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

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