The Lyman-break technique (e.g. Steidel et al. 1995) has now been proved very successful in finding large numbers of star forming galaxies at redshift (e.g. Steidel et al. 1996, 1999b). The observed number density and clustering properties of Lyman-break galaxies (hereafter LBGs, Steidel et al. 1998; Giavalisco et al. 1998; Adelberger et al. 1998) are best explained by assuming that they are associated with the most massive haloes at predicted in hierarchical models of structure formation (Mo & Fukugita 1996; Baugh et al. 1998; Mo et al. 1998b; Coles et al. 1998; Governato et al. 1998; Jing 1998; Jing & Suto 1998; Katz et al. 1998; Kauffmann et al. 1999; Moscardini et al. 1998; Peacock et al. 1998; Wechsler et al. 1998). This assumption provides a framework for predicting a variety of other observations for the LBG population. Steidel et al. (1999b and references therein) gave a good summary of recent studies on this population including the luminosity functions, luminosity densities, color distribution, star formation rates, clustering properties, and the differential evolution.
Assuming that LBGs form when gas in dark haloes settles into rotationally supported discs or, in the case where the angular momentum of the gas is small, settles at the self-gravitating radius, Mo et al. (1998b) predict sizes, kinematics and star formation rates and halo masses for LBGs, and find that the model predictions are consistent with the current (rather limited) observational data; Steidel et al. (1999a) suggest that the total integrated UV luminosity densities of LBGs are quite similar between redshift 3 and 4 although the slope of their luminosity function might have a large change in the faint-end.
Furthermore, Steidel et al. (1999b) suggest that a "typical" LBG has a star formation rate of about for and that the star formation time scale is of the order of 1Gyr based on their values of E(B-V) as pointed out by Pettini et al. (1997b) after adopting the reddening law of Calzetti (1997). Recently Friaca & Terlevichet al. (1999) used their chemodynamical model to propose that an early stage (the first Gyr) of intense star formation in the evolution of massive spheroids could be identified as LBGs.
However, Sawicki & Yee (1998) argued that LBGs could be very young stellar populations less than 0.2Gyr old, based on the broadband optical and IR spectral energy distributions. This is also supported by the work of Ouchi & Yamada (1999) based on the expected sub-mm emission and dust properties. It is worthy of note that the assumptions about the intrinsic LBG spectral shape and the reddening curve play important roles in these results.
In this paper, we study how star formation and chemical enrichment may have proceeded in the LBG population. It will be demonstrated in Sect. 2, that the observed star formation rate at requires a self-regulating process to keep the gas supply for a sufficiently long time. We will show (in Sect. 2) that such a process can be achieved by the balance between the energy feedback from star formation and gas cooling. Model predictions for the LBG population and further discussions about the results are presented in Sect. 3, a brief summary is given in Sect. 4.
As an illustration, we show theoretical results for a CDM model with cosmological density parameter , cosmological constant . The power spectrum is assumed to be that given in Bardeen et al. (1986), with shape parameter and with normalization . We denote the mass fraction in baryons by , where is the cosmic baryonic density parameter. According to the cosmic nucleosynthesis, the currently favoured value of is (Burles & Tytler 1998), where h is the present Hubble constant in units of 100 , and so . Whenever a numerical value of h is needed, we take . At the same time, we define parameter as the time scale for star formation in the LBG population throughout the paper.
© European Southern Observatory (ESO) 2000
Online publication: February 25, 2000