Ground-based Pa$\alpha$ Narrow-band Imaging of Local Luminous Infrared
  Galaxies I: Star Formation Rates and Surface Densities
  Luminous infrared galaxies (LIRGs) are enshrouded by a large amount of dust,
produced by their active star formation, and it is difficult to measure their
activity in the optical wavelength. We have carried out Pa$\alpha$ narrow-band
imaging observations of 38 nearby star-forming galaxies including 33 LIRGs
listed in $IRAS$ RBGS catalog with the Atacama Near InfraRed camera (ANIR) on
the University of Tokyo Atacama Observatory (TAO) 1.0 m telescope (miniTAO).
Star formation rates (SFRs) estimated from the Pa$\alpha$ fluxes, corrected for
dust extinction using the Balmer Decrement Method (typically $A_V$ $\sim$ 4.3
mag), show a good correlation with those from the bolometric infrared
luminosity of $IRAS$ data within a scatter of 0.27 dex. This suggests that the
correction of dust extinction for Pa$\alpha$ flux is sufficient in our sample.
We measure the physical sizes and the surface density of infrared luminosities
($\Sigma_{L(\mathrm{IR})}$) and $SFR$ ($\Sigma_{SFR}$) of star-forming region
for individual galaxies, and find that most of the galaxies follow a sequence
of local ultra luminous or luminous infrared galaxies (U/LIRGs) on the
$L(\mathrm{IR})$-$\Sigma_{L(\mathrm{IR})}$ and $SFR$-$\Sigma_{SFR}$ plane. We
confirm that a transition of the sequence from normal galaxies to U/LIRGs is
seen at $L(\mathrm{IR})=8\times10^{10}$ $L_{\odot}$. Also, we find that there
is a large scatter in physical size, different from those of normal galaxies or
ULIRGs. Considering the fact that most of U/LIRGs are merging or interacting
galaxies, this scatter may be caused by strong external factors or differences
of their merging stage.
