From molecules to Young Stellar Clusters: the star formation cycle across the M33 disk

International audienceTo shed light on the time evolution of local star formation episodes in M33, we study the association between 566 Giant Molecular Clouds (GMCs), identified through the CO (J=2-1) IRAM-all-disk survey, and 630 Young Stellar Cluster Candidates (YSCCs), selected via Spitzer-24~$\mu$m emission. The spatial correlation between YSCCs and GMCs is extremely strong, with a typical separation of 17~pc, less than half the CO(2--1) beamsize, illustrating the remarkable physical link between the two populations. GMCs and YSCCs follow the HI filaments, except in the outermost regions where the survey finds fewer GMCs than YSCCs, likely due to undetected, low CO-luminosity clouds. The GMCs have masses between 2$\times 10^4$ and 2$\times 10^6$ M$_\odot$ and are classified according to different cloud evolutionary stages: inactive clouds are 32$\%$ of the total, classified clouds with embedded and exposed star formation are 16$\%$ and 52$\%$ of the total respectively. Across the regular southern spiral arm, inactive clouds are preferentially located in the inner part of the arm, possibly suggesting a triggering of star formation as the cloud crosses the arm. Some YSCCs are embedded star-forming sites while the majority have GALEX-UV and H$\alpha$ counterparts with estimated cluster masses and ages. The distribution of the non-embedded YSCC ages peaks around 5~Myrs with only a few being as old as 8--10~Myrs. These age estimates together with the number of GMCs in the various evolutionary stages lead us to conclude that 14~Myrs is a typical lifetime of a GMC in M33, prior to cloud dispersal. The inactive and embedded phases are short, lasting about 4 and 2~Myrs respectively. This underlines that embedded YSCCs rapidly break out from the clouds and become partially visible in H$\alpha$ or UV long before cloud dispersal