Structural properties of spherical galaxies obeying the Sersic R¹/n law: a semi-analytical approach

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By considering that the distribution of measured light along any galactocentric radius of an elliptical galaxy can be well represented by a R¹/ⁿ Sersic law, we propose in this paper a ``discrete ordenate'' method, which, for any value of n, allows an explicit expression for the luminous density, rho(r), to be found that can be numerically evaluated to any required precision. Once we have this semi-analytical expression for the spatial density, rho(r), the mass distribution, M(r), the potential, phi(r), and the velocity dispersions, sigmaₛ²(r), in the space and in the observational plane, sigmaₚ²(R), can be computed in a straightforward manner.