Parameters
By treating the star as an idealized energy radiator known as a black body, the luminosity L and radius R can be related to the effective temperature by the Stefan–Boltzmann law:
- L = 4πσR2Teff4
where σ is the Stefan–Boltzmann constant. As the position of a star on the HR diagram shows its approximate luminosity, this relation can be used to estimate its radius.
The mass, radius and luminosity of a star are closely interlinked, and their respective values can be approximated by three relations. First is the Stefan–Boltzmann law, which relates the luminosity L, the radius R and the surface temperature Teff. Second is the mass–luminosity relation, which relates the luminosity L and the mass M. Finally, the relationship between M and R is close to linear. The ratio of M to R increases by a factor of only three over 2.5 orders of magnitude of M. This relation is roughly proportional to the star's inner temperature TI, and its extremely slow increase reflects the fact that the rate of energy generation in the core strongly depends on this temperature, while it has to fit the mass–luminosity relation. Thus, a too high or too low temperature will result in stellar instability.
A better approximation is to take, the energy generation rate per unit mass, as ε is proportional to TI15, where TI is the core temperature. This is suitable for stars at least as massive as the Sun, exhibiting the CNO cycle, and gives the better fit R ∝ M0.78.
Read more about this topic: Main Sequence
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