2D surface density plot in Mathematica

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SUMMARY

The discussion focuses on plotting the function \(\sigma(r, \phi) = \frac{3r^2}{\sqrt{1 - r^2}} e^{i(2 \phi - \omega t)}\) in Mathematica to visualize a "bar shape" for a galactic disk. The user expresses difficulty in generating a 2D plot, as most Mathematica plotting functions default to 3D representations. The suggestion to utilize PolarPlot is highlighted as a potential solution for achieving the desired 2D visualization while ignoring the time variable.

PREREQUISITES
  • Familiarity with Mathematica 12.0 plotting functions
  • Understanding of polar coordinates and their representation
  • Basic knowledge of complex functions and their graphical interpretation
  • Experience with mathematical functions involving multiple variables
NEXT STEPS
  • Research how to implement PolarPlot in Mathematica for complex functions
  • Explore the use of Manipulate in Mathematica to visualize changes over time
  • Learn about 2D surface density representations in astrophysics
  • Investigate alternative plotting libraries compatible with Mathematica for enhanced visualization
USEFUL FOR

Astrophysicists, data scientists, and Mathematica users interested in visualizing complex mathematical functions, particularly in the context of galactic structures.

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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