<i>Euclid</i>: Early Release Observations – Overview of the Perseus cluster and analysis of its luminosity and stellar mass functions★

The Euclid Early Release Observations (ERO) programme targeted the Perseus cluster of galaxies, gathering deep data in the central region of the cluster over 0.7 deg² , including the cluster core up to 0.25 _{r 200} . The dataset reaches a point-source depth of I_E = 28.0 ( Y_E , J_E , H_E = 25.3), AB magnitudes at 5 σ with a 0′′.16 (0′′.48) full width at half maximum (FWHM), and a surface brightness limit of 30.1 (29.2) mag arcsec⁻² for radially integrated galaxy profiles. The exceptional depth and spatial resolution of this wide-field multi-band data enable simultaneous detection and characterisation of both bright galaxies and low surface brightness ones, along with their globular cluster systems, from the optical to the near-infrared (NIR). Cluster membership was determined using several methods in order to maximise the completeness and minimise the contamination of foreground and background sources. We adopted a catalogue of 1100 dwarf galaxies, detailed in the corresponding ERO paper, that includes their photometric and structural properties. We identified all other sources in the <i>Euclid</i> images and obtained accurate photometric measurements using AutoProf or AstroPhot for 137 bright cluster galaxies and SourceExtractor for half a million compact sources. This study advances beyond previous analyses of the cluster and enables a range of scientific investigations, which are summarised here. We derived the luminosity and stellar mass functions (LF and SMF) of the Perseus cluster in the <i>Euclid</i> I_E band thanks to supplementary u, g, r, i, z , and H α data from the Canada-France-Hawai’i Telescope (CFHT). Our LF and SMF are the deepest recorded for the Perseus cluster, highlighting the groundbreaking capabilities of the <i>Euclid</i> telescope. We fit the LF and SMF with a Schechter plus Gaussian model. The LF features a dip at M ( I_E ) ≃ −19 and a faint-end slope of α_S ≃ −1.2 to −1.3. The SMF displays a low-mass-end slope of α S ≃ −1.2 to −1.35. These observed slopes are flatter than those predicted for dark matter halos in cosmological simulations, offering significant insights for models of galaxy formation and evolution.