Extrasolar enigmas: from disintegrating exoplanets to exoasteroids
EExtrasolar enigmas: from disintegratingexoplanets to exoasteroids
Jan Budaj, Petr Kabath and Enric Palle
Abstract
Thousands of transiting exoplanets have been discovered to date, thanksin great part to the
Kepler space mission. As in all populations, and certainly inthe case of exoplanets, one finds unique objects with distinct characteristics. Herewe will describe the properties and behaviour of a small group of ‘disintegrating’exoplanets discovered over the last few years (KIC 12557548b, K2-22b, and others).They evaporate, lose mass unraveling their naked cores, produce spectacular dustycomet-like tails, and feature highly variable asymmetric transits. Apart from theseexoplanets, there is observational evidence for even smaller ‘exo-’objects orbitingother stars: exoasteroids and exocomets. Most probably, such objects are also behindthe mystery of Boyajian’s star. Ongoing and upcoming space missions such as
TESS and PLATO will hopefully discover more objects of this kind, and a new era of theexploration of small extrasolar systems bodies will be upon us.
The exoplanet science discoveries kicked-in after 1992-1995 when the first exoplanetswere discovered [1] first around a pulsar and then a hot Jupiter around a solar typestar 51 Peg [2]. The exoplanet 51 Peg b was detected from observations of radial
Jan BudajAstronomical Institute, Slovak Academy of Sciences, 05960 Tatranska Lomnica, Slovakia, e-mail:[email protected] KabathAstronomcal Institute of Czech Academy of Sciences, Fričova 298, 25165, Ondřejov, Czech Re-public e-mail: [email protected] PalleInstituto de Astrofísica de Canarias, Calle Vía Láctea, s/n, 38205 San Cristóbal de La Laguna,Santa Cruz de Tenerife, Spain e-mail: [email protected] 1 a r X i v : . [ a s t r o - ph . E P ] F e b Jan Budaj, Petr Kabath and Enric Palle velocities (‘RV’) from the ground with a 1.92-m telescope located at Observatoirede Haute Provence.Later hundreds of exoplanets were discovered using the radial velocity method.In 2000, the first transiting exoplanet HD209458b, again a Jupiter-sized planet ina close-in orbit, was detected [3]. New automated ground-based projects to detecttransiting exoplanets were started in the first decade of 21st century. The mostsuccessful of such projects to date is the WASP survey which has discovered about200 transiting planets (April 2019), and there are a number of other successfulground-based exoplanet surveys as well, such as HAT [4] or KELT [5].A real breakthrough came with the launch of the CoRoT space mission in 2006.The CoRoT satellite was a french-led ESA mission carrying a 28-cm aperture tele-scope equipped with 4 CCD detectors dedicated to asteroseismology and exoplane-tary transit detections [6]. The CoRoT mission was terminated in 2013 and it reported33 exoplanets which are all fully characterized and thus we know both their massesand radii.In 2009 a very successful NASA space mission Kepler was launched carrying atelescope with a mirror of 1.4-m with a large array of CCD detectors [7].
Kepler , andlater its continuation K2 mission, discovered during their lifetimes from 2009 until2018 about 4000 transiting exoplanets. Kepler/K2 photometric data likely still containmany more new planetary candidates. However, only a few hundreds of the
Kepler/K2 planets have been fully characterized, so that we know their masses and radii. This factis due to the relative faintness of the
Kepler/K2 targets and the difficulty of carryingout ground-based follow-up spectroscopic RV observations. However, despite theselimitations,
Kepler/K2 was able to deliver extremely interesting candidates, amongthem low mass and rocky planets in the habitable zone such as Kepler-62f [8], ultra-short period planets such as Kepler-78b [9], and multiple planetary systems [10].Also, new types of objects such as Boyajian’s star [11] and ‘disintegrating’ planets[12] were found with
Kepler/K2 .In the following text, we will focus on the physics behind the more recently discov-ered enigmatic objects such as disintegrating and evaporating planets. A significantnumber of such objects are also expected to be discovered with the most recent andupcoming missions like
TESS and later
PLATO . Before discussing the physics of thedisintegrating objects, we briefly introduce the observing strategies which led to thediscoveries of these interesting types of exo-objects.In Section 2 we describe the methods and observing strategies used to discoveror characterize these ‘dusty objects’. Section 3 contains a crash course on the dustproperties which are important to understand the content of this chapter. Sections4, 5 describe the most interesting disintegrating exoplanets and minor bodies inexoplanetary systems. The special case of Boyajian’s star is discussed in the Section6. Finally, Section 7 deals with ongoing and future space missions which may bringnew fascinating discoveries and open a new era in the study of these extrasolarobjects. For a reference, another recent review of disintegrating exoplanets can befound in [13]. The most successful methods of exoplanet detection are the transit and radial velocitymeasurements. Both methods benefit from their combination, and, in general, allplanets detected by the transit method need follow-up radial velocity measurementsfor mass determination. Therefore, all exoplanetary transit space missions try toensure that the targets in their prime sample can be followed-up spectroscopicallyfrom the ground.
The method of discovering and characterizing exoplanets by precise radial velocitymeasurements is based on Kepler’s laws. If the system consists of a star and a planet,these orbit around their common center of mass causing the star to move toward andaway from the observer with a given radial velocity that is a function of the massof the planet. Detailed derivations of the expression for the semi-amplitude K of theradial velocity curve can be found in numerous publications [14, 15]; therefore, welimit ourselves here to only presenting the final expression for the semi-amplitude ofthe radial velocity curve K : K = √ − e (cid:18) π GP orb (cid:19) / M plan sin i ( M star + M plan ) / (1)where G is the gravitational constant, P orb the orbital period, M star the stellar mass, M plan the planetary mass, i planetary orbital inclination angle, and e the eccentricityof the planetary orbit. As can be seen from the above equation, the resulting radialvelocity and the corresponding semi-amplitude K can be obtained from the observedspectroscopic time series that adequately samples the orbital phases. However, thismethod can not provide a determination of the inclination, i , of the planetary orbitalplane. Therefore, the value of planetary mass M plan obtained from the RV measure-ments is only a lower limit since the value of i is unknown without making use ofthe photometric transit data. One example of an RV curve is illustrated in Fig.1The typical radial velocity semi-amplitude of a large gas planet is of order oftens to hundreds of m/s. On the other hand a typical radial velocity signature of anEarth-sized planet can be as low as few cm/s. If a planet passes in front of the stellar disc along observer’s line of sight, thenone can observe a periodic dimming of the stellar light, i.e., a transit. Typically aphotometric time series with good sampling is obtained a few hours before, then
Jan Budaj, Petr Kabath and Enric Palle
Fig. 1
Figure shows a typ-ical RV curve of a gasplanet obtained with var-ious telescopes aroundthe globe. Figure Credit:[16] DOI:10.1051/0004-6361:20052850, reproducedwith permission © ESO. during the transit, and finally a few hours after the transit ends. The basics of themethod have been described in great detail elsewhere [17]. Here we limit ourselvesto expressing the transit depth, δ , as: δ ∝ ∆ FF = R R (2)where ∆ F is the observed change of flux during a transit, F the flux of the star, R plan the planetary radius, and R star the stellar radius. An advantage of this method is thatit can be used to determine the inclination of the planet’s orbital plane if the stellarparameters of the host star are known. It is clear that the photometric transit methodneeds to be combined with spectroscopic observations of a given system in order tofully characterize the exoplanet.The detection of hot-Jupiters can be accomplished even with small-aperture tele-scopes as the typical transit depth, δ , due to a transit of a hot-Jupiter is a few percent ofthe stellar flux for a main sequence dwarf star. However, the detection of Earth-sizedplanets requires ultra-precise photometry, typically measured in parts per million(‘ppm’). CoRoT-7b was the first example of a small rocky exoplanet showing a tran-sit depth of only a few hundred ppm [18]. The smallest exoplanet currently known toorbit a solar-like star is Kepler-37b [19] and it was discovered by the transit method.Its light curve along with the light curves of two other larger planets in the systemare shown in Fig. 2. Over the past decade, the characterization of exo-atmospheres has started to gainin importance. The first detection of sodium in the exo-atmosphere of a gas giantHD209458b was made from space with the Hubble Space Telescope (HST) [20], xtrasolar enigmas: from disintegrating exoplanets to exoasteroids 5
Fig. 2
Figure shows a com-parison of light curvesobtained with
Kepler forvarious sized exoplanetsfrom the system Kepler-37, with the smallest beingKepler-37b (upper panel).Reprinted by permission fromSpringer Nature: Nature, [19]DOI: 10.1038/nature11914,© 2013. followed by the spectroscopic detection, also with HST, of an extended hydrogenatmosphere for the same planet [20, 21]. Ground based detection of exo-atmosphereswith the transmission spectroscopy method using high spectral resolving powersucceeded nearly six years later when sodium was detected in the atmosphere of HD189733b [22].Transmission spectroscopy uses the basic idea that, during a transit, the stellarlight has to pass through the exo-planetary atmosphere which forms a thin annulusaround the planet. If the atmosphere contains an absorber, such as sodium or anyother species, the radius of the planet appears larger at the corresponding wavelengthas the species blocks the stellar light.When using transmission spectroscopy, typically, a time series of spectra withlow spectral resolving power is recorded before, during, and after the transit. Eachof the observed spectra from the time series is split into defined photometric bandsand then the resulting spectrophotometric light curves are produced and evaluated.The variation in transit depth in the different spectral bands provides informationon the absorbing species. This method has successfully confirmed atmospheres fora handful of planets. A metal rich atmosphere was confirmed for the Neptune-sizedexoplanet GJ1214b from the ground [23, 24], followed by many other detections forpredominantly gas planets [25, 26]. Lately, reports of elements other than sodiumand hydrogen have been reported, such as lithium and perhaps a first detection of
Jan Budaj, Petr Kabath and Enric Palle
TiO features [26, 27]. However, this method also has potential application to rockyplanets around late type dwarfs [28] that are recently discovered by TESS and willbe found later by PLATO and ELT from the ground.A slightly different approach is to use a spectrograph with high resolving power. Aspectroscopic time series is again obtained on either side of, and during, the transit.In this case the actual spectra from in- and out-of-transit phase are directly compared.Before a search for planetary atmosphere signatures can start, a careful analysis ofthe telluric features in the spectra has to be performed and, if necessary, telluricfeatures are removed [29]. Furthermore the Rossiter-McLaughlin effect which canaffect the planetary signal needs to be taken into account [30]. Regions of prominentlines, such as the sodium doublet (NaD), or potassium region as well as hydrogenlines are typically investigated. The ratio of in- and out-of-transit spectra can reveala planetary signature [22, 31, 32, 33, 34, 35] as the in-transit spectra also possess anexcess signal from the planetary atmosphere.
The detection of exoplanets is most efficient from space with the transit method.Therefore, we will introduce the observing strategies and principles of such missions.Different space missions dedicated to the search of planets via transit detection havefollowed different observing strategies. The first one, CoRoT, monitored severalfields for a series of long (150 days) and short (30 day) periods. On the contrary,the space mission
Kepler monitored a single field for 4 years. The selected fieldin the region of the Cygnus and Lyra constellations contained more than 150,000stars [7] that were monitored. This part of the
Kepler mission yielded about 2000exoplanets and several thousand candidates. In 2013 the
Kepler team needed to adopta different observing strategy due to problems with the spacecraft gyroscopes. Themission was renamed K2 and it observed one field for typically 70 days and thenpointed towards a new field. Over the ensuing four years, the K2 mission yieldedabout 1000 exoplanets and several hundred additional candidates [36]. There werenumerous interesting discoveries among these missions, and many “firsts" reported,such as: the circumbinary planet Kepler-16b [37], the oldest known multiplanetsystem Kepler-444 [38], the first Kepler rocky planet Kepler-10b [39], and the firstplanet with a radius smaller than the Earth [40]. The K2 mission was retired in late2018 when the fuel was depleted.However, Kepler also discovered a new class of ‘disintegrating’ planets. In thefollowing text, we lay the theoretical ground for understanding these highly enigmaticplanets among the known types of exoplanetary systems. xtrasolar enigmas: from disintegrating exoplanets to exoasteroids 7
In this section we introduce the basic physical properties of astrophysical dust whichwill be important for understanding the subsequent sections. At sufficiently lowtemperatures and high density, grains of condensates can be formed out of a gasphase. Such grains are usually called “dust”, although some authors use the moregeneric term “condensates”. At the same time, the term “grain” often includes notonly solid grains but also liquid droplets. Such condensates are usually confined to“clouds”. These can not only be clouds in the atmospheres of cool objects but alsovast interstellar dust clouds.The reason why dust is so important for our objects will become obvious from thefollowing everyday experience. Our atmosphere contains water. If this water is in theform of a gas one can easily see distant mountains which are 100 km away. However,once the water condenses and forms clouds or a fog, the visibility can drop to 10meters or even less. Thus the opacity, which is a measure of the non-transparency ofthe material (see Sec.3.2), could be much higher if the material were in the form ofdust rather than gas. Figure 3 illustrates the opacity of gas and dust in the visible andnear infrared regions per gram of material. The opacity of the gas in this exampleis based on an assumed solar chemical composition and a density ρ = − g cm − [41]. For the dust opacity we used the illustrative mineral forsterite with a particlesize of about 0.1 and 1 micron [42]. It should be mentioned that, as a rule, not all thegas can turn into a condensate. For solar composition material, dust can account forroughly 1% of the mass. Still, as can be seen from the figure, the dust opacity willeasily overtake that of the gas. Fig. 3
Comparison betweenthe gas opacities at twotemperatures and dust opacityof forsterite for two particlesizes. -8-6-4-2 0 2 4 6 0.3 0.4 0.5 0.7 1 2 3 l o g o p a c i t y [ c m ^ / g ] lambda [mic]dust 0.1 micdust 1.0 micgas T=1500Kgas T=2500K The optical properties of condensates may not only influence, but fully govern, theemerging spectrum and even the structure of a dusty object. Dust can absorb the
Jan Budaj, Petr Kabath and Enric Palle impinging radiation and convert it directly into heating the grains. This process iscalled ‘absorption’ or ‘true absorption’ to emphasize that the photon is destroyed orthermalized. It is quantified by the absorption opacity.Dust can also scatter the radiation in a process called ‘scattering’. Scatteringmainly changes the direction of the photon without significantly affecting its en-ergy. So the scattered radiation is somewhat decoupled from the medium and flowsthrough and around it without heating it. This process is characterized by the scat-tering opacity. Furthermore, scattering can be highly anisotropic, a property that isdescribed by means of the phase function, which depends on the scattering angle(the deflection angle from the original direction of the impinging radiation). Themost prominent feature is a strong forward scattering peak for large values of theso-called ‘scaled particle size’, X = π a / λ where a is the particle size (radius) and λ is the wavelength of the radiation.The combined effect of absorption and scattering is referred to as the ‘extinction’.Finally, formation of dust can also affect the chemical composition of an object. Itremoves the condensed elements from the gas phase within the dust cloud. Subse-quently, various processes and forces may decouple gas and dust, creating chemicalinhomogeneities.Absorption and scattering by large particles (relative to the wavelength, i.e., large X ) is wavelength independent. However, scattering by small particles has a verystrong, λ − , dependence (Rayleigh scattering) and absorption by small particles hasa λ − dependence. Blue light is scattered and attenuated more efficiently, and for thisreason dust generally causes a reddening of the light passing through a dust cloud.The extinction at some wavelength (or filter) in magnitudes is the difference betweenthe observed and intrinsic brightness: A ( V ) = V obs − V int . Reddening (selectiveextinction/color excess) is usually expressed as a difference between the observedand intrinsic color index: E ( B − V ) = ( B − V ) obs − ( B − V ) int = A ( B ) − A ( V ) (3)A relative slope of the wavelength dependence of the extinction can be characterizedby a single parameter 1 / R ( V ) where R(V) is [43]: R ( V ) = A ( V ) E ( B − V ) = A ( V ) A ( B ) − A ( V ) (4) R ( V ) is sensitive to the particle size. The typical value of R ( V ) for interstellar dustin our Galaxy is 3 . ± .
2. The absolute amount of the extinction as a function of λ (the extinction curve) can be characterized by two parameters: R ( V ) and E ( B − V ) . The optical properties of the dust are given by the complex index of refraction of thematerial it is made from (which is a function of wavelength), and further depends on xtrasolar enigmas: from disintegrating exoplanets to exoasteroids 9 the size and shape of the particles. These properties of the grains are often expressedin the form of cross-sections for absorption, scattering, and extinction C a , C s , C e ,respectively. The cross-sections are related to the projected area of the dust particlesof radius r via efficiency factors Q a , Q s , and Q e , for absorption, scattering, andextinction, respectively: C a = Q a π r , C s = Q s π r , Q e = Q a + Q s . (5)The cross-sections are related to the absorption and scattering opacities, κ ν, a and κ ν, s , of the condensates at radiation frequency, ν , by: κ ν, { a , s } ≡ C ν, { a , s } / m g = Q ν, { a , s } ρ g r (6)where κ is the cross section per unit mass and has the dimensions of cm g − , m g is the mass of a dust grain, ρ g is the bulk material density of the grain, and wehave assumed spherical particles for simplicity. Note that κ is nearly exclusively aproperty of the material and may not depend at all on the mass in dust grains perunit volume of the medium, ¯ ρ . Finally, for completeness, we note that the quantity α ≡ ¯ ρκ is defined as the linear extinction coefficient (with units cm − ), and may beuseful in certain circumstances.Using these opacities, the monochromatic optical depth due to scattering andabsorption along the line of sight z is then given by: τ ν = ∫ ¯ ρ ( z ) (cid:2) κ ν, a ( z ) + κ ν, s ( z ) (cid:3) dz . (7)The sum of the absorption and scattering opacities is referred to as a total opacity.For the special idealized case of single-size dust particles, this reduces to τ ν = (cid:0) Q ν, a + Q ν, s (cid:1) ρ g r ∫ ¯ ρ ( z ) dz . (8)We can see from this, that for a fixed amount of dust mass per unit volume of themedium, i.e., ¯ ρ = constant, the optical depth would become monotonically largerwith decreasing particle size, as 1 / r . However, in Mie scattering, once the particlesize becomes substantially less than the radiation wavelength, λ = c / ν , then the Q factors for the cross section drop dramatically, and the optical depth stops rising withfurther decreases in particle size. This is the reason why, for observing wavelengthsin the visible, it is often stated that particle sizes comparable to a micron are themost efficient at blocking light.The angular distribution of the scattered light is described by the phase function, p ( θ ) , where θ is the scattering angle which measures the deflection of the scatteredphoton from its original direction. The phase function is normalized such that itsintegral over all solid angles is 4 π . An example of the dust phase function at smallangles is displayed in Figure 4. One can see a strong increase towards zero phase angle which is called the forward scattering peak. The amplitude and width of thispeak are quite sensitive to the particle size and wavelength. Calculations of phasefunctions usually assume an incident parallel beam of light. However, if the dustcloud were very close to the star, its angular dimension (as seen by the dust grain)could be comparable to, or wider than, the width of the forward scattering peak. Thiswill be the case in our objects and one has to take that into account [44, 45, 46]. Thesame figure also illustrates this effect on dust particles located in the atmosphere ofthe exoplanet WASP-103b [47, 48]. Fig. 4
Phase functions as-suming a point source oflight (solid) versus the phasefunctions assuming the finitedimension of the stellar disc(dotted). Example is for en-statite at 600 nm for differentdust particle radii. The verti-cal line illustrates the angularradius of the stellar disc ofWASP-103 as seen from theplanet WASP-103b. P h a s e f un c t i o n Angle [Deg.] r= 0.1 micr= 1 micr=10 mic
It is sometimes useful to define a mean cosine of the scattering angle g , alsoknown as the asymmetry parameter. It has values from -1 to 1 and is calculated fromthe phase function: g = ∫ p ( θ ) cos ( θ ) d Ω / π. (9) Let’s assume that a dust particle is irradiated by its host star with effective temperature T ∗ , solid angle Ω ∗ , and intensity approximated by the Planck function B ν ( T ∗ ) . Theparticle can scatter some of the light from the star, and we define a quantity calledsingle-scattering albedo, (cid:36) , which describes the reflecting properties of the grains.It is a fraction of the energy which is scattered by the particle: (cid:36) ν = C ν, s C ν, a + C ν, s . (10)This scattered light does not heat the particle. Apart from scattering, the particle canalso absorb the stellar radiation at a rate: Ω ∗ ∫ C ν, a B ν ( T ∗ ) d ν (11) xtrasolar enigmas: from disintegrating exoplanets to exoasteroids 11 This energy heats the particle to a temperature T g . Subsequently, the grain emitsthermal radiation and cools at a rate:4 π ∫ C ν, a B ν ( T g ) d ν, (12)A balance between the absorbed and re-radiated energy sets the grain equilibriumtemperature (provided that the grain is not also sublimating; but see Eqn. 21). It canbe obtained by solving the radiative equilibrium equation for T g : Ω ∗ ∫ C ν, a B ν ( T ∗ ) d ν = π ∫ C ν, a B ν ( T g ) d ν (13)Assuming that the opacities are grey (i.e., they do not depend of the frequency)the grain temperature is simple given by: T grey g = T ∗ (cid:18) Ω ∗ π (cid:19) / . (14)A dust grain irradiated by a star with effective temperature T ∗ , mass M ∗ , radius R ∗ ,and surface flux F ν experiences a radiative acceleration a R . It is usually expressedas a parameter β relative to the gravitational acceleration a G : β = a R a G = R ∗ GM ∗ c ∫ (cid:2) κ ν, a + ( − g ) κ ν, s (cid:3) F ν ( T ∗ ) d ν. (15)where G is gravitational constant, c is speed of light, and g is the previously men-tioned asymmetry parameter. Thus, in the two extreme cases of forward vs backscattering of the stellar radiation, the scattering adds either nothing to the radiativeacceleration or has a factor of 2 enhancement relative to the absorption term.Extensive online tables of such dust properties devoted mainly to exoplanets arepublicly available [42]. They are based on codes that calculate cross-sections of dustparticles using Mie theory such as [49] from the complex indices of refraction forspecific materials. For example, the Heidelberg - Jena - St.Petersburg - Databaseof Optical Constants is a very convenient source of refractive index measurements[50, 51]. Depending on the state quantities, such as temperature and pressure, matter composedof a single component usually exists in one particular phase, e.g. gas, liquid, or solid.The Clausius-Clapeyron equation, which gives a relation between the temperatureand pressure, marks a transition or boundaries between the different phases. Oncethe temperature drops below the condensation temperature (at a certain pressure)or the pressure exceeds the equilibrium (saturated) vapour pressure (at a particular temperature) the dust starts to condense out of the gas. Condensates may be in eitherthe liquid or solid phase. The equilibrium vapor pressure where the transition occurscan be approximated by [52, 53]: P v ( T ) = exp (− A / T + B ) (16)where A , B are material-specific sublimation parameters.Materials with low vapour pressure or high condensation temperature (refractorymaterials) condense first out of a hot cooling gas (or last to evaporate if the dust wereheated). For a solar chemical composition these are mainly calcium and aluminumoxides such as corrundum (Al O ), grossite (CaAl O ) and hibonite (CaAl O ).They are followed by titanium compounds such as perovskite (CaTiO ) or TiO atlower temperatures. The most important refractory species are usually silicates. Theyform two branches: pyroxenes (Mg x Fe − x SiO ) and olivines (Mg y Fe − y SiO ). Ineach branch a fraction of magnesium atoms can be replaced by iron. Iron free pyrox-ene is called enstatite (MgSiO ) while an iron free olivine is forsterite (Mg SiO ).The other extreme member of the olivine family is fayalite (Fe SiO ). Silicates are atype of glass and, as such, are quite transparent in the optical region, although theycan scatter light quite efficiently. The amount of iron can affect their absorption prop-erties significantly [54]. Other refractory dust species which might be encounteredin such an environment are amorphous carbon, graphite (C), silicon carbide (SiC),Quartz (SiO ), spinel (MgAl O ), or akermanite (Ca MgSi O ). At the other end ofthe condensation temperature scale are volatile species such as water and ammonia.In between are numerous compounds, depending on the chemical composition andpressure, for example sulfides and alkali halides, and troilite but we are not likely toobserve these in such hot and close disintegrating objects.Apart from the temperature, the occurrence of a particular dust component alsodepends critically on the abundances and the availability of the chemical elementswhich form the compound. The element with the lowest abundance is typically thelimiting factor for the abundance of the whole compound. The solar abundances of Ca, Al, and Ti are relatively small 6.34, 6.45, and 4.95, respectively [55]. That iswhy silicates and/or iron dust which are composed of silicon, magnesium, and ironwith abundances of 7.51, 7.60, and 7.50, respectively are usually more abundant anddominate extinction processes.The condensation properties of various compounds are nicely summarized inFigure 5. Here the condensation curves are plotted as a function of atmosphericpressure. They were calculated mainly for the atmospheres of brown dwarfs or giantexoplanets and assume a solar chemical composition [56] but contain many dustspecies which are also relevant for our objects. Note that the abundances are defined, using the element number density N , as the numberof atoms of an element per 10 atoms of hydrogen (log N / H + Fig. 5
Condensation temper-atures of several compoundsas a function of atmosphericpressure assuming a solarcomposition gas. Taken from[56]. Courtesy of ApJ.
Dust particles are also subject to sublimation [52, 53]. The mass-loss flux (rate perunit area) from a solid surfaces at temperature T in vacuum is J ( T ) = α P v ( T ) (cid:114) µ u π k B T , (17)where α is the evaporation coefficient, P v ( T ) the equilibrium vapor pressure, µ the molecular weight, u the atomic mass unit, and k B Boltzmann’s constant. Themass-loss rate from a spherical dust grain of mass m g = π r ρ g / S = π r is then dm g dt = − SJ . (18)Taking into account that dm g dr = S ρ g (19)the change in the particle radius is given by: drdt = drdm g dm g dt = − J ρ g . (20)Sublimation represents a phase transition which consumes heat and cools the par-ticle. If that heat is not negligible one has to take it into account in computing theequilibrium temperature of the grain. In such a case the energy absorbed by theparticle per unit time is balanced by the energy radiated by the particle plus the heatconsumed for the phase transition. Equation 13 then reads Ω ∗ ∫ C ν, a B ν ( T ∗ ) d ν = π ∫ C ν, a B ν ( T ) d ν − L dm g dt (21) where L is the latent heat of sublimation per unit mass. The characteristic timescalefor sublimation is τ = m g | dm g / dt | . (22) The great majority of exoplanets that we know of were discovered by the transitmethod. Nominal planet transits are symmetric and periodic without any significantvariations in their shape or depth over time. This changed in 2012 when a strangeobject named Kepler-1520-b was discovered [57].
Kepler-1520b is an exoplanet also known as KIC 12557548b (KIC1255b). It becamea prototype of a very rare new class of exoplanets called Disintegrating Exoplanets. Itwas found in the
Kepler data. The host star is a V=16 mag main sequence K4V typestar. Its effective temperature, mass, and radius are about T eff = M = . M (cid:12) ,and R = . R (cid:12) , respectively [57, 58]. The star is active and has spots which cause ∼
1% variability with a period of about 22.9 days which enabled its rotation periodto be determined [44, 59]. In its light curve, the discoverers noticed something liketransits but they were highly variable, sometimes as deep as 1.2%, sometimes evenmissing. The strictly periodic transit signal had a very short period of about 15.7hours. Figure 6 illustrates the observed data folded with this period which yields theaverage light curve. One can see a significantly increased spread of fluxes in the pointsduring the transit indicating the variability in the transit depth. Another interestingfeature becomes obvious from the binned and averaged light curve (bottom panelof Fig. 6). It is highly asymmetric and features a steeper ingress and slower egress.The strict periodicity and short period of the transits indicate that they may becaused by some body orbiting the star on a very close orbit. The fact that the transitsare sometimes missing implies that the body itself is very small, smaller than theEarth, otherwise it would be detected in every transit. Follow-up radial velocitymeasurements did not detect any reflex motion of the star which puts an upper limiton the mass of the body of 89 M ⊕ [60, 61] which places the body deep into theplanetary regime. However, what is then causing the variable asymmetric transits? The interpretation it that a body on such tight orbit around the star is heated to about2000 Kelvin. At such temperatures even rock melts and can evaporate which maydrive a thermal wind off the surface [57, 62]. Gas escapes the planet at a rate larger xtrasolar enigmas: from disintegrating exoplanets to exoasteroids 15
Fig. 6
Top: First long cadenceKepler observations of KIC1255 folded with the 15.7-hr orbital period. Bottom:Binned and averaged lightcurve. Taken from [57].Courtesy of ApJ. than 0.1 M ⊕ /Gyr dragging dust grains with it. Alternatively, the dust may condenseout of the gas when it cools during or after escape from the planet. The mixture ofgas and dust expands beyond the Hill sphere radius of the planet. It flows “down hill"out of the potential well of the planet through the L1 point towards the star or via theL2 point away from the star. Strong radiative forces on the dust cause a weakeningof the effective gravity which drives the dust into higher orbits that lag progressivelybehind the planet. It is this dust which is causing the transits and this is also thereason why we observe a steep ingress followed by a gradual egress.Once such a fine dust cloud forms around and behind the planet it may not bestable and is prone to variability. For example when the dust cloud is thin the planetsurface is intensively irradiated, which leads to more evaporation, outflows, andcondensation, thereby producing more dust. In turn, the thick dust cloud shieldsthe planet and the evaporation drops, limiting the production of dust, and the clouddissipates. This limit cycle can apparently operate, even on a timescale from orbit toorbit, but there are longer intervals of order a week where the transits are reduced toa level where they are not detected (see also the following section on the variability). Producing and maintaining a substantial outflow of gas and dust is relativelysimple in bodies with the surface gravities of asteroids, where the thermal speed ofthe material exceeds the escape speed (see, e.g., Fig. 8 of [13]). For at least somecommon minerals the vapour pressure at ∼ ∼ M ⊕ /Gyr. For more substantialbodies, e.g., Mercury, Mars, and Earth, a Jeans’ outflow of 1 M ⊕ per Gyr of heavymolecules becomes nearly impossible [57, 62, 13]. For such massive bodies, adifferent escape mechanism has been proposed, namely a Parker-type hydrodynamicwind [57, 62]. Roughly speaking this requires thermal speeds that are only ∼ M ⊕ per Gyr is that if it has of only ∼ − − − M ⊕ , then it willhave a lifetime of only 1-10 Myr. If the lifetime of the host star is measured in Gyr,then the a prior probability of seeing one of its planets in that evaporative state arerather low. However, obviously if one surveys a large number of stars, then the oddsof seeing a few such systems is non-negligible. Since such planets may have lostmost of their mass their observations open a unique window into planetary interiorsand their chemical composition [63, 64]. It was mentioned above that the transits are variable. They vary on a very shorttimescale from one orbit to another, i.e., in less than one day. This variability isstrong, sometimes more than a factor of 2 from one orbit to the next one, and appearsto be stochastic and associated with the deep core of the transit [57, 65]. However,a modulation of the transit depth was also found that appears to be anti-correlatedwith the periodic rotational variability (22.9 days) of the stellar flux[59, 66].There is also a smooth long-term variability in the egress part of the light curveassociated with the dust tail on timescales of about 1.3 yr which is not seen inthe core of the transit [44, 58]. There might also have been a period of decreasedactivity, i.e., when the transits were shallower on average, during 2013-2014 [67].This longer-term variability in the depth and shape of the transits indicates that thedust cloud associated with the planet may not be homogeneous and has at least twocomponents; an inner tail (or coma) and an outer tail which may behave differently(e.g., when subjected to magnetic fields or stellar winds) or have different properties(particle size, chemical composition) [44, 65]. On the contrary, [68] arrived at theconclusion that, as far as the pure shape of the average transit profile is concerned,it is well reproduced in their calculations and there is no need to invoke two suchconstituents. A similar long-term variability of the transit, namely a monotonicdecrease of its depth over the four-year duration of the
Kepler mission was found inanother disintegrating exoplanet, KOI 2700b [69].The reason for the above mentioned long-term variability has not been well studiedbut it has been argued that it may be associated with the magnetic activity of thestar and be analogous to the comet tail disconnection events observed in some of xtrasolar enigmas: from disintegrating exoplanets to exoasteroids 17 the comets in our Solar System [44, 59]. However, it has also been argued that themodulation of the transit depth with stellar rotation may be due to occultations ofthe stellar spots rather than the magnetic activity [66].
There is a very interesting tiny feature in the transit light curve, barely visiblein Figure 6. It is a small brightening just before the transit, already noted by thediscoverers [57], which is referred to as a pre-transit brightening. It is not due to thestar getting brighter. It is caused by the scattering properties of the dust. As shownin Figure 4, the dust does not scatter the light isotropically but mainly in the forwarddirection. For the same reason a driver gets blinded when the Sun is near, but not in,the driver’s immediate field of view, but the windshield is dirty and this nonethelessscatters the sunlight into his/her eyes.In our system, this happens mainly in the vicinity of the transit. While we cannotidentify this light during or after the transit, since it is overlaid with the ongoingabsorption, we can see it just before the transit (Figure 7). This feature is sensitiveto the particle size and it enables us to estimate that the size of particles in the tailis about 0.1-1 micron. At the same time this effect confirms that the transit eventsare caused by a dusty tail passing in front of, and close to, the star. Apart from thesefeatures in direct transits, the forward scattering effect can, in principle, be used todetect non-transiting dusty-tailed exoplanets by searching for positive bumps in thelight curves [45, 46].
Fig. 7
Kepler light curve ofKIC 1255 (red) zoomed so thatthe pre-transit brightening isclearly visible. Models (green,blue, purple) demonstrate thatthis feature is sensitive tothe particle size. Taken from[44] and reproduced withpermission ©ESO. N o r m a li ze d f l ux Phasepre-transit brightening post-transit brighteningObs.r= 0.01 micr= 0.1 micr= 1 mic
A number of authors have studied the
Kepler light curves of KIC 1255b attemptingto derive the chemical composition and grain size distribution of the transiting dustmaterial [70, 44, 65]. This problem is partially degenerate and one can fit suchmonochromatic transits with different chemical composition and particle size. Thepre-transit brightening is sensitive to the particle size and the observed brighteningindicates particles 0.1-1 micron in size. On the other hand, the length of the tail ishighly sensitive to the sublimation properties of the grains. Corundum and 0.2-5micron grains are most favoured for this reason and the mass loss rate amounts to0.6-16 Earth masses per Gyr [53, 68]. Fig. 8
Theoretical transitdepths for three species alu-mina, olivine, and iron; eachfor the particle size of 0.1(solid), 0.16 (dashed), 0.4(short-dashed), 1.0 (dotted)micron as a function of wave-length. Depth is normalizedsuch that the transit in the Ifilter is about 0.5% deep. d e p t h ( % ) wavelength[mic]U B V R I J H KAluminaOlivineIron More information and a deeper insight can be achieved with multi-wavelengthobservations. This is because the opacity of dust changes with the wavelength andthe behaviour is different for grains of different chemical composition and size. Con-sequently, under the assumption that the tail is optically thin, the transit depth woulddepend on the wavelength, the particle size, and the chemical composition. This isillustrated in Figure 8 which shows theoretical transit depths for three species: corun-dum (alumina), olivine, and iron. One can see that the transits produced by smallparticles of corundum or silicates would be much deeper at the shorter wavelengths.This is because scattering dominates extinction and scattering on small particles(relative to the wavelength) is approaching the Rayleigh regime with a strong λ − dependence. Extinction by large particles is almost grey. The problem is that theobservations must be carried out at different wavelengths simultaneously because ofthe above mentioned strong variability of the transit depths.Such observations in the optical and near-infrared regions have not detected asignificant difference in the transit depth across these wavelengths. This impliesthat the dust particle size must be larger than ∼ In this context ‘monochromatic’ means transits that are observed in only a single waveband.xtrasolar enigmas: from disintegrating exoplanets to exoasteroids 19 dust grains are lifted directly from the surface of the planet, this in turn impliesthat the planet should be less massive than Mercury otherwise its gravity wouldprevent such direct dust ejection [60, 67]. However, as mentioned above, dust mighthave also condensed later beyond the potential well of the planet. Additional multi-wavelength observations in z (cid:48) , g (cid:48) , u (cid:48) filters indicate slightly larger depths at shorterwavelengths and particle sizes of about 0.25-1 micron [71]. Recent 3D models ofthe dust dynamics including the sublimation and 3D radiative transfer pointed outthe possibility that the tail may be optically thick. In this case the transit depth mightbe constant with the wavelength even for smaller particles and mass loss rates mayreach 80 Earth masses per Gyr [64].Apart from KIC 1255b, two other systems of this kind have been discovered,KOI 2700b [69] and K2-22b [72]. The first one is similar in its transit profile toKIC1255b, and the latter system is described in more detail below. This exoplanet (also known as EPIC201637175B) was discovered with the
Kepler follow-on mission ( K2 ) by [72]. It is in some respects similar to KIC 1255b. Thehost star is cooler and smaller. It is an M0V type red dwarf (r = 15.01 mag) witheffective temperature, mass, and radius of about T eff = M = . M (cid:12) , and R = . R (cid:12) , respectively. The host star rotates with a period of 15.3 days and has a‘close’ (3 magnitudes fainter) companion, separated by about 2 (cid:48)(cid:48) . The planet K2-22bis smaller than 2.5 R ⊕ , is less massive than 1.4 M J , and has a very short orbitalperiod of only 9 . ± . ≈ × g s − [72].As in the case of KIC 1255b, the transits are asymmetric and highly variable.They are on average about 0.5% deep but the depth changes from 0 to 1.3% fromtransit to transit. The duration of the transits is about 50 minutes. The average transitshape is shown in Figure 9. The special feature of this exoplanet is that it exhibitsa post-transit brightening. Based on the lesson learned from KIC 1255b, this likelyindicates that the planet also has a dusty tail but it is pointing in the opposite direction.In other words, the planet is orbiting the star with its dust tail heading forward. Thisis most probably due to the host star being colder and fainter than KIC 1255. Itsradiation does not exert sufficient pressure on the dust grains to force them into ahigher orbit, and thereby trail the star. Thus, the dust can flow from the planet towardthe L1 point and the host star, and then descend into the potential well of the star.Since the Keplerian velocity of these orbits is higher, these grains overtake the planetand form a leading dust tail [72].The follow up multi-wavelength transit observations with the GTC in the visibleregion found no evidence for a wavelength dependence in three out of the four transitsobserved [72, 73]. One transit, however, did indicate that the transit depth is greaterat the bluer wavelengths. This sets an upper limit on the dust grains of about 0.4-0.6micron. The forward scattering peak indicates particle sizes of about 0.5 micron. Fig. 9
Binned and averaged K2 light curve of K2-22 foldedwith the orbital period. It fea-tures a post-transit brighteninglikely indicative of a leadingdust tail. Taken from [72].Courtesy of ApJ. Although the dust is the major opacity source, the gas might be detected in the coresof some strong spectral lines such as NaI in high resolution spectra. [74] searchedfor such gas absorption during the transits of K2-22b and Kepler-1520b but did notdetect any spectral signatures.
As in our solar system, minor bodies are also expected to exist in extrasolar systems.While we do not yet have the capability to detect structures similar to the mainasteroid belt or the Oort cloud in other planetary systems, the first extrasolar minorbodies have recently been detected.
In the solar system, asteroids are defined as minor bodies in the inner solar systemthat show significant departures from spherical shape dictated by hydrostatic equi-librium. The first extrasolar minor bodies were discovered by K2 [75] in the form ofdisintegrating material orbiting the white dwarf WD 1145+017.It has long been known that some white dwarfs have dusty debris disks aroundthem [76, 77], and also that many of them (about 1/4 - 1/2) have heavy elementsin their atmospheres that should have already sunk into the stellar interiors, unlessthey were replenished by infalling orbiting material [78, 79, 80]. Vanderburg et al xtrasolar enigmas: from disintegrating exoplanets to exoasteroids 21 [75] observed for the first time this process in action by detecting a white dwarfbeing transited by ‘at least one and likely multiple disintegrating planetesimals withperiods ranging from 4.5 hours to 4.9 hours’. The detected transits are marked bybeing asymmetric, and even irregular, with respect to normal transiting planets,indicating that they do not correspond to solid spherical bodies, and can be as deepat 55 per cent. In addition, most of the observed transits are much longer in durationthan the ∼ g = . L = . L (cid:12) , d =
174 pc, T eff = M = . M (cid:12) , and R = . R ⊕ , respectively. The orbital period of 4.5h corresponds to a distance ofabout 1 R (cid:12) from the star. A combination of this distance and stellar luminosityyields equilibrium temperatures of about 1400-1700 K which is similar to those ofdisintegrating planets.This object has attracted the attention of exoplanet observers. Croll et al. [81]conducted ground and space follow-up observations on WD 1145+017. The obser-vations confirmed that the white dwarf is orbited by multiple short-period objects,that egress times were longer than ingress times, and the duration of the transitswas longer than expected, pointing again to cometary tail-like structures behind thedebris fragments. These asteroids are nicely visualized with a ’waterfall’ diagrampresented in Rappaport et al. [82] showing the evolution of the phase light curve(see Fig.10). One can easily identify several objects with slightly different periodscrisscrossing the picture. Fig. 10
Waterfall diagramof WD1145 phased with thebase period of 4.49126 days.Objects with the base periodfollow the vertical line whileobjects with different periodscrisscross the diagram ondifferent tracks. Taken from[82] by permission of OxfordUniversity Press.
Croll et al. [81] also did not detect any transit chromaticity. Alonso et al [83] andIzquierdo et al [84] used the 10-m GTC telescope to check for chromaticity but foundthe transits to be gray over the optical range from 480 to 920 nm (see Figure 11),indicating that particle sizes smaller than 0.5 micron can be excluded. From theirobservations, Alonso et al [83] concluded that the radius of single-size particles inthe tail materials must be ≈ µ m or larger, or ≈ µ m or smaller. They also report low amplitude variations in the light curves suggesting that dusty material iscontinuously passing in front of the stellar disk.Zhou et al. [85] and Xu et al [86] also observed these dips in multiple photometricbands in the visible and infrared. They find no difference in the transit depths onceinfrared observations are corrected for excess emission from a dusty disk. Xu etal [86] conclude that there must be a deficit of small particles in the transitingmaterial and that only large particles can survive without sublimating at the effectivetemperatures prevalent at these short orbital periods. Fig. 11
GTC light curves of WD 1145+017 taken simultaneously in four wavebands and coveringseveral dips. The nearly identical dip profiles in the four bands can be used to constrain the dustgrain sizes to larger than 0.5 µ m. The divergence of the curves after phase 0.22 in the lower panelis due to atmospheric effects. Adapted from [83] and reproduced with permission ©ESO. Xu et al. [87] found the first detection of chromaticity, showing that UV transitdepths are always shallower than those in the optical. They proposed a model toexplain this observations by having the transiting dust clouds block a larger fractionof the circumstellar gas than of the white dwarf and by having all of them (transitingdust, circumstellar gas, and white dwarf) aligned with respect to our line of sight.The light curve of this object is extremely variable as shown by Rappaport etal. [88, 82] and Gänsicke et al. [89]. This is because (i) individual objects haveslightly different periods, (ii) the periods of some of individual objects can changeslowly with time, and (iii) their dust activity can change dramatically on timescalesof months and years.High resolution spectroscopic observations also revealed the presence of high-velocity gas orbiting the white dwarf. [90, 91].A more detailed review of this object can be found in [82, 92]. Very recently asecond white dwarf with possibly related properties was discovered [93]. This object,ZTF J013906.17+524536.89, exhibits two deep transits separated by 110 days, butit is not yet clear if this is a periodicity. xtrasolar enigmas: from disintegrating exoplanets to exoasteroids 23
The unprecedented precision of the
Kepler photometry enabled the detection ofeven smaller objects than planets or even large asteroids. Two decades ago [94]predicted that comets orbiting other stars and emitting large dusty tails might bedetected by photometry when transiting their host stars and calculated what theirlight curves could look like. In the
Kepler data, [95] detected six events in the lightcurve of KIC 3542116 (KIC3542) and one event in the light curve of KIC 11084727(KIC1108) which looked very much like the expected cometary transits. They wereabout 0.05-0.2% deep and highly asymmetric, similar in shape to the KIC1255btransits but several times more shallow (see Fig.12). The three deeper transits ofKIC3542 and that of KIC1108 lasted for about one day while the three shallowertransits of KIC3542 lasted for about half a day. There is no obvious periodicityto these events indicating that six transits of KIC3542 are caused by 2-6 distinctcomet-like bodies. The duration of the transits corresponds to a transverse speedsof about 35-50 km/s for the longer transits and about 75-90 km/s for the shortertransits. This corresponds to orbital periods of ≥
90 and ≥
50 days, respectively.Both host stars KIC3542 and KIC1108 are relatively bright (V=10mag) and hot stars
Fig. 12
Three deeper transit events found in the Kepler light curve of KIC3542 by [95] bypermission of Oxford University Press. with T eff = Kepler arecooler (or older) so the fact that they are hotter/younger, similar to each other, andalso similar to Boyajian’s star mentioned later is probably not an accident.Recently, a single comet-like transit was found in the archival lightcurve of KIC8027456 [96]. The
TESS mission also detected three other dips of this kind in β Pictoris [97]. Similar events were discovered in two stars (EPIC 205718330 andEPIC 235240266) monitored by the K2 mission [98]. The authors call these ‘littledippers’ since they resemble the so-called “dipper" stars. However, contrary to dipperstars. these dips are 1-2 orders of magnitude shallower with depths of about 0.1-1%.The dips in the ‘little dippers’ are episodic, not periodic, lasting for about 0.5-1 days,with complicated shapes resembling more WD1145 or Boyajian’s star rather thanthe typical exocomet like profile seen in Fig.12. Nevertheless, the authors argue thatexocomets are the most likely explanation. The host stars are early-K and late-F typedwarfs, not younger than 150 and 800 Myr, respectively. Recently, two other ’dipper’ stars were discovered by K2 mission. HD139139 isa normal early G-type star which shows a sequence of 28 transit like dips [99]. Theevents are about 200 ppm deep, 0.7-7 hours long, are random, and do not show asignificant asymmetry. EPIC204376071 is a young M5 dwarf which shows a single80% deep asymmetric dip [100]. There is no explanation to these phenomena yet.
We would like to introduce another star which may be related to the above mentionedobjects and which is sometimes labeled as “the most mysterious star in the Galaxy".
The
Kepler mission delivered a huge amount of high-precision photometric lightcurves for about 170,000 stars. A group of volunteers, the ‘Planet Hunters’, werereviewing the light curves by human eye and they were the first to notice that therewere some very strange dips in flux from the star KIC 8462852. A more detailedanalysis and follow-up observations resulted in a discovery paper led by TabethaBoyajian [11], and since that time the star has become known as Boyajian’s orTabby’s star.So what is so special about this star? The
Kepler light curve shows a few strongdimming events that are 10%-20% deep. They are irregular with no sign of periodicityand are clustered into four main events observed near BKJD=790, 1520, 1540, 1570days . They are shown in Figure 13. The D790 event is very smooth with a slowingress followed by a faster egress. The D1520 and D1570 events consist of asequence of dips gradually increasing in strength. D1540 is a symmetric triple dipwith the central dip being the strongest.There is another tiny feature in the Kepler data at D1210 which deserves attention.It is a symmetric triple dip with the middle one being the strongest [101]. This shaperesembles the D1540 event.This kind of variability would not be anything unusual if this were a young star.Such stars are often surrounded by protostellar disks which might cause dippingevents when seen nearly edge on. They show broad emission lines and infraredexcess. However, this star has no such features and looks like a normal F3V typemain sequence star with temperature, mass, radius, projected equatorial velocity androtational period of T eff = M = . M (cid:12) , R = . R (cid:12) , v sin i =
78 km/s,and P rot = .
88 days, respectively [11, 102]. It is a relatively bright, V = . BKJD stands for the Kepler Barycentric Julian day which is a Julian Day minus 2454833 According to [103] the 0.88 day periodicity may come from a different source, not from the targetstar.xtrasolar enigmas: from disintegrating exoplanets to exoasteroids 25 companion to the star at 1.95 (cid:48)(cid:48) which is about 3.8 mag fainter in H band. However,this star is not physically bound to Boyajian’s star [104]. N o r m a l i z e d fl u x Time [day, BKJD] N o r m a l i z e d fl u x Time [day, BKJD] N o r m a l i z e d fl u x Time [day, BKJD] N o r m a l i z e d fl u x Time [day, BKJD] N o r m a l i z e d fl u x Time [day, BKJD]
Fig. 13
The
Kepler light curve of Boyajian’s star shows irregular dips (top). A more detailed viewof the four major events is displayed in the middle and bottom panels.
Soon after the discovery of Boyajian’s star, a plethora of follow-up observationswere performed. Observations in the infrared region did not detect any infraredexcess but put constraints on the amount of dust at different distances from thestar. Spitzer/IRAC [105], NASA/IRTF 3 m SpeX [106], Millimetre (SubmillimeterArray) and submillimetre (SCUBA-2) continuum observations also did not detectany significant emission towards KIC 8462852. This places an upper limit of about10 − M ⊕ of dust lying within 2-8 AU from the star, 10 − M ⊕ located within 26 AU,and a total overall dust budget of <7.7 M ⊕ within a radius of 200 AU [107].Since the end of the Kepler space mission in 2013 May the star had been relativelyquiet. In 2017 May the dipping activity started again with four main events named‘Elsie’, ‘Celeste’, ‘Skara Brae’, and ‘Angkor’ shown in Figure 14 [108]. These dipsare about 1%-2.5% deep. The multiband photometry of the dips shows differential reddening favoring non-gray extinction. The data are inconsistent with dip modelsthat invoke optically thick material, but rather they are in-line with predictions for anocculter consisting primarily of ordinary dust, where much of the material must beoptically thin with particle sizes (cid:46) µ m. No changes in the spectrum or polarizationwere detected during these events [108, 109, 110, 102]. Spectrophotometric obser-vations of these recent dipping events with the GTC confirm that the dips are deeperin the visual than at red wavelengths. This is compatible with optically thin dustparticles having sizes of (cid:39) . − . µ m. Such particles would be quickly blownaway by the radiation pressure which indicates that the dust particles must be con-tinuously replenished [111]. Finally, we note that the radial velocities of the host staralso seem to be constant, within 2 sigma from the average value of v rad = . ± . Fig. 14
Boyajian’s star be-came active again in May2017. Ground based monitor-ing shows four dips of depth1-2.%. Taken from [108],courtesy of ApJ.
There is evidence for a long term (secular) variability of Boyajian’s star. Based onarchival photographic plates from Harvard College Observatory, [112] found thatthe star faded at an average rate of 0 . ± .
013 magnitudes per century from 1890to 1989. This result was questioned by [113, 114]. Nevertheless, a similar studyusing archival photographic plates taken at the Maria Mitchell observatory during1922-1991 found a similar trend of 0 . ± .
02 per century [115].The star’s brightness dropped significantly throughout the
Kepler mission as well.Over the first 1000 days the star faded approximately by 0.9%. It dimmed much morerapidly in the next 200 days, with its flux dropping by more than 2% [116]. A slightlydeeper 3.5% drop was found in the contemporary GALEX observation in the nearUV [117]. These results imply R V (cid:39) . xtrasolar enigmas: from disintegrating exoplanets to exoasteroids 27 seen previously in Kepler data. According to [118] the dimming rate for the entireperiod reported is "22 . ± . . ± . . ± . . ± . . ± . ± . ± .
05, and 0.31 ± .
05, respectively [123]. This implies that the dust particlescausing the long-term variability must be about 0.1 µ m in size. Such particles will beeasily blown away and must be continuously replenished. The long-term variability(dimming) has a continuum of timescales ranging from almost a century, to decades,to years, and even down to a few months. It is most probably related to the shallowdip events and caused by the same phenomena. The net result is that the star hasexperienced about a 12% long-term dimming over the past century. This has seriousimplications for the amount of the dust that must be distributed along the ellipticalorbit which now amounts to at least 10 − M ⊕ . There have been numerous models, ideas, and speculations proposed to explainthe above mentioned behaviour. It is not possible to mention and discuss all themodels here. An overview was presented in [124] and it concluded that interveninginterstellar material (ISM) is a more plausible explanation than other natural models.The discoverers themselves discussed a number of possibilities and favoured a cometscenario. Apart from that it was proposed that KIC 8462852 might be undergoinga late heavy bombardment, but is only in its very early stages [106, 125]. It isalso possible that the variability could be intrinsic to the star [126], or the dipsmight have been caused by matter in our Solar system [127]. According to [128]the secular dimming is the result of the inspiral of a planetary body or bodies intoKIC 8462852, which took place 10 − yr ago. The discoverers also proposedthat the dips observed with Kepler may be due to transits of less massive bodiesplaced on eccentric orbits by the Lidov-Kozai oscillations due to the outer M-dwarfcompanion. However, the predicted smooth decline in flux is not in agreement withthe brightening episodes [119, 120], and the M-dwarf companion turned out not to be associated with Boyajian’s star [104]. However, evidence is growing that thedipping phenomenon is due to circumstellar dust. In the next few sections we willmention three models that were developed to the point where they can be directlycompared with the observations of the dip events.
This is the scenario favoured by the discoverers and developed by [129]. In thismodel the deep
Kepler dips and long-term behaviour are due to transit of a largenumber (70-700) of comets. Such strings of comets are known from our Solarsystem so it is a natural explanation. An eccentric orbit has advantages. There isa high likelihood of the transits occurring near periastron and the material spendsmost of the time very far from the star so it can satisfy the IR limits as well as thedynamical constraints [122, 123]. These comets must have had a common progenitor.The models can fit the
Kepler dips very well. Unfortunately, the model has a fewdrawbacks. (i) It cannot reproduce the D790 event because it is very smooth andhas a slow ingress and a faster recovery, while the model features just the oppositebehaviour with a steeper ingress and a slower egress. (ii) The symmetric triple dip,D1540, would require an accidental constellation of comets. However, there are twoother events of this kind: D1210 and Skara Brae, and they would have to be theresult of an accidental grouping of comets as well. (iii) Comets can hardly produceand continuously replenish (cid:38) − M ⊕ of dust required to explain the long-termvariability [123]. (iv) The model requires many free parameters (related to a largenumber of comets) and even a perfect fit does not mean that it is correct. This ‘recipe’ can be found in [101] but it was already considered in the discoverypaper [11]. It is in many respects similar to the above mentioned scenario. Accordingto this model there are a few massive asteroids or planetesimals surrounded by dustclouds orbiting and transiting the star on eccentric orbits. Obviously, the objectsmust have originated from a common progenitor as well. The orbit and the amountof the dust required to transit the star is similar to the previous model so it alsosatisfies the IR limits and the dynamical constraints [122, 123]. The difference is inthe following. Instead of a large number of comets only four more massive objectsare sufficient to explain the four major Kepler events. A massive object means thatits gravity cannot be neglected, and it can retain a dust cloud within its Hill’s sphere(contrary to a comet). It naturally explains the smooth shape of the D790 eventand produces a slower ingress and faster egress. The symmetric triple dips: D1540,D1210, and Skara Brae are no longer due to an accidental constellation of objectsbut rather single objects surrounded by dusty disks/rings. The massive asteroids canproduce and replenish (cid:38) − M ⊕ of dust to account for the long-term variability.It was demonstrated that if the objects were initially on exactly identical orbits, and xtrasolar enigmas: from disintegrating exoplanets to exoasteroids 29 were massive enough, then they (and their dust clouds) would mutually interactand end up on a slightly different orbits. Even though the fits are not perfect, themodel requires a small number of massive objects, and hence only a handful of freeparameters. One can anticipate that massive asteroids are accompanied by a largenumber of smaller debris which would account for the smaller dips and long-termvariability. We hope the reader will not mind the ‘label’ above. The model was proposed by[130]. The authors noticed that one of the post
Kepler dips (Skara Brae, the onethat occurred around Aug 9, 2017) is very similar to the
Kepler
D1540 event, i.e.,it is a symmetric triple dip with the central dip being the deepest. The similarity isindeed striking and the authors presume that it is the transit of the same body. Thisimplies an orbital period of 1601 days. ‘The Lord’ is a dark and relatively massiveobject – a brown dwarf orbiting the star. It is accompanied by a ‘fellowship’ of about9 rings which are about 0.2 AU across. With this model the authors were able toreproduce the Skara Brae and D1540 events very well. Apart from that the modelexplains a tentative 1600 day periodicity found in the long-term variability. Theother dips observed by
Kepler were not modelled but might be understood assumingtransits of additional bodies (moons) related to the brown dwarf. The model makes avery precise and testable prediction. ‘The Return of the Lord’ should happen duringChristmas on Dec 27, 2021.A similar idea was presented earlier in [131]. The authors identified two strikinglysimilar events in the
Kepler light curve which are approximately 0.1% deep andoccurred at D216 and D1144. They show that these events could be explained by theoccultation of the star by a giant ring system or by the transit of a string of half adozen exocomets. These events occurred 928.25 days apart and the authors predictthat the next event will occur between 3-8 October 2019.More recent comparison and cross-correlation of
Kepler dips and dips observedfrom the ground indicate a similar periodicity of 1574.4 days (4.31 yr) [132]. Thisperiod also explains a few other historical dimming events of the star in the past.It predicts the next return of the D790 event on Oct 17, 2019. We would like tocomment that this idea presumes that the mutual gravitational interaction among thebodies orbiting the star must be negligible. It is not compatible with the brown-dwarfhypothesis.It remains to be established whether these models are compatible with the long-term variability, infrared limits, and various other constraints including the dynamicsof the system.
Because
Kepler played a pioneering role in the detection of a new class of ‘disinte-grating’ objects, we shall briefly discuss ongoing and future space missions in orderto present their potential for new discoveries of this particularly interesting class ofobjects.
TESS
TESS is a NASA space mission successfully launched in 2018 and planned for atleast 2 years of operations [133, 134]. The aim of the
TESS mission is the detection ofseveral thousand exoplanets, mainly Neptune- and super Earth-sized. However, sev-eral hundred Jupiter-sized planet detections are expected as well.
TESS is deliveringprecise photometry down to about 200 ppm which is sufficient to detect a transitingsuper-Earth . The first TESS planets were recently announced [135, 136]. There aremany interesting objects discovered by
TESS , such as a Neptune-sized planet HD21749b with another, Earth-sized, planet HD 21749c in the same system [37] or thefirst
TESS transiting brown dwarf [137]. Many of the
TESS planets should be suitablefor ground-based follow-up observations to detect exoplanetary atmospheres evenwith mid-sized telescopes [138] as shown in Figure 15. Furthermore, it is expectedthat
TESS will detect additional interesting systems, and among those should be thetypes of disintegrating and dusty objects which we described in this review.
Fig. 15
Expected distribu-tion of
TESS planets with theorange line representing adetection threshold for mid-sized telescopes. Figure from[138] DOI: 10.1088/1538-3873/ab2143. ©The Astro-nomical Society of the PacificReproduced by permissionof IOP Publishing. All rightsreserved.
Visual magnitude * S i g n a l https://heasarc.gsfc.nasa.gov/docs/tess/observing-technical.htmlxtrasolar enigmas: from disintegrating exoplanets to exoasteroids 31 The ESA M3 space mission PLATO (PLAnetary Transits and Oscillations of stars)will be launched in 2026. The PLATO space mission will consist of 26 telescopesmonitoring large portion of sky (about 50%) for transits with an unprecedentedphotometric accuracy of a few ppm [139]. The PLATO mission should find sev-eral thousand planetary candidates around one million bright stars from naked eyebrightness to Vmag =
11. PLATO will be able to detect even an Earth-like planeton an Earth-like orbit among the Solar type stars. PLATO will also focus on aster-oseismology of stars [140]. However, the PLATO mission will also contribute tomany other fields of astrophysics ranging from variable star research to extragalacticobjects [139]. The majority of the PLATO targets and candidates will amenable tofollow-up studies from the ground, thereby allowing for an exact determination oftheir masses and radii and thus allowing for their full characterization.
ARIEL, the Atmospheric Remote-sensing Infrared Exoplanet Large-survey, is anESA M4 mission which will be launched in 2028 and it will be dedicated to un-veiling the chemical composition of a sample of about 1000 selected transitingexoplanets [141]. ARIEL will be equipped with an off-axis Cassegrain telescopewith an elliptical primary mirror of 1.1-m × µ m, 0.8-1.0 µ m and 1.0-1.2 µ m. A spectrograph with two medium resolving power channels of1.95-3.9 µ m and 3.9-7.8 µ m and one low-resolution channel of 1.25-1.95 µ m will beavailable . The precision of ARIEL should be sufficient to detect the signature ofexo-atmospheres with a precision of at least 10 − relative to the star. The main targetswill be hot (600 K and more) planets, and it is expected that species like H O, CO ,CH , NH , HCN or even metallic compounds such as TiO and VO will be detectedand studied. Acknowledgements
The authors would like to thank Prof. Saul Rappaport for carefully reviewingthe manuscript and his help with several sections. We acknowledge the ERASMUS+ project ’Peraspera ad astra simul’ under number 2017-1-CZ01-KA203-035562 which funded the mobilitiesof the authors. Apart from that JB thanks for support the VEGA 2/0031/18 and APVV 15-0458grants. PK acknowledges the support of GACR grant number 17-01752J. E.P is partly financed bythe Spanish Ministry of Economics and Competitiveness through projects ESP2016-80435-C2-1-Rand PGC2018-098153-B-C31. http://sci.esa.int/ariel/59798-summary/2 Jan Budaj, Petr Kabath and Enric Palle References
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