We investigate the mass profile of \Lambda CDM halos using a suite of numerical simulations spanning five decades in halo mass , from dwarf galaxies to rich galaxy clusters .
These halos typically have a few million particles within the virial radius ( r _ { 200 } ) , allowing robust mass profile estimates down to radii below 1 \% of r _ { 200 } .
Our analysis confirms the proposal of Navarro , Frenk & White ( NFW ) that the shape of \Lambda CDM halo mass profiles differs strongly from a power law and depends little on mass .
The logarithmic slope of the spherically-averaged density profile , as measured by \beta = - d \ln \rho / d \ln r , decreases monotonically towards the center and becomes shallower than isothermal ( \beta < 2 ) inside a characteristic radius , r _ { -2 } .
The fitting formula proposed by NFW provides a reasonably good approximation to the density and circular velocity profiles of individual halos ; circular velocities typically deviate from best NFW fits by less than 10 \% over the radial range which is well resolved numerically .
On the other hand , systematic deviations from the best NFW fits are also noticeable .
Inside r _ { -2 } , the profile of simulated halos becomes shallower with radius more gradually than predicted and , as a result , NFW fits tend to underestimate the dark matter density in these regions .
This discrepancy has been interpreted as indicating a steeply divergent cusp with asymptotic inner slope , \beta _ { 0 } \equiv \beta ( r = 0 ) \sim 1.5 .
Our results suggest a different interpretation .
We use the density and enclosed mass at our innermost resolved radii to place strong constraints on \beta _ { 0 } : density cusps as steep as r ^ { -1.5 } are inconsistent with most of our simulations , although \beta _ { 0 } = 1 is still consistent with our data .
Our density profiles show no sign of converging to a well-defined asymptotic inner power law .
We propose a simple formula that reproduces the radial dependence of the slope better than the NFW profile , and so may minimize errors when extrapolating our results inward to radii not yet reliably probed by numerical simulations .