7.2. Star Formation Rates and the Cosmic Star Formation History
If the ionization is dominated by hot, young stars, the observed flux of the Ly emission line may be used to estimate a lower bound to the star formation rate in a galaxy. Using the case B recombination Ly / H ratio of 10 (Osterbrock 1989), and the Kennicutt (1983) conversion from H luminosity to , Madau et al. (1998) find ~ 0.7 × 10-42 h50-2 LLy M yr-1 where LLy is measured in units of ergs s-1 (q0 = 0.5; is 3.3 times larger for q0 = 0.1). The star formation rate may also be estimated from the observed UV continuum emission. Madau et al. (1998) calculate that a population older than 100 Myr will have 10-40L1500 M yr-1 where L1500, the luminosity at 1500 Å, is measured in units of ergs s-1 Å-1. Leitherer, Carmelle, & Heckman (1995) models yield similar results for a different initial mass functions (IMFs) and ages less than 10 Myr. These are lower limits to since no correction to the UV flux for either internal absorption or dust extinction has been made (see Section 7.5).
With sufficient numbers of well-observed distant systems, we may begin studying the star formation history of the universe as a function of comoving volume. The Canada-France Redshift Survey (CFRS; Lilly et al. 1995) demonstrated strong luminosity evolution in the blue field galaxy population between z = 0 and z = 1. Madau et al. (1996), using the early results of photometric selection in the HDF, integrated the results at z < 5 into a coherent picture of the star formation history of the universe and suggested that the global star formation peaks between z = 1 and z = 2, in remarkable agreement with predictions based on the comoving H I density traced by Ly absorption systems (Pei & Fall 1995), with hierarchical models in a cold dark matter dominated universe (Baugh et al. 1998), and with the quasar luminosity function (Cavaliere & Vittorini 1998).
Substantial caveats temper this result, however: (1) the number of spectroscopically measured redshifts between z = 1 and z = 2 is small. Connolly et al. (1997) use optical and near-infrared data to estimate photometric redshifts in the HDF at 1 < z < 2 in order to span this redshift "desert" for which few strong spectroscopic features are shifted into the optical regime. Until a substantial number of confirmed redshifts have been obtained, however, photometric redshifts in the 1 < z < 2 range are not well constrained. Thus the epoch thought to be the most productive in terms of star formation is also the least well measured. (2) The small area ( 5 arcmin2) covered by the HDF makes global parameters inferred from it vulnerable to perturbations from large-scale structure. (3) The existence of the peak at z ~ 1.5 is contingent upon the completeness of the estimates of global star formation at higher redshift. The z ~ 4 point in the analysis of Madau et al. (1996) was based on a single object in the HDF at z = 4.02 (Dickinson 1998) and should thus be treated as an uncertain lower limit. More recent measurements, based on larger area surveys, show that the star formation density is significantly higher at z 4 (Steidel et al. 1999). Finally, (4) both the photometric and the Ly search techniques require the objects to be UV bright. It is possible that a substantial fraction of star-forming activity in dusty high-redshift systems has been overlooked thus far. The recent discoveries of a relatively large number of resolved sources in small area sub-mm surveys performed by SCUBA suggest this to be the case (e.g., Hughes et al. 1998; Barger et al. 1998; Dey et al. 1999a).
Figure 11 illustrates a recent determination of the star formation history of the universe. In sharp contrast to the initial results of Madau et al. (1996), the UV luminosity density of the universe is approximately constant at 2 z 4. Preliminary results from the Berkeley long-slit searches suggest that it remains constant to z 5.5. The evolution of the star formation density of the universe, as probed by apparently normal, star-forming systems, implies that their evolution follows a significantly different trajectory than that of AGN, especially quasars. Both radio-quiet and radio-loud quasars show a considerable density decrease beyond z ~ 3 (cf. Dunlop & Peacock 1990; Hook & McMahon 1998; Cavaliere & Vittorini 1998), falling by a factor of ~ 3 from z = 3 to z = 4.
Figure 11. The star formation history of the universe. Points at z < 1 are from the Canada-France Redshift Survey (CFRS; Lilly et al. 1996); points at 1 z 2 are from near-infrared studies of the HDF (Connolly et al. 1997); and points at z 3 and z 4 are from studies of Lyman-break galaxies (LBGs; Steidel et al. 1999). For a Salpeter IMF, the cosmic metal ejection density, z, is 1/42 of the cosmic star formation density, * (Madau et al. 1996).