MNRAS 000,1{16 (2019) Preprint 24 February 2020 Compiled using MNRAS LATEX style file v3.0 Chemical Diversity of Super-Earths As a Consequence of Formation Jennifer Scora,1? Diana Valencia,2 Alessandro Morbidelli3 and Seth Jacobson4 1Department of Astronomy and Astrophysics, University of Toronto, Toronto, ON, Canada 2Centre for Planetary Sciences, University of Toronto, 1265 Military Trail, Toronto, ON, M1C 1A4, Canada 3Laboratoire Lagrange, Universit´eC^ote d'Azur, Observatoire de la C^ote d'Azur, CNRS, Blvd de l'Observatoire, CS 34229, 06304 Nice Cedex 4, France 4Department of Earth and Environmental Sciences, Michigan State University, East Lansing, MI 48824, USA Accepted XXX. Received YYY; in original form ZZZ ABSTRACT Recent observations of rocky super-Earths have revealed an apparent wider distribu- tion of Fe/Mg ratios, or core to mantle ratios, than the planets in our Solar System. This study aims to understand how much of the chemical diversity in the super-Earth population can arise from giant impacts during planetary formation. Planet forma- tion simulations have only recently begun to treat collisions more realistically in an attempt to replicate the planets in our Solar System. We investigate planet formation more generally by simulating the formation of rocky super-Earths with varying initial conditions using a version of SyMBA, a gravitational N-body code, that incorporates realistic collisions. We track the maximum plausible change in composition after each impact. The final planets span a range of Fe/Mg ratios similar to the Solar System planets, but do not completely match the distribution in super-Earth data. We only form a few planets with minor iron-depletion, suggesting other mechanisms are at work. The most iron-rich planets have a lower Fe/Mg ratio than Mercury, and are less enriched than planets such as Kepler-100b. This indicates that further work on our understanding of planet formation and further improvement of precision of mass and radius measurements are required to explain planets at the extremes of this Fe/Mg distribution. Key words: planets and satellites: terrestrial planets { planets and satellites: forma- tion 1 INTRODUCTION (Valencia et al. 2013). On the other hand, the composition of rocky super-Earths is a rich source of information with only Before the discovery of exoplanets, planet formation theo- minor degeneracies, and it has not yet been used to constrain ries were limited to explaining the Solar System and thus, formation scenarios. Therefore, with this study we propose were unintentionally biased. Now, with thousands of extra- to use composition of rocky super-Earths as another axes to solar planetary systems, there is a diverse set of data to test constrain formation theories. against formation theories. Models so far have been con- The reason for these fewer compositional degeneracies arXiv:2002.09042v1 [astro-ph.EP] 20 Feb 2020 structed to explain the masses and orbital architectures seen in rocky super-Earths is that the main determinant for the in the data (i.e. Hansen & Murray(2012); Ogihara et al. radius of the planet is the amount of iron (Valencia et al. (2015); Izidoro et al.(2017)), where composition is just a 2007b). In simple terms, rocky super-Earths are made of a by-product of the two. This is because composition is not a silicate-oxide mantle overlaying an iron core, and therefore useful constraint for most classes of planets. For exo-jovians, their relative masses can be inferred from measurements of the only possibility is a high H/He content, whereas for low- the total mass and radius. Hence, we can estimate the core mass exoplanets the possibilities are unconstrained (Valen- mass fraction (CMF) of the planet, and from this we can cia et al. 2007a; Rogers & Seager 2010; Vazan et al. 2018). infer the iron to silicon (Fe/Si) or the iron to magnesium In fact, the degeneracy in the composition of mini-Neptunes (Fe/Mg) ratios, where silicon and magnesium are used as arises from a trade-off between refractory material and water tracers of mantle material. In reality though, the above pic- ture is more complex because: planets generally are not ex- pected (1) to have pure iron cores { Si is a candidate among ? E-mail: [email protected] others for the Earth's core light alloy (Hirose et al. 2013), or © 2019 The Authors 2 Scora et al. (2) to be completely differentiated { some iron may remain The answer usually invokes a gas-poor environment due to in the mantle (e.g. Earth's iron content in mantle minerals is a timing issue: either because the gas disk lifetime is short about 10% (Ringwood 1970)). However, differences in total (Alibert et al. 2006; Terquem & Papaloizou 2007) or the radius for a given mass due to these complexities are minor planets formed late when there was little gas around (Lee & for rocky super-Earths. Plotnykov and Valencia (in prep) Chiang 2016; Dawson et al. 2015). Alternatively, the planets calculate a difference in radius of 0.5% and 0.8% in the ab- may accrete gas more slowly than expected (Lambrechts & sence of a light alloy in the core, and 2.6% and 2% due Lega 2017). Given that all these scenarios result in some gas to differentiation for Earth and a 5 ME -planet, respectively. envelope accretion, then how are bare rocky super-Earths Therefore, mass-radius data pairs for rocky super-Earths can formed? Two possibilities are (1) that rocky super-Earths provide valuable constraints on CMF. formed so slowly that by the time planets grew massive Furthermore, observational efforts in the last decade enough to capture gas, there was no gas around (Dawson have now yielded hundreds of rocky super-Earths with mea- et al. 2015), or (2) that they did acquire an envelope but sured masses and radii, with the more precise data pairs lost it, either due to atmospheric photo-evaporation (Owen amenable to compositional inference. The first transiting & Wu 2017; Lopez & Fortney 2013) or giant impact collisions super-Earths with measured masses were CoRoT-7b (L´eger (Inamdar & Schlichting 2016). The first theory does seem to et al. 2009; Southworth 2011; Barros et al. 2014; Stassun be challenged by the fast accretion timescales that close-in et al. 2017) and Kepler-10b (Batalha et al. 2011; Dumusque super-Earths experience (Ogihara et al. 2015) (also see Sec- et al. 2014; Fogtmann-Schulz et al. 2014; Van Eylen et al. tion4). No theory is without problems, especially once we 2016), which early on demonstrated the difficulty of collect- consider multi-planet systems (e.g. Kepler-36 (Carter et al. ing and interpreting high-quality data. The stellar activity 2012)) where both rocky super-Earths and mini-Neptunes of CoRoT-7 made it difficult to infer the mass of the planet exist with similar masses, and, of course, the same disk life- with high precision (Hatzes et al. 2011; Barros et al. 2014), time and properties. However, any successful formation the- while instead asteroseismology data on Kepler-10 allowed ory not only needs to explain the mass range and orbital for an exquisite precision of ±0:003R⊕ in planetary radius periods of super-Earths as a population distinct from mini- (Fogtmann-Schulz et al. 2014). Kepler yielded thousands of Neptunes, but it also needs to account for their chemical super-Earths' with measured radii, and hundreds of them diversity in terms of the Fe/Mg ratios seen in the data. have been followed up for mass estimates. Although, typical With this in mind, we focus on the formation of rocky data is more precise in radius than it is in mass, we are finally super-Earths and the role of collisions in growing planets at a stage where there is enough quality mass-radius data with the observed chemical make-up. Our interest in plan- that we can infer the composition of rocky super-Earths as etary collisions is highly motivated by the fact that we ob- a population, and use it to constrain formation scenarios. serve a spread in the Fe/Mg ratios for these planets which We propose to use this chemical data to inform planet seems to be beyond the spread of stellar abundances (see formation theories. That is, any successful theory that forms Section2), suggesting these planets do not have a primor- super-Earths needs to explain their chemical diversity as dial composition. seen from the Fe/Mg ratios, as well as the distribution of Collisions may be responsible for significantly altering masses (5-15 M⊕) and semi-major axes (0.01 - 0.2 AU) seen the composition of growing planets (Asphaug et al. 2006), in rocky super-Earths from the NASA Exoplanet Archive as and can vary from super-catastrophic outcomes where the of July 2019. Eccentricities and inclinations need to be ac- target is heavily disrupted to perfect mergers of the two in- counted for as well, although in reality these quantities are volved bodies and anything in between. Typical formation highly unconstrained for most low-mass exoplanets. models of growing planets by gravitational interactions in- When attempting to form super-Earth and mini- volve N-body codes that only consider perfect mergers dur- Neptune planets starting from the minimum-mass solar neb- ing encounters (for a summary see Raymond et al.(2014); ula (MMSN), followed by standard core-accretion, fails to Bond et al.(2010)). These models are severely limited for reproduce the exoplanet low-mass population (Raymond & investigating the chemical diversity of planets. It is only re- Cossou 2014). Instead, efforts to explain the formation of cently that formation simulations have begun accounting for these low-mass planets fall into two categories: either they more realistic collisions (Kokubo & Genda 2010b; Cham- form outside their current location and migrate inwards bers 2013; Haghighipour & Maindl 2019).