White dwarf v. sun magnitudes

  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
    Mbol=-2.5log(Lbol)+5+constant (absolute bolometric magnitude)
    m-M=-2.5log(d) – 5 (M=absolute magnitude, m=apparent magnitude, d=distance in parsecs)

    3. The attempt at a solution
    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
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