Establish whether and where disk thermalization surfaces exist

Establish whether and where a thermalization surface exists within each optically thick radiation-transfer column of a supermassive-black-hole circumbinary disk.

Background

The PTransX calculations solve one-dimensional radiation-transfer problems through vertical disk columns while imposing thermal and ionization balance. Some columns contain a thermalized core, whereas others remain non-thermalized throughout the computational domain.

The existence and location of a thermalization surface cannot be specified in advance because they depend on energy exchange, absorption opacity, and emissivity, all of which vary strongly with temperature. The authors therefore determine the surface during the iterative calculation and split columns when a thermalized core develops.

References

We do not know a priori whether or where a thermalization surface exists because thermal equilibrium is achieved through energy exchange, and absorption opacity, along with its inverse, the true emissivity, depends strongly on the temperature.

— Thermal and non-thermal emission from supermassive black hole circumbinary disks: Disks, Coronae, Streams, and Cavities  (2609.03140 - Nagele et al., 2 Sep 2026) in Section 2.3, PTransX