2D surface density plot in Mathematica

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thealyosha
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I am trying to plot the following function:

\sigma(r, \phi) = \frac{3r^2}{\sqrt{1 - r^2}} e^{i(2 \phi - \omega t)}

where \sigma is a surface density, r is radius, and \phi is azimuthal angle.

It is supposed to yield a "bar shape" for a galactic disk, but I'm not sure how to go about plotting it. It seems like all two-variable Mathematica plots yield 3D images, but I need a 2D image. The function also has a time variable, which I have been ignoring.
 
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Possibly using a PolarPlot would be somewhere to start?