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 with disk radius R-D = 50 and 100 AU) around protostars using a Smoothed Particle Hydrodynamic (SPH) code. We implement simple and approximate prescriptions for heating via dynamical processes in the disk. Cooling is implemented with a simple radiative cooling prescription, which does not assume that local heat dissipation exactly balances local heat generation. Instead, we compute the local vertical (z) temperature and density structure of the disk and obtain a "photosphere temperature," which is then used to cool that location as a blackbody. We synthesize spectral energy distributions (SEDs) for 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 produce less distinct spiral structure than isothermally evolved systems, especially in approximately the inner radial third of the disk. Pattern amplitudes are similar to isothermally evolved systems farther from the star, but patterns do not collapse into condensed objects. We attribute the differences in morphology to increased efficiency for converting kinetic energy into thermal energy in our current simulations. Our simulations produce temperatures in the outer part of the disk that are very low (similar to 10 K). The radial 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 heating processes (PdV work and shocks) are not responsible for generating a large 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 shocks, which provide sufficient dissipation to power a larger fraction of the near-infrared radiated energy output. In this region, the spatial and size distributions of grains can have marked consequences on the observed near-infrared SED of a given disk and can lead to increased emission and variability 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 vaporized in the midplane of a hot region of the disk, we show that they do not reform into a size distribution similar to that on which most opacity calculations are based. With rapid grain reformation into the original size distribution, the disk does not emit near-infrared photons. With a plausible modification of the opacity, it contributes much more.