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

You create a model. We know the mass, the composition, the luminosity and the radius. Maybe you don’t need that much.

If you have those values (maybe others too), you’ll be able to figure out what the core temperature is. If it’s cooler, the radius and luminosity would surely change. We can also measure the solar wind to figure out what the mass loss is, which must be somewhat related to the temperature.

We know what the minimum temperature has to be for fusion to overcome the forces pushing atoms apart, and I assume any superheat is calculated based on the other numbers I mentioned.