The high-mass microquasar Cygnus X-3 has been recently detected in a flaring
state by the gamma-ray satellites Fermi and Agile. In the present contribution,
we study the high-energy emission from Cygnus X-3 through a model based on the
interaction of clumps from the Wolf-Rayet wind with the jet. The clumps inside
the jet act as obstacles in which shocks are formed leading to particle
acceleration and non-thermal emission. We model the high energy emission
produced by the interaction of one clump with the jet and briefly discus the
possibility of many clumps interacting with the jet. From the characteristics
of the considered scenario, the produced emission could be flare-like due to
discontinuous clump penetration, with the GeV long-term activity explained by
changes in the wind properties.Comment: Contribution to the proceedings of the 25th Texas Symposium on
  Relativistic Astrophysics - TEXAS 2010, December 06-10, Heidelberg, German

Araudo, Anabella T.

Bosch-Ramon, Valenti

Romero, Gustavo E.

English

arXiv

The high-mass microquasar Cygnus X-3 has been recently detected in a flaring state by the gamma-ray satellites Fermi and Agile. In the present contribution, we study the high-energy emission from Cygnus X-3 through a model based on the interaction of clumps from the Wolf-Rayet wind with the jet. The clumps inside the jet act as obstacles in which shocks are formed leading to particle acceleration and non-thermal emission. We model the high energy emission produced by the interaction of one clump with the jet and briefly discus the possibility of many clumps interacting with the jet. From the characteristics of the considered scenario, the produced emission could be flare-like due to discontinuous clump penetration, with the GeV long-term activity explained by changes in the wind properties.Fil: Araudo, Anabella Teresa. 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: Bosch Ramon, Valentí. Dublin Institute for Advanced Studies; IrlandaFil: 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 AstrophysicsHeidelbergAlemania|Max-Planck-Institut für Kernphysi

Araudo, Anabella Teresa

Bosch Ramon, Valentí

Romero, Gustavo Esteban

CONICET Digital

arXiv:1104.1730v1  [astro-ph.HE]  9 Apr 2011Transient gamma-ray emission from Cygnus X-3Anabella T. AraudoInstituto Argentino de Radioastronomía, C.C.5, (1894) Villa Elisa, Buenos Aires, Argentina.Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo delBosque, 1900 La Plata, Argentina.E-mail: aaraudo@fcaglp.unlp.edu.arValentí Bosch-RamonDublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2.E-mail: valenti@cp.dias.ieGustavo E. RomeroInstituto Argentino de Radioastronomía, C.C.5, (1894) Villa Elisa, Buenos Aires, Argentina.Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo delBosque, 1900 La Plata, Argentina.E-mail: romero@fcaglp.unlp.edu.arThe high-mass microquasar Cygnus X-3 has been recently detected in a flaring state by thegamma-ray satellites Fermi and Agile. In the present contribution, we study the high-energyemission from Cygnus X-3 through a model based on the interaction of clumps from the Wolf-Rayet wind with the jet. The clumps inside the jet act as obstacles in which shocks are formedleading to particle acceleration and non-thermal emission. We model the high energy emissionproduced by the interaction of one clump with the jet and briefly discus the possibility of manyclumps interacting with the jet. From the characteristics of the considered scenario, the producedemission could be flare-like due to discontinuous clump penetration, with the GeV long-termactivity explained by changes in the wind properties.25th Texas Symposium on Relativistic Astrophysics - TEXAS 2010December 06-10, 2010Heidelberg, Germanyc© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licen. http://pos.sissa.it/Transient gamma-ray emission from Cygnus X-3γWindZaφBHrMassive starcsVZVjFigure 1: Left: Sketch of a HMMQ. Right: Sketch of the interaction of one clump with the jet.1. IntroductionThe mass loss in massive stars is thought to take place via supersonic inhomogeneous winds.Considerable observational evidence supports the idea that the wind structure is clumpy [1], al-though the properties of clumps are not well-known as a consequence of the very high spatialresolution necessary for clump detection. Some massive stars are accompanied by a compact ob-ject and present transfer of matter to the latter, forming anaccretion disc. When bipolar relativisticoutflows are formed, these sources are called high-mass microquasars (HMMQs). In Figure 1 (left),a sketch of a HMMQ is shown.Cygnus X-3 is a HMMQ composed by a Wolf-Rayet (WR) star and a compact object, bothbeing separated a distancea∼ 3×1011 cm. The nature of the compact object has not been deter-mined yet, but recent studies suggest that it may be a black hole (e.g. [2]). Located at a distance∼ 7−9 kpc, the system has been recently detected in a recurrent flari g state at high-energy (HE)gamma rays [3, 4]. The observed emission spectrum is a power-la with index∼ 1.7 and luminos-ity & 1036 erg s−1. The typical duration of the flares was∼ 2 days [4].In this contribution, we present a model to explain the HE emission detected in Cygnus X-3based on the interaction between its jets and wind inhomogeneiti s [5]. Some clumps can even-tually penetrate in the jet, leading to transient non-thermal activity that may release a significantfraction of the jet kinetic luminosity,Lj, in the form of synchrotron, inverse Compton (IC), andproton-proton (pp) emission.2. Jet-clump interaction in Cygnus X-3In order to study the physical processes of the jet-clump interaction, we consider the collisionof a single clump with the jet, as is shown in Figure 1 (right).A huge density contrastχ ≡ ρc/ρj2Transient gamma-ray emission from Cygnus X-3(whereρc andρj are the clump and jet densities, respectively) allows the clump to fully cross theboundary of the jet and penetrate into it. In the context of this work, thermal conduction, magneticfields and gravitational forces are not dynamically relevant for the jet-clump interaction and havebeen neglected.We consider that a clump with sizeR0c = 1010 cm (. 0.1R⋆) reaches one of the HMMQ jetsmoving at the terminal wind velocityv∞ = 2500 km s−1. At a distancer =√z2+a2 from the star,the clump density can be estimated throughρc = ρw/ f , where f < 1 is the filling factor of theclumpy wind, andρw ∼ Ṁ/(4πr2v∞) is the wind density, wherėM ∼ 10−5 M⊙yr−1 is the typicalmass loss rate of WR stars. We assume that the jet has a velocity vj ∼ c/3 (i.e. Lorentz factorΓ ∼ 1.06) and a kinetic luminosityLj = 1038 erg s−1. We fix the relation between the height (z)and the width (Rj) of the jet asRj = 0.1z.The penetration time of the clump into the jet is determined by tc ∼ 2R0c/vc ∼ 100 s, where theclump velocity isvc = v∞. As a consequence of the interaction of the jet material withthe clump,two shocks form. One of these shocks propagates back in the jet with a velocityvbs∼ vj , forminga bow shock (see Figure 1, right). This bow shock reaches the steady state configuration in a timetbs ∼ Zbs/vbs, with the stagnation point located at a distanceZbs ∼ R0c/5 from the clump. On theother hand, a shock propagates in the clump at a velocityvsc∼ vj/√χ and, in a timetsc∼ 2Rc/vsc,the whole clump is shocked. During the shock passage, the clump is compressed in the directionof the shock velocity,z, and when the whole clump is shocked, its size in thez-direction is∼ R0c/4.However, int > tsc the clump starts to expand at the sound velocity of the shocked material. Atthe same time, the acceleration exerted by the jet to the clump increases withRc. Assuming thatthe expansion is spherical, and neglecting the acceleration exerted by the jet on the clump, weobtain the following expression for the clump size:Rc(t) ∼ R0c/(1−0.4t/tsc)2 [6], which gives acharacteristic clump expansion timetexp∼ 3.5tsc. In Figure 2 (left), the evolution ofRc with timeis shown.As a consequence of the acceleration exerted by the jet on theclump, Rayleigh-Taylor (RT)instabilities can develop in the contact discontinuity. Kelvin-Helmholtz (KH) instability can alsogrow as a result of the high relative velocity between the jetshocked material and the clump.Numerical simulations show that RT and KH instabilities grow sufficiently to destroy the clump(i.e. up to a wavelength∼ Rc) in a timescaletRT ∼ tKH ∼ 5tsc [7]. If instabilities do not growfast enough, and clump expansion and acceleration are too slow, the permanence of the clumpinto the jet will be determined by the passage time of the clump through the jet:tj ∼ 2Rj/vc. InFigure 2 (right), the main dynamical timescales are plotted.2.1 Interaction heightConsidering the previous analysis on the dynamics of the jet-clump interaction, one can deter-mine the minimum interaction height,zminint , at which one clump can completely penetrate into thejet. Being the lifetime of clumps into the jettlife & tsc, to determine the interaction heightzint weimpose thatsc> tc. This constraint is fulfilled ifz> A√z2+a2, whereA∼ 0.5[(f0.01)(vjc/3)(Lj1038 erg/s)]1/2[(Γj −10.06)(Ṁ10−5 M⊙/yr)(v∞2500 km/s)]−1/2.(2.1)3Transient gamma-ray emission from Cygnus X-31 1.5 2 2.5 3 3.5 4t/tsc012345log[Rc(t)/Rc0]9 9.5 10 10.5 11 11.5 12log(z [cm])-101234log(t [s])cloud penetration (tc)bow shock (tbs)jet crossing (tj)clump shock crossing (tsc)Rc = 1010 cmvc ~ 2500 km s-1f = 10-2Figure 2: Left: Clump spherical expansion. Right: Dynamical timescales corresponding to the interactionof one clump ofR0c = 1010 cm with the jet.If, for a certain election of clump and jet parameters,A results larger than 1, the constraintsc> tcis no satisfied for any value ofz and clumps will be destroyed by the jet before fully penetratinginto it. However, for the parameters chosen in this work,A∼ 0.5 and in such a case, the minimuminteraction height resultszminint ∼ Aa/√1−A2 ∼ a/2.3. Non-thermal processesTo estimate the non-thermal emission produced by the interaction of one clump with the jet, wefix the interaction height atzint = a∼ 2zminint . At zint, the density of the clump isρc ∼ 10−12 gr cm−3(i.e. the number density isnc = ρc/(4mp)∼ 2×1011 cm−3, wheremp is the proton mass).3.1 Particle accelerationIn the bow shock, we assume that particles are accelerated upto relativistic energies beinginjected in the downstream region following a distributionQe,p ∝ E−2e,p (e and p for electrons andprotons, respectively) and with a luminosityLnt = ηnt(Rc/Rj)2Lj, where we fixηnt = 0.1. For theparameters assumed in this work,Lnt ∼ 1036(ηnt0.1)(R0c1010cm)2(zinta= 3×1011cm)−2( Lj1038ergs−1)erg s−1. (3.1)In addition, considering that the magnetic energy density in he bow-shock region,UB, is a fractionηB of the non-thermal one,Unt, we obtain a magnetic fieldB∼√ηB 2×103 G. (Bothηnt andηBare free parameters in our work.)The main radiative losses that affect the evolution of the non-thermal particles are synchrotronradiation, and synchrotron self-Compton (SSC) and external Compton (EC) scattering. For ECcooling we have considered target photons provided by the WRstar, that has a luminosityL⋆ ∼1039 erg s−1 and a temperatureT⋆ ∼ 105 K. The energy density of stellar photons atzint is U⋆ ∼3×104 erg cm−3. At electron energiesEe & 25 GeV, EC scattering with stellar photons of energyEph⋆ ∼ 3KT⋆ (whereK is the Boltzmann constant) occurs in the Klein-Nishina regime. In addition4Transient gamma-ray emission from Cygnus X-36 7 8 9 10 11 12 13log(Ee [eV])-505log(t [s])accelerationrel. BremsstrahlungadvectionEC SSCsynchrotronηB = 10-2B ~ 2x102 Gdiffusion-4 -2 0 2 4 6 8 10 12 14log(Eph [eV])2830323436log(E ph LEph [erg s-1 ]) synchrotronSSCEC (star)ppηB = 10-2B ~ 2x102 GFigure 3: Left: Timescales of the acceleration and lepton cooling losses (synchrotron, SSC, EC and relativis-tic Bremsstrahlung). Diffusion and advection escape losses ar also shown. Right: Spectral energy distribu-tion produced by one clump ofR0c = 1010 cm interacting with the jet atzint ∼ a. At energiesEph & 10 GeV,the emission is strongly absorbed. Both (left and right) plots have been produced takingB∼ 2×102 G.to radiative losses, electrons are advected away from the emitter on a timetadv∼ 4Rc/vj . In Figure 3(left), the electron cooling timescales are plotted together with the acceleration timescale. As seenin the figure, forηB = 10−2 the maximum energy is determined by synchrotron losses, yieldingEmaxe ∼ 1 TeV. To obtain the distributionNe of relativistic electrons we solve the kinetic equation [8]for a one-zone emitter, taking into account the losses mentioned above, and also the synchrotronphotons (as targets for SSC). The steady state is reached on atime≪ tsc. Ne(Ee) has a break at theenergyEb ∼ 0.1 GeV due to electron advection escape.Protons can lose energy viapp interactions in the bow-shock region, but diffusion lossesdom-inate, constraining the maximum energy toEmaxp ∼ 2.5×102√ηB TeV (for ηnt = 0.1). The mostenergetic protons,Ep & 0.1Emaxp , can diffuse up to the clump before escaping through advection,producing gamma rays viapp interactions.3.2 High-energy emissionIn the bow-shock region, using standard formulas [9] andNe, we estimate the synchrotron,SSC and EC emission; relativistic Bremmstrahlung andpp interactions are negligible there. Inthe clump, if energetic protons that arrive from the bow shock are not confined, they will escapefrom the clump in a timetcl ∼ R0c/c before radiating a significant part of their energy. Consideringthat the energy distribution of relativistic protons in theclump isNp ∼ Qp tcl, we estimate theppemission following the formulae given in [10]. In Figure 3 (right), we show the spectral energydistribution (SED) composed by the most important radiative processes in the bow-shock region(synchrotron, SSC and EC) and in the clump (pp). The synchrotron emission is self-absorbed atenergiesEph < 10−4 eV, and at photon energiesEph & 10 GeV absorption due to electron-positronpair creation in the star photon field is relevant. The achieved luminosity at energies∼ 0.1−10 GeVis LEC ∼ 2×1035 erg s−1. Regarding to thepp emission, the estimate obtained in this work is alower-limit. If the protons were confined in the clump, the radiated emission would be larger.The SED shown in Figure 3 (right) has been calculated neglecting the expansion of the clumpinside the jet (see Figure 2, right). If we consider that after tsc the cloud expands up to a size much5Transient gamma-ray emission from Cygnus X-3larger thanR0c = 1010 cm, the available non-thermal luminosity will be significantly larger and, as aconsequence, the synchrotron and IC luminosity will be higher. On the other hand, theppemissionproduced in the expanded clump will be lower, because the clump density decreases faster than theincrease of the clump surface:nc/n0c ∝ (R0c/Rc)3.Finally, note that in Figure 3 (right) we show the result of the interaction of only one clumpwith the jet, but many clumps could simultaneously interactwith the jet. The non-thermal radiationfluxes grow linearly with the number of clumps interacting with the jet,Ncj, as long as too manyclumps do not disrupt the jet. The corresponding SED will be also higher.4. DiscussionThe total luminosity produced by jet-clump interactions depends on the number of clumpsinside the jet, and on the size and density of each one. The number of clumps in the jet canbe estimated asNcj ∼ fj Vj/Vc, where fj ≤ f is the filling factor of clumps into the jet, andVjandVc are the jet and the clump volume, respectively. ConsideringVj up to z∼ 2a, Vc ∼ πR0c3(whereR0c = 1010 cm) and fj = f = 0.01, we obtainNcj ∼ 0.5 in Cygnus X-3. However, the realnumber of clumps into the jet will be smaller than the previous estimate, becausefj < f as aconsequence of the clump destruction during the penetration pr cess and inside the jet due to RTand KH instabilities. IfNcj < 1, the emission produced by the jet-clump interaction will be like aflare with a duration determined by the lifetime of the clumpsinto the jet.On the other hand, if we consider clumps with a radiusR0c = 109 cm (. 0.01R⋆), the numberof clumps into the jet grows up to∼ 104. Then, the simultaneous interaction of∼ 104 clumps withthe jet will produce significantly more luminosity than the emission produced by the interaction ofonly one clump, that is∼ 1034 erg s−1 atzint ∼ a. In that case, the final spectrum will be persistent,with a flickering due to the continuous interactions of many small clumps.However, the jet can be disrupted by the too small many clumps, in particular if the section ofclumps interacting within∆z is comparable with the section of the jet:ΣR2c ∼ R2j . This will be thecase, neglecting clump expansion, forR0c . 109 cm. Note that periods of smaller clump size maylead to jet disruption. Also, changes in the wind could lead to more clumps inside the jet and moreeffective tapping of the jet luminosity.References[1] S. Owocki, D. Cohen,The Effect of Porosity on X-Ray Emission-Line Profiles from Hot-Star Winds,ApJ, 2006 (648) 565.[2] C. Shrader, L. Titarchuk1, N. ShaposhnikovNew Evidence for a Black Hole in the Compact BinaryCygnus X-3, ApJ, 2010, (718) 488.[3] A. Abdo. et al.Modulated High-Energy Gamma-Ray Emission from the Microquasar Cygnus X-3,Science, 2009 (326) 1512.[4] M. Tavani, et al.Extreme particle acceleration in the microquasar CygnusX-3, Nature, 2009 (462)620.[5] A. Araudo, V. Bosch-Ramon, G.E. Romero,High-energy emission from jet-clump interactions inmicroquasars, A&A, 2009 (503) 673.6Transient gamma-ray emission from Cygnus X-3[6] M. Barkov, F. Aharonian, V. Bosch-Ramon,Gamma-ray Flares from Red Giant/Jet Interactions inActive Galactic Nuclei, ApJ2010 (724) 1517.[7] R. Klein, C. McKee, P. Colella,On the hydrodynamic interaction of shock waves with interstellarclouds. 1: Nonradiative shocks in small clouds, ApJ2004 (420) 213.[8] V. Ginzburg, S. Zyrovatskii,The origin of cosmic raysGordon & Breach, New York1969[9] G. Blumenthal, R. Gould,Bremsstrahlung, Synchrotron Radiation, and Compton Scattering ofHigh-Energy Electrons Traversing Dilute Gases, RvMP1970 (42) 237[10] S. Kelner, F. Aharonian, V. Bugayov,Energy spectra of gamma rays, electrons, and neutrinosproduced at proton-proton interactions in the very high energy regime, PhRvD2006 (74) 40187

Transient gamma-ray emission from Cygnus x-3

The high-mass microquasar Cygnus X-3 has been recently detected in a flaring state by the gamma-ray satellites Fermi and Agile. In the present contribution, we study the high-energy emission from Cygnus X-3 through a model based on the interaction of clumps from the Wolf-Rayet wind with the jet. The clumps inside the jet act as obstacles in which shocks are formed leading to particle acceleration and non-thermal emission. We model the high energy emission produced by the interaction of one clump with the jet and briefly discus the possibility of many clumps interacting with the jet. From the characteristics of the considered scenario, the produced emission could be flare-like due to discontinuous clump penetration, with the GeV long-term activity explained by changes in the wind properties

Bosch-Ramon, V

Romero, GE

Oxford University Research Archive

PoS(Texas 2010)184Transient gamma-ray emission from Cygnus X-3Anabella T. AraudoInstituto Argentino de Radioastronomía, C.C.5, (1894) Villa Elisa, Buenos Aires, Argentina.Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo delBosque, 1900 La Plata, Argentina.E-mail: aaraudo@fcaglp.unlp.edu.arValentí Bosch-RamonDublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2.E-mail: valenti@cp.dias.ieGustavo E. RomeroInstituto Argentino de Radioastronomía, C.C.5, (1894) Villa Elisa, Buenos Aires, Argentina.Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo delBosque, 1900 La Plata, Argentina.E-mail: romero@fcaglp.unlp.edu.arThe high-mass microquasar Cygnus X-3 has been recently detected in a flaring state by thegamma-ray satellites Fermi and Agile. In the present contribution, we study the high-energyemission from Cygnus X-3 through a model based on the interaction of clumps from the Wolf-Rayet wind with the jet. The clumps inside the jet act as obstacles in which shocks are formedleading to particle acceleration and non-thermal emission. We model the high energy emissionproduced by the interaction of one clump with the jet and briefly discus the possibility of manyclumps interacting with the jet. From the characteristics of the considered scenario, the producedemission could be flare-like due to discontinuous clump penetration, with the GeV long-termactivity explained by changes in the wind properties.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)184Transient gamma-ray emission from Cygnus X-3γWindZaφBHrMassive starcsVZVjFigure 1: Left: Sketch of a HMMQ. Right: Sketch of the interaction of one clump with the jet.1. IntroductionThe mass loss in massive stars is thought to take place via supersonic inhomogeneous winds.Considerable observational evidence supports the idea that the wind structure is clumpy [1], al-though the properties of clumps are not well-known as a consequence ofth very high spatialresolution necessary for clump detection. Some massive stars are accompanied by a compact ob-ject and present transfer of matter to the latter, forming an accretion disc. When bipolar relativisticoutflows are formed, these sources are called high-mass microquasars (HMMQs). In Figure 1 (left),a sketch of a HMMQ is shown.Cygnus X-3 is a HMMQ composed by a Wolf-Rayet (WR) star and a compactobject, bothbeing separated a distancea∼ 3×1011 cm. The nature of the compact object has not been deter-mined yet, but recent studies suggest that it may be a black hole (e.g. [2]). Located at a distance∼ 7−9 kpc, the system has been recently detected in a recurrent flaring state at high-energy (HE)gamma rays [3, 4]. The observed emission spectrum is a power-law with index∼ 1.7 and luminos-ity & 1036 erg s−1. The typical duration of the flares was∼ 2 days [4].In this contribution, we present a model to explain the HE emission detected in Cyg us X-3based on the interaction between its jets and wind inhomogeneities [5]. Some clumps can even-tually penetrate in the jet, leading to transient non-thermal activity that may release a significantfraction of the jet kinetic luminosity,Lj , in the form of synchrotron, inverse Compton (IC), andproton-proton (pp) emission.2. Jet-clump interaction in Cygnus X-3In order to study the physical processes of the jet-clump interaction, we consider the collisionof a single clump with the jet, as is shown in Figure 1 (right). A huge density contrastχ ≡ ρc/ρj2PoS(Texas 2010)184Transient gamma-ray emission from Cygnus X-3(whereρc andρj are the clump and jet densities, respectively) allows the clump to fully cross theboundary of the jet and penetrate into it. In the context of this work, thermalconduction, magneticfields and gravitational forces are not dynamically relevant for the jet-clump interaction and havebeen neglected.We consider that a clump with sizeR0c = 1010 cm (. 0.1R⋆) reaches one of the HMMQ jetsmoving at the terminal wind velocityv∞ = 2500 km s−1. At a distancer =√z2 +a2 from the star,the clump density can be estimated throughρc = ρw/ f , where f < 1 is the filling factor of theclumpy wind, andρw ∼ Ṁ/(4πr2v∞) is the wind density, wherėM ∼ 10−5M⊙ yr−1 is the typicalmass loss rate of WR stars. We assume that the jet has a velocityvj ∼ c/3 (i.e. Lorentz factorΓ ∼ 1.06) and a kinetic luminosityLj = 1038 erg s−1. We fix the relation between the height (z)and the width (Rj) of the jet asRj = 0.1z.The penetration time of the clump into the jet is determined bytc ∼ 2R0c/vc ∼ 100 s, where theclump velocity isvc = v∞. As a consequence of the interaction of the jet material with the clump,two shocks form. One of these shocks propagates back in the jet with a velocity vbs∼ vj , forminga bow shock (see Figure 1, right). This bow shock reaches the steady state configuration in a timetbs ∼ Zbs/vbs, with the stagnation point located at a distanceZbs ∼ R0c/5 from the clump. On theother hand, a shock propagates in the clump at a velocityvsc∼ vj/√χ and, in a timetsc∼ 2Rc/vsc,the whole clump is shocked. During the shock passage, the clump is compressed in the directionof the shock velocity,z, and when the whole clump is shocked, its size in thez-direction is∼ R0c/4.However, int > tsc the clump starts to expand at the sound velocity of the shocked material. Atthe same time, the acceleration exerted by the jet to the clump increases withRc. Assuming thatthe expansion is spherical, and neglecting the acceleration exerted by the jet on the clump, weobtain the following expression for the clump size:Rc(t) ∼ R0c/(1−0.4t/tsc)2 [6], which gives acharacteristic clump expansion timetexp∼ 3.5tsc. In Figure 2 (left), the evolution ofRc with timeis shown.As a consequence of the acceleration exerted by the jet on the clump, Rayleigh-Taylor (RT)instabilities can develop in the contact discontinuity. Kelvin-Helmholtz (KH) instabili y can alsogrow as a result of the high relative velocity between the jet shocked material and the clump.Numerical simulations show that RT and KH instabilities grow sufficiently to destroy the clump(i.e. up to a wavelength∼ Rc) in a timescaletRT ∼ tKH ∼ 5tsc [7]. If instabilities do not growfast enough, and clump expansion and acceleration are too slow, the permanence of the clumpinto the jet will be determined by the passage time of the clump through the jet:tj ∼ 2Rj/vc. InFigure 2 (right), the main dynamical timescales are plotted.2.1 Interaction heightConsidering the previous analysis on the dynamics of the jet-clump interaction,one can deter-mine the minimum interaction height,zminint , at which one clump can completely penetrate into thejet. Being the lifetime of clumps into the jettlife & tsc, to determine the interaction heightzint weimpose thatsc > tc. This constraint is fulfilled ifz> A√z2 +a2, whereA∼ 0.5[(f0.01)(vjc/3)(Lj1038 erg/s)]1/2[(Γj −10.06)(Ṁ10−5 M⊙/yr)(v∞2500 km/s)]−1/2.(2.1)3PoS(Texas 2010)184Transient gamma-ray emission from Cygnus X-31 1.5 2 2.5 3 3.5 4t/tsc012345log[Rc(t)/Rc0]9 9.5 10 10.5 11 11.5 12log(z [cm])-101234log(t [s])cloud penetration (tc)bow shock (tbs)jet crossing (tj)clump shock crossing (tsc)Rc = 1010 cmvc ~ 2500 km s-1f = 10-2Figure 2: Left: Clump spherical expansion. Right: Dynamical timescales corresponding to the interactionof one clump ofR0c = 1010 cm with the jet.If, for a certain election of clump and jet parameters,A results larger than 1, the constraintsc > tcis no satisfied for any value ofz and clumps will be destroyed by the jet before fully penetratinginto it. However, for the parameters chosen in this work,A∼ 0.5 and in such a case, the minimuminteraction height resultszminint ∼ Aa/√1−A2 ∼ a/2.3. Non-thermal processesTo estimate the non-thermal emission produced by the interaction of one clump withthe jet, wefix the interaction height atzint = a∼ 2zminint . At zint, the density of the clump isρc ∼ 10−12 gr cm−3(i.e. the number density isnc = ρc/(4mp) ∼ 2×1011 cm−3, wheremp is the proton mass).3.1 Particle accelerationIn the bow shock, we assume that particles are accelerated up to relativisticenergies beinginjected in the downstream region following a distributionQe,p ∝ E−2e,p (e and p for electrons andprotons, respectively) and with a luminosityLnt = ηnt(Rc/Rj)2Lj , where we fixηnt = 0.1. For theparameters assumed in this work,Lnt ∼ 1036(ηnt0.1)(R0c1010cm)2(zinta = 3×1011cm)−2( Lj1038ergs−1)erg s−1. (3.1)In addition, considering that the magnetic energy density in the bow-shock region,UB, is a fractionηB of the non-thermal one,Unt, we obtain a magnetic fieldB∼√ηB 2×103 G. (Bothηnt andηBare free parameters in our work.)The main radiative losses that affect the evolution of the non-thermal particles are synchrotronradiation, and synchrotron self-Compton (SSC) and external Compton (EC) scattering. For ECcooling we have considered target photons provided by the WR star, thathas a luminosityL⋆ ∼1039 erg s−1 and a temperatureT⋆ ∼ 105 K. The energy density of stellar photons atzint is U⋆ ∼3×104 erg cm−3. At electron energiesEe & 25 GeV, EC scattering with stellar photons of energyEph⋆ ∼ 3KT⋆ (whereK is the Boltzmann constant) occurs in the Klein-Nishina regime. In addition4PoS(Texas 2010)184Transient gamma-ray emission from Cygnus X-36 7 8 9 10 11 12 13log(Ee [eV])-505log(t [s])accelerationrel. BremsstrahlungadvectionEC SSCsynchrotronηB = 10-2B ~ 2x102 Gdiffusion-4 -2 0 2 4 6 8 10 12 14log(Eph [eV])2830323436log(E ph LEph [erg s-1 ]) synchrotronSSCEC (star)ppηB = 10-2B ~ 2x102 GFigure 3: Left: Timescales of the acceleration and lepton cooling losses (synchrotron, SSC, EC and relativis-tic Bremsstrahlung). Diffusion and advection escape losses ar also shown. Right: Spectral energy distribu-tion produced by one clump ofR0c = 1010 cm interacting with the jet atzint ∼ a. At energiesEph & 10 GeV,the emission is strongly absorbed. Both (left and right) plots have been produced takingB∼ 2×102 G.to radiative losses, electrons are advected away from the emitter on a timetadv∼ 4Rc/vj . In Figure 3(left), the electron cooling timescales are plotted together with the acceleration timescale. As seenin the figure, forηB = 10−2 the maximum energy is determined by synchrotron losses, yieldingEmaxe ∼ 1 TeV. To obtain the distributionNe of relativistic electrons we solve the kinetic equation [8]for a one-zone emitter, taking into account the losses mentioned above, andalso the synchrotronphotons (as targets for SSC). The steady state is reached on a time≪ tsc. Ne(Ee) has a break at theenergyEb ∼ 0.1 GeV due to electron advection escape.Protons can lose energy viapp interactions in the bow-shock region, but diffusion losses dom-inate, constraining the maximum energy toEmaxp ∼ 2.5×102√ηB TeV (for ηnt = 0.1). The mostenergetic protons,Ep & 0.1Emaxp , can diffuse up to the clump before escaping through advection,producing gamma rays viapp interactions.3.2 High-energy emissionIn the bow-shock region, using standard formulas [9] andNe, we estimate the synchrotron,SSC and EC emission; relativistic Bremmstrahlung andpp interactions are negligible there. Inthe clump, if energetic protons that arrive from the bow shock are not confined, they will escapefrom the clump in a timetcl ∼ R0c/c before radiating a significant part of their energy. Consideringthat the energy distribution of relativistic protons in the clump isNp ∼ Qp tcl, we estimate theppemission following the formulae given in [10]. In Figure 3 (right), we show the spectral energydistribution (SED) composed by the most important radiative processes in thebow-shock region(synchrotron, SSC and EC) and in the clump (pp). The synchrotron emission is self-absorbed atenergiesEph < 10−4 eV, and at photon energiesEph & 10 GeV absorption due to electron-positronpair creation in the star photon field is relevant. The achieved luminosity at energi s∼ 0.1−10 GeVis LEC ∼ 2×1035 erg s−1. Regarding to thepp emission, the estimate obtained in this work is alower-limit. If the protons were confined in the clump, the radiated emission would be larger.The SED shown in Figure 3 (right) has been calculated neglecting the expansion of the clumpinside the jet (see Figure 2, right). If we consider that aftertsc the cloud expands up to a size much5PoS(Texas 2010)184Transient gamma-ray emission from Cygnus X-3larger thanR0c = 1010 cm, the available non-thermal luminosity will be significantly larger and, as aconsequence, the synchrotron and IC luminosity will be higher. On the other hand, theppemissionproduced in the expanded clump will be lower, because the clump density decreas s faster than theincrease of the clump surface:nc/n0c ∝ (R0c/Rc)3.Finally, note that in Figure 3 (right) we show the result of the interaction of only e clumpwith the jet, but many clumps could simultaneously interact with the jet. The non-thermal radiationfluxes grow linearly with the number of clumps interacting with the jet,Ncj as long as too manyclumps do not disrupt the jet. The corresponding SED will be also higher.4. DiscussionThe total luminosity produced by jet-clump interactions depends on the number of clumpsinside the jet, and on the size and density of each one. The number of clumps inthe jet canbe estimated asNcj ∼ fj Vj/Vc, where fj ≤ f is the filling factor of clumps into the jet, andVjandVc are the jet and the clump volume, respectively. ConsideringVj up to z∼ 2a, Vc ∼ πR0c3(whereR0c = 1010 cm) and fj = f = 0.01, we obtainNcj ∼ 0.5 in Cygnus X-3. However, the realnumber of clumps into the jet will be smaller than the previous estimate, becausefj < f as aconsequence of the clump destruction during the penetration process andinside the jet due to RTand KH instabilities. IfNcj < 1, the emission produced by the jet-clump interaction will be like aflare with a duration determined by the lifetime of the clumps into the jet.On the other hand, if we consider clumps with a radiusR0c = 109 cm (. 0.01R⋆), the numberof clumps into the jet grows up to∼ 104. Then, the simultaneous interaction of∼ 104 clumps withthe jet will produce significantly more luminosity than the emission produced by theinteraction ofonly one clump, that is∼ 1034 erg s−1 atzint ∼ a. In that case, the final spectrum will be persistent,with a flickering due to the continuous interactions of many small clumps.However, the jet can be disrupted by the too small many clumps, in particular if the section ofclumps interacting within∆z is comparable with the section of the jet:ΣR2c ∼ R2j . This will be thecase, neglecting clump expansion, forR0c . 109 cm. Note that periods of smaller clump size maylead to jet disruption. Also, changes in the wind could lead to more clumps inside the j t and moreeffective tapping of the jet luminosity.References[1] S. Owocki, D. Cohen,The Effect of Porosity on X-Ray Emission-Line Profiles from Hot-Star Winds,ApJ, 2006 (648) 565.[2] C. Shrader, L. Titarchuk1, N. ShaposhnikovNew Evidence for a Black Hole in the Compact BinaryCygnus X-3, ApJ, 2010, (718) 488.[3] A. Abdo. et al.Modulated High-Energy Gamma-Ray Emission from the Microquasar Cygnus X-3,Science, 2009 (326) 1512.[4] M. Tavani, et al.Extreme particle acceleration in the microquasar CygnusX-3, Nature, 2009 (462)620.[5] A. Araudo, V. Bosch-Ramon, G.E. Romero,High-energy emission from jet-clump interactions inmicroquasars, A&A, 2009 (503) 673.6PoS(Texas 2010)184Transient gamma-ray emission from Cygnus X-3[6] M. Barkov, F. Aharonian, V. Bosch-Ramon,Gamma-ray Flares from Red Giant/Jet Interactions inActive Galactic Nuclei, ApJ2010 (724) 1517.[7] R. Klein, C. McKee, P. Colella,On the hydrodynamic interaction of shock waves with interstellarclouds. 1: Nonradiative shocks in small clouds, ApJ2004 (420) 213.[8] V. Ginzburg, S. Zyrovatskii,The origin of cosmic raysGordon & Breach, New York1969[9] G. Blumenthal, R. Gould,Bremsstrahlung, Synchrotron Radiation, and Compton Scattering ofHigh-Energy Electrons Traversing Dilute Gases, RvMP1970 (42) 237[10] S. Kelner, F. Aharonian, V. Bugayov,Energy spectra of gamma rays, electrons, and neutrinosproduced at proton-proton interactions in the very high energy regime, PhRvD2006 (74) 40187

Transient gamma-ray emission from Cygnus X-3

The high-mass microquasar Cygnus X-3 has been recently detected in a  flaring state by the gamma-ray satellites Fermi and Agile. In the  present contribution, we study the high-energy emission from Cygnus X-3  through a model based on the interaction of clumps from the Wolf-Rayet  wind with the jet. The clumps inside the jet act as obstacles in which  shocks are formed leading to particle acceleration and non-thermal  emission. We model the high energy emission produced by the interaction  of one clump with the jet and briefly discus the possibility of many  clumps interacting with the jet. From the characteristics of the  considered scenario, the produced emission could be flare-like due to  discontinuous clump penetration, with the GeV long-term activity  explained by changes in the wind properties.Fil: Araudo, Anabella Teresa. 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: Bosch Ramon, Valentí. Dublin Institute for Advanced Studies; IrlandaFil: 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

Transient gamma-ray emission from Cygnus X-3

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