information:classification
Measuring a supernova's photosphere

We can assume that a supernova expands in a spherically symmetric manner. If the supernova is close enough such that we can measure the angular extent, θ (t), of its photosphere, we can use the equation

ω = Δ θ Δ t, {\displaystyle \omega ={\frac {\Delta \theta }{\Delta t}}\,,} where ω is angular velocity, θ is angular extent. In order to get an accurate measurement, it is necessary to make two observations separated by time Δ t. Subsequently, we can use

d = V e j ω, {\displaystyle \ d={\frac {V_{ej}}{\omega }}\,,} where d is the distance to the supernova, V is the supernova's ejecta's radial velocity (it can be assumed that V equals V if spherically symmetric).

This method works only if the supernova is close enough to be able to measure accurately the photosphere. Similarly, the expanding shell of gas is in fact not perfectly spherical nor a perfect blackbody. Also interstellar extinction can hinder the accurate measurements of the photosphere. This problem is further exacerbated by core-collapse supernova. All of these factors contribute to the distance error of up to 25%.