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Apparent Flux and number of stars

  1. Jul 15, 2016 #1
    The stars in our Galaxy have luminosities ranging from $L_{\text{min}}$ to $L_{\text{max}}$. Suppose that the number of stars per unit volume with luminosities in the range of $L$, $L+dL$ is $n(L)dL$. The total number of stars per unit volume if clearly $$n = \int_{L_{min}}^{L_{max}} n(L)dL.$$ Show that the total number of stars with apparent flux $f \geq f_0$ is $$N(f \geq f_0) = \frac{A}{f_0^{3/2}}$$ and find $A$ in terms of $n(L)$.


    We have that the flux $f$, is given by $$f = \frac{L}{4 \pi r^2}.$$ Therefore, take $L_{min} = 4\pi r^2 f_0$ and $L_{max} = 4\pi r^2 f$. We thus have that $$N = \int_{4\pi r^2 f_0}^{4 \pi r^2 f} n(L) dL.$$ Is this on the right track?
     
  2. jcsd
  3. Jul 16, 2016 #2
    You are wrong in final equation.
    \begin{equation}
    N=n.A.l
    \end{equation}
    You know
    \begin{equation}
    n = \int_{L_{min}}^{L_{max}} n(L)dL.
    \end{equation}
    If we put this to first equation we get
    \begin{equation}
    N = \int_{L_{min}}^{L_{max}} n(L)A.LdL.
    \end{equation}

    Other equations are true, i think
     
  4. Jul 16, 2016 #3
    Where did you determine that first equation from?

    Also, do we therefore conclude that $$A = \frac{N}{\int_{L_{min}}^{L_{max}} L \cdot n(L) dL}?$$
     
  5. Jul 17, 2016 #4
    In my equations A is area. In my equation
    \begin{equation}
    A=4.\pi.r^2=S
    \end{equation}
    I should have S for this for doesn't mixing the question provided and asked constant.
    And also i had mistake in the above post
    \begin{equation}
    N=n.V
    \end{equation}
    where is V volume, n tota number of star per unit volume.
    And you have to express n(L) depends on variables we know. But i didn't found these method i think in this problem there aren't enough knowledge to get this. This question from a textbook? If yes you may look up the issues maybe n(L) defined by in the textbook.
     
    Last edited: Jul 17, 2016
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