Using clusters in Sunyaev-Zel’dovich effect plus x-ray surveys as an ensemble of rulers to constrain cosmology

Ongoing and upcoming surveys in x rays and SZE are expected to jointly detect many clusters due to the large overlap in sky coverage. We show that these clusters can be used as an ensemble of rulers to estimate the angular diameter distance, $d_{\mathrm{A}}(z)$. This comes at no extra observational cost, as these clusters form a subset of a much larger sample, assembled to build cluster number counts, $\frac{dN}{dz}$. On using this $d_{\mathrm{A}}(z)$ the dark energy constraints can be improved by factors of 1.5–4, over those from just $\frac{dN}{dz}$. Even in the presence of a mass follow-up of 100 clusters (done for mass calibration), the dark energy constraints can be further tightened by factors of 2–3 . Adding $d_{\mathrm{A}}(z)$ from clusters is similar to adding $d_{\mathrm{L}}(z)$, from the SNe observations; for eg., $\frac{dN}{dz}$ (from ACT/SPT) plus $d_{\mathrm{A}}(z)$ is comparable to $\frac{dN}{dz}$ plus $d_{\mathrm{L}}(z)$ in constraining ${\Omega }_m$ and ${\sigma }_8$.

Figure 1

(a) $M_{\lim }$ as a function of redshift plotted for various x-ray and SZE surveys. The $d_{\mathrm{A}}(z)$ mock catalog is created by using the effective $M_{\lim }(z)$, which is the maximum of the $M_{\lim }$ corresponding to a given $N_{\mathrm{beam}}$, the $M_{\lim }$ for determining temperature of the clusters detected through eROSITA, and the $M_{\lim }$ for detecting clusters through Planck/SPT. (b) A mock $d_{\mathrm{A}}(z)$ catalog of 578 clusters (as found from an overlap of ACT/SPT with eROSITA) with 25% Gaussian errors plus scatter. The thick line indicates the $d_{\mathrm{A}}$ from fiducial cosmology.

Figure 2

Cosmological constraints from ACT/SPT: The $1\mathrm{\text{−}}\sigma$ regions in the order of overlap (decreasing area) are number counts—with mass follow-up (no priors on $A$ and $\alpha$) with $\Delta M\sim 30–100\%$ (red) and $\Delta M\sim 15–50\%$ (dark blue); only number counts (light green); with $d_{\mathrm{A}}(z)$ ($N_{\mathrm{beam}}=2$, 578 clusters) (dark green); with CMB priors on ${\Omega }_m$ and ${\sigma }_8$ (orange); with 557 SNe from SCP Union 2 data set (light blue).

Figure 3

Constraints obtained from Planck $\frac{dN}{dz}$ added to $d_{\mathrm{A}}(z)$ measured from the overlap of Planck plus eROSITA survey areas. The figures show $1\mathrm{\text{−}}\sigma$ regions in the order of overlap (decreasing area) as follows: just $\frac{dN}{dz}$ (yellow); $\frac{dN}{dz}$ with $d_{\mathrm{A}}(z)$ for $N_{\mathrm{beam}}=4$ (light green), 3 (indigo), and 2 (magenta), respectively.