Relation between polycyclic aromatic hydrocarbon, Br$\alpha$ and infrared luminosity of local galaxies observed with AKARI

We produce a catalogue of polycyclic aromatic hydrocarbon (PAH) 3.3 $\mu$m, Br$\alpha$ and infrared luminosity ($L$(IR)) of 412 local galaxies, and investigate a relation between these physical parameters. We measure the PAH 3.3 $\mu$m and Br$\alpha$ flux using AKARI 2-5 $\mu$m spectra and the $L$(IR) using the AKARI-all-sky-survey data. The $L$(IR) and redshift ranges of our sample are $L$(IR)=$10^{9.7-12.8}$L$_\odot$ and $z_{\rm spec}=0.002-0.3$, respectively. We found that the ratio of $L$(PAH 3.3 $\mu$m) to $L$(IR) is constant at $L$(IR) $