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.
