formedthrough a combination of a core accumulation process and planetary migration.Modeling the formation of these objects requires the simulation of the collisionalgrowth of planetary embryos and their subsequent interactions with the pro-toplanetary disk. A realistic model requires global treatment of the disk andinclusion of large numbers of planetesimals and planetary embryos. In practice,such simulations are computationally expensive. To avoid such complications,most of the current models of super-Earth formation include only small numbersof objects (e.g., cores, progenitors, protoplanets, planetesimals). As shown byMcNeil & Nelson (2010), in systems with large numbers of bodies (e.g., severalthousand planetesimals and larger objects), the combination of traditional coreaccretion and type I planet migration may not produce objects larger than 3-4 M ⊕ in close-in (e.g., ≤ . I am grateful to J¨orgen Blum, Alan Boss, Andre Izidoro, Scott Kenyon, Fr´ed´ericMass´et, and Ji-Lin Zhou for kindly providing figures. uper-Earths Adams FC, Hollenbach D, Laughlin G, GortiU. 2004. Photoevaporation of cir-cumstellar disks due to external far-ultraviolet radiation in stellar aggregates.Astrophys. J. 611:360-79Agnor CB, Canup RM, Levison HF. 1999. On the character and consequences oflarge impacts in the late stage of terrestrial planet formation. Icarus 142:219-37Agnor CB, Lin DNC. 2012. On the migration of Jupiter and Saturn: constraintsfrom linear models of secular resonant coupling with the terrestrial planets. As-trophys. J. 745:143Alibert Y, Mordasini C, Benz W. 2004. Migration and giant planet formation.Astron. Astrophys. 417:L25-28Anglada-Escud´e G, Arriagad P, Vogt SS, Rivera E, Butler RP. 2011. A planetarysystem around the nearby M dwarf GJ 667C with at least one super-Earth in itshabitable zone. Astrophys. J. 751:L16Armitage PJ. 2010. The early evolution of planetary systems. In Astrophysicsof Planet Formation, pp. 218-62. Cambridge, UK: Cambridge Univ. PressAumatell G, Wurm G. 2011. Breaking the ice: planetesimal formation at thesnowline. MNRAS 418:L1-5Barge P, Sommeria J. 1995. Did planet formation begin inside persistent gaseousvortices? Astron. Astrophys. 295:L1-4Baruteau C, Masset F. 2013. Recent developments in planet migration theory. InTides in Astronomy and Astrophysics (Lecture Notes in Physics), ed. J Souchay,S Mathis, T Tokieda, p. 201. Berlin: Springer-VerlagBean JL, D´esert J-M, Kabath P, Stalder B, Seager S, et al. 2011. The opticaland near-infrared transmission spectrum of the super-Earth GJ 1214b: furtherevidence for a metal-rich atmosphere. Astrophys. J. 743:92Bean JL, Miller-Ricci Kempton E, Homeier D. 2010. A ground-based transmis-sion spectrum of the super-Earth exoplanet GJ 1214b. Nature 468:669-72Beitz E, G¨uttler C, Blum J, Meisner T, Teiser J,Wurm G. 2011. Low-velocitycollisions of centimeter-sized dust aggregates. Astrophys. J. 736:34Berta ZK, Charbonneau D, D´esert J-M, Miller-Ricci Kempton E, McCulloughPR, et al. 2012. The flat transmission spectrum of the super-Earth GJ1214bfrom Wide Field Camera 3 on the Hubble Space Telescope. Astrophys. J. 747:35Blum J. 2006. Dust agglomeration. Adv. Phys. 55:881-9476
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Table 1: Currently known extrasolar planets with masses up to 10 Earth-masses.The quantities
M, P, a and e represent the mass (in terms of Earth’s mass M ⊕ ),orbital period, semimajor axis, and orbital eccentricity of the planet. The massof the central star is shown by M ∗ and is given in the units of solar-masses ( M ⊙ ).Planet M ( M ⊕ ) P (day) a (AU) e Stellar Type M ∗ ( M ⊙ )KOI-55 c 0.6678 0.34289 0.0076 - 0.496 sdBKepler-42 d 0.954 1.856169 0.0154 - 0.13 -Kepler-42 c 1.908 0.45328509 0.006 - 0.13 -Gl 581 e 1.9398 3.14945 0.028 0.32 0.31 M2.5VKepler-11 f 2.301366 46.68876 0.25 0 0.95 GHD 20794 c 2.4168 40.114 0.2036 0 0.7 G8VHD 20794 b 2.703 18.315 0.1207 0 0.7 G8VHD 215152 b 2.7666 7.2825 0.0652 0.34 - K0Kepler-42 b 2.862 1.2137672 0.0116 - 0.13 -HD 215152 c 3.0846 10.866 0.0852 0.38 - K0Kepler-20 e 3.0846 6.098493 0.0507 0.912 G8MOA-2007-BLG 3.18 - 0.66 - 0.06 M-192-L bKepler-32 b 3.4 5.90 0.0519 - 0.54 M1VHD 85512 b 3.498 58.43 0.26 0.11 0.69 K5VHD 39194 b 3.7206 5.6363 0.0519 0.2 - K0VKepler-32 c 3.8 8.75 0.067 - 0.54 M1VPSR 1257 +12 d 3.816 98.2114 0.46 0.025 - -PSR 1257 +12 c 4.134 66.5419 0.36 0.018 - -HD 156668 b 4.1658 4.646 0.05 0 0.772 K3VHD 40307 b 4.1976 4.3115 0.047 0 0.77 K2.5VGJ 667C c 4.2612 28.13 0.1251 0.34 0.33 M1.5VKepler-11 b 4.30254 10.30375 0.091 0 0.95 GKOI-55 b 4.452 0.2401 0.006 - 0.496 sdBKepler-10 b 4.5474 0.837495 0.01684 0 0.895 GHD 20794 d 4.77 90.309 0.3499 0 0.7 G8VCoRoT-7 b 4.8018 0.853585 0.0172 0 0.93 K0V61 Vir b 5.088 4.215 0.050201 0.12 0.95 G5VHD 39194 d 5.1516 33.941 0.172 0.2 - K0VHD 136352 b 5.2788 11.577 0.0933 0.18 - G4VGl 581 c 5.406 12.9182 0.073 0.07 0.31 M2.5V uper-Earths M, P, a and e represent the mass(in terms of Earth’s mass M ⊕ ), orbital period, semimajor axis, and orbital ec-centricity of the planet. The mass of the central star is shown by M ∗ and is givenin the units of solar-masses ( M ⊙ ).Planet M ( M ⊕ ) P (day) a (AU) e Stellar Type M ∗ ( M ⊙ )OGLE-2005-390L b 5.406 3500 2.1 - 0.22 MGJ 667C b 5.46324 7.199 0.0504 0.09 0.33 M1.5VGJ 433 b 5.7876 7.3709 0.058 0.08 0.48 M1.5HD 1461 c 5.9148 13.505 0.1117 0 1.08 G0VHD 39194 c 5.9466 14.025 0.0954 0.11 - K0VGl 581 d 6.042 66.64 0.22 0.25 0.31 M2.5VKepler-11 d 6.10242 22.68719 0.159 0 0.95 GHD 154088 b 6.1374 18.596 0.1316 0.38 - K0IVGJ 1214 b 6.36 1.58040482 0.014 0.27 0.153 MHD 215497 b 6.36 3.93404 0.047 0.16 0.87 K3VHD 97658 b 6.36 9.4957 0.0797 0.13 0.85 K1VGl 876 d 6.678 1.93778 0.0208 0.21 0.334 M4 VHD 40307 c 6.8688 9.62 0.081 0 0.77 K2.5VKepler-18 b 6.9006 3.504725 0.0447 - 0.972 -GJ 3634 b 6.996 2.64561 0.0287 0.08 0.45 M2.5Kepler-9 d 6.996 1.592851 0.0273 - 1 -HD 181433 b 7.5684 9.3743 0.08 0.39 0.78 K3IVHD 1461 b 7.6002 5.7727 0.063 0.14 1.08 G0VHD 93385 b 8.3634 13.186 0.1116 0.15 - G2VCoRoT-7 c 8.3952 3.698 0.046 0 0.93 K0VKepler-11 e 8.40474 31.9959 0.194 0 0.95 GGJ 176 b 8.427 8.7836 0.066 0 0.49 M2.5V55 Cnc e 8.586 0.7365449 0.0156 0.06 0.905 K0IV-VKepler-20 b 8.586 3.6961219 0.0453 0.32 0.912 G8HD 96700 b 9.0312 8.1256 0.0774 0.1 - G0VHD 40307 d 9.1584 20.46 0.134 0 0.77 K2.5VHD 7924 b 9.222 5.3978 0.057 0.17 0.832 KOVHD 134606 b 9.2856 12.083 0.102 0.15 - G6IVHD 136352 d 9.54 106.72 0.411 0.43 - G4VHD 189567 b 10.0488 - 14.275 0.11 0.23 G2VHD 93385 c 10.1124 - 46.025 0.21 0.24 G2V2 Nader Haghighipour
Figure 1: Coagulation of dust particles to fractal aggregates. Figure courtesy ofJ. Blum. uper-Earths − . − . Mean-motion and secular resonances withJupiter and Saturn are also shown. Figure courtesy of A. Izidoro.4 Nader Haghighipour
Figure 3: Type I (top) and type II (bottom) planetary migration. Figures cour-tesy of F. Mass´et. uper-Earths . M ⊙ M star (Haghighipour & Rastegar 2011).6
Nader Haghighipour
Figure 5: Accretion of protoplanetary bodies during the migration of two giantplanets around a 0 . M ⊙ M star. As shown here, the system becomes stable withtwo giant planets in a 1:2 MMR and a super-Earth in a short-period orbit (e.g.,GJ 876). uper-Earths M ⊕ object at 0.5 AU. The super-Earth has two giant companions, one at 10 AU (not shown here) and one at 4 AUwith a mass of 1,200 M ⊕ . Figure courtesy of S. Kenyon. Bottom: A combinationof the migration and accretion of embryos to super-Earth bodies and their capturein MMR resonances. Figure courtesy of J.-L. Zhou.8 Nader Haghighipour
Figure 7: A snapshot of a simulation of the formation of super-Earths around a0.5 M ⊙⊙