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

Stellar cores for normal stars are actually not super complex. We can make very good models fairly simply, and the temperature can be found using them. The main question is how hot and dense does something have to be for fusion to occur, which we’ve been able to model and calculate for quite some time. This exercise is often done early in undergraduate astrophysics classes, so it’s really not too hard at all (relative to other things). It turns out that the middle layers are much more complicated, and things change as stars get older.