How do we know the temperature of the Sun’s core, if we can’t even go near it?

Question

I’ve read a lot of astronomy, and it’s always been emphasized how hot the Sun’s core is, 15 million C.

But HOW did we get to that number? Why specifically 15 million and not scientists ballparking it as ‘more than a million’?

I’ve studied transport phenomena in university, so I guessed that maybe they constructed an equation of temperature as a function of radius, and substituted r=0 to get 15 million. But it can’t possibly be that simple, as the Sun has different layers of unknown size (and if known, how do we know?) that we aren’t even about the properties.

If possible, explain this to me as simple as possible, while still describing simply the math that caused the scientist to arrive at the 15 million number

In: Planetary Science

Answer 1

The sun is in a state called “thermal equilibrium,” which is just a fancy way of saying that it isn’t heating up or cooling down (at least not very quickly). Since we know that it isn’t heating up or cooling down, we must *also* know that the amount of heat that it is releasing from its surface is equal to the amount of heat it is creating in its core.

This should make some inuitive sense. For example, if the sun was creating more heat in its core than it was releasing from the surface, that would mean the sun would heat up. Otherwise, where would that extra energy be going? Likewise, if the sun was creating less heat in its core than it was releasing from the surface, then that would mean the sun would have to cool down. Otherwise, what source of energy would keep the sun at the same temperature?

As you mentioned, we can’t directly measure the temperature at the core of the sun, but we *can* measure how much energy is being released by the *surface* of the sun. Since we know that the amount of energy being released at the surface of the sun must be the same amount of energy being released at the core of the sun, we can calculate how much energy is being created at the sun’s core. We can then take this amount of energy, do some fancy math based on thermodynamics and the phsyical properties of the sun (like volume, density, etc.), and calculate that the core of the sun *must* be a certain temperature based on how much energy it is releasing.