The Gas Temperature in the Surface Layers of Protoplanetary Disks

Models for the structure of protoplanetary disks have so far been based onthe assumption that the gas and the dust temperature are equal. The gastemperature, an essential ingredient in the equations of hydrostaticequilibrium of the disk, is then determined from a continuum radiative transfercalculation, in which the continuum opacity is provided by the dust. It hasbeen long debated whether this assumption still holds in the surface layers ofthe disk, where the dust infrared emission features are produced. In this paperwe compute the temperature of the gas in the surface layers of the disk in aself-consistent manner. The gas temperature is determined from aheating-cooling balance equation in which processes such as photoelectricheating, dissociative heating, dust-gas thermal heat exchange and line coolingare 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, Fe (Kamp & Bertoldi 2000). The underlying disk models to ourcalculations are the models of Dullemond, van Zadelhoff & Natta (2002). We findthat in general the dust and gas temperature are equal to withing 10% for A_V>~ 0.1, which is above the location of the `super-heated surface layer' inwhich the dust emission features are produced (e.g. Chiang & Goldreich 1997).High above the disk surface the gas temperature exceeds the dust temperatureand can can become -- in the presence of polycyclic aromatic hydrocarbons -- ashigh as 600 K at a radius of 100 AU. This is a region where CO has fullydissociated, but a significant fraction of hydrogen is still in molecular form.The densities are still high enough for non-negligible H_2 emission to beproduced(see paper for full abstract)Comment: 28 pages, 8 figures, accepted for publication in Ap