High-Energy Neutrinos from NGC 1068
HHigh-Energy Neutrinos from NGC 1068
Luis A. Anchordoqui *1 , , , John F. Krizmanic , , and Floyd W. Stecker , Department of Physics, Lehman College, City University of New York, NY 10468, USA Department of Physics, Graduate Center, City University of New York, NY 10016, USA Department of Astrophysics, American Museum of Natural History, NY 10024, USA NASA / Goddard Space Flight Center, Greenbelt, MD 20771, USA Department of Physics, University of Maryland, Baltimore, MD 21250, USA Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA
IceCube has observed an excess of neutrino events over expectations from the isotropicbackground from the direction of NGC 1068. The excess is inconsistent with backgroundexpectations at the level of 2 . σ after accounting for statistical trials. Even though theexcess is not statistical significant yet, it is interesting to entertain the possibility thatit corresponds to a real signal. Assuming a single power-law spectrum, the IceCubeCollaboration has reported a best-fit flux φ ν ∼ × − ( E ν / TeV) − . (GeV cm s) − , where E ν is the neutrino energy. Taking account of new physics and astronomy developmentswe give a revised high-energy neutrino flux for the Stecker-Done-Salamon-SommersAGN core model and show that it can accommodate IceCube observations. * Speaker. © Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/ a r X i v : . [ a s t r o - ph . H E ] F e b igh-Energy Neutrinos from NGC 1068 Luis A. Anchordoqui
A search for astrophysical point-like neutrino sources using 10 yr of data collected bythe IceCube detector (between April 6, 2006 and July 10, 2018) finds an excess of clusteredevents (with energies E ν (cid:38) . σ after accounting for statistical trials. When the distributions of theobserved events as a function of their distance from NGC 1068 and their estimated angu-lar uncertainties are weighted by a signal-over-background likelihood characterizing thepoint-like source hypothesis give a best fit spectrum ∝ E − . ν . On the assumption of a singlepower-law spectrum IceCube finds a best-fit flux φ ν ∼ × − ( E ν / TeV) − . (GeV cm s) − ;the reconstructed muon neutrino spectrum with its large uncertainty is shown in Fig. 1. Apoint worth noting at this juncture is that the favored soft spectrum for NGC 1068 is con-sistent with the shape of the high-energy starting event all-sky neutrino spectrum, whichis compatible with an unbroken power-law spectrum, with a preferred spectral index of2 . + . − . for the 68.3 % confidence interval [5].Recently, the MAGIC Collaboration reported a search for gamma-ray emission inthe very-high-energy band [4]. No significant signal was detected during 125 hours ofobservation of NGC 1068. The null result provides a 95% CL upper limit to the gamma-rayflux above 200 GeV of 5 . × − (cm s) − . This limit improves an earlier upper boundfrom H.E.S.S. [3] and set tight constraints on the theoretical models that could explainthe NGC 1068 IceCube’s “signal.” More concretely, the gamma rays accompanying theneutrino flux must be significantly attenuated; see Fig. 1. The gamma-ray optical depth iswell-known, τ γγ ( ε ) ∼ σ γγ π c L X ε R ∼ (cid:18) ε (cid:19) − (cid:32) L X L Edd (cid:33) (cid:18) R S R (cid:19) , (1)where ε is the typical energy of the target photon background, σ γγ is the scattering crosssection, L X is the X -ray luminosity, R is the size of the region carrying the dense X -raytarget photons, R S = GM / c is the is the Schwarzschild radius, L Edd = π GMm p c /σ T is theEddington luminosity (i.e., the maximum steady state luminosity that can be producedbefore radiation pressure disrupts the accretion flow), and σ T is the Thomson cross section,with M and m p the black hole and proton mass, respectively. It is straightforward to seeusing (1) that to have significant absorption of the gamma rays R must characterize acompact region in the vicinity of the black hole.In 1991, Stecker, Done, Salamon, and Sommers proposed a model featuring all ofthese characteristics [6]. The high-energy neutrino flux originates in the core of the activegalactic nucleus (AGN). Protons can reach very high energies through accretion-diskshock-acceleration at the inner edge of the black hole [7]. The relativistic protons undergoinelastic collisions with the thermal photon background to produce charged and neutralpions, which, in turn, decay into neutrinos, electrons, and gamma-rays. The non-thermalelectrons generate gamma rays via inverse Compton scattering on disk photons. Whileall the gamma rays cascade down to the MeV energy range because of the strong internalattenuation e ff ect [8] neutrinos escape the source en route to Earth. Taking account ofnew physics and astronomy developments, in this communication we give a revised highenergy neutrino flux for the AGN core model and show that it can accommodate IceCube1 igh-Energy Neutrinos from NGC 1068 Luis A. Anchordoqui
Figure 1:
AGN-core model prediction of the muon neutrino spectrum from NGC 1068; pp inter-actions (dot-dashed line), p γ interactions (dashed line), and total (solid line). For comparison,we overplot the best-fit time-integrated astrophysical power-law neutrino flux obtained using the10 yr IceCube data [1]. We also show measurements and bounds on the gamma-ray flux fromFermi [2], H.E.S.S. [3] and MAGIC [4]. We have set b = data. Observational studies and theoretical modeling are used to guide us in choosing themodel parameters. Before proceeding, we pause to note that related ideas for modellingneutrino emission from NGC 1068 have been discussed in [9–12]. X -ray absorbers are classified as Compton-thick or -thin, according to whether theircolumn density N H is larger or smaller than σ − T (cid:39) . × cm − . Back in the 90s, therewas a lack of evidence for strong X -ray absorption features in AGN spectra [13, 14], andthis was taken as an indication that the secondary X -rays are produced in regions of lowcolumn density. If this were the case, the amount of target gas for pp collisions would bevery limited and the very large photon density in the AGN core would make photopionproduction, predominantly through the resonant process p γ → ∆ + → n π + or p π , theleading mechanism for energy loss. Because of resonant scattering the mean pion energyis kinematically determined by requiring equal boosts for the decay products of the ∆ + ,giving (cid:104) E π (cid:105) ∼ E p / π + → µ + ν µ → e + ν e ν µ ν µ (and the charge-conjugate processes)share similar amounts of energy (cid:104) E ν (cid:105) (cid:39) (cid:104) E π (cid:105) / (cid:39) E p /
20. For the neutral pions π → γγ , wesimilarly find (cid:104) E γ (cid:105) (cid:39) E p /
10. The threshold condition for pion production in p γ scattering isgiven by ( p γ + p p ) > ( m p + m π ) , which leads to ζ > (2 m π m p + m π ) / m p ≡ ζ (cid:39) . ζ ≡ ε E p / m p characterizes the center-of-mass total energy squaredof the interaction and where we have taken m ± π (cid:39) m π (cid:39)
137 MeV and m p (cid:39) m n (cid:39)
938 MeV.For UV photons, with a mean energy (cid:104) ε (cid:105) ∼
40 eV, this translates into a characteristic protonenergy E p , min >
70 PeV / ( ε/ eV) ∼ O (TeV)2 igh-Energy Neutrinos from NGC 1068 Luis A. Anchordoqui neutrinos from the direction of NGC 1068 pose unique challenges for predictive modeling.Over the past decades, multiple space-missions and ground-based experiments (in-cluding BeppoSAX, Chandra, MERLIN, the Very Long Baseline Array, NuSTAR, andXMM-Newton [16–21]) have performed an extensive observing campaign aimed at thecharacterization of NGC 1068. Collectively, these observations call for a recalibration ofthe AGN-core-model parameters. In particular, NuSTAR detected a flux excess above20 keV with respect to both the December 2012 observation and a later observation per-formed in February 2015. The most plausible explanation of the NuSTAR transient excessis that for a short time interval the total absorbing column, probably composed by a num-ber of individual clouds, became less thick so as to allow the radiation from the AGN coreto pierce through it, supporting the hypothesis of a clumpy structure of the obscuringmaterial along the line of sight. The inferred column gas density from NuSTAR obser-vations, which varies in the range 5 . × (cid:46) N H / cm (cid:46) . × [21], seems to indicatethat the target proton gas in the AGN core is much denser than previously thought [14].If this were the case, NGC 1068 should be reclassified as an optically thick absorber. For pp collisions, threshold e ff ects are insignificant and so for column densities N H > σ − T , pp scattering could produce a TeV neutrino population to explain the low-energy tail of Ice-Cube’s “signal” [1]. Moreover, after correction for absorption, the inferred intrinsic X -rayluminosity of NGC 1068 (in the 2 −
10 keV range) is L X = + − × erg s − [21], aboveabout 2 orders of magnitude than previous estimates [17]. It is important to note that theintrinsic L X of NGC 1068 is roughly an order of magnitude larger than the L X of NGC4151 [22, 23], which is the brightest Seyfert in X -rays. Since both these two sources arelocated at about 14 Mpc from Earth [24], the L X recalibration of [21] makes NGC 1068 theintrinsically brightest Seyfert galaxy in the sky, and explains why it could become the firstneutrino source to be uncovered using (only) IceCube data. To develop some sense for the orders of magnitude involved, we begin by notingthat first-order Fermi acceleration of protons in strong (non-relativistic) shocks producesa power-law proton energy spectrum ∝ E − p up to a maximum energy E p , max . The protonacceleration time-scale is given by t acc ( E p ) ∼ × − b (cid:32) R shock R S (cid:33) (cid:18) B G (cid:19) − (cid:32) E p m p (cid:33) s , (2)where B (cid:39) . × Q − / ( R shock / R S ) − / L − / X G is the magnetic field, R shock is the shockradius, Q = − . R shock / R S ) . is the e ffi ciency of conversion of bulk kinetic energy ofaccreting plasma into energetic particles at the shock, and b is a numerical factor that givesa measure of the particle’s mean free path (in gyroradii) for scattering o ff the magneticfield inhomogeneities [26, 27]. Based on the assumption L X ∼ L Edd /
20 (which correspondsto M ∼ M (cid:12) ) we fix the shock radius to R shock ∼ R S [6]. Multimessenger observations of TXS 0506 +
056 provided 3 σ evidence of neutrino emission from theflaring blazar [25]. However, the association of the Texas source with neutrino emission in IceCube’s 10 yrdata sample is less significant [1] than the reported significance of the time-dependent flare associating bothneutrino and gamma-ray production. igh-Energy Neutrinos from NGC 1068 Luis A. Anchordoqui
The pp energy-loss rate is given by t pp ( E p ) = n p σ pp c κ pp ∼ s , (3)where σ pp ( E p ) ∼ [34 . + .
88 ln( E p / TeV) + .
25 ln ( E p / TeV)] × − cm is the inelastic pp cross section [28], κ pp ∼ . n p ∼ N H R themean proton density. Following [6], we take R ∼ R S .The p γ energy-loss rate is evaluated by t − p γ ( E p ) = c (cid:90) ∞ d ε n ( ε ) γ ε (cid:90) γε d ε (cid:48) ε (cid:48) κ p γ σ p γ ( ε (cid:48) ) , (4)where γ = E p / m p c is the Lorentz boost, ε (cid:48) is the photon energy in the proton rest frame, n ( ε ) is the di ff erential number density of photons, and σ p γ and κ p γ are the cross sectionand inelasticity for photopion production, respectively [30]. We approximate the p γ crosssection by interactions with the ∆ + resonance of mass m ∆ (cid:39) .
232 GeV. Since the decaywidth Γ ∆ (cid:39)
150 MeV is much smaller than the resonance mass the cross section can besafely approximated by the single pole of the narrow-width approximation, σ p γ ( ε (cid:48) ) = π σ Γ δ ( ε (cid:48) − ε ) , (5)where σ (cid:39) × − cm is the resonance peak and ε = ( m ∆ − m p ) / (2 m p ) (cid:39)
340 MeV thepole. The factor of π/ t − p γ ( E p ) ≈ c π σ ε Γ ∆ κ p γ γ (cid:90) ∞ d εε n ( ε ) Θ (2 γε − ε ) = c π σ ε Γ ∆ κ p γ γ (cid:90) ∞ (cid:15) / γ d εε n ( ε ) = c π σ ( m ∆ − m p ) Γ ∆ κ p γ m p (cid:32) m p E p (cid:33) (cid:90) ∞ ε min d εε n γ ( ε ) , (6)where ε min = ( m ∆ − m p ) / (4 E p ) [31]. We assume that the spectrum of the external UVradiation field arises from a Shakura-Sunyaev optically-thick accretion disk model that isscattered by clouds [32]. For calculations, we approximate the AGN continuum n ( ε ) bytwo components: (i) a power-law spectrum ∝ ε − . which extends up to 1 MeV and (ii) ablack body spectrum with temperature T = × K used to represent the UV / optical bumpwhich is thought to be thermal emission from the accretion disk [27]. For normalization,we assume that the total X -ray luminosity is roughly the same as that in the UV-bump L X ∼ L UV and so L C ∼ π R c (cid:82) ε n ( ε ) d ε = L Edd /
10, where L C is the luminosity in the infraredto hard X -ray continuum [6].Now, by equating (2) to (3) + (6) with b = E p , max is O (10 GeV).The order of magnitude estimate from this back-of-the-envelope calculation is consistentwith the result from a Monte Carlo simulation, which gives E p , max (cid:39) . × GeV (6 / b ) α , (7)4 igh-Energy Neutrinos from NGC 1068 Luis A. Anchordoqui where α = .
52 for b < α = .
18 for b > pp [28, 34] and p γ [34, 35] collisions it is straightforward to calculate themuon neutrino yield from NGC 1068. Our results are encapsulated in Fig. 1. At lowenergies the spectrum ∝ E − ν from pp interactions dominates; at high energies the spectrumfrom p γ interactions dominates. Corrections due to kaon decay and threshold e ff ects are O (10%) [36] and fall within erros. We have accounted for a reduction in the muon-neutrinoflux at production by a factor of 2 due to neutrino oscillations (whose discovery was madeafter the publication of [6]). From (1) we can see that the accompanying photons from π decay cascade down to lower energies, in agreement with the upper limits from H.E.S.S. [3]and MAGIC [4].We now turn to compare our results with recent estimates of the neutrino flux fromNGC 1068. The predicted neutrino flux is in agreement with the estimates of [9–11]. How-ever, it is important to stress that the acceleration rate adopted in our study is significantlyfaster than the one used in [9–11]. This implies that the maximum energy is always con-trolled by p γ interactions. In particular, t p γ ( E p , max ) (cid:28) t pp ( E p , max ) even when considering theupper bound of n p ∼ × cm − . For the acceleration mechanisms entertain in [9–11], thecolumn density cannot (significantly) surpass σ − T otherwise pp collisions would controland largely reduce E p , max . The neutrino flux predicted by the AGN-core model is about anorder of magnitude larger than the estimate in [12], which is normalized to accommodategamma-ray observations.Although there are a few other nearby AGN of this magnitude which can potentiallybe detected as point sources, one can integrate over the estimated AGN population outto the horizon to obtain a prediction for the di ff use neutrino flux. The result is simple: Φ ν ∼ π R n AGN (cid:104) L ν (cid:105) , where R (cid:39) (cid:39) n AGN ∼
800 Gpc − is the number densityof AGN with L X > erg / s [37], and (cid:104) L ν (cid:105) is an average AGN neutrino luminosity (allflavors). What has become of the energy red-shifting of the neutrino? A more carefulcalculation must include an additional factor, H (cid:82) dz H − ( z ) L ν ( z ) / L ν (0), to account fore ff ects of the expanding universe ( viz. , loss of energy associated with the redshift z andalso depending on a choice of Hubble parameter H ) and possible source evolution [6,38,39].However, given the large uncertainty in the energy spectrum, we will ignore this order ofmagnitude “correction” and just note that if (cid:104) L ν (cid:105) ∼ − L X E − ν , the di ff use neutrino fluxexpected on Earth from the AGN population, E ν Φ ν ∼ − GeV (cm sr s) − , would be inthe ballpark of IceCube observations [5]. Curiously though, there is a seemingly bumpy-structure in the spectrum of the high-energy starting event sample around the 100 TeVenergy bin. Coincidentally, this is the energy range in which photopion production on thedisk photons turns on. It is then tempting to speculate that if not all AGN are Compton-thick we would expect a bump in the spectrum when AGN sources producing neutrinosonly via p γ interactions come into play.In summary, IceCube has detected an intriguing excess of events above the isotropicbackground from the direction of NGC 1068. We have shown that the origin of theseneutrinos can be traced back to a Fermi engine at the core of this AGN. Absorption andinteractions intrinsic to the source due to the high opacity, will result in a suppressed5 igh-Energy Neutrinos from NGC 1068 Luis A. Anchordoqui
TeV gamma-ray flux to accommodate H.E.S.S. and MAGIC upper limits. The neutrinoAGN-core model is fully predictive and will be confronted with future IceCube data.
Acknowledgments
LAA is supported by NSF Grant PHY-1620661 and NASA Grant 80NSSC18K0464.JFK is supported by NASA Grant 80NSSC19K0626. FWS is suppoorted by NASA FermiGrant 80NSSSC20K0413.
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