CLASH-VLT: constraints onf(R) gravity models with galaxy clusters using lensing and kinematic analyses

Abstract

We perform a maximum likelihood kinematic analysis of the two dynamically relaxed galaxy clusters MACS J1206.2-0847 at z = 0.44 and RXC J2248.7-4431 at z = 0.35 to determine the total mass profile in modified gravity models, using a modified version of the MAMPOSSt code of Mamon, Biviano and Boué. Our work is based on the kinematic and lensing mass profiles derived using the data from the Cluster Lensing And Supernova survey with Hubble (hereafter CLASH) and the spectroscopic follow-up with the Very Large Telescope (hereafter CLASH-VLT). We assume a spherical Navarro-Frenk-White (NFW hereafter) profile in order to obtain a constraint on the fifth force interaction range λ for models in which the dependence of this parameter on the environment is negligible at the scale considered (i.e. λ = const) and fixing the fifth force strength to the value predicted in f (R) gravity. We then use information from lensing analysis to put a prior on the other NFW free parameters. In the case of MACSJ 1206 the joint kinematic+lensing analysis leads to an upper limit on the effective interaction range λ ≤ 1.61 Mpc at ∆χ 2 = 2.71 on the marginalized distribution. For RXJ 2248 instead a possible tension with the ΛCDM model appears when adding lensing information, with a lower limit λ ≥ 0.14 Mpc at ∆χ 2 = 2.71. This is consequence of the slight difference between the lensing and kinematic data, appearing in GR for this cluster, that could in principle be explained in terms of modifications of gravity. We discuss the impact of systematics and the limits of our analysis as well as future improvements of the results obtained. This work has interesting implications in view of upcoming and future large imaging and spectroscopic surveys, that will deliver lensing and kinematic mass reconstruction for a large number of galaxy clusters.

Calibration of systematics in constraining modified gravity models with galaxy cluster mass profiles

“…It is worth to point out the RXJ 2248 is an overall relaxed cluster (see ref. [18] and references therein) as the dynamics and lensing mass profiles obtained in GR are in agreement within 68% C.L. However, it is worth to remind that possible MG signatures are expected to be very small (e.g.…”

“…The joint lensing and dynamics analysis in linear f (R) gravity of ref. [18] on the data of two CLASH clusters MACS 1206 and RXJ 2248, indicates agreement with GR in the case of MACS 1206, while a slight preference of λ > 0 has been found for the cluster RXJ 2248. In particular, at ∆χ 2 = 2.71 they obtain λ 1206 ≤ 1.61 (345 galaxy cluster members available in the MG-MAMPOSSt fit), λ 2248 ≥ 0.14 (981 members available in the MG-MAMPOSSt fit) respectively.…”

“…We applied the MG-MAMPOSSt method (refs. [18,22]) to reconstruct the cluster mass profile in modified gravity models with a Maximum Likelihood approach, by solving the spherical Jeans' equation in the projected phase space (R, v los ) of member galaxies. The method assumes dynamical relaxation and spherical symmetry of the total matter distribution.…”

“…Ref. [18] developed an extension of MAMPOSSt (MG-MAMPOSSt hereafter) by introducing a generic parametric form for the gravitational potential Φ. In the case of a NFW density profile for the matter perturbation the expression of Φ reads:…”

“…Ref. [18] performed a joint lensing and dynamics analysis on the data of two relaxed galaxy clusters MACS J1206.2-0847 (hereafter MACS 1206) at redshift z = 0.44, and RXC J2248.7-4431 (hereafter RXJ 2248) at z = 0.35, aimed at constraining the interaction range λ in the framework of linear f (R) gravity. An interesting behavior has been found in the case of the cluster RXJ 2248, where a slight preference of MG with respect to GR suggests that some effects, whose contribution can be negligible in the framework of General Relativity, may become relevant source of systematics when searching for small deviations, such as those induced by the additional degrees of freedom in non-standard gravity.…”