Gravitational Instability

1. Gravitational Instability Can Giant Planet Form by Direct Gravitational Instability? Roman Rafikov (CITA)

2. Gravitational Instability 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. Gravitational Instability (GI)

3. Gravitational Instability • Pros: • allows planets to form quickly ( yr) • explains distant planetary companions Mayer et al. 2002 • 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 TreeSPH, isothermal EOS, • 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

4. Gravitational Instability • 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 Planet Formation

5. Gravitational Instability Gammie ‘01 Fragmentation No 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 fragmentation Gammie (2001) showed that for fragmentation to set in one needs

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

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

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

9. 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 an alternative view.

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

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

12. Gravitational Instability For more general opacity need for convection (Lin & Papaloizou 1980; Rafikov 2006). In cold gas opacity is determined by dust so that and convection is possible. Important point is that still with so that again Cooling time by convection is (Rafikov 2006)

13. Gravitational Instability Rafikov (2006) Alexander et al 2005 MMSN With realistic opacities find that planet formation still requires extreme properties of protoplanetary disks! ( Cf. Boss 2004 )

14. Gravitational Instability Rafikov 2006 Rafikov 2006 Photospheric temperature Disk and clump masses Where (and when) formation of compact objects by GI could be possible: in the Galactic Center, in the outer parts of protoplanetary disks (100 AU), during the embedded (Class 0) phase (?).

15. Gravitational Instability • 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 External Irradiation.

16. Gravitational Instability Alexander et al 2005 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) Opacity gaps. • Opacity gaps promote fragmentation: • contracting object heats up, enters the gap • cooling time goes down • fragment looses pressure support, collapses

17. Gravitational Instability • Opacity drop is smoother than J&G assumed, lowers • J&G used 2D approximation – qualitatively different in the 3D case • Would need initial T around 1000 K to be important – not very likely in protoplanetary disks anyway • Right below the opacity gap not only is high but f is huge too, which compensates the opacity gap’s effect. but as well ! Why this objection is not so serious:

18. Gravitational Instability Conclusions • Planet formationby 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!

19. For and