Heating and Cooling Protostellar Disks

We examine heating and cooling in protostellar disks using 3-D radiation-MHD calculations of a patch of the Solar nebula at 1 AU, employing the shearing-box and flux-limited radiation diffusion approximations. The disk atmosphere is ionized by stellar X-rays, well-coupled to magnetic fields, and sustains a turbulent accretion flow driven by magneto-rotational instability, while the interior is resistive and magnetically dead. The turbulent layers heat by absorbing the light from the central star and by dissipating the magnetic fields. They are optically-thin to their own radiation and cool inefficiently. The optically-thick interior in contrast is heated only weakly, by re-emission from the atmosphere. The interior is colder than a classical viscous model, and isothermal. The magnetic fields support an extended atmosphere that absorbs the starlight 1.5 times higher than the hydrostatic viscous model. The disk thickness thus measures not the internal temperature, but the magnetic field strength. Fluctuations in the fields move the starlight-absorbing surface up and down. The height ranges between 13% and 24% of the radius over timescales of several orbits, with implications for infrared variability. The fields are buoyant, so the accretion heating occurs higher in the atmosphere than the stresses. The heating is localized around current sheets, caused by magneto-rotational instability at lower elevations and by Parker instability at higher elevations. Gas in the sheets is heated above the stellar irradiation temperature, even though accretion is much less than irradiation power when volume-averaged. The hot optically-thin current sheets might be detectable through their line emission.