Estimation of the Mass of the Very Massive Galaxy Cluster SRGe CL2305.2-2248 from Strong Lensing

Abstract

SRGe CL2305.2–2248 (SPT-CL J2305–2248, ACT-CL J2305.1–2248) is one of the most massive galaxy clusters at high redshifts ($z\simeq 0.76$) and is of great interest for cosmology. Deep images have been obtained at the Russian–Turkish 1.5-m telescope (RTT-150) for an optical identification of this cluster. In combination with the open Hubble Space Telescope archival data, they have made it possible to select candidates for gravitationally lensed images of distant blue galaxies in the form of arcs and arclets. The observed giant arc near the brightest cluster galaxies allows the Einstein radius to be estimated, $9.8\pm 1.3$ arcsec. The photometric redshift of the lensed source has been found ($z_{s}=2.44\pm 0.07$). Its use in combination with the Einstein radius estimate has made it possible to independently estimate the mass of SRGe CL2305.2–2248 by extrapolating the strong-lensing results to large radii and using model density profiles in relaxed clusters. This extrapolation leads to mass estimates smaller than those obtained from X-ray and microwave observations by a factor of ${\sim}1.5{-}3$. A probable cause of this discrepancy may be the galaxy merger process, which is also confirmed by the morphology of SRGe CL2305.2–2248 in the optical range.

APPENDIX

The analytical expressions describing the positions of tangential arcs in a spherically symmetric gravitationally lensed system, in which the lens density profile is described by the Navarro–Frenk–White profile, are presented in Bartelmann (1996). The properties of axisymmetric gravitational lenses are determined by their surface density $\kappa(x)=\Sigma(x)/\Sigma_{\textrm{cr}}$, where

$$\Sigma_{\mathrm{\textrm{cr}}}=\frac{c^{2}}{4\pi G}\frac{D_{\mathrm{s}}}{D_{\mathrm{d}}D_{\mathrm{ds}}},$$

(4)

$x$ is the coordinate along the radius in units of $R_{\textrm{s}}$, $c$ is the speed of light, $G$ is the gravitational constant, $D_{\textrm{d}}$ and $D_{\textrm{s}}$ are the angular diameter distances from the observer to the lens and the source, respectively, and $D_{\textrm{ds}}$ is the angular diameter distance from the lens to the source. The mass within a circle of radius $x$ is specified by the expression

$$m(x)\equiv 2\int\limits_{0}^{x}dyy\kappa(y).$$

(5)

In the case of spherically symmetric lenses, source images in the form of tangential arcs arise close to the tangential critical curve defined by the condition $m(x)=x^{2}$. The dimensionless surface density

$$\kappa(x)=2\kappa_{\mathrm{s}}\frac{f(x)}{x^{2}-1},$$

(6)

where $\kappa_{\mathrm{s}}\equiv\rho_{\mathrm{s}}r_{\mathrm{s}}\Sigma_{\mathrm{cr}}^{-1}$, corresponds to the volume density $\rho(r)$ defined by Eq. (2). The dimensionless mass $m(x)$ is specified by the expression

$$m(x)=4\kappa_{\mathrm{s}}g(x),$$

(7)

where

$$g(x)=\ln\frac{x}{2}+\begin{cases}\dfrac{2}{\sqrt{x^{2}-1}}\arctan\sqrt{\dfrac{x-1}{x+1}},\quad x>1\\ \dfrac{2}{\sqrt{1-x^{2}}}\mathrm{arctanh}\sqrt{\dfrac{1-x}{1+x}},\quad x<1\\ 1,\quad x=1.\end{cases}$$

(8)