Context : The density structure of molecular clouds determines how they will evolve .

Aims : To 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 \textrm { H } _ { 2 } \textrm { CO } , radio recombination lines , and the radio continuum in the W51 star forming complex acquired with Arecibo and the Green Bank Telescope at \sim 50 \mbox { $ { } ^ { \prime \prime } $ } resolution .
We use \textrm { H } _ { 2 } \textrm { CO } absorption to determine the relative line-of-sight positions of molecular and ionized gas .
We measure gas densities using the \textrm { H } _ { 2 } \textrm { CO } densitometer , including continuous measurements of the dense gas mass fraction ( DGMF ) over the range 10 ^ { 4 } \textrm { cm } ^ { -3 } < n ( \textrm { H } _ { 2 } ) < 10 ^ { 6 } \textrm { 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 \gtrsim 70 \% above n > 10 ^ { 4 } \textrm { cm } ^ { -3 } , while it is low , f < 20 \% , in W51 B .
We did not detect any \textrm { H } _ { 2 } \textrm { CO } 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 .
The data set has been made public at http : //dx.doi.org/10.7910/DVN/26818 .

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 \gtrsim 1 \times 10 ^ { 5 } \textrm { cm } ^ { -3 } gas .
Gas with n > 10 ^ { 4 } \textrm { 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 \textrm { H } _ { 2 } \textrm { CO } 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 H ii regions have their emission suppressed .