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

There are layers but the sun is in equilibrium, the power radiated from the surface is equal to the power generated in the core and the energy flux through all the layers is in a steady state.