Gaussian random field power spectrum and the S\'ersic law

TL;DR

This paper demonstrates through simulations that the Sersic index of galaxy profiles naturally arises from Gaussian random field initial conditions, linking initial density fluctuations to galaxy structure.

Contribution

It confirms that the Sersic profiles of galaxies can be explained by Gaussian random field initial conditions in a dissipationless collapse framework, showing a range of possible indices.

Findings

Higher small-scale power in GRFs leads to higher Sersic index m.

Dissipationless collapse can produce Sersic index as low as 2.

High Sersic index systems may result from multiple mergers.

Abstract

The surface-brightness profiles of galaxies are well described by the S\'ersic law: systems with high S\'ersic 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 (2014, ApJL, 790, L24) 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 S\'ersic index is in the range 2<m<6.5. It follows that systems with S\'ersic 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).