1. Mayer et al. 2002
Viability of Giant Planet Formation 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 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 (?)

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
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.

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 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 )

13. 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

14. 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)

15. 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

16. 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!