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
We have models based on our understanding of the relationship of energy and matter in a hydrogen fusion process (what the source of energy in the Sun is), and we can calculate based on those models.
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.
We certainly can’t put a thermometer there, but we can directly measure lots of things about the sun, such as the power density of radiation it produces, the color temperature and size. From this and other variables we can be fairly certain of its mass and composition, then we can model the fusion reaction powering the sun, how much energy is dissipated, density, etc. There’s lots of complex modeling but that’s the eli5.
We sort-of know what the sun is made of, partly because we’ve measured its “size”, “mass” and “spectral lines”, which gave us density which we can compare to materials we have on earth.
We also know the “temperature” of the sun’s surface due to black body radiation math and the colour of the light it produces.
Then, we know how much energy leaves the sun every second because we can measure it on earth and its result on other planets.
We can use all of this information to formulate a rate at which heat has to leave the core to sustain the size, density, colour and heat of the sun.
And lastly, we know from modelling and experimentation how quickly heat can flow from hydrogen to other hydrogen – thermal conductivity, which depends on a temperature gradient.
If the core is colder than that, the rate at which heat could leave would be too low to sustain the colour and size of the sun.
> 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.
This works pretty well, and it was the main method until recently.
The Sun has a couple of different fusion processes, their rate all depends on the temperature. Some of these processes emit neutrinos (or produce things that then decay and emit neutrinos), and different processes have a different energy distribution for the neutrinos. We can measure that energy distribution, compare it to our expectation for different temperatures, and see what fits best. That confirms the 15 million we already calculated with a completely independent method.
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.
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.
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.
Without visiting the core of the sun and taking a physical reading it is very much hard to record and state for a fact it is 15 million degrees or whatever
To my knowledge no one has stated the suns core is 15 million degrees as fact
But a lot of science has gone into figuring out a range of what it would most likely be and then that gets simplified so our text books would read 15 million degrees because that’s all anyone would need to know unless they were to get into the field itself in which they would then research the relevant papers and data and make their own observations
Science often isn’t down to exact sometimes it’s about ranges and probabilities until new data and/or analysis proves otherwise, we still learn something new here n there even within our own planet let alone the solar system or the universe for that matter
We can measure how much energy the sun is releasing as light, and how much mass it has. From those can calculate what the temperatures and pressures need to be for fusion to produce the amount of energy the sun emits.
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