Comparing the $M_{gas}-N_{yso}$ Relation inside a Giant Molecular Cloud

Abstract

In this paper we present a simple analysis around scaling relations derived from the Schmidt conjecture for star-forming molecular clouds, at the intra-cloud scale. Using a hierarchical tree (dendrograms) above a constant threshold ($A_V$ = 7 mag), we separate individual gas structures in a column density map of the nearby Giant Molecular Cloud Orion A, constructed from Herschel far-infrared maps. These structures define regions of dense molecular gas that can actively form stars. We also estimate their current embedded population using a list of known young stars. From the combined analysis of the column density map and the young star catalog, we construct a series of plots that show the intra-cloud level behavior of three well-known scaling relations: $N_{yso}$ vs. $M_{gas}$, $Σ_{SFR}$ vs. $Σ_{gas}$ and $R_{eq}$ vs. $M_{gas}$. Our dataset, along with other sets from literature, show the validity of a linear relation for $N_{yso}$ vs. $M_{gas}$, from intra-cloud to inter-cloud scales, over three orders of magnitude. We also especulate on the possibility that the relation could be valid over an even larger scale range. Additionally, our data are consistent with the $R_{eq}$ vs. $M_{gas}$ discussed in previous studies. However, our data is not quite in agreement with previously proposed fits for the $Σ_{SFR}$ vs. $Σ_{gas}$ relation, and we discuss the implications of using the free-fall timescale as the main parameter defining the star-forming efficiency in dense gas regions.

Figures (11)

• Figure 1: HP2 extinction map of the Orion A Cloud. The grayscale shows extinction values from 0.5 to 20 mag in logarithmic scale. The red colored contour delineates the $A_V=7$ mag level on the map. The orange colored contours delineate the boundaries of branch type objects. The yellow colored contours delineate the boundaries of leaf type objects.
• Figure 2: The image illustrates how a group of YSO positions is matched inside the boundaries of a pixel structure in one of our maps. Gray dots trace the pixel positions of a clump in the extinction map. The red dots and line indicate the positions of pixels used to define the polygon boundary of the structure. The green dots are objects falling inside the boundary. Orange dots are rejected as they do not fall completely inside the boundary.
• Figure 3: The histogram shows the distribution of YSO mass values estimated by the method described in section \ref{['s:datamethods:ss:clumpprops:sss:ysoagemass']}. The solid red line is a Kernel Density Estimate of the same distribution made with a 3$\sigma$ truncated Gaussian.
• Figure 4: $N_{\rm yso}$vs.$M_{\rm gas}$ relationship as derived for the inter-cloud studies of Lada+10 and Gutermuth+11, the intra-cloud study of Jorgensen+08 and the individual clump determinations in the studies of Palau+15 and Palau+21. The blue line shows a general fit to the data of the form $N_{\rm yso}=0.15 \cdot M_{\rm gas}^{1.0}$.
• Figure 5: $N_{\rm yso}$vs.$M_{\rm gas}$ relation for the intra-cloud dataset presented in this study. The red symbols in two shapes (circles and diamonds) separate branches and leaves in the A$_V>7.0$ dendrogram object list obtained from the Orion A map. The yellow symbols represent counts with only Class I and II sources. We show, for comparison, the same literature datasets as in Fig. \ref{['fig:McNyso_lit']} respecting the same symbols but using a single color. The solid lines are linear best fits for the data groups $(y=Ax;\ A={0.15, 0.035, 0.014})$.