  [abridged] 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, which are meant
to describe nonlocal effects. 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 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.
