A3 - lifetimes of stars

• luminosity depends on the amount of fuel, or mass, $M:$

• the Stefan-Boltzmann law relates the luminosity to the temperature, assuming a star is a black body:

where, $\sigma$ is the Stefan-Boltzmann constant, $R_{\ast }$ is the stellar radius

• the lifetime is proportional to fuel over rate of consumption, ie. $L:$

• thus, massive stars live for shorter

• this can be used to categorise stars:

  • older, redder and fainter
  • younger, bluer, and brighter

• the colours and luminosities map out the evolutionary state (HR diagram)

• it can be further used to derive distance and probe the structure of the local universe