Radiative signatures of circumplanetary disks and envelopes during the late stages of giant planet formation

During the late stages of giant planet formation, protoplanets are surrounded by a circumplanetary disk and an infalling envelope of gas and dust. For systems with sufficient cooling, material entering the sphere of influence of the planet falls inward and approaches ballistic conditions. Due to conservation of angular momentum, most of the incoming material falls onto the disk rather than directly onto the planet. This paper determines the spectral energy distributions of forming planets in this stage of evolution. Generalizing previous work, we consider a range of possible geometries for the boundary conditions of the infall and determine the two-dimensional structure of the envelope, as well as the surface density of the disk. After specifying the luminosity sources for the planet and disk, we calculate the corresponding radiative signatures for the system, including the emergent spectral energy distributions and emission maps. These results show how the observational appearance of forming planets depend on the input parameters, including the instantaneous mass, mass accretion rate, semimajor axis of the orbit, and the planetary magnetic field strength (which sets the inner boundary condition for the disk). We also consider different choices for the form of the opacity law and attenuation due to the background circumstellar disk. Although observing forming planets will be challenging, these results show how the observational signatures depend on the underlying properties of the planet/disk/envelope system.