Galaxy number counts -: V.: Ultradeep counts:: The Herschel and Hubble Deep Fields

We present u, b, r and i galaxy number counts and colours from both the North and South Hubble Space Telescope Deep Fields and the William Herschel Deep Field. The latter comprises a 7 x 7 arcmin(2) area of sky, reaching b similar to 28.5 at its deepest. Following Metcalfe et al., we show that simple Bruzual & Chariot evolutionary models which assume exponentially increasing star formation rates with look-back time and q(0) = 0.05 continue to give excellent fits to galaxy counts and colours in the deep imaging data. With q(0) = 0.5, an extra population of 'disappearing dwarf' galaxies is required to fit the optical counts. We further find that the (r - i) : (b - r) colour-colour diagrams show distinctive features corresponding to two populations of early- and late-type galaxies which are well fitted by features in the Bruzual & Chariot models. The (r - i) :(b - r) data also suggest the existence of an intrinsically faint population of early-types at z similar to 0.1 with similar properties to the 'disappearing dwarf' population required if q(0) = 0.5. The outstanding issue remaining for the early-type models is the dwarf-dominated initial mass function (IMF) which we invoke to reduce the numbers of z > 1 galaxies predicted at K < 19. For the spiral models, the main issue is that even with the inclusion of internal dust absorption at the A(B) = 0.3 mag level, the model predicts too blue (u - b) colours for late-type galaxies at z 1. Despite these possible problems, we conclude that these simple models with monotonically increasing star formation rates broadly fit the data out to z similar to 3. We compare these results for the star formation rate history with those from the different approach of Madau et al. We conclude that when the effects of internal dust absorption in spirals are taken into account the results from this latter approach are completely consistent with the tau = 9Gyr, exponentially rising star formation rate density out to z approximate to 3 which fits the deepest, optical/IR galaxy count and colour data. When we compare the observed and predicted galaxy counts for UV dropouts in the range 2 less than or similar to z less than or similar to 3.5 from the data of Steidel et al. and Madau et al., and new data from the Herschel and HDF-S fields, we find excellent agreement, indicating that the space density of galaxies may not have changed much between z = 0 and z = 3, and identifying the Lyman-break galaxies with the bright end of the evolved spiral luminosity function. Making the same comparison for B dropout galaxies in the range 3.5 less than or similar to z less than or similar to 4.5 we find that the space density of intrinsically bright galaxies remains the same, but the space density of faint galaxies drops by a factor of similar to5, consistent with the idea that L* galaxies were already in place at z approximate to 4 but that dwarf galaxies may have formed later at 3 less than or similar to z less than or similar to 4.