# Why are main sequence stars more massive than the Sun less dense? e.g. Vega, Spica etc

Why do main sequence stars more massive than the Sun have lower densities? e.g. Vega, Spica etc.

• You need to be clearer. Average densities? Core densities? Is there any source that this is typical among more massive stars, or are you just using a sample of 2? – Sir Cumference Oct 31 '16 at 5:05
• yes, fair enough. I'm referring to average density among the most commonly cited examples of main sequence stars where I notice that volume increases much faster than mass. – Arvind H Nov 1 '16 at 4:16

To see the scaling approximately, use the virial theorem, which says that the energy per particle in the core (roughly set by the need for fusion) is about $GMm/R$, where $M$ is the mass of the star, and $m$ is the mass of a proton. Expressed in terms of density $\rho$ instead of radius $R$, that's proportional to $M^{\frac{2}{3}}\rho^{\frac{1}{3}}$. Ergo, $\rho$ drops when $M$ rises.