The gas temperature in the surface layers of protoplanetary disks

Models for the structure of protoplanetary disks have thus far been based on the assumption that the gas and dust temperatures are equal. The gas temperature, an essential ingredient in the equations of hydrostatic equilibrium of the disk, is then determined from a continuum radiative transfer calculation, in which the continuum opacity is provided by the dust. It has long been debated whether this assumption still holds in the surface layers of the disk, in which the dust infrared emission features are produced. In this paper we compute the temperature of the gas in the surface layers of the disk in a self-consistent manner. The gas temperature is determined from a heating-cooling balance equation in which processes such as photoelectric heating, dissociative heating, dust-gas thermal heat exchange, and line cooling are included. The abundances of the dominant cooling species such as CO, C, C+, and O are determined from a chemical network based on the atomic species H, He, C, O, S, Mg, Si, and Fe. The underlying disk models to our calculations are the models of Dullemond, van Zadelhoff, & Natta. We find that in general the dust and gas temperatures are equal to within 10% for A(V) greater than or similar to 0.1, which is above the location of the superheated surface layer'' in which the dust emission features are produced. High above the disk surface the gas temperature exceeds the dust temperature and can become-in the presence of polycyclic aromatic hydrocarbons-as high as 600 K at a radius of 100 AU. This is a region in which CO has fully dissociated, but a significant fraction of hydrogen is still in molecular form. The densities are still high enough for nonnegligible H-2 emission to be produced. At radii inward of 50 AU, the temperature of the gas above the photosphere can reach up to similar to10(4) K. In the disk surface layers, the gas temperature exceeds the virial temperature of hydrogen. Some of this material could possibly evaporate, but firm conclusions have to await fully self-consistent disk models, in which the disk structure and gas temperature determination will be solved iteratively.