Night Sky
Just after the Sun is gone below the horizon, the sky keeps lit during a few moments. During that period of time, the sky appears mainly blue and is known as twilight. This is due to ozone and is taken into account in our model.
During the night, the Sun has gone far under the horizon. The only potential source of visible direct light is the Moon (reflecting the light it receives from the sun hidden to the observer). Even during the day, the Moon can be visible.
Other major components of the night sky are the stars. Note that the stars are only visible under clear sky, with no Moon and after some eye adaptation. In our model, this means that you need to remove the Moon from the viewing pyramid, try to keep the sky turbidity low and increase the exposure of the tone mapping operator used. Stars are several times of magnitude darker than the Sun or the Moon and you may need to multiply the day exposure by around 10000-100000 to get a correct night exposure with stars.