We have recently shown that both the Prugniel-Simien model and Sérsic ’ s function ( hereafter referred to as the Einasto model when applied to internal density profiles ) describe simulated dark matter halos better than an NFW-like model with equal number of parameters .
Here we provide analytical expressions for the logarithmic slopes of these models , and compare them with data from real galaxies .
Depending on the Einasto parameters of the dark matter halo , one can expect an extrapolated , inner ( 0.01–1 kpc ) , logarithmic profile slope ranging from \sim - 0.2 to \sim - 1.5 , with a typical value at 0.1 kpc around -0.7 .
Application of this ( better fitting ) model therefore alleviates some of the past disagreement with observations on this issue .
We additionally provide useful expressions for the concentration and assorted scale radii : r _ { s } ,r _ { -2 } ,r _ { e } ,R _ { e } ,r _ { vir } , and r _ { max } — the radius where the circular velocity profile has its maximum value .
We also present the circular velocity profiles and the radial behavior of \rho ( r ) / \sigma ( r ) ^ { 3 } for both the Einasto and Prugniel-Simien models , where \sigma ( r ) is the velocity dispersion associated with the density profile \rho ( r ) .
We find this representation of the phase-space density profile to be well approximated by a power-law with slope slightly shallower than -2 near r = r _ { -2 } .