Transcript Slide 1
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 - Planet formation - Star Formation in the Galactic Center Gravitational Instability Gravitational Instability (GI) When a disk patch with size L starts collapsing it has the following contributions to energy. To collapse need Egr Eth Eth ~ L2cs2 2 2 G L Egr ~ G 2 L3 L 2 2 Erot ~ L L 2 L4 Egr Erot AND G 2 L3 2 L4 G 2 L3 L2cs2 cs2 G L 2 G Thus, gravitational instability requires cs 1 G Gravitational Instability Gravitational Instability (GI) Q 1 2G | k | k c 2 Get 2 2 2 s 0 2 Q 1 2 Dispersion relation for density waves in disk 2 and instability when cs Q 1 G Toomre Q parameter Q 1 k Gravitational Instability Greaves, Richards, Rice & Muxlow (2008) Gravitational Instability Observational Evidence 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 Gravitational Instability Stellar Disks in the Galactic Center Genzel et al 2003 • Galactic Center contains a supermassive black hole (SMBH) with a mass of M SMBH 3106 M sun • 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 disklike geometry (Genzel et al 2003) Gravitational Instability Stellar Rings • Contain no more than M d 10 4 M sun 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 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 Hubble Galactic disks Kennicutt Gravitational Instability Fragmentation vs Gravitoturbulence Gravitational Instability Disk fragmentation Gammie (2001) showed that for fragmentation to set in one needs tc 50 No fragmentation tc 3 Gammie ‘01 tc 2 Fragmentation 2D hydro 1 When tc ~ fragments lose thermal support at the same rate at which they collapse. Isothermal gas effectively has tc 0. Gravitational Instability 3D simulations confirm this general picture (tc 3 5). Rice et al 2003 tcool 5 1 tcool 3 1 Gravitational Instability Gravitoturbulent disks Gravitational Instability Gravitoturbulent disks GM * 2 F ~ 3 M M r • Dissipated energy is radiated locally • Angular momentum conservation • By definition cs2 M ~ & Prescription for the angular momentum transfer by gravitoturbulence Fragmentation happens when 1 ! tcool cs2 F 1 ~ tcool Gravitational Instability External Irradiation. Toomre Q Q Rafikov 2009 1 T Tirr r - parameter 1 T Tirr r 3 103 , Tirr 30K Gravitational Instability External Irradiation. Toomre Q Q Rafikov 2009 1 T Tirr r - parameter 1 T Tirr r 3 103 , Tirr 30K Gravitational Instability External Irradiation. Toomre Q Q Rafikov 2009 fragmentation 1 r - parameter 1 fragmentation r 3 103 , Tirr 30K 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 Gravitational Instability Fragmenting disks Gravitational Instability Disk cooling. Most unstable (to fragmentation) situation corresponds to the shortest cooling time 4 Eth c c k 1 tc 6 Fcool Fcool T cs 2 s Fcool T 2 s 4 4 T cs2 k Requirement that fragmentation takes place and planets may be born then implies 4 k 6 3 tc cS or c 3 6 s k 4 Gravitational Instability Fragmentation + GI Instability requires High T needed for short cooling: k c 3 4 cs Q 1 G 6 s Fragmentation condition then sets a lower limit on k 3 tc 3 cs : This sets an upper limit on c s : 4 1/ 6 cs k 3 cs + 4 1/ 6 cs G G Gravitational Instability Thermodynamical constraints cs GI planet formation Constraint on follows: fragmentation Rafikov 2005 k 3 naturally 4 1/ 6 G As a result, giant planet formation by GI requires k 6 3 (G ) 7 k T 3G 2 4 1/ 5 21/ 10 3 105 g cm 2 a AU 3/ 2 2 / 5 6 / 5 2200 K a AU ( ~ 100 MMSN) ~T Sun ! !!! Gravitational Instability Rafikov (2007) With realistic opacities f 1 Alexander et al 2005 find that planet formation still requires extreme properties of protoplanetary disks! ( Cf. Boss 2004 ) Prad MMSN Prad f 1 Gravitational Instability Numerical results: grid based Boss 2003 Boley et al 2006 Boss (2003) sees fragmentation and formation of bound objects BUT Boley (2006) do not observe fragmentation Gravitational Instability Numerical results: SPH Mayer et al 2007 Disks fragment in simulations of Mayer et al (2007) Stamatellos et al 2008 BUT They don’t in simulations of Stamatellos & Whitworth (2008) 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 !!! 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 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