Context. The star formation rate (SFR) linearly correlates with the amount of dense gas mass (Mdg) involved in the formation of stars both for distant galaxies and clouds in our Galaxy. Similarly, the mass accretion rate (Ṁacc) and the disk mass (Mdisk) of young, Class II stars are also linearly correlated.
Aims. We aim to explore the conditions under which the previous relations could be unified.
Methods. Observational values of SFR, Mdg, Ṁacc, and Mdisk for a representative sample of galaxies, star forming clouds, and young stars have been compiled from the literature. Data were plotted together in order to analyze how the rate of gas transformed into stars and the mass of dense gas directly involved in this transformation relate to each other over vastly different physical systems.
Results. A statistically significant correlation is found spanning ~16 orders of magnitude in each axis, but with large scatter. This probably represents one of the widest ranges of any empirical correlation known, encompassing galaxies that are several kiloparsec in size, parsec-size star-forming clouds within our Galaxy, down to young, pre-main sequence stars with astronomical unit-size protoplanetary disks. Assuming that this global correlation has an underlying physical reason, we propose a bottom-up hypothesis suggesting that a relation between Ṁacc and the total circumstellar mass surrounding Class 0/I sources (Mcs; disk + envelope) drives the correlation in clouds that host protostars and galaxies that host clouds. This hypothesis is consistent with the fact that the SFRs derived for clouds over a timescale of 2 Myr can be roughly recovered from the sum of instantaneous accretion rates of the protostars embedded within them, implying that galactic SFRs averaged over ~10–100 Myr should be constant over this period too. Moreover, the sum of the circumstellar masses directly participating in the formation of the protostellar population in a cloud likely represents a non-negligible fraction of the dense gas mass within the cloud.
Conclusions. If the fraction of gas directly participating in the formation of stars is ~1–35% of the dense gas mass associated with star-forming clouds and galaxies, then the global correlation for all scales has a near unity slope and an intercept consistent with the (proto-)stellar accretion timescale, Mcs/ Ṁacc. Therefore, an additional critical test of our hypothesis is that the Ṁacc−Mdisk correlation for Class II stars should also be observed between Ṁacc and Mcs for Class 0/I sources with similar slope and intercept.
Relationship between the system of Astronomical constants and the radar determinations of the Astronomical Unit