Measuring the Two-Dimensional Thermal Structures of Protoplanetary Disks

Abstract

We present a flexible, annulus-by-annulus method to constrain the 2-D thermal structure of a protoplanetary disk from optically thick spectral line emission. Using synthetic disk models with a known temperature and density structure, we extracted the vertical emission surfaces and brightness temperatures in radial annuli for multiple CO isotopologue transitions and used them to infer the vertical temperature profiles. This approach reliably recovers the injected temperature structure despite noise and finite resolution. We demonstrated that even a modest set of emission lines can constrain the temperature across a wide range of radii and elevations. Nevertheless, biases in the extracted emission surfaces constitute a major source of systematic error. Finally, we applied this method to archival ALMA observations of the HD 163296 disk, revealing that simple parametric radial temperature models may obscure the complexity of real disks and that additional observations are necessary to distinguish between different models of the vertical structure. This flexible framework can be readily applied to other systems, helping to characterize the thermal environments that shape planet formation.