  Models for the structure of protoplanetary disks have so far been based on
the assumption that the gas and the dust temperature 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
been long debated whether this assumption still holds in the surface layers of
the disk, where 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, Fe (Kamp & Bertoldi 2000). The underlying disk models to our
calculations are the models of Dullemond, van Zadelhoff & Natta (2002). We find
that 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' in
which the dust emission features are produced (e.g. Chiang & Goldreich 1997).
High above the disk surface the gas temperature exceeds the dust temperature
and can can become -- in the presence of polycyclic aromatic hydrocarbons -- as
high as 600 K at a radius of 100 AU. This is a region where CO has fully
dissociated, but a significant fraction of hydrogen is still in molecular form.
The densities are still high enough for non-negligible H_2 emission to be
produced.....(see paper for full abstract)
