We present results of a study of non-thermal, time-dependent particle
injection in a corona around an accreting black hole. We model the spectral
energy distribution of high-energy flares in this scenario. We consider
particle interactions with magnetic, photon and matter fields in the black hole
magnetosphere. Transport equations are solved for all species of particles and
the electromagnetic output is predicted. Photon annihilation is taken into
account for the case of systems with early-type donor stars.Comment: 7 pages, 7 figures. Accepted for publication in the Proceedings of
  the 25th Texas Symposium on Relativistic Astrophysics, held in Heidelberg,
  December 06-10, 201

Romero, Gustavo E.

Vieyro, Florencia L.

English

arXiv

We present results of a study of non-thermal, time-dependent particle injection in a corona around an accreting black hole. We model the spectral energy distribution of high-energy ﬂares in this scenario. We consider particle interactions with magnetic, photon and matter ﬁelds in the black hole magnetosphere. Transport equations are solved for all species of particles and the electromagnetic output is predicted. Photon annihilation is taken into account for the case of systems with early-type donor stars.Fil: Vieyro, Florencia Laura. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaFil: Romero, Gustavo Esteban. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; Argentina25th Texas Symposium on Relativistic AstrophysicsHeidelbergAlemaniaMax-Planck-Institut für Kernphysi

Vieyro, Florencia Laura

Romero, Gustavo Esteban

CONICET Digital

PoS(Texas 2010)174Gamma-ray flares from black hole coronae.Gustavo E. RomeroInstituto Argentino de Radioastronomía (IAR-CONICET)Facultad de Ciencias Astronómicas y Geofísicas (FCAG, UNLP)E-mail: romero@iar-conicet.gov.arFlorencia L. VieyroInstituto Argentino de Radioastronomía (IAR-CONICET)Facultad de Ciencias Astronómicas y Geofísicas (FCAG, UNLP)E-mail: fvieyro@iar-conicet.gov.arWe present results of a study of non-thermal, time-dependent particle injection in a corona aroundan accreting black hole. We model the spectral energy distribution of high-energy flares in thisscenario. We consider particle interactions with magnetic, photon and matter fields in the blackhole magnetosphere. Transport equations are solved for allspecies of particles and the electro-magnetic output is predicted. Photon annihilation is takeninto account for the case of systemswith early-type donor stars.25th Texas Symposium on Relativistic Astrophysics - TEXAS 2010December 06-10, 2010Heidelberg, Germanyc© Copyright owned by the author(s) under the terms of the CreativCommons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(Texas 2010)174Gamma-ray flares from black hole coronae1. IntroductionThe existence of a broad-band X-ray/soft gamma-ray spectra of accreting black holes in binarysystems strongly suggest the presence of a very hot plasma (corona) aund the central object.The soft X-ray photons produced in the inner accretion disk are Comptonized by the corona [1]producing a power-law, high-energy feature in the spectrum.The effects of a non-thermal population of electrons in a hot corona were considered byKunusose & Mineshige [2] and more recently by Belmont et al. [3] and Vurm & Poutanen [4].Romero et al. [5] have studied the case of a steady state magnetized coronawith injection of bothrelativistic electrons and protons. In the present work we extend the latterwork to time-dependentinjection and calculate the expected electromagnetic emission during a transientevent in a hot mag-netized corona around a galactic black hole. We also study the absorbing effect of an anisotropicphoton-field, provided by the companion star.This paper is motivated by the recent detections of very high energy emission from severalX-ray binaries. For example, the detection of the well known source Cygnus X-1 during a flareepisode constitutes the first putative evidence of very high-energy gamma-ray emission producedaround galactic black hole [6]. More recently, the flaring nature of Cyg X-1 in gamma rays hasbeen confirmed with the AGILE satellite [7]. In addition, four gamma-ray flares w re detected byAGILE satellite from the X-ray binary Cygnus X-3 [8]. The Fermi Large Area Telescope (LAT)has also detected a variable high-energy source coinciding with the positionof Cyg X-3 [9].Here, we apply our model to the X-ray binary Cyg X-1.2. Steady state modelWe consider a spherical corona with a radiusRc = 35Rg, and a luminosity of 1 % of theEddington luminosity of a 10M⊙ black hole. Since the corona is in steady state, by consideringequipartition of energy we can estimate the values of magnetic field and plasma density, whichresult inB= 5.7×105 G andne∼ ni = 6.2×1013cm−3, respectively. It is assumed that the coronais composed of a two-temperature plasma, with an electron temperatureTe = 109 K and an iontemperatureTi = 1012 K (e.g., [10],[11]). The X-ray emission of the corona is characterized by apowerlaw with an exponential cut-off at high energies.We consider an static corona where relativistic particles can be removed bydiffusion. In theBohm regime, the diffusion coefficient isD(E) = rgc/3, whererg = E/(eB) is the gyro-radius ofthe particle.For further details on the static corona model we refer the reader to [5].In this scenario it is expected that relativistic particles lose energy mainly becaus of syn-chrotron radiation and inverse Compton scattering, for electrons and muons, whereas for protonsand charged pion the relevant cooling processes are synchrotron radiation, inellastic proton-protoncollisions, and photomeson production. Figure (1) shows the cooling time fordif e ent radiativeprocesses together with the diffusion rate for primary particles.2.1 Spectral energy distributionWe study the effect of the injection of a power-law distribution of relativistic ele trons and pro-2PoS(Texas 2010)174Gamma-ray flares from black hole coronae6 7 8 9 10 11 12 13 14 15 16 17-3-2-10123456789 Bremsstrahlung IC Synchrotron Acceleration rate Diffusive rate  Log (t-1  / s-1)Log (Ee / eV)(a) Electron losses.9 10 11 12 13 14 15 16 17 18 19-3-2-1012345 p+ p+p Synchrotron Acceleration rate Diffusive rate  Log (t-1  / s-1)Log (Ep / eV)(b) Proton losses.Figure 1: Radiative losses in the static corona previously described[5].tons. The main products of hadronic interactions are charged pions, which then decay producingmuons and neutrinos. Neutral pions yield gamma-rays, that are a source of secondary pairs. There-fore, we also include the effect of the presence of all these secondary particles in our treatment. Wesolve the transport equation in steady state obtaining particle distributions forthe different species.2.1.1 Internal absorptionGamma-rays produced in the corona can be absorbed by different mechanisms. The most rel-evant mechanism in this scenario is photon-photon annihilation. The absorption can be quantifiedby the absorption coefficient or opacityτ. In Fig. (2) we show the opacity due to the interactionbetween gamma-rays and thermal X-ray photons from the corona, which are by far the dominantelectromagnetic component.5 6 7 8 9 10 11 12 13 140255075100125150175  Log (E  / eV) r = 0.1 Rc r = 0.25 Rc r = 0.5 Rc r = RcFigure 2: Internal absorption due to photon-photon pair production.Because of the high values of the opacity, it is expected a great number ofs c ndary pairs tobe created. The effects of internal absorption and the radiation emitted by secondary pairs are alsoinclude in the final SED, which is shown in Fig. (3). This figure also shows the spectrum of thewell-known source Cygnus X-1, detected by COMPTEL [12] and INTEGRAL [13].3PoS(Texas 2010)174Gamma-ray flares from black hole coronae-2 0 2 4 6 8 10 12 14 16303132333435363738  Log (L / erg s-1 )Log (E  / eV) Static corona model Cygnus X-1 CTA MAGIC FermiFigure 3: Spectral energy distribution obtained with the steady state model of a static corona. The predictionfits the observation made by COMPTEL andINTEGRALof Cygnus X-1 ([12, 13]).2.1.2 Gamma-ray opacity due to photopair-production in the stellar radiation fieldThe binary system Cygnus X-1 is composed by a massive star and a compact object. Themassive star is an O9.7 Iab of 40±10M⊙ [14]. The orbit of the system is circular, with a period of5.6 days and an inclination between 25◦ and 65◦ [15].The star provides an intense radiation field that can absorb gamma-rays bypair creation withinthe binary system. The photon field provided by the star is anisotropic, becaus it depends on theposition of the black hole in its orbit (see Fig. 4). We consider the opacity treatment for gamma-rayabsorption in Cygnus X-1 as in [16].The star has a radiusR∗ = 1.5×1012 cm, and for simplicity we asume a blackbody densityradiation of a temperatureT∗ = 3×104 K. The orbital radius isrorb = 3.4×1012 cm. The value ofthe orbital phaseφ = 0 corresponds to the compact object at opposition (Fig. 4).In Fig. (5) we show the gamma-ray emission of the corona in steady state at a given energy.The modulation is due to the photon absorption in the stellar field.3. Flare modelThe temporal dependence of the particle injection is characterized by a FRED (Fast Rise andExponential Decay) behavior, whereas the energy dependence is a power-law. The transient injec-tion can be represented by [17]Q(E, t) = Q0E−αe−E/Emax(1−et/τrise)[π2−arctan( t − τplatτdec)], (3.1)4PoS(Texas 2010)174Gamma-ray flares from black hole coronaeFigure 4: Sketch of the geometry considered for the gamma-ray absorption in the stellar photon field [16].0 50 100 150 200 250 300 350-505101520253035 Log (L / erg s-1 )Orbital Phase [degree]Figure 5: Modulation of gamma-ray emission in steady state atE ∼ 50 GeV by the anisotropic photon fieldof the companion star.whereτrise= 30min, τdec= 1h andτplat= 2h. The power-law has the standard index ofα = 2.2. Thenormalization constantQ0 can be obtained from the total power injected in relativistic protons andelectrons,Lrel = Lp+Le. This power is assumed to be a fraction of the luminosity of the corona,Lrel = qrelLc. In the steady state the best fit to the observations is obtained withqrel = 0.2. Duringthe flare the number of relativistic particles increases. In our model, the powr injected in the flaredoubles of that injected in steady state.In order to obtain the evolution of particle distributionsN(E, t) for each type of particle, wesolve the transport equation given by [18]∂N(E, t)∂ t+∂∂E(b(E)N(E, t))+N(E, t)tesc= Q(E, t). (3.2)whereb(E) = dEdt∣∣∣loss.5PoS(Texas 2010)174Gamma-ray flares from black hole coronaeFig. (6) shows the evolution of the electromagnetic emission during a day, notcorrected bythe absorption in the photon field of the star. For this purpose, in Fig. (7) weshow the absorptioncoefficient due to the stellar field. We estimate the opacity for flares occurring at different orbitalphases, and we conclude that for some values ofφ the absorption of the star is almost negligible.-4 -2 0 2 4 6 8 10 12 14 1626283032343638  Log (L / erg s-1 )Log (E  / eV) t = 1 h t = 6 h t = 24 hFigure 6: Evolution of the luminosity during the flare, without consider the absorption due to the star.4. Summary and conclusionsWe have estimated the electromagnetic output produced in the corona during atransient out-burst. Our study is based on a steady state model of an accreting black hole, w ich is in agreementwith the observations of Cygnus X-1 [5]. We consider both internal and external absorption. Wehave included the effect of the presence of an anisotropic stellar photon-field. The absorptionproduced by this field results almost negligible for certain positions of the compact objects; never-theless it affects the electromagnetic emission atE ∼ 30 GeV for the most of the orbit.In a future work, we will study the modulation in the emission for objects in which the orbitalperiod is comparable with the flare duration.References[1] Shakura, N. I., Sunyaev, R. A., 1973, A&A, 24, 337[2] Kusunose, M., Mineshige S., 1995, ApJ, 440, 100[3] Belmont, R., Malzac, J., Marcowith, A., 2008, A&A, 491, 617[4] Vurm, I., Poutanen, J., 2009, ApJ, 698, 293[5] Romero, G. E., Vieyro, F. L., Vila, G. S., 2010, A&A, 519, A109[6] Paredes, J. M., 2008, AIP Conference proceedings, 1085,1576PoS(Texas 2010)174Gamma-ray flares from black hole coronae9 10 11 12020406080100120140160180200220 t = 0 h t = 4 h t = 8 h t = 12 h t = 16 h  Log (E / eV)(a) φ0 = 0.09 10 11 12020406080100120140160180200220   t = 0 h t = 4 h t = 8 h t = 12 h t = 16 hLog (E / eV)(b) φ0 = π/29 10 11 12020406080100120140160180200220   t = 0 h t = 4 h t = 8 h t = 12 h t = 16 hLog (E / eV)(c) φ0 = π9 10 11 12020406080100120140160180200220   t = 0 h t = 4 h t = 8 h t = 12 h t = 16 hLog (E / eV)(d) φ0 = 3π/2Figure 7: Opacity due to the presence of an anisotropic photon field.[7] Sabatini, S., et al. 2010, ApJ, 712, L10[8] Tavani, M. et al. (AGILE coll.) 2009, Nature, 462, 620[9] Abdo, A.A. et al (Fermi LAT coll.) 2009, Science, 326, 1512[10] Narayan, R., Yi, I., 1995a, ApJ, 444, 231[11] Narayan, R., Yi, I., 1995b, ApJ, 452, 710[12] McConnell, M. L., et al. 2000, ApJ, 543, 928[13] Cadolle Bel, M., et al. 2006, A&A, 446, 591[14] Ziólkowski, J., 2005, MNRAS, 358, 851[15] Gies, D. R., Bolton C. T., 1986, ApJ, 304, 371[16] Romero, G. E., del Valle, M. V., Orellana, M., 2010, A&A,518, A12[17] Reynoso, M., Romero, G. E., 2009, A&A, 493, 1, 1[18] Ginzburg, V. L., Syrovatskii S. I., 1964,The Origin of Cosmic Rays, Macmillan, New York7

Gamma-ray flares from black hole coronae

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Gamma-ray flares from black hole coronae

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