X-ray flux -- mass relation for $z\gtrsim 0.7$ galaxy clusters

TL;DR

This work tests and calibrates the use of the observed X-ray flux F_X in the 0.5–2 keV band as a mass proxy for distant galaxy clusters (z ≳ 0.6–0.7). By combining eROSITA X-ray data with SZ-based ACT DR5 masses and MaDCoWS co-detections, the authors derive a modified F_X–M_{500c} scaling M_{500c} = 1.2×10^{14} M_⊙ · η · (F_X/10^{−14} erg s^{−1} cm^{−2})^{0.57} · z^{0.5}, where η captures survey- and method-dependent offsets. For the calibration sample (36 clusters, z > 0.7), they find η ≈ 0.80 with a scatter of ~34% between F_X-predicted and SZ masses; when using weak-lensing-calibrated masses, η increases to ≈1.13. Extending the calibration to ~400 ACT DR5 clusters confirms that F_X serves as a crude but practical mass proxy at high redshift, offering a ~34% RMS accuracy and valuable utility for pre-selecting massive clusters for follow-up studies. These results provide a cost-effective path to mass estimates from all-sky X-ray data, complementing SZ and WL measurements for cosmological applications.

Abstract

We use a subsample of co-detections of the ACT and MaDCoWS cluster catalogs to verify the predicted relation between the observed X-ray flux $F_X$ in the 0.5-2~keV band and the cluster mass $M_{\rm 500c}$ for halos at $z>0.6-0.7$. We modify this relation by introducing a correction coefficient $η$, which is supposed to encapsulate factors associated with a particular method of flux estimation, the sample selection function, the definition of the cluster mass, etc. We show that the X-ray flux, being the most basic X-ray observable, serves as a convenient and low-cost mass indicator for distant galaxy clusters with photometric or even missing redshifts (by setting $z=1$) as long as it is known that $z\gtrsim 0.6-0.7$. The correction coefficient $η$ is $\approx 0.8$ if $M^{\rm UPP}_{\rm 500c}$ from the ACT-DR5 catalog are used as cluster masses and $η\approx 1.1$ if weak-lensing-calibrated masses $M^{\rm Cal}_{\rm 500c}$ are used instead.

Figures (8)

• Figure 1: SZ and X-ray views on the galaxy cluster ACT-CL J0105.8-1839. Left panel: the Planck + ACT Compton-y map (2024PhRvD.109f3530C). Middle panel: the eROSITA 0.4--2.3 keV image. We use a ring with $6'<R<20'$ to estimate the background, which is then subtracted from the source region marked as a white circle. The right panel illustrates the source removal procedure.
• Figure 2: ACT cluster masses $M^{\rm UPP}_{\rm 500c}$ vs the eROSITA fluxes in the 0.5--2.0 keV energy band for the subsample of ACT/MaDCoWS co-detections from 2021AA...653A.135O. X-ray fluxes have been corrected for the expected bias arising from the different resolved fractions of compact sources in the cluster and background regions (see Appendix \ref{['sec:bias']}). The best-fit relation (\ref{['eq:xmass']}) with $\eta = 0.8\pm 0.03$ is shown with a black line and grey shaded area. The dashed and dash-dotted lines illustrate $\eta=1$ and 0.6, respectively. Cluster redshifts are shown with color.
• Figure 3: ACT masses $M^{\rm UPP}_{\rm 500c}$ vs cluster masses estimated from the calibrated $F_{\rm X}$-$M_{\rm 500c}$ relation for the 2021AA...653A.135O subsample. Cluster redshifts are shown with color.
• Figure 4: ACT masses $M^{\rm UPP}_{\rm 500c}$ for the subsample of the ACT DR5 clusters with 0$^{\circ}$ < $l$ < 180$^{\circ}$ vs eROSITA 0.5-2.0 keV fluxes extracted from a circle of $R=2'$ arcmin centered at a cluster. The dashed, solid and dotted lines show the $F_{\rm X}$-$M_{\rm 500c}$ relation (equation \ref{['fig:fxm']}) with $\eta = 1.0$, 0.8 and 0.6, correspondingly. Cluster redshifts are shown with color.
• Figure 5: Expected deviation of the X-ray-flux-based mass estimate from the true (input) mass. Triangles show the ratio of the mass predicted by eq. (\ref{['eq:CVS2015']}) to the true $M_{500c}$ value for clusters that follow adopted scaling relations from 2009ApJ...692.1033V. Solid circles show the same ratio when the factor $z^{0.5}$ (as in eq. \ref{['eq:xmass']}) is accounted for. Different colors indicate the mass range of clusters that are expected to be present above a given redshift.