Mayer et al. 2002 Viability of Giant Planet Formation by Direct Gravitational Instability Roman Rafikov (CITA)

Gravitational Instability (GI) Dispersion relation for density waves in disk Get and instability when Toomre Q parameter Objects with size and mass form, with roughly equal thermal, gravitational and rotational energy contributions. Collapse further if thermal and rotational support can be removed.

does extremely poor job accounting for the cores of Neptune and Uranus Gravitational Instability requires extremely massive protoplanetary disks : between 4 and 20 AU (typical observed disk masses are within 100 AU) has been demonstrated to robustly operate only in simulation using isothermal equation of state Cons: does not naturally explain cores (and high-Z element enhancements) of Jupiter and Saturn does extremely poor job accounting for the cores of Neptune and Uranus Pros: allows planets to form quickly ( yr) explains distant planetary companions Mayer et al. 2002 TreeSPH, isothermal EOS,

Gravitational Instability Planet Formation GI generates overdensities but does not guarantee their strongly nonlinear development. Even if the disk is gravitationally unstable (Q<1) gas pressure and rotation can stop collapse. Thus, in general, To be able to form bound objects (planets) disk must be able to fragment, i.e. Gravitational Instability Planet Formation Gravitational Instability + Fragmentation = Planet Formation

Gravitational Instability Disk fragmentation Gammie (2001) showed that for fragmentation to set in one needs Gammie ‘01 No fragmentation Fragmentation 2D hydro When fragments lose thermal support at the same rate at which they collapse. Isothermal gas effectively has . 3D simulations confirm this general picture . Rice et al 2003

Disk cooling (radiative). Gravitational Instability Disk cooling (radiative). If the disk is optically thick (optical depth ) If the disk is optically thin ( ) General formula covering both possibilities where

Fragmentation + GI Express : Instability requires Gravitational Instability Fragmentation + GI Express : Instability requires Fragmentation condition then sets a lower limit on : This sets an upper limit on :

Thermodynamical constraints Gravitational Instability Thermodynamical constraints Rafikov 2005 fragmentation GI planet formation Constraint on naturally follows: As a result, giant planet formation by GI requires ( ~ 100 MMSN) ! !!!

These are rather unusual parameters for a protoplanetary disk! Gravitational Instability These are rather unusual parameters for a protoplanetary disk! These are the minimum requirements ! With realistic opacity find even more extreme requirements for giant planet formation by gravitational instability (even at 10 AU)! Incompatible with our knowledge of protoplanetary disk properties Supported by recent simulations (Mejia et al 2005, Cai et al 2006, Boley et al 2006) , but see Boss for alternative view Where (and when) could be possible: in the Galactic Center, in the outer parts of protoplanetary disks (100 AU), during the embedded (Class 0) phase (?)

Disk cooling (convective). Gravitational Instability Disk cooling (convective). Transport of energy from the midplane to the photosphere can also be done by convection (not radiation). Convection sets in when For if - convective (Lin & Papaloizou 1980) ( for thus convective). midplane photosphere For a given midplane the shortest is for the highest effective temperature realized for the most shallow Isentropic profile guarantees fastest possible convective cooling.

At the photosphere thus Gravitational Instability At the photosphere thus At the midplane so that for constant opacity and shallowest temperature gradient Then The only difference with the case of radiative cooling is in the exponent of otherwise expression for is the same!

For more general opacity find similarly (Cassen’93) Gravitational Instability For more general opacity find similarly (Cassen’93) and for convection. For and Important point is that still with so that again Analogous to the radiative case find that planet formation requires extreme properties of protoplanetary disks! ( Cf. Boss 2004 )

Gravitational Instability External Irradiation. External irradiation (by the central star or by dusty envelope) modifies thermal structure of the disk. It raises the photospheric temperature of the disk. Unlikely to affect how the disk cools – extra loss due to higher is compensated by the gain due to irradiation. Cooling is still going to be determined by and the temperature gradient that establishes during the nonlinear evolution of the fragments. In that case all previous arguments fully apply. moderate strong

Opacity gaps. Opacity gaps promote fragmentation: Gravitational Instability Opacity gaps. Alexander et al 2005 Opacity gaps promote fragmentation: contracting object heats up, enters the gap cooling time goes down fragment looses pressure support, collapses Johnson & Gammie 2003 Important only near the gap (initial K) Analytical arguments show that existence of opacity gaps still does not relax constraints on disk properties needed for planet formation (Rafikov, in preparation)

Compressed fragment still must reach for collapse Gravitational Instability but as well ! Compressed fragment still must reach for collapse In a compressed state column of material is higher – works against rapid cooling

None of the following seem to relax these requirements: Gravitational Instability Conclusions Planet formation by gravitational instability is possible only when collapsing objects can cool rapidly Simple analytical arguments (supported by simulations) demonstrate that this requires extreme properties of protoplanetary disks None of the following seem to relax these requirements: - Convective cooling - External irradiation - Realistic opacity with gaps Need more careful simulations with realistic physics to check these predictions – comparison projects!