Mathematica 2D surface density plot in Mathematica

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The discussion focuses on plotting the function σ(r, φ) = (3r²/√(1 - r²)) e^(i(2φ - ωt)) in Mathematica, which represents a surface density for a galactic disk. The user seeks a 2D representation, expressing concerns that typical Mathematica plots produce 3D images. They suggest that a PolarPlot might be a viable starting point for achieving the desired 2D visualization. The function's time variable is currently being disregarded in the plotting process. Overall, the goal is to effectively visualize the "bar shape" characteristic of the galactic disk.
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?
 

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