How do you model an NFW Dark Matter Halo?

Mike Doonsebury 08/25/2017. 0 answers, 132 views
astrophysics computational-physics dark-matter galaxy-rotation-curve

I am trying to reproduce the results of Sofue's 2016 paper ( 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:

$$M_h(R)=4 \pi \rho_0h^3\left(\ln\left(1+X\right)-\frac{X}{1+X}\right)$$ $$V_h(R)=\sqrt{\frac {G M_h(R)}{R}}$$

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 Navarro-Frenk-White (NFW) halo so that it matches the data but has a reasonable density?

Update: 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.

Kyle Kanos 08/26/2017
Model how? Like plotting the distribution? For use in $n$-body simulations?
Mike Doonsebury 08/27/2017
@KyleKanos - To compare observed velocity against predicted you need to determine the masses for the bulge, disk and halo components of a galaxy. Typically you use properties like the bulge mass, bulge scale radius, disk central density, disk scale radius, halo representative density, halo scale radius to model the total mass at a given radius. This mass tells you the predicted velocity of an object in orbit at that radius. The model velocity can then be compared to the measured velocity.

No Answers Yet

Related questions

Hot questions


Popular Tags