Annu. Rev. Astron. Astrophys. 1994. 32: 531-590 Copyright © 1994 by Annual Reviews. 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 10⁵ 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.