The Carbon-to-H$_2$, CO-to-H$_2$ Conversion Factors and Carbon Abundance
  on Kiloparsec Scales in Nearby Galaxies
  Using the atomic carbon [CI](1$-$0) and [CI](2$-$1) emission maps observed
with the $Herschel\ Space\ Observatory$, and CO(1$-$0), HI, infrared and submm
maps from literatures, we estimate the [CI]-to-H$_2$ and CO-to-H$_2$ conversion
factors of $\alpha_\mathrm{[CI](1-0)}$, $\alpha_\mathrm{[CI](2-1)}$, and
$\alpha_\mathrm{CO}$ at a linear resolution $\sim1\,$kpc scale for six nearby
galaxies of M 51, M 83, NGC 3627, NGC 4736, NGC 5055, and NGC 6946. This is
perhaps the first effort, to our knowledge, in calibrating both [CI]-to-H$_2$
conversion factors across the spiral disks at spatially resolved $\sim1\,$kpc
scale though such studies have been discussed globally in galaxies near and
far. In order to derive the conversion factors and achieve these calibrations,
we adopt three different dust-to-gas ratio (DGR) assumptions which scale
approximately with metallicity taken from precursory results. We find that for
all DGR assumptions, the $\alpha_\mathrm{[CI](1-0)}$,
$\alpha_\mathrm{[CI](2-1)}$, and $\alpha_\mathrm{CO}$ are mostly flat with
galactocentric radii, whereas both $\alpha_\mathrm{[CI](2-1)}$ and
$\alpha_\mathrm{CO}$ show decrease in the inner regions of galaxies. And the
central $\alpha_\mathrm{CO}$ and $\alpha_\mathrm{[CI](2-1)}$ values are on
average $\sim 2.2$ and $1.8$ times lower than its galaxy averages. The obtained
carbon abundances from different DGR assumptions show flat profiles with
galactocentric radii, and the average carbon abundance of the galaxies is
comparable to the usually adopted value of $3 \times 10^{-5}$. We find that
both metallicity and infrared luminosity correlate moderately with the
$\alpha_\mathrm{CO}$ whereas only weakly with either the
$\alpha_\mathrm{[CI](1-0)}$ or carbon abundance, and not at all with the
$\alpha_\mathrm{[CI](2-1)}$.
