Hadronic origin of multi-TeV gamma rays and neutrinos from low-luminosity active galactic nuclei: implications of past activities of the Galactic center
aa r X i v : . [ a s t r o - ph . H E ] J u l Hadronic origin of multi-TeV gamma rays and neutrinos from low-luminosity activegalactic nuclei: implications of past activities of the Galactic center
Yutaka Fujita
Department of Earth and Space Science, Graduate School of Science,Osaka University, Toyonaka, Osaka 560-0043, Japan
Shigeo S. Kimura
Frontier Research Institute for Interdisciplinary Sciences,Tohoku University, Sendai, 980-8578, Japan andAstronomical Institute, Tohoku University, Sendai 980-8578, Japan
Kohta Murase
Center for Particle and Gravitational Astrophysics; Department of Physics; Department of Astronomy & Astrophysics,The Pennsylvania State University, University Park, Pennsylvania, 16802, USA andInstitute for Advanced Study, Princeton, New Jersey 08540, USA (Dated: August 29, 2018)Radiatively inefficient accretion flows (RIAFs) in low-luminosity active galactic nuclei (LLAGNs)have been suggested as cosmic-ray and neutrino sources that may largely contribute to the observeddiffuse neutrino intensity. We show that this scenario naturally predicts hadronic multi-TeV gamma-ray excesses around Galactic centers. The protons accelerated in the RIAF in Sagittarius A ∗ (SgrA ∗ ) escape and interact with dense molecular gas surrounding Sgr A ∗ , which is known as the centralmolecular zone (CMZ), and produce gamma rays as well as neutrinos. Based on a theoretical modelthat is compatible with the IceCube data, we calculate gamma-ray spectra of the CMZ and find thatthe gamma rays with > ∼ ∗ was more active in the past than it is today as indicated by various observations.Our model predicts that neutrinos should come from the CMZ with a spectrum similar to thegamma-ray spectrum. We also show that such a gamma-ray excess is expected for some nearbygalaxies hosting LLAGNs. I. INTRODUCTION
Recently, the IceCube Collaboration reported the dis-covery of extraterrestrial neutrinos [1–3]. The origin ofthe neutrinos is a matter of a debate ([4–19] for reviews,see [20, 21]). The data so far are compatible with anisotropic distribution, which suggests that neutrinos areof extragalactic origin. Diffuse gamma-ray data also sup-port this idea [6, 10]. However, the sources have notbeen identified because of poor angular information andstatistics for the neutrinos. One way of improving thissituation may be detection of counterparts through elec-tromagnetic waves.Low-luminosity active galactic nuclei (LLAGNs) are acandidate for the source of the neutrinos. The LLAGNsare expected to have radiatively inefficient accretion flows(RIAFs), which are realized when the mass accretion rateinto the supermassive black hole (SMBH) is relativelysmall ( ˙
M / ˙ M Edd < ∼ . M Edd = L Edd /c isthe Eddington accretion rate, and L Edd is the Eddingtonluminosity [22]. In the tenuous and turbulent plasmain the RIAFs, cosmic ray (CR) protons may be accel-erated via stochastic acceleration or magnetic reconnec-tion [19]. These CR protons interact with other nucleons( pp interaction) and photons ( pγ interaction) in the flowand generate neutrinos. Although the production rateof the neutrinos per an LLAGN is not large compared with other more energetic sources such as quasistellarobjects (QSOs), the abundance of LLAGNs can repro-duce observed neutrino flux on the Earth [19]. Even if itis difficult to resolve LLAGNs as point neutrino sources,gamma rays from them could be used to test this model.In particular, the gamma rays that are a byproduct of the pp interactions have energies comparable to those of theneutrinos, which means that the gamma-ray spectrumshould reflect the neutrino spectrum unless the gammarays are not absorbed.Sagittarius A ∗ (Sgr A ∗ ) is the SMBH at the center ofthe Galaxy and it is known as an LLAGN. The currentmass accretion rate of Sgr A ∗ is very small and the accre-tion flow is thought to be a RIAF [23]. The current pro-duction rate of CR protons in the RIAF is expected to besmall because of the small accretion rate [24]. Thus, thegamma-ray luminosity of the RIAF in the TeV band isalso expected to be small because of inefficient pion pro-duction [19]. However, it has been indicated that Sgr A ∗ was much more active in the past [25–28]. During thoseactivities, a large amount of protons could have been ac-celerated and escaped from the RIAF. Moreover, observa-tions have revealed that there is a huge amount of molec-ular gas surrounding Sgr A ∗ . This gas concentration isknown as the central molecular zone (CMZ) with the sizeof R CMZ ∼
100 pc and the mass of M CMZ ∼ M ⊙ [29].Strong turbulence and magnetic fields in the CMZ maydelay the diffusion of the CR protons that have plungedinto the CMZ, and those protons may stay in the CMZfor a long time. In this paper, we calculate the diffusionof the protons in the CMZ that have accelerated andescaped from the RIAF in Sgr A ∗ . We estimate gamma-ray and neutrino emissions created through pp interac-tions between the CR protons and protons in the CMZ.We show that TeV gamma rays from the CMZ aroundSgr A ∗ and nearby LLAGNs observed with the High En-ergy Stereoscopic System (HESS) may be produced bythis mechanism. Previous studies have shown that thegamma-ray excess observed in those objects at > ∼ pp interactions in the CMZ by different approaches [32–36]. II. COSMIC-RAY PROTON ACCELERATION INRADIATIVELY INEFFICIENT ACCRETIONFLOWS OF SGR A ∗ In our model, protons are accelerated in the RIAF ofSgr A ∗ . Since the acceleration is confined in a small re-gion on a scale of a few tens of the Schwarzschild radiusof the SMBH, we consider the acceleration based on aone-zone model as previous studies [19, 37, 38]. Accord-ing to the model of Ref. [19], the typical energy of theaccelerated protons is determined by the balance betweenthe acceleration time of the protons in a RIAF ( t acc , R )and their escape time from the RIAF. The escape timeis comparable to the diffusion time of the protons in theRIAF ( t diff , R ). Thus, the Lorentz factor correspondingto the typical energy is obtained by solving the equationof t acc , R = t diff , R and the result is E p, eq m p c ∼ . × (cid:18) ˙ m . (cid:19) / (cid:18) M BH × M ⊙ (cid:19) / × (cid:16) α . (cid:17) / (cid:18) ζ . (cid:19) (cid:18) β (cid:19) − (cid:18) R acc R S (cid:19) − / , (1)where m p is the proton mass, ˙ m is the normalized accre-tion rate ˙ m = ˙ M / ˙ M Edd , α is the alpha parameter of theaccretion flow [39], ζ is the ratio of the strength of tur-bulent fields to that of the nonturbulent fields, β is theplasma beta parameter, R acc is the typical radius whereparticles are accelerated, and R S is the Schwarzschildradius of the black hole [19]. For the parameters ofthe RIAF, we take α = 0 . ζ = 0 . β = 3, and R acc = 10 R S as fiducial parameters, because the neu-trino flux at ∼ L p, tot = η cr ˙ M c , where η cr is theparameter and we take η cr = 0 .
015 as the fiducial valuefollowing Ref. [19]. When only stochastic acceleration is effective, the production rate of protons in the momen-tum range p to p + dp is˙ N ( x ) dx ∝ x (7 − q ) / K ( b − / ( x ) dx , (2)where x = p/p cut , K ν is the Bessel function, and b =3 / (2 − q ) [40]. The power-law index of turbulence re-sponsible for the acceleration is assumed to be q = 5 / p cut = (2 − q ) / (2 − q ) p eq = p eq /
27, where p eq = E p, eq /c [19, 40]. We determine the normalization of Eq. (2) sothat the total power of the protons is L p, tot . III. DIFFUSION OF PROTONS IN THE CMZ
Protons accelerated in Sgr A ∗ leave the accelerationsite (RIAF) and disperse into the interstellar space. Someof them would enter the CMZ surrounding Sgr A ∗ . Wesolve a diffusion-convection equation for the CR protonsin the CMZ. For the sake of simplicity, we solve a spher-ically symmetric equation: ∂f∂t = 1 r ∂∂r (cid:18) r κ ∂f∂r (cid:19) − u ∂f∂r + 13 r (cid:20) ∂∂r ( r u ) (cid:21) p ∂f∂p + Q , (3)where f = f ( t, r, p ) is the distribution function, r is thedistance from the Galactic center, p is the momentum ofparticles, κ is the diffusion coefficient, u is the velocityof the background gas, and Q is the source term for theparticles (Sgr A ∗ ). We assume that u = 0, because we areinterested in the CRs inside the CMZ, which is too heavyto be moved by possible outflows from Sgr A ∗ . We donot consider CRs carried by the outflows without enteringinto the CMZ. We assume that the CMZ is uniform andits dense gas occupies at r < R CMZ .The actual CMZ has a disclike structure and does notentirely cover Sgr A ∗ [29]. Thus, we expect that mostof the CR protons do not plunge into the CMZ, and weassume that only a fraction λ of the protons acceleratedin the RIAF are injected into the CMZ. Thus, the sourceterm in Eq. (3) is written as R πcp Qdp = λL p, tot = λη cr ˙ M c . Since the size of the CMZ ( R CMZ ∼
100 pc)is much larger than that of the RIAF, we treat Q as apoint source.We assume that the diffusion coefficient of CRs outsidethe RIAF is given by κ = 10 (cid:18) E p
10 GeV (cid:19) . (cid:18) B µ G (cid:19) − . cm s − , (4)where E p is the particle energy. This coefficient is forthe ordinary interstellar space in the Galactic disc [41].We only consider resonant scattering, which is valid atsufficiently low energies. Although the diffusion coeffi-cient in the CMZ is not known, we apply Eq. (4) tostronger magnetic field cases. If there are strong mag-netic fields ( B ∼ mG) in the CMZ [29], the coefficient ismuch smaller than that in the intercloud space aroundthe Galactic center ( B ∼ µ G) [42]. In fact, it has beenindicated that the diffusion coefficient in molecular gasaround supernova remnants is much smaller than the or-dinary value [43]. From now on, we fix magnetic fields at B = 1 mG for r < R CMZ and 10 µ G for r > R
CMZ . We donot consider stochastic acceleration in the CMZ. This isbecause the diffusion coefficient we assumed in Eq. (4) istoo large for effective particle acceleration. In fact, previ-ous studies have shown that the diffusion coefficient mustbe as small as that for the Bohm diffusion for particlesto be accelerated up to > ∼ TeV [34, 44]. It is not certainwhether such a small coefficient is realized by turbulencein and around the CMZ. We do not include cooling ofthe protons in Eq. (3), because the cooling time is largerthan the diffusion time estimated based on Eq. (4) (seelater).CR protons interact with protons in the CMZ. For agiven distribution function f , we calculate the produc-tion rate of gamma-ray photons using the code providedby [45] and the formula provided by [46] for E p < E p > ∼
10 eVcm − ) is much smaller than that of the assumedmagnetic field ( ∼ mG) [48]. Thus, the gamma-ray emis-sion via inverse Compton scattering by secondary elec-trons can be ignored. IV. GAMMA RAYS FROM THE CMZ AROUNDSGR A ∗ Observations showed that the radius of the CMZ atthe Galactic center is R CMZ , obs = 200 pc, the thick-ness is H CMZ , obs = 75 pc, and the mass is M CMZ =2 × M ⊙ [49, 50]. Thus, the average density is ρ CMZ = M CMZ / ( πR , obs H CMZ , obs ) = 1 . × − gcm − . SinceEq. (3) assumes spherical symmetry, we define an effec-tive radius R CMZ ≡ (cid:18) M CMZ πρ CMZ (cid:19) / = 130 pc , (5)and we use this as the radius of the CMZ inthe following calculations. The covering factorof the CMZ for r < R CMZ , obs is f CMZ = πR , obs H CMZ , obs / (4 πR , obs /
3) = 0 .
5, The fractionof CR protons that enter into the CMZ, λ , may be com-parable to f CMZ . However, if the protons are not spheri-cally emitted and they are, for example, carried by strongoutflows perpendicular to the disclike CMZ, the fraction may be much smaller. Moreover, the inner edge of theCMZ may not have contact with Sgr A ∗ . Thus, we as-sume that λ ≤ .
5, and λ ≪ . M BH =4 . × M ⊙ [51], and the current mass accretion rate is˙ M = 4 × − M ⊙ yr − [23]. Since the Eddington luminos-ity is given by L Edd = 1 . × ( M BH /M ⊙ ) erg s − , theEddington accretion rate is ˙ M Edd = 9 . × − M ⊙ yr − .Thus, the normalized accretion rate is written as ˙ m =4 . × − . For these and the fiducial parameters, weobtain E p, eq = 0 . t = 0 to 10 yr. There are no CRs at t = 0. Thedistribution of CRs has achieved a steady state at theend of the simulation because the diffusion time of CRsis only t diff , C = R / (6 κ ) ∼ . × yr at E p ∼ t = 10 yr. Since thistime scale is much larger than t diff , C , the energy spec-trum of the CR protons is almost uniform in the CMZ[43, 52]. As long as the spectrum of the injected CRsdoes not vary significantly, our model does not expectsubstantial variation in the gamma-ray spectrum acrossthe CMZ (see later), which is consistent with observa-tions. The distance to Sgr A ∗ and the CMZ is assumedto be 8.5 kpc.The inverse of the cooling time of CR protons due to pp interactions is t − pp ∼ n CMZ σ pp cK pp , (6)where n CMZ = ρ CMZ /m p and K pp ( ∼ .
5) is the protoninelasticity of the process. The total cross section of theprocess is given by σ pp = (34 . . L + 0 . L ) " − (cid:18) E th E p (cid:19) mb , (7)where E th = 1 .
22 GeV is the threshold energy of produc-tion of π mesons and L = ln( E p / t pp ∼ × yr at E p ∼ t diff , C . Since t pp > t diff , C is satisfied inthe energy of interest ( E p > ∼ m = 4 . × − and λ = 0 .
01 regardless of t . Other parameters are the fidu-cial ones. For comparison, we show the GeV and TeVgamma-ray fluxes obtained with Fermi and HESS obser-vations [53, 54]. The predicted gamma-ray flux is muchsmaller than the observations. The fraction of λ ∼ . E ∼ λ = 0 . ∗ is exceptionally small, and that the average -10 -8 E (GeV) E d N / d E ( G e V c m - s - ) γν i FIG. 1. Predicted gamma-ray flux (dashed line) and neutrinoflux (two-dot dashed line) from the CMZ when ˙ m = 4 . × − and λ = 0 .
01. Filled circles and squares are the Fermi andHESS observations, respectively [53, 54]. -10 -8 E (GeV) E d N / d E ( G e V c m - s - ) γν i FIG. 2. Same as Fig. 1 but for ˙ m = 0 . λ = 5 × − . accretion rate more than ∼
100 yrs ago might be muchlarger and it could be as much as 10 –10 times the cur-rent one [25–28]. Thus, we calculate the gamma-ray andneutrino fluxes when ˙ m = 0 .
001 and λ = 5 × − re-gardless of t . The drop of activity in the past ∼
100 yrsdoes not affect the results because the diffusion time ofCRs is much larger than 100 yrs. Other parameters arethe same as the fiducial ones. These give the typical en-ergy of E p, eq = 3 . m and M BH , any combinations of parameters ( α , ζ , β ,and R acc /R S ) that give the same E p, eq give the samespectrum. Moreover, any combinations of λ and η cr thatgive the same λη cr give the same spectrum. Figure 2shows the results of this model; the gamma-ray spectrumat E ∼ . E > ∼
10 TeV become available -10 -8 E (GeV) E d N / d E ( G e V c m - s - ) γν i FIG. 3. Same as Fig. 1 but for ˙ m = 0 . λ = 3 × − , ζ = 0 .
18, and η cr = 6 × − . -10 -8 E (GeV) E d N / d E ( G e V c m - s - ) γ outin FIG. 4. Same as Fig. 1 but when ˙ m is variable (see text).Thick dashed line is the total gamma-ray flux. Thin dottedline (out) is the gamma-ray flux from 0 . R CMZ < r < R
CMZ .Thin dot-dashed line (in) is that from 0 < r < . R CMZ . in the future (e.g. Cherenkov Telescope Array; CTA [55],High Altitude Water Cherenkov detector; HAWC [56]),our model predicts a soft gamma-ray spectrum in thatenergy band. Since the designed sensitivities of CTA andHAWC at E ∼ ∼ ◦ × . ◦ , it can be wellresolved by CTA with a resolution of ∼ ′ [55]. Detailedmaps of gamma rays will reflect not only the distributionof molecular gas but that of CRs. The latter may reflectthe history of Sgr A ∗ activities, if the activities signifi-cantly change on the diffusion time scale of the CRs.From the current neutrino observations with IceCube,the flux of ∼ × − GeVcm − s − can be attributed tothat from the Galactic center [10]. Since the predictedfluxes in Figs. 1 and 2 are smaller than that, they areconsistent with the observations. However, as the statis-tics of neutrinos improve, we may detect an excess inthe direction of the Galactic center in the future. Inparticular, observations with KM3NeT would be usefulto detect the CMZ as a neutrino source if the flux is > ∼ − GeV cm − s − [57]. Our model predicts that theneutrino image should coincide with the gamma-ray im-age because both are the results of pp interactions.Since parameters for the RIAF have some uncertain-ties, we adopt another model that can reproduce the neu-trino flux at ∼ ζ = 0 . η cr = 6 × − . We take ˙ m = 0 . λ = 3 × − so that the flux at E ∼ E p, eq = 160 TeV (Eq. 1),which is much larger than that of the model in Fig. 2.The results are shown in Fig. 3. If this is the case, a rel-atively hard gamma-ray spectrum would be observed byCTA at ∼ E < ∼ m ,is constant. Here, we discuss the effects of variable ˙ m .The x-ray light curve of Sgr A ∗ in the past 500 yrs wasderived in Ref. [28]. They showed that the x-ray lu-minosity is L X ∼ erg s − in the past 50–500 yrs,and then it dropped to the current value of L X ∼ –10 erg s − . The x-ray luminosity before 500 yrs agois less constrained. Upper limits are placed to down toabout 8 × erg s − for several periods within the past4 × yrs [58, 59]. Before that, upper limits are ∼ –10 erg s − [58, 59]. The x-ray luminosity of a RIAF isproportional to ˙ m [22]. Assuming that the x-ray lu-minosity follows the above observations and upper lim-its, and that t = 10 yr is the current time, we set˙ m = 0 .
03 for 0 < t < t − × yr, ˙ m = 0 .
01 for t − × yr < t < t − × yr, ˙ m = 0 .
001 for t − × yr < t < t −
50 yr, and ˙ m = 4 . × − for t −
50 yr < t < t . Other parameters, including the fidu-cial values, are time-independent, except for λ = 4 × − and ζ = 0 . E ∼ . m decreases as time advances, the typicalenergy of the CRs, E p, eq , in the CMZ should decreasefrom the outer region to the inner region [Eq. (1)]. Weobtain E p, eq = 2 . m = 0 .
03. However, theshape of gamma-ray spectrum from 0 < r < . R CMZ isnot much different than that from 0 . R CMZ < r < R
CMZ . The peak gamma-ray energy of the former is only a fac-tor of 2 smaller than the latter. Most of the gamma-rayflux from the CMZ is associated with CRs injected when˙ m = 0 .
03, because they are injected during most of thepast diffusion time ( t − t diff , C < t < t − × yr), where t diff , C = R / (6 κ ) ∼ . × yr (at E p ∼ E < ∼ m ≤ .
001 are locatedat r < ∼ . R CMZ . However, their short injection timescale compared with t diff , C and the smaller injection rate( L p, tot ∝ ˙ m ) make their contribution to the gamma-rayflux smaller. In other words, the contribution of CRs isrepresented in the form of R λL p, tot dt integrated for thepast diffusion time. Moreover, since the higher-energyCRs ( ≫ E p, eq , sig-nificantly varies in the past, while ˙ m does not muchdecrease [see (Eq. 1)], the gamma-ray spectrum canchange across the CMZ. Note that the gamma-ray lu-minosity of the RIAF is proportional to ˙ m and it is ∼ . L p, tot ∼ erg s − when ˙ m = 0 .
001 [19]. Al-though this is larger than the current total gamma-rayluminosity of the CMZ at ∼ ∼ × erg s − ),the gamma-rays from the RIAF cannot be observed atpresent. This is because the gamma-ray luminosity ofthe RIAF almost immediately changes with ˙ m , owing tothe short ( < V. GAMMA RAYS FROM THE CMZ AROUNDCENTAURUS A
Since some LLAGNs other than Sgr A ∗ also have theirown CMZs, gamma rays and neutrinos may be createdthere. As for neutrinos from their RIAFs, LLAGNs with˙ m ∼ . m and RIAFs are realized when ˙ m < ∼ . λ < ∼ − of the CR protons acceler-ated in those RIAFs enter their CMZs as is the case ofSgr A ∗ , the production rate of neutrinos in the CMZs issmaller than that in the RIAFs. Thus the contributionof the former to the overall neutrino flux on the Earth isexpected to be smaller than the latter. However, if theRIAF in a nearby galaxy is well covered with massivemolecular gas or a CMZ and ˙ m is relatively large, thegamma rays from the CMZ may still be detectable as anindividual source.In Fig. 5, we show as an example the gamma-ray fluxfrom Centaurus A (Cen A), which is a nearby radiogalaxy and for which the origin of the gamma rays isunder debate [62, 63]. The distance to Cen A is assumedto be 3.84 Mpc. We do not include the absorption of -10 -8 E (GeV) E d N / d E ( G e V c m - s - ) γ ν i FIG. 5. Predicated gamma-ray flux (dashed line) and neu-trino flux (two-dot dashed line) from Cen A. Parameters areshown in the text. Filled circles and squares are the Fermiand HESS observations, respectively [60, 61]. the gamma rays. The radius, thickness, and mass ofthe CMZ are R CMZ , obs =195 pc, H CMZ , obs =195 pc, and M CMZ = 8 . × M ⊙ , respectively [64]. The mass of theSMBH is M BH = 5 × M ⊙ [65]. We choose ˙ m = 0 . λ = 0 .
02, and ζ = 0 .
03 in order to reproduce the HESSresults. Other parameters are the same as the fiducialones. These give the typical energy of E p, eq = 7 . λ may be largerthan that of Sgr A ∗ . Figure 5 shows that our modelcan reproduce the HESS observations at E > ∼ E < ∼ VI. SUMMARY
We have shown that TeV gamma rays from theGalactic center can be used to test a model in whichlow-luminosity active galactic nuclei (LLAGNs) are thesource of neutrinos observed with IceCube. In this model,protons are accelerated in the radiatively inefficient ac-cretion flows (RIAFs) in the LLAGNs, and neutrinos arecreated through pp and pγ interactions in the flows. SinceSgr A ∗ at the center of the Galaxy is an LLAGN, we ex-pect that the protons are being accelerated in Sgr A ∗ andinjected into the interstellar space.In this study, we found that the central molecular zone(CMZ) surrounding Sgr A ∗ works as an effective targetof the high-energy protons escaped from the RIAF and gamma rays and neutrinos are created there through pp interactions. We showed that our model can explain thegamma rays observed by HESS at E ∼ . ∗ was ∼ times largerin the past than it is today as indicated by previousstudies, and if the typical energy of the CR protons is ∼ TeV. 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