4. Comparison with observation
To begin with we adopt the population 1 dust grains, identical to those considered in MR, and the new abundance numbers of Snow & Witt (1996). Inserting into Eq. (3), and substituting this into the intensity integral (1) along with the gas extinction (2), we obtain the results shown in Fig. 2 (after OW). In this plot the dashed, long-dashed and heavy solid lines are predicted intensities of the EBL due to decaying neutrinos (after absorption by gas and dust) for dust opacity models A, B and C respectively. There are two groups of lines; these have been obtained by letting the model parameters and theoretical uncertainties in Sect. 2 take their maximum and minimum possible values, as appropriate. The faint dotted line is included for comparison purposes and illustrates the effects of ignoring dust (absorption by hydrogen gas only). The remaining curves (labelled) are observational upper limits on EBL intensity in this waveband reported by Bowyer (1991; "Bo91"), Edelstein et al. (1997; "Ed97"), Fix et al. (1989; "Fi89"), Henry (1991; "He91"), Holberg (1986; "Ho86"), Hurwitz et al. (1991; "Hu91"), Korpela & Bowyer (1998; "Ko98"), Martin et al. (1991; "Ma91"), Murthy et al. (1991; "Mu91"), Murthy et al. (1999; "Mu99") and Wright (1992; "Wr92"). Most of these limits have been discussed in OW. The curve marked "Ed97" has come down somewhat from that based on preliminary data (OW, "Ed96"), however. And one important new limit has been included: that of Murthy et al. (1999), who have re-analyzed the data from Voyager and now find a 1 upper limit of 30 continuum units (photons cm-2 s-1 sr-1 Å-1) over the waveband 912-1150 Å. This is by far the strongest limit yet reported on the intensity of the EBL at FUV wavelengths (see Henry 1999 for discussion).
Several things can be noted about Fig. 2. Firstly, the overall picture has not changed significantly from that described in OW, despite the inclusion of dust extinction. This is particularly true for dust models A and B, the lower limit and best-fit models. For model C, which represents an upper limit on the amount of dust compatible with observation (FP), the neutrino decay signal is noticeably reduced at wavelengths longward of 1216 Å. Constraints on the theory in this region were already weak, however, in comparison to those at shorter wavelengths (OW). Constraints shortward of Ly are hardly affected at all by dust, essentially because dust extinction only becomes important at large redshifts: for model A, for model B, and for model C.
Next, we move to the population 3 dust grains, with very small radii [as an approximation to the nanoparticle populations discussed by Duley & Seahra (1998)]. This model, with its strong FUV extinction, is able to hide a good deal more of the neutrino decay signal and should thus lead to the most conservative constraints on Sciama's model. Inserting into Eq. (3), and substituting this into the intensity integral (1) along with the gas extinction (2), we obtain the results shown in Fig. 3. The format of this figure is exactly the same as that of Fig. 2 (see description above). As expected, reductions in EBL intensity are significant. Longward of Ly, in particular, we find that the strength of the neutrino decay signal is cut (at 1600 Å) by 4%, 17% and 56% for dust models A,B and C respectively. At these wavelengths, we therefore approach the factor-two reduction in intensity attributed to dust extinction by Sciama (1992) - if one adopts the upper limits on dust density consistent with quasar obscuration (FP, model C), and if the dust grains are extremely small.
Shortward of 1216 Å, the neutrino decay signal is cut (at 1000 Å) by only 1%, 3% and 10% respectively. This is not enough to alter the findings in OW. As before, our ability to rule out Sciama's hypothesis stands or falls on the validity of the Voyager limits . The new limit derived by Murthy et al. (1999), in particular, is crucial - if valid, it is more than an order of magnitude below the minimum intensity consistent with the theory. The only non-Voyager data in this region (Korpela et al. 1998) remains marginally consistent with the theory. New observations by the EURD instrument aboard Spain's MINISAT 01 satellite (Bowyer et al. 1999) could help settle the issue decisively.
By comparing the minimum predicted intensities in Figs. 2 and 3 to the observational upper limits, one can obtain constraints on the neutrino decay lifetime. Results are summarized in Table 1 (for standard grain sizes, 50-2500 Å) and Table 2 (for the nanoparticle-sized grains, 3-150 Å). These figures - especially the ones in Table 2 - are conservative lower limits, and may be compared with the neutrino decay lifetime of s required in Sciama's theory (Sciama 1997). Tables 1 and 2 confirm that the strongest constraints come from the new limit of Murthy et al. (1999). This is inconsistent with the decaying neutrino hypothesis, even assuming the most conservative dust model (C) and the smallest possible dust grains (population 3). The other limits, however, do not rule out the theory under these assumptions. Assuming the best-fit (B) or least conservative model (A), the theory is inconsistent with three of the Voyager-based limits (Mu99,He91 below Ly, and Mu91), but remains compatible with the other data (for both standard and small sized dust grains).
Table 1. Lower limits on neutrino lifetime ( s), with extinction due to dust grains of standard size (population 1)
Table 2. Lower limits on neutrino lifetime ( s), with extinction due to very small dust grains (population 3)
© European Southern Observatory (ESO) 1999
Online publication: August 25, 1999