Galaxy number counts - IV. Surveying the Herschel Deep Field in the near-infrared

We present results from two new near-infrared imaging surveys. One survey covers 47.2 arcmin(2) to K(3 sigma) = 20 mag whilst a second, deeper catalogue covers a subarea of 1.8 arcmin(2) to K(3 sigma) = 22.75 mag. Over the entire area we have extremely deep optical photometry in four bandpasses (UBRI), allowing us to track the colour evolution of galaxies to very faint magnitude limits. Our K-band number counts are consistent with the predictions of non-evolving models with 0 less than or equal to q(0) less than or equal to 0.5. The K-selected (B - K) galaxy colour distributions from our surveys move sharply bluewards fainter than K similar to 20. At brighter magnitudes (K < 20 mag) our K-selected (B - K) distributions indicate a deficiency of red, early-type galaxies at z similar to 1 compared with the predictions of passively evolving models, which implies either a pure luminosity evolution (PLE) model, where star formation continues at a low level after an initial burst, or dynamical merging. At fainter magnitudes, the continuing bluewards trend observed in (B - K) can be explained purely in terms of passively evolving PLE models. We detect 0.5 +/- 0.1 galaxy arcmin(-2) with (I - K) > 4 and 19 < K < 20 mag. Although this is a factor of similar to 3 (2 sigma) more objects than in the recent survey of Berger et al., this is still lower than the predictions of standard passively evolving models and more consistent with PLE models containing small amounts of ongoing star formation. Our observed numbers of (I - K) > 4 galaxies at K - 20 are lower than the predictions of passively evolving models or PLE models with a low level of continuing star formation, suggesting that at least part of the larger deficiency observed in (B - K) at K - 20 may be caused by star formation rather than dynamical merging. As we and others have noted, the number redshift distribution at 18 < K < 19 of recent, deep K-selected redshift surveys is well fitted by non-evolving models, and passively evolving models with a Salpeter or Scale initial mass functions predict too many galaxies with z > 1. Dynamical merging is one possible solution to reduce the numbers of these galaxies but las we have suggested previously) a dwarf-dominated initial mass function for early-type galaxies could offer an alternative explanation; we show here that such a model reproduces well the optical-infrared colour distributions and K-band galaxy counts.