This is a good question! As far as I have learnt from my dive into cosmic structure growth, I would say that NFW profiles work well if the structure you consider is dominated by gravitational self-interactions. Here is a short video how I derived the NFW (and NFW-like) profiles:
https://youtu.be/WhxyVvO1YjA?si=NDYk7IEJN9mKEkb2
...and here are the two corresponding papers, with the details of maths:
Article Cosmic structures from a mathematical perspective 1: dark ma...
...and the details of physical reasoning:
https://ui.adsabs.harvard.edu/abs/2020IJMPD..2943017W/abstract
Hope that helps, Peyman Zakeri !
Jenny Wagner Thank you so much for your response. I appreciate it. I check your video and papers.
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? How about the formula ρ(z)=ρ_0*(1+z)^3
Peyman Zakeri : have a look at the video, then you will find the criteria when you can use NFW. You need to know the properties of the host galaxy, what's its size, what is the AGN-, SNe-feedback, etc... besides that, the props of the observation is important: what are the constraints on the profile that we know (at high res, Einasto profiles might be preferred).
And you can always use a chi-squared fit, it will tell you whether a single power law is sufficient compared to NFW. (BIC/AIC for Bayesian analyses also work in a similar way, if you use Bayesian stats).
From my experience, it will rather be a rho \propto r^(-a) with a somewhere between 0 and 2 and not 3 with r being a dimensionless radius and not the redshift...
Jenny Wagner Thank you so much for your explanation. It's very useful in my project!
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