High-energy radiation from the relativistic jet of Cygnus X-3
aa r X i v : . [ a s t r o - ph . H E ] J u l SF2A 2010
S. Boissier, M. Heydari-Malayeri, R. Samadi and D. Valls-Gabaud (eds)
HIGH-ENERGY RADIATION FROM THE RELATIVISTIC JET OF CYGNUS X-3
Cerutti, B. , Dubus, G. and Henri, G. Abstract.
Cygnus X − Fermi found definitiveevidence that high-energy emission is produced in this system. We propose a scenario to explain the GeVgamma-ray emission in Cygnus X −
3. In this model, energetic electron-positron pairs are accelerated at aspecific location in the relativistic jet, possibly related to a recollimation shock, and upscatter the stellarphotons to high energies. The comparison with
Fermi observations shows that the jet should be inclinedclose to the line of sight and pairs should not be located within the system. Energetically speaking, amassive compact object is favored. We report also on our investigations of the gamma-ray absorption ofGeV photons with the radiation emitted by a standard accretion disk in Cygnus X −
3. This study showsthat the gamma-ray source should not lie too close to the compact object.
Cygnus X-3 is an accreting high-mass X-ray binary with relativistic jets, i.e. a microquasar. This system iscomposed of a Wolf-Rayet star (see e.g. van Kerkwijk et al. 1996) and an unknown compact object, probably ablack-hole, in a tight 4.8 hours orbit and is situated at about 7 kpc from Earth (Ling et al. 2009). The gamma-rayspace Telescopes
AGILE (Tavani et al. 2009) and
Fermi (Fermi LAT Collaboration et al. 2009) have detectedgamma-ray flares at GeV energies in the direction of Cygnus X − Fermi dataset. This is the first unambigous detection of a microquasar in high-energy gammarays. The gamma-ray emission in Cygnus X − − − The model relies on simple assumptions. Energetic electron-positron pairs are located at a specific altitude H along the jet and symmetrically (with respect to the compact object) in the counter-jet. These accelerationsites could be related to recollimation shocks as observed in some AGN such as M87 (Stawarz et al. 2006),possibly produced by the interaction of the dense Wolf-Rayet star wind and the jet. This possibility seems to becorroborated by recent MHD simulations (see Perucho et al. 2010). Pairs are isotropic in the comoving frameand follow a power-law energy distribution. The total power injected into pairs is P e . The jet is relativistic (witha bulk velocity β = v/c >
0) and inclined in an arbitrary direction parameterized by the spherical angles φ j (polar angle) and θ j (azimuth angle). The orbit of the compact object is circular with a radius d = 3 × cm.We define here the orbital phase φ such as φ ≡ .
25 at superior conjunction and φ ≡ .
75 at inferior conjunction. Laboratoire d’Astrophysique de Grenoble, UMR 5571 CNRS, Universit´e Joseph Fourier, BP 53, 38041 Grenoble, Francec (cid:13)
Soci´et´e Francaise d’Astronomie et d’Astrophysique (SF2A) 2010
SF2A 2010The Wolf-Rayet star (effective temperature T ⋆ ∼ K, stellar radius R ⋆ ∼ R ⊙ ) provides a high density ofseed photons for inverse Compton scattering on the relativistic pairs injected in the jet ( n ⋆ ≈ ph cm − atthe compact object location). Because of the relative position of the star with respect to the energetic pairsand the observer, the inverse Compton flux is orbital modulated. This is a natural explanation for the orbitalmodulation of the gamma-ray flux observed in Cygnus X −
3. Other sources of soft radiation ( e.g. accretiondisk, CMB) can be excluded to account for the modulation, and could instead contribute to the DC component.In addition to anisotropic effects, the relativistic motion of the flow should be considered in the calculation ofthe Compton emissivity (Doppler-boosting effects, see Dubus et al. 2010a for technical details).
We applied this model to Cygnus X − i = 30 o ), the compact object is a 20 M ⊙ black hole orbiting a 50 M ⊙ Wolf-Rayet star. In the second solution ( i = 70 o ), the system is composed of a 1.4 M ⊙ neutron star and a 5 M ⊙ star. Fig. 1.
High-energy gamma-ray flux ( >
100 MeV) as a function of the orbital phase (two full orbits) for the black holesolution in Cygnus X −
3. Example of a good fit solution of the theoretical model (blue solid line) to the folded
Fermi lightcurve (data points). The contribution from the jet (red solid line) and the counter-jet (red dashed line) are shownfor comparison. Set of parameters: β = 0 . , H = 3 d, φ j = 12 o , θ j = 106 o and P e = 10 erg s − . In order to constrain the orientation of the jet, we carried out an exhaustive exploration of the spaceparameter. The theoretical solutions are compared with the
Fermi lightcurve using a χ test. The best fitsolutions to observations are given by those minimizing the χ . Many sets of parameters reproduce correctlythe observed gamma-ray modulation. Fig. 1 shows one possible solution. Fig. 2 presents the full distribution ofmodels leading to a good fit, i.e. contained in the 90% confidence region .It appears from this study that the jet should be inclined close to the line of sight. The jet is mildlyrelativistic ( β < .
9) and pairs should not be located within the system (0 . d < H < d ). We favor a massivecompact object in the system ( i.e. a black hole) as the energy budget required to reproduce the GeV flux canbe only a small fraction of the Eddington luminosity. This work reveals also that the gamma-ray modulation(amplitude and shape) is very sensitive to the polar angle θ j , i.e. if the jet precesses. The non-detectionby COS B (Hermsen et al. 1987) and EGRET (Mori et al. 1997) may be the consequence of a non favorableorientation of the jet. The controversial results by
SAS-2 (Lamb et al. 1977) might actually be a real detection. In Dubus et al. (2010b), we implicitly assumed fast cooling such that P e ≈ R + ∞ γ min K e γ − pe dγ e /t ic where t ic ≈ . γ e / ) − ( R/d ) s is the inverse Compton cooling timescale at γ min = 10 (see § R/d ) wasnot properly taken into account in our calculation of the distribution of acceptable parameters. The corrected distribution allowsfor a greater range of solutions with electrons injected at a large distance from the compact object. The corrected Figure 3 is shownhere on the left panel in Fig. 2. The parameters of the best fit model and our conclusions are unchanged. igh-energy radiation from the relativistic jet of Cygnus X-3 3 Fig. 2.
Distribution of good fit models contained in the 90% confidence region of the χ statistics for the black hole (leftpanel) and the neutron star orbital solutions (right panel), for the parameters of the jet β ( top panels), H, φ j , and θ j ( bottom panels). Filled regions correspond to a total power injected into pairs P e < L edd (light gray), < . L edd (gray)and < . L edd (dark gray), where L edd is the Eddington luminosity. High-energy photons of 100 MeV-1 GeV can be absorbed by ∼ −
3, themain source of soft X-rays could be provided by an accretion disk around the compact object. FollowingZhang & Cheng (1997), we compute the gamma-ray opacity in the thermal radiation field emitted by a standardaccretion disk (optically thick, geometrically thin) in Cygnus X −
3. The inner radius of the disk R in is set at thelast stable orbit. Assuming that the total luminosity of the disk is radiated in X-rays L disk ≈ L X ≈ erg s − ,the accretion rate is ˙ M ≈ − M ⊙ yr − for the black hole solution. The source of gamma rays is assumedpoint-like and located above the disk at an altitude z . The disk is inclined at an angle ψ with respect to theobserver. Fig. 3 presents the gamma-ray opacity map of a 1 GeV photon in the radiation field of the accretion disk inCygnus X −
3. Photons are injected on the revolution axis of the disk. Gamma-ray photons are highly absorbedif the source lies in a compact region around the compact object ( z < − R in ). Similar maps were obtainedby Sitarek & Bednarek (2010) in the context of AGN with an application to Centaurus A. In addition to thethermal component in soft X-rays, the spectrum of Cygnus X − e.g. Szostek et al. 2008). This component might be related to the emission from a hot corona of electronsabove the accretion disk (see e.g.
Coppi 1999). These photons could also contribute significantly to increase SF2A 2010the gamma-ray opacity in the system at MeV and GeV energies. More theoretical endeavors are required inthis direction.
Fig. 3.
This map gives the gamma-ray opacity exp ( − τ γγ ) as a function of the viewing angle ψ and the altitude of thesource above a standard accretion disk z for a 1 GeV gamma-ray photon. The calculation is applied here to Cygnus X − τ γγ ≫
1) and bright regions to low opacity ( τ γγ ≪ R in = 10 cm and R ext = 10 cm. The white dashed line indicates z ≡ R in and the black dotted line z ≡ d . Doppler-boosted Compton emission from energetic pairs accelerated at a specific location far from the compactobject, in an inclined and mildly relativistic jet explains convincingly the gamma-ray modulation in Cygnus X − − cm above theaccretion disk. Microquasars provide a nearby and well constrained environment to study accretion-ejectionmechanisms and acceleration processes in relativistic jets. Acknowledgements:
This work was supported by the
European Community via contract ERC-StG-200911.