The Near-Infrared Number Counts and Luminosity Functions of Local Galaxies

This study presents a wide-field near-infrared (K-band) survey in two fields; SA 68 and Lynx 2. The survey covers an area of 0.6 deg.$^2$, complete to K=16.5. A total of 867 galaxies are detected in this survey of which 175 have available redshifts. The near-infrared number counts to K=16.5 mag. are estimated from the complete photometric survey and are found to be in close agreement with other available studies. The sample is corrected for incompleteness in redshift space, using selection function in the form of a Fermi-Dirac distribution. This is then used to estimate the local near-infrared luminosity function of galaxies. A Schechter fit to the infrared data gives: M$^\ast_K = -25.1 \pm 0.3$, $\alpha = -1.3\pm 0.2$ and $\phi^\ast =(1.5\pm 0.5)\times 10^{-3}$ Mpc$^{-3}$ (for H$_0=50$ Km/sec/Mpc and q$_0=0.5$). When reduced to $\alpha=-1$, this agrees with other available estimates of the local IRLF. We find a steeper slope for the faint-end of the infrared luminosity function when compared to previous studies. This is interpreted as due to the presence of a population of faint but evolved (metal rich) galaxies in the local Universe. However, it is not from the same population as the faint blue galaxies found in the optical surveys. The characteristic magnitude ($M^\ast_K$) of the local IRLF indicates that the bright red galaxies ($M_K\sim -27$ mag.) have a space density of $\le 5\times 10^{-5}$ Mpc$^{-3}$ and hence, are not likely to be local objects.