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

2. 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.

3. 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,

4. 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

5. 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

6. 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

7. 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 :

8. 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) !
!!!

9. 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 an alternative view.

10. 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
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.

11. 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!

12. For more general opacity need
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.
Cooling time by convection is (Rafikov 2006)
Important point is that still with
so that again

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

14. Photospheric temperature Disk and clump masses
Gravitational Instability
Photospheric temperature
Disk and clump masses
Rafikov 2006
Rafikov 2006
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.
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

16. 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)

17. Why this objection is not so serious:
Gravitational Instability
Why this objection is not so serious:
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 !

18. 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!

19. For
and