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A star's temperature

  1. Mar 26, 2014 #1
    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=M^3.5 (not too sure about this one)

    3. The attempt at a solution

    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:
    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.

    im lost on this part of the question, any help will be appreciated

  2. jcsd
  3. Mar 27, 2014 #2


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    Staff: Mentor

    Do the units make sense?

    In that equation, what is A? What is σ?
  4. Mar 27, 2014 #3
    Im missing some units, in which case L ∝ M^3.5
    I was quoting the mass-luminosity relation M/M_solar =(L/L_solar)^a, what i wasnt sure about was using a=3.5 since there is not information regarding the type of star.
    A is the surface area of the star=4piR^2 and σ is the stefan boltzmann constant
  5. Mar 27, 2014 #4


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    Staff: Mentor

    Then you got all you need to calculate ##T##.
  6. Mar 27, 2017 #5
    For part b, use the temperature gradient and treat the opacity as a constant.
  7. Mar 27, 2017 #6


    User Avatar

    Staff: Mentor

    Please do not revive dead threads. The OP hasn't been here in almost three years.

    Thread closed.
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