DARK COLLAPSE OF GAS GIANT PLANETS
Sergei Nayakshin, University of Leicester Seung-Hoon Cha, Mark Fletcher “GI works for far away planets only”
CA (Core Accretion) <— GI (Gravitational Instability)—>
✤ Gammie 01, Rice + 05, Rafikov 05: fragmentation at a > 50 AU or so
✤ Meru (talk here) a ~ 20 AU fragmentation GI PLANET MIGRATION
1. GI gives birth to fragments in the outer disc 2. Fragments migrate inward in ~ 10 orbits
Boley+ 2010 Cha & Nayakshin 11
–34– Vorobyov & Basu 06
Fig. 2.— ConfigurationMachida of protostellar outflow + at t c =11 843 yr is shown by yellow volume, in which color indicates outflow speed. The density distributions (colors) are projected on each wall surface. The velocity vectors (arrows) on the equatorial plane are plotted on bottom surface. The magnetic field lines integrated from each planet are plotted by yellow lines. The box size is 100 AU. Migration of GI planets may explain all giant planets, including hot Jupiters Giant planets need ~ 1 Myr to cool
✤ GI fragments are basically First Cores (Larson 69, Masunaga & Inutsuka 00) 4 S. Nayakshin PTEP 2012,01A307 S.Inutsuka ✤ Fragments must heat up to ~ 2000tions K mayto becollapse the origin of or ”hot” else sub-giant they planets are such disrupted as hot Super-Earths or hot Neptunes. Another point worth noting from figure 1 is that the as- a = 10 AU trophysical metal components of the protoplanet (that is, all ] 1000 elements heavier than H and He) can settleEffective into the centre Ratio of Specific Heats of it provided that condensation temperature of the compo- Jupiter γ =1.1 < γ =4/3 a = 1 AU nents is higher than the central temperature of theeff planet. eff 100 In this paper we limit our attention to three dominant grain species: water ice, organics called CHON, and a mix of Fe Second and silicates (cf. 4.3 below). The condensation tempera- Core § o tures for these species are marked approximately by the po- 10 a = 0.05 AU = 7/5 sition of the respective text in the bottom panelγeff of figure 1. Second Collapse
Planet Radius [R Note that the planet spends little time in the cold config- uration, since it cools relatively rapidly initially. From this 1 one can expect water to be the least able to condense down in TD planets, whereas Fe and silicates be the most able to Dissociation of H2 Fe and silicates γeff = 5/3 do so (this agrees with results of Forgan & Rice 2013b, that Ebind = 4.48 eV 1000 TD cores are mainly composedFirst of rocks Collapse ). Grain sedimentation may lead to core formationFirst in- Core side of the protoplanetdense (e.g., McCrea & Williams 1965; CHON (organics) Boss 1997; Helledcore & Schubert 2008). If the gaseous com- Downloaded from ponent of the protoplanet is then disrupted by the tides, the nearly “naked” core survives, since its density is much Temperature [K] Water Ice higher. Such disruptions may be an alternative to CA origin for terrestrial-likeFig. 1. Temperature planets (Kuiper evolution 1951; at the Boley center et of al. the 2010; gravitationally collapsing cloud obtained by Masunaga and
100 Nayakshin 2010a). http://ptep.oxfordjournals.org/ Inutsuka in their radiation hydrodynamical calculation of protostellar collapse in spherical symmetry [19]. The 0.0 0.5 1.0 1.5 2.0 first collapse phase corresponds to the formation of the first core,whichconsistsmainlyofhydrogenmolecules. time [Myr] Inutsuka 2012 The dissociation of hydrogen molecules triggers the second collapse,whicheventuallyproducesthesecond 2.3 TDcore modelor a protostar. possible Each outcomes phase of the temperature evolution is characterized by the effective ratio of specific Figure 1. Radiative cooling of an isolated Jupiter mass gas giant heats, γeff. planet. The planet is coreless and of Solar composition. The upper It is clear that the fate of a gas fragment formed in the outer panel shows planet’s radius (black curve). The three horizontal disc by GI is sealed (Boley et al. 2010; Forgan & Rice 2013b) lines depict the planet’s Hills radius if the planet were in orbit by the ratios of the various time scales: tcoll,theplanet’scon-
around a 1 M mass star at distances indicated just above the tractionρ and1g/cc, collapse and time the second scale; tmigr adiabatic, the planet’s core or migra- a protostar forms. Further periods of evolution include a by guest on June 27, 2015 ∼ lines. The lower panel shows evolution of the central temperature tion timeT-Tauri scale; phase and tsed on, the the grain Hayashi growth track, and the sedimentation timescale of which is about two orders of magnitude longer of the planet. During the first Million years, the planet is dom- time scale. Qualitatively, there are several possibilities:5 inated by molecular hydrogen. The three di↵erent grain species than the dynamical timescale ( 10 year) of protostellar collapse, which is only accessible by steady ∼ considered here condense out below temperatures indicated ap- (i) Ifstate the calculations migration time (see, is the e.g., shortest the review of the by three, Chabrier the and Baraffe [21]). The time evolution of the SED proximately by the location of the species name in the panel. fragment is disrupted with essentially nothing remaining of it; obtained from the self-consistent RHD calculation is also shown in Ref. [19]. Molecular emission (ii) lineif tsed profiles
TABLE 3 Stars with Uniform Planet Detectability
Star ID Planet/Star
HD 142 ...... P HD 2039 ...... P HD 4203 ...... P HD 8574 ...... P HD 10697 ...... P
Note.—Table 3 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content.
more than 100 metal-poor stars (Mayor et al. 2003). In addition, a Fig. 5.—Same results as Fig. 4, but divided into 0.1 dex metallicity bins. The Doppler survey of 150 low-metallicity stars has been underway increasing trend in the fraction of stars with planets as a function of metallicity is at Keck for the past two years (Sozzetti et al. 2004). No planets well fitted with a power law, yielding the probability that an FGK-type star has a 2:0 gas giant planet: (planet) 0:03 (NFe=NH)=(NFe=NH) . have been announced from either of these surveys, suggesting P ¼ ½ that the rate of occurrence of Jovian-mass planets with orbital periods less than 3 yr does not exceed (and is likely lower than) often as they orbit solar-metallicity stars, it seems very likely that afewpercentaroundmetal-poorstars. they would have been detected by now. A single substellar object, HD 114762b, with M sin i 11MJ has been found orbiting a metal-poor ( Fe/H 0:655) 3.2. The Volume-limited Sample field star (Latham et al. 1989). Interestingly,½ we measure¼À a low 1 Avolume-limited sample is often desirable as an unbiased sam- v sin i (1.7 km sÀ )forthisF-typestar.Fewerthan5%ofthestars 1 ple, and virtually all spectroscopic investigations of the planet- with comparable spectral type have v sin i < 2:0kmsÀ ,sug- metallicity correlation have referenced such a sample as a control. “Giant problems” of GI gesting that this particular star may be viewed close to pole-on. We contend that a volume-limited sample is not the best com- Assuming that the stellar rotation axis is aligned with the orbital parison sample for this investigation because it does not nec- rotation axis, it is possible that the companion to HD 114762 essarily represent the stars on Doppler surveys. To investigate may have a substantially higher mass, conceivably even a stellar this, we defined a volume-limited subset of 230 FGK-type stars mass, a suggestion first made by Cochran et al. (1991). analyzed with SME. Figure 6 shows the density of the entire ✤ Clumps are disrupted too easily (Zhu et al 12, ItVazan has been & suggested Helled that 12). the paucity Difficult of spectral to lines in metal- (1040 star) planet search sample as a function of distance for poor stars results in poorer detectability that impedes the detec- specified ranges of absolute visual magnitude. The points on explain hot Jupiters. tion of Jovian-mass planets. To address this issue, we calculated each curve mark the distance where the sample size increments the mean radial velocity error for stars in each 0.25 dex metal- by about 40 stars. Intrinsically faint stars dominate the 20 pc licity bin. For [Fe/H]dEtot between 0.75 and 0.5,1 the mean Doppler ✤ 1 À sample, and the sample composition gradually shifts to earlier Gas fragments collapse faster at low metallicitiesprecision is 4 m sÀ .Thelowestmetallicitybinonlysuffersa= Lrad 1 type, intrinsically bright stars at larger distances. We define the modest degradationdt in velocity precision/ toZ6msÀ .Thus, volume-limited sample to have a radius of 18 pc, inside of which there is no significant detectability bias against the detection of ✤ Negative giant planet -- metallicity correlation is expected (Helled & Bodenheimer the number of FGK-type stars per unit volume on the planet planets in the parameter space that we have defined to have uni- search programs is nearly constant as a function of distance. Be- 2011), but a positive one is observed (Fischerform & Valenti detectability. 2005) If gas giant planets orbit metal-poor stars as yond this distance the number density of intrinsically faint stars begins to decline rapidly.
Fig. 4.—Percentage of stars with detected planets rises with iron abundance. In all, a subset of 850 stars were grouped according to metallicity. This subset of stars had at least 10 Doppler measurements over 4 yr, providing uniform de- Fig. 6.—Stellar density for a range of absolute visual magnitudes calculated tectability for the presence of planets with velocity amplitudes greater than in distance bins, each with 41–43 stars. Intrinsically faint stars dominate the 1 30 m sÀ and orbital periods less than 4 yr. The numbers above each bar on the nearby solar neighborhood but are rapidly lost beyond 20 pc. Intrinsically bright histogram indicate the ratio of planets to stars in each bin. Thirteen stars had stars become the dominant constituent of the planet search samples at distances Fe/H < 1:0, and no planets have been discovered around these stars. greater than about 40 pc. ½ À Solid accretion on GI fragments
✤ Rice, Lodato +04 found solids (1-10m) concentrate in spiral arms, clumps
✤ Boley, Helled & Payne 2011 found same for 10 cm grains
✤ Johansen & Lacerda 2010, Ormel and Klarh 2010, … Lambrechts & J 12, 14— CA context The Astrophysical Journal,735:30(12pp),2011July1 Boley, Helled, & Payne Planet embedded in a disc
Pebbles of a few mm in size tend to decouple from gas and sink towards and into massive objects
Figure 2. Similar to Figure 1, but later in the disk’s evolution after additional fragmentation has occurred. Left: there are three regions of interest that are highlighted by boxes A, B, and C. Box A shows to clumps that are about to merge and become one object. Box B shows two clumps that just missed merging. One is becoming disrupted and releasing its gas solids back into the disk. In box C, three clumps are about to merge. Right: the boxes represent the same objects 200 yr later. Boxes A and C show that the clumps have completed their mergers. The clump in box C is now 32 MJ with 270 M of total heavy elements. In contrast, one of the clumps in ⊕ box B has survived, while the other was tidally disrupted. The clump is 11 MJ with 100 M of heavy elements. ∼ ⊕ (A color version of this figure is available in the online journal.)
Figure 3. Similar to Figure 2,butforSIM1mu1.5Z.TheclumpsinboxAareverysimilartothoseinFigure2,buttheclumpsinboxBmerge.Attheendofthe simulation (right panel), the clump in Box C is 26 MJ with 370 M total in solids, giving the clump a total enrichment of about 1.5 over the nebular value. ∼ ⊕ (A color version of this figure is available in the online journal.)
Figure 4. Three snapshots of SIM2kmv2. The center panel is roughly at the same time that SIM2km ends. As a result, BD2010 did not capture the formation of the second clump, but noted that the arm showed signs of fragmentation. The solids do not collect in the spiral arms, and arms of planetesimals can even be offset from 2 the gaseous arms (color bar, log [g cm− ]). (A color version of this figure is available in the online journal.)
enrichment at birth seems to scale with the fraction of solids that This capture efficiency may not continue to scale to very large can be aerodynamically captured by the spiral arms. The result metallicities, e.g., when the back reaction of the large solids on is consistent with the enrichment being pushed toward twice the the gas becomes more appreciable in the dense, spiral arms. nebular value in the limit that all solids can be aerodynamically For example, one large difference between the SIM1mu and captured by spiral arms. SIM1mu1.5Z is the frequency of knotty structure in remnant
4 GI planets contract when accreting pebbles Dark collapse of giant planets 5
0 2 4 6 8 10 12 0 2 4 6 8 ✤ 1D RHD simulation of (a) (c) a GI clump evolution 1000 1000
✤ Metallicity z=const on T [K] T [K] Z=ZSol tz=250 the left, dz/dt > 0 on the 500 Z=ZSol 1000 right 0.5 ZSol 2000 2 ZSol 4000 100 100 (b) (d) ✤ z=const confirms Helled 0.10 0.10 & Bodenhemier’s results
✤ But dz/dt > 0 planets contract faster than 0.01 0.01 z=z_0 one! Planet metallicity Planet metallicity
0 2 4 6 8 10 12 0 2 4 6 8 time [kyr] time [kyr]
Figure 2. Top left panel (a): evolution of the central temperature versus time for constant metallicity planets of 4 MJ masses. The bottom left panel (b) shows the (constant in time) metallicity, z,oftheplanets.Rightpanels(c)and(d):samebutforplanetsloaded by grains at constant rates parameterised by the metallicitNayakshinydoublingtime 201tz.Notethatthefasterthemetalsareaddedtotheplanet,5a the quicker it collapses.
Tc = 700 K. The exact numerical value of the termina- index γ =1+1/n. The equation of state (EOS) of the gas tion temperature is not important. Figure 3 shows that once in the sphere is grain accretion stops, contraction of the cloud continues at aslowerrate than that for a non-metal-polluted planet, i.e., P = Kργ , (8) one recovers the main result of the fixed metallicity cases shown in figure 2a and 2b. For example, for the case of the where P and ρ and the total (gas plus metals) pressure and most rapid metal loading, tz = 250 years, the fragment col- density, respectively, and K is a constant throughout all of lapsed at less than 2,000 years in figure 2(a), but collapses the planet. Constancy of K is assumed to be maintained only at t ≈ 9, 000 years when grain accretion is discontinued. by convection that is known to be the main energy trans- These results indicate that grain deposition into a pre- fer mechanism within H2 dominated planets (e.g., Helled & collapse planet produces two opposing effects, one delay- Schubert 2008). ing contraction of the planet, and the other speeding it up. The theory is only approximate, since there is no single The former effect is due to the increase in the dust opacity value of γ that could describe a planet dominated by molec- which slows down radiative contraction of the fragment. In ular hydrogen exactly. For gas dominated by molecular hy- our opacity model, this effect depends on the instantaneous < drogen, γ varies from γ =5/3 at T ∼ 100 K to γ =7/5ina amount of dust in the planet, that is, its metallicity. The lat- < < relatively broad temperature range, 200 ∼ T ∼ 1000 K, and ter effect however depends not on the amount of dust in the > finally drops to γ ≈ 1.1−1.2 at T ∼ 1500 K (see figure 5a be- planet but on the rate of grain deposition into the planet, low, and Boley et al. 2007). An H2 dominated gas fragment as hinted in the Introduction. spans a range of temperatures, from the maximum at the centre, Tc, to the minimum at the atmosphere of the planet, Teff , which may be as low as tens of K (Vazan & Helled 2012), so γ varies within the planet significantly. However, qualitatively, H2 dominated gas fragments behave as poly- 5 A TOY MODEL tropes with γ varying from 5/3 at low Tc to γ < 4/3 at > To understand how grain accretion can accelerate collapse Tc ∼ 2000 K. of a planet we turn to a simple analytical model in which The total energy of a polytrope of mass Mp and radius the planet is modelled as a polytropic sphere of adiabatic Rp is (e.g., Chandrasekhar 1957)
⃝c 2008 RAS, MNRAS 000,1–?? GI planets collapse faster due to pebble accretion Dark collapse of giant planets 7
where z⊙ =0.015, the Solar metallicity. This suggests that over-abundance of metals by a factor of 5 − 10 in a gas frag- ment dominated by molecular hydrogen may significantly in- 0 5 10 15 > crease Tc, taking the planet closer to the desired Tc ∼ 2000 K ✤ accretion of grainspoint at at low which velocities it can collapse brings to much higher mass densities. but not (a) Figure 4 show a comparison of the analytical theory kinetic energy -->(equation effective 16) with cooling numerical integrations of the metal load- ing effect performed with our code, except that the H/He 1000 mix EOS was replaced by the polytropic gas equation with dEp a fixed γ. FiveGM valuesp ofMγ˙arez considered, as labelled on the = Lfigure.rad The metal loading time is tz = 300 years for all of T [K] the curves. The black curves in top panel, fig. 4a, are numer- dt Rp γ = 1.37 ical integrations, whereas red lines are equation 16. Figure 1.40 4b shows the metallicity evolution of the planets,1 which is 1.46 ✤ 1+ n 1.58 Considering a polytropicidentical, all givensphere by same (P value = of K t z =⇢ 300 years. ), The 5/3 agreement between the theory and numerical simulations is and exact solutionacceptable for metal to us. The loading curves show, is justfound as equation 16 does, that the smaller the value of γ, the stronger the planet reacts (b) to addition of grains. This is because n =1/(γ − 1) edges closer to the unstable value,6/(3n = 3,n as) γ approaches 4/3 1 z0 from above, and even a small amount of metals can cause a 0.10 Tc = significantT0 contraction of the planet. The same1 resultz (equation 16) can be also obtained from a polytropic sphere relation between planet’s radius, mass, and the ”constant” K, if the latter is allowed to vary as z 1+1/n 1+1/n ✤ changes. Namely, K = P/ρ = K0[(1−z)/(1−z0)] for H2 gas n=2.5, so the exponent is 12 Planet metallicity Nayakshin 2015a in this case, where K0 is the polytropic constant at z = z0. Since K is related to entropy per unit mass of the planet, this provides another interpretation of the metal loading effect: 0.01 ✤ Adding ~10% of massadding metalsin metals decreases can entropy make of the cloud,the fragment just as radia- 0 5 10 15 tive cooling does, so metal accretion is effectively a cooling time [kyr] collapse mechanism. Figure 4. Evolution of polytropic gas fragments for five different values of γ, as labelled in the figure, when loaded with grains ho- mogeneously throughout the cloud. The solid red lines are predic- 6 REAL H2-DOMINATED POLYTROPES tions of the analytical model (equation 16), whereas black curves Having explored idealised polytropic models with a fixed are the results of the numerical integration. value of γ (or n), we turn to more realistic cases of H/He- dominated pre-collapse planets. Figure 5a shows adiabatic
index γ versus gas temperature for a Solar composition similar all the way to Tc ≈ 2000 K. As can be expected, γeff H/He plus metals mix for the ideal EOS used in this pa- for a planet bears a strong resemblance to the γ(T )func- −7 3 per calculated for a fixed gas density of ρ = 10 g/cm . tion (the solid curve), except smoothed out somewhat due < As expected, γ =5/3 at T ∼ 100 K when rotational and vi- to the presence of a range of temperatures inside a planet, brational degrees of freedom of molecular hydrogen are not and also shifted to higher temperatures since Tc represents yet excited; then at higher T , γ drops to ≈ 7/5 appropri- the maximum temperature in a given planet, whereas γeff is ate for diatomic gas. This persists until T ∼ 1500 K when probably related more closely to a mean temperature in the H2 dissociation becomes energetically possible. Due to H2 planet. dissociation at temperatures around 2000 K, γ plunges to Now, the analytical theory developed in §5 predicts how about 1.1. the central temperature of a polytropic planet varies with Clearly, each pre-collapse planet configuration spans a its metallicity when grains are added to the planet, e.g., −σz range of densities and temperatures, from the maximum in Tc ∝ (1−z) (equation 16), where we defined ”metallicity the centre to the minimum in the atmosphere. To relate exponent” to the analytical theory derived in §5, we define effective γ d ln Tc 6 and n for a planet by computing the gravitational potential σz = − = . (20) energy of that planet and then comparing it with that of a d ln(1 − z) 3 − n
polytropic planet of the same mass and radius, e.g., The dependence of σz on central temperature is plotted in 2 figure 5b for the two planetary masses, and also for the solid 3 GMp Egrav = − , (19) curve from figure 5a (corresponding to fixed gas density of 5 − n Rp − ρ = 10 7 g/cm3). where n =1/(γ − 1). The values of the γeff versus planet’s The dash-dotted curve passing through red triangles central temperature are plotted in figure 5a for two plane- in the panel shows −[d ln Tc/d ln(1 − z)] actually measured tary masses, Mp =1MJ and Mp =4MJ. These are very in simulations of planets of mass Mp =4MJ loaded with
⃝c 2008 RAS, MNRAS 000,1–?? “Giant problems” of GI solved by pebble Positive GI planet -- metallicity correlation accretion Dark collapse of GI planets: positive metallicity correlation 9 Dark collapse of GI planets: positive metallicity correlation 7
Pebble accretion, Mp = 1 MJ Planet survival vs metallicity, M =1 M ✤ Planets are over-abundant in metals p J 100.0 1.0 (a) a (Miller & Fortney 2011) RH R H 10.0 p , R p 0.8 1.0 ✤ Clumps are disrupted a, R easily at low Z. 0.1
Zd = 2 (b) Z = 1 0.6 0.10 d ✤ average Gas fragments collapse faster at high fp0=0.05 z Zd = 0.5 fp0=0.2 metallicities. Positive giant planet -- 0.4 metallicity correlation0.01 (Nayakshin 2015b). Fraction survived (c) 0.2
[K] 1000 c T
0.0 6 10 1 (d) time tmigr Z tz Nayakshin105 2014c, subm.
104 Thursday, 18 September 14 Figure 3. Planet survival probability versus Z, the metallicity in Solar units, for a planet of Mp =1MJ mass and disc
time scales [years] 3 parameters covering a range of properties. The black diamonds show the full grid of models, while the blue and the red symbols 10 20 show40 results for60fp0 =0.05 and fp0 =0.2 (low and high pebble content, respectively). There is a strong positive planet survival timecorrelation [kyr] with the metallicity of the host disc.
Figure 2. Evolution of a gas fragment accreting grains from the disc at three different disc metallicities (Zd =2,1and 0.5, for solid, dotted and dashed curves, respectively). Panels show: (a) planet-star separation, a,Hill’sandplanet’sradii;(b)8 planet’s metallicity, z;(c)centraltemperatureoftheplanet;(d)migrationandgrain loading time scales. For all three cases, the fragment mass is 1 MJ,birthlocationa =120AU,discmass100MJ within 150 AU, viscosity parameter αSS =0.02, pebble7 fraction fp0 =0.1, and planet opacity parameter fop =0.3. Zd =2fragmentcontractsrapidly,reaching2000Kandcollapsing ≈ at t 32, 000 years. The metallicity of the planet is about 10z⊙ at the point of collapse. The Zd =1and0.5fragmentscontract1.0 6 less rapidly due to lower metal supply (resulting in longer tz,seepaneld),andaretidallydisruptedata =1.7and3.3AU, respectively. The Zd = 1 planet would have actually collapsed if not for a deep gap inthedisc,openedatt ≈ 55, 000 years, which cuts off grain accretion to almost zero. 5 p Z 4 0.8 3
⃝c 2008 RAS, MNRAS 000,1–10 2
1 0.6 0 1 2 3 4 Mp [MJ]
Fraction survived 0.4
0.2
Mp = 1 MJ = 0.5 = 2 0.0 1 Z
Figure 4. Planet survival probability versus Z for a range of planet’s masses, as labelled on the figure. The redinsetshows planet metal over-abundance over its host star, z/z∗ at the point of fragment collapse, averaged over all survived fragments. Lower mass giants are much more metal rich than more massive ones, as observed (Miller & Fortney 2011).
⃝c 2008 RAS, MNRAS 000,1–10 Migration of GI planets may explain all giant planets. But what about smaller planets? CORE FORMATION INSIDE GI FRAGMENTS
Kuiper 51, McCrea Williams 65, Cameron+ 82, Boss 98
Grain sedimentation Envelope disruption Migration and disruption of GI planets may explain all planets
1.“Tidal Downsizing”
2.Boley et al 2010, Nayakshin 2010
3.Note: parts of this were suggested by Kuiper 1951, McCrea & Williams 1965, Boss 1998 PLANET FORMATION DEBRIS
Incomplete grain/planetesimal sedimentation into the core creates a core and planetesimal debris ring DEBRIS DISCS MADE BY GI
Nayakshin & Cha 2012 — Alternative to Safronov 1969 TIDAL DOWNSIZING (MODERN GI)
1.GI gives birth to fragments in the outer disc 2./3. Fragments migrate in/Cores form inside 4a. Disrupted fragments — rocky planets + debris discs 4b. Collapsed fragments — gas giants
Can potentially explain everything. How do we test it? RESEARCH LETTER metallicity correlations
M. Mayor et al.: The HARPS search for southern extra-solar planets 120 0.6 0.3 15
100 0.4
0.2 Number of planets 80 0.2 10 0.0 0.1 60 0.0 Metallicity # planets Fe/H [dex] 40 Metallicity –0.2 5 0.0 20 –0.4 −0.5 0 Buchhave et al (2012) –0.1 –0.6 Mayor et al 2011 0 2 4 6 8 10 12 0 −0.5 0.0 0.5 10.0 100.0 1000. Radius of planet (R⊕) 0 5 10 15 Fe/H [dex] M2sini [Earth Mass] Radius of planet (R⊕) Figure 1 | Average host-star metallicities. Stellar metallicity is defined as Fig. 16. Histograms of host star metallicities ([Fe/H]) for giant Fig. 17. Estimation of the planetary-mass limit between the two gaseous planets (black), for planets less massive than 30 M [m/H] 5 log10(Nm/NH)star 2 log10(Nm/NH)Sun, where Nm and NH are regimes for the metallicity dependance of host stars. A vertical Figure 3 | Individual host-star metallicity(red), and foras the a function global combined of planet sample stars radius. (blue). The lat- line at 30 M distinguishes the two populations. We should note respectively the number densities of metal atoms (all elements more massive The black dots represent single-planetter histogram systems, has whereas been multiplied the green by 0.1 dotsfor visual comparison that such a limit also corresponds to the gap in the mass distribu- than helium) and hydrogen atoms. Red points represent the average metallicity representGas the largest giants planet and thecorrelate redreason. dots represent all the with smaller planets Z, in sub-Neptunestion (see Fig.10 and 12). On the right sidedo of the verticalnot. line we of the host stars with planets of different radii grouped in 1.33R and 4R bins. • do not observe significant changes of the metallicity distribution › › multiple-planet systems. The confirmed, published Kepler planets in our above 30 M . We remark that stars with metallicity exceeding The bin size is indicated by the length of the horizontal line and the uncertainty set at about 30-40 M . At the exception of a single star, all the 0.15 are for their huge majority associated with planets more samples are plotted as squares with thestars samehosting colour planets less code massive as the than dots. 40 M have Planet metallicities in the average metallicity is given by the standard error. The shaded grey massive than 30 M . candidatesMaldonado in multiple systems are et eachbelow addedal [Fe/H] = to2012:0.20. the This sample is well withinDebris contrast the with same the situation discs do not histogram shows the number of planets in each bin, and illustrates the large •host-star metallicity. In Supplementaryfor stars Information, hosting more massivewe consider planets. systemsInterestingly of this mass number of small planets in the Kepler sample. The average metallicity of host correlate withcorresponds Z. about to local the minimum in the mass distribu- planets as opposed to individual planetstion between by neglecting Neptunes andall but gaseous the giants largest (see planet e.g. Fig. 10 or suing a still more di cult challenge, the detection of Earth twins, stars with smaller planets (R , 4R ) is lower ([m/H] 520.01 6 0.02) than Fig. 11). P › in each system. The vertical dotted line indicates the division of the sample at rocky planets orbiting stars in the so-called habitable zone, and that of host stars with larger planets ([m/H] 510.15 6 0.03). Some of the The correlation between the occurrence of giant planets and possibly around stars as close as possible to the Sun. This last R 5 4.0R . The data show that Keplerthe metallicity detects small of the hostplanets star (i.e. around the metallicity stars with of the ma- planetary candidates in the Kepler sample are expected to be false positives that P › condition is of special importance for future experiments aiming a wide range of metallicities (20.6 ,terial[m/H] in the, proto-planetary0.5), and that disc) larger is a natural planets outcome are of the at the spectroscopic follow-up of the planet, in order to e.g. char- core accretion planet formation theory. In this paradigm, mas- do not turn out to be transiting planets, such as occurs when the reduced signal found preferentially around stars with solar metallicity or higher. The average acterize its atmosphere. For this long-term goal we would like sive gaseous planets form by runaway gas accretion onto cores to contribute to an ”input catalogue” with a significant number from a background eclipsing binary is by chance contained within the exceeding a critical mass, typically of the order of 10 20 M . uncertainty in the individual measurements in metallicity is 0.08 dex and that in of entries. Would Doppler spectroscopy have a chance to fulfill photometric aperture of the foreground target star. The false-positive rate of the The gas accretion from the disc goes on until the disc vanishes, such an ambitious goal? planetary radius is 12%. typically after a few million years. Hence, the sooner in the evo- candidates that pass the standard vetting procedures applied by the Kepler team lution of the disk a critical-mass core can form, the larger the At present, already 2 super-Earths located in the habitable has been estimated to be less than 10% (ref. 26). Therefore, such a low false- amount of gas that will still be available for accretion. A high zone of their host star have been detected with the HARPS in- needed better to understand themetallicity seemingly (interpreted diverse as a large regime dust-to-gas of ratio small in the mod- strument. The first one, Gl 581 d is part of a multi-planetary sys- positive rate is not expected to impact our results and interpretation. We have els) and/or massive discs favors the early growth of such critical tem hosting 4 low-mass planets. Gl 581 d has been detected by thus ignored possible contamination by false positives. We do not derive planets. cores. Conversely, lower-mass planets that do not accrete signifi- Udry et al. (2007). As a result of the aliasing with the sideral year, its orbital period had to be corrected later (Mayor et al. absolute probabilities or occurrence rates of planets and therefore do not attempt cant amount of gas, can grow their cores over a longer timescale Our data show that the well-establishedand therefore do not depend correlation as critically upon between the metallicity. 2009a). The minimum mass and orbital period of Gl 581 d are to eliminate the many strong bias and selection effects that, for example, These e↵ects have1–3 been born out in the population synthesis 7M and 66 days. Despite its rather short period the planet ap- metallicity and occurrence of giant planets does not extend into pears as the first super-Earth discovered in the habitable zone completeness studies (for example ref. 27) must take into account. We have models by Mordasini & al. (2011). the smaller planet regime below RP , 4R›, where the host stars due to the very late spectral type and low mass of Gl 581 (M5V, explored the possibility that correlations between planet size and parameters 0.3 M ). Models of the atmosphere of Gl 581 d have demon- instead have a wide range of metallicities. This observation implies 6. Planets in the habitable zone of solar-type stars strated the possibility of habitability (Kaltenegger et al. 2011a; such as orbital semi-major axis are the source of the apparent dependence on that, by contrast with smaller planets, gas giants require exceptional Wordsworth et al. 2011; Hu & Ding 2011). The discovery metallicity, but find no evidence for such an effect (Supplementary Information). All the very specific properties of the population of low-mass of another super-Earth in the habitable zone of the same star conditions to trigger their formation.planets (super-EarthsOur findings and Neptune-mass agree well planets) with are the of special (G 581 g) was claimed by (Vogtet al. 2010). Statistical reanalysis interest for constraining the formation of planetary systems. In of the published velocity data could unfortunately not confirm core accretion theory for planetaddition formation, to this, the whereby surveys targeting high-metallicity low-mass planets, in the the detection (Andrae et al. 2010; Gregory 2011; Tuomi 2011). environments allow planetary coressame way to grow as the parallel rapidly e↵orts to aiming reach to increase approxi- the precision Doubling the number of available precise HARPS measurements 50 mately ten times the mass of theof Earth, spectrographs continue optimized to for accrete Doppler measurements a gaseous are pur- Forveille & al. (2011) ruled out the existence of Gl 581 g. 5 envelope and evolve to gas giants of several hundred Earth masses . 11 40 Gas disks around young stars are observed to dissipate within a few million years15, requiring the cores of their planets to reach ten Earth masses within that time if they are to become gas giants. Planets 30 forming in low-metallicity environments, however, may not reach large enough core masses before the dissipation of the gas disk, which 20 could explain why we find very few gas giants around low-metallicity stars. Planetary accretion cannot compete with gas dissipation around Number of planets low-metallicity stars because the number density of planetesimals is 10 low16–18 and gas disks dissipate sooner around low-metallicity stars19,20. The semi-major axes of the orbits of the majority of the Kepler 0 planets analysed in this work are less than 0.5 AU, so the detected gas –0.5 0.0 0.5 giants in our sample were probably brought into orbits within 1 AU by Metallicity migration21. A decreased efficiency of migration in low-metallicity Figure 2 | Comparison of host-star metallicities for small and large planets. disks could partly explain the observed deficiency of gas giants around The histograms compare the metallicities of two samples of stars hosting the low-metallicity stars. The formation of gas giants late in the lifetime planets by dividing the sample at RP 5 4R›. The host stars of the gas giant of the protoplanetary gas disk would reduce their subsequent migra- planets (RP $ 4R›; red histogram) are clearly more metal rich than those of the tion because the gas disk is diluted at that stage. This could partly , smaller planets (RP 4R›; blue histogram), which have a much wider range of explain why we observe so few gas giants in close orbits. However, late metallicities. The hatched area represents the area where the histograms planet formation will in itself suppress formation of gas giants because overlap. A Kolmogorov–Smirnov test shows that the probability that the two distributions are not drawn randomly from the same parent population is some cores are formed after the disappearance of the gas disk. Hence, greater than 99.96%; that is, the two distributions differ by more than 3.5s.The migration cannot be the only reason for the small number of gas giants average metallicity of the stars with small planets ([m/H] 520.01 6 0.02; that we observe around low-metallicity stars. blue histogram) differs by almost 5s from that of the larger planets During the initial stages of planet formation, dust grains collide to ([m/H] 510.15 6 0.03; red histogram). form planetesimals, which represent the kilometre-sized building
376 | NATURE | VOL 486 | 21 JUNE 2012 ©2012 Macmillan Publishers Limited. All rights reserved classic GI model fails completely
Observations TD CA
Gas giants Positive Positive
Sub-Neptunes No ?
Debris Discs No ? A detailed TD pop synthesis model
1. Planet-disc (migration) model (Nayakshin & Lodato 2012) •1D viscous disc evolution •type II + type I migration 2. Planet contraction + grain physics •radiative cooling/external irradiation from the disc •grain (3 species) growth, sedimentation, vaporisation •core formation and energy release 3. No gas accretion on planets (N & Cha 2013) but see D. Stamatellos talk 4. Pebble accretion on GI planets (Nayakshin 2015a,b).
Note: Forgan & Rice 2013, Galvagni & Mayer 2014 presented semi-analytical population synthesis models for TD. TD = GI + MANY “CA PROCESSES”
• Fragment formation by GI (Rice, Forgan, Stamatellos, Inutsuka et al, Meru, Z. Zhu, Boley, Durisen…) • Fragment contraction, grain growth, core growth (Bodenheimer et al 1970-is; Helled et al 2008, 2010, 2011; N 2010, 2011, 2014) • Fragment migration in the disc (Crida, Baruteau, Matsunaga+) • Disc evolution in 1D (Shakura, Sunyaev … Clarke, Armitage, Alexander) • Population synthesis — Ida, Lin, Mordasini, Alibert (CA context); Forgan & Rice, Galvagni & Mayer (TD context) • Pebble accretion (Johansen, Lambrechts….) • Massive atmosphere formation around the core (Mizuno, Stevenson…) Example: formation of a Hot Super Earth
Disc evolution
1000 t= 0.18 Myr 0.23 Myr 1. Fragment forms at 110 AU 1.20 Myr ]
-2 1.50 Myr 100 Tidal disruption
2. [g cm Gap closed Fragment migrates to ~3 AU Σ
10 3. Tidal forces destroy the envelope
0.1 1.0 10.0 100.0 4. A core of ~ 6 Earth masses remains R, AU Super Earth planet formation 5. 100.0 The core migrates to 0.23 AU Gap openned 10.0 before the disc dissipates Tidal disruption Gap closed 6. Need ~ 4 CPU hours per run 1.0
Separation, a Radius, R Separation and radii [AU] 0.1 (a) p Hill’s radius, RH ] Earth 1.0 Total Core mass Rocks CHON Nayakshin 2015c, subm. Core mass [M
0.1
0 100 200 300 400 500 600 time [103 years] 20,000 planet formation experiments7
1/20 sample Planet Mass vs Separation 1/2 sample 10.000
1000
1.000
100 ] ] Earth Jup 0.100 [M p M
10 Mass [M
0.010
1 Zl < -0.25 -0.25 < Zl < 0 1/20 sample 0 < Z < 0.25 0.001 l Nayakshin & Fletcher, Zl > 0.25 2015, MNRAS 0.1 1.0 10.0 100.0 a [AU]
Figure 2. Simulated planets in the planet mass versus planet-host separation plane. The symbols and colors reflect the metallicity of the host stars. For the sake of clarity, only 1/20th fraction of planets is shown to the left of the vertial line and also below the horisontal line. 1/2ofallplanetsisshownintherighttopquartileoftheplane.
(b) Gas Fragment Fate (a) Planet disruption outcomes 1.00 Z < -0.25 1500 All l Metal rich -0.25 < Zl < 0 Metal poor Initial Fragments 0 < Zl < 0.25 Zl > 0.25
1000
0.10
500 Relative fraction Number of planets
0 a=Rin Surviving giants 0.01 -1 0 1 2 3 4 Disrupted Assimilated Cold Giants Hot Giants log Planet mass, MEarth
Figure 3. (a) Comparison of the initial mass spectrum of fragments (black diagram) to the final distribution of planetary masses. The colours group the results by metallicity, with low metallicities defined as Zl < 0andhighdefinedasZl > 0. (b) The outcome of gas fragment migration experiments in terms of the fraction of the initial fragments that are tidally disrupted, pushed all the way into the star (”assimilated”), survive as gas giant planets at all separations, or survive as ”hot giants” here defined as planets at separations less than 10 AU.
c 2008 RAS, MNRAS 000,1–?? 7
1/20 sample Planet Mass vs Separation 1/2 sample 7 10.000 1/20 sample Planet Mass vs Separation 1000 1/2 sample 10.000 1.000 1000
100 ] ]
1.000 Earth Jup 0.100 [M p
100 ] M ] Earth Mass [M Jup 10 0.100 [M p
0.010 M 10 Mass [M
0.010 1 Zl < -0.25 -0.25 < Zl < 0 1/20 sample 0 < Z < 0.25 0.001 l 1 Zl > 0.25 Zl < -0.25 -0.25 < Z < 0 1/20 sample l 0.001 0 < Zl < 0.25 0.1 1.0 10.0 100.0 Zl > 0.25 a [AU] 0.1 1.0 10.0 100.0 a [AU] Figure 2. Simulated planets in the planet mass versus planet-host separation plane. The symbols and colors reflect the metallicity of the host stars. For the sake of clarity, only 1/20th fraction of planets is shown to the left of the vertial line and also below the horisontal line. 1/2ofallplanetsisshownintherighttopquartileoftheplane.Planet Mass FigureFunction 2. Simulated planets in the planet mass versus planet-host separation plane. The symbols and colors reflect the metallicity9 of the host stars. For the sake of clarity, only 1/20th fraction of planets is shown to the left of the vertial line and also below the horisontal line. 1/2ofallplanetsisshownintherighttopquartileoftheplane. Simulated Planets, a < 5 AU Atmospheres and Cores, a < 5 AU (b) Gas Fragment Fate 1200 (a) Planet disruption outcomes 1.00 Cores No selection (b) Gas Fragment FateGas (a) Planet disruptionv = 1 m/s Zselection outcomes< -0.25 1500 All 300 * l 1000 1.00 Metal rich -0.25 < Zl < 0 Zl < -0.25 Metal poor Initial Fragments 1500 All 0 < Zl < 0.25 Metal rich -0.25 < Zl < 0 Zl > 0.25 Metal poor Initial Fragments 800 0 < Zl < 0.25 Tidal disruption desert Zl > 0.25 200 1000 600
1000 Number 0.10 0.10 400 Number of planets
Relative fraction 100
500 Relative fraction
Number of planets 500
Number of planets 200
0 0 0 0 a=Rin Surviving giants -4 -2 a=Rin 0 Surviving2 giants4 0.01 0.01 1.0 1.5 2.0 2.5 3.0 3.5 4.0 log Mass, MEarth -1 0 1 2 3 4 Disrupted -1Assimilated0 Cold1 Giants 2 Hot Giants3 4 Disrupted Assimilated Cold Giants Hot Giants log Planet mass, M log Planet mass, MEarth N & Fletcher 2015 Observed planets,Earth a < 5 AU 100 Figure 3. (a) Comparison of the initial mass spectrum of fragments (black diagram)Figure to3. (a) the Comparison final distribution of the initial of planetary mass spectrum masses. of ThefragmentsFigure (black 5. diagram)Mass function to the of final bound distribution gas in the of simulations planetary (red masses. The colours group80 the results by metallicity, with low metallicities definedhistogram), as Zl < compared0andhighdefinedas with that of the coresZl > (shaded0. (b) green). The outcome The of gas colours group the results by metallicity, with low metallicities defined as Zl < 0andhighdefinedasZl > 0. (b) The outcome of gas fragment60 migration experiments in terms of the fraction of the initiallatter fragments is scaled down that byare a tidally factor of disrupted, 3 for clarity. pushed The bound all the gas way is into the fragment• PMF migration desert experiments at in terms ~ 20 of the to fraction 100 of the Mearth initial fragments predictedstar that (”assimilated”), are tidally disrupted, surviveby Ida as gas pushed giant& Lin planetsall the 2004 at way all into separations, the either or survive self-bound as ”hot (the giants” high mass here peak defined to the as right) planets or is at attached separations less 40 star (”assimilated”),(also Mordasini survive as gas giant planetset al at all2009) separations, or survive asthan ”hot 10 giants” AU. here defined as planets at separations less to numerous low mass cores (low mass part of the red histogram), than 10 AU. 20 with little in between. 0 Frequency of planets TD also has the desert, for a physically1.0 opposite1.5 2.0 2.5reason3.0 3.5 4.0 • log Planet mass, M dense gas envelopes bound to the core as explained in sec- Earth tion 2.2.3. The gas masses of these envelopes are comparable to or a few times larger than their core masses. We find that • M_gas ~ M_core planets are rare no Figurematter 4. Planet masshow function you (PMF) make from simulations them (top such planets are rare. panel) and observations (bottom panel) at the high mass end. The To expand on this point, fig. 5 compares the mass simulations reproduce the “tidal disruption desert” naturally, but function of all gaseous envelopes at Rin
c 2008 RAS, MNRAS 000,1–?? 13
Simulated cores, a < 5 AU Simulated Planets 1.0 0.1200 Hot giants 600 Zl < -0.25 -0.25 < Z < 0 Cold giants l 0.8 0 < Zl < 0.25 0.1000 Zl > 0.25 400 0.0800 0.6
0.0600 200 Number of cores 0.4 0.0400 Frequency of planets 0 0.2 Cumulative Probability 0.0200 -1.0 -0.5 0.0 0.5 1.0 log Planet mass, M Earth 0.0000 0.0 -0.4 -0.2 0.0 0.2 0.4 0.1500 [Z/H]
Figure 11. Same as fig. 8 but now comparing the metallicity 0.1000 distribution of gas giant planets in the inner 5 AU (hot giants) with those in the ”cold” region, a>10 AU (red histogram). Note that cold giants show no metallicity preference. 0.0500 Frequency of cores The interpretation of this result is straightforward. 0.0000 Most of the fragments that stayed behind 10 AU did not -1.0 -0.5 0.0 0.5 1.0 come close enough to the parent star to experience tidal log Planet mass, M Earth forces su ciently strong to rip the fragments apart. There- fore, these planets survive irrespectively of how much peb- Figure 9. Number (top panel) and fractional (lower panel) mass distributions for cores found in the inner 5 AU for four di↵erent bles was accreted. They are therefore insensitive to the metal metallicity groups. content of the parent discs. TD z-correlations:12 Nayakshin as & Fletcherobserved
5.3 Most massive giants are metal insensitive Cores and low mass giants vs Zl 1.00 Simulated Planets, hot region because super Earths are the remnants of these disruptions: Finally, we come to the most massive planets studied in 1.0 no disruptions, no super-Earths. this0.1400 paper. A visualGiants, inspection moderate of themass top left hand corner of Figure 2 shows thatSuper metal Earths poor massive giants (Mp 10 MJ) We now investigate the relative importance of these two ⇠ are0.1200 about as abundant as metal rich planets of same mass. 0.8 e↵ects. The top panel of Fig. 9 shows the mass function of This appears true for planets at the inner disc edge and also 0.1000 cores found in our simulation in the inner 5 AU for four 0.10 in the inner few AU, so it may be general for the whole hot 0.6 metallicity bins as specified in the legend. This panel shows sample0.0800 of the most massive planets. Figure 12 shows that this is indeed the case. Similar to that most of the super Earths form at metallicity not too fig.0.0600 10, this figure shows how frequency of an initial frag- 0.4 dissimilar from the Solar metallicity (the blue and the green ment becoming a given type of planet changes with the host histograms). The curves are normalised by the total integral
Fractional outcome star0.0400 metallicity. Three groups of gas giants is considered in Frequency of planets 0.01 0.2 Cumulative Probability giving the total number of cores, of course. The bottom panel Giants, a = Rin fig. 12. The fraction of survived moderately massive giants Giants, Rin < a < 5 (the0.0200 blue diamonds curve) is a rapidly increasing function of the figure shows the distribution of frequency of planet Super Earths (roughly a power law z5/4, where z = z 10Zl ), reflect- masses for the curves in the top panel; the histograms on the All cores 0.0000 / 0.0 ing the strong positive correlation for the hot moderately bottom are normalised on unity for each metallicity bin. It is massive giants-0.4 discussed in-0.25.1. However,0.0 the black0.2 squares 0.4 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 § curve shows the survival fraction for[Z/H] more massive giants, clear from the bottom panel of fig. 9 that the mean mass of Zl N & Fletcher 2015 [Z/H] Mp > 5MJ. We see that the probability of these massive the core increases with metallicity rapidly while Zl < 0.25. Figure 8. The fractional distribution of gas giant planets (blue Figure 10. Frequency of a fragment becoming a planet of a given fragments surviving the disc migration phase inside the hot However, the mean core mass increases less between the two type, as shown in the legend, as a function of the host star metal- filled-inregion is histogram) actually flat and with super metallicity. Earths Further (red histogram) to that, the over metal- metal rich bins. There is thus indeed a certain saturation licity.• NoteAt thatlow at the z, highest most metallicity fragments bins, most fragments arelicitiesred destroyed crosses of the show host the stars. fraction — Onlyfew of the planets initialgiants fragments in the but inner in the 5lots AU are se- in the cores mass growth at high metallicities, although the are ableof to migratecores in to a = Rin and hence only a few super lected.massive The sample curves that of migrated the respective all the way colours to the show innermost the cumulative Earths are made. disc radius. The curve has a depression at metallicities just mean core mass still increases with Zl.Thuse↵ect (a) is not distributions of same planet groups. Note strong positive metallic- below the Solar value, which is to say that fragments around actually that strong. ity correlation for gas giants and absence of such for super Earths. At high z, very few fragmentsstars are of nearly disrupted Solar composition — are few the most massive likely to be The main driver of the poor correlation between super • See text in 5.1 for more detail. Figurecores 11 compares the metallicity distributions of the tidally disrupted§ before they arrive at a = Rin. Earths and host’s metallicity in our models turns out to be hot and cold giants. As was the case with super Earths dis- For the most massive fragments, therefore, very high or cussed in 5.1, the cold giants show little metallicity prefer- very low metallicity environments are actually pre↵errable (b), e.g., that the number of tidal disruptions is just too § ¯ ence.• ThePeak mean ofof the massive hot giant distribution core is at productionZl =0.12, (although — not intermediate by much, e.g., less than by z a factor of 2). This low at high Zl, yielding too few cores (although on average clearly showing a significant positive metallicity preference, bi-modalityFig. 8 of shows metallicity how preferences these two of groups high mass of planets giants are dis- they are more massive than the cores at lower metallicities). whereas for the cold giants we find Z¯l = 0.01. forming in the context of TD was hinted on in Nayakshin tributed over the host star metallicities. The blue line his- Figure 10 shows the frequency of the fragment becoming a c 2008 RAS, MNRAS 000,1–?? togram shows the giants, whereas the red histogram shows given planet type as shown in the legend versus metallicity the super Earths. The curves of the same colour show the of the host star. In particular, the black connected diamonds respective cumulative distributions with the scale on the show the frequency of obtaining a super Earth in the inner right vertical axis. It is evident that gas giants appear pref- disc. The red crosses show the frequency of the fragment erentially around metal-rich hosts, whereas super Earths migrating through all of the disc to r = Rin without be- are spread about the mean (zero, that is Solar) metallicity ing disrupted. Notice the anti-correlation between such un- roughly simmetrically. disrupted fragments and the number of super Earths. In par- As explained in Nayakshin (2015b) and papers I and II, ticular, at the highest metallicities, as much as 70 80% ⇠ the positive metallicity correlation for giants is due to peb- of our initial fragments manage to collapse and migrate all ble accretion rate onto the fragment being larger at higher the way in, avoiding tidal disruption. This of course must metallicities, which leads to the fragment contracting faster. mean that fewer core-dominated planets are made in this Faster contraction implies fewer tidal disruptions, and hence environment because there are fewer tidal disruptions. more gas giants surviving at higher metallicities. The physi- Summarising these findings, we conclude that super cal reason for pebble accretion being so influential in control- Earths do not correlate with metal abundance of host star ling the rate of the fragment’s contraction os that pebbles in our models because gas giant planets do. The presence bring in additional mass into the fragment (but not kinetic of a gas giant planet indicates that its predecessor, a pre- energy since they sediment onto the cloud gently or else they collapse molecular fragment, was successful in avoiding the break up in high speed collisions). Gas clumps dominated by tidal disruption. Since gas giants are most frequent at high molecular hydrogen turn out to be very sensitive to addition metallicities, gas fragment disruptions must be much less of mass in this way and collapse when the mass of the extra ubiquitous at high Zl, and hence there should be fewer super metals reaches 5% to 20% of the initial fragment mass. Earths. On the other hand, we note that the mean mass of ⇠ ⇠ This picture also has implications for metal overabundance the cores does increase with metallicity. Thus, super Earths in giant planets as a function of their mass as we shall see made by TD model may be said to correlate in mass (some- in 8. The more massive the fragment is, the hotter it is what weakly at high core masses) but not in numbers with § at birth, the less pebbles is required to bring it to the H2 the metallicity of the host star. dissociation instability point (when the central fragment’s The histogram distribution for our simulated planets temperature is 2000 K). shown in fig. 8 looks quantitatively similar to fig. 2 in Buch- ⇡ The metallicity correlation for super Earths turns out to have et al. (2012), even though we did not make any attempt be a much subtler matter. Fig. 8 shows that high metallicity to arrive at such an agreement specifically. environments are no more preferable for formation of cores in the mass range 2 M
c 2008 RAS, MNRAS 000,1–?? Z-CORRELATIONS OF SMALL THINGS
Sub-Neptune planets and debris disc are created when gas giants are destroyed —> They cannot correlate same way with z as giants! Debris disc correlations
Number of tidal disruptions with Mz > 0.1 Mj
Fletcher & N, in prep.
-0.6 [Fe/H] 0.6 Z-correlations
Observations TD CA
Gas giants Positive Positive Positive(?)
Sub-Neptunes No No ?
Debris Discs No No Yes Conclusion
✤ TD explains Z-correlations of exoplanets/debris discs better than CA
✤ TD pop. synthesis models are very promising 940 R. Helled, P. Bodenheimer / Icarus 211 (2011) 939–947
of a few thousand times Jupiter’s present radius (RJ), with hydrogen ent. At present, the topic of fragmentation’s sensitivity to metallic- being in molecular form (H2). The clump contracts quasi-statically ity is still unsolved. on time scales of 104–106 years, depending on mass, and as it con- Thus, metallicity can also be significant in the context of the tracts its internal temperatures increase. Once a central tempera- protoplanets’ evolution. Planetary metallicity (opacity) has a fun- ture of 2000 K is reached, the molecular hydrogen dissociates, damental role in governing the cooling timescale of the planetary and a dynamical collapse of the entire protoplanet occurs (the sec- object and therefore the protoplanet’s contraction. As a result, met- ond stage). The extended phase is known as the ‘pre-collapse stage’ allicity has a direct impact on the pre-collapse evolution of the (Decampli and Cameron, 1979), and during that phase the object is newly-formed planets, and possibly their survival. at most risk to be destroyed by tidal disruption and disk interac- In this section we present the pre-collapse evolution (ending tions. After the dynamical collapse the planet becomes compact when central temperatures reach 2000 K) for different planetary and dense, with the radius being a few times RJ. During this third masses assuming different metallicities. Extrasolar planets have stage it is therefore less likely to be disrupted, although the plane- been detected around stars with very different metallicities, with tary object still has the danger of falling into its parent star due to the metallicity of the parent stars ranging between [Fe/H] 1 À inward migration. The protoplanet then continues to cool and and [Fe/H] +0.5. Here, to model protoplanets with different contract on a much longer timescale (109 years). metallicities, we simply multiply the grain opacity, calculated with During the extended state the protoplanet is most vulnerable to an interstellar size distribution and solar abundances, by the disk torques and tidal encounters, and therefore its survival is corresponding metallicity. The Rosseland mean opacities are ob- questionable. Shortening the pre-collapse timescale may reduce tained from Pollack et al. (1985) and Alexander and Ferguson the risk of disruption since the transition to a ‘‘point-like” (gravita- (1994). Thus, to model the evolution of a planetary object with tionally bound) protoplanet occurs faster. The time scale of the [Fe/H] = 0.477, we multiply the solar grain opacity by a factor À pre-collapse stage is also important with respect to the final plan- of 1/3 everywhere. The planets are assumed to have solar abun- etary composition and structure. During the extended phase the dances of hydrogen and helium; the equation of state is essentially protoplanet can capture heavy elements in the form of planetesi- an ideal gas of neutral He and molecular H. The standard stellar mals and enrich the interior with these elements (e.g., Helled structure equations are solved (Bodenheimer et al., 1980), with et al., 2006). Cores can be formed in these objects by settling of surface boundary conditions appropriate for a gray photosphere heavy elements to the planetary center as long as the internal temperatures are low (e.g., Helled et al., 2008). As a result, a longer 2 4 2 L 4pR rBTeff and jRP g 1 extended phase could lead to further enrichment with heavy ¼ ¼ 3 ð Þ elements and would provide more time for forming cores. The where L is the total luminosity, R is the outer radius, is the more massive the protoplanet, the shorter the pre-collapse rB Stefan–Boltzmann constant, T is the surface temperature, and g, timescale (Helled and Bodenheimer, 2010, hereafter paper I). This eff P, and are, respectively, the acceleration of gravity, the pressure, may imply that in the disk instability scenario more massive plan- jR and the Rosseland mean grain opacity at the surface. etary objects are likely to survive while lower mass planets (if they The initial radii of the protoplanets were chosen to fall inside survive) will tend to be enriched with heavy elements and contain the tidal radius at 20 AU for a 3 M protoplanet. Since all of the cores. J planets have an initial radius of 2 AU they all fall within the Hill An important parameter that controls the contraction timescale radius at distances larger than 20 AU. At smaller radial distances, is the planetary opacity. Lower opacity leads to faster cooling and planets could be tidally disrupted. Our initial radii are in good therefore shortens the pre-collapse phase (e.g., Pollack et al., 1996). agreement with 3D numerical simulations of clump formation in Below we investigate the effects of opacity reduction due to differ- gravitationally unstable disks (Boley et al., 2010). ent metallicities (Section 2) and grain growth and sedimentation Figs. 1–3 present the evolutionary tracks for three planetary (Section 3) on the planetary evolution. The results are discussed Giant planets collapsemasses: slower 3, 5 and 7 MatJ, with higher solar, 3 solar and,opacity solar/3 composi- in Section 4 and the conclusions summarized in Section 5. Â tions ( [Fe/H] = 0, +0.477, and 0.477, respectively). More massive À protoplanets have shorter pre-collapse evolutions. Protoplanets 2. Planetary metallicity
3 MJup The question✤ ofContraction whether stellar due (and disk)to radiative metallicity cooling affects the frequency of giant planet formation by gravitational instabilities has been investigated by different authors. Boss (2002) varied 3.5 the assumed opacity indE thetot models by factors of 10 and1 0.1, and 3Z found little difference in the results.= As aL result,rad Boss (2002) sug- gested that gravitationaldt collapse is insensitive/ to theZ system’s metallicity. Cai et al. (2006a,b) investigated the sensitivity to opac- 3.0 ity in their models, but found that changing the opacity by factors ✤ of 0.25–2 led to enhancedGas fragment fragmentation contracts when faster the opacity at low was Z lowered. Meru and Bate (2010) also find, from three-dimensional 2.5 radiation-hydrodynamic simulations, that low disk opacity tends ✤ to allow the diskHelled to cool & faster Bodenheimer and promotes 11 predicted fragmentation a (Gammie, 2001); thereforenegative lower GI metallicityplanet vs is Z more correlation likely to result in fragmentation. Finally, Mayer et al. (2007) found enhanced frag- 0 50 000 100 000 150 000 200 000 mentation when the mean molecular weight l was increased, but Time years required rather large increases in l (with no change of opacity), from 2.4 to 2.7, to make a significant effect, and concluded that Fig. 1. Physical properties as a function of time for three Jupiter mass protoplanets with solar (blue), three times solar (red) and solar/3 (black) compositions. The increasing metallicity would result in more fragmentation. All dashed, dotted, and dot-dashed curves represent Log(Tc) (K), Log(R/RJup) (cm), and 26 1 these groups reached different conclusions in some sense, though Log(L/10 ) (erg sÀ ), respectively. (For interpretation of the references to color in it should be noticed that the investigations were somewhat differ- this figure legend, the reader is referred to the web version of this article.) (a) 600
500 0.3 < Mp < 2 ME All 400 Zl > 0 300 Zl < 0 Additional slides 200 100
Number of Earths 0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 log a [AU] (b) 2000 Obs. (Silburt et al) Planet to Star metallicity ratio 1500 1000
100 500 2 < Mp < 15 ME
Zl < -0.25 Super Earths -0.25 < Zl < 0 0 0 < Zl < 0.25 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 log a [AU] Zl > 0.25 (c) 250 200 50 ME < Mp < 5 MJ
10 150 star
/Z 100 Obs. Giants pl
Z 50 0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 log a [AU] 1 (d) 50
40 50 ME < Mp < 5 MJ 30 Obs. x 0.1 20 Giants 0.1 1.0 10.0 10 0 Mp [MJup] -1.0 -0.5 0.0 0.5 1.0 (e) log a [AU] 50 40 M > 5 M 30 p J 20
Super Giants 10 More results from N & Fletcher 2015 0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 log a [AU]