Radiative Transfer in the Vicinity of a Protoplanet

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We calculate the effect of stellar irradiation on the temperature structure of the photosphere of a circumstellar disk in the vicinity of a protoplanet. We restrict our study to small protoplanets that perturb the disk locally but are too small to open a gap. These protoplanets induce a compression of the disk material near it, resulting in a decrement in the density at the disk's surface. Thus, an isodensity contour at the height of the photosphere takes on the shape of a well. When such a well is illuminated by stellar irradiation at grazing incidence, it results in cooling in a shadowed region and heating in an exposed region. Using a method we have developed for calculating three-dimensional radiative transfer on a perturbed surface, we examine the variation of this effect with protoplanetary mass and distance. We conclude that even relatively small protoplanets can induce significant temperature variations in a passive disk, up to ±30% for planets at the gap-opening threshold. Therefore, many of the processes involved in planet formation should not be modeled with a locally isothermal equation of state. Although the temperature perturbation is unlikely to be observable, it may affect accretion of disk material onto the planet or the rate of Type I migration.

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