Recently, in Benetti et al. (Astrophys. J. 2023, 949, 65), we suggested that the dark matter (DM) component in galaxies may originate fractional gravity. In such a framework, the DM component exists, but the gravitational potential associated to its density distribution is determined by a modified Poisson equation including fractional derivatives (i.e., derivatives of noninteger type),
which are meant to describe nonlocal effects; as such, this scenario is different from theories where baryonic matter emulates DM-like effects via modifications of gravity (e.g., MONDian frameworks).
In Benetti et al., we showed that fractional gravity worked very well for reproducing the kinematics of disk-dominated galaxies, especially dwarfs; there is also preliminary evidence that the strength of fractional effects tends to weaken toward more massive systems. Here, we aim to test fractional
gravity in galaxy clusters, with a twofold aim: (i) perform an independent sanity check that it can accurately describe such large and massive structures; (ii) derive a clear-cut trend for its strength in systems with different DM masses. To this purpose, we forward model the density and pressure
distributions of the intracluster medium (ICM), working out the hydrostatic equilibrium equation in fractional gravity. Then, we perform a Bayesian analysis of the X-COP galaxy cluster sample and infer constraints on the fractional gravity parameters, for individual clusters as well as stacked
clusters. We find that fractional gravity performs remarkably well in modeling the ICM profiles for the X-COP sample. We also check that the DM concentration vs. mass relation is still consistent with the expectations of N-body simulations in the standard cosmological scenario. Finally, we
confirm the weakening of the fractional gravity effects toward more massive systems and derive the overall scaling of the fractional gravity parameters from dwarf galaxies to massive clusters, spanning six orders of magnitude in DM mass. Such an overall trend implies that fractional gravity
can substantially alleviate the small-scale issues of the standard DM paradigm, while remaining successful on large cosmological scales.
