Stellar lifetime and mass-luminosity relation · CAP 2013 #28
Physics · modern-physics
Problem
The luminosity of a star is defined as the energy it emits per unit time. We know from astronomical observations that the luminosity L of the stars that have a mass M < 10M_S is approximately related to their mass as:
LSL=(MSM)3.5
where LS and MS are the luminosity and mass of the Sun.
Furthermore, we know from Einstein's theory of relativity that the energy released from converting a mass M into energy is given by E = Mc². In this problem, we assume that all stars burn almost the same fraction of their mass during their active life.
a) If the fraction of the mass converted into energy is α ≪ 1, first find an expression for the lifetime of a star in terms of its mass, luminosity, α and physical constants.
b) Using the luminosity-mass equation, find the lifetime of a star as a function of its mass.
c) If we know that the lifetime of our Sun is about 10 billion years, what is the lifetime of a star with a mass M = 5M_S?