1. The problem statement, all variables and given/known data Consider a star with a density distribution ⍴ = ⍴_0(R/r), where R is the star’s outer radius. The star’s luminosity is L, and all of its energy is generated in a small region near r = 0. Outside that region the heat ﬂow is constant. a) Find the surface temperature of the star T_s assuming a black body. b) Assuming the opacity is dominated by electron scattering at all radii (i.e., a constant κ_es), solve for the temperature as a function of radius inside the star, excluding the energy-generating region. (Hint: the algebra will be easier if you rewrite the heat ﬂow in terms of Ts.) 2. Relevant equations L=AσT^4 L=M^3.5 (not too sure about this one) 3. The attempt at a solution a) Im given a density profile and so i find the mass m(r)=∫4πR2ρ_0 (R/r)dr (since we're finding the surface temperature I figured the limits will be from 0→R therefore M=2πR3ρ0 then I sub in the the 2 equations in the relevant equations part and M from above: L=Aσ(T^4)=M^3.5=(2πR3ρ0)^3.5 and then rearrange to find T (I dont get anything simple/neat so that throws me off a little) Im wondering if this method is wrong in tackling this problem. b) im lost on this part of the question, any help will be appreciated thanks!