Euclid Quick Data Release (Q1). A systematic study of the intracluster light fraction at 0.2 < z < 1.5

We present a homogeneous analysis of the intracluster light (ICL) in approximately 300 galaxy clusters spanning 0.2<z<1.5, combining Sunyaev-Zeldovich-selected clusters from the South Pole Telescope and optically selected clusters from Euclid, and comparing results with Hydrangea simulations. We measured the brightest cluster galaxy (BCG) within elliptical isophotes of semi-major axis 50 kpc, and ICL between 50 and 200 kpc. We show that the Euclid Wide Survey can detect ICL in individual massive clusters (M 500 10 14.2,M) out to at least z about1.5, with detection rates of 70-80%. This indicates that diffuse stellar envelopes are common, although not ubiquitous, in massive clusters throughout this redshift range. Using a uniform methodology, we place improved constraints on ICL fraction evolution. ICL contributes about 40% of the combined BCG and ICL light and 20% of the total cluster stellar light, with both fractions remaining approximately constant across 0.2<z<1.5 at fixed cluster mass. This implies that the relative partitioning of stellar mass between the BCG, ICL, and satellite populations is largely established by z about1.5. However, the ICL properties of individual clusters may still change as they evolve, since the sample does not represent an evolutionary sequence. This behaviour is consistent with a scenario in which the BCG and ICL are assembled together through the accretion, stripping, and eventual merging of the same population of massive galaxies (>10 10,M). The inferred ICL fraction also depends systematically on wavelength, while remaining largely insensitive to the adopted outer integration radius of 200-600 kpc. These results highlight the importance of homogeneous ICL analyses and constrain the evolution of diffuse stellar components in clusters.