The Synchrotron Proton Blazar model is a promising model to explain high
energy emission from gamma-ray loud BL Lac objects like Mkn 421. In contrast to
leptonic models, the hadronic explanation of gamma-ray emission predicts
ultrahigh energy neutrinos.
  The predicted neutrino spectra from a typical High-energy cutoff BL Lac
Object (HBL) and a Low-energy cutoff BL Lac Object (LBL) are presented. We find
that cooling due to muon synchrotron radiation causes a cutoff of the neutrino
spectrum at $\sim 10^{18}$ eV, with the exception of $\nu_\mu$ from kaon decay
which may extend to higher energies if meson production takes place in the
secondary resonance region of the cross section.
  The impact of the neutrino output from both source populations to the diffuse
neutrino background is discussed.Comment: 4 pages, 3 figures, to appear in: Proc. 27th Int. Cosmic Ray Conf.,
  Hamburg/German

Muecke, A.

Protheroe, R. J.

English

arXiv

© Copernicus Gesellschaft 2001 Submitted to Cornell University’s online archive www.arXiv.org in 2001 by A. G. Mucke, Post-print sourced from www.arxiv.orgThe Synchrotron Proton Blazar model is a promising model to explain high
energy emission from gamma-ray loud BL Lac objects like Mkn 421. In contrast to
leptonic models, the hadronic explanation of gamma-ray emission predicts
ultrahigh energy neutrinos.
  The predicted neutrino spectra from a typical High-energy cutoff BL Lac
Object (HBL) and a Low-energy cutoff BL Lac Object (LBL) are presented. We find
that cooling due to muon synchrotron radiation causes a cutoff of the neutrino
spectrum at $\sim 10^{18}$ eV, with the exception of $\nu_\mu$ from kaon decay
which may extend to higher energies if meson production takes place in the
secondary resonance region of the cross section.
  The impact of the neutrino output from both source populations to the diffuse
neutrino background is discussed.A. Mucke and R.J. Prothero

Mucke, A.

Protheroe, R.

Adelaide Research &amp; Scholarship

arXiv:astro-ph/0105543v1  30 May 2001Proceedings of ICRC 2001: 1 c© Copernicus Gesellschaft 2001 ICRC 2001Neutrino Emission from HBLs and LBLsA. Mu¨ckea1 and R.J. Protheroe21De´partement de Physique, Universite´ de Montre´al, Montre´al, Que´bec, H3C 3J7, Canada2Department of Physics and Mathematical Physics, The University of Adelaide, Adelaide, SA 5005, AustraliaaNow at: Institut fu¨r Theoretische Physik, Lehrstuhl IV: Weltraum- & Astrophysik, Ruhr-Universita¨t Bochum, D-44780Bochum, GermanyAbstract. The Synchrotron Proton Blazar model is a promis-ing model to explain high energy emission from γ-ray loudBL Lac objects like Mkn 421. In contrast to leptonic models,the hadronic explanation of γ-ray emission predicts ultrahighenergy neutrinos.The predicted neutrino spectra from a typical High-energycutoff BL Lac Object (HBL) and a Low-energy cutoff BLLac Object (LBL) are presented. We find that cooling due tomuon synchrotron radiation causes a cutoff of the neutrinospectrum at ∼ 1018 eV, with the exception of νµ from kaondecay which may extend to higher energies if meson pro-duction takes place in the secondary resonance region of thecross section.The impact of the neutrino output from both source popu-lations to the diffuse neutrino background is discussed.1 IntroductionMost models of gamma ray emission from blazar jets con-sider Inverse Compton scattering of energetic electrons offlow energy photons as the main gamma ray production mech-anism. In the Synchrotron-Proton Blazar (SPB) model, re-cently proposed by, e.g., Mu¨cke & Protheroe (2001) acceler-ated protons interact with the synchrotron radiation field pro-duced by the co-accelerated electrons via meson photopro-duction and Bethe-Heitler pair production, and more impor-tantly, with the strong ambient magnetic field, emitting syn-chrotron radiation (pions and muons also emit synchrotronradiation). Since this model neglects external photon fieldcomponents, it is most applicable to BL Lac objects whichhave weak accretion disks. Mu¨cke & Protheroe (2001) haveshown that this model can reproduce the commonly observeddouble-humped blazar spectral energy distribution (SED).Gamma ray loud BL Lac objects are commonly classi-fied as HBLs or LBLs on the basis of their ratio of radioto X-ray flux i.e. HBLs have a broad-band spectral indexCorrespondence to: muecke@astro.umontreal.ca (Email)αRX ≤ 0.75 and LBLs have αRX > 0.75 (Padovani &Giommi, 1995). Consequently, for LBLs, the synchrotronpeak is generally observed at optical/IR-frequencies whilethe X-ray band covers the local minimum of νLν between thetwo spectral humps. LBLs are thought to represent an inter-mediate object class between quasars, which have generallya much higher bolometric luminosity than BL Lac objects,such that νLν peaks in the IR and at MeV-GeV-energies, andHBLs, which are the least luminous blazars, and have νLνspectral peaks at soft to medium-energy X-rays and GeV-TeV gamma rays.In this paper we present for the first time the predictedneutrino emission from a typical HBL and LBL in the SPBmodel, assuming that Mkn 421 and PKS 0716+714 are typi-cal for each source population, respectively.2 The modelWe inject an spectrum of E′−2p protons into the jet (primedquantities are in the jet frame), and they are assumed to re-main quasi-isotropic in the jet frame due to pitch-angle scat-tering. The co-accelerated relativistic electrons radiate syn-chrotron photons which serve as the target radiation fieldfor proton-photon interactions, and for the subsequent pair-synchrotron cascade which develops as a result of photon-photon pair production in the highly magnetized environ-ment. In the SPB model, the target photon density u′photis much smaller than the magnetic field energy density, andthus Inverse Compton losses can be neglected. The pair-synchrotron cascade redistributes the photon power to lowerenergies where the photons escape from the emission region,or “blob”, of size R′ which moves relativistically in a direc-tion closely aligned with our line-of-sight.The proton energy loss processes considered in the modelare photomeson production, Bethe Heitler pair production,proton synchrotron radiation and adiabatic losses due to jetexpansion. Synchrotron radiation from µ± and π± (fromphotomeson production) prior to their decay becomes impor-2tant in highly magnetized environments with B′ > severaltens of Gauss (Rachen & Me´sza´ros, 1998), and is taken intoaccount in our calculations. The acceleration rate for anyacceleration mechanism is dE′/dt′ = η(E′)ec2B′ whereη(E′) ≤ 1 describes the efficiency, and B′ is the magneticfield in the blob. The maximum proton energy is limited bythe balance between energy gain and loss rates.Direct proton and muon synchrotron radiation seems tobe mainly responsible for the high energy hump whereasthe low energy hump is dominanted by synchrotron radiationfrom the directly accelerated e−, with a contribution of syn-chrotron radiation from secondary electrons produced by theproton- and µ±-synchrotron initiated cascade. The contribu-tion from Bethe-Heitler pair production turned out to be neg-ligible. For our calculations we use a Monte-Carlo methodand utilize the recently developed SOPHIA code for the pho-tohadronic event generation (Mu¨cke et al., 2000).3 HBLs and LBLs in the SPB Model: the case Mkn 421and PKS 0716+714Mkn 421 is a well-known TeV-blazar, and is classified as anHBL. We have used the average SED published by Ghiselliniet al. (1998) to derive its model parameters in the frameworkof our model.The observed low energy hump, identified as synchrotronradiation, serves as the target photon field in our model forpion photoproduction and cascading. We have parametrizedthe observations by a broken power law with photon spectralindex –1.5 below the lab frame break energy ǫb ≈ 100 eV,and index –2.25 up to the cutoff energy of ǫc ≈ 40 keV.Our model represents the data well (Mu¨cke et al., in prep.)for Doppler factor D ≈ 10, ǫ′b ≈ 10 eV, and ǫ′c ≈ 4 keV,u’phot ≈ 109 eV/cm3, an emitting volume of ≈ 109AU3,B′ ≈ 50G, ambient proton energy density u′P ≈ 102 ergcm−3 and η ≈ 0.8 . Fig. 1 shows the relevant time scales.The clear dominance of the proton synchrotron radiation athigh energies is apparent, while pion production is rather ofminor importance. The proton spectrum is cut off at γ′p ≈1010.5 due to proton synchrotron radiation. Significant π±synchrotron losses do not occur below the proton cutoff, whileµ± synchrotron radiation cannot be neglected.The LBL PKS 0716+714 has been chosen for its well-defined low-energy synchrotron component (Ghisellini et al.,1998). Again, the same power-law spectral indices has beenused as before to represent this component, a lab-frame breakenergy ǫb ≈ 0.7 eV and cutoff energy ǫc ≈ 3.5 keV. Ourmodel parameters used are: u′phot ≈ 1011 eV/cm3, D ≈ 7,R′ ≈ 1017cm, B′ ≈ 30G, u′p ≈ 40 erg cm−3 and η ≈ 10−2.In this environment, losses due to photo-meson productionlimit the injection proton spectrum to about γp,max ≈ 109(see Fig. 2). With proton synchrotron radiation being ratherunimportant here, photo-pion production dominates the elec-tromagnetic energy output, and is responsible for a strongerneutrino flux than in the HBL case (see Sect. 4). Due to thelow cutoff of the proton spectrum, pion synchrotron radiationFig. 1. Mean (jet frame) energy loss and acceleration time scalesfor the HBL Mkn 421 as modeled in Mu¨cke et al. (in prep.): pi-photoproduction (pi), Bethe-Heitler pair production (e+e−) andproton synchrotron radiation (syn); pi±- and µ± for synchrotronradiation (syn pi, syn µ) are also shown and compared with theirmean decay time scales (decay pi, decay µ). The acceleration timescale (acc) is indicated as a thick straight line. Model parametersare: B′ = 50 G, D = 10, R′ ≈ 1016 cm, u′phot = 2 × 109 eVcm−3, u′p ≈ 100 erg cm−3, γ′p,max = 3× 1010, η = 0.8.can again be neglected.Our modeling seems to favour the hypothesis that the lowluminosities observed from HBLs might be due to an intrin-sically low jet-frame target photon density while the more lu-minous LBLs may possess rather intrinsically high jet-frametarget photon fields. The consequences of this hypothesis forthe Synchrotron-Proton Blazar model will be presented else-where (Mu¨cke et al., in prep.).4 Neutrino SpectraHadronic blazar models produce neutrino emission mainlythrough the production and decay of charged mesons, e.g.π± → µ±+ νµ/ν¯µ followed by µ± → e±+ νe/ν¯e+ νµ/ν¯µ.The neutrinos escape without further interaction.Fig. 3 shows the predicted neutrino output from Mkn 421,which is considered as a typical HBL, and the typical LBLPKS 0716+714. We give the predicted neutrino emissionfrom the objects themselves, and do not consider here anyadditional contribution from escaping cosmic rays interact-ing while propagating through the cosmic microwave back-ground radiation.The clear dominance of neutrino emission from LBLs incomparison to HBLs is obvious. The reason for this is thehigher meson production rate in the LBL source population(see also Fig. 1 and 2) due to their higher target photon fieldsin comparison to the HBL population.The proton injection spectrum is modified by photohadroniclosses. For Mkn 421 the photopion production rate approx-imately follows a broken power law, t−1pi ∝ γ1.25p for pro-3Fig. 2. Mean (jet frame) energy loss and acceleration time scalesfor the LBL PKS 0716+714 as modeled in Mu¨cke et al. (in prep.).Annotations are the same as in Fig. 1. Model parameters are: B′ =30 G, D ≈ 7, R′ ≈ 1017 cm, u′phot = 4× 1011 eV/cm3, u′p = 40erg/cm−3, γ′p,max = 3× 109, η ≈ 10−2.ton energies below ∼ 107 GeV, and ∝ γ0.5p above E′p ∼107 GeV (see Fig. 1) due to the break in the target photonspectrum. This leads to a break in the neutrino spectrumat ∼ 107 GeV (observer frame), from power spectral indexαν ≈ 1.25 to αν ≈ 0.5 ((E2dN/dE) ∝ Eαν ). The cut-off at ∼ 109 GeV in the observer’s frame is caused by µ±-synchrotron losses, whereas π±-synchrotron emission turnsout to be unimportant. Another important source of high en-ergy neutrinos is the production and decay of charged kaonsif the proton-photon interaction takes place predominantly inthe secondary resonance region of the cross section (Mu¨ckeet al., 2000). This might be the case for HBLs because theirtarget photon field can extend up to X-ray energies. Thepositively charged kaons decay in ∼ 64% of all cases intomuons and direct high energy muon-neutrinos. In contrastto the neutrinos originating from π± and µ±-decay, thesemuon-neutrinos will not have suffered energy losses throughπ±- and µ±-synchrotron radiation, and therefore appear asan excess in comparison to the remaining neutrino flavors atthe high energy end (Eν ≈ 109–1010 GeV) of the emergingneutrino spectrum, and in addition cause the total neutrinospectrum to extend to ∼ 1010 GeV.In contrast, the neutrino emission from PKS 0716+714 iscutoff at∼ 109 GeV (observer frame) for all neutrino flavors(see Fig. 3) due to a roughly one order of magnitude lowerproton cutoff. Also µ± synchrotron losses may play a rolehere. The neutrino spectrum follows a power law with indexαν ≈ 1.25 below the cutoff, and is caused by photohadronicinteractions with the target photon field above ǫ′b. Because ofthe π-production threshold and the relatively low proton cut-off in LBLs, meson production in the photon field below ǫ′bcannot occur, leading to a simple power law for the neutrinospectrum.The photon-hadron interactions for both, LBLs and HBLs,take place predominantly in the resonance region. Here, π−,and thus ν¯e production is suppressed (see Fig. 3).Previous hadronic jet models expected equal photon andneutrino energy fluxes (e.g. Mannheim (1993)). Our modelpredicts for HBLs a peak neutrino energy flux approximatelytwo to three orders of magnitude lower than high energygamma rays (qγν ≈ 102...3), while for LBLs the neutrino andgamma ray output is approximately comparable (qγν ≈ 1).5 Diffuse neutrino backgroundFrom inspecting Fig. 3 it is immediately clear that LBLswould dominate the BL Lac contribution to the diffuse neu-trino background unless HBLs turn out to be significantlymore numerous than LBLs.A commonly used method to estimate the diffuse neutrinobackground due to unresolved blazars is to determine the ra-tio gamma ray to neutrino emission, qγν , in the objects inquestion, and then normalize to the observed extragalacticgamma ray background (e.g. Mannheim (1995)). The dif-ferent photon to neutrino ratio we found in HBLs and LBLsleads to various implications for the diffuse neutrino emis-sion.The extragalactic diffuse gamma ray background (EGRB)as detected by EGRET is (1.45±0.05)×10−5 photons cm−2s−1 sr−1 above 100 MeV (Sreekumar et al., 1998). Thus, theextragalactic neutrino background (ENB) due to unresolvedEGRET blazars can be estimated by: (E2dN/dE)ENB ≈7.4(1 + f)qsq−1γν × 10−7 GeV cm−2 s−1 sr−1 where f <1 is the fraction of photon power lost in the cosmic back-ground matter and radiation field, and qs ≈ 0.25 is the pre-sumed blazar contribution to the EGRET EGRB (Chiang &Mukherjee, 1998). Propagation of gamma rays at ≤ 100GeV is relatively unattenuated, and is therefore comparableto neutrino propagation, so we set f = 0. Since LBLs areEGRET-sources, and with qγν ≈ 1, a diffuse neutrino fluxof (E2dN/dE)ENB ≈ 2 × 10−7 GeV cm−2 s−1 sr−1 fol-lows if LBLs dominate the blazar contribution to the EGRETdiffuse gamma ray background. This is slightly above theneutrino upper bound derived using cosmic ray constraintsby Waxman & Bahcall (1999) and Mannheim, Protheroe &Rachen (2001) for optically thin sources, but well below theupper bound for optically thick sources. Thus, we concludethat either LBLs do not dominate the blazar contribution tothe EGRET EGRB, or LBLs are rather thick sources (likequasars).Our estimate of the ENB due to HBLs follows a similarprocedure. Since HBLs emit, however, most of their pho-ton power at TeV-energies, we extrapolate the E−2.1 EGRBspectrum as observed by EGRET up to 25 TeV, the highestenergy observed from any HBL, to estimate the unattenu-ated EGRB flux in the ≥ 100 GeV energy range. The re-sulting ENB from HBLs is then (E2dN/dE)ENB ≈ 3qs ×(10−9 . . . 10−10) GeV cm−2 s−1 sr−1, where qs is here theHBL contribution to our estimated diffuse TeV-background.Even for qs = 1 the predicted ENB intensity lies several4Fig. 3. Predicted neutrino spectra for the HBL Mkn 421 (lower curves)and the LBL PKS 0716+714 (upper curves) as modeled in Mu¨cke et al. (inprep.).orders of magnitude below the neutrino upper bounds (Wax-man & Bahcall 1999; Mannheim et al. 2001, MPR), and isalso lower than the estimate from MPR of the BL Lac contri-bution to the ENB using the observed XBL luminosity func-tion. Note, however, that MPR assumed pion photoproduc-tion was the main proton loss process, whereas in the SPBmodel for HBLs proton synchrotron losses dominate at theexpense of pion (and neutrino) production. The same is truefor Mu¨cke et al. (1999), where one to two order of magnitudehigher contribution from TeV-blazars to the diffuse neutrinobackground was estimated in comparison to this work.6 SummaryNeutrino production spectra of BL Lac objects are calculatedin the framework of the Synchrotron-Proton Blazar model(Mu¨cke & Protheroe, 2001) using the SOPHIA event gener-ator for photomeson production (Mu¨cke et al., 2000). Theν spectra presented here for Mkn 421 and PKS 0716+714,typical of HBLs and LBLs, respectively, are modeled usinga parameter set which reproduces well the average SED ofthose blazars. We find higher pion production rates for LBLsin comparison to the HBLs, and this leads a higher neutrinooutput for a typical LBL by∼ 106 compared to HBLs. Muonsynchrotron losses are responsible for a spectral cutoff in theneutrino SED at ∼ 1018 eV, with a possible extension of νµsup to ∼ 1019 eV, due to kaon decay.The total power deposited in gamma rays and neutrinos isapproximately equal for LBLs, while a two to three order ofmagnitude smaller neutrino peak flux is predicted in HBLs incomparison to their peak photon power. This leads to a sig-nificantly higher LBL contribution to the extragalactic dif-fuse neutrino background than from HBLs, when the methodof normalizing to the observed EGRB is used for estimatingthe diffuse neutrino flux.Acknowledgements. AM acknowledges a postdoctoral bursary fromthe Que´bec Government. The research of RJP is funded by a grantfrom the Australian research Council.ReferencesChiang J. & Mukherjee R., ApJ, 496, 752, 1998.Ghisellini G. et al., MNRAS, 301, 451, 1998.Mannheim K., A&A, 269, 67, 1993.Mannheim K., Astropart.Phys., 3, 295, 1995.Mannheim K., Protheroe R.J. & Rachen J.P., Phys. Rev. D, 63,023003, 2001. (MPR)Mu¨cke A., Engel R.R., Protheroe R.J., Rachen J.P. & Stanev T.,in: Proc. 26th Int. Cosmic Ray Conf., Salt Lake City/Utah, 236,1999.Mu¨cke A., Engel R.R., Rachen J.P., Protheroe R.J.& Stanev T.,Comm.Phys.Comp., 124, 290, 2000.Mu¨cke A. & Protheroe R.J., Astropart. Phys., 15, 121, 2001.Mu¨cke A., Protheroe R.J., et al., in preparationPadovani P. & Giommi P., ApJ, 444, 567, 1995.Rachen J.P. & Me´sza´ros P., Phys. Rev. D, 58, 123005, 1998.Sreekumar P. et al., ApJ, 494, 523, 1998.Waxman E. & Bahcall J., Phys. Rev. D, 59, 023002, 1999.

Neutrino Emission from HBLs and LBLs

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