$Z$-bursts from the Virgo cluster

Resonant annihilation of ultrahigh energy cosmic neutrinos ($\mathrm{UHEC}\nu$) on the cosmic neutrino background ($\mathrm{C}\nu \mathrm{B}$) into $Z$ bosons—the $Z$-burst mechanism—and its associated absorption and emission phenomenology provide a unique, albeit indirect, probe of the $\mathrm{C}\nu \mathrm{B}$ in its present state. In this paper, we examine the implications of gravitational clustering of the $\mathrm{C}\nu \mathrm{B}$ in nearby galaxy clusters for the $Z$-burst phenomenology. In particular, we study the emission features of the $Z$-decay products originating from the Virgo cluster, and the potential of future cosmic ray experiments to observe clustering-enhanced $Z$-burst rates. We find that a detector with an exposure equivalent to three years of observations at the Extreme Universe Space Observatory (EUSO) will very likely measure these enhanced rates together with the associated $\mathrm{UHEC}\nu$ flux, provided that the latter saturates current observational limits and the neutrino masses are quasidegenerate, $m_{{\nu }_i}\gtrsim 0.1\mathrm{eV}$. In the case of $\mathrm{UHEC}\nu$ fluxes below the electromagnetic cascade limit, or a hierarchical neutrino mass spectrum, an experimental sensitivity exceeding that of EUSO by at least 2 orders of magnitude is required to detect the clustering enhancements with any certainty.

Figure 1

Upper limits on the diffuse neutrino flux per flavor $F_{{\nu }_{\alpha }}+F_{{\overline{\nu }}_{\alpha }},\alpha =e,\mu ,\tau$, from RICE [46], GLUE [47], Fly’s Eye+AGASA [48], FORTE [49] and AMANDA (assuming an $E^{-2}$ differential spectrum) [50], assuming full flavor mixing en route to Earth. Also shown are the projected sensitivities of Auger in ${\nu }_e,{\nu }_{\mu }$ modes and in ${\nu }_{\tau }$ mode (bottom swath) [51], ANITA [52], EUSO [53], IceCube [54], and SalSA [55], i.e., one event per energy decade for the indicated duration. A prototype of the full ANITA experiment, ANITA-lite [56], should constrain the ${10}^{19}÷{10}^{22}\mathrm{eV}$ region in the very near future.

Figure 2

Prospects for ultrahigh energy neutrino detection in the next decade (fluxes required to produce one event per energy decade). For the year 2008 (long dashed/red line), we assume three years of Auger data and one 15-day ANITA flight. For 2013 (dash-dot/blue line), we assume 8/3/3/4 yr Auger/EUSO/IceCube/SalSA, and three ANITA flights. These curves are indicative only. The sensitivity will improve if we consider also the Westerbork radio observatory [45], if further projects such as Auger North and OWL [43] are realized, or if the EUSO or ANITA flight times are extended. Also shown are a wide sample of $\mathrm{UHEC}\nu$ flux predictions, the current observational upper bound (solid shade) from Fig. 1, and the electromagnetic cascade limit from EGRET [33, 35]. The points labeled “$Z$-burst” (green) denote the $\mathrm{UHEC}\nu$ fluxes required to explain the post-GZK events observed by AGASA in terms of $Z$-burst secondaries [25].

Figure 3

Relic neutrino number density per mass eigenstate, $n_{{\nu }_i}=n_{{\overline{\nu }}_i}$, as a function of the radial distance from the halo center, for halo virial masses (top to bottom) ${10}^{15},{10}^{14},{10}^{13},{10}^{12}$, in units of $(0.7/h)M_{\odot }$, and neutrino masses indicated in the figure. All curves are normalized to the expected mean density ${\overline{n}}_{{\nu }_i}={\overline{n}}_{{\overline{\nu }}_i}\simeq 56{\mathrm{cm}}^{-3}$.

Figure 4

$Z$-burst nucleon and photon fluxes from the Virgo cluster ($M_{\mathrm{vir}}={10}^{15}{M}_{\odot },D=15\mathrm{Mpc}$) per neutrino species for three URB scenarios (minimal, moderate, and high), assuming the EM cascade limited $\mathrm{UHEC}\nu$ fluxes. Red (solid) lines represent photon fluxes originating from points located at angular distances (top to bottom) $\theta =0°,4°,10°$, and $180°$ (i.e., an unclustered $\mathrm{C}\nu \mathrm{B}$) from galaxy M87. Blue (dashed) lines denote the corresponding nucleon fluxes. The Akeno+AGASA (upper) and Fly’s Eye+HiRes (lower) normalized extragalactic proton fluxes are shown in green (dotted lines).

Figure 5

Energy-integrated $Z$-burst fluxes (nucleons plus photons) above $E_{\mathrm{th}}=2\times {10}^{20}\mathrm{eV}$ as functions of angular distance from the center of Virgo, normalized to their corresponding values at $\theta =0°$. Red (solid), blue (dashed) and green (dotted) lines denote, respectively, the minimal, the moderate and the high URB scenarios.

Figure 6

Number of $Z$-burst events per neutrino species originating within $\theta =10°$ from M87 expected at EUSO in three years, assuming $\mathrm{UHEC}\nu$ fluxes at the current observational limits. Solid red squares denote the photon events, while solid blue triangles refer to the nucleons. The corresponding predictions for an unclustered $\mathrm{C}\nu \mathrm{B}$ in the same solid angle $\Delta \Omega \simeq 0.1$ ster are indicated by the open red squares and open blue triangles. The number of extragalactic background protons anticipated in $\Delta \Omega$, assuming the Akeno+AGASA (upper) and the Fly’s Eye+HiRes (lower) normalizations, are represented by the green crosses.

Figure 7

Same as Fig. 6, but for the EM cascade limited $\mathrm{UHEC}\nu$ fluxes.

Figure 8

Number of $Z$-burst events, for three quasidegenerate neutrinos, originating within $\theta =10°$ from M87 expected at EUSO in three years, assuming the cascade limited UHEC$\nu$ fluxes. Triangles denote the nucleon events, while the squares, pentagons and hexagons refer, respectively, to the photon events for the minimal, moderate and high URB scenarios. The stars indicate the number of events observed by AGASA in the same energy range (${10}^{20}÷{10}^{20.5}\mathrm{eV}$) projected for three years of EUSO observations in the same solid angle.