Dynamics of circumstellar disks. II. Heating and cooling

We present a series of two-dimensional (r, phi) hydrodynamic simulations of marginally self-gravitating disks (M-D/M* = 0.2, with M-* = 0.5 M. and wit h disk radius R-D = 50 and 100 AU) around protostars using a Smoothed Parti cle Hydrodynamic (SPH) code. We implement simple and approximate prescripti ons for heating via dynamical processes in the disk. Cooling is implemented with a simple radiative cooling prescription, which does not assume that l ocal heat dissipation exactly balances local heat generation. Instead, we c ompute the local vertical (z) temperature and density structure of the disk and obtain a "photosphere temperature," which is then used to cool that lo cation as a blackbody. We synthesize spectral energy distributions (SEDs) f or our simulations and compare them to fiducial SEDs derived from observed systems, in order to understand the contribution of dynamical evolution to the observable character of a system. We find that these simulations produc e less distinct spiral structure than isothermally evolved systems, especia lly in approximately the inner radial third of the disk. Pattern amplitudes are similar to isothermally evolved systems farther from the star, but pat terns do not collapse into condensed objects. We attribute the differences in morphology to increased efficiency for converting kinetic energy into th ermal energy in our current simulations. Our simulations produce temperatur es in the outer part of the disk that are very low (similar to 10 K). The r adial temperature distribution of the disk photosphere is well fitted to a power law with index q similar to 1.1. Far from the star, corresponding to colder parts of the disk and long-wavelength radiation, known internal heat ing processes (PdV work and shocks) are not responsible for generating a la rge fraction of the thermal energy contained in the disk matter. Therefore gravitational torques responsible for such shocks cannot transport mass and angular momentum efficiently in the outer disk. Within similar to 5-10 AU of the star, rapid breakup and reformation of spiral structure causes shock s, which provide sufficient dissipation to power a larger fraction of the n ear-infrared radiated energy output. In this region, the spatial and size d istributions of grains can have marked consequences on the observed near-in frared SED of a given disk and can lead to increased emission and variabili ty on similar to 10 yr timescales. The inner disk heats to the destruction temperature of dust grains. Further temperature increases are prevented by efficient cooling when the hot disk midplane is exposed. When grains are va porized in the midplane of a hot region of the disk, we show that they do n ot reform into a size distribution similar to that on which most opacity ca lculations are based. With rapid grain reformation into the original size d istribution, the disk does not emit near-infrared photons. With a plausible modification of the opacity, it contributes much more.