The dense gas mass fraction in the W51 cloud and its protoclusters

Context. The density structure of molecular clouds determines how they will evolve. Aims. We map the velocity-resolved density structure of the most vigorously star-forming molecular cloud in the Galactic disk, the W51 giant molecular cloud. Methods. We present new 2 cm and 6 cm maps of H2CO, radio recombination lines, and the radio continuum in the W51 star forming complex acquired with Arecibo and the Green Bank Telescope at similar to 50 '' resolution. We use H2CO absorption to determine the relative line-of-sight positions of molecular and ionized gas. We measure gas densities using the H2CO densitometer, including continuous measurements of the dense gas mass fraction (DGMF) over the range 10(4) cm(-3) < n(H-2) < 10(6) cm(-3) - this is the first time a dense gas mass fraction has been measured over a range of densities with a single data set. Results. The DGMF in W51 A is high, f greater than or similar to 70% above n > 10(4) cm(-3), while it is low, f < 20%, in W51 B. We did not detect any H2CO emission throughout the W51 GMC; all gas dense enough to emit under normal conditions is in front of bright continuum sources and therefore is seen in absorption instead. Conclusions. (1) The dense gas fraction in the W51 A and B clouds shows that W51 A will continue to form stars vigorously, while star formation has mostly ended in W51 B. The lack of dense, star-forming gas around W51 C indicates that collect-and-collapse is not acting or is inefficient in W51. (2) Ongoing high-mass star formation is correlated with n greater than or similar to 1 x 10(5) cm(-3) gas. Gas with n > 10(4) cm(-3) is weakly correlated with low and moderate mass star formation, but does not strongly correlate with high-mass star formation. (3) The nondetection of H2CO emission implies that the emission detected in other galaxies, e.g. Arp 220, comes from high-density gas that is not directly affiliated with already-formed massive stars. Either the non-star-forming ISM of these galaxies is very dense, implying the star formation density threshold is higher, or HII regions have their emission suppressed.