On high-energy particles in accretion disk coronae of supermassive black holes: implications for MeV gamma rays and high-energy neutrinos from AGN cores
Yoshiyuki Inoue, Dmitry Khangulyan, Susumu Inoue, Akihiro Doi
DDraft version June 5, 2019
Typeset using L A TEX twocolumn style in AASTeX62
On high-energy particles in accretion disk coronae of supermassive black holes:implications for MeV gamma rays and high-energy neutrinos from AGN cores
Yoshiyuki Inoue,
1, 2
Dmitry Khangulyan, Susumu Inoue, and Akihiro Doi
4, 5 Interdisciplinary Theoretical & Mathematical Science Program (iTHEMS), RIKEN, 2-1 Hirosawa, Saitama 351-0198, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583,Japan Department of Physics, Rikkyo University, Nishi-Ikebukuro 3-34-1, Toshima-ku, Tokyo 171-8501, Japan Institute of Space and Astronautical Science JAXA, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan Department of Space and Astronautical Science, The Graduate University for Advanced Studies (SOKENDAI),3-1-1 Yoshinodai,Chuou-ku, Sagamihara, Kanagawa 252-5210, Japan
Submitted to ApJABSTRACTRecent observations with ALMA have revealed evidence for non-thermal synchrotron emission fromthe core regions of two nearby Seyfert galaxies. This suggests that the coronae of accretion disks inactive galactic nuclei (AGNs) can be conducive to the acceleration of non-thermal electrons, in additionto the hot, thermal electrons responsible for their X-ray emission through thermal Comptonization.Here we investigate the mechanism of such particle acceleration, based on observationally inferredparameters for AGN disk coronae. One possibility to account for the observed non-thermal electronsis diffusive shock acceleration, as long as the gyrofactor η g does not exceed ∼ . These non-thermalelectrons can generate gamma rays via inverse Compton scattering of disk photons, which can appearin the MeV band, while those with energies above ∼
100 MeV would be attenuated via internal γγ pairproduction. The integrated emission from all AGNs with thermal and non-thermal Comptonizationcan reproduce the observed cosmic background radiation in X-rays as well as gamma-rays up to ∼
10 MeV. Furthermore, if protons are accelerated in the same conditions as electrons and η g ∼ Keywords: accretion, accretion disks — black hole physics — galaxies: active — (galaxies:) quasars:supermassive black holes — acceleration of particles — neutrinos INTRODUCTIONActive galactic nuclei (AGNs) are powered by massaccretion onto supermassive black holes (SMBHs). Theyemit intense electromagnetic radiation in broad rangeof frequencies. Measurements of X-ray spectra of AGNsallow us to study various aspect of SMBHs such as blackhole spins (e.g., Reynolds 2014), geometrical structures(e.g., Ramos Almeida & Ricci 2017), and cosmologicalevolution (e.g., Ueda et al. 2014).A key for understanding these phenomena is primaryX-ray radiation of the accretion disk which arises fromComptonization of disk photons in moderately thickthermal plasma, namely coronae, above an accretion [email protected] disk (see, e.g., Katz 1976; Bisnovatyi-Kogan & Blin-nikov 1977; Pozdniakov et al. 1977; Galeev et al. 1979;Takahara 1979; Sunyaev & Titarchuk 1980). X-ray ob-servations have indicated the coronal temperature of ∼ K and the Thomson scattering opacity of (cid:38) ∼
10 G witha size of 40 R s , where R s is the Schwartzschild radius, forboth active SMBHs with a mass of ∼ M (cid:12) . It is alsofound that coronae of Seyferts contain both thermal and a r X i v : . [ a s t r o - ph . H E ] J un Inoue et al. non-thermal electrons. This implies that acceleration ofhigh energy particles happens in AGN coronae.High energy particles in the nuclei of Seyferts havebeen discussed for a long time . In the past, it wasargued that primary X-ray emission comes from paircascades induced by high energy particles acceleratedin and/or around accretion flows (e.g., Zdziarski 1986;Kazanas & Ellison 1986; Ghisellini et al. 2004). In thepair cascade model, particles are accelerated by shockdissipation in accretion flows (e.g., Cowsik & Lee 1982;Protheroe & Kazanas 1983; Zdziarski 1986; Kazanas &Ellison 1986; Sikora et al. 1987; Begelman et al. 1990).However, the detection of the AGN spectral cutoffs (e.g.,Madejski et al. 1995; Zdziarski et al. 2000) and non-detection of Seyfert AGNs in the gamma-ray band (e.g.,Lin et al. 1993) ruled out the pair cascade scenario as adominant source for the primary X-ray emission .In this paper, we investigate the production mecha-nism of the observed high energy particles in AGN coro-nae. As an example, we consider those high energy par-ticles are supplied by diffusive shock acceleration (DSA)processes (e.g., Drury 1983; Blandford & Eichler 1987)in the coronae. Contrary to the previously discussedAGN accretion shock models, the required shock poweris much lower in order to explain the observed non-thermal species and to be in concordance with the cur-rent picture of coronal X-ray emission. Moreover, pre-vious studies of high energy particles in AGN accretiondisks have treated as free parameters corona size andmagnetic field, which are important parameters for theunderstandings of particle acceleration. The ALMA ob-servations allowed us to determine both of them (Inoue& Doi 2018). Most critically, the observationally de-termined strength of the magnetic field appeared to besignificantly smaller than the one previously consideredin the literature. We take into account these newly de-termined coronal parameters.Thermal coronal emission from Seyferts is known toexplain the entire cosmic X-ray background radiation(e.g., Ueda et al. 2014). In contrast, the origin of the cos-mic MeV background radiation from 0.1 MeV to severaltens MeV is still unknown (see e.g., Inoue 2014). Here,the non-thermal electrons in coronae seen by ALMA willinvoke power-law MeV gamma-ray emission via Comp-tonization of disk photons. Such non-thermal emission issuggested as a possible explanation for the cosmic MeVgamma-ray background radiation (Inoue et al. 2008).However, non-thermal electron species in the previous High energy particles in the coronae of X-ray binaries havebeen also discussed in literature (e.g., Bhattacharyya et al. 2003,2006). TeV gamma rays are measured from the Galactic center(HESS Collaboration et al. 2016). This detection indicated possi-ble particle acceleration in accretion flow, even though accretionrate in the Galactic center is several orders of magnitude lowerthan that in standard disks. work were included in an ad hoc way. In this work, we re-visit the contribution of Seyferts to the MeV gamma-raybackground radiation by considering the particle accel-eration of non-thermal populations in coronae togetherwith the latest X-ray luminosity function of Seyferts(Ueda et al. 2014).High energy particles around accretion disks ofAGNs also generate intense neutrino emission throughhadronuclear ( pp ) and photomeson ( pγ ) interaction pro-cesses by interacting accreting gas and photon fields(e.g., Eichler 1979; Begelman et al. 1990; Stecker et al.1992; Alvarez-Mu˜niz & M´esz´aros 2004). Although theseoriginally predicted fluxes have been significantly con-strained by high energy neutrino observations (TheIceCube Collaboration 2005), recent studies have re-visited the estimated fluxes and found that AGN coremodels are still viable (Stecker 2005, 2013; Kalashevet al. 2015). However, normalization of neutrino fluxesfrom AGNs and acceleration properties of high energyparticles in those models are assumed to match with theobservation. In this work, we also discuss the possiblecontribution from AGN cores given our ALMA observa-tions and investigate the required parameter spaces forthe explanation of the IceCube diffuse neutrino fluxes.We describe general particle acceleration processes inAGN coronae in §
2. The broadband emission spectrumof the central region of AGNs and physical properties ofAGN coronae are presented in §
3. Relevant timescalesand steady-state particle spectra are discussed in § §
5, respectively. § § §
8, and conclusions are in § h, Ω M , Ω Λ ) = (0 . , . , . PARTICLE ACCELERATION IN NUCLEI OFSEYFERTSAs non-thermal coronal synchrotron emission is seenin nearby Seyferts (Inoue & Doi 2018), particle acceler-ation should occur in AGN coronae, even though ther-mal populations are energetically dominant. Particleacceleration mechanism in the coronae is highly uncer-tain. Various acceleration mechanisms can take place inthe coronae such as DSA mechanism (e.g., Drury 1983;Blandford & Eichler 1987), turbulent acceleration (e.g.,Zhdankin et al. 2018), magnetosphere acceleration (e.g.,Beskin et al. 1992; Levinson 2000), and magnetic recon-nection (e.g., Hoshino & Lyubarsky 2012). In this work,for simplicity, we consider the DSA as the fiducial par-ticle acceleration process. We discuss the other possibleacceleration processes in § n the high energy particles in massive black hole coronae R c ≡ r c R s . r c is the dimensionless parameter of thecorona size and R s = 2 GM BH /c , where G is the gravi-tational constant, M BH is the mass of the central SMBH, c is the speed of light. Coronae are also set to be in asteady state. We also do not consider positrons in coro-nae. Thus, the proton number density n p is equal tothe electron density n e in this work, which gives themaximum number of protons in coronae. n e is definedthrough the Thomson scattering opacity in coronae, τ T as n e = τ T σ T R c (1) (cid:39) . × (cid:16) τ T . (cid:17) (cid:16) r c (cid:17) − (cid:18) M BH M (cid:12) (cid:19) − cm − , where σ T is the Thomson scattering cross section.2.1. Dynamical Timescale
The gas is assumed to be spherically accreted on to theSMBH with free-fall velocity v ff = (cid:112) GM BH /R c . Thefree-fall timescale from the coronal region is estimatedto be t fall = R c /v ff (cid:39) . × (cid:16) r c (cid:17) / (cid:18) M BH M (cid:12) (cid:19) [s] . (2)2.2. Radiative Cooling
High energy particles loose their energies through ra-diative cooling processes. In AGN coronae, high-energyelectrons mainly lose their energies via synchrotron andinverse Compton (IC) radiation. The synchrotron cool-ing rate for an electron with a Lorentz factor of γ e is t syn ,e ( γ e ) = 34 m e cσ T U B γ − e , (3) (cid:39) . × (cid:18) B
10 G (cid:19) − (cid:16) γ e (cid:17) − [s] , where m e is the electron rest mass and U B = B / π is the magnetic field energy density of magnetic fieldstrength B .The inverse Compton cooling rate including theKlein–Nishina (KN) cross section (Jones 1968; Mod-erski et al. 2005; Khangulyan et al. 2014) is t IC ( γ e ) = 3 m e c σ T ∞ (cid:90) d(cid:15)f KN (˜ b ) U ph ( (cid:15) ) (cid:15) − γ − e , (4) where ˜ b ≡ γ e (cid:15)/m e c and f KN (cid:39) / (1 . b ) (Moderskiet al. 2005). (cid:15) is the target photon energy and U ph is thephoton energy density given as U ph ( (cid:15) ) = L ph ( (cid:15) ) / πR c c .The total AGN disk luminosity, L ph , which includes con-tribution from the accretion disk and corona, is definedin § ∼ .
24 on average (Atoyan & Aharonian 1996).For the typical characteristics of the coronae, the en-ergy density of the photon field is U ph , tot = (cid:90) d(cid:15) U ph ( (cid:15) ) (5) ∼ × L ph , bol × erg s − (cid:16) r c (cid:17) − (cid:18) M BH M (cid:12) (cid:19) − [erg cm − ] . For the magnetic field strength inferred with ALMA, B (cid:39)
10 G for M BH = 10 M (cid:12) SMBHs, the energy den-sity of the photon field exceeds the magnetic field energydensity if L ph , bol ≥ × erg s − . We note that thedominance of photon fields over magnetic field does notnecessary prevents particle acceleration as such condi-tions are met in some efficient non-thermal sources, e.g.,in gamma-ray binary systems (Aharonian et al. 2006;Khangulyan et al. 2008). Moreover, high density of tar-get photons can enable the converter acceleration mech-anism if a relativistic velocity jump present in the system(Derishev et al. 2003).Relativistic protons are predominately cooled thoughinelastic pp interactions, pγ reactions, and protonIC/synchrotron channels. Since only the Thomsonregime might be relevant for the proton IC cooling,the proton synchrotron and IC cooling time-scales are t IC / syn ,p = 34 (cid:18) m p m e (cid:19) m e c cσ T U ph / B γ − p , (6)where m p is the proton rest mass and γ p is the protonLorentz factor. In the case of the synchrotron losses,this yields t syn ,p (cid:39) . × (cid:18) B
10 G (cid:19) − (cid:16) γ p (cid:17) − [s] . (7)Given the higher energy density of the photon field, theIC cooling time can be up to ∼ times faster. Theseelectrodynamic cooling channels are inefficient as com-pared to the hardronic mechanisms below. Hereinafter,we do not consider proton IC/synchrotron coolings.The pp cooling time can be expressed as t pp = 1 n p σ pp cκ pp , (8) (cid:39) . × (cid:16) τ T . (cid:17) − (cid:16) r c (cid:17) (cid:18) M BH M (cid:12) (cid:19) [s] . Inoue et al. where κ pp ∼ . σ pp = 3 × − cm . Below we adopt theformalism developed by Kelner et al. (2006). The totalcross section of the inelastic pp process σ pp is representedas a function of the proton energy E p = γ p m p c , σ pp (cid:39) (9) (cid:16) . . L + 0 . L (cid:17) (cid:34) − (cid:18) E pp, thr E p (cid:19) (cid:35) mbfor E p ≥ E pp, thr , where 1 mb = 10 − cm , L =log( E p / E pp, thr = 1 .
22 GeV (Kelner et al.2006).The pγ cooling time via photomeson interactions is t − pγ = c γ p ∞ (cid:90) ¯ ε thr d ¯ εσ pγ (¯ ε ) K pγ (¯ ε )¯ ε ∞ (cid:90) ¯ ε/ (2 γ p ) d(cid:15) U ph ( (cid:15) ) (cid:15) , (10)where ¯ ε and (cid:15) are the photon energy in the protonrest frame and the black hole frame, respectively, U ph is the energy density of the photon target, and ¯ ε thr =145 MeV. For numerical calculation we follow the for-malism suggested by Kelner & Aharonian (2008).The pγ interaction also generates pairs, so-called theBethe-Heitler pair production process and its coolingtimescale is approximated as (Gao et al. 2012) t − ≈ m e c ) α f σ T c √ πm p c γ p (cid:90) ∞ m e c /γ p d(cid:15) U ph ( (cid:15) ) (cid:15) (11) × (cid:40)(cid:18) γ p (cid:15)m e c (cid:19) / (cid:20) log (cid:18) γ p (cid:15)m e c (cid:19) − / (cid:21) + 2 / (cid:41) , where α f is the fine-structure constant.2.3. Acceleration
In the frame work of DSA (e.g., Drury 1983; Bland-ford & Eichler 1987), the acceleration time scale can beapproximated as t DSA (cid:39) η acc D ( E CR ) v sh , (12)where D is the diffusion coefficient, E CR is the particleenergy, and v sh is the shock speed. η acc is a numericalfactor that depends on the shock compression ratio andthe spatial dependence of D (Drury 1983). We set η acc =10. Assuming a Bohm-like diffusion, D ( E CR ) (cid:39) η g cE CR eB , (13)where e is the electric charge and η g is the gyrofactorwhich is the mean free path of a particle in units ofthe gyroradius. η g characterizes the efficiency of the acceleration. η g = 1 corresponds to the Bohm limitcase. The DSA time can be written as t DSA (cid:39) η g cR g v sh , (14) (cid:39) . × − (cid:16) η g (cid:17) (cid:18) m p/e m e (cid:19) (cid:16) r c (cid:17) (cid:18) B
10 G (cid:19) − (cid:16) γ p/e (cid:17) [s] . where R g is the gyro radius and v sh is set as v ff ( R c ). η g varies in different astrophysical environments. η g ∼ η g ∼ is seen in thecase of blazars in the framework of one-zone leptonicmodels (e.g., Inoue & Takahara 1996; Finke et al. 2008;Inoue & Tanaka 2016). PROPERTIES OF ACTIVE SUPERMASSIVEBLACK HOLESIn this section, we summarize the general observa-tional properties of the central region of AGNs relatedto high-energy particles in coronae.3.1.
Broadband Emission from the Core Region
Emission from the AGN core region mainly arises fromtwo components (Elvis et al. 1994). First is the geo-metrically thin and optically thick standard accretiondisks (Shakura & Sunyaev 1973). This standard ac-cretion disk generates a big blue bump from opticalto UV attributed by multi-color blackbody radiation.Second is the Comptonized accretion disk photons fromthe coronal regions above the accretion disk (Katz 1976;Bisnovatyi-Kogan & Blinnikov 1977; Pozdniakov et al.1977; Sunyaev & Titarchuk 1980). This Comptonizedemission appears in the X-ray band together with emis-sion reprocessed by the surrounding cold materials, aso-called Compton reflection component (e.g., Lightman& White 1988; Magdziarz & Zdziarski 1995; Ricci et al.2011).In this work, for the primary X-ray emission fromcoronae, we assume a cut-off power-law model in theform of E − Γ exp( E/E c ), where we set Γ = 1 . E c = 300 keV (Ueda et al. 2003, 2014). For the Comp-ton reflection component, we use the pexrav modelMagdziarz & Zdziarski (1995) assuming a solid angleof 2 π , an inclination angle of cos i = 0 .
5, and the so-lar abundance for all elements. Since we consider thephotons only around the core regions, we ignore the ab-sorption by torus.The optical-UV accretion-disk spectral energy distri-butions (SEDs) are taken from Elvis et al. (1994). Here,the primary 2 keV X-ray disk luminosity is connected tothe accretion-disk luminosity at 2500 ˚A aslog L = 0 .
760 log L ˚ A + 3 .
508 (15)based on the study of 545 X-ray selected type 1 AGNsfrom the XMM-COSMOS survey (Lusso et al. 2010). n the high energy particles in massive black hole coronae [Hz]10 L [ e r g / s ] log L = 46log L = 44log L = 42 Figure 1.
The typical broadband spectral energy distri-bution arising from the core region of AGNs. From top tobottom, each curve corresponds to 2-10 keV luminosity of10 , 10 , 10 erg s − , respectively. Between UV and X-ray, following Lusso et al. (2010),we linearly connect the UV luminosity at 500 ˚A to theluminosity at 1 keV. Figure 1 shows the broadband AGNSED arising from the core region for various X-ray lumi-nosities. AGN core SEDs typically have a spectral peakat ∼
30 eV corresponding to ∼ K (Fig. 1), whichcorresponds to the emission radius at around ∼ R s .3.2. Physical Properties of Coronae
X-ray spectral studies allow us to determine someof the coronal parameters such as the coronal electrontemperature kT e and the Thomson scattering opticaldepth τ T (e.g., Brenneman et al. 2014). k is the Boltz-mann constant and T e is the electron temperature inKelvin. The spectral cutoff at ∼
300 keV of AGNcore spectra corresponds to the electron temperature of kT e ∼
100 keV. The process of Comptonization by ther-mal plasma is described by the Kompaneets equation(Kompaneets 1957). Here, the photon index of the pri-mary emission is assumed to be 1.9 in this work. Thiscorresponds to τ T ∼ . (cid:115)
94 + 1 θ e [ τ T ( τ T + 1 / − , (16)where the dimensionless electron temperature θ e ≡ kT e /m e c . Therefore, in this work, we adopt kT e =100 keV and τ T = 1 .
1. These values are consistent withthe results from detailed X-ray spectral analysis (e.g.,Fabian et al. 2015).Recently, utilizing X-ray and radio data, Inoue & Doi(2018) found that the coronal magnetic field strength B is approximately 10 Gauss on scales of ∼ R s from theSMBHs for two nearby Seyferts whose BH masses are ∼ M (cid:12) . This coronal size is consistent with optical–X-ray spectral fitting studies (Jin et al. 2012) and mi-corolensing observation (Morgan et al. 2012). Thus, inthis paper, we set the coronal size as 40 R s for all SMBHsand B = 10 G for 10 M (cid:12) SMBHs.Inoue & Doi (2018) also suggested that the coronae arelikely to be advection heated hot accretion flows (Katoet al. 2008; Yuan & Narayan 2014) rather than magneti-cally heated corona (Haardt & Maraschi 1991; Liu et al.2002) because the measured magnetic field strength istoo weak to keep the coronae hot and is rather consistentwith the value based on the self-similar solutions of hotaccretion flows (Kato et al. 2008; Yuan & Narayan 2014).Thus, we assume that coronal magnetic field strengthscales as B ∝ M − / BH , (17)following the self-similar solution for the hot accretionflow (Yuan & Narayan 2014) where we ignore depen-dence on accretion rate and other parameters for sim-plicity.Mayers et al. (2018) have recently investigated a re-lation between the intrinsic 2–10 keV X-ray luminosityand the mass of central SMBHs using AGNs from theXMM-Newton Cluster Survey. The empirical relationfound in Mayers et al. (2018) is given as M BH = 2 × M (cid:12) (cid:20) L −
10 keV . × erg s − (cid:21) . . (18)Using this relation, we can convert X-ray luminositiesto masses of central SMBHs.3.3. Internal Gamma-ray Attenuation in Coronae
Accelerated electrons and protons in coronae wouldemit gamma rays (see § γγ → e + e − ) with low-energy photons. For isotropic target photons the pairproduction cross section achieves its maximum of ≈ . σ T when a gamma-rays of energy E γ interacts witha low-energy photon with energy (see, e.g., Aharonian2004) (cid:15) peak (cid:39) . m e c E γ (cid:39) (cid:18) E γ (cid:19) eV . (19)In terms of wavelength, λ peak (cid:39) . E γ [TeV]) µ m.Abundant photons are emitted from the AGN coreregion (Fig. 1). From the SED of AGN core regions asgiven in § γγ pair production interactions. Contrary to this observational result, recent numerical simu-lations of the hot accretion flows (e.g., Kimura et al. 2019) showsthe magnetic field enhanced more by the magnetorotational insta-bility (MRI; Balbus & Hawley 1991, 1998).
Inoue et al. Photon Energy [GeV]10 I n t e r na l G a mm a -r a y O p t i c a l D ep t h log L = 46log L = 44log L = 42 Figure 2.
Internal gamma-ray optical depth in the core re-gion of AGNs. From top to bottom, each curve correspondsto 2-10 keV luminosity of 10 , 10 , 10 erg s − , respec-tively. The horizontal dot-dashed line represents τ γγ = 1. The cross section for this process is (Breit & Wheeler1934; Heitler 1954) σ γγ ( E γ , (cid:15), θ ) = 3 σ T
16 (1 − β ) × (cid:20) β ( β −
2) + (3 − β ) ln (cid:18) β − β (cid:19)(cid:21) , (20)where β is β ≡ (cid:115) − m e c (cid:15)E γ (1 − µ ) ; µ ≡ cos θ. (21)where θ is the angle between the colliding photons’ mo-menta.For a photon with an energy of E γ , the γγ opticaldepth is τ γγ ( E γ ) = (cid:90) − dµ ∞ (cid:90) (cid:15) th d(cid:15) − µ U ph ( (cid:15) ) (cid:15) σ γγ ( E γ , (cid:15), θ ) R c (22)where (cid:15) th is the pair production threshold energy, (cid:15) th = 2 m e c E γ (1 − µ ) . (23)Integration over the interaction angle in Eq. (22) can beperformed analytically resulting in the angle averaged γγ cross section (Aharonian 2004): σ γγ = 3 σ T s (cid:20)(cid:18) s + 12 ln s −
16 + 12 s (cid:19) ln( √ s + √ s − − (cid:18) s + 49 − s (cid:19) (cid:114) − s (cid:35) , (24) where s = E γ (cid:15)/m e c .Figure 2 shows the internal gamma-ray optical depthin the core region for various X-ray luminosities. Thecore region is expected to be optically thick againstgamma-ray photons above 10–100 MeV depending ondisk luminosities. Such high optical thicknesses againstpair production in AGN coronae are well known (e.g.,Bonometto & Rees 1971; Done & Fabian 1989; Fabianet al. 2015) based on the compactness parameter argu-ment (Guilbert et al. 1983). TIMESCALESGiven the observed properties of AGN core regions, wecan estimate the various timescales of high energy par-ticles in the coronae. Figure 3 shows the cooling ratesof electrons in the coronae for different energy-loss pro-cesses, together with the acceleration rate and the free-fall timescale following § §
3. We set η g = 30 in the figure, which reproduces theIceCube neutrino background fluxes as discussed laterin §
7. Each panel corresponds to 2-10 keV X-ray lumi-nosity of 10 , 10 , 10 erg s − .Due to the intense broadband radiation field, the cool-ing is dominated by the Compton cooling. However, athigher energy regions, the main cooling channel is re-placed by synchrotron cooling because of the KN effect.The more luminous AGNs tend to have more efficientIC cooling effect, as the target photon density increases.When we assume η g = 30, electron acceleration up to γ e ∼ ( ∼
50 GeV) is feasible in AGN coronae atvarious luminosities. Therefore, synchrotron radiationthrough coronal magnetic fields and gamma-ray emis-sion by Comptonization of disk photons are naturallyexpected in AGN coronae.ALMA spectra of two nearby Seyferts, whose X-rayluminosities are about 10 erg s − , extends their radiosynchrotron power-law spectra at least up to 230 GHz,which corresponds to γ e ∼
80 given the magnetic fieldstrength of 10 G (Inoue & Doi 2018) . As shown in thetop right panel (the case of log L X = 44) in Fig. 3,relativistic electrons with γ e ∼
80 seen by ALMA canbe easily accelerated in AGN coronae. Notably, suchelectrons can be accelerated even by a low efficiency ac-celeration process, e.g., with η g ∼ . For this energy,Compton cooling is the dominant energy loss process.As the cooling timescale for γ e ∼
80 is about 100 s, fluxvariability in the radio synchrotron emission is expected,some Seyferts are already known to show a flux varia-tion at least in day scales (Baldi et al. 2015). Furtherdense light curve observations may see shorter timescalevariabilities. This frequency limit is due to the instrumental coverage of theALMA band-6 receiver. Therefore, the emission itself is likely toextend to higher frequencies, even though those emission signalswould be buried in thermal dust emission. n the high energy particles in massive black hole coronae e T i m e sc a l e [ s ] log L X = e T i m e sc a l e [ s ] log L X = e T i m e sc a l e [ s ] log L X = t acc ( g = 30) t syn t IC t cool t fall Figure 3.
Electron energy losses in AGN coronae together with acceleration and dynamical timescales. Each panel correspondsto different 2–10 keV X-ray luminosity as indicated in panels. Thin solid line shows the acceleration timescale assuming DSA.Dashed, dotted, and thick solid curve corresponds to synchrotron cooling, IC cooling, and total cooling timescale, respectively.Dot-dashed curve shows the free-fall timescale. In these plots, we set τ T = 1 . R c = 40 R s , kT e = 100 keV, and η g = 30. Wenote that the vertical axis ranges are different in each panel. Similar to Fig. 3 for electrons, Fig. 4 shows thetimescales for high energy for various luminosities. Asin Fig. 3, we set η g = 30. Since synchrotron and Comp-ton cooling are not effective for protons in our case, wedo not show these timescales in the figure.It is evident that protons can be accelerated up to γ p ∼ ( ∼ L X < erg s − ), acceleration is limited by the dy-namical timescale rather than radiative cooling, while itbecomes limited by the Bethe-Heitler cooling for higherluminosity objects. As the luminosity increases, pγ andBethe-Heitler cooling effects become more prominent.At higher luminosities, the Bethe-Heitler processes dom-inate the energy loss process of high energy particles.Therefore, in cases of high luminosity objects, resultinghadronic gamma-ray and neutrino spectra in the TeVband will show spectral suppression due to the Bethe-Heitler processes (see e.g., Murase 2008, for the cases ofgamma-ray burst). PARTICLE SPECTRUM The steady state particle distributions n = dN/dγ canbe derived from the solution of the transport equation(Ginzburg & Syrovatskii 1964) ∂∂γ ( ˙ γ cool n ) + nt fall = Q ( γ ) , (25)where ˙ γ cool is the total cooling rate, Q ( γ ) is the injec-tion function, which describes phenomenologically someacceleration process, e.g., DSA. The injection functionfor non-thermal protons and electrons is set as Q ( γ ) = Q γ − p inj exp( − γ/γ max ). Here, γ max is the maximumLorentz factor determined by balancing the accelerationand cooling time scales (Figures. 3 and 4). The corre-sponding solution is n = 1˙ γ cool ∞ (cid:90) γ Q ( γ (cid:48) ) e − T ( γ,γ (cid:48) ) dγ (cid:48) , (26)where T ( γ , γ ) = 1 t fall γ (cid:90) γ dγ ˙ γ cool (27) Inoue et al. p T i m e sc a l e [ s ] log L X = p T i m e sc a l e [ s ] log L X = p T i m e sc a l e [ s ] log L X = t acc ( g = 30) t pp t p t BH t cool t fall Figure 4.
Same as in Fig. 3, but for protons. Dashed, dotted, double-dot-dashed, and thick solid curve corresponds to pp cooling, pγ cooling, BH cooling, and total cooling timescale, respectively. e e d N e / d e [ c m ] p inj = 2.0 IC 4329A (Inoue & Doi 2018)ALMA Coverage
Figure 5.
The steady-state electron spectral distribution inAGN coronae. Solid curve corresponds to the model with p inj = 2 .
0. We set M BH = 10 M (cid:12) , r c = 40, B = 10 G, kT e =100 keV, τ T = 1 .
1, and η g = 30. Dashed curve correspondsto the observationally determined electron distribution forIC 4329A (Inoue & Doi 2018). The shaded region shows theLorentz factors responsible for the observed radio spectrum. By solving Equation. 26, we obtain a steady-state spec-trum of the non-thermal particles. Fig. 5 shows the steady-state non-thermal electronspectrum obtained for the injection spectral index of p inj = 2 . M BH = 10 M (cid:12) , r c = 40, B = 10 G, kT e = 100 keV, τ T = 1 .
1, and η g = 30. The synthetic electron distribu-tion obtained for p inj = 2 . γ e > be-comes softer than observationally determined index at50 (cid:46) γ e (cid:46)
80. This is because of the influence ofthe cutoff imposed by the particle cooling. Therefore,if we consider the high energy synchrotron or IC spec-tral shapes, the cooling effects should be taken into ac-count accurately. Even though the electron spectrumextends down to lower energies, it is hard to see thecorresponding synchrotron emission due to synchrotronself-absorption effect (Inoue & Doi 2014). n the high energy particles in massive black hole coronae f nth = 0 .
03 of the energy in thermal leptons. We notethat, in order to define the energy content in the non-thermal particles, we formally integrate above γ e = 1 inthis study. We keep this fraction for non-thermal elec-tron energy fixed in calculations below for all Seyferts.The energy fraction of non-thermal electrons was fixedto ξ nth = 0 .
04 in Inoue & Doi (2018). ξ nth is definedbeyond the break electron Lorentz factor, while f nth isabove γ e = 1. That amount of non-thermal electronsoverproduces the MeV background flux given the mea-sured electron spectral index (see § . 7). To be consistentwith the observed cosmic MeV gamma-ray backgroundflux, we set ξ nth = 0 .
015 in this work, which corre-sponds to f nth = 0 .
03. The obtained best fit parameterswith this fraction for the radio spectrum of IC 4329A is p = 2 . ± . B = 11 . ± . r c = 42 . ± . ξ nth = 0 .
04. We adopt these parameters for the obser-vationally determined electron distribution in the Fig.5. Fitting results for the other parameters were also thesame as those with ξ nth = 0 . P sh can be estimated as P sh = 4 πR c n p m p v / (cid:39) . × (cid:16) τ T . (cid:17) (cid:16) r c (cid:17) − / (cid:18) M BH M (cid:12) (cid:19) erg s − . For objects with L X = 10 erg s − , f nth = 0 .
03 cor-responds to ∼
5% of the shock power is injected intoacceleration of electrons. This high value implies thatif DSA is responsible for particle acceleration in AGNcoronae then processes regulating injection of electronsinto DSA are very efficient. For example in the caseof DSA in supernovae remnants non-thermal electronsobtain only ∼
1% of energy transferred to non-thermalprotons (Ackermann et al. 2013). Detailed considera-tion of the reasons of this unusually high efficiency ofelectron acceleration is beyond the scope of this paper,however we note that a significant presence of positronsmay affect the ratio (see, e.g., Park et al. 2015). Giventhese uncertainties, for protons we set that the sameenergy injection rate is achieved as for electrons. Thispower appears to be sufficient to explain the observedIceCube neutrino fluxes.For the other object, NGC 985, the observed electronspectral index is 2 . ± .
28 (Inoue & Doi 2018), whichis hard considering the radiative cooling effect. Cascadecomponents would have such a hard spectrum below thethreshold energy (see, e.g., Aharonian & Plyasheshnikov2003). In addition, due to the quality of data at lowfrequencies, we could not precisely determine the othercomponents such as free-free emission and synchrotronemission from star formation activity, and synchrotronemission from the jet. Those uncertainties may resulted in a less reliable measurement of the corona emissionspectrum slope. Further observations are required todetermine the radio spectral properties in NGC 985 pre-cisely. GAMMA RAYS AND NEUTRINOS FROM AGNCORONAEAccelerated electrons and protons in AGN coronaegenerate gamma-ray and neutrino emission through ICscattering, pp interaction, and pγ interaction. Adoptinga steady-state particle spectrum, we calculate the result-ing gamma-ray and neutrino spectra from AGN coronae.We follow Blumenthal & Gould (1970) for the gamma-ray emission due to the IC scattering by non-thermalelectrons. We calculate the gamma-ray and neutrinoemission induced by hadronic interactions following Kel-ner et al. (2006) for pp interactions and Kelner & Aha-ronian (2008) for pγ interactions. For simplicity, we donot take into account IC scattered emission by secondaryelectrons and positrons. For the thermal Comptoniza-tion spectra, we adopt the AGN SED shown in Fig. 1which takes into account reflection components but doesnot account for attenuation by torus. The torus atten-uation is mainly relevant for (cid:46)
30 keV, which is belowthe range of our interest.Figure 6 shows the resulting gamma-ray and neutrinospectra for two cases. The neutrino flux is shown in theform of per flavour. The left panel of the figure showsthe case with a 2-10 keV luminosity of 10 erg s − ata distance of 14 Mpc, while the right panel shows thecase with a luminosity of 10 erg s − at a distance of69 Mpc. The former and the latter roughly correspondsto NGC 4151 and IC 4329A, respectively. NGC 4151 isthe brightest Seyfert in the X-ray sky (Oh et al. 2018).For the comparison, the overall fluxes of both panelsare renormalized to match with the Swift /BAT flux ofNGC 4151 and IC 4329A, respectively, at 14-195 keV(Oh et al. 2018). We note that we do not calculate thedetailed X-ray spectra of each objects, which is beyondthe scope of this paper.We set the injection spectral index of p inj = 2 . η g = 30 for both electrons and protons(See § § . 5. The targetphoton density for IC scatterings and pγ interactions isdefined as U ph ( (cid:15) ) (See § u int ( τ int ) /τ int , where u int ( τ ) = 1 / − τ ) /τ − [1 − exp( − τ )] /τ (See Sec.7.8 in Dermer & Menon 2009), where τ int is the internalgamma-ray optical depth (See § . 3.3). Gamma rays arealso attenuated by the extragalactic background light(EBL) during the propagation in the intergalactic space.We adopt Inoue et al. (2013a) for the EBL attenuation.For the comparison, we also show the expectedsensitivity curve of planned MeV missions: COSI-X Inoue et al. Energy [GeV] F l u x F [ e r g / c m / s ] COSI-X(300 days)e-ASTROGAM(3 yrs) GRAMS(35 days)GRAMS(3 yrs) Fermi/LAT(10 yrs) log L X = 43 , d=14 Mpc, g = 30 IceCube(North, 7 yrs)IceCube-Gen2(North, 15 yrs)-ray : ICIC (intrinsic)IC (thermal) pp + p pp + p (intrinsic): pp + pppp Energy [GeV] F l u x F [ e r g / c m / s ] COSI-X(300 days)e-ASTROGAM(3 yrs) GRAMS(35 days)GRAMS(3 yrs) Fermi/LAT(10 yrs) IceCube(South, 7 yrs)IceCube-Gen2(South, 15 yrs) log L X = 44 , d=69 Mpc, g = 30 -ray : ICIC (intrinsic)IC (thermal) pp + p pp + p (intrinsic): pp + pppp Figure 6.
Left : Gamma-ray and neutrino spectrum per flavour from an AGN coronae with p inj = 2 . η g = 30. We set2-10 keV luminosity of 10 erg s − at a distance of 14 Mpc, which roughly corresponds to NGC 4151. We renormalize theoverall fluxes in order to match the Swift /BAT flux of NGC 4151 at 14-195 keV (Oh et al. 2018). The thick black solid and thickdot curve shows gamma rays from IC interaction and pp + pγ interaction including internal and EBL attenuation effect. Eachthin curve shows the spectrum before the attenuation. The black dashed curve shows the IC spectrum considering only thermalelectrons, in which the effect of reflection is taken into account. The blue dot-dashed, double-dot-dashed, and solid curve showsthe neutrino contribution per flavour of pp interaction, pγ interaction, and the sum of the two, respectively. The non-thermalelectrons in coronae are assumed to carry 3% of the total lepton energies. We assume the injection powers in electrons andprotons are the same. For the comparison, we overplot the sensitivity curve of COSI-X (300 days), e-ASTROGAM (3 yrs; DeAngelis et al. 2017),
GRAMS (35 days; Aramaki et al. 2019),
GRAMS (3 yrs; Aramaki et al. 2019), and
Fermi /LAT (10 yrs).We also plot the sensitivity of IceCube and IceCube-Gen2 at δ = 30 ◦ (van Santen & IceCube-Gen2 Collaboration 2017). Right:
The same as the
Left panel, but we set 2-10 keV luminosity of 10 erg s − at a distance of 69 Mpc which roughly correspondsto IC 4329A. We renormalize the overall fluxes in order to match the Swift /BAT flux of IC 4329A at 14-195 keV (Oh et al.2018). For the IceCube sensitivity, we show that at δ = − ◦ . (300 days) , e-ASTROGM (3 yrs, De Angelis et al.2017) , GRAMS (35 days, Aramaki et al. 2019), and
GRAMS (3 yrs, Aramaki et al. 2019). 10-yr sensitivityof
Fermi /LAT is also shown. We also plot the sensitiv-ity of neutrino detectors: IceCube and IceCube-Gen2(van Santen & IceCube-Gen2 Collaboration 2017). Forthe left panel, we assume the declination δ of 30 ◦ , while − ◦ for the right panel.Since the spectral index of electrons is ∼ νF ν in the MeV band which appearsafter the thermal cutoff. Given the cooling limited max-imum energy γ e ∼ , the intrinsic IC spectrum canextend up to ∼
100 GeV. However, due to the stronginternal gamma-ray attenuation effect, the spectra willhave a cutoff around 100 MeV in both cases. In thesub-MeV band, the spectrs show super-thermal tails dueto the combination of thermal and non-thermal compo- COSI collaboration website (The Compton Spectrometer andImager http://cosi.ssl.berkeley.edu/ e-ASTROGAM collaboration website (enhanced AS-TROGAM http://eastrogam.iaps.inaf.it/ Fermi IceCube collaboration website (https://icecube.wisc.edu/ nents and a spectral hardening at ∼ GRAMS (Aramaki et al. 2019) and
SMILE (Takadaet al. 2011; Komura et al. 2017) may be able to catchthis superthermal tail. And, satellite-class MeV mis-sions such as e-ASTROGAM (De Angelis et al. 2017), AMEGO , and GRAMS (Aramaki et al. 2019) will beable to see also the non-thermal power-law tail. Forthe case of NGC 4151,
Fermi /LAT may be able to seethe signature with its 10 yrs survey. However, the ex-pected flux is almost at the sensitivity limit. Thus, itmay need further exposures for
Fermi /LAT to see thecoronal emission.The pp and pγ production efficiency is given by theratio between the dynamical timescale (Eq. 2) and theinteraction timescales (Eqs. 8 and 10). The pp produc-tion efficiency is analytically given as f pp = t fall t pp (cid:39) . (cid:16) τ T . (cid:17) (cid:16) r c (cid:17) − / . (29) SMILE AMEGO collaboration website (The All-sky Medium EnergyGamma-ray Observatory https://asd.gsfc.nasa.gov/amego/ n the high energy particles in massive black hole coronae / / ∼
5% and ∼
3% of the in-trinsic proton luminosity, respectively. Since we assumethe same energy injection to electrons and protons andthe coronal Thomson scattering optical depth is 1.1, be-fore the attenuation, we have hadronic gamma-ray andneutrino fluxes are ∼
5% and ∼
3% of the IC gamma-rayfluxes.The pp and pγ induced gamma rays are also mostly at-tenuated by the internal photon fields. Thus, we do notexpect any (cid:38) GeV gamma-ray emission from Seyferts.Moreover, the intrinsic gamma-ray energy fluxes due tohadronic interactions is about a factor of 10 less thanthat by primary electrons because of radiative efficiencydifferences between protons and electrons. This impliesthat gamma rays produced by secondary pairs shouldnot significantly alter the resulting spectra. Therefore,we can safely ignore the cascade contribution.On the contrary to gamma rays, neutrinos induced byhadronic interactions can escape from the system with-out any attenuation. Since we adopt the same p inj = 2for protons as for electrons, we expect a flat νF ν spec-trum for neutrinos, to which pp makes dominant con-tribution. At higher energies, especially in the case ofIC 4329A, pp and pγ spectra are suppressed due to theBethe-Heitler cooling process. The exact position of thecutoff energy depends on the assumed η g . Here, as de-scribed later, we set η g = 30 in order to be consistentwith the IceCube background flux measurements. Thisgyrofactor results in a neutrino spectral cutoff around100 TeV. Although it is difficult to see neutrino signalsfrom individual Seyferts with the current generation ofIceCube, it would be possible to see bright Seyferts inthe northern hemisphere in the era of IceCube-Gen2 (seealso Murase & Waxman 2016, for more general argu-ments). Therefore, even though Seyferts are faint in theGeV gamma-ray band, future MeV gamma-ray and TeVneutrino observations can test our scenario. COSMIC GAMMA-RAY AND NEUTRINOBACKGROUND FLUXES FROM HIGH ENERGYPARTICLES IN AGN CORONAEIn this section, we calculate the cosmic gamma-rayand neutrino background spectra from AGN coronae.For the cosmological evolution of AGNs, we follow Uedaet al. (2014) in which the evolutionary functions are de-fined at 2–10 keV intrinsic X-ray luminosity. We brieflyreview their formalism here.Based on the luminosity-dependent density evolutionmodel, the AGN X-ray luminosity function at a givenluminosity L X and a given redshift z is defined as d Φ X ( L X , z ) d log L X = d Φ X ( L X , d log L X e ( z, L X ) , (30) where d Φ X ( L X , /d log L X is the luminosity function inthe local universe defined as d Φ X ( L X , z = 0) d log L X = A [( L X /L ∗ ) γ + ( L X /L ∗ ) γ ] − , (31)where A is the normalization and L ∗ is the break lumi-nosity. e ( z, L X ) is the evolution factor represented as e ( z, L X ) = (32) (1 + z ) p [ z ≤ z c ( L X )] , (1 + z c ) p (cid:16) z z c (cid:17) p [ z c ( L X ) < z ≤ z c ] , (1 + z c ) p (cid:16) z c z c (cid:17) p (cid:16) z z c (cid:17) p [ z > z c ] . Here the luminosity dependence for the p p L X ) = p ∗ + β (log L X − log L p ) , (33)where we set log L p = 44. Both cutoff redshifts are givenby power law functions of L X as z c1 ( L X ) = (cid:40) z ∗ c1 ( L X /L a1 ) α [ L X ≤ L a1 ] ,z ∗ c1 [ L X > L a1 ] , (34)and z c2 ( L X ) = (cid:40) z ∗ c2 ( L X /L a2 ) α [ L X ≤ L a2 ] ,z ∗ c2 [ L X > L a2 ] . (35)The parameters are summarized in Table. 4 in Uedaet al. (2014). There is also a substantial fraction ofCompton-thick AGNs in the universe (e.g., Ueda et al.2003; Ricci et al. 2015). In order to take into accountthis population, we multiply the normalization factor bya factor of 1.5 (see Ueda et al. 2014, for details).The cosmic gamma-ray background fluxes are calcu-lated as E dNdE = c π (cid:90) . dz (cid:90) d log L X (cid:12)(cid:12)(cid:12)(cid:12) dtdz (cid:12)(cid:12)(cid:12)(cid:12) d Φ X ( L X , z ) d log L X × L γ ( E (cid:48) , L X )1 + z u int ( τ int [ E (cid:48) , log L X ]) τ int ( E (cid:48) , log L X ) × exp( − τ EBL [ E, z ]) , (36)where E (cid:48) = (1 + z ) E and L γ ( E, L X ) is the gamma-rayluminosity at energy E for a given X-ray luminosity of L X . The redshift and luminosity ranges are selected tobe the same as in Ueda et al. (2014). τ int and τ EBL isthe gamma-ray optical depth due to the internal pho-ton field and the EBL. We do not consider the cascadegamma-ray photons (e.g., Inoue & Ioka 2012) becausethe gamma-ray energy fluxes due to hadronic interac-tions is already subdominant compairing to that by pri-mary electrons.2
Inoue et al. Energy [GeV] F l u x E d N / d E [ G e V / c m / s / s r ] -ray : ICIC (intrinsic)IC (thermal) pp + p pp + p (intrinsic): pp + pppp Figure 7.
The cosmic gamma-ray and neutrino background spectrum from AGN coronae with p inj = 2 . η g = 30 assumingthat the injection powers in electrons and protons are the same. The thick black solid and thick dot curves show the gamma-raycontribution of IC interaction and pp + pγ interaction, respectively, in which internal and EBL attenuation effects are taken intoaccount. Corresponding thin curves show the spectra before the attenuation. The black dashed curve shows the IC spectrumconsidering only thermal electrons. The blue dot-dashed, double-dot-dashed, and solid curve shows the neutrino contributionsper flavour produced via pp interactions, pγ interactions, and the sum of the two, respectively. The circle and square data pointscorrespond to the total cosmic gamma-ray background spectrum measured by the Fermi /LAT (Ackermann et al. 2015) and thecosmic neutrino background spectrum by the IceCube (Aartsen et al. 2015), respectively. The cosmic X-ray and MeV gamma-ray background spectrum data of
HEAO -1 A2 (Gruber et al. 1999),
INTEGRAL (Churazov et al. 2007),
HEAO -1 A4 (Kinzeret al. 1997),
Swift -BAT (Ajello et al. 2008),
SMM (Watanabe et al. 1997), Nagoya–Ballon (Fukada et al. 1975), COMPTEL(Weidenspointner et al. 2000) are also shown in the figure.
The neutrino background fluxes can be also calculatedin the same manner ignoring the gamma-ray attenu-ation terms and replacing L γ ( E, L X ) with L ν ( E, L X ). L ν ( E, L X ) is the neutrino intensity at an energy of E for a given X-ray luminosity of L X .Figure 7 shows the cosmic X-ray/gamma-ray and neu-trino background spectra from AGN coronae assumingthe case of p inj = 2 . η g = 30. We also plot the ob-served background spectrum data by HEAO -1 A2 (Gru-ber et al. 1999),
INTEGRAL (Churazov et al. 2007),
HEAO -1 A4 (Kinzer et al. 1997),
Swift -BAT (Ajelloet al. 2008),
SMM (Watanabe et al. 1997), Nagoya–Ballon (Fukada et al. 1975), COMPTEL (Weidenspoint-ner et al. 2000),
Fermi -LAT (Ackermann et al. 2015),and IceCube (Aartsen et al. 2015).Figure 8 shows the cosmic MeV gamma-ray back-ground spectrum only from Figure 7. By setting f nth = 0 .
03, the gamma-ray fluxes from AGNs coronae dueto IC scattering by thermal and non-thermal electronscan nicely explain the observed cosmic MeV gamma-raybackground radiation in an extension from the cosmicX-ray background radiation, which is known to be ex-plained by Seyferts (Ueda et al. 2014). Since the spec-tral index of non-thermal electrons in the coronae is ∼
3, the resulting MeV gamma-ray background spec-trum becomes flat in E dN/dE (See Fig. 8). Here, thecosmic X-ray background spectrum by Seyferts has aspectral cutoff above ∼
300 keV because of temperatureof thermal electrons ∼
100 keV (Ueda et al. 2014). Bysumming up these two thermal and non-thermal compo-nents, superthermal tail appears in the sub-MeV bandas observed by Fukada et al. (e.g., 1975); Kinzer et al.(e.g., 1997); Watanabe et al. (e.g., 1997). Since the dom-inant IC contributors switches from thermal electrons to n the high energy particles in massive black hole coronae Energy [MeV] F l u x E d N / d E [ M e V / c m / s / s r ] TotalThermalNon-thermalIntrinsicSMMSwift/BAT INTEGRALHEAO-1 A4HEAO-1COMPTELNagoya
Figure 8.
Same as Figure 7, but enlarging the cosmicMeV gamma-ray background spectrum from 0.03 MeV to100 MeV. The thick black solid curve shows the total (ther-mal + non-thermal) contribution of IC interaction where in-ternal and EBL attenuation effects are taken into account.Thin curve shows the spectrum before the attenuation. Thedashed and dotted curve shows the contribution from ther-mal electrons and non-thermal electrons, respectively. Con-tribution of reflection is included in the thermal contribution.The cosmic X-ray and MeV gamma-ray background spec-trum data of
HEAO -1 A2 (Gruber et al. 1999),
INTEGRAL (Churazov et al. 2007),
HEAO -1 A4 (Kinzer et al. 1997),
Swift -BAT (Ajello et al. 2008),
SMM (Watanabe et al. 1997),Nagoya–Ballon (Fukada et al. 1975), COMPTEL (Weidens-pointner et al. 2000) are also shown in the figure. non-thermal electrons at around 1 MeV, the MeV back-ground spectrum may have spectral hardening featureat ∼ η g = 30. The resultdoes not significantly change as far as η g < η g > f nth .Due to the internal gamma-ray attenuation effect,these non-thermal gamma rays can not contribute tothe emission above GeV. Because of the same reason,most of hadronic gamma-ray photons are attenuated byinternal photon fields, resulting in generation of multiplesecondary particles. Since calculation of those popula-tions are beyond the scope of this paper, we ignore thosepopulations in our estimate. Moreover, as we describeabove, the intrinsic hadronic fluxes are already an orderof magnitude below the leptonic fluxes. Thus, pairs in-duced by hadronic cascades will not significantly changeour results.Here, IC emission due to non-thermal electrons alsocontribute in the X-ray band. Their contribution isabout ∼
5% at 30 keV of the observed cosmic X-raybackground flux, which may reduce the required num-ber of the Compton-thick population of AGNs.The model curve at ∼
10 keV slightly overproducesthe measured background spectrum. This is because Energy [GeV] F l u x E d N / d E [ G e V / c m / s / s r ] g = 1 g = 10 g = 30 g = 10 g = 10 IceCube
Figure 9.
The cosmic neutrino background spectrum perflavour from AGN coronae. The dashed, dotted, solid, dot-dashed, and double-dot-dashed curve shows the pp + pγ con-tribution with η g =1 (Bohm limit), 10, 30, 10 , and 10 ,respectively. The square data points correspond to the cos-mic neutrino background spectrum by the IceCube (Aartsenet al. 2015). we do not take into account X-ray attenuation by torus.However, the treatment of those soft X-ray photons doesnot affect our results at all.For neutrinos, the combination of pp and pγ inter-actions can nicely reproduce the IceCube fluxes below100–300 TeV by assuming η g = 30 and about 5% ofthe shock power into proton acceleration, same as elec-trons. pp interactions dominate the flux at (cid:46)
10 TeV,while pγ interactions prevail above this energy. Becauseof the target photon field SED, pγ is subdominant inthe GeV-TeV band. If we inject more powers into pro-tons, it inevitably overproduces the IceCube backgroundfluxes. As (cid:38) GeV gamma rays are internally attenu-ated, AGN coronae emission will not be seen in GeVgamma-rays, even though they can make the IceCubeneutrino fluxes. Such hidden cosmic-ray accelerators aresuggested as a possible origin of the IceCube neutrinos(see Murase et al. 2016, for a general argument).Figure 9 shows the cosmic neutrino background spec-tra from AGN cores with various gyro factors rang-ing from 1 (Bohm limit) to 10 . It is clear that if η g (cid:28)
30, the resulting neutrino fluxes overproduce themeasured fluxes. On the contrary, if η g (cid:29)
30, AGNcoronae can not significantly contribute to the observedneutrino background fluxes. Thus, in order to explainthe IceCube neutrino background fluxes by AGN cores, η g ∼
30 is required. However, we note that these esti-mates are based on the assumed energy injection fractionto protons. Recent particle-in-cell simulations of proton-electron plasma considering radiatively inefficient accre-tion flows (RIAFs) showed that protons will carry haveseveral factors more energies than electrons (Zhdankinet al. 2018). If this is the case, larger η g is favored.4 Inoue et al. DISCUSSION8.1.
Comparison with Previous works on High EnergyNeutrinos
In literature, it has been argued that high energyparticles in the core of AGNs generate intense neu-trino emission (e.g., Eichler 1979; Begelman et al. 1990;Stecker et al. 1992; Alvarez-Mu˜niz & M´esz´aros 2004).These originally predicted fluxes have been ruled out byhigh energy neutrino observations (The IceCube Collab-oration 2005). However, recent studies have revisitedthe estimated fluxes and found that AGN core modelscan account for the whole measured fluxes (Stecker 2013;Kalashev et al. 2015). In this section, we would like tocompare our results with those recent studies (Stecker2013; Kalashev et al. 2015).The model suggest by Stecker (2013) is very similarto the originally proposed one (Stecker et al. 1992), butthe background flux is assumed to be lower by a factorof 20. The original model is motivated by the modelsexplaining AGN X-ray spectra by the electromagneticcascade emission of secondary particles (Zdziarski 1986;Kazanas & Ellison 1986), which is not the case basedon current X-ray and gamma-ray observational results.The shock radius and the magnetic field strength wasassumed to be 10 R s and 10 G in the model by Steckeret al. (1992).The model in Kalashev et al. (2015) is an extension ofStecker et al. (1992) taking into radial emission profile inthe standard accretion disk for the consideration of the pγ cooling processes. In our modeling, we do not takeinto account such anisotropic radiation field. However,given the observationally determined corona size, thedominant photon targets are likely to be generated inthe inner region of the coronae. The particle spectrain Kalashev et al. (2015) are fixed to match with theIceCube data.Neutrino fluxes or cosmic-ray spectra are fixed tomatch with the latest IceCube data in Stecker (2013);Kalashev et al. (2015). In this work, we take more phys-ical approach. Corona plasma density, corona size, andmagnetic field strength are determined from observa-tions (Inoue & Doi 2018) in our work. For example, weset R c = 40 R s and B = 10 G based on ALMA obser-vations (Inoue & Doi 2018). With those parameters, wecan follow the acceleration processes in coronae in theframework of DSA. We found the AGN coronae can ex-plain the IceCube neutrino background in the TeV band,if the gyrofactor is η g = 30 and about 5% of the shockenergy goes into proton acceleration. We also predictthat next generation MeV gamma-ray and neutrino ex-periments can test our model by observing nearby brightSeyferts such as NGC 4151 and IC 4329A.8.2. Plasma Condition in Coronae
Considering the plasma density in the accreting coro-nae, high energy particles may have sufficient time to redistribute their kinetic energy through thermalizationby elastic Coulomb (EC) collisions before the gas reachesthe event horizon (Takahara & Kusunose 1985; Mahade-van & Quataert 1997). In this section, we discuss ther-malization timescales of electrons and protons in theAGN coronae.First, the electron thermalization timescale in the non-relativistic regime is estimated to be (Spitzer 1962; Step-ney 1983) t EC , ee (cid:39) √ πn e σ T c ln Λ θ / e (37) (cid:39) . × (cid:16) τ T . (cid:17) − (cid:16) r c (cid:17) (cid:18) M BH M (cid:12) (cid:19) (cid:18) kT e
100 keV (cid:19) / [s] , where ln Λ ≈
20 is the Coulomb logarithm. For relativis-tic electrons with Lorentz factors γ e (cid:29) θ e the ther-malization timescale due to interactions with the back-ground plasma becomes (Dermer & Liang 1989) t EC , ee ( γ e ) = 43 K ( θ − e ) γ e n e σ T c (ln Λ + 9 / − ln √ × (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) ∞ (cid:90) dγ (cid:48) e exp( − u ee )[ θ e (1 + 2 u ) − γ e ] (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) − , (38)where K n is the modified Bessel function of order n ,and parameter u ee = ( γ e /γ (cid:48) e + γ (cid:48) e /γ e ) / θ e . This equa-tion can be approximated as t EC , ee ( γ e ) ≈ (39)23 γ e n e σ T c (ln Λ + 9 / − ln √ (cid:12)(cid:12)(cid:12)(cid:12) K ( θ − e ) K ( θ − e ) − γ e (cid:12)(cid:12)(cid:12)(cid:12) − . This is a good analytic approximation at θ e (cid:38) . γ e (cid:38) t EC , pp (cid:39) √ πn p σ T c ln Λ (cid:18) m p m e (cid:19) θ / p (40) (cid:39) . × (cid:16) τ T . (cid:17) − (cid:16) r c (cid:17) (cid:18) M BH M (cid:12) (cid:19) (cid:18) kT p
100 keV (cid:19) / [s] , where θ p ≡ kT p /m p c is the dimensionless proton tem-perature. At high kinetic energies, nuclear interactionbecomes important (see Gould 1982, for details). In themildly relativistic case, the elastic proton-proton relax-ation timescale approximately becomes (Gould 1982) t EC , pp (cid:39) n p σ h c β p γ p γ p − , (41)where σ h ∼ . × − cm . This approximation is validat 70 MeV (cid:46) ( γ − m p c (cid:46)
500 MeV. Above 500 MeV,inelastic processes start to dominate. n the high energy particles in massive black hole coronae T i m e sc a l e [ s ] t freefall t syn t IC t EC,ee t EC,pp t EC,ep t pp Figure 10.
Electron and proton thermalization timescalesin AGN coronae together with radiative cooling and dy-namical timescales. Thick solid curve shows the free-falltimescale. Dashed, dotted, and dot-dashed curve corre-sponds to synchrotron cooling, IC cooling, and ee EC ther-malization timescale for electrons, respectively. Double-dot-dashed, triple-dot-dashed, and thin solid curve correspondsto pp EC thermalization, pe EC thermalization, and pp in-elastic interaction timescale for protons, respectively. Weset log L X = 44, τ T = 1 . R c = 40 R s , and kT e = kT p =100 keV. Lastly, the proton-electron thermalization timescaledue to EC collisions in the non-relativistic regime is es-timated to be (Spitzer 1962; Stepney 1983) t EC , ep (cid:39) (cid:112) π/ n e σ T c ln Λ (cid:18) m p m e (cid:19) ( θ e + θ p ) / (42) (cid:38) . × (cid:16) τ T . (cid:17) − (cid:16) r c (cid:17) (cid:18) M BH M (cid:12) (cid:19) (cid:18) kT e
100 keV (cid:19) / [s] , where we assume θ p = θ e . The temperature of ahot accretion can roughly reach to virial temperature T p (cid:39) GM BH m p / kR ∼ × ( R/R s ) − K. At suchhigher temperature, t EC , ep becomes longer. In the caseof relativistic protons, the energy loss timescale throughEC interactions is given as (Mannheim & Schlickeiser1994; Dermer et al. 1996) t EC , ep (cid:39) . × (3 . θ / e + β p )( γ p − n p σ T cβ p ln Λ , (43)where β p = (cid:113) − /γ p . At γ p (cid:29) θ e (cid:28)
1, the rel-ativistic EC scattering relaxation time can be approxi-mated as t EC , ep (cid:39) . × (cid:16) τ T . (cid:17) − (cid:16) r c (cid:17) (cid:18) M BH M (cid:12) (cid:19) (cid:16) γ p (cid:17) [s] . (44) Fig. 10 shows EC thermalization timescales forelectrons and protons for the luminosity of L X =10 erg s − . Since EC thermalization is effective atlow energy particles, the horizontal axis is shown in γβ .Around γ e β e ∼ t EC ,ee shows a sharp feature, whichis related to the temperature of the background plasma, kT e = 100 keV. At this temperature, the electron dis-tribution has a peak around ∼ kT e corresponding to γ e β e ∼ .
2. Thus, around this energy, mean energytransfer is small. We note that below this energy, elec-trons gain energies from the background plasma throughelastic ee scatterings rather than loosing their energies(Dermer & Liang 1989), however, this energy gain pro-cess is not considered in our work, since it is not relevantfor our energy range of interest. As seen in the Fig. 10,the energy loss process of electrons is dominated by theCompton cooling at γ e β e (cid:38) pp timescale in the mildly relativistic regime. Since it as-sumes an incident proton has much higher kinetic en-ergy than background plasma, we combine the non-relativistic t EC ,pp (Equation. 40) and that from Gould(1982). As discussed above, inelastic processes startto dominate at the kinetic energies of (cid:38)
500 MeV( γ p β p (cid:38) . pp interaction timescale t pp .As the proton-electron Coulomb timescale ( t EC ,pe ) islonger than t fall , protons and electrons may not be inthe thermal equilibrium in AGN coronae. The pro-ton temperature of a hot accretion can roughly reachto virial temperature T p (cid:39) GM BH m p / kR ∼ × ( R/R s ) − K, which is (cid:29) T e . And, the existenceof pairs in coronae can reduce n p . Moreover, the shockheated proton temperature becomes kT p ∼ m p v ∼ r c / − MeV. Those shock heated protons and elec-trons also gain and loose their energies through the pro-cesses and would contribute as a thermal populationin the coronae. These electrons are heated and cooledthrough EC proton-electron thermalization and Comp-tonization, respectively (e.g., Katz et al. 2011; Muraseet al. 2011). The heating rate can be written as − dT p dt = dT e dt = T p t EC ,pe (cid:39) n e σ T c ln Λ (cid:112) π/ (cid:18) m e m p (cid:19) T p θ − / e , (45)assuming θ e (cid:29) θ p . The cooling rate through Comp-tonization is dT e dt ≈ − σ T U ph , tot T e m e c (46)By equating these two heating and cooling rates of ther-mal electrons, the shock heating electron temperature is6 Inoue et al. estimated to be kT e (cid:39) k (cid:32) (cid:112) π/ m e m p n e U ph , tot T p (cid:33) / (47) (cid:39) (cid:16) τ T . (cid:17) / [keV] , where we assume L ph , bol ∝ M BH . This temperature isclose to the measured coronal temperature. Therefore,such shock heating mechanism may be able to explainthe current observed coronal temperature. For the un-derstanding the detailed nature of thermal coronae, fur-ther studies including thermodynamical processes arerequired.8.3. Other Particle Acceleration Mechanisms
In this paper, we consider the DSA as fiducial accel-eration mechanism. However, other acceleration mech-anisms such as turbulent acceleration, magnetosphereacceleration, and magnetic reconnection can also oper-ate in AGN coronae. We briefly discuss these processeshere.First, turbulent acceleration is considered for low-accretion rate objects such as low-luminosity AGNs(e.g., Kimura et al. 2015; Zhdankin et al. 2017, 2018;Wong et al. 2019). In this scenario, particles are ac-celerated stocastically by turbulence and magnetic re-connection in accretion disk or coronae. Recently, Zh-dankin et al. (2018) investigated electron-ion plasmaenergization via turbulent dissipation in RIAFs usingparticle-in-cell simulations for the ion temperature T i inthe range of m e c (cid:46) k B T i (cid:46) m p c . Turbulent electron-ion plasma driven by MRIs generate power-law spectrafor both species and the indices depends on the initialion temperature. The fraction of the kinetic energy inthe non-thermal ions and electrons are ∼
60% and 6%for ions and electrons at k B T i ∼ m e c , respectively. Thefraction in non-thermal electrons is close to the requiredvalue for the MeV background (See § D p (cid:39) ( m p c ) ( ck min ) (cid:16) v A c (cid:17) ζ ( r L k min ) q − γ q , (48)where k min ∼ R − c is the minimum wave number ofturbulence spectrum (corresponding to the size of thecorona), v A = B/ (cid:112) πm p n p is the Alfv´en speed, r L = m p c /eB is the Larmor radius, and ζ = δB /B is theratio of strength of turbulence fields against the back-ground. Then, the acceleration timescale is estimatedto be t StA (cid:39) p D p (cid:39) ζ (cid:16) v A c (cid:17) − R c c (cid:18) r L R c (cid:19) − q γ − q (49) Assuming the Kolomogorov spectrum for the turbu-lent ( q = 5 /
3) and ζ = 1, the timescale becomes t StA (cid:39) . × (cid:16) τ T . (cid:17) (cid:16) r c (cid:17) − / (cid:18) M BH M (cid:12) (cid:19) − / × (cid:18) B
10 G (cid:19) − / (cid:16) γ p (cid:17) / [s] . (50)Thus, stochastic acceleration appears to be inefficientas compared to the typical cooling rates. This is causedby the measured weak magnetic fields, which results insmall Alfv´en speed. If the magnetic fields are ampli-fied by MRIs, more efficient acceleration can be realized(e.g., Zhdankin et al. 2018) .Second, magnetosphere acceleration can also acceler-ate particles in the vicinity of SMBHs (e.g., Beskin et al.1992; Levinson 2000; Neronov & Aharonian 2007; Levin-son & Rieger 2011; Rieger 2011). At low accretion rates,the injection of charges into the BH magnetosphere isnot sufficient for a full screening of the electric field in-duced by the rotation of the compact object. The re-gions with unscreened electric field, so-called gaps, areable to accelerate charged particles effectively.In order to have gaps, the maximum allowed accretionrate is (Levinson & Rieger 2011; Aleksi´c et al. 2014;Aharonian et al. 2017)˙ m < × − (cid:18) M BH M (cid:12) (cid:19) − / , (51)where ˙ m is the accretion rate in the Eddington units.Since we are considering the standard accretion diskregime ˙ m (cid:38) .
01, particle acceleration by gaps will notbe operated in our case.Lastly, magnetic reconnection would accelerate parti-cles (see e.g., Hoshino & Lyubarsky 2012, for reviews).Reconnection would naturally happens in coronae asthey are magnetized and radiative magnetic reconnec-tion is suggested as an origin of the X-ray emissionseen in accreting black hole systems (Beloborodov 2017).However, even in the case of solar flares, particle accel-eration mechanisms in magnetic reconnection is still un-certain (e.g., Liu et al. 2008; Nishizuka & Shibata 2013).Although quantitative discussion is not easy here, the After we submitted our paper to the journal and arXiv, sim-ilar study on AGN coronae by Murase et al. (2019) appeared onarXiv. Both studies are independent and the most different pointis the assumed particle acceleration processes. In our paper, weconsider DSA, while Murase et al. (2019) consider stochastic accel-eration motivated by recent numerical simulations (Kimura et al.2019). However, as we discussed in this section, stochastic accel-eration may not work given the ALMA results of weak coronalmagnetic field. n the high energy particles in massive black hole coronae P B = B R c v A (cid:39) . × (cid:16) τ T . (cid:17) − / (cid:16) r c (cid:17) / (cid:18) M BH M (cid:12) (cid:19) / × (cid:18) B
10 G (cid:19) [erg s − ] . This power is not sufficient for providing the non-thermal particle energies. For detailed estimation, wemay need to consider spatial distribution fo magneticfield. However, such information is not currently avail-able.8.4.
Cosmic MeV Gamma-ray Background Radiation
It is known that Seyferts generate the cosmic X-raybackground radiation (Ueda et al. 2014). The cosmicgamma-ray background at 0.1–820 GeV is believed tobe explained by three components: blazars (e.g., Inoue& Totani 2009; Ajello et al. 2015), radio galaxies (In-oue 2011), and star-forming galaxies (Ackermann et al.2012a), even though the contributions of radio galax-ies and star-forming galaxies are still uncertain due to asmall number of gamma-ray detected samples. On thecontrary to the cosmic X-ray and GeV background ra-diation, the origin of the cosmic MeV gamma-ray back-ground radiation is still veiled in mystery.As a possible scenario, non-thermal IC emission fromcoronae in Seyferts has been suggested (Inoue et al.2008). The MeV tail extended from the X-ray back-ground spectrum is generated by non-thermal electronswith very soft spectral index (Inoue et al. 2008). How-ever, non-thermal electrons are included in an ad hocway. In our work, we consider the particle accelera-tion and cooling processes given the latest observations.The tail is due to the superposition of thermal Comp-tonization cut-off spectrum and γγ attenuated flat non-thermal IC component. We can distinguish these twoscenarios by observing individual objects in radio andX-ray bands.Not only Seyferts, but also blazars are considered as acandidate as the origin of the MeV background (Ajelloet al. 2009). In order to distinguish Seyferts and blazars,we need to resolve the MeV sky. However, it is not easyeven with future MeV instruments (Inoue et al. 2015).Here, it is suggested that anisotropy measurements maydistinguish these two scenarios (Inoue et al. 2013b) be-cause blazar background should feature stronger Pois-son fluctuations. Future MeV gamma-ray anisotropyobservations will be important to understand the par-ticle acceleration in coronae and the origin of the MeVgamma-ray background radiation.8.5. Gamma-ray Observations toward Seyferts
Gamma rays from Seyfert galaxies are not robustlydetected yet (Lin et al. 1993; Teng et al. 2011; Ack-ermann et al. 2012b). Possible signature of gamma-rayemission above 0.1 GeV have been reported for ESO 323-G077 and NGC 6814 (Ackermann et al. 2012b), whoseX-ray luminosities are about 10 erg s − . The re-quired luminosity ratio between X-ray and gamma-ray L . −
10 GeV /L −
195 keV for these sources is about 0.1(Ackermann et al. 2012b). Our model estimates this ra-tio as ∼ .
01. Therefore, coronal gamma-ray emission ismost-like not able to account for the observed gamma-ray fluxes from those Seyfert galaxies.Although gamma rays from other Seyferts have notbeen detected yet,
Fermi /LAT has set upper limits ontheir gamma-ray fluxes (Teng et al. 2011; Ackermannet al. 2012b). Based on the analysis of the first 2-3years data, L . −
10 GeV /L −
195 keV < . L . −
10 GeV /L −
195 keV < . Fermi /LAT may be able to see NGC 4151 (Figure. 1),even though the expected flux is almost at the sensitivitylimit. 8.6.
Fraction of Non-thermal Electrons
We set the energy fraction of non-thermal electrons inAGN coronae as f nth = 0 .
03 because it nicely reproducesthe observed MeV gamma-ray background radiation. Asdiscussed in Inoue & Doi (2018), f nth , B , and R c areclosely tied, current radio and X-ray data do not allow usto solve these three parameters simultaneously withoutdecoupling thermal and non-thermal components.Observationally, f nth is constrained as < . NuSTAR ob-servations (Fabian et al. 2017). If f nth is significantlylower, it becomes difficult for Seyfert to explain the MeVgamma-ray background radiation. However, too muchlower f nth contradicts with other observations since itrequires a bigger R c based on the radio spectral fitting.If we set f nth = 10 − and 10 − , R c becomes ∼ R s and ∼ R s , respectively. The size of coronae is also con-strained as an order of ∼ R s by optical–X-ray spectralfitting studies (Jin et al. 2012) and micorolensing obser-vation (Morgan et al. 2012). Therefore, f nth can notbecome much smaller than the adopted value.8.7. Nuclear Spallation in AGNs
Given the ALMA results, particle accelerations oc-curs in AGN coronae. As we demonstrated, high en-ergy protons are easily accelerated in coronae. Thesehigh energy protons can be also traced by future high-resolution calorimeter spectroscopy in the X-ray bandsuch as
XRISM (Tashiro et al. 2018) and
Athena (Nan-8
Inoue et al. dra et al. 2013) . As narrow line features are seen inAGN X-ray disk spectra, there are abundant metal ele-ments in AGN cores. Accelerated protons also interactwith those nuclei and induce nuclear spallation. The nu-clear spallation in AGN disks will result in enhancementof emission lines from Mn, Cr, V, and Ti (Gallo et al.2019). Those signatures will be another clue for the testof our model. CONCLUSIONRecently, Inoue & Doi (2018) has reported the coro-nae of Seyferts are composed of both thermal and non-thermal electrons based on ALMA observations, whichimplies that particle acceleration occurs in AGN coro-nae. In order to investigate the production mechanismof those high energy particles, we study the particle ac-celeration process in AGN coronae. We consider particleacceleration by the DSA process in the coronae as an ex-ample. By taking into account the observationally deter-mined coronal properties, such as temperature, density,size, and magnetic field strength, we found that stan-dard DSA processes can easily reproduce the observednon-thermal electron in the coronae with an injectionelectron spectral index of p inj = 2. Even in low ac-celeration efficiency cases ( η g ∼ ), such populationscan be realized in coronae. Given the observed mag-netic field strength of 10 G and accretion rates, we alsofound that other possible acceleration mechanisms suchas turbulent acceleration, magnetosphere acceleration,and magnetic reconnection confront difficulty in repro-ducing the observed non-thermal electrons.The accelerated non-thermal electron populations willgenerate a MeV gamma-ray power-law spectrum in theAGN SEDs up to ∼ . ∼ f nth ∼ ∼
5% of the shock energy in electronacceleration, AGN coronae can explain the MeV back-ground in an extension of the X-ray background contri- bution of Seyferts. Due to a strong internal gamma-rayattenuation effect, the contribution of AGN coronae tothe GeV background is negligible.Accelerated particles would also result in neutrino pro-duction through hadronic processes. Intense neutrinoemission has been expected to be produced in AGN coro-nae once hadrons are accelerated together (e.g., Begel-man et al. 1990; Stecker et al. 1992; Alvarez-Mu˜niz &M´esz´aros 2004). Recent studies have proposed thatthese AGN core models could reproduce the high energyneutrino fluxed measured by IceCube (Stecker 2005,2013; Kalashev et al. 2015). However, normalization ofneutrino fluxes from AGNs and acceleration propertiesof high energy particles in those models are assumed tomatch with the observation.We found that AGN coronae can explain the diffuseneutrino fluxes below 100–300 TeV under specific pa-rameters of energy injection rates in protons and gyrofactors. The allowed parameter regions are quite nar-row. Protons and electrons should have the same energyinjection rate and the gyro factor η g should be ∼
30. Ice-Cube Gen-2 will be able to test this scenario by search-ing the neutrino signal from nearby Seyfert galaxies suchas NGC 4151 and IC 4329A.In summary, Seyfert coronae are feasible sites for par-ticle acceleration. If the energy injection rate is 5%for both protons and electrons and the gyro factor is η g = 30, they may be able to simultaneously explainthe cosmic X-ray, MeV gamma-ray, and TeV neutrinobackground radiation. Future MeV gamma-ray and TeVneutrino observations will be able to test this scenarioby observations of nearby bright Seyferts.We thank the anonymous referee for his/her helpfulcomments which improved the manuscript. We alsowould like to thank Tsuguo Aramaki, Mitch Begel-man, Norita Kawanaka, Shigeo Kimura, Ari Laor, KohtaMurase, Satomi Nakahara, and Marek Sikora for usefuldiscussions and comments. YI is supported by JSPSKAKENHI Grant Number JP16K13813, JP19K14772,program of Leading Initiative for Excellent Young Re-searchers, MEXT, Japan, and RIKEN iTHEMS Pro-gram. DK is supported by JSPS KAKENHI GrantNumbers JP18H03722, JP24105007, and JP16H02170.REFERENCES Aartsen, M. G., Abraham, K., Ackermann, M., et al. 2015,ApJ, 809, 98 Ackermann, M., Ajello, M., Allafort, A., et al. 2012a, ApJ,755, 164—. 2012b, ApJ, 747, 104—. 2013, Science, 339, 807Ackermann, M., Ajello, M., Albert, A., et al. 2015, ApJ,799, 86 n the high energy particles in massive black hole coronae Aharonian, F., Anchordoqui, L., Khangulyan, D., &Montaruli, T. 2006, in Journal of Physics ConferenceSeries, Vol. 39, Journal of Physics Conference Series, ed.A. Bottino, E. Coccia, J. Morales, & J. Puimed´onv,408–415Aharonian, F. A. 2004, Very high energy cosmic gammaradiation : a crucial window on the extreme Universe(World Scientific Publishing Co), doi:10.1142/4657Aharonian, F. A., Barkov, M. 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