  The disk instability mechanism for giant planet formation is based on the
formation of clumps in a marginally-gravitationally unstable protoplanetary
disk, which must lose thermal energy through a combination of convection and
radiative cooling if they are to survive and contract to become giant
protoplanets. While there is good observational support for forming at least
some giant planets by disk instability, the mechanism has become theoretically
contentious, with different three dimensional radiative hydrodynamics codes
often yielding different results. Rigorous code testing is required to make
further progress. Here we present two new analytical solutions for radiative
transfer in spherical coordinates, suitable for testing the code employed in
all of the Boss disk instability calculations. The testing shows that the Boss
code radiative transfer routines do an excellent job of relaxing to and
maintaining the analytical results for the radial temperature and radiative
flux profiles for a spherical cloud with high or moderate optical depths,
including the transition from optically thick to optically thin regions. These
radial test results are independent of whether the Eddington approximation,
diffusion approximation, or flux-limited diffusion approximation routines are
employed. The Boss code does an equally excellent job of relaxing to and
maintaining the analytical results for the vertical (theta) temperature and
radiative flux profiles for a disk with a height proportional to the radial
distance. These tests strongly support the disk instability mechanism for
forming giant planets.
