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Galaxy rotation curve: Applicability of formula

  1. Feb 2, 2007 #1
    1. The problem statement, all variables and given/known data
    Derive and plot the rotation curve of a galaxy with logarithmic potential:
    [tex]\Phi(R, z) = \frac{v_0^2}{2}\ln{(R_c^2 + R^2 + q_{\phi}^{-2} z^2)}[/tex]
    where [tex]R_c =[/tex] 2 kpc, [tex]q_{\phi} =[/tex] const. and [tex]v_o = 200 kms^{-1}[/tex]. Note that [tex]v_c[/tex] is defined for z = 0 only.

    2. Relevant equations
    [tex]v_c^2 = -2 \Phi(R, z)[/tex]

    3. The attempt at a solution
    I'm just wondering if the above equation for circular velocity is applicable in this case. All signs point to yes, but I'm just worried about additional criteria that I may be overlooking.
  2. jcsd
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