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Tidal Downsizing Model. II. Planet-Metallicity Correlations

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Tidal Downsizing Model. II. Planet-Metallicity Correlations Mon. Not. R. Astron. Soc. 000, 1–13 (2008) Printed 26 March 2021 (MN LATEX style file v2.2) Tidal Downsizing model. II. Planet-metallicity correlations Sergei Nayakshin Department of Physics & Astronomy, University of Leicester, Leicester, LE1 7RH, UK E-mail: [email protected] Received ABSTRACT Core Accretion (CA), the de-facto accepted theory of planet formation, requires for- mation of massive solid cores as a prerequisite for assembly of gas giant planets. The observed metallicity correlations of exoplanets are puzzling in the context of CA. While gas giant planets are found preferentially around metal-rich host stars, planets smaller than Neptune orbit hosts with a wide range of metallicities. We propose an alternative interpretation of these observations in the framework of a recently developed planet formation hypothesis called Tidal Downsizing (TD). We perform population synthesis calculations based on TD, and find that the connection between the populations of the gas giant and the smaller solid-core dominated planets is non linear and not even monotonic. While gas giant planets formed in the simulations in the inner few AU region follow a strong positive correlation with the host star metallicity, the smaller planets do not. The simulated population of these smaller planets shows a shallow peak in their formation efficiency at around the Solar metallicity. This result is driven by the fact that at low metallicities the solid core’s growth is damped by the scarcity of metals, whereas at high metallicities the fragments within which the cores grow contract too quickly, cutting the core’s growth time window short. Finally, simulated giant gas planets do not show a strong host star metallicity preference at large separa- tions, which may explain why one of the best known directly imaged gas giant planet systems, HR 8799, is metal poor. Key words: 1 INTRODUCTION than positive giant planet–metallicity correlation since plan- ets’ radiative cooling is the fastest at low dust opacities Given the bewildering diversity of exoplanet system archi- (Helled & Bodenheimer 2011), increasing planet’s chances tectures (e.g., Batalha et al. 2013; Winn & Fabrycky 2014), of survival. it is clear that the outcome of planet formation is a highly arXiv:1502.07585v1 [astro-ph.EP] 26 Feb 2015 However, there are both observational and theoretical stochastic process. Any statistical trends found in the ob- reasons to study the issue further. Radial velocity observa- served planetary populations have special significance as tions show that Neptune-mass planet occurrence does not they testament to planet-forming processes so robust that seem to correlate with the host star’s metallicity for FGK they rise above the stochasticity. A successful planet forma- stars (Sousa et al. 2008). Similarly, transit method observa- tion theory must reproduce such trends. tions with Kepler, sensitive to the planet’s radius rather than Metallicity correlations of the observed planets is one its mass, show (Buchhave et al. 2012) that planets smaller such correlation. Giant planets are detected much more fre- than 4R⊕ form around hosts with a wide range of metallic- quently around metal-rich stars than around metal-poor ities, with the average close to the Solar metallicity. This is ones (Gonzalez 1999; Fischer & Valenti 2005). This correla- clearly surprising in the context of CA, since these smaller tion has been argued to provide a direct support to Core Ac- planets are the precursors of the gas giant planets. If CA’s cretion theory for planet formation (e.g., Pollack et al. 1996) explanation for the positive gas giant planet correlation with since metal-rich environments assemble massive cores much metallicity is correct then there should be more cores at more readily (e.g., Ida & Lin 2004, 2008; Mordasini et al. higher metallicities, which is not what is observed. 2009). These cores are the crucial step towards forming On the theoretical side, several important extensions a gas giant planet in CA framework, thus a positive gi- to the classical variant of the Gravitational Instability (GI) ant planet–metallicity correlation ensues. Gravitational disc model for planet formation have been recently proposed. Instability model for planet formation (e.g., Boss 1998; In particular, GI model that includes planet migration and Helled et al. 2013) was argued to produce a negative rather pebble accretion was showed to produce a strong posi- c 2008 RAS 2 S. Nayakshin tive and not negative correlation with the star’s metallicity more rapidly (e.g., see Nayakshin 2015a). Also, radiative col- (Nayakshin 2015a,b) for coreless gas giant planets. The goal lapse of H2-dominated fragments produces a negative planet of this paper is to extend this recent work on giant planets frequency – metallicity correlation (Helled & Bodenheimer with cores and also on core-dominated (smaller) planets and 2011) because radiative cooling is more rapid at low metal- to compare the results with the observations. licities. That is clearly at odds with observations (Gonzalez The key reason why GI theory may require a major 1999; Fischer & Valenti 2005). overhaul is the realisation that GI gas fragments can also We (Nayakshin 2015a), however, considered accre- migrate from ∼ 100 AU all the way into the inner disc tion of ∼< 1 cm sized grains (usually called ”pebbles”; (Boley et al. 2010). While planet migration was a standard Johansen & Lacerda 2010; Ormel & Klahr 2010) onto the feature for the CA model since 1996 (Lin et al. 1996), GI pre-collapse fragments. While gas has pressure gradient planets were somehow thought to not migrate until recently. forces that may prevent its accretion from the proto- If this were true than GI could at best account for important planetary disc onto the fragments (e.g., Nayakshin & Cha but rare giant planet systems like HR 8799 imaged directly 2013), pebbles weakly coupled to the gas by aerodynam- (e.g., Marois et al. 2008), and could never explain the Solar ical forces can still accrete onto the fragment in an anal- System: massive self-gravitating proto-planetary discs can ogy to the pebble accretion process onto massive solid cores hatch clumps only at R ∼> many tens of AU (e.g., Rice et al. (Lambrechts & Johansen 2012) in the context of the CA 2005; Rafikov 2005). model. However, simulations, starting with Vorobyov & Basu Surprisingly, pebble accretion on GI fragments was (2005, 2006), showed that massive gas fragments do migrate found to accelerate their contraction despite increasing their inward. Furthermore, Boley et al. (2010) suggested a new metallicity and hence opacity. Physically, addition of peb- way of forming terrestrial-like planets inside ∼ a few Jupiter bles to the fragment increases its weight without increasing masses gas clumps by grain growth and sedimentation (see its thermal energy1. Since pre-collapse molecular gas frag- also Williams & Crampin 1971; Boss 1997), and then releas- ments are polytropes with an effective polytropic index γ ing them back into the disc by destroying the gas clumps edging ever closer to the unstable value of 4/3 as the cen- via tidal forces from the host star. Nayakshin (2010a) used tral temperature of the fragment increases towards 2000 K analytical estimates of the relevant processes and arrived at (see Nayakshin 2015a), addition of a relatively small, ∼ 10%, similar ideas, proposing the Tidal Downsizing (TD) hypoth- amount of mass in metals to the fragment usually tips it over esis for formation of all types of planets observed so far. into collapse. Higher metallicity environments provide larger The key question for a planet forming in the framework pebble accretion rates, hence Nayakshin (2015b) found, via of the TD hypothesis is how does the clump’s inward mi- a population synthesis like study of coreless gas fragments, gration time scale, which may be as short as ∼ 104 years that the frequency of gas giants survived the initial tidal (Baruteau et al. 2011; Michael et al. 2011), compare with disruption increases as metallicity of the host increases. the time scale for its internal evolution? If the fragment con- An important issue not considered by Nayakshin traction time is shorter than the inward migration time, then (2015a,b) is formation of a core within the fragment. If peb- the fragment collapses, becoming a bona fide ”hot start” bles entering the fragment accrete onto the core, the core’s protoplanet, which may mature into a gas giant planet. If accretion luminosity may be significant and this may lead the fragment contraction time is long, then the host’s tidal to expansion of the fragment instead of its contraction. A forces catch up with the fragment when the latter migrates similar effect – accretion of planetesimals onto the grow- too close to the star, and the fragment is disrupted. The ing core – is well known in the context of the CA model fragment’s short existence may however not be all in vain as and has to be taken into account when determining the fate there could be a remnant. If grains within the fragment had of the planet (e.g., Pollack et al. 1996; Alibert et al. 2005). a sufficient time to grow and sediment to the centre, getting Nayakshin (2015c, paper I hereafter) has recently presented locked into a self-gravitating massive core (see also Kuiper numerical algorithms that extend the work of Nayakshin 1951; McCrea & Williams 1965; Williams & Crampin 1971; (2015b) by adding the core formation and growth inside the Boss 1997; Helled & Schubert 2008), then the remnant of pre-collapse fragments. the disruption is the core – a practically ready rocky planet. Here we use that framework to study the planet fre- No planetesimal accretion is required for the planet to sur- quency of survival versus metallicity dependence for all types vive at that stage, although ”veneer accretion” of them or of planets rather than just the coreless giants.
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