Statistics of gravitational potential perturbations: A novel approach to deriving the X-ray temperature function

TL;DR

This paper presents a new method to derive the X-ray temperature function of galaxy clusters directly from gravitational potential statistics, bypassing the need for poorly defined mass measurements, and aligns well with classical models.

Contribution

It introduces an analytical approach to obtain the X-ray temperature function from gravitational potential fluctuations without relying on halo mass definitions.

Findings

Derived temperature function agrees with Press-Schechter results

Method avoids using poorly defined halo masses

Potential-based approach reduces scatter in cluster data

Abstract

Context. While the halo mass function is theoretically a very sensitive measure of cosmological models, masses of dark-matter halos are poorly defined, global, and unobservable quantities. Aims. We argue that local, observable quantities such as the X-ray temperatures of galaxy clusters can be directly compared to theoretical predictions without invoking masses. We derive the X-ray temperature function directly from the statistics of Gaussian random fluctuations in the gravitational potential. Methods. We derive the abundance of potential minima constrained by the requirement that they belong to linearly collapsed structures. We then use the spherical-collapse model to relate linear to non-linear perturbations, and the virial theorem to convert potential depths to temperatures. No reference is made to mass or other global quantities in the derivation. Results. Applying a proper high-pass filter that removes large enough modes from the gravitational potential, we derive an X-ray temperature function that agrees very well with the classical Press-Schechter approach on relevant temperature scales, but avoids the necessity of measuring masses. Conclusions. TThis first study shows that and how an X-ray temperature function of galaxy clusters can be analytically derived, avoiding the introduction of poorly defined global quantities such as halo masses. This approach will be useful for reducing scatter in observed cluster distributions and thus in cosmological conclusions drawn from them.