We present the identifications of two z ~ 3·8 quasars from a deep UBI imaging survey with the Palomar 5·1 m Telescope. The survey covers an area of 0·25 degree2 around a sample of ten z =0·2–0·3 luminous X-ray clusters. The QSOs were identified on the basis of their stellar morphologies, relatively blue optical and very red UV–optical colours. The two objects are Q 1322+5034, with total magnitudes of B =20·8, I =18·3 and (U–B) > 4·7, and Q 1722+3211, which has total magnitudes of B =21·8, I =19·7 and (U–B) > 3·2. Subsequent spectroscopic observations with the 4·2 m William Herschel Telescope have confirmed the identity of these two sources as QSOs at z =3·82 and z =3·73 respectively. Our spectroscopic observations identify a damped Lyman-α absorber in the spectrum of Q 1322+5034 at z =3·439, as well as a second absorption system at z =2·700, which may be either a single very high column density, damped Lyman-α system, or more likely a blend of a number of high column-density absorbers spread over a distance of ~10 Mpc.

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.