The Star Formation Rate History in the FORS Deep and GOODS-South Fields

We measure the star formation rate (SFR) as a function of redshift z up to z ≈ 4.5, based on B -, I -, and ( I + B )-selected galaxy catalogs from the FORS Deep Field (FDF) and the K -selected catalog from the GOODS-South field. Distances are computed from spectroscopically calibrated photometric redshifts accurate to Δ z /( z spec + 1) ≤ 0.03 for the FDF and ≤0.056 for the GOODS-South field. The SFRs are derived from the luminosities at 1500 Å. We find that the total SFR estimates derived from B , I , and I + B catalogs agree very well (≲0.1 dex), while the SFR from the K catalog is lower by ≈0.2 dex. We show that the latter is due solely to the lower star-forming activity of K -selected intermediate- and low-luminosity ( L < L * ) galaxies. The SFR of bright ( L > L * ) galaxies is independent of the selection band, i.e., the same for B -, I -, ( I + B )-, and K -selected galaxy samples. At all redshifts, luminous galaxies ( L > L * ) contribute only approximately one-third to the total SFR. There is no evidence for significant cosmic variance between the SFRs in the FDF and in the GOODS-South field, ≲0.1 dex, consistent with theoretical expectations. The SFRs derived here are in excellent agreement with previous measurements, provided that we assume the same faint-end slope of the luminosity function as previous works (α ~ -1.6). However, our deep FDF data indicate a shallower slope of α = -1.07, implying a SFR lower by ≈0.3 dex. We find the SFR to be roughly constant up to z ≈ 4 and then to decline slowly beyond, if dust extinctions are assumed to be constant with redshift.