Time and cylindrically averaged density (as background colour) and temperature (in contours) distributions as functions of r and z and the optically thin–thick transition surface measured from the simulation boundary. Parameters are well resolved (N_c = 100) runs of opacity Set 1 and gravitational smoothing . The time-average ran over ten orbits with ten output samples per orbit. Near the planet, density and temperature are both radially distributed. Farther away from the planet, the density stratifies in z in order to connect to the gap. Moving outward radially in the disc midplane, the temperature becomes quasi-isothermal as r moves into the optically thin gap. In the z-direction however, heavy cooling bends the iso-T planes upwards. The luminosity required for Eq. (16) is computed for the κ = 0.01 cm² g⁻¹ cases in the approximation ∑dAσT⁴, which is possible as in those cases the planetary gap is optically thin. Luminosities and accretion rates vs. time are shown in Fig. 10.