Characteristic density of a Navarro--Frenk--White profile (${\rho }_s$)

The characteristic density of a Navarro--Frenk--White profile is its normalization ${\rho }_s$ at fixed scale radius of a Navarro--Frenk--White profile $r_s$. It is not the density at that radius: substituting $r=r_s$ in the NFW profile gives $\rho (r_s)={\rho }_s/4$. Once $r_s$ is fixed, doubling ${\rho }_s$ doubles the enclosed mass at every radius. This separates a profile's density normalization from its radial scale.