Membership analysis and 3D kinematics of the star-forming complex around Trumpler 37 using Gaia-DR3

Identifying and characterizing young populations of star-forming regions is crucial to unravel their properties. In this regard, Gaia-DR3 data and machine learning tools are very useful for studying large star-forming complexes. In this work, we analyze the $\rm \sim7.1degree^2$ area of one of our Galaxy's dominant feedback-driven star-forming complexes, i.e., the region around Trumpler 37. Using the Gaussian mixture and random forest classifier methods, we identify 1243 high-probable members in the complex, of which $\sim60\%$ are new members and are complete down to the mass limit of $\sim$0.1 $-$ 0.2~$\rm M_{\odot}$. The spatial distribution of the stars reveals multiple clusters towards the complex, where the central cluster around the massive star HD 206267 reveals two sub-clusters. Of the 1243 stars, 152 have radial velocity, with a mean value of $\rm -16.41\pm0.72~km/s$. We investigate stars' internal and relative movement within the central cluster. The kinematic analysis shows that the cluster's expansion is relatively slow compared to the whole complex. This slow expansion is possibly due to newly formed young stars within the cluster. We discuss these results in the context of hierarchical collapse and feedback-induced collapse mode of star formation in the complex.