- #1
zephyr5050
- 21
- 0
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
\rho (r) = \frac{\delta_c \rho_c}{(r/r_s)(1+r/r_s)^2}
where
\delta_c = \frac{200}{3} \frac{c^3}{ln(1+c)-c/(1+c)}
r_s = r_{200}/c
and \rho_c is the critical density of the universe (as a function of redshift). The parameter r_{200} is the virial radius which is defined as the radius at which the mass density of the halo is 200\rho_c.
Now we can't really talk about the mass of this halo because the integral from 0 to \infty diverges. Instead, we use the fiducial radius r_{200} and define the quantity M_{200} to be the mass inside the radius r_{200}. It can be shown that
M_{200} = \frac{800\pi}{3}\rho_c r_{200}^3
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 r_{200} \equiv 200 \rho_c? Is there any logic to this, is it historical, arbitrary? What's going on here?
\rho (r) = \frac{\delta_c \rho_c}{(r/r_s)(1+r/r_s)^2}
where
\delta_c = \frac{200}{3} \frac{c^3}{ln(1+c)-c/(1+c)}
r_s = r_{200}/c
and \rho_c is the critical density of the universe (as a function of redshift). The parameter r_{200} is the virial radius which is defined as the radius at which the mass density of the halo is 200\rho_c.
Now we can't really talk about the mass of this halo because the integral from 0 to \infty diverges. Instead, we use the fiducial radius r_{200} and define the quantity M_{200} to be the mass inside the radius r_{200}. It can be shown that
M_{200} = \frac{800\pi}{3}\rho_c r_{200}^3
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 r_{200} \equiv 200 \rho_c? Is there any logic to this, is it historical, arbitrary? What's going on here?