The Hubble Deep Field (HDF) is the deepest set of multicolor optical photometric observations ever undertaken, and it offers a valuable data set with which to study galaxy evolution. Combining the optical WFPC2 data with ground-based near-infrared photometry, we derive photometrically estimated redshifts for HDF galaxies with J < 23.5. We demonstrate that incorporating the near-infrared data reduces the uncertainty in the estimated redshifts by approximately 40% and is required to remove systematic uncertainties within the redshift range 1 < z < 2. Utilizing these photometric redshifts, we determine the evolution of the comoving ultraviolet (2800 Angstrom) luminosity density (presumed to be proportional to the global star formation rate) from a redshift of z = 0.5 to z = 2. We find that the global star formation rate increases rapidly with redshift, rising by a factor of 12 from a redshift of zero to a peak at z approximate to 1.5. For redshifts beyond 1.5, it decreases monotonically. Our measures of the star formation rate are consistent with those found by Lilly et al. from the Canada-France Redshift Survey at z < 1 and by Madau et al. from Lyman break galaxies at z > 2, and they bridge the redshift gap between those two samples. The overall star formation or metal enrichment rate history is consistent with the theoretical models of White and Frenk and the predictions of Pei and Fall based on the evolving H I content of Ly alpha QSO absorption line systems.
