Ultrahigh-energy neutrino follow-up of Gravitational Wave events
GW150914 and GW151226 with the Pierre Auger Observatory

On September 14, 2015 at 09:50:45 UTC the Advanced LIGO detectors observed the first gravitational-wave transient GW150914 LIGO_GW150914 . The GW was inferred to have arisen from the merger of black holes in a binary system at a luminosity distance $D_{s}=410^{+160}_{-180}$ Mpc. The estimated amount of energy released in the form of gravitational waves was $E_{\rm GW}=3.0^{+0.5}_{-0.5}\leavevmode\nobreak\ M_{\odot}c^{2}$ solar masses LIGO_GW150914 ; LIGO_GW150914_Properties . A second GW event GW151226 LIGO_GW151226 was detected at 03:38:53 UTC on December 26, 2015, also inferred to be produced by the merger of two black holes at a distance $D_{s}=440^{+180}_{-190}$ Mpc. In this case the amount of energy released in the form of GW was $E_{\rm GW}=1.0^{+0.1}_{-0.2}\leavevmode\nobreak\ M_{\odot}c^{2}$ LIGO_GW151226 . A third candidate event, LVT151012, was observed on October 12, 2015 at 09:54:43 UTC. Although LVT151012 is consistent with a binary black-hole merger it is not significant enough to claim an unambiguous detection LIGO_3GW .

The observation of GW events with LIGO has motivated several models on the production of electromagnetic counterparts to GW in binary black-hole mergers Bartos_BH ; Stone_BH . Moreover, observations with the Fermi GBM detector have revealed the presence of a transient source above 50 keV, only 0.4 s after GW150914, with localization consistent with its direction Fermi_GBM_GW and with a possible association with a short gamma-ray burst Meszaros_GW_GRB ; Perna_GW_GRB ; Murase_GW_GRB . On the other hand, other gamma-ray and X-ray observatories did not find any potential counterpart either for GW150914 INTEGRAL_GW ; Fermi_LAT_GW ; XMM_GW ; AGILE_GW or for GW151226 Fermi_LAT_GBM_GW .

Mergers of black holes are a potential environment where cosmic rays can be accelerated to ultrahigh-energies (UHEs) provided there are magnetic fields and disk debris remaining from the formation of the black holes Kotera-Silk ; Murase_GW_GRB . These are two necessary ingredients to accelerate cosmic rays to ultrahigh energies through the Fermi mechanism at astrophysical sources (see for instance Gaisser_review ). The estimated rate of this type of mergers can account for the total energy observed in ultrahigh-energy cosmic rays (UHECRs) and their distribution in the sky Kotera-Silk . The UHE cosmic rays can interact with the surrounding matter or radiation to produce ultrahigh-energy gamma rays and neutrinos Kotera-Silk ; Murase_GW_GRB . Other models speculate on the possibility that protons could be accelerated up to $\sim 10$ EeV energies in a one-shot boost Anchordoqui_GW . Collisions of UHE protons with photon backgrounds and gas surrounding the black hole would produce UHE neutrinos. The remarkable power of GW150914 could produce a proton spectrum peaked at EeV energies with a lesser emission of neutrinos in the PeV energy range Anchordoqui_GW . Neutrino experiments with peak sensitivities in the TeV-PeV energy range such as IceCube and ANTARES have reported no neutrino candidates in spatial and temporal coincidence with GW150914 GW_IceCube_ANTARES .

With the surface detector (SD) of the Pierre Auger Observatory Auger_detector we can identify neutrino-induced air showers in the energy range above 100 PeV combined . Showers induced by neutrinos at large zenith angles can start their development deep in the atmosphere so that they have a considerable amount of electromagnetic component at the ground (“young” shower front). On the other hand, at large zenith angles the atmosphere is thick enough that the electromagnetic component of the more numerous nucleonic cosmic rays, which interact shortly after entering the atmosphere, gets absorbed and the shower front at ground level is dominated by muons (“old” shower front). The SD consists of $1660$ water-Cherenkov stations spread over an area of ${\sim}3000\leavevmode\nobreak\ {\rm km^{2}}$, separated by $1.5\leavevmode\nobreak\ {\rm km}$ and arranged in a triangular grid. Although the SD is not separately sensitive to the muonic and electromagnetic components of the shower, nor to the depth at which the shower is initiated, the signals produced by the passage of shower particles, digitized with 25 ns time resolution Auger_detector , allow us to distinguish narrow traces in time induced by inclined showers initiated high in the atmosphere, from the broad signals expected in inclined showers initiated close to the ground. Applying this simple idea, with the SD of the Pierre Auger Observatory Auger_detector we can efficiently detect inclined showers and search for two types of neutrino-induced showers at energies above 100 PeV:

1. 1.

   Earth-skimming (ES) showers induced by tau neutrinos ($\nu_{\tau}$) that travel in a slightly upward direction. A $\nu_{\tau}\leavevmode\nobreak\$can skim the Earth’s crust and interact near the surface, inducing a tau lepton which escapes the Earth and decays in flight in the atmosphere, close to the SD. Typically, only $\nu_{\tau}\leavevmode\nobreak\$-induced showers with zenith angles $90^{\circ}<\theta<95^{\circ}$ may be identified.

2. 2.

   Showers initiated by neutrinos of any flavor moving down at large zenith angles $75^{\circ}<\theta<90^{\circ}$ with respect to the vertical and that interact in the atmosphere close to the surface-detector array through charged-current or neutral-current interactions. These will be referred to as downward-going high zenith angle (DGH) neutrinos.

In previous publications combined ; DGH ; PRL_nutau ; nu_tau_long methods were established to identify inclined and deeply-initiated showers with the SD of the Pierre Auger Observatory. These were applied blindly to search for ES and DGH neutrinos in the data collected with the SD up to 20 June 2013. No neutrino candidate was found. As a result an upper limit to the diffuse flux of UHE neutrinos (i.e., from an ensemble of unresolved sources) was obtained in combined . Also the same analysis was applied to place upper limits on continuous (in time) point-like sources of UHE neutrinos Auger_PS .

In this paper we use the same identification criteria as in combined to search for neutrinos in temporal and spatial coincidence with GW150914 and GW151226, as well as with the GW candidate event LVT151012 LIGO_3GW . The search was performed within $\pm 500$ s around the time of either GW event as well as in the period of 1 day after their occurrence. The choice of these two rather broad time windows is motivated by the association of mergers of compact systems and gamma-ray bursts (GRBs) Meszaros_GW_GRB ; Perna_GW_GRB ; GRB_review . The $\pm 500$ s window Baret corresponds to an upper limit on the duration of the prompt phase of GRBs, when typically PeV neutrinos are thought to be produced in interactions of accelerated cosmic rays and the gamma rays within the GRB itself. The choice of the 1-day window after the GW event is a conservative upper limit on the duration of GRB afterglows, where ultrahigh-energy neutrinos are thought to be produced in interactions of UHECRs with the lower-energy photons of the GRB afterglow (see GRB_review for a review).

The results of the search allow us to set constraints on the emission of UHE neutrinos from the merger of two black holes. These constraints apply in the energy range [$\sim$ 100 PeV, $\sim$ 25 EeV] and are complementary to those of IceCube/ANTARES GW_IceCube_ANTARES which apply in the energy range [$\sim$ 100 GeV, $\sim$ 100 PeV].

The neutrino identification criteria applied to data collected with the Pierre Auger Observatory are summarized in reference combined . Firstly, inclined showers are selected in the different angular ranges of the ES and DGH channels. Secondly, deeply-penetrating showers are identified in the inclined-event sample through the broad time structure of the signals expected to be induced in the water-Cherenkov SD stations indicative of the presence of an electromagnetic component combined .

The sensitivity to UHE neutrinos in Auger is limited to large zenith angles. As a consequence at each instant in time, neutrinos can be detected efficiently only from a specific portion of the sky. A source at declination $\delta$ and right ascension (RA) $\alpha$ (in equatorial coordinates) is seen at the latitude of Auger ($\lambda=-35.2^{\circ}$) and at a given sidereal time $t$ with a zenith angle $\theta(t)$ given by:

where $T$ is the duration of one sidereal day. From Eq. (1) it is straigthforward to calculate the fraction of a sidereal day a source at declination $\delta$ is visible in the ES angular range $(90^{\circ},\leavevmode\nobreak\ 95^{\circ})$ and in the DGH one $(75^{\circ},\leavevmode\nobreak\ 90^{\circ})$. In Fig. 1 we show two sky maps in equatorial coordinates where the color scale indicates the fraction of a sidereal day during which each declination is seen in the ES (top plot) and DGH (bottom plot) field of view. The positions of GW150914 and GW151226 are not well constrained by data collected with the Advanced LIGO detectors but 90% CL contours are provided and are also shown in Fig. 1. At 90% CL the declination of the source of GW150914 can be between $\delta\sim-1.0^{\circ}$ and $\sim-14.5^{\circ}$ or between $\delta\sim-38.5^{\circ}$ and $\sim-78.0^{\circ}$, and that of GW151226 between $\delta\sim-72.7^{\circ}$ and $\sim 60.9^{\circ}$ as can be seen in Fig. 1. Both 90% CL declination ranges overlap with the field of view of the ES and DGH channels for fractions of one sidereal day that can reach up to $\sim 17\%$ and $\sim 35\%$, respectively. If the emission took less time than a day these numbers could change significantly, depending on the sky position of the GW event relative to Auger during the emission time. The overlapping between the Auger field of view in the inclined directions and the 90% CL contour position of the GW event is larger for GW151226 as seen in Fig. 1 and also for LVT151012.

The results in this work represent the first upper limits on UHE neutrino emission from an identified source of GW - the merger of two black holes - and the first follow-up of GW events with neutrinos of energies above 100 PeV.

The upper limits on fluence emitted in the form of UHE neutrinos are strongly declination-dependent. With the SD of the Pierre Auger Observatory we are sensitive to a large fraction of the declination range in which the sources of GW150914 and GW151226 could be located at the 90% CL as shown in Fig. 1.

While our most stringent upper limit to the total energy in the form of UHE neutrinos for the GW150914 event is $\sim 7.7\times 10^{53}$ erg per flavor at $\delta_{0}=-53^{\circ}$, the IceCube/ANTARES best upper limit $(\nu_{\mu}+\bar{\nu}_{\mu})$ is $\sim 5.4\times 10^{51}$ erg at declinations close to the equator GW_IceCube_ANTARES . However, the IceCube/ANTARES limits apply in the energy range [100 GeV, 100 PeV] while the Auger limits apply in the complementary energy range [100 PeV, 25 EeV].

In Kotera-Silk it was argued that black-hole mergers would have sufficient luminosity to power the acceleration of cosmic rays up to 100 EeV. With a modest efficiency $\lesssim 0.03$ per GW event per unit of gravitational-wave energy release radiated in the form of UHECRs and given the inferred rate of BH mergers LIGO_3GW , a source population of this type could achieve the energy budget needed to explain the observed UHECRs Kotera-Silk . In this work we place a most stringent upper limit on the fraction of GW energy channeled into neutrinos of $\sim 14\%$. If only $3\%$ of the energy of the GW is channeled into UHECRs Kotera-Silk , and the same energy goes into UHE neutrinos, then we would expect at most on the order of $0.5$ events in Auger in coincidence with GW150914.

An upper bound to the diffuse single-flavor neutrino flux integrated over a source population of this type was estimated also in Kotera-Silk ,

depending on the evolution with redshift of the sources and assuming an optical depth $\tau=1$ to neutrino production in the debris surrounding the BH mergers. This upper bound is a factor between $\sim 3$ and 10 above the limit to the diffuse flux of UHE neutrinos obtained with Auger data up to 20 June 2013 in combined , namely,

It is possible that there are no significant fluxes of UHE neutrinos associated with the coalescence of black holes, more phenomenological work in this area is needed. In the case that cosmic rays are indeed accelerated as suggested in Kotera-Silk , our constraints on the diffuse flux of UHE neutrinos would imply that either (1) the optical depth to neutrino production is significantly smaller than 1 as expected in GRB models; or (2) only a fraction of the luminosity that can be extracted from the BH can be invested in UHECRs acceleration, or (3) only a fraction of the energy of the protons goes into charged pions (that are the parents of the neutrinos); or (4) a combination of the three possibilities.

The Advanced LIGO-Virgo detection of GW150914 and GW151226 represents a breakthrough in our understanding of the Universe. Similar analyses to those presented in this work will be important to provide constraints on the progenitors of the GW emission. Given the inferred rate of events $9-240\leavevmode\nobreak\ {\rm Gpc^{-3}yr^{-1}}$ LIGO_3GW new GW events can be expected in the near future, closer to Earth and/or more energetic, and/or produced by another type of source that is more likely to accelerate UHECRs and produce UHE neutrinos than the merger of two black holes, such as for instance binary neutron-star mergers, and core-collapse supernovae with rapidly-rotating cores NS_GW ; GW_review .

Finally, the detection of UHE neutrino candidates in Auger in coincidence with GW events could help in pinpointing the position of the source of GW with an accuracy that depends on the shower zenith angle and energy, ranging from less than $\sim 1\leavevmode\nobreak\ {\rm deg}^{2}$ to order $10\leavevmode\nobreak\ {\rm deg}^{2}$ in the least favourable cases. This is to be compared with the currently known position of the two GW events, namely a few $100\leavevmode\nobreak\ {\rm deg}^{2}$. Observations with Auger can significantly constrain the position of the source and help the follow-up of the GW events with optical and other observatories of electromagnetic radiation. This is an example where multimessenger observations (GW, neutrinos and photons) can reveal properties of the sources which may not be discerned from one type of signal alone.

The successful installation, commissioning, and operation of the Pierre Auger Observatory would not have been possible without the strong commitment and effort from the technical and administrative staff in Malargüe. We are very grateful to the following agencies and organizations for financial support:

Comisión Nacional de Energía Atómica, Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Gobierno de la Provincia de Mendoza, Municipalidad de Malargüe, NDM Holdings and Valle Las Leñas, in gratitude for their continuing cooperation over land access, Argentina; the Australian Research Council; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (FINEP), Fundação de Amparo à Pesquisa do Estado de Rio de Janeiro (FAPERJ), São Paulo Research Foundation (FAPESP) Grants No. 2010/07359-6 and No. 1999/05404-3, Ministério de Ciência e Tecnologia (MCT), Brazil; Grant No. MSMT CR LG15014, LO1305 and LM2015038 and the Czech Science Foundation Grant No. 14-17501S, Czech Republic; Centre de Calcul IN2P3/CNRS, Centre National de la Recherche Scientifique (CNRS), Conseil Régional Ile-de-France, Département Physique Nucléaire et Corpusculaire (PNC-IN2P3/CNRS), Département Sciences de l’Univers (SDU-INSU/CNRS), Institut Lagrange de Paris (ILP) Grant No. LABEX ANR-10-LABX-63, within the Investissements d’Avenir Programme Grant No. ANR-11-IDEX-0004-02, France; Bundesministerium für Bildung und Forschung (BMBF), Deutsche Forschungsgemeinschaft (DFG), Finanzministerium Baden-Württemberg, Helmholtz Alliance for Astroparticle Physics (HAP), Helmholtz-Gemeinschaft Deutscher Forschungszentren (HGF), Ministerium für Wissenschaft und Forschung, Nordrhein Westfalen, Ministerium für Wissenschaft, Forschung und Kunst, Baden-Württemberg, Germany; Istituto Nazionale di Fisica Nucleare (INFN),Istituto Nazionale di Astrofisica (INAF), Ministero dell’Istruzione, dell’Universitá e della Ricerca (MIUR), Gran Sasso Center for Astroparticle Physics (CFA), CETEMPS Center of Excellence, Ministero degli Affari Esteri (MAE), Italy; Consejo Nacional de Ciencia y Tecnología (CONACYT) No. 167733, Mexico; Universidad Nacional Autónoma de México (UNAM), PAPIIT DGAPA-UNAM, Mexico; Ministerie van Onderwijs, Cultuur en Wetenschap, Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Stichting voor Fundamenteel Onderzoek der Materie (FOM), Netherlands; National Centre for Research and Development, Grants No. ERA-NET-ASPERA/01/11 and No. ERA-NET-ASPERA/02/11, National Science Centre, Grants No. 2013/08/M/ST9/00322, No. 2013/08/M/ST9/00728 and No. HARMONIA 5 – 2013/10/M/ST9/00062, Poland; Portuguese national funds and FEDER funds within Programa Operacional Factores de Competitividade through Fundação para a Ciência e a Tecnologia (COMPETE), Portugal; Romanian Authority for Scientific Research ANCS, CNDI-UEFISCDI partnership projects Grants No. 20/2012 and No.194/2012 and PN 16 42 01 02; Slovenian Research Agency, Slovenia; Comunidad de Madrid, Fondo Europeo de Desarrollo Regional (FEDER) funds, Ministerio de Economía y Competitividad, Xunta de Galicia, European Community 7th Framework Program, Grant No. FP7-PEOPLE-2012-IEF-328826, Spain; Science and Technology Facilities Council, United Kingdom; Department of Energy, Contracts No. DE-AC02-07CH11359, No. DE-FR02-04ER41300, No. DE-FG02-99ER41107 and No. DE-SC0011689, National Science Foundation, Grant No. 0450696, The Grainger Foundation, USA; NAFOSTED, Vietnam; Marie Curie-IRSES/EPLANET, European Particle Physics Latin American Network, European Union 7th Framework Program, Grant No. PIRSES-2009-GA-246806; and UNESCO.