# How to plot the freeze out equation for massive particle species in Mathematica? [closed]

I want to recreate the figure . This comes from the Cosmological Boltzmann equation which can be modified as the number density equation as

$$\frac{dY}{dx}=-\frac{s(m)<{\sigma}|v|>[y^2-Y_{eq}^2]}{x^2 H(m)}.$$

The equation is attached (Mathematica Codes):

ClearAll["Global`"]; m = 1000; sigmav = 0.0000000001; gstar = 106; mpl = 2.410^18, Sm = (2 pi^2)/45gstarm^3; Hm = 1.67*[gstar]^(1/2)m^2/mpl; Yeq[x_] = 0.145x^(3/2)*Exp[-x];

(s1=LogLogPlot[0.145x^(3/2)Exp[-x],{x,3,1000},PlotRange[Rule]All,
Frame[Rule]True,PlotStyle[Rule]Thick];
) s2 = NDSolve[{Y'[x] == x^-2Sm/Hmsigmav*(Y[x]^2 - (0.145*x^(3/2)*Exp[-x])^2), Y1 == Yeq1}, Y, {x, 1, 1000}]; LogLogPlot[{Evaluate[Y[x] /. s2], Yeq[x]}, {x, 1, 1000}, PlotRange -> All, AxesLabel -> Automatic, Frame -> True]

These results are derived using the help of "[The Early Universe]" by Kolb and Turner

Question: How to plot the freeze-out equation for massive particle species in Mathematica?

• @ProfRob I've adjusted the wording to make the question clearer (I hope!)
– uhoh
May 22 at 2:13
• @TrinayanSaikia Welcome to Astronomy Stack Exchange! I've made some small edits to help your question fit the site's format better, please check it and feel free to edit further. Thanks! Also, when we include figures we need to credit the source - is the plot you show from Kolb and Turner?
– uhoh
May 22 at 2:14
• I’m voting to close this question because this is question about Mathematica, not astronomy. May 22 at 7:13
• As this is purely a programming question, the main, SO, site might be appropriate. May 22 at 7:36
• It currently takes (AFAIK) 5 votes to close a question on Astronomy SE (only 3 on Physics SE by the way) so there's usually plenty of time for someone to change their question to meet objects. I did also explain my close vote (and members do not have to explain their votes, BTW), and I don't (at this time) see any great improvement. You need to edit the question to update it, not just comment. Comments are not considered permanent on SE and can be deleted or purged at any time. May 22 at 22:17