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IV. Destructive Feedback in Planets MNRAS 461, 3194–3211 (2016) doi:10.1093/mnras/stw1404 Advance Access publication 2016 June 15 Tidal Downsizing model – IV. Destructive feedback in planets Sergei Nayakshin‹ Department of Physics and Astronomy, University of Leicester, Leicester LE1 7RH, UK Accepted 2016 June 8. Received 2016 June 8; in original form 2015 July 31 ABSTRACT The role of negative feedback from a massive solid core on its massive gas envelope in the Tidal Downsizing scenario of planet formation is investigated via one-dimensional planet evolution models followed by population synthesis calculations. It is shown that cores more massive Downloaded from than ∼10 M⊕ release enough energy to reverse contraction of their parent gas envelopes, culminating in their destruction. This process may help to explain why observed gas giant planets are so rare, why massive cores are so ubiquitous, and why there is a sharp rollover in the core mass function above ∼20 M⊕. Additionally, the short time-scales with which these massive cores are assembled in TD may help explain formation route of Uranus, Neptune and http://mnras.oxfordjournals.org/ the suspected HL Tau planets. Given the negative role of cores in assembly of gas giants in the model, an antimony is found between massive cores and gas giants: cores in survived gas giant planets are on average less massive than cores free of massive envelopes. In rare circumstances when core feedback self-regulates, extremely metal-rich gas giants, such as CoRoT-20b, a gas giant made of heavy elements by up to ∼50 per cent, can be made. Key words: planets and satellites: formation – protoplanetary discs – planetary systems. at University of Leicester on August 11, 2016 dominated fragments; (ii) massive cores are the sources of negative 1 INTRODUCTION and destructive feedback on their parent gas fragments. From a single star to a cluster of galaxies, large self-gravitating Point (i) has been discussed previously. In TD, Gravitational astrophysical systems are similar in two ways. First, gravitational Instability (GI) of cold massive protoplanetary disc hatches gas collapse is the first step towards formation of these systems (e.g. fragments at distances of tens to hundreds of au from the host star see Larson 1969; Sunyaev & Zeldovich 1972; White & Rees 1978; (Kuiper 1951;Boss1997; Rice, Lodato & Armitage 2005; Helled Fall & Rees 1985, for formation of stars, galaxies and globular et al. 2014; Kratter & Lodato 2016). As fragments migrate to- clusters). Secondly, most of these systems suffer from energetic wards the host (e.g. Baruteau, Meru & Paardekooper 2011; Michael, feedback released by very compact sub-parts of the systems. For Durisen&Boley2011; Tsukamoto et al. 2015), massive solid cores example, red giants are stars which experience a sudden increase in are assembled inside them by grain sedimentation (Helled, Podolak the rate of nuclear reactions in or near the core. They swell by up & Kovetz 2008; Nayakshin 2011). Fragments that are disrupted by to ∼100 times and eventually loose (e.g. Vassiliadis & Wood 1993) tidal forces from the host stars leave their rocky cores behind, which most of their envelope, leaving behind very dense cores composed are, by large, fully made planets with mass from sub-Earth to many of heavy elements, the white dwarfs. Negative feedback is also times larger (e.g. Boley et al. 2010; Nayakshin 2011). Fragments important during formation of stars and star clusters (e.g. Krumholz that managed to stay intact mature into jovian gas planets. et al. 2009; Dale & Bonnell 2008). Similarly, galaxies, including The main focus of this paper is point (ii). Although planets burn our own, miss a significant amount of primordial gas believed to no nuclear fuel while cooling off from their initial extended, high have been expelled by energetic feedback (Cen & Ostriker 1999) entropy, state (Bodenheimer 1974; Spiegel & Burrows 2012), the due to stars (e.g. Agertz et al. 2013) and supermassive black holes amount of specific energy needed to disrupt a very young planet (King & Pounds 2015). is tiny compared to that for a star or galaxy. The depth of the In this paper, it is shown that in the context of the recently devel- potential well of a pre-collapse planet is GMp/Rp, which is only oped Tidal Downsizing (TD) theory (Boley et al. 2010; Nayakshin ∼(10−5–10−4) of the Sun’s potential well, ∼G M/R. This vul- 2010a), planet formation process also follows these general rules nerability of very young gas giant planets to internal energy release since (i) all planets begin forming by gravitational collapse of gas- was already appreciated by Handbury & Williams (1975), who pro- posed that ice giants of the Solar system, Uranus and Neptune, were formed when their 10 M⊕ mass cores disrupted their ∼ Jupiter mass envelopes. Nayakshin & Cha (2012) also investigated E-mail: [email protected] a scenario in which core-induced disruptions of pre-collapse gas C 2016 The Author Published by Oxford University Press on behalf of the Royal Astronomical Society Self-destruction of giant planets 3195 giants may leave behind rings of minor (1 or more km sized) bod- total energy of the envelope, Etot, changes with time according to ies, similar to the Kuiper belt and the debris ring systems around the following equation, stars other than the Sun. However, thus far there has not been a dEtot GMp GMc wider investigation on what the role of negative core feedback on =−Lrad − M˙ z + M˙ c. (1) dt R R properties of planets made by TD is. p c The goal of this paper is to deliver such a study. We consider Here the first term on the right is the usual radiative luminosity of analytical arguments in Section 2, then go on to numerical experi- the planet, the next term is the change in the potential energy of ments with contracting isolated planets in 1D (Section 3) and planets the planet as solids settle on to it. This term will be called pebble embedded in an evolving protoplanetary disc. Finally, Section 4 in- ‘luminosity’ due to its physical units, troduces a population synthesis model that is used to study planet GM M˙ L = p z . formation outcomes of the model in a statistical sense. In Section 5, peb R (2) results of the simulations are discussed in detail. To expose effects p of core feedback in the sharpest possible light, population synthesis Finally, the last term in equation (1) is the accretion energy of is performed with three varying assumptions about massive core the core due to the accretion rate M˙ c, assumed to be released formation and its luminosity output. Finally, Section 6 considers instantaneously. One term that should be in equation (1) but is observational implications of this paper’s results. neglected is the kinetic energy that solids bring with them into the envelope. In the case of Core Accretion, this term is always Downloaded from small compared to the last one because the core’s potential is very 2 ANALYTICAL ARGUMENTS deep. In the case of TD, grains settle on to the planet at sedimen- tation velocity which is much smaller than the first term on the 2.1 Pebble accretion versus accretion of the core left (cf. section 2 in Nayakshin 2015b), so again making this term Newly made GI fragments have virial temperatures in hundreds of negligible. http://mnras.oxfordjournals.org/ Kelvin, when Hydrogen is molecular, and gas densities ∼10 or- ders of magnitude lower than the density of present day Jupiter 2.1.1 Core Accretion case (Bodenheimer 1974; Helled et al. 2008; Nayakshin 2010b). De- pending on fragment mass and dust opacity (e.g. Helled & Boden- In the most widely used scenario, planetesimals accrete on to the ∼ heimer 2011), it takes them 1 Myr to contract and collapse by H2 core efficiently, so that M˙ c = M˙ z. Furthermore, the envelope’s ra- molecule dissociation into the ‘hot start’ stage usually taken as the dius is orders of magnitude larger than Rcore (e.g. see fig. 1 in Pollack beginning of a GI planet’s life (e.g. Marley et al. 2007). The cool et al. 1996), and Menv Mcore in the most interesting pre-runaway and extended stage of GI fragment evolution is logically called the configuration. Thus, the energy balance for the envelope is well pre-collapse stage. To become a hot Jupiter, the fragment needs to approximated by collapse or else it is disrupted, typically at a few au distance from at University of Leicester on August 11, 2016 dE GM the star (Nayakshin 2010a). tot =−L + c M˙ . (3) dt rad R c Accretion of grains or planetesimals from the surrounding disc c (Boley & Durisen 2010; Boley, Helled & Payne 2011) may modify It is obvious from this equation that planetesimal accretion yields a the fate of the fragments strongly by changing its opacity (Helled & heating term since it increases Etot. The only physical way to counter Bodenheimer 2011), weight and energy balance Nayakshin (2015a). balance overheating of the envelope because of core’s luminosity is The range of possible outcomes here is very broad – from a more to radiate the excess heat away. This is not trivial; in order to allow rapid planet contraction to a slower one, and even a complete the envelope to collapse within the few Million years of the disc planet’s destabilization. Therefore, we pause here to explain the lifetime, the grain opacity in the envelope needs to be reduced by different sides of solid accretion on to a gas fragment. factors of ∼100 (Pollack et al. 1996; Helled & Bodenheimer 2014), In what follows we shall call ‘pebbles’ large grains of ∼10– perhaps due to grain growth (Mordasini 2014).
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