# Surface vs Apparent Brightness

1. Nov 10, 2015

### Huej

I'm confused what the difference between the two are...I thought surface brightness was luminosity, but apparently it's not: L=Surface brightess x Area...But I came across a similar equation that seems to assume surface brightness is the same as apparent brightness. Please help!
Edit: Also, why does temperature increase towards the core of a star but also increase in density? Shouldn't they be inversely related?

Last edited: Nov 10, 2015
2. Nov 10, 2015

### davenn

https://www.e-education.psu.edu/astro801/content/l4_p4.html

does it help ?

because only in the core is where the nuclear reactions are occurring and heat is transported to the surface by 2 methods
firstly by a radiative zone then finally to the surface by a convective zone .....

why would you think that ?

Dave

3. Nov 15, 2015

### vela

Staff Emeritus
Because the pressure increases as well. Remember a volume in the interior has to support the weight of all of the mass above it.

4. Nov 16, 2015

### Huej

The ideal gas law would show an inverse relationship.

5. Nov 17, 2015

Staff Emeritus
The sun is not an ideal gas.

6. Nov 17, 2015

### phyzguy

I don't think the answer to the OP's question is that the sun is not an ideal gas. The sun is actually quite well described by the ideal gas laws. The answer is that the ideal gas laws do not imply an inverse relationship between density and temperature unless the pressure is constant, as vela said a couple of posts ago. The ideal gas law is usually written P V = n k T, so if we define the density as ρ = n/V, then we can write it as P = k ρ T. In the sun, P, T, and ρ all increase monotonically as we move from the outside to the interior, and they increase in such a way that the ideal gas laws are satisfied at all radii. There is no contradiction here to the ideal gas laws.

As far as the original question on surface brightness and apparent brightness, try reading the Wikipedia article on luminosity and magnitude here. Luminosity refers to the total amount of radiation a star emits, whereas brightness depends on how far away it is. A 100 Watt light bulb has a specific luminosity, but its brightness gets less as you move away from it. If you have specific questions on this, come back and ask.

7. Nov 17, 2015

### SteamKing

Staff Emeritus
Well, a star is a big collection of hydrogen gas, initially. What keeps all this hydrogen together to form the star is gravity. Since the gravity in the ball of hydrogen never shuts off, the ball of hydrogen wants to get smaller and smaller, and this means that the hydrogen in the center is going to get hotter and denser as the ball gets smaller. After a certain point, the hydrogen at the very core of the ball of gas will 'ignite' in a series of nuclear fusion reactions, the chief result of which is that the temperature at the core of the star gets really hot, like millions of degrees hot, and it stays hot, as long as there is hydrogen in the core to keep feeding the fusion reactions.

Now, this hot ball of fusing hydrogen gas wants to expand, because of the high temperature, but if it expands beyond a certain point, the fusion reactions will stop, gravity takes over again, the core gets smaller and hotter, and the fusion reactions start again, making the core want to expand. After a certain time, some of the energy produced by the fusing hydrogen at the core of the star eventually reaches the outer, less dense layers, and is radiated into space. In other words, a system is set up, whereby the star is continually kept from collapsing onto itself by the high temperatures at the core wanting to expand the star and thus serving to counterbalance the attractive nature of gravity.

https://en.wikipedia.org/wiki/Stellar_structure

The study of the mechanism of how stars work, how they form, and how they age and eventually die is covered by stellar astrophysics.

8. Nov 17, 2015

### davenn

Thanks for the additional posts guys

9. Nov 17, 2015

### D H

Staff Emeritus
That's only if you ignore gravity, adiabatic compression, and fusion. That is essentially ignoring everything that happens inside the Sun.

Any point in the interior of the Sun must be close to being in an equilibrium state, where the outward forces due to pressure more or less balance the inward forces due to gravitation. (Justification: The Sun has remained more or less unchanged for about for 4.6 billion years.) This leads to the hydrostatic equilibrium condition: The pressure at any point inside the Sun is just enough to counteract the weight of all of the stuff above that point. As the temperature of a gas increases as it is compressed adiabatically, the temperatures in the interior of the Sun should be (and are) much higher than the surface temperature.

This compression would ultimately lead to a gravitational collapse if it weren't for fusion in the Sun's core. Suppose the fusion rate drops at some point in the Sun's core. This would in turn make the temperature drop, which in turn would pressure drop, which would in turn result in in-falling material, which would in turn increase the pressure, which would in turn increase the temperature, which would in turn increase the fusion rate. Fusion represents a built-in negative feedback regulator.

As an aside, the lack of such a negative feedback regulatory mechanism is what makes very massive stars turn into neutron stars or black holes at the end of their lives.