A Modified Conveyor Belt Model: Implications for Surface Density Thresholds for Massive Star Formation

Abstract

Recent models and simulations of cluster formation within molecular clumps consider multi-scale, hierarchical accretion, which leads to clump mass growth over time. This mode of mass accumulation could have implications regarding the evolution of observable properties such as mass and radius, bringing into question the interpretation of commonly cited thresholds for high-mass star formation. In this paper, we use the conveyor belt model of cluster formation to create synthetic cores/clumps and derive physical and observational properties. We show that while this model successfully predicts many observed trends, modifications are required to match properties of high-mass prestellar clumps. When the model clumps are observationally classified as intermediate- or high-mass star-forming, the threshold delineating these two groups agrees with those found in the literature; however, results show that high-mass clumps at early evolutionary stages can be misclassified using standard surface density thresholds. Our logistic regression analysis reveals the quantity of material to ever enter a star-forming region is the most important factor in differentiating intermediate- and high-mass star-forming regions. This implies observations characterising the environment surrounding star-forming regions are crucial, especially at early evolutionary stages.

Figures (17)

• Figure 1: The evolution of the gas (black) and stellar (red) mass for the CBD model with representative values of $M_{g,0}$. These plots illustrate that in the CBD model the cloud mass is never fully assembled at a given time, and therefore does not initially need to be as massive as the final stellar mass. The orange dashed line indicates the minimum total stellar mass at which a model beings to populate a clump with YSOs (see text for details).
• Figure 2: Example of an evolved clump populated with YSOs. The dots represent the YSO positions as a projection on the y-z plane, and extinction is calculated along the x-axis towards the 'observer'. The background gradient represents the density profile of the clump, while the YSOs are colour-coded by their visual extinction (see text for details).
• Figure 3: Example SED evolution of a clump from birth to the end of the model run. The SEDs are colour coded by age. This model spends $\sim$7 Myr in the prestellar phase before enough material is accumulated for YSOs to populate the clump, causing a sharp jump in luminosity, and emitting significant flux at shorter wavelengths.
• Figure 4: Left: Evolutionary tracks for the accreting protostellar portion of the CBD model. The post-$\tau_\text{acc}$ phase is shown at a higher transparency in the background as to not take away from the structure. The prestellar phase is omitted from the evolutionary tracks as they begin at arbitrarily small values and increase up to the lowest protostellar points shown around $\sim1-10$ L$_\odot$. The evolutionary tracks from M08 are overlaid in orange. The red dashed line indicates the average location of a model at $\tau_\text{acc}$, or where the transition from an accretion dominated phase to an 'envelope clean up' phase begins. This is consistent with the M08 transition point, where their evolutionary tracks shift from vertical to horizontal. Right: Histograms comparing the prestellar (blue) and protostellar (red) distributions for Hi-GAL clumps and CBD model clumps (i.e., those with radii between 0.1 and 1.5 pc), with a 0.25 bin width. The lack of prestellar points in the CBD distributions is due to the fact that none of the models become large enough to be classified as clumps before star formation begins. Instead gray histograms show where all non-clump prestellar CBD models lie.
• Figure 5: Surface density distribution for the CBD model. Points are defined as follows: HII region candidates are those with ZAMS, high-mass stars (B3-O9 or earlier). Protostellar clumps are those with a total stellar mass above 0.1 M$_\odot$, and prestellar are those with less than 0.1 M$_\odot$.