A necessary condition for best fitting analytical to simulated density profiles in dark matter haloes
Generalized power-law (GPL) density profiles are compared with simulated dark haloes (SDH) density profiles, and nonlinear least-squares fits are prescribed, involving five parameters which specify the fitting profile (RFSM5 method). More specifically, the validity of a necessary condition for the occurrence of an extremal point, is related to the existence of an intersection between three surfaces in a 3-dimension space. An application is made to a sample of 17 SDHs on the scale of cluster of galaxies, within a flat /\CDM cosmological model. In dealing with the averaged SDH density profile (ADP), a virial radius, equal to the mean over the whole sample, is assigned, which allows the calculation of the remaining parameters. The exponents of both the best fitting GPL density profile to ADP and related averages calculated over the whole halo sample, are far from their NFW counterparts. Values of asymptotic inner slope of fitting logarithmic density profiles, are consistent with results from recent high-resolution simulations.