Two stars have the following properties: Star
1 has Ms = 1 Solar Mass (denote M), T = 1.5 × 107 K, and is composed almost wholly
of hydrogen with a small admixture of heavy elements. Star 2 has
Ms = 0.5 Solar masses, Tc = 108 K, and is composed almost wholly of helium
with the same small admixture of heavy elements. Given that 0
varies with composition as Z(1 + X), where X and Z are the mass
fractions of hydrogen and heavy elements respectively, use the same
order of magnitude approach and the equation of radiative transport
to estimate the relative luminosities of the two stars.

Question

Two stars have the following properties: Star
1 has Ms = 1 Solar Mass (denote M), T = 1.5 × 107 K, and is composed almost wholly
of hydrogen with a small admixture of heavy elements. Star 2 has
Ms = 0.5 Solar masses, Tc = 108 K, and is composed almost wholly of helium
with the same small admixture of heavy elements. Given that 0
varies with composition as Z(1 + X), where X and Z are the mass
fractions of hydrogen and heavy elements respectively, use the same
order of magnitude approach and the equation of radiative transport
to estimate the relative luminosities of the two stars.

anonymous · Answer

luminosity will vary roughly $$L \alpha k_0^{-1}\mu^7M^5T^{0.5}$$