Dense Gas in a Giant Molecular Filament

Recent surveys of the Galactic plane in the dust continuum and CO emission lines reveal that large ($\gtrsim 50$~pc) and massive ($\gtrsim 10^5$~$M_\odot$) filaments, know as giant molecular filaments (GMFs), may be linked to galactic dynamics and trace the mid-plane of the gravitational potential in the Milky Way. We have imaged one entire GMF located at $l\sim$52--54$^\circ$ longitude, GMF54 ($\sim$68~pc long), in the empirical dense gas tracers using the HCN(1--0), HNC(1--0), HCO$^+$(1--0) lines, and their $^{13}$C isotopologue transitions, as well as the N$_2$H$^+$(1--0) line. We study the dense gas distribution, the column density probability density functions (N-PDFs) and the line ratios within the GMF. The dense gas molecular transitions follow the extended structure of the filament with area filling factors between 0.06 and 0.28 with respect to $^{13}$CO(1--0). We constructed the N-PDFs of H$_2$ for each of the dense gas tracers based on their column densities and assumed uniform abundance. The N-PDFs of the dense gas tracers appear curved in log-log representation, and the HCO$^+$ N-PDF has the largest log-normal width and flattest power-law slope index. Studying the N-PDFs for sub-regions of GMF54, we found an evolutionary trend in the N-PDFs that high-mass star forming and Photon-Dominate Regions (PDRs) have flatter power-law indices. The integrated intensity ratios of the molecular lines in GMF54 are comparable to those in nearby galaxies. In particular, the N$_2$H$^+$/$^{13}$CO ratio, which traces the dense gas fraction, has similar values in GMF54 and all nearby galaxies except ULIRGs.