6.1.6. A Possible Decaying Particle Background

During the period 1990-1995, the British Cosmologist Dennis Sciama introduced an important new idea of cosmological significance. Sciama surmised that the current level of ionization in the Galaxy seemed to be higher than could be accounted for by the known contribution of young, ionizing stars in the Galactic disk. In particular, the free electron scale height in the galaxy is observed to be approximately 900 pc and its difficult to account for ionizing radiation that would make it this high above the thin ( 100 pc) plane defined by young stars. In addition to this, it has always been unclear if the combined ionizing flux of QSOs was sufficient to produce the partial ionization states of the Lyman forest clouds and/or the metallic line systems. To account for a possible extra source of ionization in the Universe, Sciama hypothesized the existence of a neutrino with a non-zero rest mass whose principle decay channel was that of an ionizing photon. The foundation of this idea, that some massive particle might experience late decay though photon channels does have significant cosmological consequences and so its important to rigorously test this idea.

The basis of the idea is well grounded in particle physics theory. One of the main ingredients of the standard model for particle physics is the existence of 3 families of neutrinos, the electron, muon and tau neutrinos. If say, the tau neutrino was unstable then it could decay along a channel

(3)

The decay lifetime could be anything depending upon unknown details in the standard model of particle physics. In order to conserve energy and momentum, the energy of the decay photon is given by

(4)

where m₁ refers to the heavier neutrino species (e.g., ) and m₂ refers to the lighter species (_µ or _e). To be consistent with the solar neutrino experiment one requires m₁ >> m₂ so that

(5)

Since we require E to be larger than the ionization energy of hydrogen (13.6 eV), this leads to a lower limit on the mass of the tau neutrino of 27.2 eV. This is a cosmologically interesting mass which allows theses neutrinos to have a significant contribution to . However, the decay time of these neutrinos must be quite long, on order of 10²³ seconds (see Sciama 1990). Recall that the expansion age of the Universe is of order 10¹⁷ seconds. This long decay time is set by the requirement that too short of decay time produces much too large of UV background and too long of decay time means there is insufficient ionization photons at z = 0 to account for the large free electron scale height (900 pc - Lyne et al. 1990), in our Galaxy as inferred from dispersion measures to globular clusters. Indeed, it is difficult to understand this large of scale height if the ionization is solely due to young OB stars in the galactic disk which have a scale height 100 pc.

The main aesthetic complaint to this particular theory is that two very disconnected physical properties of the Universe, i.e. the ionization potential of hydrogen and are now strongly coupled leaving only a very small range of neutrino masses than can satisfy both conditions. When one considers recent observational data on the metagalactic ionizing UV radiation this small range becomes even more narrow. Vogel et al. (1995) report on observations of a large intergalactic H I cloud discovered originally by Giovanelli and Haynes (1989) (see also Impey et al. 1990, Salzer et al. 1991, Chengular et al. 1995). This cloud, which may be a form of LSB galaxy (see below), represents an ideal laboratory for determining the metagalactic UV flux because it has no identifiable internal sources of ionization. The limits on H recombination from the Vogel et al. study constrain the flux of ionizing radiation of be 1.6 x 10⁵ photons cm^-2 s^-1. The flux of decaying neutrinos is given by

(6)

where N is the number density of neutrinos at z = 0 ( 100 cm^-3) and is the decay lifetime. From chapter 1 we have that c / H₀ is the horizon scale or the radius of the observable Universe. Since the decaying neutrinos have some redshift distribution associated with them (due to a distribution of decay times) then

(7)

where represents the fractional volume of the Universe over which the neutrinos can decay and still have 13.6 eV of energy at z = 0. We thus have the firm observational constraint that

(8)

which leads to in the range 0.2-0.4 eV. Thus, if this theory is correct, observations have fixed the mass of the neutrino to be 27.6 - 28.0 eV. We have either now solved cosmology or dismissed the decaying neutrino hypothesis (see also Sciama 1995).

There are other observational constraints that are also inconsistent with this hypothesis. The first of these involves the ionization of nitrogen which requires photons of energy greater than 14.5 eV. Under the current constraints, the decaying neutrino hypothesis would not result in the ionization of nitrogen. In our Galaxy, nitrogen is observed to be partially ionized when there are no apparent local sources of ionization. In addition, as discussed above, the observed UV background flux is quite consistent with the integrated contribution of galaxies and doesn't appear to require extra sources. For the decay parameters presented here, decay photons would end up providing approximately 70% of the extragalactic background at 1500 Å (see Sciama 1995). Finally, if decaying massive neutrinos contribute most of the binding mass to clusters of galaxies, then very massive clusters (which have a high density of neutrinos) should be sources of weak UV emission at the specific wavelength of ₀ = _e(1 + z) where _e corresponds to a photon of energy 13.8-14.0 eV. HUT observations of A665, at z = 0.18, failed to detect any emission at the predicted wavelength (Davidsen et al. 1991). To explain this non-detection requires a longer neutrino decay time. However, a longer neutrino decay time will not supply the needed ionizing photons to account for the 900 pc free electron scale height in the Galaxy. On balance, this intriguing idea does not appear to be viable.