Abstract Gaps and rings are commonly seen in recent high-resolution ALMA observations of protoplanetary disks. Ice lines of volatiles are one of the mechanisms proposed to explain the origin for these substructures. To examine the ice line hypothesis, literature studies usually parameterize the midplane temperature with the analytic formula of a passively heated, flared disk. The temperature in this simplified expression is basically dependent on the stellar luminosity. I have built a grid of self-consistent radiative transfer models that feature the same stellar properties, but different disk parameters. The midplane temperature of these models shows a large dispersion over a wide range of radii, indicating that besides the stellar luminosity, the disk parameters also play an important role in determining the thermal structure. Comparing the mid-plane temperature from radiative transfer simulation with the analytic solution shows a large difference between both approaches. This result suggests that special care on the assumed temperature profile has to be taken in the analysis of gap/ring origins, and conclusions drawn in previous works on the basis of the analytic temperature should be revisited. I further took the AS 209 disk as an example, and conducted a detailed radiative transfer modeling of the spectral energy distribution and the ALMA Band 6 image. The D137, D24 and D9 gaps are associated with the ice lines of major volatiles in the disk according to such a thorough analysis. However, if the temperature profile simply follows the analytic formula, none of these gaps matches the ice lines of the species considered here.
Keywords protoplanetary disks — radiative transfer — stars: formation
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