Gaussian Random Field Power Spectrum and the Sérsic Law

The surface-brightness profiles of galaxies are well described by the Sérsic law: systems with high Sérsic index m have steep central profiles and shallow outer profiles, while systems with low m have shallow central profiles and steep outer profiles. R. Cen has conjectured that these profiles arise naturally in the standard cosmological model with initial density fluctuations represented by a Gaussian random field (GRF). We explore and confirm this hypothesis with N-body simulations of dissipationless collapses in which the initial conditions are generated from GRFs with different power spectra. The numerical results show that GRFs with more power on small scales lead to systems with higher m. In our purely dissipationless simulations, the Sérsic index is in the range 2 ≤ m ≤ 6.5. It follows that systems with Sérsic index as low as m = 2 can be produced by coherent dissipationless collapse, while high-m systems can be obtained if the assembly history is characterized by several mergers. As expected, dissipative processes appear to be required to obtain exponential profiles (m = 1).