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I have currently been reading up on dark matter halos as I’m considering doing a small project on them for my degree. I plan to use an (approximated) analytical equation for the density at r of an isothermal halo in terms of the halos central density and core radius.

density(r) = density(0) * (a^2)/(a^2+r^2)

where a = core radius.

How would I be able to fix either the core radius or central density of in order to model the Milky Way?

I would love to compare this result with a model of the milky way that has an NFW profile.

Regarding the NFW halos, I’m having trouble with the virial radius. The virial radius is needed in order to calculate the scale radius, which is used in the equation for the density at r. I understand the virial radius is the radius of a sphere that encompasses around 200 times the critical density. But how does the virial radius compare to the physical radius of a halo. For instance, I've read the virial radius for the Milky Way was 428 kpc or so. Much larger than the radius of the milky way, which is around 15 kpc. Do I need the physical radius of the milky way in order to model it as an NFW halo?

Any help will be very much appreciated.

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# Isothermal v NFW halos

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