Thermal time scale

Stellar astrophysics

The size of a star as well as its energy output generally determine a star's thermal lifetime because the measurement is independent of the type of fuel normally found at its center. Indeed, the thermal time scale assumes that there is no fuel at all inside the star and simply predicts the length of time it would take for the resulting change in outputted energy to reach the surface of the star and become visually apparent to an outside observer.

$${\displaystyle {\tau }_{\text{th}}=\frac{\text{total kinetic energy}}{\text{rate of energy loss}}\approx \frac{G{M}^2}{2RL}}$$

where G is the gravitational constant, M is the mass of the star, R is the radius of the star, and L is the star's luminosity. As an example, the Sun's thermal time scale is approximately 15.7 million years.