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 IR galaxy LFs at redshifts of z<=0.3 from AKARI space telescope, which performed an all-sky survey in six IR bands (9, 18, 65, 90, 140, and 160um) with 10 times better sensitivity than its precursor Infrared Astronomical Satellite. Availability of 160um 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 (DR 13), six-degree Field Galaxy Survey and the 2MASS Redshift Survey, we created a sample of 15638 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+/-0.05x10^8^L_{sun}/Mpc^3^. The contributions from luminous IR galaxies and ultraluminous IR galaxies to {OMEGA}_IR are very small, 9.3 per cent and 0.9 per cent, respectively. There exists no future all-sky survey in far-IR wavelengths in the foreseeable future. The IR LFs obtained in this work will therefore remain an important benchmark for high-redshift studies for decades.

Cone search capability for table J/MNRAS/474/5363/table1 (AKARI-SDSS-6dFGS-2MRS sample)