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Gravitationally Unstable Accretion Disks. Roman Rafikov (Princeton). Gravitational Instability. Outline. Evidence for the gravitationally unstable disks Gravitoturbulence vs fragmentation Properties of gravitoturbulent disks Constraints on fragmentation Applications - PowerPoint PPT Presentation
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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