NFW mass and circular-speed profile
= NFW mass and circular-speed profile
{c}
{title2=$M(r)=4\pi\rho_s r_s^3[\log(1+x)-x/(1+x)]$}
For an <NFW profile>, $x=r/r_s$ and $v_c^2=GM(r)/r$. The <circular speed> rises as $r^{1/2}$ at small radius and eventually decreases as $[\log(r/r_s)/r]^{1/2}$. Its maximum occurs at $x\simeq2.16258$, with $v_{c,\max}^2\simeq2.71706G\rho_s r_s^2$.