- Email: [email protected]
The Search for Ultra-High Energy Neutrinos at the Pierre Auger Observatory
Available online at www.sciencedirect.com
Nuclear Physics B (Proc. Suppl.) 237–238 (2013) 236–238 www.elsevier.com/locate/npbps
The Search for Ultra-High Energy Neutrinos at the Pierre Auger Observatory S. Navas1 Dpto. de F´ısica Te´orica y del Cosmos & C.A.F.P.E., Universidad de Granada, 18071 Granada, Spain
for the Pierre Auger Collaboration2 Av. San Mart´ın Norte 304 (5613) Malarg¨ue, Prov. de Mendoza, Argentina
Abstract The Pierre Auger Observatory is the largest cosmic ray observatory ever built. Even though designed and optimized to investigate the origin and nature of ultra-high energy cosmic rays, the Observatory is well suited also to search for ultra-high energy neutrinos (UHEνs). Neutrinos of extraterrestrial origin can interact in the atmosphere (downwardgoing ν) or in the Earth’s crust (Earth-skimming ν), producing air showers that can be observed with the Surface Detector Array. The distinguishing signature for neutrino events is the presence of inclined showers produced close to the ground. In this paper we review the procedure established to search for UHEνs and report the results obtained after analyzing the data collected by the Pierre Auger Observatory. Moreover, the sensitivity to point-like sources of neutrinos is presented as a function of the source declination. The result shows that with the Surface Detector Array we are sensitive to a large fraction of the sky spanning ∼ 100◦ in declination. Keywords: astroparticle physics, cosmic rays, neutrinos, telescopes
1. Introduction After a hundred years since the discovery of cosmic rays, the identification of the nature and production mechanisms of ultra-high energy cosmic rays (UHECRs), with energies above 1018 eV, are still a challenge. The Pierre Auger Observatory [1] was built by an international collaboration to study the properties of such UHECRs with high performances and unprecedented statistics. Due to its capability of investigating different aspects of the extensive air showers (EAS) produced by UHECRs as they enter the atmosphere, many of the open questions in cosmic ray physics can nowadays be addressed by the Pierre Auger Observatory [2]. The observation of UHECRs makes an associated flux of ultra-high energy cosmic neutrinos (UHEνs) [3]
1 Email
address: [email protected] http://www.auger.org/archive/authors 2012 11.html
2 Full author list:
0920-5632/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nuclphysbps.2013.04.096
very likely. All models of UHECR production predict neutrinos as a result of the decay of charged pions generated in interactions of cosmic rays within the sources themselves (“astrophysical” neutrinos), and/or in their propagation through background radiation fields (“cosmogenic” neutrinos). Also, charged pions, which are photoproduced by UHECR protons interacting with the Cosmic Microwave Background radiation, decay into UHEνs. However, the predicted flux has large uncertainties, since it depends on the UHECR spectrum and on the spatial distribution and cosmological evolution of the sources [3, 4, 5]. The observation of UHE neutrinos would open a new window to the Universe since they travel unaffected by magnetic fields and can give information on astrophysical regions that are otherwise hidden from observation by large amounts of matter. The Pierre Auger Observatory [1] – located in the province of Mendoza, Argentina, at a mean altitude of 1400 m above sea level (∼875 g cm−2 ) – was designed to
S. Navas / Nuclear Physics B (Proc. Suppl.) 237–238 (2013) 236–238
measure EAS induced by UHECRs. The Fluorescence Detector of the Observatory [6] comprises a set of imaging telescopes to measure the light emitted by excited atmospheric nitrogen molecules as the EAS develops. A Surface Detector Array (SD) measures EAS particles at ground with an array of water-Cherenkov detectors (“stations”). Each SD station contains 12 tonnes of water viewed by three 9” photomultipliers. Arranged on a triangular grid with 1.5 km spacing, 1660 SD stations are deployed over an area of ∼ 3000 km2 which is overlooked by 27 fluorescence telescopes. Although the primary goal of the SD is to detect UHECRs, it can also identify ultra-high energy neutrinos. Neutrinos of all flavours can interact at any atmospheric depth through charged or neutral currents and induce a “downward-going” (DG) shower. In addition, tau neutrinos can undergo charged current interactions in the Earth’s crust and produce a tau lepton which, after emerging from the Earth’s surface and decaying in the atmosphere, will induce an “Earth-skimming” (ES) upward-going shower. Neutrino candidate events must be identified against the much higher background of showers initiated by standard UHECRs (protons or other nuclei). 2. The search for UHE neutrinos Highly inclined ES and DG neutrino-induced showers initiated close to observation level will present a significant electromagnetic component at the ground (“young” showers), producing signals spread over hundreds of nanoseconds in the triggered SD stations. Inclined showers initiated by standard UHECRs are, by contrast, dominated by muons at ground level (“old” showers), with signals typically spread over only tens of nanoseconds. This is the key to separate neutrino candidates from nuclear background. Candidates for UHEνs are searched for in inclined showers in the ranges 75◦ < θ < 90◦ and 90◦ < θ < 96◦ for the DG and ES analyses, respectively. Thanks to the fast sampling (25 ns) of the SD digital electronics, several observables sensitive to the signal time structure can be used to discriminate between young and old showers, allowing for detection of UHEνs. Two sets of conditions constituting the ES and DG neutrino identification criteria have been designed and optimized to select showers induced by UHE neutrinos, rejecting those induced by UHECRs. A fraction of the data (“training” period) is dedicated to define and optimize the selection algorithm. The remaining fraction (“search” sample) is not used until the selection procedure is established, and then it is “unblinded” to search
237
for neutrino candidates. The search sample reported here in the ES (DG) mode corresponds to 3.5 yr (2 yr) of a full Auger SD working without interruption. The observables used to select highly inclined showers are associated with the pattern (footprint) of triggered stations at ground (from which we can extract a length L along the arrival direction of the event and a width W perpendicular to it characterizing the shape of the footprint [7]) and with the apparent speed of the trigger from a station i to a station j, averaged over all pairs (i, j) of stations in the event. Very inclined events typically have large values of L/W and apparent speeds concentrated around the speed of light. The selection of young showers is done by requiring a significant contribution from the electromagnetic component in some stations in the event. In the ES mode, a given percentage of the stations in the event is required to pass the time over threshold (ToT) local trigger condition. In the DG mode, the selection is optimized with a Fisher discriminant method which uses the so-called Area-over-Peak (ratio of the integrated signal over the peak height) signals of the first four (time-ordered) stations [8]. In practice, the cut in the Fisher value is fixed so that the estimated number of background events is 1 in 20 yr of data taking by a full Auger SD. In general, the neutrino identification efficiencies depend on many parameters like the energy of the primary neutrino (DG) or tau lepton (ES), the neutrino flavour and type of interaction (DG), the depth in the atmosphere of the ν interaction (DG) or the altitude above ground of the tau decay point (ES). The efficiencies are estimated through MC simulations of the first neutrino interaction and the development of the shower in the atmosphere, and from the response of the SD. The calculation of the exposures for the ES and DG channels (described with detail in [7] and [8], respectively) involves folding the SD array aperture with the ν interaction probability and the identification efficiency, and integrating in time. The dominant sources of systematic uncertainties for DG neutrinos come from [8] the hadronic models and the neutrino-induced shower simulations (+9%, −33%), and from the neutrino interaction cross-section (±7%). For the ES channel, they are dominated by the tau energy losses (+25%, −10%), the shower simulations (+20%, −5%) and the topography (+18%, 0%) [7]. 3. Results A blind scan over the search data period until 31 May 2010 reveals no neutrino candidates [8, 11]. Assuming a differential spectrum Φ(Eν ) = dNν /dEν = k · Eν−2
238
S. Navas / Nuclear Physics B (Proc. Suppl.) 237–238 (2013) 236–238
for the diffuse flux of UHEνs and zero background, we place a 90% C.L. upper limit on the integral single flavor neutrino flux of k < 3.2 × 10−8 GeV cm−2 s−1 sr−1 based on ES neutrinos and k < 1.7 × 10−7 GeV cm−2 s−1 sr−1 based on DG neutrinos. These limits, shown as two horizontal lines in Figure 1, are valid in the energy ranges 1.6 × 1017 eV ≤ Eν ≤ 2.0 × 1019 eV (ES) and 1 × 1017 eV ≤ Eν ≤ 1 × 1020 eV (DG), where ≈ 90% of neutrino events would be detected for a Eν−2 flux . Also shown are the 90% C.L. upper limits in differential form, where the limits are calculated independently in each energy bin of width 0.5 in log10 Eν . Notice that the maximum sensitivity of the Pierre Auger Observatory, obtained for Eν ∼ 1018 eV, matches well the peak of the expected neutrino flux.
Assuming a differential flux F(Eν ) = kPS (δ) · Eν−2 , and a 1:1:1 neutrino flavour ratio, the 90% C.L. upper limits on kPS derived from the ES and DG modes are shown in Figure 2 as a function of source declination. The sensitivity has a broad plateau spanning Δδ ∼ 100◦ in declination and two peaks where limits at the level of ≈ 5 × 10−7 (ES) and 2.5 × 10−6 GeV cm−2 s−1 (DG) are obtained. The shape of the declination-dependent upper limits is largely determined by the fraction of time a source is within the field of view of the ES or DG analyses, and, to a lesser extent, by the zenith angle dependence of the exposure. These are the best limits around 1 EeV. Single flavour neutrino limits (90% CL) Auger downward-going
10-5 [GeV cm-2 s-1] kPS = E2ν F(Eν)
10-6 10-7 10-8
k = Eν2 Φ(Eν)
[ GeV cm-2 s-1 sr -1 ]
Auger Earth-skimming
Single flavour neutrino limits (90% CL)
10-5
10-6
10-7
10-9
10-10 10-11
-80 ν limits Auger downward-going 2011 Auger Earth-skimming this work IceCube 2011a Anita 2009
1017
1018
-60
-40 -20 0 20 40 Source declination δ [deg]
60
80
Cosmogenic models Ahlers 2010 Kotera 2010
1019
1020
1021
Eν [eV]
Figure 1: Differential and integrated upper limits at 90% C.L. on the single flavour E−2 ν neutrino flux from the search for DG and ES neutrinos at the Pierre Auger Observatory (search data period until 31 May 2010). Limits from the IceCube Neutrino Observatory [9] and from the ANITA experiment [10] are also shown, as well as predictions for cosmogenic neutrinos under different assumptions [4, 5].
It is also possible to place a limit on the UHEν flux from a source at declination δ. The sensitivity to neutrinos originated at a given point source is a function of the local sidereal time. At each instant, neutrinos can be detected only from a specific portion of the sky corresponding to the zenith angle ranges covered by the ES and DG channels. The SD of the Pierre Auger Observatory is sensitive to point-like sources of neutrinos over a broad declination range spanning north of δ ∼ −65◦ and south of δ ∼ 55◦ . The regions of the sky close to the Northern (δ = 90◦ ) and Southern (δ = −90◦ ) Terrestrial Poles are not accessible by this analysis. As an example, Centaurus A (δ ∼ −43◦ ) is observed ∼ 7% (∼ 15%) of one sidereal day in the range of zenith angles corresponding to the ES (DG) search.
Figure 2: Upper limits at 90% C.L. on a single flavour Eν−2 flux from a specific point-like source as a function of the source declination [11]. The bounds from the Earth-skimming and downward-going neutrino analyses hold for a neutrino energy range 1017 − 1020 eV.
4. Acknowledgements The author thanks the organizers of the conference for the opportunity to present recent results on behalf of the Pierre Auger Collaboration, and acknowledges support from Spanish Ministerio de Ciencia e Innovaci´on grants FPA2009-07187 and AIC-B-2011-0700. References [1] The Pierre Auger Collab., Nucl. Instr. and Meth. A 523, 2004 50. [2] The Pierre Auger Collab., 2011, Proc. 32nd ICRC, Beijing, China. arXiv:1107.4809, arXiv:1107.4804 and arXiv:1107.4805. [3] J.K. Becker, Phys. Rep. 458, 2008 173. [4] M. Ahlers et al., Astropart. Phys. 34, 2010 106. [5] K. Kotera et al., JCAP 10, 2010 013. [6] The Pierre Auger Collab., Nucl. Instr. Meth. A 620, 2010 227. [7] The Pierre Auger Collab., Phys. Rev. D 79, 2009 102001. [8] The Pierre Auger Collab., Phys. Rev. D 84, 2011 122005. [9] The IceCube Collab., Phys. Rev. D 83, 2011 092003. [10] The ANITA Collab., Phys. Rev. D 82, 2010 022004. Erratum arXiv:1011.5004v1 [astro-ph]. [11] The Pierre Auger Collab., Astrophys. J. Lett. 755, 2012 L4.
Nuclear Physics B (Proc. Suppl.) 237–238 (2013) 236–238 www.elsevier.com/locate/npbps
The Search for Ultra-High Energy Neutrinos at the Pierre Auger Observatory S. Navas1 Dpto. de F´ısica Te´orica y del Cosmos & C.A.F.P.E., Universidad de Granada, 18071 Granada, Spain
for the Pierre Auger Collaboration2 Av. San Mart´ın Norte 304 (5613) Malarg¨ue, Prov. de Mendoza, Argentina
Abstract The Pierre Auger Observatory is the largest cosmic ray observatory ever built. Even though designed and optimized to investigate the origin and nature of ultra-high energy cosmic rays, the Observatory is well suited also to search for ultra-high energy neutrinos (UHEνs). Neutrinos of extraterrestrial origin can interact in the atmosphere (downwardgoing ν) or in the Earth’s crust (Earth-skimming ν), producing air showers that can be observed with the Surface Detector Array. The distinguishing signature for neutrino events is the presence of inclined showers produced close to the ground. In this paper we review the procedure established to search for UHEνs and report the results obtained after analyzing the data collected by the Pierre Auger Observatory. Moreover, the sensitivity to point-like sources of neutrinos is presented as a function of the source declination. The result shows that with the Surface Detector Array we are sensitive to a large fraction of the sky spanning ∼ 100◦ in declination. Keywords: astroparticle physics, cosmic rays, neutrinos, telescopes
1. Introduction After a hundred years since the discovery of cosmic rays, the identification of the nature and production mechanisms of ultra-high energy cosmic rays (UHECRs), with energies above 1018 eV, are still a challenge. The Pierre Auger Observatory [1] was built by an international collaboration to study the properties of such UHECRs with high performances and unprecedented statistics. Due to its capability of investigating different aspects of the extensive air showers (EAS) produced by UHECRs as they enter the atmosphere, many of the open questions in cosmic ray physics can nowadays be addressed by the Pierre Auger Observatory [2]. The observation of UHECRs makes an associated flux of ultra-high energy cosmic neutrinos (UHEνs) [3]
1 Email
address: [email protected] http://www.auger.org/archive/authors 2012 11.html
2 Full author list:
0920-5632/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nuclphysbps.2013.04.096
very likely. All models of UHECR production predict neutrinos as a result of the decay of charged pions generated in interactions of cosmic rays within the sources themselves (“astrophysical” neutrinos), and/or in their propagation through background radiation fields (“cosmogenic” neutrinos). Also, charged pions, which are photoproduced by UHECR protons interacting with the Cosmic Microwave Background radiation, decay into UHEνs. However, the predicted flux has large uncertainties, since it depends on the UHECR spectrum and on the spatial distribution and cosmological evolution of the sources [3, 4, 5]. The observation of UHE neutrinos would open a new window to the Universe since they travel unaffected by magnetic fields and can give information on astrophysical regions that are otherwise hidden from observation by large amounts of matter. The Pierre Auger Observatory [1] – located in the province of Mendoza, Argentina, at a mean altitude of 1400 m above sea level (∼875 g cm−2 ) – was designed to
S. Navas / Nuclear Physics B (Proc. Suppl.) 237–238 (2013) 236–238
measure EAS induced by UHECRs. The Fluorescence Detector of the Observatory [6] comprises a set of imaging telescopes to measure the light emitted by excited atmospheric nitrogen molecules as the EAS develops. A Surface Detector Array (SD) measures EAS particles at ground with an array of water-Cherenkov detectors (“stations”). Each SD station contains 12 tonnes of water viewed by three 9” photomultipliers. Arranged on a triangular grid with 1.5 km spacing, 1660 SD stations are deployed over an area of ∼ 3000 km2 which is overlooked by 27 fluorescence telescopes. Although the primary goal of the SD is to detect UHECRs, it can also identify ultra-high energy neutrinos. Neutrinos of all flavours can interact at any atmospheric depth through charged or neutral currents and induce a “downward-going” (DG) shower. In addition, tau neutrinos can undergo charged current interactions in the Earth’s crust and produce a tau lepton which, after emerging from the Earth’s surface and decaying in the atmosphere, will induce an “Earth-skimming” (ES) upward-going shower. Neutrino candidate events must be identified against the much higher background of showers initiated by standard UHECRs (protons or other nuclei). 2. The search for UHE neutrinos Highly inclined ES and DG neutrino-induced showers initiated close to observation level will present a significant electromagnetic component at the ground (“young” showers), producing signals spread over hundreds of nanoseconds in the triggered SD stations. Inclined showers initiated by standard UHECRs are, by contrast, dominated by muons at ground level (“old” showers), with signals typically spread over only tens of nanoseconds. This is the key to separate neutrino candidates from nuclear background. Candidates for UHEνs are searched for in inclined showers in the ranges 75◦ < θ < 90◦ and 90◦ < θ < 96◦ for the DG and ES analyses, respectively. Thanks to the fast sampling (25 ns) of the SD digital electronics, several observables sensitive to the signal time structure can be used to discriminate between young and old showers, allowing for detection of UHEνs. Two sets of conditions constituting the ES and DG neutrino identification criteria have been designed and optimized to select showers induced by UHE neutrinos, rejecting those induced by UHECRs. A fraction of the data (“training” period) is dedicated to define and optimize the selection algorithm. The remaining fraction (“search” sample) is not used until the selection procedure is established, and then it is “unblinded” to search
237
for neutrino candidates. The search sample reported here in the ES (DG) mode corresponds to 3.5 yr (2 yr) of a full Auger SD working without interruption. The observables used to select highly inclined showers are associated with the pattern (footprint) of triggered stations at ground (from which we can extract a length L along the arrival direction of the event and a width W perpendicular to it characterizing the shape of the footprint [7]) and with the apparent speed of the trigger from a station i to a station j, averaged over all pairs (i, j) of stations in the event. Very inclined events typically have large values of L/W and apparent speeds concentrated around the speed of light. The selection of young showers is done by requiring a significant contribution from the electromagnetic component in some stations in the event. In the ES mode, a given percentage of the stations in the event is required to pass the time over threshold (ToT) local trigger condition. In the DG mode, the selection is optimized with a Fisher discriminant method which uses the so-called Area-over-Peak (ratio of the integrated signal over the peak height) signals of the first four (time-ordered) stations [8]. In practice, the cut in the Fisher value is fixed so that the estimated number of background events is 1 in 20 yr of data taking by a full Auger SD. In general, the neutrino identification efficiencies depend on many parameters like the energy of the primary neutrino (DG) or tau lepton (ES), the neutrino flavour and type of interaction (DG), the depth in the atmosphere of the ν interaction (DG) or the altitude above ground of the tau decay point (ES). The efficiencies are estimated through MC simulations of the first neutrino interaction and the development of the shower in the atmosphere, and from the response of the SD. The calculation of the exposures for the ES and DG channels (described with detail in [7] and [8], respectively) involves folding the SD array aperture with the ν interaction probability and the identification efficiency, and integrating in time. The dominant sources of systematic uncertainties for DG neutrinos come from [8] the hadronic models and the neutrino-induced shower simulations (+9%, −33%), and from the neutrino interaction cross-section (±7%). For the ES channel, they are dominated by the tau energy losses (+25%, −10%), the shower simulations (+20%, −5%) and the topography (+18%, 0%) [7]. 3. Results A blind scan over the search data period until 31 May 2010 reveals no neutrino candidates [8, 11]. Assuming a differential spectrum Φ(Eν ) = dNν /dEν = k · Eν−2
238
S. Navas / Nuclear Physics B (Proc. Suppl.) 237–238 (2013) 236–238
for the diffuse flux of UHEνs and zero background, we place a 90% C.L. upper limit on the integral single flavor neutrino flux of k < 3.2 × 10−8 GeV cm−2 s−1 sr−1 based on ES neutrinos and k < 1.7 × 10−7 GeV cm−2 s−1 sr−1 based on DG neutrinos. These limits, shown as two horizontal lines in Figure 1, are valid in the energy ranges 1.6 × 1017 eV ≤ Eν ≤ 2.0 × 1019 eV (ES) and 1 × 1017 eV ≤ Eν ≤ 1 × 1020 eV (DG), where ≈ 90% of neutrino events would be detected for a Eν−2 flux . Also shown are the 90% C.L. upper limits in differential form, where the limits are calculated independently in each energy bin of width 0.5 in log10 Eν . Notice that the maximum sensitivity of the Pierre Auger Observatory, obtained for Eν ∼ 1018 eV, matches well the peak of the expected neutrino flux.
Assuming a differential flux F(Eν ) = kPS (δ) · Eν−2 , and a 1:1:1 neutrino flavour ratio, the 90% C.L. upper limits on kPS derived from the ES and DG modes are shown in Figure 2 as a function of source declination. The sensitivity has a broad plateau spanning Δδ ∼ 100◦ in declination and two peaks where limits at the level of ≈ 5 × 10−7 (ES) and 2.5 × 10−6 GeV cm−2 s−1 (DG) are obtained. The shape of the declination-dependent upper limits is largely determined by the fraction of time a source is within the field of view of the ES or DG analyses, and, to a lesser extent, by the zenith angle dependence of the exposure. These are the best limits around 1 EeV. Single flavour neutrino limits (90% CL) Auger downward-going
10-5 [GeV cm-2 s-1] kPS = E2ν F(Eν)
10-6 10-7 10-8
k = Eν2 Φ(Eν)
[ GeV cm-2 s-1 sr -1 ]
Auger Earth-skimming
Single flavour neutrino limits (90% CL)
10-5
10-6
10-7
10-9
10-10 10-11
-80 ν limits Auger downward-going 2011 Auger Earth-skimming this work IceCube 2011a Anita 2009
1017
1018
-60
-40 -20 0 20 40 Source declination δ [deg]
60
80
Cosmogenic models Ahlers 2010 Kotera 2010
1019
1020
1021
Eν [eV]
Figure 1: Differential and integrated upper limits at 90% C.L. on the single flavour E−2 ν neutrino flux from the search for DG and ES neutrinos at the Pierre Auger Observatory (search data period until 31 May 2010). Limits from the IceCube Neutrino Observatory [9] and from the ANITA experiment [10] are also shown, as well as predictions for cosmogenic neutrinos under different assumptions [4, 5].
It is also possible to place a limit on the UHEν flux from a source at declination δ. The sensitivity to neutrinos originated at a given point source is a function of the local sidereal time. At each instant, neutrinos can be detected only from a specific portion of the sky corresponding to the zenith angle ranges covered by the ES and DG channels. The SD of the Pierre Auger Observatory is sensitive to point-like sources of neutrinos over a broad declination range spanning north of δ ∼ −65◦ and south of δ ∼ 55◦ . The regions of the sky close to the Northern (δ = 90◦ ) and Southern (δ = −90◦ ) Terrestrial Poles are not accessible by this analysis. As an example, Centaurus A (δ ∼ −43◦ ) is observed ∼ 7% (∼ 15%) of one sidereal day in the range of zenith angles corresponding to the ES (DG) search.
Figure 2: Upper limits at 90% C.L. on a single flavour Eν−2 flux from a specific point-like source as a function of the source declination [11]. The bounds from the Earth-skimming and downward-going neutrino analyses hold for a neutrino energy range 1017 − 1020 eV.
4. Acknowledgements The author thanks the organizers of the conference for the opportunity to present recent results on behalf of the Pierre Auger Collaboration, and acknowledges support from Spanish Ministerio de Ciencia e Innovaci´on grants FPA2009-07187 and AIC-B-2011-0700. References [1] The Pierre Auger Collab., Nucl. Instr. and Meth. A 523, 2004 50. [2] The Pierre Auger Collab., 2011, Proc. 32nd ICRC, Beijing, China. arXiv:1107.4809, arXiv:1107.4804 and arXiv:1107.4805. [3] J.K. Becker, Phys. Rep. 458, 2008 173. [4] M. Ahlers et al., Astropart. Phys. 34, 2010 106. [5] K. Kotera et al., JCAP 10, 2010 013. [6] The Pierre Auger Collab., Nucl. Instr. Meth. A 620, 2010 227. [7] The Pierre Auger Collab., Phys. Rev. D 79, 2009 102001. [8] The Pierre Auger Collab., Phys. Rev. D 84, 2011 122005. [9] The IceCube Collab., Phys. Rev. D 83, 2011 092003. [10] The ANITA Collab., Phys. Rev. D 82, 2010 022004. Erratum arXiv:1011.5004v1 [astro-ph]. [11] The Pierre Auger Collab., Astrophys. J. Lett. 755, 2012 L4.