2.2. The cosmic-averaged star formation history
A complementary way to understand the star formation history of the Universe is to explore the build-up in stellar mass with cosmic time. This integral over the cosmic SFR contains the same information (under the assumption of a reasonably well-behaved stellar IMF), yet suffers from completely different systematic uncertainties and is therefore an invaluable probe of the broad evolution of the stellar content of the Universe.
Ideally stellar masses would be estimated from spectroscopic data (e.g., velocity fields, rotation curves, and/or stellar velocity dispersions) coupled with multi-waveband photometry, under some set of assumptions about the dark matter content of the galaxy. Unfortunately, measurements of such quality are relatively uncommon, even in the local Universe.
In the absence of velocity data, one can attempt to estimate stellar masses using photometric data alone with the aid of stellar population synthesis models ([Fioc & Rocca-Volmerange (1997), Bruzual & Charlot (2003)]). In these models, increasing the mean stellar age or the metallicity produces almost indistinguishable effects on their broad-band optical colors, and indeed even in their spectra with the exception of a few key absorption lines ([Worthey (1994)]). Increasing dust extinction produces very similar effects at least some of the time ([Tully et al. (1998)]), although the relationship between reddening and extinction is rather sensitive to star/dust geometry ([Witt & Gordon (2000)]). An increase in stellar population age, metallicity or dust content reddens and dims the stellar population, at a fixed stellar mass. Crucially, the relationship between reddening and dimming is similar for all three effects. While this makes it extremely challenging to measure the age, metallicity or dust content of galaxies using optical broad-band colors alone, it does mean that one can invert the argument and use color and luminosity to rather robustly estimate stellar mass, almost independent of galaxy SFH, metallicity or dust content (e.g., [Bell & de Jong (2001)]).
The slope of the relationship between color and mass-to-light ratio (M/L) is passband-dependent (steeper in the blue, shallower in the near-infrared) but does not strongly depend on stellar IMF. In contrast, the zero point of the color-M/L relation depends strongly on stellar IMF, especially to its shape at masses 1 M where the bulk of the stellar mass resides but the contribution to the total luminosity is low. There are important sources of systematic error: dust does not always move galaxies along the same color-M/L relation as defined by age and metallicity (e.g., [Witt & Gordon (2000)]), and most importantly, significant contributions from young stellar populations (either because the galaxy is truly young or because of recent starburst activity) can bias the stellar M/Ls at a given color towards lower values. Recently, a number of methodologies have been developed to address these limitations by inclusion of important variations in star formation history (e.g., [Papovich, Dickinson, & Ferguson (2001)]) or by using spectral indices and colors to account for bursts and dust more explicitly (e.g., [Kauffmann et al. (2003)]).
The basic methodology has been applied in the last several years to a wide variety of galaxy surveys to explore the stellar mass density in the local Universe (e.g., [Cole et al. (2001)]; [Bell et al. (2003)]), its evolution out to z ~ 1 (e.g., [Brinchmann & Ellis (2000)]; [Drory et al. (2004)]; Borch et al., in preparation) and even out to z ~ 3 (e.g., [Rudnick et al. (2003)]; [Dickinson et al. (2003)]; [Fontana et al. (2003)], [Glazebrook et al. (2004)]). In Fig. 2, I show a compilation of some of these stellar mass estimates, all transformed to a [Kroupa (2001)] IMF. The error bars in all cases give a rough idea of the uncertainties in stellar mass; the error bars for [Drory et al. (2004)], [Glazebrook et al. (2004)], and Borch et al. include contributions from cosmic variance also.
Figure 2. The evolution of the cosmic-averaged stellar mass density. Stellar masses assume a [Kroupa (2001)] IMF and H0 = 70 km s-1 Mpc-1. The data are taken from Rudnick et al. (2003, normalized to reproduce the z = 0 stellar mass density from Cole et al. 2001 & Bell et al. 2003), [Dickinson et al. (2003)], [Drory et al. (2004)], [Glazebrook et al. (2004)], and Borch et al.'s (in preparation) measurements from the COMBO-17 photometric redshift survey. The solid line shows the integral of the SFR from Fig. 1.
From Figs. 1 and 2, it is clear that the epoch z 1 is characterized by rapid star formation, with roughly 2/3 of the stellar mass in the Universe being formed in the first 5 Gyr. In contrast, from z ~ 1 to the present day, one witnesses a striking decline in the cosmic SFR, by a factor of roughly 10. Despite this strongly suppressed SFR, roughly 1/3 of all stellar mass is formed in this interval, owing to the large amount of time between z ~ 1 and the present day.