1. Eduard Vorobyov and Shantanu Basu
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) and HD (Grady et al. 2001) HD

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. Evolution of the protostellar disk Mass infall rate onto the protostar
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
Smooth mode
Burst 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