2. Contributions of neutrino decay to the EBL intensity
The spectral intensity of the neutrino decay signal at observed wavelength (including the effects of extinction) is given by Eqs. (12) and (17) of OW:
where z refers to redshift and we have assumed an Einstein-de Sitter cosmology, as befits the fact that neutrinos in Sciama's theory provide enough dark matter to close the Universe.
The parameters in Eq. (1) are given as follows: is the redshift beyond which neutrino contributions to the observed EBL become negligible. It may be confirmed numerically (by evaluating the integral for various values of ) that for the neutrinos and waveband of interest here; we take in our calculations. (The fact that the signal is dominated by nearby neutrino decays plays a crucial role in limiting the effects of obscuration by intergalactic dust, since the latter in most cases becomes important only at and higher.) In Sciama's theory (Sciama 1997), each decay [of lifetime s] produces a eV photon, implying a peak decay wavelength Å. To this we associate a 3 uncertainty of 30 Å (OW). The (redshifted) waveband of interest therefore stretches across the FUV region, from Å to about 2000 Å.
The mean number density of eV neutrinos required to close the Universe is about 100 cm-3; whereas the number density of neutrinos responsible for the ionization of the local interstellar medium in Sciama's theory is about cm-3. This implies that a significant fraction of the decaying neutrinos are bound in galactic halos. The integral (1) must therefore incorporate contributions from both bound and free-streaming neutrinos. Since we are concerned only with the total extragalactic background signal, however, the two components may be pulled out of the integral and absorbed into the constant ; ie, . It turns out that is much greater than , partly because the free-streaming neutrinos are more numerous, and partly because many of the decay photons from bound neutrinos are absorbed within their host galaxies before they can contribute to the EBL. More detailed investigation (OW) leads to the expressions and respectively, where the are factors reflecting various uncertainties in the model. In particular, , , and refer to the mass of galactic dark matter halos, the extent to which decay photons given off by bound neutrinos are absorbed by neutral hydrogen in their host galaxies, the neutrino decay lifetime, and the neutrino rest energy, respectively. We will allow these factors to take their upper and lower limits in order to arrive at minimum and maximum possible EBL contributions from neutrino decay. We also allow the Hubble parameter to vary within the narrow range , consistent with a critical density in the context of Sciama's theory.
where Å and (Zuo & Phinney 1993, Model 1, assuming ).
A new feature of our analysis is . Little is known about the distribution of dust between galaxies, and we proceed to discuss this critically before presenting our model. The simplest possibility, and the one which should be most effective in obscuring a diffuse signal like that considered here, would be for dust to be spread uniformly through intergalactic space. A quantitative estimate of opacity due to a proposed uniform dusty intergalactic medium has in fact been suggested (Ostriker & Cowie 1981), but is regarded as an extreme upper limit because it would lead to excessive reddening of quasar spectra (Wright 1981). Subsequent discussions have tended to treat intergalactic dust as clumpy (Ostriker & Heisler 1984), with significant debate about the extent to which such clumps would redden and/or hide background quasars, possibly helping to explain the "turnoff" in quasar population at around (Wright 1986 , Wright & Malkan 1987 , Heisler & Ostriker 1988 , Wright 1990). Most of these models assume a critical density of matter () with no cosmological term (). There is evidence that and/or might enhance the effects of dust obscuration (Heisler & Ostriker 1988). We will ignore this possibility here, because neutrinos (not ) are assumed to make up the critical density in Sciama's theory.
© European Southern Observatory (ESO) 1999
Online publication: August 25, 1999