High Energy Neutrinos from the Gravitational Wave event GW150914 possibly associated with a short Gamma-Ray Burst
High-energy neutrino (HEN) and gravitational wave (GW) can probe astrophysical sources in addition to electromagnetic observations. Multimessenger studies can reveal nature of the sources which may not be discerned from one type of signal alone. We discuss HEN emission in connection with the Advanced Laser Interferometer Gravitational-wave Observatory (ALIGO) event GW150914 which could be associated with a short gamma-ray burst (GRB) detected by the Fermi Gamma-ray Burst Monitor (GBM) 0.4 s after the GW event and within localization uncertainty of the GW event. We calculate HEN flux from this short GRB, GW150914-GBM, and show that non-detection of a high-energy starting event (HESE) by the IceCube Neutrino Observatory can constrain the total isotropic-equivalent jet energy of this short burst to be less than erg.
pacs:95.85.Ry, 98.70.Sa, 14.60.Pq
The detection of GW150914 on September 14, 2015 at 09:50:45 UTC is a watershed event Abbott:2016blz (). A sweeping up of the GW frequency and subsequent ringdown heralded formation of a black hole from a binary merger in a split second. GW has long been hypothesized as a cosmic messenger and detection of GW150914 has opened a new window to the universe. A few years earlier the IceCube Neutrino Observatory detected cosmic high-energy neutrinos for the first time Aartsen:2013bka () and ushered an era of multimessenger astronomy.
Binary mergers of neutron stars (NSs) or black hole (BH) and NS systems have been proposed to be the progenitors of short GRBs Eichler:1989ve (); Narayan:1992iy (). Since GW is naturally produced in binary mergers, it has been predicted to be coincident with the short GRBs Eichler:1989ve (); Kobayashi:2002by (); Rezzolla:2011da (). Detection of a short GRB of duration 1 s, GW150914-GBM within 0.4 s and from within square degree arrival direction uncertainty of the GW150914 by the Fermi-GBM Connaughton:2016umz () is therefore very intriguing. GW150914-GBM could not be characterized very well due to large uncertainty in the Fermi-GBM position, (RA, Dec) = (, ) with a uncertainty region over 9000 square degrees in the standard 50-300 keV analysis; (RA, Dec) = (, ) with a uncertainty region about 3000 square degrees for 100-1000 keV analysis. GW150914-GBM was outside of the field of view of the Fermi Large Area Telescope (LAT) initially and no GeV afterglow was detected when it could observe Fermi-LAT:2016qqr (). A joint LIGO-Fermi analysis reduces the confidence region for GW150914 to 199 square degrees and located in the Southern hemisphere (see, Fig. 8 bottom right panel in Ref. Connaughton:2016umz ()). The INTEGRAL/SPI-ACS also observed the GW150914 localization region in hard X-ray without detection Savchenko:2016kiv ().
The isotropic-equivalent luminosity of GW150914-GBM in the 1 keV to 10 MeV energy range was erg/s Connaughton:2016umz () using a Mpc distance inferred from the GW150914 event Abbott:2016blz (). The true luminosity and hence the true energy radiated, depending on the GRB jet opening angle, is much lower. As for comparison, the total energy radiated in GW was erg Abbott:2016blz ().
A binary merger of two BHs, as proposed for the origin of the GW150914 event Abbott:2016blz (), is traditionally thought to produce no electromagnetic counterpart due to a lack of accretion material. Detection of GW150914-GBM Connaughton:2016umz (), however, have raised the possibility that the binary BH systems may also possess some accretion material. In a recent work, the authors of Ref. Perna:2016jqh () modeled that one of the BHs of the binary system could possess a long-lived dormant accretion disk created from the explosion of its low-metallicity progenitor star. This disk is fully revived only during the final merger of the BHs and is accreted rapidly to power a short GRB. In the particular case of GW150914, an accretion disk of mass around a BH may exist Perna:2016jqh (), which is sufficient to power GW150914-GBM with a significant baryon load in its jet.
High energy neutrinos can be produced in the GRB jet from interactions of shock-accelerated protons with the observed rays Waxman:1997ti (); Dermer:2003zv (); Razzaque:2003uw (); Guetta:2003wi (); Murase:2005hy (); Moharana:2011hh (); Hummer:2011ms (). Detection of HEN from GW150914-GBM could potentially measure the total jet power and yet uncertain jet bulk Lorentz factor for the short GRBs. The ANTARES and IceCube Neutrino Observatories have searched for HEN in coincidence with the GW150914 but no detection has been reported Adrian-Martinez:2016xgn ().
In this work we calculate the HEN flux using the short GRB characteristics of GW150914-GBM and estimate the corresponding number of HESE events at the IceCube detector. Using the fact that no HEN event was detected, we put constraints on the power and bulk Lorentz factor of the short GRB jet.
Ii Neutrino flux and HESE
We calculate the HEN flux from the short GRB (duration s) detected by the Fermi GBM Connaughton:2016umz () in-coincidence with the GW event. The isotropic-equivalent electromagnetic luminosity of the short burst is erg/s Connaughton:2016umz (). We assume protons, accelerated in the internal shocks, interact with these photons () to produce neutrinos Waxman:1997ti () and calculate their flux following Refs. Gupta:2006jm (); Moharana:2011hh ().
The target photon density for interactions can be written in terms of a broken power-law with indices , and break energy in the GRB jet frame as
The normalization constant is given by,
where is the internal energy density in photons with flux , luminosity distance , jet radius and bulk Lorentz factor . The efficiency for pion production, with a fractional energy transfer from a proton to a pion from interaction can be written, using Eq. (2), as
Here the prefactor is given by
where erg/s, and s is the flux variability time. The factor is the average fraction of energy lost to the pions. The proton break energy in Eq. (3), corresponding to the photon break energy in Eq. (2), is GeV. The pion production efficiency in Eq. (3) is restricted as . Note that the jet radius at which emission takes place is .
We calculate the neutrino flux in this -resonance channel for a proton spectrum. The HEN flux for one neutrino flavor from the pion decay () or muon decay () is given by
where is the energy in protons, is a normalization factor since is the bolometric luminosity in the 1 keV to 10 MeV range Gupta:2006jm (). In Eq. (5) is a break energy arising from synchrotron cooling of pions and muons in the magnetic field of the jet Rachen:1998fd (). We assume the energy density in the magnetic field is . We use this magnetic field to calculate the pion and muon synchrotron break energies by equating their respective synchrotron cooling time scales with the dynamic time scale in the jet frame. We also calculate the maximum accelerated proton energy in this magnetic field which is limited by proton cooling time scales and/or the jet dynamic time scale. See also Ref. Petropoulou:2014awa () for the role of in case of proton acceleration.
Figure 1 shows the neutrino fluxes for different model parameters, considering GW150914-GBM as a short GRB. Here we have used , and MeV, erg/sec and . We have plotted the HEN flux for three different jet radius by varying while keeping fixed s. Although the values of the parameters , , and are not well-constrained from the Fermi GBM observations of the GW150914-GBM Connaughton:2016umz (), they are within typical ranges of their values for short GRBs. Figure 1 also shows conventional atmospheric neutrino flux Honda:2006qj () which has been measured by IceCube up to 400 TeV Abbasi:2010ie ().
Finally we calculate the HESE number (cascade or track) at the IceCube detector from GW150914-GBM using the corresponding neutrino effective area , averaged over the full sky in the TeV - 1 PeV energy range Aartsen:2013jdh (), as
where s. Note that the confidence region of the joint LIGO-Fermi localization of the GW150914 event (bottom right panel of Fig. 8 in Ref. Connaughton:2016umz ()) lies entirely in the Southern hemisphere at . Neutrinos with PeV energy in the upper limit of integration in Eq. (6) suffers negligible absorption inside the earth for this source localization region. The atmospheric neutrino flux is much lower than the flux from the GW150914-GBM in this energy range for cm (see Fig. 1).
Iii Results and Discussion
Our main results are shown in Fig. 2 where we have plotted the number of HESE (cascade- or track-type) in IceCube from the short burst GW150914-GBM in coincidence with the gravitational wave detection. In the top panel we plot the bulk Lorentz factor of the GRB jet in the -axis, which is the most-sensitive parameter for calculating the interaction efficiency in Eq. (3). We have kept the flux variability time s fixed. In the bottom panel we plot the flux variability time in the -axis, which is the other sensitive parameter. We have kept fixed in this case. The -axis of Fig. 2 (both panels) shows the ratio of the proton to photon energy in Eq. (5). Different shading in the plot represents different number of events as indicated in the sidebars. The contour lines indicate number of HESE as 1, 2, 3, etc. from the bottom and above.
Note in Fig. 2 (top panel) that the event number is lower for higher , as expected, and deduced from non-detection of GRBs in neutrinos Ahlers:2011jj (); He:2012tq (); Gao:2013fra (). For , the peak in Fig. 1 shifts to further below the 25 TeV threshold energy for HESE detection. Thus the HESE detection is the most effective for . The dependence (bottom panel) is milder than the dependence, with a preference for tens of ms variability. The preferred range of radii for HEN production is therefore between cm and cm. The atmospheric neutrino flux is lower than the HEN flux in the energy range of Eq. (6) for these radii even in case of (see Fig. 1).
The plots in Fig. 2 allow us to put constraints on the and parameter spaces using non-detection of any HEN by IceCube in coincidence with the GW event Adrian-Martinez:2016xgn (). The minimum parameter values for detection of 1 HESE is (top panel) and (bottom panel). The value kept fixed in the top panel is largely consistent with the value in the bottom panel where is the minimum. Similarly the value kept fixed in the bottom panel is largely consistent with the value obtained in the top panel where is the minimum. As a result the minimum values are also consistent with each other. A detection of at least 1 HESE would then require or erg/s, at least. Given that the short GRB had a duration of s, the upper limit on the isotropic-equivalent proton energy is then erg. Because of the relativistic beaming effect the true GRB jet energy must be smaller by roughly two orders of magnitude. This implies that of the energy was emitted as kinetic energy as compared to the GW energy.
High-energy neutrino emission from gravitational wave sources has been discussed recently Razzaque:2006ju (); Murase:2006mm (); Wang:2007ya (); Murase:2009pg (); Bartos:2011aa (). Short GRBs can potentially be the multimessenger sources of electromagnetic, neutrino and gravitational wave. Detection of 100 GeV rays simultaneously with neutrinos from short GRBs Razzaque:2006ju () might be possible as well in near future with sensitive ground-based Cherenkov -ray detector such as the High Altitude Water Cherenkov (HAWC) Observatory Abeysekara:2011yu ().
We thank Kohta Murase and Maria Petropoulou for useful comments. This work was supported in part by the National Research Foundation (South Africa) grants no. 87823 (CPRR) and no. 93273 (MWGR) to SR. PM acknowledges support from a NASA grant NNX13AH50G.
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