Neutrinos as a diagnostic of cosmic ray galactic-extragalactic transition

Motivated by a recent change in viewing the onset of the extragalactic component in the cosmic ray spectrum, we have fitted the observed data down to ${10}^{8.6}\mathrm{GeV}$ and have obtained the corresponding power emissivity. This transition energy is well below the threshold for resonant $p\gamma$ absorption on the cosmic microwave background, and thus source evolution is an essential ingredient in the fitting procedure. Two-parameter fits in the spectral and redshift evolution indices show that a standard Fermi $E_i^{-2}$ source spectrum is excluded at larger than 95% confidence level (CL). Armed with the primordial emissivity, we follow Waxman and Bahcall to derive the associated neutrino flux on the basis of optically thin sources. For $pp$ interactions as the generating mechanism, the neutrino flux exceeds the AMANDA-B10 90% CL upper limits. In the case of $p\gamma$ dominance, the flux is consistent with AMANDA-B10 data. In the new scenario the source neutrino flux is considerably enhanced, especially below ${10}^9\mathrm{GeV}$. Should data from AMANDA-II prove consistent with the model, we show that IceCube can measure the characteristic power law of the neutrino spectrum, and thus provide a window on the source dynamics.

Figure 1

The goodness-of-fit test of the low crossover scenario, using the method outlined in Ref. 13. In the left panel we show the 95% CL allowed regions in the $n-\gamma$ plane, obtained with Fly’s Eye & HiRes and Akeno & AGASA data. In the right panel we show the corresponding 68% CL obtained from Fly’s Eye & HiRes data. In the fitting procedure we used data in the energy interval from $E_{-}={10}^{8.6}\mathrm{GeV}$ to $E_{+}={10}^{11}\mathrm{GeV}$, taking $z_{\min }=0.012$ and $z_{\max }=2.$

Figure 2

Best fits to the ultra-high energy cosmic ray spectrum in the energy interval $[E_{-},E_{+}]$ as observed by Akeno & AGASA and Fly’s Eye & HiRes. We set $E_{-}={10}^{8.6}\mathrm{GeV}$, $E_{+}={10}^{11}\mathrm{GeV}$, $z_{\min }=0.012,$ $z_{\max }=2$, and $E_{i,\max }={10}^{12.5}\mathrm{GeV}$.

Figure 3

Neutrino fluxes (summed over all flavors) from optically thin sources for ${ϵ}_{\pi }=0.28$. The horizontal solid line indicates the WB prediction which corresponds to a galactic/extragalactic crossover energy at the ankle, $\sim {10}^{10}\mathrm{GeV}$. The falling solid lines indicate the expected neutrino flux normalized to HiRes (lower) and AGASA (upper) data, if one assumes the onset of dominance by the extragalactic component is at ${10}^{8.6}\mathrm{GeV}$. The dash-dotted lines indicate the fluxes of cosmogenic neutrinos associated with flux predictions given by the falling solid lines. The cross-hatched region excludes an $E^{-2}$ spectrum at the 90% CL by measurements of AMANDA-B10 [50]. The single hatched region, obtained by rescaling the AMANDA integrated bolometric flux limit to an $E^{-2.54}$ power law, is the exclusion region for the low crossover model. The shaded region indicates the cascade limit (see text for details).

Figure 4

Best fit to HiRes data (solid line), assuming dominance of the extragalactic component above $E_{-}={10}^{8.2}\mathrm{GeV}$ (top) and $E_{-}={10}^{8.6}\mathrm{GeV}$ (bottom). Also shown is the associated cosmogenic neutrino flux for all flavors (dashed line).

Figure 5

Upper panel: Differential event rate at IceCube for the different neutrino flux predictions from AGASA (top), HiRes (middle) and WB (bottom) obtained in Sec. 3. Lower panel: Expected bin-by-bin event rates for 10 years of operation. The bin partition interval is taken as $\Delta {log}_{10}E=0.5.$