Deep galaxy counts in the K band with the Keck telescope

We present deep galaxy counts in the K (⋋ 2.2 micrometer) band, obtained at the W. M. Keck 10 m telescope. The data reach limiting magnitudes K approximately 24 mag, about 5 times deeper than the deepest published K-band images to date. The counts are performed in three small (approximately 1 min), widely separated high-latitude fields. Extensive Monte Carlo tests were used to derive the completeness corrections and minimize photometric biases. The counts continue to rise, with no sign of a turnover, down to the limits of our data, with the logarithmic slope of d log N/dm = 0.315 +/- 0.02 between K = 20 and 24 mag. This implies a cumulative surface density of approximately 5 x 10^5 galaxies/sq deg, or approximately 2 x 10^10 over the entire sky, down to K = 24 mag. Our counts are in good agreement with, although slightly lower than, those from the Hawaii Deep Survey by Cowie and collaborators; the discrepancies may be due to the small differences in the aperture corrections. We compare our counts with some of the available theoretical predictions. The data do not require models with a high value of Omega_0, but can be well fitted by models with no (or little) evolution, and cosmologies with a low value of Omega_0. Given the uncertainties in the models, it may be premature to put useful constrains on the value of Omega_0 from the counts alone. Optical-to-IR colors are computed, using CCD data obtaind previously at Palomar. We find a few red galaxies with (r-K) approximately greater than 5 mag, or (i-K) approximately greater than 5 mag; these may be ellipticals at z approximately 1. While the redshift distribution of galaxies in our counts is still unknown, the flux limits reached would allow us to detect unobscured L_* galaxies out to substantial redshifts (z greater than 3?