Hadronic-origin TeV flare of M87 in April 2010

M87 is a giant radio galaxy with FR-I morphology. It underwent three episodes of TeV flaring in recent years with the strongest one in April 2010 which was jointly monitored by MAGIC, VERITAS and H.E.S.S. We explain its spectral energy distribution in the energy range 0.3 TeV to 5 TeV by assuming that the flaring occurs in the innermost region of the jet. In this region the low energy SSC photons serve as the target for the Fermi-accelerated high energy protons of energy<30 TeV to form a delta resonance. The TeV photons are produced from the subsequent decay of the delta resonance to neutral pions. In this scenario the observed TeV flux of the 2010 flare is fitted very well.

M87 is a giant radio galaxy with FR-I morphology. It underwent three episodes of TeV flaring in recent years with the strongest one in April 2010 which was jointly monitored by MAGIC, VERITAS and H.E.S.S. We explain its spectral energy distribution in the energy range 0.3 TeV to 5 TeV by assuming that the flaring occurs in the innermost region of the jet. In this region the low energy SSC photons serve as the target for the Fermi-accelerated high energy protons of energy 30 TeV to form a delta resonance. The TeV photons are produced from the subsequent decay of the delta resonance to neutral pions. In this scenario the observed TeV flux of the 2010 flare is fitted very well.

I. INTRODUCTION
M87 is a giant radio galaxy in the Virgo cluster at a luminosity distance of 16.7 ± 0.2 Mpc[1] and a redshift of z = 0.00436. The mass of the central supermassive black hole (SMBH) is estimated be M BH = (3 − 6)× 10 9 M ⊙ [2]. Based on its radio morphology it is classified as FR-I galaxy [3]. The radio images and modeling of its interaction with the surrounding environment suggests that the jet is misaligned with respect to the line of sight [3,4]. The substructures in the plasma jet originated from the center of M87 is resolved at different wavelengths (radio [5], optical [3] and x-ray [6]). Due to the harboring of SMBH in the center and the presence of the jet, M87 was considered as a potencial candidate of TeVemission. The evidence for very high energy (VHE) γrays (E γ > 100 GeV) emission from M87 was reported by the HEGRA Collaboration in 2003 [7] and was later confirmed by H.E.S.S., VERITAS [8,9] and MAGIC. The AGN M87 is normally a weak VHE source, but this source shows strong variability at VHE with time scales of the order of days, which indicates a compact emission region < 5 × 10 15 D cm, (where D is the Doppler factor of the emitting plasma), corresponding to only a few Schwarzschild radii R s = 2GM BH /c 2 ≃ 10 15 cm.
So far, there are three episodes of enhanced VHE γ-ray emission observed from the AGN M87 in the years 2005 [10,11], 2008 [8] and 2010 [8,12]. The latest one of April 2010, is the strongest TeV γ-ray flare ever detected from the AGN M87 with a peak flux of (2.7 ± 0.68) × 10 −11 cm −2 s −1 for E γ > 350 GeV [8,9,13]. The detected single isolated flare is well described by two sided exponential functions with significantly different flux rise and decay times [8]. The rising (5 to 8 of April), peak (9 to 10 of April) and falling (11 to 15 of April) parts of the flux during the flare are consistent with power-law behavior. This flare was detected simultaneously by VERITAS, MAGIC and H.E.S.S. [9,12], and triggered further multi-wavelength observations in radio, optical and x-ray. This was also observed by Fermi-LAT at MeV-GeV energies but could not observe day-scale variability [13].
Different theoretical models have been proposed to explain the flaring in M87. Wagner et al. [14] have complied the multi-wavelength data sets spanning almost all the energy range and presented a spectral energy distribution (SED) of M87 along with leptonic and hadronic models predictions. The hadronic synchrotron-proton blazar model [15] suggests emission of synchrotron photons from protons, charged pions and muons in the jet magnetic field. However the SED produced using the archival data before 2004 shows a steep drop-off at TeV energies and to explain above TeV energy a strong Doppler boosting in needed which is not the case in M87. So this model is not compatible with any of the VHE spectral measurements after 2004. The leptonic decelerating inner jet model by Georganopoulos et al. [16] does not describe the hard TeV spectra well as it has a strong cut-off. The multiblob synchrotron self Compton (SSC) model by Lenain et al. [7] needs a low magnetic field in the VHE emitting region which is unlikely because this region is of the order of the Schwarzschild radius and is expected to have strong field. Thus the so called one-zone homogeneous leptonic models of Georganopoulos et al. [16] and Lenain et al. [7] are very unlikely to reproduce the observed VHE spectrum. The lepto-hadronic model [17] fits to the low energy γ-ray spectrum by Fermi/LAT and HESS low state but not the flaring state. The spine-sheath model by Tavecchio and Ghiselline [18] has difficulties to achieve a harder spectrum in the VHE range due to strong absorption of the TeV photons from interactions with the optical-infra red (IR) photons from the spine. In the jet-in-jet model of Giannios et al. [19] minijets are formed within the jet due to flow instabilities and these minijets move relativistically with respect to the main jet flow. The interaction of the daughter jets with the main jet are responsible for the production of VHE gamma rays. While the minijets are aligned with our line of sight, the VHE gamma rays are beamed with large Doppler factor. This scenario can explain the 2010 flare but does not provide a quantitive prediction of the light curve of the flare. Similarly, the magnetosphere model [20][21][22] can explain the hard TeV spectrum but in this case also there is no detailed quantitive predication for the VHE light curve. Similarly in the work by Cui et al. [23] can explain the VHE gamma ray flare in an external inverse Compton model with a very wide jet to have a Doppler boosting. Borkov et al. [24] have proposed a scenario where a red giant star with a loosely bound envelope of mass ∼ 10 29 g interacts with the base of the M87 jet. The VHE emission is produced near the SMBH due to the interaction of the cosmic ray protons emerging from the jet with the disrupted dense cloud of the red giant through proton-proton interaction. This model reproduced well the light curve and the energy spectrum of the April 2010 flare. But how universal is this scenario ? Can we be sure that VHE flaring in other AGNs/Blazars happen only due to the interaction of respective jet with the intervening cloud from a foreign object ? If so, can we be able to explain the multiple episodic flaring of these objects. Possibly, the 2010 flaring of M87 might be due to the jet cloud interaction, but it is unlikely to be universal. Limitations of the above discussed models and the non-universality of the jet cloud scenario can be overcome in an alternative scenario presented and applied to the orphan TeV flaring of the blazar 1ES 1959+650 [25]. A similar scenario is also invoked to explain the multi-TeV emission from Centaurus A [26]. In this mechanism, the low energy tail of the SSC photons or the SSC peak serves as the target for the Fermi-accelerated high energy protons to produce the pions through delta resonance and their subsequent decay to high energy photons and neutrinos. This scenario neither needs any intervening foreign object nor any special jet cloud geometry [27] to produce the high energy photons.
The plan of the paper is as follows: In Sec.II we review in detail the flaring model and the kinematical condition for the production of ∆-resonance. The results are discussed in Sec.III and we briefly conclude in Sec.IV.

II. THE FLARING MODEL
In a recent paper Sahu et al. [25] have explained the orphan TeV flare of 4th June, 2002, from the blazar 1ES1959+650 through hadronic model. In this work they use the standard interpretation of the leptonic model to explain both, low and high energy peaks, by synchrotron and SSC photons respectively as in the case of any other AGNs and Blazars. Thereafter, they propose that the low energy tail of the SSC photons in the blazar jet serve as the target for the Fermi-accelerated high energy protons of energy ≤ 100 TeV, within the jet to produce TeV photons through the decay of neutral pions from the delta resonance. This model explains very nicely the observed TeV flux from the orphan flare. Also it is interesting to note that, this scenario is self sufficient and does not need any external medium for the production of gamma rays. As discussed, the flaring occurs within a compact and confined volume of radius R ′ f inside the blob of radius Figure  1 of ref. [25] . Both the internal and the external jets are moving with the same bulk Lorentz factor Γ and the Doppler factor D as the blob. In normal situation within the jet, we consider the injected spectrum of the Fermi accelerated charged particles having a power-law spectrum dN/dE ∝ E −α with the power index α ≥ 2. But in the flaring region we assumed that the Fermi accelerated charged particles have a power-law with an an exponential cut-off spectra [25,28], it is given as where the high energy proton has the cut-off energy E p,c and again the spectral index has the restriction α > 2. Also probably due to the copious annihilation of electron positron pairs, splitting of photons in the magnetic field, enhance IC photons and Poynting flux dominated flow from the magnetic reconnection in the strongly magnetized plasma around the base of the jet [19,29], the comoving photon density n ′ γ,f (flaring) in the flaring region is much higher than the rest of the blob n ′ γ (non-flaring) i.e. n ′ γ,f (ǫ γ ) ≫ n ′ γ (ǫ γ ). Here we assume that the ratio of photon densities at two different background energies ǫ γ1 and ǫ γ2 in flaring and non-flaring states remains the same, that is In general, in the leptonic one-zone synchrotron and SSC jet model the emitting region is a blob with comoving radius R ′ b moving with a velocity β c corresponding to a bulk Lorentz factor Γ and seen at an angle θ ob by an observer which results with a Doppler factor D = Γ −1 (1 − β c cos θ ob ) −1 . The emitting region is filled with an isotropic electron population and a randomly oriented magnetic field B ′ . The electrons have a power-law spectrum. The energy spectrum of the Fermi-accelerated protons in the blazar jet is also assumed to be of powerlaw. Due to high radiative losses, electron acceleration is limited. On the other hand, protons and heavy nuclei can reach UHE through the same acceleration mechanism.
Due to photohadronic interaction in the jet, the pions are produced through the intermediate ∆-resonance and is given by which has a cross section σ ∆ ∼ 5 × 10 −28 cm 2 . Subsequently, the charged and neutral pions will decay through π + → e + ν e ν µνµ and π 0 → γγ respectively. The produced neutrinos and photons are in the GeV-TeV range energy. For the production of ∆-resonance, the kinemat-ical condition is where E ′ p and ǫ ′ γ are respectively the proton and the background photon energies in the comoving frame of the jet. We define the quantities with a prime in the comoving frame and without prime in the observer frame. For high energy protons we assume β p ≃ 1. Since in the comoving frame the protons collide with the SSC photons from all directions, in our calculation we consider an average value (1 − cos θ) ∼ 1 (θ in the range of 0 and π). Going from comoving frame to observer frame, the proton and photons energies can be written as respectively and the kinematical condition given in Eq.(4) can be written in the observer frame as In the jet comoving frame, each pion carries ∼ 0.2 of the proton energy while 50% of the π 0 energy will be given to each γ. So the relationship between high energy γray and the E p is E γ = DE p /10. From these relations we can express the ∆-resonance kinematical condition in terms of photon energies (target photon energy ǫ γ and the observed photon energy E γ ) as The optical depth to produce the ∆-resonance is given as The comoving photon number density within the confined volume can be given in terms of the luminosity L γ as with κ ∼ (0 − 1) (depending on whether the jet is continuous or discrete) and η ∼ 1 . Here in this work we consider κ = 0. For κ = 1, the photon density will be reduced by a of factor D −1 in the discrete jet as compared to continuous one. The relationship between observed γray flux F γ , high energy proton flux and the background SSC photon density in the flaring region is given as [25] Then the observed high energy γ-ray flux at two different energies will scale as −α+2 e −(Eγ 1 −Eγ 2 )/Ec , (12) where E γ1,2 are two different γ-ray energies and correspondingly the proton energies are E p1,2 . In the above equation (12) we have used the relations in Eq. (2) and From an observed flux in a given energy, we can calculate the fluxes at other energies by using Eq. (12). The optical depth τ pγ implies that out of τ −1 pγ many protons, one will interact with the SSC background photons to produce ∆-resonance. In this case the fluxes of the TeV photons and the Fermi accelerated high energy protons F p , are related through Like photons, the proton fluxes at different energies E p1 and E p2 , scale as From this relation we can calculate the proton fluxes at different energies.

III. RESULTS
With the homogeneous leptonic one-zone synchrotron and SSC jet model [30] the SED is fitted assuming the viewing angle 10 o and bulk Lorentz factor Γ = 2.3 which corresponds to a Doppler factor D = 3.9 which is shown in Figure 4 of Ref. [10]. Based on the multi-band correlations detected in the 2005 and 2008 flaring events of M87, the core and the HST-1 are favored as the emitting regions. But during the VHE flare of 2008 and 2010, Chandra detected an enhanced x-ray flux from the core region which are the two highest measurements since the start of its observation in 2002. During these time HST-1 remained in a low state [6]. During the 2005 VHE flaring episode no enhanced x-ray emission from the core was detected. On the other hand, at that time, HST-1 was more than 30 times brighter than the core region in xrays leading to uncertainty in the flux estimation of the core [31] . The coincidence in x-ray and VHE emission as well as the observed timescales of short variability (∼ day) at VHE/x-ray suggests that the size of the emitting region is compact lead to believe that the 2010 VHE flare probably originates in the innermost region of the jet. So here we assume that the flaring occurs within the confined volume of radius R ′ f = 5 × 10 15 cm which is in the core region. For the fit to the multi-wavelength SED in ref. [10], the source radius is taken to be R ′ b = 1.4 × 10 16 cm which is consistent with the few day timescale variability in TeV and the magnetic field is B = 55 mG. Also this is consistent with R ′ f < R ′ b . In this work we use the SED and parameters of the one-zone synchrotron model given in ref. [10].
During the flaring in April 2010, the high energy γ-ray flux was observed in the energy range 0.3 TeV E γ 5 TeV. Also the flaring had distinct rise time and fall time of the spectra. The rising, the peak and the falling of the flux are fitted with power-law with different flux normalization and the spectral index α [8]. In the hadronic model, the above E γ range corresponds to the proton energy in the range 1.9 TeV E p 30 TeV. Protons in this energy range will collide with the background photons in the energy range 1.5 MeV(3.7 × 10 20 Hz) ǫ γ 0.1 MeV(2.3 × 10 19 Hz) to produce ∆-resonance and subsequent decay of it will produce both γ-rays and neutrinos through neutral and charged pion decay respectively. We can observe that the above ǫ γ lie in the rising part of the SSC photons shown as shaded region in Figure 1. The number density of these photons are also calculated which lie in the range 72 cm −3 n ′ γ 516 cm −3 . As discussed in the ref. [25] for the calculation of the TeV flux, first we take into account one of the observed flaring fluxes with its corresponding energy for normalization e.g. F γ (E γ2 = 3.18 TeV) ≃ 3.8×10 −12 TeV cm −2 s −1 and n ′ γ (ǫ γ2 = 0.15MeV) ≃ 387 cm −3 and using it calculate the flux for other energies with the Eq.(12). This we have done for different observed fluxes for a better fit. The spectral index α and the cut-off energy E c are the free parameters in the model and the best fit is obtained for α = 2.83 and E c ≃ 12 TeV. The γ-ray cut-off energy of ∼12 TeV corresponds to E p,c ≃ 71 TeV and above the cut-off energy the flux decreases rapidly which is clearly shown in Figure 1. With the same α = 2.83 and E c ≃ 12 TeV but different normalized flux we fitted the rising, the peak and the falling flux which are shown in Figure  2. The rising flux is fitted with two different normalized flux to have a better picture. In Figure 3, the fitting of the peak flux in our model is compared with the cloudjet interaction model [24]. It is interesting to note that the spectral index α fitted to the TeV flaring SEDs of M87 and the blazar 1 ES 1959+650 have the same value 2.83 which probably hints for a common mechanism of particle acceleration during the flaring [25].
We have also plotted the ratio of photon densities n ′ γ (ǫ γ1 )/n ′ γ (ǫ γ2 ) of Eq. (12 ) for a given value n ′ γ (ǫ γ2 = 3.7×10 19 Hz) ≃ 386 cm −3 in Figure 4 as a function of SSC photon energy. It shows that the density ratio is almost a linear function of energy. We have specifically chosen the energy range in the vicinity of the shaded region of  [24] for two different injection spectra and fitted to the peak SED of the flare. The continuous curve is the hadronic model fit. Figure 1 which is responsible for the TeV spectra. The standard power-law fitting with an exponential cut-off to the SED [28] is expressed as where F 0 is a constant. But here F 0 is replaced by energy dependent photon density of the background and due to this energy dependent coefficient, fitting to SED in this model is different from the standard one. During the flaring period, not only protons but also electrons are Fermi-accelerated in the inner jet with the same energy as the protons. The e + produced during the π + decay has energy in the range 0.095 TeV E γ 1.5 TeV. These electrons and positrons will produce synchrotron radiation in the jet magnetic field. While the Fermi-accelerated electrons will emit synchrotron photons in the frequency band 2.5 × 10 18 Hz ǫ γ 6.3 × 10 20 Hz, the positrons will radiate in the frequency band 6.3 × 10 15 Hz ǫ γ 1.6 × 10 18 Hz. So the flaring in the TeV energy should be accompanied by a simultane-ous enhanced synchrotron emission in the frequency band 6.3 × 10 15 Hz ǫ γ 6.3 × 10 20 Hz. FIG. 4. The ratio of photon densities n ′ γ (ǫγ 1 )/n ′ γ (ǫγ 2 ) for a given value n ′ γ (ǫγ 2 = 3.7 × 10 19 Hz) is plotted as a function of SSC photon energy. The points are the density ratios for observed data points. The curve is fitted with a straight line.

IV. CONCLUSIONS
The strongest TeV flaring of the radio galaxy M87 in April 2010 is explained by assuming it to be due to the photohadronic interaction of the Fermi-accelerated protons of energy 30 TeV with the SSC photons in the energy range ∼ (0.1 − 1.5)M eV . In this scenario the proton spectrum is a power-law with an exponential cut-off. For the fitting of the rising, the peak and the falling parts of the TeV flare we use the same spectral index α = 2.83 and the γ−ray cut-off energy E c ≃ 12 TeV. Our results fit well to these distinct phases of the flare.