Euclid Quick Data Release (Q1). A probabilistic classification of quenched galaxies
Investigating what drives the quenching of star formation in galaxies is key to understanding their evolution. The Euclid mission will provide rich data from optical to infrared wavelengths for millions of galaxies, and enable precise measurements of their star formation histories. Using the first Euclid Quick Data Release (Q1), we developed a probabilistic classification framework that combines the average specific star-formation rate inferred over two timescales ($10^8,10^9$ yr) to categorise galaxies as `ageing' (secularly evolving), `quenched' (recently halted star formation), or `retired' (dominated by old stars). Two classification methods were employed: a probabilistic approach, which integrates posterior distributions, and a model-driven method, which optimises sample purity and completeness using IllustrisTNG. At $z<0.1$ and $M_\ast \gtrsim 3\times10^{8}\,M_\odot$, we obtain Euclid class fractions of 68-72\%, 8-17\%, and 14-19\% for ageing, quenched, and retired populations, respectively. Ageing and retired galaxies dominate at the low- and high-mass end, respectively, while quenched galaxies surpass the retired fraction for $M_\ast \lesssim 10^{10}\,\rm M_\odot$. The evolution with redshift shows increasing and decreasing fractions of ageing and retired galaxies, respectively. More massive galaxies usually undergo quenching episodes at earlier times than to their low-mass counterparts. In terms of the mass-size-metallicity relation, ageing galaxies generally exhibit disc morphologies and low metallicities. Retired galaxies show compact structures and enhanced chemical enrichment, while quenched galaxies form an intermediate population that is more compact and chemically evolved than ageing systems. This work demonstrates Euclid's great potential for elucidating the physical nature of the quenching mechanisms that govern galaxy evolution.