The Formation and Long-term Evolution of Circumstellar Disks

1. The Formation and Long-term Evolution of Circumstellar Disks Shantanu Basu The University of Western Ontario, Canada & Eduard Vorobyov (ICA, St. Mary’s U., Canada) Isaac Newton Institute DDP Program seminar September 24, 2009

2. The Envelope-Disk Connection Calvet, Hartmann, & Strom (1999) FU Ori C. Briceno FUor’s are YSO’s with significant circumstellar material. Typical disk accretion: FU Ori:

3. Empirical Inference of YSO Accretion History Hartmann (1998), based on Kenyon et al. (1990) New evidence from Spitzer (very low luminosity objects – VeLLO’s; Enoch et al. 2008) also reveals need for episodic accretion Observed frequency of FU Ori eruptions (last 50 years) is several times greater than the low-mass star formation ratewithin 1 kpc  It is thought that all YSO’s undergo multiple eruptions.

4. Gravitational instability of a gaseous disk • The stability properties of gas disks are often expressed in terms of the Toomre Q-parameter (Toomre 1964) • If Q > 2 the disk is stable (but still may have low-amplitude non-axisymmetric density perturbations). • If 1 < Q < 2 the disk is unstable and can develop observationally meaningful non-axisymmetric structure. • If Q < 1 the disk is vigorously unstable and can fragment into self-gravitating clumps. Fragment formation ultimately depends also upon cooling and heating rates (Gammie 2001; also, Lodato, Rice, Durisen, Pickett, Boss, and others) and/or upon mass accretion onto the disk (Vorobyov, Basu)

5. Global Core  Disk Formation/Accretion Simulations We Employ the Thin-Disk Approximation Vorobyov & Basu (2006): • Our model is global, nonaxisymmetric, and includes disk self-gravity. Outer boundary at ~ 104 AU, i.e. prestellar core. • Integrate vertically (in z-direction) through cloud. Solve time-dependent equations for profiles in (r,f) directions. IC’s from self-similar core collapse calculations. • With nonuniform mesh, can study large dynamic range of spatial scales, ~ 104 AU down to several AU • Allows efficient calculation of long-term evolution even with very small time stepping due to nonuniform mesh. Can study disk accretion for ~ 106 yr rather than ~103 yr (for 3D) • Can run a very large number of simulations – for statistics and parameter study • Last two still not possible for 3D simulations

6. What’s not included in this model (for now) • Magnetic braking • Ambipolar diffusion, Ohmic dissipation, Hall term • Model for inner disk (~ 5 AU) inside central sink cell • Magnetorotational instability (can’t occur in thin-disk model) • Stellar irradiation effects on disk • Radiative transfer in disk - we use P= P(r), barotropicrelation • Photoevaporation of outer disk Schematic from Armitage, Livio, & Pringle (2001)

7. Basic Equations 2D convolution theorem (Binney & Tremaine, Galactic Dynamics) very useful to model isolated objects

8. Core initial conditions These profiles represent best analytic fits (Basu 1997) to axisymmetric models of magnetically supercritical core collapse (e.g. Basu & Mouschovias 1994). All scale as r -1 at large radii. Pick r0, W0,a, so that core is mildly gravitationally unstable initially. Basic qualitative results are independent of details of initial profiles.

9. Self-consistent formation of the protostellar disk and envelope-induced evolution Evolution of the protostellar disk Mass infall rate onto the protostar

10. Early (Burst Mode) Disk Evolution

11. Mass accretion bursts and the Q-parameter Black line - mass accretion rate onto the central sink;Red line– the Q-parameter Smooth mode Burst mode Vorobyov & Basu (2006) The disk is strongly gravitationally unstable when the bursts occur

12. Accretion history of young protostars Burst mode Residual accretion , self-regulated mode FU Ori outburst disk accretion envelope accretion VeLLO’s? Vorobyov & Basu (2007)

13. Disk mass stays well below central mass M = 1 M8, rout = 0.05 pc, b = 0.275% disk formation at 10 AU Gravitational instability and clump formation can occur in low-mass protostellar disks.

14. Azimuthally Averaged Spatial Profiles – Into the Late Phase Keplerian W Accretion and instability help to self-regulate disks to a near-uniform Qdistribution Sharp edge! S Slope of MMSN  Disk weakly nonisothermal T Nonaxisymmetry is essential for this result. Vorobyov & Basu (2007) Q Self-regulation

15. Two Modes of Disk Accretion Early burst mode Episodic vigorous gravitational instability (GI). Distinct spiral modes Clumps form and accreted inward Binary formation may occur here Late self-regulated mode Gravitational torque driven accretion, Q ~ 1, not GI Diffuse spiral structure VB06

16. The Swing Amplifier – why fluctuations persist in self-regulated mode Leading spiral waves can be unwound into trailing spiral waves. During the process, a transient instability feeds energy into the spiral mode. For the process to work continuously, need a feedback loop, i.e. fresh sources of leading waves in the system. Where from?? Toomre (1981), based on work by Zang and Toomre. Also, Goldreich & Lynden-Bell (1965).

17. Compile accretion rates for various initial core masses Solid circles: time-average (class II phase, 0.5 to 3 Myr) values from models with differing initial mass. Bars represent variations from mean during same time period. All other symbols: data from Muzerolle et al. (2005) and Natta et al. (2006). Blue line – best fit to simulation averages. Black line – best fit to all data points. Red lines – best fits to low and higher mass regimes of data. Blue line: Vorobyov & Basu (2008)

18. Some key results • Can fit mean observed T Tauri star (TTS) accretion rates using a model of gravitational torque driven accretion • Model also produces near-Keplerian rotation and r-3/2 surface density profile in disk • However, disk masses and disk-to-star mass ratios are a factor ~10 greater than observational estimates for TTSs and BDs (Andrews & Williams 2005; Scholz et al. 2006)

19. Observed disk masses underestimated? • Grain growth in disks already significant. Standard opacity requires grain growth to 1 mm at ~100 AU, but what if they grow further? Larger grains would lead to higher disk mass estimates (Andrews & Williams 2007; Hartmann et al. 2006) • Upper envelope of TTS accretion rate dM/dt ~ 10-7Msun/yr implies Mdisk ~ dM/dt x 1 Myr ~ 0.1 Msun • MMSN contains ~ 0.01 Msun material, barely enough to make Jupiter. Extrasolar systems with M sin i up to several Jupiter masses imply Mdisk >> 0.01 Msun • Chondrule formation models (Desch & Connolly 2002; Boss & Durisen 2005) require a high density and Mdisk ~ 0.1 Msun

20. Basic Equations with Viscosity unit tensor

21. Radial distance (AU) The Additional Effect of a-viscosity Red lines, a = 0. Solid black lines, a = 0.01. Vorobyov & Basu (2009, MNRAS, 393, 822) Distances on horizontal axis in AU. Density drops and disk is larger in viscous disk. Self-regulated disk structure is lost, and it is clearly gravitationally stable.

22. An effective alpha for models Vorobyov & Basu (2009) at inner sink

23. Can viscous approach model gravitational instability/torques? In Burst mode: No! Global (mostly m=1) mode dominates Burst mode Self-regulated mode  many higher order modes dominate Vorobyov & Basu (2009)

24. Viscous approach may be useful for self-regulated mode In self-regulated mode, many high order spirals, lots of mode-mode interaction  a local approximation more suitable, e.g., Lin & Pringle (1987,1990), Lodato & Rice (2004), Vorobyov (2010). Lodato & Rice 2004 – a self-regulated disk, Q ~ 1 Vorobyov & Basu (2007) – evolution of a ring

25. Summary • Circumstellar disks that form self-consistently enter an early burst modeof episodic vigorous gravitational instability  formation of clumps  FU Ori-type bursts. Very low accretion states may correspond to VeLLO’s. • At late (~ Myr) stages, disks enter a self-regulated mode, have a sharp edge and maintain persistent nonaxisymmetric density fluctuations  non-radial gravitational forces  torques that drive accretion at rates comparable to that of TTSs • Self-regulation of disk in late phase leads to Q ~ const. and to surface density profile S ~ r -3/2 ; same slope as MMSN • For models with ~ 0.5 Msun and above, can fit observed dM/dt vs. M* relation. • Disk mass stays well below central mass, but factor ~ 10 larger than observational estimates. Observed disk masses systematically underestimated? • Addition of a-viscosity increasingly undermines all of the above effects, and dominates even for a = 10-2 . Other parametrizations of viscosity (Q -dependent) may provide a reasonable approximation to the self-regulated mode.