The K-band galaxy luminosity function

We measured the K-band luminosity function using a complete sample of 4192 morphologically typed 2MASS galaxies with mu (K s) = 20 mag arcsec(-2) isophotal magnitudes 7<K-20<11.25 mag spread over 2.12 sr. Early-type (T <less than or equal to> -0.5) and late-type (T > -0.5) galaxies have similarly shaped luminosity functions, alpha (e) = -0.92 +/-0.10 and alpha (l) = -0.87 +/-0.09. The early-type galaxies are brighter, M-K*e = -23.53 +/-0.06 mag compared to M-K*l = -22.98 +/-0.06 mag, but less numerous, n(*e) = (0.45 +/-0.06)x10(-2) Mpc(-3) compared to N-*l = (1.01 +/-0.13)x10(-2) h(3) Mpc(-3) for H-0 = 100 h km s(-1) Mpc(-1), such that the late-type galaxies slightly dominate the K-band luminosity density, j(late)/j(early) = 1.17 +/-0.12. Including a factor of 1.20 +/-0.04 correction for the conversion of the isophotal survey magnitudes to total magnitudes, the local K-band luminosity density is j = (7.14 +/-0.75)x10(8) h L-circle dot Mpc(-3), which implies a stellar mass density relative to critical of Omega (*)h = (1.9 +/-0.2)x10(-3) for a Kennicutt initial mass function (IMF) and Omega (*)h = (3.4 +/-0.4)x10(-3) for a Salpeter IMF. Our morphological classifications are internally consistent, are consistent with previous classifications, and lead to luminosity functions unaffected by the estimated uncertainties in the classifications. These luminosity functions accurately predict the K-band number counts and redshift distributions for K less than or similar to 18 mag, beyond which the results depend on galaxy evolution and merger histories.