How do you model an NFW Dark Matter Halo? - Physics Stack Exchange most recent 30 from physics.stackexchange.com 2019-09-17T19:10:23Z https://physics.stackexchange.com/feeds/question/353679 https://creativecommons.org/licenses/by-sa/4.0/rdf https://physics.stackexchange.com/q/353679 1 How do you model an NFW Dark Matter Halo? Quarkly https://physics.stackexchange.com/users/32023 2017-08-25T12:47:07Z 2017-08-28T15:29:28Z <p>I am trying to reproduce the results of Sofue's 2016 paper (<a href="https://arxiv.org/abs/1510.05752" rel="nofollow noreferrer">https://arxiv.org/abs/1510.05752</a>). I'm able to use least squares minimization to model the bulge and disk effectively, but I get into trouble with the halo. By simply minimizing the residuals of this equation:</p> <p>$$M_h(R)=4 \pi \rho_0h^3\left(\ln\left(1+X\right)-\frac{X}{1+X}\right)$$ $$V_h(R)=\sqrt{\frac {G M_h(R)}{R}}$$</p> <p>I can match the data pretty well, except I get a density that is far less dense than critical, which is impossible (you can't have a halo that is less dense than the surrounding universe). Sofue provides some equations describing $M_{200}$, $R_{200}$ and $X_{200}$, but I can't connect the dots. How do you model an <a href="https://en.wikipedia.org/wiki/Navarro%E2%80%93Frenk%E2%80%93White_profile" rel="nofollow noreferrer">Navarro-Frenk-White (NFW) halo</a> so that it matches the data but has a reasonable density?</p> <p><strong>Update:</strong> Sofue has an $R_{MAX}$ value which limits the size of the halo scale radius, but even using this, the minimization always hits $R_{MAX}$ as a limit for the halo scale radius. It appears that any attempt to simply match a dark matter halo to a velocity curve is going to dilute the dark matter to an unreasonable quantity.</p>