1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Galaxy Luminosity Function

  1. Mar 7, 2009 #1


    User Avatar

    1. The problem statement, all variables and given/known data

    The galaxy luminosity function [tex] \phi(L) [/tex] tells us the number density of galaxies as a function of luminosity L. The luminosity density of the universe l is thus given by the expression
    [tex] l = \int^{\infty}_{0}L\phi(L)dl [/tex]

    For a Schechter luminosity function,

    [tex] \Phi(L)dL = \phi^*(\frac{L}{L^*})^aexp(-\frac{L}{L^*}d(\frac{L}{L^*})) [/tex]

    Show that

    [tex] l = \phi^*L^*\Gamma(a + 2) [/tex]

    where the gamma function [tex] \Gamma(x) = \int^{\infty}_{0}t^{x - 1}e^{-t}dt [/tex]


    The Sloan Digital Sky Survey (SDSS) has recently measured the following Schechter
    parameters in the r passband: a = -1.16 [tex]\pm[/tex] 0.03, [tex]M^*[/tex] = -20.80 [tex]\pm[/tex] 0.03, [tex]\phi^*[/tex] = (1.50 [tex]\pm 0.13) * 10^2 h^3 Mpc^{-3}[/tex] 0.13). Given that the sun has absolute magnitude M = 4.62 in the SDSS r band, calculate the luminosity density in this band in solar units. Estimate the error on this quantity.
    [tex]\Gamma[/tex](0.84) = 1.122, [tex]\Gamma[/tex](0.81) = 1.153, [tex]\Gamma[/tex](0.87) = 1.094.

    2. Relevant equations

    Given in Question

    3. The attempt at a solution

    Okay, I am on the first part, but I am slightly unsure what to do. They give us

    [tex] \Phi(L)dL = \phi^*(\frac{L}{L^*})^aexp(-\frac{L}{L^*}d(\frac{L}{L^*})) [/tex]


    [tex] l = \int^{\infty}_{0}L\phi(L)dl [/tex]

    do we have to put these two equations together? How do we get Gamma out?
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads - Galaxy Luminosity Function Date
Luminosity problem Feb 16, 2017
Weight of object in outer space away from galaxies Sep 6, 2015
Active galaxies Apr 21, 2015
Astronomy: Speed at the edge of the galaxy Apr 7, 2015
Find the speed of a galaxy Feb 28, 2015