I've been working with NFW Dark Matter Halos recently. This is a particular density model for the halo developed by Navarro, Frenk, & White (NFW). The density structure has the form(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \rho (r) = \frac{\delta_c \rho_c}{(r/r_s)(1+r/r_s)^2} [/tex]

where

[tex] \delta_c = \frac{200}{3} \frac{c^3}{ln(1+c)-c/(1+c)} [/tex]

[tex] r_s = r_{200}/c [/tex]

and [itex] \rho_c [/itex] is the critical density of the universe (as a function of redshift). The parameter [itex] r_{200} [/itex] is the virial radius which is defined as the radius at which the mass density of the halo is [itex] 200\rho_c [/itex].

Now we can't really talk about the mass of this halo because the integral from 0 to [itex]\infty[/itex] diverges. Instead, we use the fiducial radius [itex]r_{200}[/itex] and define the quantity [itex]M_{200}[/itex] to be the mass inside the radius [itex]r_{200}[/itex]. It can be shown that

[tex] M_{200} = \frac{800\pi}{3}\rho_c r_{200}^3 [/tex]

While all this makes sense to me, there's one thing that I don't understand here. Where does this 200 come from? Why say [itex] r_{200} \equiv 200 \rho_c [/itex]? Is there any logic to this, is it historical, arbitrary? What's going on here?

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# NFW Dark Matter Halos and Virial Radius

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