Dynamics of Circumstellar Disks

Abstract

We present a series of two-dimensional hydrodynamic simulations of massive disks around protostars. We simulate the same physical problem using both a Piecewise Parabolic Method (PPM) code and a Smoothed Particle Hydrodynamic (SPH) code and analyze their di †erences. The disks studied here range in mass from to and in initial minimum Toomre Q value from 1.1 to 3.0. We adopt 0.05M * 1.0M * simple power laws for the initial density and temperature in the disk with an isothermal (c \ 1) equation of state. The disks are locally isothermal. We allow the central star to move freely in response to growing perturbations. The simulations using each code are compared to discover di †erences due to error in the methods used. For this problem, the strengths of the codes overlap only in a limited fashion, but similarities exist in their predictions, including spiral arm pattern speeds and morphological features. Our results represent limiting cases (i.e., systems evolved isothermally) rather than true physical systems. Disks become active from the inner regions outward. From the earliest times, their evolution is a strongly dynamic process rather than a smooth progression toward eventual nonlinear behavior. Processes that occur in both the extreme inner and outer radial regions a †ect the growth of instabilities over the entire disk. E †ects important for the global morphology of the system can originate at quite small distances from the star. We calculate approximate growth rates for the spiral patterns ; the one-armed (m \ 1) spiral arm is not the fastest growing pattern of most disks. Nonetheless, it plays a signiÐcant role because of factors that can excite it more quickly than other patterns. A marked change in the character of spiral structure occurs with varying disk mass. Low-mass disks form Ðlamentary spiral structures with many arms while high-mass disks form grand design spiral structures with few arms. In our SPH simulations, disks with initial minimum Q \ 1.5 or lower break up into protobinary or protoplanetary clumps. However, these simulations cannot follow the physics important for the Ñow and must be terminated before the system has completely evolved. At their termination, PPM simulations with similar initial conditions show uneven mass distributions within spiral arms, suggesting that clumping behavior might result if they were carried further. Simulations of tori, for which SPH and PPM are directly comparable, do show clumping in both codes. Concerns that the pointlike nature of SPH exaggerates clumping, that our representation of the gravitational potential in PPM is too coarse, and that our physics assumptions are too simple suggest caution in interpretation of the clumping in both the disk and torus simulations.

The spectral energy distribution of self-gravitating protostellar disks

“…In particular, several numerical studies have addressed directly the issue of the energy budget when dynamical instabilities are involved (for some recent studies, see Pickett et al 1998Pickett et al , 2000Nelson et al 1998Nelson et al , 2000.…”

Fragmentation of Kozai–Lidov Disks

“…The exact condition for the development of disk GI into disk fragmentation is still an active area of research. Nevertheless, it is generally agreed that a necessary condition for GI against non-axisymmetric perturbations is Q 1.5 (Papaloizou & Savoije 1991;Nelson et al 1998;Mayer et al 2004). For non-isothermal disks, the Q criterion is not sufficient for fragmentation because fragmentation depends also on the details of the disk thermodynamics (Gammie 2001;Rice et al 2005;Lodato & Clarke 2011;Paardekooper et al 2011;Kratter & Lodato 2016).…”

Convergence Studies of Mass Transport in Disks With Gravitational Instabilities. I. The Constant Cooling Time Case

“…Thermal processes play the primary role in regulating the amplitude and outcome of these instabilities (Pickett et al 1998(Pickett et al , 2000(Pickett et al , 2003Nelson et al 1998Nelson et al , 2000Mejía et al 2005). A disk's susceptibility to GIs can be parameterized by the Toomre Q-parameter (Toomre 1981); Q = c s κ/πGΣ, where c s is the sound speed, κ is the epicyclic frequency (∼ the rotation frequency Ω in a nearly Keplerian disk), and Σ is the disk surface mass density.…”