Protoplanetary Embryo Formation via Gravitational Instability

1. Envelope-Induced Gravitational Instability and the Ultimate Fate of Protoplanetary Embryos Eduard Vorobyov and Shantanu Basu Department of Physics and Astronomy University of Western Ontario London, Canada

2. Protostellar disks can be gravitationally unstable on large scales! • Theoretical models (e.g. Larson 1984) • Numerous numerical simulation(Bodenheimer, Boss, Laughlin, Bate, Wadsley, Rice, Lodato, Durisen, Basu, Vorobyov, and many others) • Observations of non-axisymmetric structures in protostellar disks of AB Aurigae (Fukagawa et al. 2004) andHD 100546 (Grady et al. 2001) HD 100546

3. Gravitational instability of a gaseous disk • The stability properties of gas disks are often expressed in terms of the Toomre Q-parameter (Toomre 1964) Q= • 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 the observationally meaningful non-axisymmetric structure. • If Q<1 the disk is vigorously unstable and can fragment into self-gravitating clumps. Cs k π G Σ Cooling and heating effects (Durisen, Pickett, Boss, Gammie, Mejia, Rice, and others)

4. Numerical simulations of a cloud core collapse. Flattened molecular cloud core Magnetohydrodynamic equations in the thin-disk approximation ~ 0.1 pc ~ 1-2 M8 Infalling envelope • Logarithmically spaced grid in the r-direction. • Fast convolution method to find the gravitational • potential F. No restrictive periodic boundaries; • Self-consistent treatment of the disk-envelope interaction; • Long integration times (several Myr). ~ 100 AU disk Protostar (sink cell)

5. Spiral structure and protoplanetary embryo formation

6. Self-consistent formation of the protostellar disk around the protostar Evolution of the protostellar disk Mass infall rate onto the protostar

7. Mass accretion bursts and the Q-parameter Black line - mass accretion rate onto the protostar; Red line – the Q-parameter Burst mode Smooth mode The disk is strongly gravitationally unstable when the bursts occur

8. FU Ori-like luminosity outbursts and the gravitational torque Black line – the accretion luminosity Red line – the integrated gravitational torque Spiral gravitational field is responsible for the outbursts

9. The effect of rotation on the mass accretion bursts Black line – mass accretion rate onto the protostar Red line – the envelope mass The envelope mass at the time of disk formation is the key element for the burst phenomenon

10. Accretion history of young protostars Hartmann (1998) – empirical inference, based on ideas advocated by Kenyon et al. (1990). Vorobyov & Basu (2006) – theoretical calculation of disk formation and evolution

11. Conclusions • Protostellar disks are gravitationally unstable and can form protoplanetary embryos via direct gravitational instability. This can only happen in the early phase of the disk evolution when the envelope contains a substantial (≥20%) portion of the initial cloud mass. • However, most embryos will be driven onto the protostar due to the efficient exchange of angular momentum between embryos and the spiral arms! Only those embryos that form in the outer parts of spiral arms may ultimately survive. • The episodes of embryo infall provide an explanation for the FU Ori eruptions. The authors are thankful to Takahiro Kudoh and Sergey Khan for the help with preparing the animation of protostellar disks