Giant Planet Formation by Gravitational Instability

“There are essentially two main and competitive planet formation models: the core-accretion model (e.g. Pollack et al. 1996; Ida & Lin 2004; Mordasini et al. 2009) and the disk instability model (e.g. Boss 1997;2002).”

“…e.g., Tomley et al. &1991, 1994 ; Adams Benz or if the initial temperature of the disk is very1992) low (see, e.g., & Ro z5 yczka InLaughlin 1996 ; Boss 1997). adiabatic calculations, the strongest instabilities lead to mass and angular momentum transport through the disk, which may radically…”

“Other aspects are of importance if a planet forms via gravitational instability (GI; see Boss 1997).”

“Rapid formation of a giant planet in a gravitationally unstable inner disk is nearly instantaneous (Boss 1997), although only a minority of disks may be massive enough to suffer gravitational instability (Andrews & Williams 2007).”

“…explain the lower mass planets found to be orbiting with short periods (Pollack et al. 1996; Hubickyj et al. 2005), and gravitational instability during the early life time of a massive protoplanetary disc to explain the systems with long period gas giant planets (Boss 1997; Forgan and Rice 2013).”

“Companions near or below the deuterium-burning limit might form like stars in gravitational collapse or fragmentation (Boss 1997; Vorobyov 2013), by core-accretion in-situ (Pollack et al. 1996; Alibert et al. 2005), or they might form in a location more conducive to planet formation and…”

“Formation via gravitational instability (Boss 1997, Rafikov 2005, Boss 2006, Stamatellos & Whitworth 2008) require large massive disks (>0.2-0.35 M⊙) and thus also do not provide an obvious solution, given the low mass of the primary star.”

“…disk, disk fragmentation, which is a promising mechanism for the formation of binaries or wide-orbit planets (Marois et al. 2010), possibly occurs in the subsequent evolution (Boss 1997; Inutsuka et al. 2010; Machida et al. 2011a; Tsukamoto & Machida 2011, 2013; Tsukamoto et al. 2013b, 2015b).”

“…the evolution of the gasto-dust ratio, the evolution of gas surface density distribution with time and the gas dispersal timescale all influence how many and what types of planets can form in a stellar system (e.g., Pollack et al. 1996; Boss 1997; Mordasini et al. 2012; Alexander et al. 2014).”

“A gravitational instability in a disk (Boss 1997) would be a fast process but probably is not achievable, except in the outer regions of a disk (beyond 30 AU; see x 2.1), because of the requirement that the cooling rate by radiation be comparable to or shorter than the orbital timescale (Gammie…”

“Several formation mechanisms have been proposed to account for the diversity of these objects: core accretion (Pollack et al. 1996), gravitational instability (Boss 1997), and binarylike formation.”

“Another possibility is that gas giant-planet formation occurs by the disk instability model (Boss 1997, 1998, 2010).”

“…in which particles build from millimeter-sized dust grains to kilometer-sized planetesimals and eventually to planetary cores (Wetherill 1990); and gravitational instability, in which part of a massive disk quickly collapses to form giant planets by gravitational self-attraction (Boss 1997).”

“In the alternative disk-instability scenario, a rather massive protoplanetary disk is subject to gravitational instabilities leading to the direct formation of (possibly multiple) Jupiter-sized objects (Cameron 1978; Boss 1997, 2000; Armitage & Hansen 1999; Mayer et al. 2002; Lufkin et al. 2003).”

“…formation mode; in the former case the planet is likely to have been formed via core accretion of solid material and subsequent accretion of a massive atmosphere (Pollack et al. 1996), while the absence of a core supports the gravitational collapse hypothesis of giant planet formation (Boss 1997).”

“Also, many of the planets seem to move in orbits with eccentricies significantly larger than those observed in the Solar System (where e < 0.1, except for Mercury which has e ∼ 0.2), This result poses a problem for the planet formation theories of Core Accretion (Pollack et al. 1996) and Disk Instability (Boss 1997),…”

“Such discontinuities may artificially favor gas giant formation by disk instability, because isothermal (Γ1) gas behavior favors fragmentation (Boss 1997, 2000; Pickett et al. 1998).”

“Conversely, in the gravitational instability (GI) paradigm (Cameron 1978; Boss 1997), planetary-mass objects are assembled in a top-down fashion through fragmentation of the gaseou protostellar disc.”

“…considerations based on the competing gravitational instability model where giant planets form directly from a gravitational instability in the protoplanetary gas disc (Cameron 1978; Boss 1997) were recently made in Janson et al. (2011, 2012); Forgan & Rice (2013) and Galvagni & Mayer (2013).”

“In the disc instability scenario (Kuiper 1951; Cameron 1978; Boss 1997),giant planets form through a gravitational instability in a gaseous disc.”

“With outer disk temperatures of ∼28 K (Kawakita et al. 2001), such a disk would be marginally gravitationally unstable to the growth of density per- turbations that would form strong spiral arms and possibly lead to the rapid formation of Jupiter (Boss 1997, 2002).”

“Dynamical instability models develop the idea that part of an evolving disk can collapse directly into a Jupiter-mass planet (e.g., Ward 1989; Cameron 1995; Boss 1997, 2000).”

“While we focus here on core accretion formation, which is likely most relevant for planets forming closer than several tens of AU from their host star, formation through gravitational instability (Boss 1997) may be important at larger orbital distances (Boley 2009).”

“More recently, models were also based on core accretion with pebbles (Ormel & Klahr 2010; Johansen & Lambrechts 2017), and on planet formation via gravitational instability (Kuiper 1951; Cameron 1978; Boss 1997).”

“In the disk instability model, giant planets directly form from gas as a result of gravitational instabilities in a cold disk with a mass comparable to that adopted in the core accretion model (Boss, 1997; Mayer et al., 2002).”

“It seems very difficult to explain the in situ formation of this object in a disk by core accretion (Pollack et al. 1996) or disk instability (Boss 1997).”

“…Boulder CO 80309; pja@jilau1.colorado.edu 3Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder CO 80309 10 − 30 M⊕ core predicted by Pollack et al. (1996), and has led to renewed interest in models for massive planet formation via disk instability (Boss 1997).”

“…shocks to such an extent that disk temperatures increased enough (to 200 K at 10 AU) not only to prevent gas giant planet formation by disk gravitational instability (Boss 1997) but also to vaporize volatile solids and thereby prevent gas giant planet formation by core accretion (Mizuno 1980).”

“Although revived by Boss (1997), the disc instability model suffered a blow when it was realized that very efficient cooling was needed for it to operate (Gammie 2001).”

“For the color equation (e.g., Foster & Boss 1997), which gives an Eulerian description of the movement of tracers (representing the dust grains carrying the short-lived isotopes) throughout the nebula, this means adding to the right-hand side of the equation a diffusion term: a second space…”

“The first multidimensional hydrodynamic models used the ‘‘locally isothermal’’ approximation (Boss 1997, 1998, 2000; Nelson et al. 1998; Pickett et al. 1998), which is most permissive of clump formation.”

“…based on two scenarios: (1) disk instability, which states that planets form through the collapse and fragmentation of the circumstellar disk (Boss 1997; Cameron 1978), and (2) core accretion, which states that a planetary core forms first through the slow accretion of solid material and…”

“Although the model we present is the current paradigm, we note that there exists an alternate “top-down” model for giant planet formation that invokes gravitational instability in the gas disk (Boss 1997).”

“Most theories presume that planets grow by accretion of small planetesimals in a gaseous circumstellar disk (Safronov 1969; Goldreich & Ward 1973; see also Lissauer & Stewart 1993, Boss 1997, and references therein).”

“…favor the formation of planets within a protoplanetary disk by accretion of solids, building up a 10 to 15 M⊕ core followed by rapid agglomeration of gas (Pollack et al. 1996; Alibert et al. 2004), or by gravitational instability of the gas (Boss 1997; Stamatellos & Withworth 2008; Vorobyov 2013).”

“A disk fragmentation scenario (Boss 1997; Nero & Bjorkman 2009; Dodson-Robinson et al. 2009; Helled & Bodenheimer 2009) may be able to more naturally explain the massive planets and their location.”

“In thismechanism, matter accumulates in the vortex until it is dense enough to collapse into a planet through gravitational self-attraction (Boss 1997).”

“Technique Previous calculations of disk instabilities by Boss (1997, 1998, 2000, 2001, 2002a, 2002b, 2003, 2004) all used uniformly spaced radial grids.”

“Indeed the companions to 70 Vir (M sin i = 6.8 MJUP ) and to HD114762 (M sin i = 11 MJUP ) may also represent “brown dwarfs” (Marcy & Butler 1996, Mazeh et al. 1997, Latham et al. 1989, Boss 1997).”

“The occurrence and properties of planets formed in binary systems may also provide a way to discriminate between the two most widely supported planet formation models: core accretion (e.g., Pollack et al. 1996) and gravitational instability (e.g., Boss 1997; Mayer et al. 2002).”

“Two models of giant planet formation have gained preeminence over the last decade: core accretion theory (reviewed by Lissauer 1993) and the disk instability mechanism proposed by Boss (1997).”

“…1996) occur on timescales of ∼ 1– 10 Myr, comparable with or longer than the age of the system; the much more rapid gravitationalinstability mechanism (Boss 1997, 2000) occurs on timescales orders of magnitudes shorter, and may thus perhaps be favored (see Baraffe et al. 2010, for a brief overview…”

“However, in systems where giants were formed through GI (Boss 1997), such an association would be coincidental.”

“…theories of giant planet formation, because the core accumulation scenarios (Pollack et al. 1996; Wuchterl et al. 2000; Alibert et al. 2004) require at least a few million years for a core to form, whereas planet formation from a disk instability (Boss 1997;Mayer et al. 2002) can require much less.”

“Thermal Energy Generation and Dissipation In this work we relax the common practice (see e.g. Paper I , Pickett et al. 1998, Boss 1997) of predefining the temperature or adiabatic constant, K, at each location in the disk.”

“In contrast with the core accretion model, giant planets form rather rapidly in tens of thousand years directly from gas as a result of gravitational instabilities in a disk (Boss 1997; Mayer et al. 2002).”

“One possible alternative to form giant planets at large orbital separation (40–100 au) is by the gravitational instability (Boss 1997; Clarke 2009).”

“Another possible pathway to form giant planets is via gravitational instability (e.g., Boss 1997, 2001).”

“Equations (12) indicate that Q• ∝∼ r−3/4, 13 implying that like in the case of circumstellar nebulae (see e.g., Boss 1997), gravitational collapse is more easily activated in the outer regions of our model circumplanetary disk.”

“For both objects, the probable ages correspond roughly to the timewhen grain growth into larger bodies (i.e., cometesimals) has been operating, and in some models (Boss 1997) planetary embryos and perhaps true planets have already formed.”

“…by a type of gravitational disk instabilities leading to a “top-down” collapse and rapid formation of the gas giant without the need of a rocky core (e.g. Boss 1997), reliable theoratical predictions on the frequency of planetary systems depending on initial conditions like stellar primary and…”

“…financial support of the W.M. Keck Foundation. sible (and non-mutually exclusive) routes have been proposed: core accretion plus gas capture (Pollack et al. 1996; Alibert et al. 2005), disk instability (Cameron 1978; Boss 1997), and direct collapse from molecular cloud fragmentation (Bate 2009).”

“…is the regime in which the giant planet/brown dwarf boundary is located, this has interesting ramifications for planet formation theory, in particular for the canonical disc instability theory (Boss 1997), and the related, more recent tidal downsizing theory (Boley et al. 2010; Nayakshin 2010).”

“A well-known stability criterion for differentially rotating discs was introduced by Toomre (1964), and is frequently used to understand simulation results (Boss 1997).”

“The discovery of extrasolar giant planets led to the reinvigoration of the disk fragmentation hypothesis, which states that giant (exo)planets may form as a disk gravitational instability that collapses on itself in the outer protoplanetary disk (Boss 1997, 2000).”

“The alternative giant planet formation mechanism is disk instability (Boss 1997).”

“This treatment remedies a major shortcoming of previous models (Nelson et al. 1998; Pickett et al. 1998; Boss 1997) which used a “locally isothermal” or “locally adiabatic” approximation to show that relatively lowmass disks can undergo fragmentation and/or collapse, despite earlier claims…”

“Determining what sets thbound- ⋆ E-mail: wkmr@roe.ac.uk ary between these outcomes is important for understanding angul r momentum transport (Armitage 2011) and planet formation inprotoplanetary disks (Boss 1997), and star formation in discs around AGN (Bonnell & Rice 2008).”

“This has become known as the disk instability hypothesis for the formation of gas giant planets (Kuiper 1951; Cameron 1978; Boss 1997, 1998).”

“…model, one can also imagine a hybrid scenario wherein the first giant planet forms rapidly via the competing disk instability model (Cameron 1978; Boss 1997; Mayer et al. 2002), thus avoiding the Type I issue altogether, and subsequently facilitates the formation of its successors by core…”

“…of protoplanet embryos: gravitational instability followed by fragmentation, which forms gas giant planets, or (sub-)stellar mass companions (e.g., Boss 1997; Kratter et al. 2010); and bottom-up growth by core accretion, which forms terrestrial and icy planets, or the cores of giant planets…”

“There are two ways in which giant planets have been hypothesised to form: core accretion (Safronov 1969; Goldreich & Ward 1973; Pollack et al. 1996) and gravitational instability (Cameron 1978; Boss 1997; review by Durisen et al. 2007).”

“It has been hypothesisized that giant planets can form by gravitational fragmentation of protoplanetary gas disks (Boss, 1997).”

“There are two main scenarios for giant planet formation known as “core accretion” (e.g., Bodenheimer and Pollack, 1986; Pollack et al., 1996; Alibert et al., 2005) and “disk instability” (e.g., Boss, 1997, 2000; Mayer et al., 2002; Durisen et al., 2007).”

“The gravitational fragmentation of protoplanetary discs is key to the disc instability theory of giant planet formation (Boss 1997).”

“…the disc instability model, in which giant planets arise in only a few disc orbital times (less than a thousand years) from the fragmentation of a massive, gravitationally unstable disc (Boss 1997, 2002; Pickett et al. 2000, 2003) has gained new attention (Mayer et al. 2002; Rice et al. 2003a,b).”

“The Gravitational Instability (GI) model for giant planet formation (e.g., Bodenheimer 1974; Boss 1997) is one of the two well known models for planet formation (e.g., Wetherill 1990).”

“Rice et al. (2003c)M 5Mp J and Rafikov (2005) argue instead that giant planets formed by disk instability (e.g., Boss 1997, 2001, 2004; Mayer et al. 2002) should preferentially populate the high-mass tail ( )M 5Mp J of the planet mass distribution, while Mayer et al. (2004) indicate the possibility…”

“Whether the planets were formed due to core accretion (Pollack et al. 1996) or gravitational instability (Boss 1997), the composition of the star and planet are inextricably linked.”

“Simulations by Boss (1997, 2007) predict lowerdensity and colder protoplanets than the simulations of Mayer et al. (2002, 2004).”

“Therefore, the model of Boss (1997, 1998) did not seem to find support from detailed independent simulations.”

“…disk; how formation occurs, i.e., via the classical core accretion process (Pollack et al. 1996) or a modified version of that process (e.g., pebble accretion, Lambrechts & Johansen 2012) or direct gravitational collapse (Boss 1997); and the properties of the suspected circumplanetary disks (CPDs).”

“…on 19 February 2018 Modern planet formation theories, such as the core accretion scenario (e.g. Mizuno 1980; Bodenheimer & Pollack 1986) and the disc-fragmentation scenario (e.g. Boss 1997), were inspired by the Nebular Hypothesis proposed independently by Immanuel Kant and Pierre-Simon Laplace.”

“An alternative explanation for the observed populations calls for the disk instability process (e.g. Boss 1997).”

“On the other hand, the “disk instability” model suggests that giant planets may be the outcome of direct gravitational instability of the gas (Boss 1997; Mayer et al. 2002).”

“Their range of masses (2–15MJ) and orbital separations (10–150 au) make them key probes of jovian planet formation models (e.g. Boss 1997; Kenyon and Bromley 2009).”

“INTRODUCTION Gas Giants form in protoplanetary disks, through core accretion followed by runaway gas accretion, or through gravitational instabilities (Lissauer 1987; Boss 1997; Boley 2009).”

“Disk instabilities, on the other hand, can form planets much more quickly ( 1 Myr), well before circumstellar disks are dispersed (Boss 1997, 2004; Mayer et al. 2002; Meru & Bate 2010; but see also Stamatellos & Whitworth 2008; Meru & Bate 2011).”

“Boss (2002) varied the assumed opacity in the models by factors of 10 and 0.1, and found little difference in the results. As a result, Boss (2002) suggested that gravitational collapse is insensitive to the system’s metallicity. Cai et al. (2006a,b) investigated the sensitivity to opacity in their models, but found t…”

“…et al. 1996; Alibert et al. 2005; Dodson-Robinson et al. 2009) and models of disk instability are most efficient at smaller separations of tens of AU where protoplanetary disks are both massive and cold enough to gravitationally collapse (Boss 1997; Mayer 2002; Kratter et al. 2010; Boss 2011).”

“Gravitational instability was thought to be the only potential pathway towards in-situ formation at tens of au (Boss 1997; Boley 2009), but the revisited growth timescale of embryos through pebble accretion could be fast enough to form ice giants or the core of gas giants during the disc lifetime…”

“…et al. 2004), where gas from the protoplanetary disk is accreted around a previously formed rocky/icy core; and the disk instability model (e.g. Boss 1997; Mayer et al. 2002), where a planet is formed because of a direct gravitational instability in the protoplanetary disk, in the same way as…”

“In contrast, the Gravitational Instability (GI) model suggests that giant planets form “big”, e.g., directly by contraction of gaseous condensations born in a massive selfgravitating disc (e.g., Bodenheimer 1974; Boss 1997).”

“On the other hand, Laughlin & Bodenheimer (1994), Boss (1997, 2002),Mayer et al. (2002, 2004), Johnson&Gammie (2003), Pickett et al. (2003), and Mejia et al. (2005) describe the evolution of gravitationally unstable gaseous protoplanetary disks using two- and three-dimensional hydrodynamic…”

“…perhaps the first direct evidence for large-scale gravitational instability in a circumstellar disk, and they suggest that the competing mechanism for gas giant planet formation, disk gravitational instability (Cameron 1978; Boss 1997, 2003), might be able to operate at distances of∼100 AU or more.”