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Dust-to-gas ratio, $X_{\rm CO}$ factor and CO-dark gas in the Galactic anticentre: an observational study

We investigate the correlation between extinction and H~{\sc i} and CO emission at intermediate and high Galactic latitudes ($|b|>10\degr$) within the footprint of the Xuyi Schmidt Telescope Photometric Survey of the Galactic anticentre (XSTPS-GAC) on small and large scales. In Paper I (Chen et al. 2014), we present a three-dimensional dust extinction map within the footprint of XSTPS-GAC, covering a sky area of over 6,000\,deg$^2$ at a spatial angular resolution of 6\,arcmin. In the current work, the map is combined with data from gas tracers, including H~{\sc i} data from the Galactic Arecibo L-band Feed Array H~{\sc i} survey and CO data from the Planck mission, to constrain the values of dust-to-gas ratio $DGR=A_V/N({\rm H})$ and CO-to-$\rm H_2$ conversion factor $X_{\rm CO}=N({\rm H_2})/W_{\rm CO}$ for the entire GAC footprint excluding the Galactic plane, as well as for selected star-forming regions (such as the Orion, Taurus and Perseus clouds) and a region of diffuse gas in the northern Galactic hemisphere. For the whole GAC footprint, we find $DGR=(4.15\pm0.01) \times 10^{-22}$\,$\rm mag\,cm^{2}$ and $X_{\rm CO}=(1.72 \pm 0.03) \times 10^{20}$\,$\rm cm^{-2}\,(K\,km\,s^{-1})^{-1}$. We have also investigated the distribution of "CO-dark" gas (DG) within the footprint of GAC and found a linear correlation between the DG column density and the $V$-band extinction: $N({\rm DG}) \simeq 2.2 \times 10^{21} (A_V - A^{c}_{V})\,\rm cm^{-2}$. The mass fraction of DG is found to be $f_{\rm DG}\sim 0.55$ toward the Galactic anticentre, which is respectively about 23 and 124 per cent of the atomic and CO-traced molecular gas in the same region. This result is consistent with the theoretical work of Papadopoulos et al. but much larger than that expected in the $\rm H_2$ cloud models by Wolfire et al.