Modelling clusters of galaxies by f(R)-gravity

We consider the possibility that masses and gravitational potentials of galaxy cluster, estimated at X-ray wavelengths, could be explained without assuming huge amounts of dark matter, but in the context of $f(R)$-gravity. Specifically, we take into account the weak field limit of such theories and show that the corrected gravitational potential allows to estimate the total mass of a sample of 12 clusters of galaxies. Results show that such a gravitational potential provides a fair fit to the mass of visible matter (i.e. gas + stars) estimated by X-ray observations, without the need of additional dark matter while the size of the clusters, as already observed at different scale for galaxies, strictly depends on the interaction lengths of the corrections to the Newtonian potential.