Annu. Rev. Astron. Astrophys. 2000. 38: 761-814 Copyright © 2000 by Annual Reviews. All rights reserved

4.3. Star Formation at High Redshift: A Synthesis

From the survey of the 1415+52 CFRS field, Flores et al (1999b) concluded that 60 ± 25% of the star formation at z 1 is associated with infrared emission. Including the dusty luminous starbursts detected by ISOCAM, the total star formation rate (per unit comoving volume) at z 1 is 2.9 ± 1.3 times as large as that deduced from the CFRS rest-frame UV observations (without correction for extinction). Rowan-Robinson et al (1997) found an even larger correction factor from an analysis of the ISOCAM HDF(N) data. If the ISOPHOT 175 µm sources are ultraluminous starburst galaxies at z ~ 1, the far-IR data require a star formation rate also ~ 3 times larger than predicted by UV observations (not extinction-corrected) interpolated into this redshift regime. Finally, the 850 µm source detections with the SCUBA bolometer camera require a star formation rate at z ~ 3 that is ~ 3.5 times greater than that derived from Lyman-dropout galaxies (Hughes et al 1998, Barger et al 1998, Ivison et al 1998). This assumes that the 850 µm sources are powered by star formation. To explain the entire COBE far-IR/submm background requires that the star formation rate at z 1 be greater by another factor 2 (Lagache et al 1999b). The recent H-based star formation rate at z ~ 1.3 (Yan et al 1999), on the other hand, is in good agreement with the far-IR/submm estimates. The large discrepancy between the UV and IR/submm estimates disappears if the star formation rates estimated from the Lyman-dropout galaxies are corrected for extinction (Pettini et al 1998, Meurer et al 1999, Steidel et al 1999). The data are summarized in Figure 17 (the Madau plot, see color insert; adapted from Lagache et al 1999b, Steidel et al 1999).

Figure 17. Cosmic star formation rate (per unit comoving volume, h = 0.6, q0 = 0.5) as a function of redshift (the 'Madau' plot, Madau et al 1996). The black symbols (with error bars) denote the star formation history deduced from (non-extinction corrected) UV data (Steidel et al 1999 and references therein). Upward pointing dotted green arrows with open boxes mark where these points move when a reddening correction is applied. The green, four arrow symbol is derived from (non-extinction corrected) H NICMOS observations (Yan et al 1999). The red, three arrow symbol denotes the lower limit to dusty star formation obtained from SCUBA observations of HDF (N) (Hughes et al 1998). The continuous line marks the total star formation rate deduced from the COBE background and an 'inversion' with a starburt SED (Lagache et al 1999b). The filled hatched blue and yellow boxes denotes star formation rate deduced from ISOCAM (CFRS field, Flores et al 1999b) and ISOPHOT-FIRBACK (Puget et al 1999, Dole et al 1999). The light blue, dashed curve is model 'A' (no ULIRGSs) and the red dotted curve model 'E' (with ULIRGs) of Guuiderdoni et al (1998).

The good agreement between the UV/optical and IR/submm star formation histories shown in Figure 17 may be a lucky coincidence, however. The IR/submm and UV/optical measurements likely trace different source populations. At the level expected from the extinction-corrected UV star formation rates, Chapman et al (1999) detected at 850 µm only one of about a dozen Lyman break galaxies. The reddening of the ISOCAM galaxies is only slighty higher than average (Elbaz et al 2000), and thus their true output cannot be correctly derived from optical and UV data alone. The extinction corrections in the UV/optical are poorly known. In the case of the far-IR/submm sources the redshifts are uncertain, and the contribution of AGNs is unknown. Based on the X-ray background, Almaini et al (1999) set a limit of ~ 20% to the AGN contribution to the far-IR/submm background. Only 10-40% of the far-IR/submm background are resolved into individual sources. The derivation of star formation histories from the overall far-IR/submm background depends crucially on the (uncertain) source SEDs used.

Nevertheless, a reasonably consistent picture seems to emerge. The cosmic star formation rate steeply increases between the current epoch and z ~ 1, and stays flat from z ~ 1 to at least 4. The "quiescent" mode of disk star formation (with typical gas exhaustion time scales of several Gyr) cannot explain the z 1 data. Such a scenario (model A of Guiderdoni et al 1998; dashed line in Figure 17) can definitely be excluded by the extinction-corrected UV points, the mid-infrared points, and the far-IR/submm points. A rapidly evolving "burst" mode (exhaust time scales a few hundred Myrs) is required, probably associated with the much increased merger rate at high redshift [ (1 + z), = 2..6; Zepf & Koo 1989, Carlberg 1990, Abraham et al 1996]. In the semi-analytic models of Guiderdoni et al (1998) the fraction of this burst mode in the numbers of stars formed increases with (1 + z)⁵ and dominates the cosmic star formation at z 1. To fit the far-IR/submm data as well, the fraction of violent mergers within the starburst population leading to ultraluminous starbursts must rapidly increase with redshift (Guiderdoni et al 1998, Blain et al 1999). In model E of Guiderdoni et al, the fraction of star formation in ULIRGs increases from 8% at z = 1 to 27% at z = 3. Blain et al (1999) introduced an activity parameter of mergers, defined as the inverse of the product of the fraction of mergers leading to luminous starbursts/AGNs f_b and the duration of an activity event t_b. In the Blain et al models, the activity parameter must increase by a factor of about 3 from the present day to z ~ 0.7 [the "15 µm (ISOCAM) epoch"], by ~ 10 to z ~ 1 (the "ISOPHOT epoch"?) and by ~ 160 to z ~ 3 (the "SCUBA epoch"). Hence, the relative contribution of ULIRGs to the luminosity function increases by a factor of several hundred between the local Universe and z ~ 2-3. The models of Blain et al and Guiderdoni et al are thus quite consistent with each other and with the observations. The starburst galaxies sampled by ISOCAM have characteristic ages less than a few hundred Myr (Flores et al 1999b, Aussel et al 1999b), at least an order of magnitude smaller than the gas exhaustion timescale in present-day quiescent disks. The characteristic ages of nearby ULIRGs (100 L_*) that may be representative of the 175 µm and 850 µm populations are 10 Myr (Genzel et al 1998, Tecza et al 2000), and they probably make up only a small fraction of all merger events. The ultraluminous mergers may be related to the formation of large elliptical galaxies and bulges (Kormendy & Sanders 1992). As a result of these powerful mergers, the cosmic star formation rate may stay flat or even increase to redshifts z 4 (Blain et al 1999, Pei & Fall 1995).