Consider a star of mass M = 10M⊙, composed entirely of fully ionized 12C. Its core temperature is Tc = 6 × 108 K (compared to Tc,⊙ = 1.5 × 107 K for the Sun). Use the classical ideal gas law, the dimensional relation between mass, density, and radius, and the virial theorem to find the scaling of the stellar radius r∗ with total mass M, mean particle mass m , and core temperature Tc. Using the values of these parameters for the Sun, find the radius of the star.

Consider a star of mass M = 10M⊙, composed entirely of fully ionized 12C. Its core temperature is Tc = 6 × 108 K (compared to Tc,⊙ = 1.5 × 107 K for the Sun). Use the classical ideal gas law, the dimensional relation between mass, density, and radius, and the virial theorem to find the scaling of the stellar radius r∗ with total mass M, mean particle mass m , and core temperature Tc. Using the values of these parameters for the Sun, find the radius of the star.