Question

2.) Explain why a star ceases to contract when the deBroglie wavelength of its electrons approximately
    equals the average distance between electrons.

Answer 1

to calculate the luminosity produced by fusion, in addition to understanding how luminous a star needs to be from energy transport. We have

and

When the fusion luminosity is equal to the luminosity that can leak out, then the star is in steady state. This condition, plus hydrostatic equilibrium, give the properties of stars on the main sequence. In other words, given the mass, you can solve for L,T_c,T_eff,R.

We can start with an object that is not fusing, but is radiating energy away. That is, it is undergoing Kelvin Helmholtz contraction. As the object contracts, its central temperature increases, which in turn increases the luminosity due to fusion (once it is hot enough for at least some fusion to occur). This fusion luminosity will eventually increase to the point that it is equal to the luminosity being radiated away, at which point the object ceases contracting. Once this happens, the star ceases contracting, the central temperature stays fixed, the luminosity is fixed, and the star is on the main sequence. Well, almost fixed. The composition of the star will change as it fuses, which will cause very slow changes in these properties even while it is on the main sequence. This phase of hydrogen fusing lasts longer than any other stage of a star