# Visibility of a super-massive star

I heard that mass and distance are the only deciding criteria for determining the gravitational pull. Keeping the distance constant, if mass would be the only deciding factor for gravitational pull, then every super-massive star capable of forming a black hole would absorb light in the first place, and thus it would already look like a black hole throughout it's whole life cycle, even before being formed into one. This is based on the fact that black holes can absorb light rays due to it's immense gravitational pull.

• But the Schwarzchild radius is much smaller than the radius of a star. – lemon Apr 4 '15 at 23:40
• Self-promotion, I guess, but I answered this on Astronomy. – HDE 226868 Apr 5 '15 at 0:19

## 1 Answer

You are correct that the status of a black hole is determined by its mass, but also by its radius. The gravitational field becomes stronger the bigger the mass and the closer you can get to that mass.

A black hole forms once a mass $M$ is compressed inside the Schwarzschild radius $r_s = 2GM/c^2$. i.e. once its density achieves $$\rho > \frac{3M}{4\pi r_s^{3}}$$ i.e. when a central mass $M$ has a density that exceeds $$\rho > \frac{3}{32\pi} \frac{c^6}{G^3 M^2} = 1.8\times10^{19} \left(\frac{M}{M_{\odot}}\right)^{-2}\ {\rm kg/m}^3$$ This is a ball park figure and assumes spherical symmetry and neglects any detailed GR treatment, but is more or less correct - a few times higher than typical neutron star densities.

In other words it is the density of the material that largely determines whether something becomes a black hole. The mass is only an indirect parameter.

At the start of its life, the density of a super-massive star is actually lower (on average, and at the core) than the density of the Sun, so nowhere near high enough to form a black hole. Later in its (relatively) short life, after several nuclear burning stages, the core becomes very much denser - of order $10^{12}$ kg/m$^{3}$ and has a mass of just over a solar mass. This is still way to small to form a black hole. But what happens then is that once the core consists of iron (and other iron-peak elements), there is no further energy generation and electron degeneracy pressure is no longer capable of supporting the core against its weight and it collapses. If that collapse results in densities exceeding about $10^{18}$ kg/m$^3$ then a black hole can form at the centre.