  (abridged) 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 (Macc)
and the disk mass (Mdisk) of young, Class II stars are also linearly
correlated. We plotted the corresponding observational data together, finding a
statistically significant correlation that spans ~ 16 orders of magnitude. This
probably represents one of the widest ranges of any empirical correlation
known, encompassing galaxies that are several kpc in size, pc-size star-forming
clouds within our Galaxy, down to young, pre-main sequence stars with au-size
protoplanetary disks. We propose a bottom-up hypothesis suggesting that a
relation between Macc and the total circumstellar mass surrounding Class 0/I
sources (Mcs; disk+envelope) drives the correlation in protostellar-hosting
clouds and cloud-hosting galaxies. This 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 Macc values 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 Mcs values directly participating in
the formation of the protostellar population in a cloud likely represents a
non-negligible fraction of the Mdg within the cloud. If such fraction is ~
1-35% of the Mdg 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/Macc. Therefore,
an additional critical test of our hypothesis is that the Macc-Mdisk
correlation for Class II stars should also be observed between Macc and Mcs for
Class 0/I sources with similar slope and intercept.
