and Cosmology

9.5 The Cosmic Star-Formation History
line was detected from the most distant QSO known, at
z = 6.42, where it is redshifted into the submillimeter
part of the spectrum. This not only suggests that the host
galaxy of the QSO undergoes an intense burst of star
formation, but also that the material in this host galaxy
is already significantly enriched with metals.
9.5.2 Redshift Dependence of the Star Formation:
The Madau Diagram
The density of star formation, ρ SFR ,isdefinedasthe
mass of newly formed stars per year per unit (comoving)
volume, typically measured in M ⊙ yr −1 Mpc −3 .
Therefore, ρ SFR as a function of redshift specifies how
many stars have formed at any time. By means of the
star-formation density we can examine the question, for
instance, of whether the formation of stars began only at
relatively low redshifts, or whether the conditions in the
early Universe were such that stars formed efficiently
even at very early times.
Investigations of the SFR in galaxies, by means of
the above indicators, and source counts of such starforming
galaxies, allow us to determine ρ SFR . The plot
of these results (Fig. 9.33) is called a “Madau diagram”.
In about 1996, Piero Madau and his colleagues accomplished,
for the first time, a determination of the SFR at
high redshifts from Lyman-break galaxies, where the intrinsic
extinction was neglected in these first estimates.
Correcting for this extinction (for which the progress
in submillimeter astronomy has been extremely important,
as we saw in Sect. 9.2.3), a nearly constant ρ SFR is
found for z 1, together with a decline by about a factor
of 10 from z ∼ 1 to the present time. These results have
more recently been confirmed by investigations with
the Spitzer satellite, observing a large sample of galaxies
at FIR wavelengths. Whereas the star-formation rate
density at low redshifts is dominated by galaxies which
are not very prominent at FIR wavelength, this changes
drastically for redshifts z 0.7, above which most of
the star-formation activity is hidden from the optical
view by dust. From this we conclude that most stars in
our neighborhood were already formed at high redshift:
star formation at earlier epochs was considerably more
active than it is today.
Although the redshift-integrated star-formation rate
and the mass density of stars determined from galaxy
surveys, as displayed in Fig. 9.34, slightly deviate from
each other, the degree of agreement is quite satisfactory
if one recalls the assumptions that are involved
in the determination of the two quantities: besides the
uncertainties discussed above in the determination of
the star-formation rate, we need to mention in particular
the shape of the IMF of the newly formed stars for
the determination of the stellar mass density. In fact,
Fig. 9.34 shows that we have observed the formation of
essentially the complete current stellar density.
389
Fig. 9.33. The comoving star-formation density ρ SFR as
a function of redshift, where the different symbols denote
different indicators used for the determination of the starformation
rate. This plot, known as the “Madau diagram”,
shows the history of star formation in the Universe. Clearly
visible is the decline for z < 1; towards higher redshifts,
ρ ∗ seems to remain nearly constant. The curve is an empirical
fit to the data
Fig. 9.34. Redshift evolution of the mass density in stars,
as measured from various galaxy surveys. The solid curve
specifies the integrated star-formation density from Fig. 9.33