Simplified galaxy rotation curves with and without dark matter and their visual impact, Mathematica

rotationcurves.txt

Galaxy rotation curves in Mathematica
Author: Rodrigo Nemmen
Visually illustrating the impact of the presence of dark matter in speeding up the 
rotation of test particles in galaxies

Input
nϕ=15;
rmin=1;rmax=50; nr=40;
tmin=0; tmax=15Pi; 

Rotation curves
Only visible matter
Mvis=Piecewise[{{r^2,r<5},{25,r>5}}];
vvis=Sqrt[Mvis/r];
ωvis=vvis/r;

Dark matter
Mdm=Piecewise[{{r^2,r<5},{5*r,r>5}}];
vdm=Sqrt[Mdm/r];
ωdm=vdm/r;

Rigid body
vrigid=2*(r/50);
ωrigid=vrigid/r;

Plots: rotation curves
Plot[vrigid,{r,0,rmax},AxesStyle->Black,PlotStyle->Green]

Plot[{vdm,vvis,vrigid},{r,0,rmax},AxesStyle->Black]

Animation: rigid body 
Animate[ListLinePlot[
  ParallelTable[{r Cos[\[Omega]rigid*t + \[Phi]], 
    r Sin[\[Omega]rigid*t + \[Phi]]}, {\[Phi], 0, 2 Pi, 
    2 Pi/n\[Phi]}, {r, rmin, rmax, rmax/nr}],
  PlotRange -> {{-rmax, rmax}, {-rmax, rmax}}, AspectRatio -> 1],
 {t, tmin, tmax}, DefaultDuration -> 40, AnimationRunning -> False]

Animation: galaxies with and without dark matter
 Animate[Magnify[
  GraphicsGrid[{{
     ListLinePlot[
      ParallelTable[{r Cos[\[Omega]vis*t + \[Phi]], 
        r Sin[\[Omega]vis*t + \[Phi]]}, {\[Phi], 0, 2 Pi, 
        2 Pi/n\[Phi]}, {r, rmin, rmax, rmax/nr}],
      PlotRange -> {{-rmax, rmax}, {-rmax, rmax}}, AspectRatio -> 1],
     ListLinePlot[
      ParallelTable[{r Cos[\[Omega]dm*t + \[Phi]], 
        r Sin[\[Omega]dm*t + \[Phi]]}, {\[Phi], 0, 2 Pi, 
        2 Pi/n\[Phi]}, {r, rmin, rmax, rmax/nr}],
      PlotRange -> {{-rmax, rmax}, {-rmax, rmax}}, AspectRatio -> 1]
     }}]
  ],
 {t, tmin, tmax}, DefaultDuration -> 40, AnimationRunning -> False]