Predicting the Scaling Relations between the Dark Matter Halo Mass and Observables from Generalised Profiles II: Intracluster Gas Emission

TL;DR

This paper develops an analytic model linking dark matter halo properties to observable intracluster gas emissions, providing refined scaling relations for X-ray and SZ measurements with quantified uncertainties.

Contribution

It introduces a novel analytic model connecting halo structure to gas emission observables, improving the accuracy of mass-observable scaling relations.

Findings

Constrains X-ray temperature scaling relations within 57.3% and 41.6%.

Refines SZ scaling relations with uncertainties around 17-31%.

Finds gas fraction influences SZ constraints more than gas profile form.

Abstract

We investigate the connection between a cluster's structural configuration and observable measures of its gas emission that can be obtained in X-ray and Sunyaev-Zeldovich (SZ) surveys. We present an analytic model for the intracluster gas density profile: parameterised by the dark matter halo's inner logarithmic density slope, $\alpha$, the concentration, $c$, the gas profile's inner logarithmic density slope, $\varepsilon$, the dilution, $d$, and the gas fraction, $\eta$, normalised to cosmological content. We predict four probes of the gas emission: the emission-weighted, $T_\mathrm{X}$, and mean gas mass-weighted, $T_\mathrm{m_g}$, temperatures, and the spherically, $Y_\mathrm{sph}$, and cylindrically, $Y_\mathrm{cyl}$, integrated Compton parameters. Over a parameter space of clusters, we constrain the X-ray temperature scaling relations, $M_{200} - T_\mathrm{X}$ and $M_{500} - T_\mathrm{X}$, within $57.3\%$ and $41.6\%$, and $M_{200} - T_\mathrm{m_g}$ and $M_{500} - T_\mathrm{m_g}$, within $25.7\%$ and $7.0\%$, all respectively. When excising the cluster's core, the $M_{200} - T_\mathrm{X}$ and $M_{500} - T_\mathrm{X}$ relations are further constrained, to within $31.3\%$ and $17.1\%$, respectively. Similarly, we constrain the SZ scaling relations, $M_{200} - Y_\mathrm{sph}$ and $M_{500} - Y_\mathrm{sph}$, within $31.1\%$ and $17.7\%$, and $M_{200} - Y_\mathrm{cyl}$ and $M_{500} - Y_\mathrm{cyl}$, within $25.2\%$ and $22.0\%$, all respectively. The temperature observable $T_\mathrm{m_g}$ places the strongest constraint on the halo mass, whilst $T_\mathrm{X}$ is more sensitive to the parameter space. The SZ constraints are sensitive to the gas fraction, whilst insensitive to the form of the gas profile itself. In all cases, the halo mass is recovered with an uncertainty that suggests the cluster's structural profiles only contribute a minor uncertainty in its scaling relations.