The Infrared Luminosity Function of AKARI 90$\mu$m Galaxies in the Local
  Universe
  Local infrared (IR) luminosity functions (LFs) are necessary benchmarks for
high-redshift IR galaxy evolution studies. Any accurate IR LF evolution studies
require accordingly accurate local IR LFs. We present infrared galaxy LFs at
redshifts redshifts of $z \leq 0.3$ from AKARI space telescope, which performed
an all-sky survey in six IR bands (9, 18, 65, 90, 140 and 160 micron) with 10
times better sensitivity than its precursor IRAS. Availability of 160 micron
filter is critically important in accurately measuring total IR luminosity of
galaxies, covering across the peak of the dust emission. By combining data from
Wide-field Infrared Survey Explorer (WISE), Sloan Digital Sky Survey (SDSS)
Data Release 13 (DR13), 6-degree Field Galaxy Survey (6dFGS) and the 2MASS
Redshift Survey (2MRS), we created a sample of 15,638 local IR galaxies with
spectroscopic redshifts, factor of 7 larger compared to previously studied
AKARI -SDSS sample. After carefully correcting for volume effects in both IR
and optical, the obtained IR LFs agree well with previous studies, but comes
with much smaller errors. Measured local IR luminosity density is
$\Omega_{IR}=$ 1.19$\pm$0.05 $\times 10^{8}$ L$_{\odot}$ Mpc$^{-3}$. The
contributions from luminous infrared galaxies and ultra luminous infrared
galaxies to IR are very small, 9.3 per cent and 0.9 per cent, respectively.
There exists no future all sky survey in far-infrared wavelengths in the
foreseeable future. The IR LFs obtained in this work will therefore remain an
important benchmark for high-redshift studies for decades.
