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We categorized clumps, embedded clusters, and open clusters and conducted a comparative analysis of their physical properties. Overall, the radii of open clusters are significantly larger than those of embedded clusters and clumps. The radii of embedded clusters are larger than those of clumps, which may be due to the expansion of embedded clusters. The open clusters have significantly higher masses than embedded clusters, by about one order of magnitude. Given the current mass distribution of clumps in the Milky Way, the evolutionary sequence from a single clump evolving into an embedded cluster and subsequently into an open cluster cannot account for the observed open clusters with old ages and high masses, which is also supported by N-body simulations of individual embedded clusters. To explain the mass and radius distributions of the observed open clusters, initial embedded clusters with masses higher than 3000 M$_ odot $ are necessary. However, the upper limit of the embedded cluster sample is less than 1000 M$_ odot $, and only a few ATLASGAL clumps have a mass higher than 3000 M$_ odot $. Thus, the currently observed clumps cannot be the "direct" precursors of the currently observed open clusters. If the Milky Way has a burst-like and time-dependent star formation history, the currently observed open clusters with old ages and high masses may come from massive clumps in the past. There is also a very real possibility that these open clusters originate from post-gas expulsion coalescence of multiple embedded clusters. We compared the separation of open clusters and the typical size of molecular clouds, and find that most molecular clouds may only form one open cluster, which supports the scenario of post-gas expulsion coalescence. Further study is necessary to distinguish between the different scenarios.
We categorized clumps, embedded clusters, and open clusters and conducted a comparative analysis of their physical properties. Overall, the radii of open clusters are significantly larger than those of embedded clusters and clumps. The radii of embedded clusters are larger than those of clumps, which may be due to the expansion of embedded clusters. The open clusters have significantly higher masses than embedded clusters, by about one order of magnitude. Given the current mass distribution of clumps in the Milky Way, the evolutionary sequence from a single clump evolving into an embedded cluster and subsequently into an open cluster cannot account for the observed open clusters with old ages and high masses, which is also supported by N-body simulations of individual embedded clusters. To explain the mass and radius distributions of the observed open clusters, initial embedded clusters with masses higher than 3000 M$_ odot $ are necessary. However, the upper limit of the embedded cluster sample is less than 1000 M$_ odot $, and only a few ATLASGAL clumps have a mass higher than 3000 M$_ odot $. Thus, the currently observed clumps cannot be the "direct" precursors of the currently observed open clusters. If the Milky Way has a burst-like and time-dependent star formation history, the currently observed open clusters with old ages and high masses may come from massive clumps in the past. There is also a very real possibility that these open clusters originate from post-gas expulsion coalescence of multiple embedded clusters. We compared the separation of open clusters and the typical size of molecular clouds, and find that most molecular clouds may only form one open cluster, which supports the scenario of post-gas expulsion coalescence. Further study is necessary to distinguish between the different scenarios.
The initial mass--radius relation of embedded star clusters is an essential boundary condition for understanding the evolution of embedded clusters in which stars form to their release into the galactic field via an open star cluster phase. The initial mass--radius relation of embedded clusters deduced by Marks2012-543 is significantly different from the relation suggested by Pfalzner2016-586 . Here, we use direct N-body simulations to model the early expansion of embedded clusters after the expulsion of their residual gas. The observationally deduced radii of clusters up to a few million years old, compiled from various sources, are well fitted by N-body models, implying that these observed very young clusters are most likely in an expanding state. We show that the mass--radius relation of Pfalzner2016-586 reflects the expansion of embedded clusters following the initial mass--radius relation of Marks2012-543 . We also suggest that even the embedded clusters in ATLASGAL clumps with HII regions are probably already in expansion. All the clusters collected here from different observations show a mass--radius relation with a similar slope, which may indicate that all clusters were born with a profile resembling that of the Plummer phase-space distribution function.
1226 ATLASGAL clumps with H ii regions (H ii-clumps) were matched with radio sources in the CORNISH-North/South surveys, and 392 of them have corresponding radio sources. We determined the stellar luminosity L *,T84 according to the Lyman continuum flux N Ly. When the bolometric luminosity of H ii-clumps is less than log10(L bol,obs/L ⊙) ≈3.7, corresponding to a clump mass log10(M cl/M ⊙) ≈ 2.55, the values of L *,T84 derived from N Ly overestimate the actual stellar luminosities, because the accretion onto the protostars contributes significantly to the radio emission. After subtracting the accretion luminosity from L *,T84, we obtained reasonable estimates of the stellar luminosity. Using the 0.5 Myr isochrone, we calculated the stellar masses according to the stellar luminosities, and found that they roughly follow the m max − M ecl relation of embedded clusters, consistent with the ionizing sources representing the most massive stars in the embedded clusters of H ii-clumps. We also studied the contribution of the possible flaring activity to the observed stellar luminosity and found that they can be neglected. We further studied the change of SFE with the clump mass. According to the derived mass of the most massive star in each HII-clump, using the theoretical m max − M ecl relation, we calculated the mass of the corresponding embedded cluster and then the SFE of the clump. The SFE decreases with increasing clump mass, with a median value of ≈0.3. We also independently derived the SFE for each H ii-clump based on the model developed in our previous work. The SFEs of H ii-clumps derived from the observation and the model are in good agreement. Concerning the star formation histories of the ATLASGAL clumps, low-mass clumps may reach the peak of star formation earlier than high-mass clumps, consistent with the shorter free-fall time of low-mass clumps.
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