4.1. Stellar Populations and the Initial Mass Function
Among the thousand or so known Lyman break galaxies (LBGs), one, designated MS 1512-cB58 (or cB58 for short) has provided data of exceptional quality, thanks to its gravitationally lensed nature. Discovered by Yee et al. (1996), cB58 is, as far as we can tell, a typical ~ L* galaxy at a redshift z = 2.7276 magnified by a factor of ~ 30 by the foreground cluster MS 1512+36 at z = 0.37 (Seitz et al. 1998). This fortuitous alignment makes it by far the brightest known member of the LBG population and has motivated a number of studies from mm to X-ray wavelengths.
When we record the spectrum of a z = 3 galaxy at
optical wavelengths, we are in fact observing the
redshifted far-UV light produced by a whole population
of O and early B stars. Such spectra are most effectively analysed with
population synthesis models,
the most sophisticated of which is Starburst99 developed by the
Baltimore group
(Leitherer et al. 1999).
In Figure 23 we compare
Starburst99 model predictions
for different IMFs with a portion of the moderate resolution Keck LRIS
spectrum of cB58 obtained by
Pettini et al. (2000b),
encompassing the C IV
1548, 1550 doublet.
 |
Figure 23. Comparisons between Starburst99 (Leitherer et al. 1999) population synthesis models with different IMFs (green lines) and the Keck spectrum of MS 1512-cB58 analysed by Pettini et al. (2000b) in the region near the C IV doublet (black histogram). The y-axis is residual intensity. |
It is important to realise
that the comparison only refers to stellar spectral features
and does not include the interstellar lines,
readily recognisable by their narrower widths
(the interstellar lines are much stronger in cB58, where we
sample the whole ISM of the galaxy, than in the models which are based on
libraries of nearby Galactic O and B stars). With this clarification,
it is evident from Figure 23 that the spectral
properties of at least
this Lyman break galaxy are remarkably similar to those of present-day
starbursts - a continuous star formation model with a Salpeter IMF
provides a very good fit to the observations.
In particular, the P-Cygni profiles of C IV, Si IV and
N V are
sensitive to the slope and upper mass limit of the IMF; the best fit in
cB58 is obtained with a standard Salpeter IMF with
slope 
= 2.35
and Mup = 100
M
(top
panel of Figure 23).
IMFs either lacking in the most massive stars
or, conversely, top-heavy seem to be excluded by the data
(middle and bottom panels of Figure 23
respectively).
The only significant difference between the observed and synthesised
spectra is in the optical depth of the P-Cygni absorption trough
which is lower than predicted (top panel of
Figure 23).
A possible explanation is that this is
an abundance effect - the strengths of the wind lines
are known to be sensitive to the metallicity of the stars,
since it is through absorption and scattering of photons
in the metal lines that momentum is transferred
to the gas and a wind is generated. The Starburst99 spectra shown in
Figure 23
are for solar metallicity, but a recent update
(Leitherer et al. 2001)
now includes stellar libraries compiled with HST
observations of hot stars in the Large and
Small Magellanic Clouds, taken to be representative
of a metallicity
Z 
1/3
Z.
When these are compared with a higher resolution spectrum of cB58, obtained with the new Echelle Spectrograph and Imager (ESI) on the Keck II telescope, the match to the observed spectrum is improved (Figure 24). The emission component of the P-Cygni profile is perhaps underestimated by the model, but we suspect that there may be additional nebular C IV emission from the H II regions in the galaxy, superposed on the broader stellar P-Cygni emission. We take the good agreement in Figure 24 as an indication that the young stellar population of cB58 has reached a metallicity comparable to that of the Magellanic Clouds. This conclusion is reinforced by measurements of element abundances in the interstellar gas, as we shall see in Section 4.2 below.
 |
Figure 24. A portion of the high resolution
spectrum of MS 1512-cB58 obtained by
Pettini et al. (2002b),
encompassing the C IV
|
Before leaving this topic, it is worth noting that with a modest amount of effort (and luck in the form of gravitational lensing) it is now possible to obtain spectra of high redshift galaxies of sufficient quality to distinguish between the OB stellar populations of the Milky Way and of the Magellanic Clouds. As a matter of fact, it is evident from Figure 24 that the resolution of the ESI spectrum of cB58 is superior to those of Magellanic Cloud stars (and of nearby starburst galaxies) with which we would like to compare it!