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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=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!
     
  2. jcsd
  3. Mar 27, 2014 #2

    DrClaude

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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

    DrClaude

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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

    DrClaude

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    Staff: Mentor

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

    Thread closed.
     
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