Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

White dwarf v. sun magnitudes

  1. May 7, 2011 #1
    1. The problem statement, all variables and given/known data
    This is a past exam question that I am trying to get my head around but keep getting stuck
    Show that if a white dwarf were at the centre of the solar system instead of the sun, it would have an apparent visual brightness of -18.6mag.
    Assume that the white dwarf has surface temperature 3 times that of the sun and a radius 0.01 times that of the sun.
    The sun has absolute bolometric magnitude 4.75mag and the visual magnitude of the white dwarf will be 3 times smaller than it's bolometric magnitude.

    2. Relevant equations
    L=4πR2σT4
    Mbol=-2.5log(Lbol)+5+constant (absolute bolometric magnitude)
    m1-m2=-2.5log(L1/L2)
    m-M=-2.5log(d) – 5 (M=absolute magnitude, m=apparent magnitude, d=distance in parsecs)



    3. The attempt at a solution
    L(sun)=4πR2σT4
    L(dwarf)= 4π(0.01R)2σ(3T)4=34 *0.012 *Lsun
    M(dwarf)-M(sun)=- 2.5log(L(dwarf)/L(sun))=-2.5log(34*0.012)=5.23
    M(dwarf)=5.23 +M(sun)=-5.23+ 4.75= 9.98
    m=5log(d) – 5 +M
    d=1AU =4.84813681 × 10-6 Parsecs
    m=5log(4.84813681 × 10-6) – 5 + 9.98=-21.6
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted