We use Navarro–Frenk–White (NFW) to calculate Dark Matter (DM) density. Can we use it for DM halo in any galaxy or is it used only for Milky Way (MW)?
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$\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$– Community BotCommented Sep 9, 2023 at 5:44
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$\begingroup$ I want to calculate the halo DM mass density at special location in the cosmos (at redshift z=0.151 in a galaxy) $\endgroup$– PeymanCommented Sep 9, 2023 at 5:51
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$\begingroup$ @Peyman The NFW profile is dependent on the characteristic overdensity of the halo. The latter is a function of the matter density parameter $\Omega_m$ value of the Universe. A quick search gives me this note, which may be useful for your purpose (astro.yale.edu/vdbosch/jerusalem_lecture3.pdf) $\endgroup$– S.GCommented Sep 9, 2023 at 7:04
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$\begingroup$ Thank you so much for your explanation. I appreciate it. $\endgroup$– PeymanCommented Sep 10, 2023 at 13:37
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The NFW profile doesn't work for all galaxies, and it doesn't work for the Milky Way either.
The NFW profile is a pretty good fit to the structures of simulated dark-matter-only systems. In practice, that means it's a reasonably good description of galaxy clusters, because ordinary matter behaves like dark matter at such scales, and of small, dark-matter-dominated dwarf galaxies.
The dark matter halos of larger galaxies, like the Milky Way, are significantly altered by the dynamics of the ordinary matter. The main effect is that the formation of the galaxy, which is much more compact than the halo, causes the halo to contract. This is called "adiabatic contraction" and results in the halo being more compact than the NFW paradigm would predict. For example, based on the observationally constrained mass model of Cautun et al. (2020), here is the mass distribution of the Milky Way halo (solid blue curve), compared to the original NFW density profile (dotted green curve).
The contracted halo has more mass near the center of the system and less mass farther out. However, the effect is only significant below around 10 kpc, where baryons either dominate the density or come close to it. (The orange dashed curve shows the spherically averaged baryon density.)
Many works still approximate NFW profiles for galactic halos, though. It's simple, and a lot of calculations don't need accuracy badly enough to justify a more careful description.
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$\begingroup$ Thank you for your response. I appreciate it. So, what should I do if I want to calculate the halo DM mass density at special location in the cosmos? $\endgroup$– PeymanCommented Sep 9, 2023 at 7:11
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$\begingroup$ @Peyman That's a really broad question! What sorts of details do you know about the system? The most careful approach would be to find systems similar to the one you are interested in within cosmological hydrodynamic simulations. Lots of simulation data are publicly available (example). Failing that, you could adopt an NFW profile and apply a semi-analytic model for adiabatic contraction (see for example the approach used by this paper). Alternatively, if accuracy isn't critical, just use an NFW profile. $\endgroup$– StenCommented Sep 9, 2023 at 15:54
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$\begingroup$ Actually, I want to calculate the halo DM mass density (ρ(r)) at redshift z=0.151 where GRB221009A is located. Can I use NFW formula? How about the formula ρ(z)=ρ_0*(1+z)^3 $\endgroup$– PeymanCommented Sep 11, 2023 at 4:22
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$\begingroup$ @Peyman $\rho=\rho_0 (1+z)^3$ (where $\rho_0$ is the mean DM density today) gives the mean dark matter density at redshift $z$. However, a gamma-ray burst presumably came from a galaxy, since that's where stars are. Are the galaxy it originated in and its position therein known? Without information, I'd probably approximate that the DM density near the gamma-ray burst is around $10^5$ or $10^6$ times the mean dark matter density at that redshift. That's about how much more dense our dark matter environment is than the present-day average. But you can do better with knowledge of environment. $\endgroup$– StenCommented Sep 12, 2023 at 2:09
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$\begingroup$ Thank you for your explanation. Unfortunately, we have no information about a galaxy where gamma-ray burst is located. In this way, what should I do? I think its better to approximate DM density at that redshift (i.e. z=0.151) $\endgroup$– PeymanCommented Sep 12, 2023 at 4:50