A NUMERICAL FIT OF ANALYTICAL TO SIMULATED DENSITY PROFILES IN DARK MATTER HALOES

SUMMARY: Analytical and geometrical properties of generalized power-law (GPL) density proles are investigated in detail. In particular, a one-to-one cor-respondence is found between mathematical parameters (a scaling radius, r0, a scaling density, 0, and three exponents, , , ), and geometrical parameters (the coordinates of the intersection of the asymptotes, xC, yC, and three verti-cal intercepts, b, b, b , related to the curve and the asymptotes, respectively): (r0; 0; ; ; ) $ (xC; yC; b; b; b). Then GPL density proles are compared with simulated dark haloes (SDH) density proles, and nonlinear least-absolute val-ues and least-squares ts involving the above mentioned ve parameters (RFSM5 method) are prescribed. More specically, the sum of absolute values or squares of absolute logarithmic residuals, Ri = log SDH(ri) log GPL(ri), is evaluated on 105 points making a 5-dimension hypergrid, through a few iterations. The size is progressively reduced around a ducial minimum, and superpositions on nodes of earlier hypergrids are avoided. An application is made to a sample of 17 SDHs on the scale of cluster of galaxies, within a at CDM cosmological model (Rasia et al. 2004). In dealing with the mean SDH density prole, a virial radius, rvir, averaged over the whole sample, is assigned, which allows the calculation of the remaining parameters. Using a RFSM5 method provides a better t with respect to other methods. The geometrical parameters, averaged over the whole sample of best tting GPL density proles, yield (; ; ) (0:6; 3:1; 1:0), to be compared wit