Does the Sun have enough gravitation to bind its hydrogen/helium plasma?

Question

"Does the Sun have enough gravitation to bind its hydrogen/helium plasma?"
So my question arises from the fact that high energy (or high temperature in other words) hydrogen or helium gas just explodes, instead of being bounded in one place. Then I guess the Sun has enough gravitation to bound the ionized particles. I want to calculate the gravitational potential energy and compare it with kinetic energy of the plasma, but I just don't have enough information on the density of the Sun at each radius (layer).

probably_someone · Accepted Answer

Thermodynamics gives us the virial theorem: for any spherical, stable, self-gravitating distribution of particles, we know that its average total kinetic energy $langle Trangle$ and its average total potential energy $langle Urangle$ are related as follows:
$$2langle Trangle=-langle Urangle$$
In other words, the total kinetic energy of any such body is roughly half of what it would take to unbind the system. The Sun is a stable, self-gravitating spherical distribution of particles, so the virial theorem applies.

G. Smith · Answer

I just don't have enough information on the density of the Sun at each radius (layer).

According to NASA, the density profile is well-approximated by
$$D(x)=519x^4 −1630x^3 +1844x^2 −889x+155,$$
where $D$ is in grams per cubic centimeter and $x$ varies from $0$ at the center to $1$ at the surface.

Does the Sun have enough gravitation to bind its hydrogen/helium plasma?

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