Constraints on the fuzzy dark matter mass using globular clusters in dwarf galaxies from Euclid ERO data

Abstract: We constrain the particle mass of the fuzzy dark matter model using globular cluster candidates in dwarf galaxies, from the Euclid Early Release Observations, within the Fornax and Perseus galaxy clusters. We model the orbital evolution of globular clusters by combining fuzzy dark matter density profiles with the corresponding dynamical friction formalism, and integrate their orbits using galpy. In the fuzzy dark matter framework, both the halo density profile and the dynamical friction force are modified by the wave-like nature of the ultra-light dark matter particle, whose mass is parameterized as $m_{22}=m_χ/10<sup>{-22},\mathrm{eV}$ and explored over the range $0.1 \leq m_{22} \leq 100$. This framework naturally alleviates the long-standing globular cluster timing problem originally identified in the Fornax dSph. We find that globular clusters no longer experience orbital decay toward the centers of their host galaxies for $m_{22}\leq1.46<sup>{+0.51}_{-0.32}$ in the Fornax cluster and $m_{22}\leq1.09<sup>{+0.14}_{-0.21}$ in the Perseus cluster. Future Euclid data releases, providing substantially larger samples of globular cluster candidates, will enable significantly tighter constraints on the dark matter particle mass within the fuzzy dark matter scenario.