The mass distribution in the outskirts of clusters of galaxies as a probe of the theory of gravity

Abstract

We show that $\varsigma$, the radial location of the minimum in the differential radial mass profile $M^{\prime }(r)$ of a galaxy cluster, can probe the theory of gravity. We derived $M^{\prime }(r)$ of the dark matter halos of galaxy clusters from N-body cosmological simulations that implement two different theories of gravity: standard gravity in the $\Lambda$CDM model, and $f(R)$. We extracted 49169 dark matter halos in 11 redshift bins in the range $0\le z\le 1$ and in three different mass bins in the range $0.9<M_{200c}/10^{14}{h}^{-1}$M${}_{\odot }<11$. We investigated the correlation of $\varsigma$ with the redshift and the mass accretion rate (MAR) of the halos. We show that $\varsigma$ decreases from $\sim 3R_{200c}$ to $\sim 2R_{200c}$ when $z$ increases from 0 to $1$ in the $\Lambda$CDM model. At $z\sim 0.1$, $\varsigma$ decreases from $2.8R_{200c}$ to $\sim 2.5R_{200c}$ when the MAR increases from $\sim 10^4{h}^{-1}$M${}_{\odot }$~yr${}^{-1}$ to $\sim 2\times 10^5{h}^{-1}$M${}_{\odot }$~yr${}^{-1}$. In the $f(R)$ model, $\varsigma$ is $\sim 15$% larger than in $\Lambda$CDM. The median test shows that for samples of $\gtrsim 400$ dark matter halos at $z\le 0.8$, $\varsigma$ is able to distinguish between the two theories of gravity with a $p$-value $\lesssim 10^{-5}$. Upcoming advanced spectroscopic and photometric programs will allow a robust estimation of the mass profile of enormous samples of clusters up to large clustercentric distances. These samples will allow us to statistically exploit $\varsigma$ as probe of the theory of gravity, which complements other large-scale probes.

Accepted in A&A. 13 pages, 6 figures, 4 tables