Be/X-ray binaries are systems formed by a massive Be star and a magnetized neutron star, usually in an eccentric orbit. The Be star has strong equatorial winds occasionally forming a circumstellar disk. When the neutron star intersects the disk the accretion rate dramatically increases and a transient accretion disk can be formed around the compact object. This disk can last longer than a single orbit in the case of major outbursts. If the disk rotates faster than the neutron star, the Cheng-Ruderman mechanism can produce a current of relativistic protons that would impact onto the disk surface, producing gamma-rays from neutral pion decays and initiating electromagnetic cascades inside the disk. In this paper we present calculations of the evolution of the disk parameters during both major and minor X-ray events, and we discuss the generation of gamma-ray emission at different energies within a variety of models that include both screened and unscreened disks.Facultad de Ciencias Astronómicas y Geofísica

Orellana, Mariana Dominga

Romero, Gustavo Esteban

Astrophysics and Space Science

Servicio de Difusión de la Creación Intelectual

GAMMA-RAY EMISSION FROM Be/X-RAY BINARIESM. ORELLANA1,2 and G.E. ROMERO1,2,31Instituto Argentino de Radioastronomı́a, C.C. 5, 1894 Villa Elisa, Argentina2Facultad de Ciencias Astronómicas y Geofı́sicas, UNLP, Paseo del Bosque,1900 La Plata, Argentina3Member of CONICET; E-mail: romero@irma.iar.unlp.edu.ar(Received 4 June 2004; accepted 14 July 2004)Abstract. Be/X-ray binaries are systems formed by a massive Be star and a magnetized neutronstar, usually in an eccentric orbit. The Be star has strong equatorial winds occasionally forming acircumstellar disk. When the neutron star intersects the disk the accretion rate dramatically increasesand a transient accretion disk can be formed around the compact object. This disk can last longerthan a single orbit in the case of major outbursts. If the disk rotates faster than the neutron star, theCheng-Ruderman mechanism can produce a current of relativistic protons that would impact onto thedisk surface, producing gamma-rays from neutral pion decays and initiating electromagnetic cascadesinside the disk. In this paper we present calculations of the evolution of the disk parameters duringboth major and minor X-ray events, and we discuss the generation of gamma-ray emission at differentenergies within a variety of models that include both screened and unscreened disks.Keywords: X-ray binaries, neutron stars, gamma-rays1. IntroductionA significant number of variable gamma-ray sources of likely galactic origin hasbeen found by satellite-borne experiments such as COMPTEL and EGRET (e.g.Torres et al., 2001; Zhang, et al. 2002; Nolan et al., 2003). These sources varytheir flux on timescales from weeks to months, similar to the timescales exhibitedby X-ray transients at lower energies. The fact that some Be/X-ray binaries withmajor X-ray outbursts are located within the positional error boxes of unidentifiedand variable gamma-ray sources (e.g. Zhang et al., 2002; Romero et al., 2001,2004) posits the problem of whether such systems are capable of generating non-thermal high-energy emission. In this paper we discuss how MeV, GeV and evenTeV gamma-rays might be produced by accreting neutron stars in some Be/X-raybinaries and what is the expected time evolution of the high-energy radiation.2. Be/X-Ray BinariesBe/X-ray binaries are the most abundant type of massive X-ray binary systems inthe Galaxy, with an inferred population in the range 103–104. These systems areAstrophysics and Space Science 297: 167–178, 2005.C° Springer 2005168 M. ORELLANA AND G.E. ROMEROFigure 1. Sketch of a Be/X-ray binary system.formed by a rapidly rotating Be star and a neutron star, which is usually observedin an eccentric orbit. In some cases, known as Transient X-Ray Sources (TXRS),significant long-term X-ray variability is observed. These sources can vary from 1to 3 orders of magnitude going from a quiescent phase to a major outburst, overtimescales that can go from days to a few years. Sometimes, a major outburst isfollowed by a series of smaller bursts. Perhaps the most extensively studied sourceof this class is A0535 + 26 (e.g. Giovanelli and Sabau Graziati, 1992), although afew tens are known.The general situation in a TXRS is depicted in Figure 1. The Be star loses mass inthe form of a thick equatorial disk with a low expansion velocity and a low-density,fast polar wind. Far from the Be star, the neutron star accretes in the Bondi-Hoyleregime. Usually, X-ray flares occur once per orbit when the accretion rate increasesdramatically close to the periastron passage. Occasionally, the equatorial disk of theprimary can extend beyond the orbit of the compact star, which can then penetratethe disk leading to a major outburst. A transient accretion disk can be formed aroundthe neutron star in such systems. The disk can survive during more than a singleorbit in the case of a major outburst or it can last only for a fraction of the orbitin the case of minor outbursts. Evidence for the existence of such transient diskshas been found through the detection of quasi-periodic oscillations (QPOs) in thepower spectra of the hard X-ray flux of some objects (e.g. Finger et al., 1996a).When the equatorial disk of the Be star retracts a major outburst may be followedby a series of minor ones in the same object, as observed, for instance, in the system2S 1417-64 (Finger et al., 1996b).3. The Magnetosphere of Accreting Neutron StarsOnce formed, the accretion disk can penetrate the magnetosphere of the rotatingneutron star (Gosh and Lamb, 1979). This penetration creates a broad transitionGAMMA-RAY EMISSION FROM Be/X-RAY BINARIES 169region between the unperturbed disk flow and the co-rotating magnetospheric flow.In this transition zone, at the inner radius R0 the angular velocity is still Keplerian.Between R0 and the co-rotation radius Rco there is a thin boundary layer where theangular velocity departs from the Keplerian value. At Rco the disk is disrupted bythe magnetic pressure and the matter is channeled by the magnetic field lines to theneutron star polar cap, where it impacts producing hard X-ray emission.Cheng and Ruderman (1989, 1991) have studied the magnetosphere of accretingneutron stars when the disk rotates faster than the star, showing that three definiteregions are formed: 1. A region coupled to the star by the magnetic field lines thatdo not penetrate the disk, 2. An equatorial region linked to the disk by the fieldattached to it, and 3. A gap entirely empty of plasma separating both regions. Inthis gap E · B 6= 0 and a strong potential drop 1V is established (see Figure 3 inRomero et al., 2001 for a sketch of the situation). For typical parameters in Be/X-ray binaries, 1V ∼ 1013−14 V (Romero et al., 2001). Protons entering into the gapfrom the stellar co-rotating region will be accelerated to multi-TeV energies anddirected to the accretion disk by the field lines, where they will impact producingπ± and π0 in pp interactions with the disk material. These pions will decay insidethe disk producing electron-positron pairs, high-energy (TeV) photons, and neutri-nos. The neutrinos will escape from the system (see Anchordoqui, et al., 2003 forestimates of the neutrino flux), but the pairs and the gamma-rays initiate electro-magnetic cascades that will degrade the energy of the gamma-ray photons to forma standard cascade spectrum with a cut-off at MeV-GeV energies. The leptons inthe disk will lose energy by inverse Compton (IC) interactions with the thermalX-ray photons, by synchrotron radiation in the field that penetrates the disk, andby relativistic Bremsstrahlung in the ions of the accreting gas. The details of thecascade development will be determined by the relative ratios of the cooling timesamong all these processes and the opacities for the produced photons in the specificcases.4. Gamma-Ray Production in the Accretion DiskProtons entering into the gap from the stellar co-rotating region are accelerated upto energies E p ∼ e Vmax, where the potential drop Vmax is given by Cheng andRuderman (1991):Vmax ∼ 4 × 1014β−5/2µM∗M¯¶1/7R−4/76 L5/737 B−3/712 V. (1)Here, M∗ ∼ 1.4 M¯ is the mass of the neutron star, R6 is its radius in units of 106cm, B12 is the magnetic field in units of 1012 G, and L37 is the X-ray luminosity inunits of 1037 erg s−1. The parameter β ≡ 2r0/rA ∼ 1 is twice the ratio of the inneraccretion disk radius to the Alfvén radius (Gosh and Lamb, 1979). The Alfvén radius170 M. ORELLANA AND G.E. ROMEROfor spherical accretion can be determined by the condition that the unscreened mag-netic energy density of the stellar field, B2/8π , becomes comparable to the kineticenergy density of the accreting matter, ρv2/2, i.e. B(rA)2/8 π = ρ(rA) v(rA)2/2 ,which yields rA = µ4/7 Ṁ−2/7 (2 G M∗)−1/7, with µ being the dipolar magneticmoment and Ṁ the accretion rate.The ultra-relativistic proton flux will be directed to the accretion disk by thefield lines. The maximum current that can flow through the gap can be determinedfrom the requirement that the azimuthal magnetic field induced by the current doesnot exceed that of the initial field B: Jmax ∼ B∗ R3∗r−20 (Cheng and Ruderman,1989).The number of protons that impact on the disk per unit of time is huge: Np =Jmax/e ∼ O (1033) s−1 and the total power injected in the disk results: Ėinj ∼JmaxVmax ∼ O (1036) erg s−1.Since all protons arrive to the disk surface with basically the same energy, wecan estimate the proton flux as:Jp(E) ∼ δ(E − E p)2πJmaxπeR20protonss cm2 sr. (2)These protons will have a probability of penetrating up to a distance L in the diskgiven by P(L) = 1 − e−L/λpp , with λpp = (σppndiskp )−1. At the relevant energiesσpp ∼ 4 × 10−26 cm2. Once the protons interact, neutral and charged pions areproduced. The decay of the charged pions leads to neutrino production in the disk(Cheng et al., 1990; Anchordoqui et al., 2003) and the injection of new e±-pairs.The gamma-ray emissivity from the neutral pions is:qγ (Eγ ) = 2Z ∞Eminπqπ (Eπ )pE2π − m2πc4d Eπ , (3)where Eminπ (Eγ ) = Eγ + m2π c44Eγ, andqπ (Eπ ) =Zδ(Eπ − fπ (E − m pc2))σpp(E)Jp(E) d E= 1fπσppµm pc2 + Eπfπ¶Jpµm pc2 + Eπfπ¶. (4)Here fπ is the fraction of the kinetic energy of the proton that goes into theneutral pion (and then to gamma-rays). Then, using expression (2) we obtain:qγ (Eγ ) ' Jmaxe πσpp(E p)fπ E pδ(Eγ − fπ E p) phatom eV s sr. (5)GAMMA-RAY EMISSION FROM Be/X-RAY BINARIES 171The intensity of the gamma-ray emission generated in the disk through π0-decaysresults:I oγ (Eγ ) =Z 2h0qγ (Eγ )Eγ2n p e−z/λpp dz. (6)The energy released per unit of time in the disk by these photons isLπ0(Eγ ) = 2 fπ Ėinj¡1 − e−2h/λpp¢, (7)and the gamma-ray luminosity emerging from the other side of the disk is:Lπ0esc(Eγ ) = Lπ0(Eγ )e−2hσγ pn p . (8)Here, σγ p ∼ 10−26 cm2. The gamma-rays that are absorbed can initiate electro-magnetic cascades inside the disk.5. Time-Dependent EstimatesIn order to calculate the evolution of all relevant parameters during both a major anda normal outburst, we have adopted the X-ray light curves observed for the Be/X-ray transient 2S 1417-624 (Finger et al., 1996b), with a normalization1 such thatat the peak of the major outburst, which is coincident with the periastron passage,the luminosity is L37 = 1. The light curves are shown in Figure 2.In Figures 3–6 we show the evolution of different parameters that characterizesthe system and the high energy emission for the cases of an unscreened disk (η = 1)and a partially screened disk (η = 0.2). The relation of the screening factor η andFigure 2. Time evolution of the X-ray luminosity of the disk for a major (Lpeak37 = 1) and a normaloutburst (Lpeak37 = 0.2, dashed curve). t = 0 corresponds to the periastron passage.172 M. ORELLANA AND G.E. ROMEROFigure 3. Time-evolution of disk parameters during a major outburst for models with η = 1 (dashedcurve) and η = 0.2 (solid curve). t = 0 corresponds to the periastron passage. 1. Inner radius of theaccretion disk (R0). 2. Half-height of the accretion disk at R0. 3. Magnetic field inside the disk at R0.4. Particle density of the disk at R0. 5. Photon density in the disk at R0. 6. Average energy of the diskphotons at R0.the inner radius of the accretion disk is given by Wang (1996):R0 = 1.35γ 2/70 η4/7rA, (9)where γ0 = −Bφ0/Bz0 ∼ 1 is the magnetic pitch angle.In the figures we show, for each case, the evolution of the inner radius of theaccretion disk, the half-height of the disk, the z-component of the magnetic field,the particle density inside the disk, the photon density, the average energy of thephotons, the energy of the first-generation gamma-rays inside the disk, the injectedenergy into the disk in the form of relativistic particles, the opacity of the diskto proton propagation, the gamma-ray luminosity produced inside the disk as aconsequence of the π0-decays, the opacity of the disk to these high-energy gamma-rays, and the luminosity of the gamma-rays that finally emerge from the other sideof the disk. All values are given at R0.GAMMA-RAY EMISSION FROM Be/X-RAY BINARIES 173Figure 4. Time-evolution of different parameters related to the high-energy emission during a majoroutburst for models with η = 1 (dashed curve) and η = 0.2 (solid curve). t = 0 corresponds to theperiastron passage. 1. Energy of the first-generation photons from π0-decays. 2. Power injected intothe disk in the form of relativistic protons. 3. Opacity to proton propagation in the disk. 4. Gamma-raypower from π 0-decays produced inside the disk. 5. Opacity to TeV gamma-ray propagation in thedisk. 6. High-energy gamma-ray luminosity that emerges from the other side of the disk.As we have already mentioned, those gamma-rays that are absorbed in the diskcan initiate an electromagnetic cascade if the secondary pairs are energetic enoughas to generate a second generation of gamma-rays. In Figure 7 we show the evolutionof the different ratios of cooling times for secondary pairs in the disk. During majoroutbursts in models with η = 0.2 three generations of pairs are created. The firstgeneration cools mainly by synchrotron radiation, whereas in the other generationsthe cooling is dominated by relativistic Bremsstrahlung. The GeV gamma-raysproduced by the last generation of pairs escape from the disk but not necessarilyfrom the system. Inverse Compton losses, which were not dominant inside the disk,are now responsible for further cascades in the photosphere (see next section). Inmodels of major outbursts with η = 1 only two generations of pairs are producedclose to the periastron, and just one when the disk is far from it. These pairs coolby synchrotron radiation mainly, although Bremsstrahlung takes over far in the174 M. ORELLANA AND G.E. ROMEROFigure 5. Same as Figure 3, but for a normal outburst.extremes of the light curve. During minor outbursts cascades cannot be sustained:TeV gamma-rays from π -decays and MeV-GeV photons from synchrotron andBremsstrahlung cooling of pairs originated in the π±-decays are directly injectedthrough the disk into the photosphere.6. Absorption in the PhotosphereThe optical depth for a photon with energy Eγ in the photosphere of the accretingneutron star isτ (Ro, Eγ ) =Z ∞Emin(Eγ )Z ∞Ronph(EX, r )σe−e+(EX, Eγ )dr d EX, (10)where EX is the energy of the ambient thermal X-ray photons, nph(EX, r ) is theirdensity, andσe−e+(EX, Eγ ) is the photon-photon pair creation cross section given by:σe+e−(EX, Eγ ) = πr202(1 − ξ 2)·2ξ (ξ 2 − 2) + (3 − ξ 4) lnµ1 + ξ1 − ξ¶¸, (11)GAMMA-RAY EMISSION FROM Be/X-RAY BINARIES 175Figure 6. Same as Figure 4, but for a normal outburst.where r0 is the classical radius of the electron andξ =·1 − (mec2)2EX Eγ¸1/2. (12)In Eq. (10), Emin is the threshold energy for pair creation in the X-ray field. Thisfield can be considered as formed by two components, one from the disk and theother from the neutron star: nph = nph,1 + nph,2. Here,nph,1(EX, r ) =µπ B(EX)hc EX¶R2or2, (13)withB(EX ) = 2E3X(hc)2¡eEX/kTdisk − 1¢ (14)176 M. ORELLANA AND G.E. ROMEROFigure 7. Evolution of the different ratios of cooling times for secondary pairs in an average electro-magnetic cascade developed in the accretion disk of a system with screening factor η = 0.2 (dashed)and η = 1 (solid) during normal (upper panels) and major (lower panels) outbursts.and Tdisk = Eph,disk/k, is the disk contribution. The emission from the heated polarcaps of the star can be approximated by a Bremsstrahlung spectrum:nph,2(EX, r ) = Lo4πc r2 E2X eEX/kTfor EX ≥ 2 keV, (15)where Lo is the total luminosity in hard X-rays and kT ∼ 100 keV.In Figure 8 we show the opacity to gamma-ray propagation at the periastronpassage as a function of the gamma-ray energy for major and normal outburstsin both models with η = 0.2 and η = 1. We see that gamma-rays with energiesbetween ∼ 1 GeV and ∼ 1 TeV energies are absorbed. These gamma-rays initiateFigure 8. Opacity to gamma-ray propagation in the photosphere at the periastron passage for bothmajor (solid) and normal (dashed) outbursts and disks with η = 0.2 (left) and η = 1 (right).GAMMA-RAY EMISSION FROM Be/X-RAY BINARIES 177Figure 9. Time evolution of the opacity to gamma-ray propagation in the photosphere for a majoroutburst in disks with η = 0.2 (solid curve) and η = 1 (dashed curve) at two different energies.inverse Compton cascades that degrade their energy. The final spectrum will besoft with an index of ∼ 2.5 and a high-energy cutoff around ∼ 2m2ec4/ hEXi ≈250(hEXi /1 keV)−1 MeV (Aharonian et al., 1985; Aharonian and Plyasheshnikov,2003). In Figure 9 we show the time evolution of the opacity at 1 GeV and 1 TeVfor different models during a major outburst. Photons with energies above 10 TeVand below 500 MeV always can escape from the photosphere.7. DiscussionThe variability pattern of a given source at gamma rays will depend on both thephysical parameters that characterize the particular system and the energy band ofthe observations. For instance, almost all GeV sources will be strongly absorbed intheir X-ray photosphere during major outbursts. In some normal outbursts, however,a flaring GeV event might be observable. At TeV energies the gamma rays arepartially absorbed in the disks, especially during major outbursts (a fact alreadynoticed by Cheng et al., 1991). The TeV flux can be detectable for sources in theinner spiral arms of the Galaxy, once again, mainly during normal outbursts. Duringmajor flaring X-ray events, the TeV gamma rays can be variable or not, dependingon the particular combination of parameters. At MeV energies the sources shouldbe detectable for a wide range of parameters, for both normal and major bursts. Acorrelation between the X-ray and the MeV gamma-ray flux should be observed inthese systems, whereas an anti-correlation should be the case in GeV sources, dueto the different absorptions.Future detection of Be/X-ray binaries by GLAST and Cherenkov telescopesmight be favored by the observation of the candidates during normal X-rayoutbursts.AcknowledgementsWe have benefited from illuminating discussions with Felix Aharonian, Luis An-chordoqui, K.S. Cheng, and Diego Torres. This work has been supported by178 M. ORELLANA AND G.E. ROMEROFundación Antorchas, ANPCyT (PICT 03-13291), and CONICET. GER thanksthe SECyT (Argentina) for a Houssay Prize.Note1. The distance to this source is not well-establishedReferencesAharonian, F.A.: 1985, Ap&SS 115, 201.Aharonian, F.A. and Plyasheshnikov, A.V.: 2003, Astrop. Phys. 19, 525.Anchordoqui, L.A.: 2003, ApJ 589, 481.Cheng, K.S.: 1991, ApJ 379, 290.Cheng, K.S., Cheung, T. and Lau, M.M.: 1990, J. Phys. G 6, 1115.Cheng, K.S. and Ruderman, M.: 1989, ApJ 337, L77.Cheng, K.S. and Ruderman, M.: 1991, ApJ 373, 187.Finger, M.H.: 1996a, ApJ 459, 288.Finger, M.H.: 1996b, A&AS 120, 209.Giovannellli, F. and Sabau Graziati, L.: 1992, Sp. Sci. Rev. 59, 1.Gosh, P. and Lamb, F.K.: 1979, ApJ 234, 296.Nolan, P.L.: 2003, ApJ 597, 615.Romero, G.E.: 2001, A&A 376, 599.Romero, G.E.: 2002, A&A 393, L61.Romero, G.E.: 2004, ESA-SP, in press.Torres, D.F.: 2001, A&A 370, 478.Wang, Y.M.: 1996, ApJ 465, L111.Zhang, S.: 2002, A&A 396, 923.

Gamma-Ray Emission From Be/X-Ray Binaries

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Gamma-Ray Emission From Be/X-Ray Binaries

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