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We present comprehensive characterization of the Galactic open cluster M 36.Some two hundred member candidates, with an estimated contamination rate of$\sim$8%, have been identified on the basis of proper motion and parallaxmeasured by the $Gaia$ DR2. The cluster has a proper motion grouping around($\mu_{\alpha} \cos\delta = -$0.15 $\pm$ 0.01 mas yr$^{-1}$, and $\mu_{\delta}= -$3.35 $\pm$ 0.02 mas yr$^{-1}$), distinctly separated from the fieldpopulation. Most member candidates have parallax values 0.7$-$0.9 mas, with amedian value of 0.82 $\pm$ 0.07 mas (distance $\sim$1.20 $\pm$ 0.13 kpc). Theangular diameter of 27$'$ $\pm$ $0\farcm4$ determined from the radial densityprofile then corresponds to a linear extent of 9.42 $\pm$ 0.14 pc. With anestimated age of $\sim$15 Myr, M 36 is free of nebulosity. To the south-west ofthe cluster, we discover a highly obscured ($A_{V}$ up to $\sim$23 mag),compact ($\sim$ $1\farcm9 \times 1\farcm2$) dense cloud, within which threeyoung stellar objects in their infancy (ages $\lesssim$ 0.2 Myr) areidentified. The molecular gas, 3.6 pc in extent, contains a total mass of(2$-$3)$\times$10$^{2}$ M$_{\odot}$, and has a uniform velocity continuityacross the cloud, with a velocity range of $-$20 to $-$22 km s$^{-1}$,consistent with the radial velocities of known star members. In addition, thecloud has a derived kinematic distance marginally in agreement with that of thestar cluster. If physical association between M 36 and the young stellarpopulation can be unambiguously established, this manifests a convincingexample of prolonged star formation activity spanning up to tens of Myrs inmolecular clouds.

Sustaining Star Formation in the Galactic Star Cluster M 36?