Wednesday, October 30, 2013

galaxy rotation curves at large radii

can you give an expression $\upsilon_\mathrm{rot}(r)$ of how a galaxy rotation curve should look like far away from the centre of the galaxy?

1 comment:

1. at large distances, the density profile of NFW-spheres drops, $\rho(r) \propto r^{-3}$. equating the centripetal and gravitational forces yields: $$\upsilon_\mathrm{rot}(r)^2 = \frac{4\pi G}{r}\int\mathrm{d}r\:\rho(r) r^2 = 4\pi G\frac{\ln(r)}{r},$$ yielding $\upsilon_\mathrm{rot}(r)\propto\sqrt{\ln(r)/r}$