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Context. The Doppler shift predicted by general relativity for light escapinga gravitational potential has been observed on Earth as well as in thedirection of various stars and galaxy clusters at optical wavelengths. Aims.Observing the gravitational redshift in the X-ray band within galaxy clusterscould provide information on their properties and, in particular, theirgravitational potential. We present a feasibility study of such a measurement,using the capabilities of the next-generation European X-ray observatoryAthena. Methods. We used a simple generalized Navarro-Frenk-White potentialmodel along with a beta-model for the density of baryonic matter, which setsthe emission to provide an estimation of the observed redshift in the simplestof cases. We generated mock observations with the Athena X-ray Integral FieldUnit (X-IFU) for a nearby massive cluster, while seeking to recover thegravitational redshift along with other properties of the toy model cluster.Results. We investigated the observability of the gravitational redshift in anidealized test case of a nearby massive cluster with the Athena X-IFUinstrument, as well as its use in probing the properties of the potential well.We were also able to constrain the mass to a 20 % level of precision and thecosmological redshift to less than 1%, within a simplified and idealizedobservational framework. More refined simulations accounting for furthereffects such as the internal gas motions and the actual shape of the potentialwell are required to fully investigate the feasibility of measuring thegravitational redshift for a single target or statistically over a sample ofgalaxy clusters.

Observing gravitational redshift with X-Ray emission in galaxy clusters with Athena X-IFU