Supernova Heating

One of the sources of heat energy that can change the temperature of an object is heat received from a recent supernova in the simulation. This energy is produced by the supernova explosion and radiated in all directions out into space. Any object with a direct line-of-sight to the supernova will receive a fraction of the energy.

Properties

 * The rate at which energy is added to the object from supernova sources is shown in the Supernova Power property.
 * The amount of heating depends on the Luminosity of the supernova.
 * Supernova heating will affect an object's Average Surface Temperature.

Models
Every supernova in a simulation radiates energy out into space. The rate at which the energy is emitted, also known as the emitted power, is called the supernova's Luminosity. The luminosity of a supernova will change over time, increasing rapidly until it peaks and then slowly fading with time. For an object located a distance $$D$$ from the supernova with luminosity $$L$$, the power per area received by the object is
 * $$F_{nova} = \frac{L}{4 \pi D^2}.$$

Power per area is sometimes called flux density or irradiance.

The larger the object is, the more total power it will receive from the supernova. This total power depends on the cross-sectional area of the object. For a sphere (like a planet or moon) with radius $$R$$, the total power received from the supernova is
 * $$P_{rec} = F_{nova} 4 \pi R^2 = \frac{L^2 R^2}{D^2}.$$

A fraction of the received energy will be absorbed by the object, and the rest will be reflected back into space. Only the absorbed energy will affect the object's temperature. The fraction of energy reflected into space is represented by the object's albedo, $$a$$, so the rate at which energy is absorbed from the supernova, or the Supernova Power, is
 * $$P_{nova} = P_{rec}(1 - a) = \frac{L^2 R^2}{D^2} (1 - a).$$