Gravitationally Unstable Accretion Disks

Gravitationally Unstable Accretion Disks

Roman Rafikov (Princeton)

Outline

• Evidence for the gravitationally unstable disks

• Gravitoturbulence vs fragmentation

• Properties of gravitoturbulent disks

• Constraints on fragmentation

• Applications

- Planet formation

- Star Formation in the Galactic Center

Gravitational Instability

Gravitational Instability (GI)

Gravitational Instability

22~ sth cLE

4222~ LLLErot

32

22

~ LGL

LGEgr

When a disk patch with size L starts collapsing it has the following contributions to energy.

To collapse need

2232scLLG 4232 LLG

2

2

GL

G

cs

thgr EE rotgr EE AND

1G

csThus, gravitational instability requires

Gravitational Instability (GI)

Dispersion relation for density waves in disk

2222 ||2 sckkG

Get and instability when 02

1

G

cQ s

Toomre Q parameter

2

2

k

1Q

1Q

1Q

Gravitational Instability

Greaves, Richards, Rice & Muxlow (2008) Gravitational Instability

Observational Evidence

Gravitational Instability

Planets: HD 8799 (Marois 2009)

• 3 young giant planets in almost circular orbits around A star

• Masses around 10 M_J

• Star is 1.5 M_Sun, 40 pc away, age 30-160 Myrs

• Projected separations between 24 AU (innermost) and 70 AU (outer)

• Keplerian motion detected

• Probably the most compelling case of a pristine system

Stellar Disks in the Galactic Center

Genzel et al 2003• Galactic Center contains a supermassive black hole (SMBH) with a mass of

• Black hole’s gravity dominates within roughly 1 pc from the center

• Inner 0.5 pc contain more than 80 young bright O and B stars

• Some arranged in disk-like geometry (Genzel et al 2003)

sunSMBH MM 6103

Gravitational Instability

Stellar Rings

• Contain no more than in stars (Nayakshin et al 2005) – otherwise rings would preccess excessively in the neighbor’s fiels

• extend from 0.05 pc to 0.5 pc (Paumard et al 2006)

• have small geometric thickness, <h/r> ~ 0.14

sund MM 410

Levin & Beloborodov 2003 Stars in disks are

• very young, with ages of about 6 Myrs

• very massive, typically tens of solar masses.

• lifetimes are less than 100 Myrs

• likely formed by gravitational instability

Gravitational Instability

Gravitational Instability

Galactic disks

Kennicutt

Hubble

Fragmentation vs Gravitoturbulence

Gravitational Instability

Gravitational Instability

Disk fragmentation

Gammie (2001) showed that for fragmentation to set in one needs

When fragments lose thermal support at the same rate at which they collapse. Isothermal gas effectively has .

1~ ct0ct

3 ct

Gammie ‘01

50 ct No fragmentation 2 ct Fragmentation

2D hydro

Gravitational Instability

3D simulations confirm this general picture .)53( ctRice et al 2003

15 coolt 13 coolt

Gravitoturbulent disks

Gravitational Instability

Gravitoturbulent disks

Gravitational Instability

• Dissipated energy is radiated locally

MMr

GMF 2

3*~

~M• Angular momentum conservation

2sc

F

ct scool

2• By definition &

coolt1

~Prescription for the angular momentum transfer by gravitoturbulence

Fragmentation happens when !1

Gravitational Instability

External Irradiation.

Rafikov 2009

KTirr 30,103 3 r

Q

1

rirrTT

irrTT

1

Toomre Q

- parameter

Gravitational Instability

External Irradiation.

KTirr 30,103 3

Rafikov 2009

irrTT

Q

1

r

Toomre Q

- parameter

irrTT

1

r

Gravitational Instability

External Irradiation.

KTirr 30,103 3

Rafikov 2009Q

1

r

Toomre Q

- parameter

1

r

fragmentation

fragmentation

Gravitational Instability

External Irradiation.

• Disk can remain gravitationally unstable in the presence of external irradiation

• Irradiation suppresses fragmentation

• Fragmentation is possible only at high mass accretion rates

• In cold disks with dust opacity fragmentation is possible in the earliest phases of disk formation, far from the star (> 100 AU)

• At very low accretion rates disks remain viscous everywhere

Fragmenting disks

Gravitational Instability

Gravitational Instability

Disk cooling.

6

4

4

22 1

s

s

cool

s

cool

thc c

k

T

c

F

c

F

Et

k

cT s

24TFcool

Requirement that fragmentation takes place and planets may be born then implies

6

4

3

Sc c

kt

Most unstable (to fragmentation) situation corresponds to the shortest cooling time

4

6

3

k

csor

Gravitational Instability

Fragmentation

1

G

cQ s

GI

4

6

3

k

cs

High T needed for short cooling:

Fragmentation condition then sets a lower limit on :

3 ctsc

Instability requires

This sets an upper limit on : sc

Gc

ks

6/14

3

sck

6/14

3

G

cs

+

+

Gravitational Instability

As a result, giant planet formation by GI requires

10/2125

5/14

6

7

103)(3

AUacmg

k

G

5/6

5/22/32

22003

AUaK

k

GT

( ~ 100 MMSN) !

!!!

SunT~

Thermodynamical constraints Rafikov 2005

Gk

6/14

3

Constraint on naturally follows:

sc

fragmentation

GIplanet

formation

Gravitational Instability

With realistic opacities

find that planet formation still requires extreme properties of protoplanetary disks!

( Cf. Boss 2004 )

Alexander et al 2005

Rafikov (2007)

MMSN

radP

radP

1f

1f

Gravitational Instability

Numerical results: grid based

Boss 2003

Boley et al 2006

Boss (2003) sees fragmentation and formation of bound objects

Boley (2006) do not observe fragmentation BUT

Gravitational Instability

Numerical results: SPH

Disks fragment in simulations of Mayer et al (2007)

They don’t in simulations of Stamatellos & Whitworth (2008)

BUT

Mayer et al 2007 Stamatellos et al 2008

Numerical results: summary

Gravitational Instability

Can’t draw any robust conclusions!

• Results depend on which method is used and which group gets them

• No convergence between different groups

• Need to be EXTREMELY CAREFUL regarding resolution and radiative transfer treatment (Nelson 2006)

Need numerical comparison projects !!!

ConclusionsGravitational Instability

• Gravitational instability is important for accretion disks is a variety of settings, from protoplanetary to galactic

• Gravitational instability results in two outcomes depending on the cooling time: gravitoturbulence or fragmentation

• Properties of gravitoturbulent disks can be derived analytically

• Planet formation by gravitational instability requires extreme properties of protoplanetary disks, but is feasible beyond 100 AU from the star

• Star formation around SMBH in the Galactic Center is natural at distances of 0.1 pc