Predicting the scaling relations between the dark matter halo mass and observables from generalised profiles II: Intracluster gas emission

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, epsilon, the dilution, d, and the gas fraction, eta, normalised to cosmological content. We predict four probes of the gas emission: the emission-weighted, T-X, and mean gas mass-weighted, Tm-g, temperatures, and the spherically, Y-sph, and cylindrically, Y-cyl, integrated Compton parameters. Over a parameter space of clusters, we constrain the X-ray temperature scaling relations, M-200-T(X )and M-500-T-X, within 57.3%57.3% and 41.6%41.6%, and M-200-Tm-g and M-500-Tm-g, within 25.7%25.7% and 7.0%7.0%, all respectively. When excising the cluster's core, the M-200-T-X and M-500-T-X relations are further constrained, to within 31.3%31.3% and 17.1%17.1%, respectively. Similarly, we constrain the SZ scaling relations, M-200-Ys(ph) and M-500-Y-sph, within 31.1%31.1% and 17.7%17.7%, and M-200-Y-cyl and M-500-Y-cyl, within 25.2%25.2% and 22.0%22.0%, all respectively. The temperature observable Tm-g places the strongest constraint on the halo mass, whilst T(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.