On the detectability of BL Lac objects by IceCube
aa r X i v : . [ a s t r o - ph . H E ] A ug ON THE DETECTABILITY OF BL LAC OBJECTS BY ICECUBE
C. RIGHI , , F. TAVECCHIO Universit´a degli studi dell’Insubria, DiSAT, Via Valleggio, 11 - 22100 Como, Italy INAF - Osservatorio Astronomico di Brera, Via E. Bianchi 46, I-23807 Merate, Italy
Since 2010 IceCube observed around 50 high-energy neutrino events of cosmic origin above 60TeV, but the astrophysical sources of these events are still unknown. We recently proposedhigh-energy emitting BL Lac (HBL) objects as candidate emitters of high-energy neutrinos.Assuming a direct proportionality between high-energy gamma-ray and very-high energy neu-trino fluxes, we calculated the expected neutrino event number in a year for IceCube and thepresently under construction Km3NeT. To give a value of the significance of a detection weconsidered also the background for the single sources. To this aim we derived the through-going muon rate, generated by muon neutrino including the effect of Earth absorption, thedensity of the Earth and the cross section νN . Applying this calculation both to HBL sourcesand the atmospherical neutrino background, we can calculate the expected significance of thedetection by IceCube, showing that our scenario is compatible with a no detection of HBL. In 2010 Ice Cube started to reveal neutrinos in clear excess to the expected atmospheric flux atvery-high energy ( &
100 TeV); this marked the beginning of the neutrino astrophysics era1 2. IceCube is able to reconstruct some of the most relevant quantities (energy, E ν , and direction, α ν and δ ν ) of the incoming neutrino. There are two types of events: the high-energy starting events(HESE, or contained-vertex event) with a high angular uncertainty ( > ◦ ) and the high-energythrough-going muons, produced only by ν µ (and ¯ ν µ ) a and with a good angular uncertainty( ≤ ◦ ). Today we have ≈
50 events of different neutrino flavours b at these energies (60 TeV -2 . c to produce pions ( p + p → X + π or p + γ → X + π ).Charged pions, in turn, decay in muon and neutrinos ( π ± → µ ± + ν µ → e ± + 2 ν µ + ν e ). The p + p reaction could take place in regions with high barion density (such as galactic regions or starforming regions); meanwhile the photo-meson reaction is favoured in case of high photon densityregions. After 5 years of data taking the sky distribution of the detected events is consistentwith isotropy. The lack of a strong anisotropy suggests that the sources are not only galactic,but a mixed galactic and extragalactic origin can not be excluded. Recent studies suggest apossible contribution at “low energy” (30 −
100 TeV) by galactic sources and an extragalacticcomponent emission above 100 TeV 3. Among the possible extragalactic sources there are starforming galaxies 4 5, active galactic nuclei (AGN) 6 7 8 9, galaxy clusters 10. Among AGN, a We will not distinguish from neutrino and antineutrino. b The tau neutrino ν τ is not been yet observed. c For E p ∼ eV the required photon energy E γ is in the UV-X-ray range. lazars are often considered the most probable candidate because of their jet pointed towardthe line of sight to the Earth 11. These objects present peculiar characteristics such as variabilityat all frequencies and an intense emission in the γ -ray band 12 13 14. This makes blazars themost numerous extragalactic γ -ray sources. Because of the beaming, the emission observed fromblazars is dominated by the non-thermal continuum produced in the jet. This characterises theso-called spectral energy distribution, SED, typically showing a “double hump” shape. Thelow energy component, peaking between IR and soft-X rays, is explained by the synchrotronradiation of relativistic electrons inside the jets, while the second component, usually peakingin γ -ray band, has not a completely clear origin. The most popular scenario is the leptonicmodel, where the second component is due to the Inverse Compton (IC) radiation from thesame electrons producing the first component. In hadronic scenarios, instead, the second peakof SED is thought to originate from high-energy protons loosing energy through synchrotronemission or photo-meson reactions. Assuming a coexistence of both electrons and protons insidethe jet, the favourite mechanism to produce high-energy neutrino from blazars is pγ reaction.Blazars are divided in two subclasses, flat spectrum radio quasar (FSRQ), characterised bybroad emission lines typical of quasars, and BL Lacertae (BL Lac), showing extremely weakor absent emission lines in their optical spectra. FSRQs are generally more powerful thanBL Lacs. The distinct difference between the two subclasses can be interpreted by a differentnature of the the accretion flow 15 16. At a first sight, FSRQ, characterised by intense thermalradiation, providing an ideal photon target field, seems the best blazar subclass to host pγ reactions and produce neutrinos. Kadler et al.17 found a coincidence in time between a long-lasting ( ∼ months) outburst of the FSRQ PKS B1414-418 and the arrival time of an HESEneutrino with an uncertainty region of ∼ ◦ . However, there are several arguments againstthe possibility of FSRQs being the sources of the neutrinos revealed by IceCube. If FSRQscan produce neutrinos, the photon involved in the photo-meson reaction are most likely the UVphotons of the broad line region (BLR). This implies a very-high energy E p of parent protons andthus of the neutrinos d . Precisely, the energy of the proton must follow the photopion thresholdcondition E p ǫ > m π m p c with ǫ , the energy of the interacting photons, m π and m p the massesof pion and proton. Indeed, the spectra of neutrinos produced by FSRQs is predicted to be hardin the range of energy observed by IceCube 8, that instead reveals a relatively flat-soft spectrum.BL Lac objects seem disfavoured as ν emitters, mainly because their low luminosity hintsto inefficient photo-meson production 8. However Tavecchio et al.18 showed that if the jet isstructured with a fast core (spine) and a slower layer, the neutrino emission from these objectcould match the observed intensity with an acceptable value of the cosmic ray power for the jet.This thesis is supported by Padovani et al.19 which present the evidence for a significant spatialcorrelation between the reconstructed arrival direction of neutrinos (including both hemispheres,thus both HESE and through-going muon) and BL Lac objects emitting very high-energy γ -rays( >
50 GeV).
In Righi et al.20, based on the results of [19] and [18], we selected a sample of high-energy emittingBL Lac (HBL) objects from the 2FHL catalogue and linked the emission of muon neutrinoscoming from the photo-meson reaction to the γ -ray from Inverse Compton. We accept a leptonicscenario for the HBL electromagnetic emission; in this way we assume that any electromagneticcomponent associated to hadronic reactions, such as the decay of π (and hence to neutrinoemission) does not dominate the SED. We refer to Righi20 for a complete description of thescenario. Here we just recall the key points to find the linear relation between the bolometricneutrino flux F ν for a given HBL source and its high-energy γ -ray flux F γ . The total, energyintegrated, neutrino luminosity L ν can be expressed as L ν = ǫ p Q p δ s ; where ǫ p is the averaged d For photo-meson reactions the approximate relation is E ν ∼ E p / able 1: Expected 0.1-10 PeV flux (in units of 10 − GeV cm − s − ) and detection rate (yr − ) ofmuon neutrino ˙ N ν for the brightest 2FHL BL Lacs with IceCube at different declinations (top)and with Km3NeT with the horizon as thresholds on the zenith angle (bottom). IceCube Km3NeT New approachName F ν R ν R ν N µ source N µ back Mkn421 8.77 4.89 4.59 10.23 8.46PG1553+113 1.89 2.47 1.42 4.00 8.87Mkn501 3.41 1.90 1.65 3.86 8.44PKS1424+240 1.00 1.30 0.67 1.61 8.71PG1218+304 0.92 1.20 0.55 1.27 8.60TXS0518+211 0.87 1.14 0.59 1.48 8.743C66A 0.87 0.49 0.38 1.00 8.40PKS2155-304 2.15 2.23 3.00 8.60 efficiency for ν production, Q p the total cosmic ray injected power in the spine region and δ s is the beaming factor determining the amplification of the emission always in the spine region.The high-energy γ -ray luminosity due to IC can be expressed in the same way but consideringthe relativistic electrons L γ = ǫ e Q e δ s ; where ǫ e measures the efficiency for γ -ray production.Hence we have a relation of the ratio of the luminosities (and then of the fluxes): F ν F γ = L ν L γ = ǫ p Q p ǫ e Q e (1)We assume that both efficiencies ǫ p and ǫ e depend on the same photon field (the layer radiation),and thus their ratio, ǫ p /ǫ e , is constant in first approximation. The same approximation couldbe done for Q p /Q e . In this case both can be linked to the total power carried by the jet Q p,e = η p,e P jet with the ratio η p /η e ≈ const , hence F ν = k νγ F γ . In Righi et al.20 we derivedthe average value of k νγ comparing the total neutrino diffuse flux measured by IceCube andthe entire high-energy γ -ray emission of HBL detected by Fermi. With this calculation we werelikely overestimating the neutrino flux for each sources because we didn’t consider the unresolvedHBL sources by Fermi. In fact we calculated the total γ -ray flux F γ by summing the fluxes ofHBLs catalogued in the 2FHL22 that includes all the sources detected above 50 GeV. It shouldbe taken into account that, from the results by Ackermann et al.21, the derived neutrino fluxescould be lower by a factor ≈
3. It further should be noted that in Righi et al.20 we used k νγ tocalculate the neutrino flux for each HBL source, F ν i = k νγ F γ i , assuming that k νγ is the exactlysame for all sources.We can calculate the expected neutrino rate, R ν , in IceCube and Km3NeT for the brightest2FHL HBL using the neutrino flux F ν i and the effective area of the instrument A eff (IceCube23and Km3NeT24): R ν = Z E E F ν i ( E ν ) A eff ( E ν ) dE ν (2)where T exp is the integration time, one year in this case. The effective area A eff for IceCube isgiven in range of declinations (0 ◦ < δ < ◦ ,30 ◦ < δ < ◦ ,60 ◦ < δ < ◦ ) while for Km3NeT A eff is full-sky averaged. In table 1 we reported the main results of Righi et al. for IceCubeand Km3NeT. We remark that we calculated the expected muon neutrino flux and the muonneutrino rate for each source because the good angular resolution ( ≤ ◦ ) of the through-goingmuon permits a possibile spatial correlation between the position of a source and the directionof the incoming neutrinos. For this reason, in the case of IceCube, we consider only the muonneutrinos coming from the northern hemisphere (this is the reason why for the last three sourcesin table 1 we do not report the expected rate number R ν for IceCube). Our calculations predictthat only for a few γ -ray bright HBL we expect a rate numbers R ν detectable in few years ofperation. For IceCube, in particular, there are only two sources, Mkn 421 and PG 1553+113,that show a rate exceeding 1 event yr − . For Mkn 421 we obtained a relatively large expectedrate, 4.89 yr − . However, the declination of Mkn 421 is +38 ◦ ′ . ′′ , close to the lowerlimit of declination range validity of the effective area (30 ◦ < δ < ◦ ). A finer binning ofthe effective area could be used to find a more precise expected neutrino rate number for thesources by IceCube. For Km3NeT instead we obtain an appreciable neutrino flux for severalsources. While for IceCube the sources have the same visibility during the year because IceCubeis located at South Pole, the analysis for Km3NeT is more complicated because the sources arepartially visible (i.e. stays below the horizon) during the year. Km3NeT collaboration give thevisibility as a function of source declination for the muon-track analysis for tracks below thehorizon and up to 10 ◦ above the horizon. Table 1 shows only the expected rate number R ν fortracks below the horizon.This work is missing of an analysis of the background due to the atmospheric neutrinosand an estimate of the sensitivity of a possible detection of the sources. Furthermore recentlysome arguments against BL Lac objects as candidates neutrino emitters have been raised. Inparticular Murase & Waxman 25 presented an analysis of the constraints that can be put onthe average luminosity and the local volume density of high-energy neutrino sources, based onthe non-detection of multiplets in the detector (or, equivalently, on the non-detection of “pointsources” associated to high-energy neutrino-induced muon tracks). In this way they are ableto rule out some of the possible source classes, in particular those characterised by a largeluminosity and a low cosmic density. Their calculation lead to exclude blazar (both FSRQ andBL Lac) as principal neutrino emitting source class. We note however that the BL Lac samplethey consider as representative the BL Lacs population belonging to the 1FGL catalogue26.This sample includes all the BL Lac objects detected by Fermi /LAT in the band 0 . − )passing through the detector (we will consider only IceCube) without using the effective area ofthe detector, but performing a calculation starting on first principle. Although simplified, thisapproach provides an acceptable estimate28 29 25 and, importantly, it allows one to calculatea significance of the possible detection considering also the background rate for each direction(and so for each source). The number of interactions ( ν µ X → µ Y) per unit time ˙ N is given by the cross section σ timesthe incident flux. In our case we consider only through-going events, and so ν µ , because of theirassociated small angular uncertainty ( ≤ ◦ ). In this context the number of muons per unit timecrossing the detector is given by: d ˙ N = F ν ( E ν ) e − τ ( x,E ν ) A ρ ( x ) m p σ CC ( E ν ) dx (3)where σ CC is the cross section of charged current e , F ν is the neutrino flux in GeV − cm − s − sr − , τ takes into consideration the neutrino flux attenuation and depends on the path x , of theneutrino, inside the Earth (and so it depends on the zenith angle Θ) and the energy of flux E ν ; e We’ll consider only the charged current interaction between ν µ N . t corresponds to: τ ( x, E ν ) = Z x ρ ( x ′ ) m p σ CC ( E ν ) dx ′ (4)The number of target nucleons per dx is given by A ρ ( x ) m p dx , where m p is the mass of proton, A is the detector projected area (which in principle depends on the zenith angle) that weapproximate to ≃ . ρ is the Earth density (in g cm − ) and depends on the path inside theEarth x . Defining dX = ρ ( x ) dx and dividing both members of equation 3 for dX we obtain d ˙ N /dX . We want to study the rate of muon neutrino per energy d ˙ N /dE µ , that it’s equal to: d ˙ NdE µ = d ˙ NdX dXdE µ (5)The first term right of equation 5 is given by equation 3, while the second term derives from theinverse of the average muon energy-loss rate − dE µ dX = α + βE µ where α is the ionization termwhile βE µ is the radiative term at TeV range α and β are respectively equal to ≃ · − GeVcm g − and ≃ · − cm g − . Replacing previous equations in eq.5 we obtain: d ˙ NdE µ = 1 α + βE µ Am p Z E νmax E µ F ν ( E ν ) σ CC ( E ν ) e − τ ( x,E ν ) dE ν (6)We have to integrate between the minimum and maximum value of the incoming neutrino toproduce a muon of energy E µ . The minimum value of neutrino energy to produce a muon withenergy E µ corresponds to E ν min = E µ corresponding to neutrinos with energy E µ interactingjust before the detector.Integrating for all possible E µ , we obtain the number of muon (or neutrino) produced in atime T for every source: N = εT Z E µmax E µmin d ˙ NdE µ dE µ (7)where ε σ CC ( E ν ) of eq.6 given in Connolly et al. 30, the neutrino flux F ν ( E ν )found in Righi et al. and the Earth density ρ ( x ) reported by Dziewonski & Anderson31. Mainbackgrounds to the search for astrophysical neutrinos are high-energy atmospheric neutrinos andmuons produced by cosmic-ray interactions in the Earth’s atmosphere. There are two atmo-spherical neutrinos components: the conventional neutrinos and the prompt neutrinos producedin the atmosphere by the decay of charmed particles. To find the number of background muonproduced in a time T at the same declination angle of the BL Lac sources, we have to considerthe dependence on the solid angle d Ω. For this reason the background flux to use in eq.6 is F ( E ν ) Back = 2 π Z Θ0 φ B (Ω , E ν ) d Ω ≈ π Θ φ B ( E ν ) (8)where we consider Θ = 1 ◦ and φ B ( E ν ) the flux of background given by Aartsen (2016) in GeV − cm − s − sr − . The energy range of background neutrinos is 10 GeV < E ν back < GeV.In this procedure we do not include a detailed analysis of the efficiency of the detector. Forthis reason the expected muon rates N will be likely overestimated.Last two columns of table 1 show the expected muon rate produced by muon neutrinos ofthe sources and the background passing through the detector. These numbers are subject tostochastic fluctuations, for this reason they need to be treated with Poisson distribution. Li andMa32 gives a formulae to estimate the significance S of observations.We assume a Poisson distribution around the number of muon for the sources Mkn 421 andPG 1553+113 and the corresponding background; we extract randomly a value from the Poissonigure 1: same figure with draft option (left), normal (center) and rotated (right)distributions and we calculate the significance S . We repeat this procedure 10000 times, in thisway we obtain a distribution around the most probable significance for the two sources. Figures1 shows the position of the peak of the distribution for Mkn 421 and PG 1553+113. Solid lineconsider the efficiency ε = 1, while dashed lines consider an efficiency of the instrument of 30%, ε = 0 . References
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