Formation rate of gravitational structures and the cosmic X-ray background radiation

TL;DR

This paper derives analytical formulas for the formation and destruction rates of gravitational structures from primordial density fluctuations, enabling predictions of their observable effects, such as contributions to the cosmic X-ray background.

Contribution

It provides a new analytical framework linking structure formation rates with cosmological observations, specifically modeling galaxy cluster contributions to X-ray background.

Findings

Clusters of galaxies can explain a significant part of the soft X-ray background.

The model aligns with COBE normalization in a cold dark matter universe with specific parameters.

The derived formulas reproduce the time derivative of the Press-Schechter mass function.

Abstract

Analytical expressions for the rates of formation and destruction of gravitationally bound systems are derived assuming that they are originated from primordial random-Gaussian density fluctuations. The resulting formulae reproduce the time derivative of the Press-Schechter mass function in a certain limit. Combining a theoretical model for the evolution of structures with the formation rate, we can make various cosmological predictions which are to be compared with observations. As an example to elucidate such applicability, we evaluate the contribution of clusters of galaxies to the cosmic X-ray background radiation. With the {\it COBE} normalization, we find that the significant fraction of the observed soft X-ray background is accounted for by clusters of galaxies in a cold dark matter universe with $\Omega_0 \sim 0.2$, $\lambda_0 =1- \Omega_0$ and $h \sim 0.8$.