Luminosity functions and IMF variations from large samples of HII regions and molecular clouds

Abstract

Large high-quality samples of HII regions and their parent Giant Molecular Clouds (GMC) are now available for local galaxies. It is therefore possible to investigate links between the CO and H$α$ luminosity functions and whether massive stars form in GMCs of all masses. The CO luminosity functions (LF), representing the distribution of GMC masses, are consistently steeper than the H$α$ luminosity functions. The CO LF invariably steepens in the outer disk where fewer massive GMCs are present beyond the median cloud galactocentric distance. The H$α$ LF also steepens in the outer disk for most of the galaxies examined. Using Salpeter, Kroupa, and Chabrier Initial Mass Functions (IMF) along with stellar mass-luminosity-radius relations, we compute numerically the bolometric luminosity and H$α$ emission from young star clusters. The cluster masses are linked to the GMC mass by assuming that the cluster mass is a constant fraction (3\%) of the parent cloud mass. In particular, results for a fully stochastic IMF are compared to suggestions that very massive stars only form in massive clusters or clouds. Within the limits of the observations -- no small molecular clouds or low-luminosity HII regions can be detected at the typical $\sim 10$~Mpc distance of the sample galaxies -- we find no evidence for a maximum stellar mass which varies with cloud or cluster mass.

Figures (14)

• Figure 1: Initial Mass Functions used in this work. Black line is Salpeter, red is Kroupa, and green the Chabrier IMF. The plot shows the number of stars per logarithmic mass interval for each mass. Clearly, the Kroupa and Chabrier IMFs are similar and have significantly fewer low-mass stars than the Salpeter IMF. The dashed and dotted lines show the Kroupa IMF with somewhat higher characteristic masses. The effect of increasing the characteristic mass is that there are fewer low mass stars so the L/M ratio of the stellar population increases from about 900 L$_{\odot}$/M$_{\odot}$ to 1500 L$_{\odot}$/M$_{\odot}$.
• Figure 2: Link between spectral index measured with powerlaw.py and $L_{\rm min}$ for the 19 galaxies from data given in Table 2 of Santoro2022. $L_{\rm min}$ is normalized by the completeness limit $L_{\rm compl}$ to be comparable from one galaxy to another.
• Figure 3: Probability density functions of H$\alpha$ fluxes from NGC0628, NGC3627m and M 33, the three galaxies for which both HII region and GMC catalogs are available. Results of powerlaw.py (red line) and Maschberger09 fit (blue line) along with observational data for NGC0628, NGC3627, and M33 from Santoro2022 and Lin2017 are shown. NGC0628 and NGC3627 are the two PHANGS galaxies for which both the HII region and GMC samples are available. H$\alpha$ data for M33 are from Lin2017 The adopted completeness limit for the fits (equivalent of $L_{\rm min}$ in Santoro2022) are shown as a green dashed line and given in Table 1. The errorbars are proportional to $1/sqrt(N)$ where $N$ is the number of points in the bin. When no errorbar is plotted, it means $N=1$.
• Figure 4: Probability density functions of CO luminosities from NGC0628, NGC3627m and M 33, the three galaxies for which both HII region and GMC catalogs are available. Results of powerlaw.py (red line) and Maschberger09 fit (blue line) along with observational data for NGC0628, NGC3627, and M33 from Rosolowsky2021 and Corbelli17. NGC0628 and NGC3627 are the two PHANGS galaxies for which both the HII region and GMC samples are available. CO data for M33 are from Druard14 and Corbelli17. The adopted completeness limits for the fits are the first of the limits given in Table 5 of Rosolowsky2021 and are shown as a green dashed line and given in Table 2. The errorbars are proportional to $1/sqrt(N)$ where $N$ is the number of points in the bin. When no errorbar is plotted, it means $N=1$.
• Figure 5: Results of fits to the distribution of H$\alpha$ and GMC CO luminosities of star forming regions. For each galaxy, the name is indicated followed by (1) the whole-galaxy GMC spectral index (2) the whole-galaxy H$\alpha$ spectral index (3) the inner and outer GMC spectral index, connected by a line, and (4) the same for the H$\alpha$ luminosities of HII regions. In each case, the triangles indicate the values obtained from the two independent fitting methods and the average by the short horizontal line. When the line goes up, the distribution in the outer part is steeper (relatively more small objects). A horizontal dashed line at a value of 1.5 is plotted to allow easy appraisal of the values.