Annu. Rev. Astron. Astrophys. 1994. 32:
531-590
Copyright © 1994 by . All rights reserved |

**5.1. Background Light Constraints**

An effect that constrains the number of Population III objects over
every mass range between 0.1 and 10^{5}
*M*_{} is the
generation of background light during
stellar main-sequence phase. The fact that the observed background
radiation density over all wavebands cannot exceed
_{RO}
10^{-4} in
units of the
critical density (and it is smaller in most bands) permits a general
constraint
on _{*}(*M*). One can obtain more precise
constraints by using information
about the waveband in which the radiation is expected to reside
(Peebles & Partridge 1967.
Thorstensen & Partridge
1975,
Carr et al 1984,
McDowell 1986,
Negroponte 1986)
but an integrated background light limit has the virtue of generality.

For stars larger than 0.8
*M*_{}, which
have already burnt their nuclear fuel,
one just compares their total light production to
_{RO} to
obtain a constraint on
_{*}(*M*). Since 7 MeV per baryon is
released in burning hydrogen to helium,
the background light density generated should be
_{R} = 0.007
_{*}*f*_{b}(1 +
*z*_{*})^{-1}
in units of the critical density, where *z*_{*} is
the redshift at which the stars burn
their fuel (the minimum of the formation redshift *z*_{f}
and the redshift *z*_{MS} at
which the age of the Universe equals their main-sequence time) and
*f*_{b} is the
fraction of the star's mass burnt into helium. By using the known dependence
of *f*_{b} and *z*_{MS} on *M*, one can
predict the value of
_{R} as a
function of
_{*},
*M*,
and *z*_{f}. Since the observed background density over all
wavebands does not exceed 10^{-4}, this implies a constraint on
_{*}
as function of *M* and *z*_{f}. For
stars with *M* < 0.8
*M*_{}, which
are still burning, one compares the product
of the luminosity *L(M)* and the age of the Universe to
_{RO}. The
resulting constraints on
_{*}(*M,
z*_{*}) are shown in
Figure 2; these are somewhat stronger
than indicated by
Carr et al (1984)
because the limits on
_{RO} have
improved (See Section 6.1).
Peebles & Partridge (1967)
used this argument to preclude stars in the mass range 0.3-2.5
*M*_{} from
having the critical density.