Abstract
This chapter summarises current theoretical concepts and methods to deter- mine the gas temperature structure in protoplanetary disks by balancing all relevant heating and cooling rates. The processes considered are non-LTE line heating/cooling based on the escape probability method, photo-ionisation heating and recombination cooling, free-free heating/cooling, dust thermal accommodation and high-energy heat- ing processes such as X-ray and cosmic ray heating, dust photoelectric and PAH heating, a number of particular follow-up heating processes starting with the UV excitation of H2, and the release of binding energy in exothermal reactions. The resulting thermal structure of protoplanetary disks is described and discussed.
Highlights
The temperature of the gas in protoplanetary disks is important for its chemical composition, the production of emission lines connected to the observability of the gas phase, and the gas temperature is essential to predict the pressure structure in disks which determines the vertical stratification and shape of the disk
There is often a disk layer where the densities are high, so the level populations are close to local thermodynamical equilibrium (LTE), i.e. strong, and a lot of line photons are emitted from the top of that layer into the optically thin model volume above
In case of CO ro-vibrational cooling, which is a superposition of hundreds of individual lines, we find ncr > nthick
Summary
The temperature of the gas in protoplanetary disks is important for its chemical composition, the production of emission lines connected to the observability of the gas phase, and the gas temperature is essential to predict the pressure structure in disks which determines the vertical stratification and shape of the disk. In order to determine the temperature of the gas, we consider the first law of thermodynamics d(ρe) = −p dV +. The −pdV work is usually not important in disks, because there is no expansion or contraction of the gas in stable Keplerian orbits. In order to assess the importance of the −pdV work we can compare the cooling relaxation timescale τcool with the dynamical timescale τdyn, given e.g. by the evolutionary timescale in case of a stable 2D disk in Keplerian rotation, or by the orbital timescale in case of a strongly time-dependent situation like a disk with spiral waves. In most cases, heating/cooling will be rapid and we will find τcool τdyn, so the −pdV work can be neglected, and Eq (1) simplifies to de = Q = dt. Note that Eq (2), in principle, may have several temperature solutions (“thermal bifurcations”)
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