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Gravitationally Unstable Accretion Disks

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

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Gravitationally Unstable Accretion Disks

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  1. Gravitationally Unstable Accretion Disks Roman Rafikov (Princeton)

  2. Gravitational Instability 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

  3. Gravitational Instability AND Thus, gravitational instability requires Gravitational Instability (GI) When a disk patch with size L starts collapsing it has the following contributions to energy. To collapse need

  4. Gravitational Instability Get and instability when Gravitational Instability (GI) Dispersion relation for density waves in disk Toomre Q parameter

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

  6. Gravitational Instability Observational Evidence

  7. 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

  8. Gravitational Instability 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) Stellar Disks in the Galactic Center

  9. Gravitational Instability Levin & Beloborodov 2003 • Contain no more than in stars (Nayakshin et al2005)– 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 Stellar Rings • 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

  10. Gravitational Instability Hubble Kennicutt Galactic disks

  11. Gravitational Instability Fragmentation vs Gravitoturbulence

  12. Gravitational Instability Fragmentation Gammie ‘01 2D hydro No fragmentation When fragments lose thermal support at the same rate at which they collapse. Isothermal gas effectively has . Disk fragmentation Gammie (2001) showed that for fragmentation to set in one needs

  13. Gravitational Instability 3D simulations confirm this general picture . Rice et al 2003

  14. Gravitational Instability Gravitoturbulent disks

  15. Gravitational Instability • Dissipated energy is radiated locally • Angular momentum conservation • By definition & Prescription for the angular momentum transfer by gravitoturbulence Fragmentation happens when Gravitoturbulent disks

  16. Gravitational Instability Toomre Q Q Rafikov 2009 r 1 - parameter 1 External Irradiation. r

  17. Gravitational Instability Toomre Q Q Rafikov 2009 1 r - parameter 1 r External Irradiation.

  18. Gravitational Instability Q Rafikov 2009 1 r - parameter 1 r External Irradiation. Toomre Q fragmentation fragmentation

  19. 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

  20. Gravitational Instability Fragmenting disks

  21. Gravitational Instability Disk cooling. Most unstable (to fragmentation) situation corresponds to the shortest cooling time Requirement that fragmentation takes place and planets may be born then implies or

  22. Gravitational Instability + This sets an upper limit on : Fragmentation condition then sets a lower limit on : + Fragmentation GI Instability requires High T needed for short cooling:

  23. 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

  24. Gravitational Instability Rafikov (2007) With realistic opacities find that planet formation still requires extreme properties of protoplanetary disks! Alexander et al 2005 MMSN ( Cf. Boss 2004 )

  25. Gravitational Instability Boss 2003 Boley et al 2006 Boss (2003) sees fragmentation and formation of bound objects Boley (2006) do not observe fragmentation BUT Numerical results: grid based

  26. Gravitational Instability Mayer et al 2007 Stamatellos et al 2008 Disks fragment in simulations of Mayer et al (2007) They don’t in simulations of Stamatellos & Whitworth (2008) BUT Numerical results: SPH

  27. Gravitational Instability Numerical results: summary • 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 !!!

  28. Gravitational Instability Conclusions • 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 formationby 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

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