The relativistic jet of Cygnus X-3 in gamma rays

High energy gamma-rays have been detected from Cygnus X-3, a system composed of a Wolf-Rayet star and a black hole or neutron star. The gamma-ray emission is linked to the radio emission from the jet launched in the system. The flux is modulated with the 4.8 hr orbital period, as expected if high energy electrons are upscattering photons emitted by the Wolf-Rayet star to gamma-ray energies. This modulation is computed assuming that high energy electrons are located at some distance along a relativistic jet of arbitrary orientation. Modeling shows that the jet must be inclined and that the gamma ray emitting electrons cannot be located within the system. This is consistent with the idea that the electrons gain energy where the jet is recollimated by the stellar wind pressure and forms a shock. Jet precession should strongly affect the gamma-ray modulation shape at different epochs. The power in non-thermal electrons represents a small fraction of the Eddington luminosity only if the inclination is low i.e. if the compact object is a black hole.

💡 Research Summary

Cygnus X‑3 is a high‑mass X‑ray binary consisting of a Wolf‑Rayet (WR) star and a compact object (either a black hole or a neutron star) in a tight 4.8 h orbit. The system is a bright X‑ray source (L_X ≈ 10³⁸ erg s⁻¹) and exhibits powerful radio flares (up to 20 Jy) associated with a relativistic jet expanding at 0.3–0.7 c. In 2009 the AGILE and Fermi‑LAT collaborations reported the detection of high‑energy (HE) γ‑rays (>100 MeV) from Cygnus X‑3. The γ‑ray flux is strongly modulated with the orbital period, with an amplitude close to 100 % after background subtraction, and the modulation is almost anti‑phased with the X‑ray modulation (γ‑ray minimum occurs ≈0.3–0.4 in phase after the X‑ray minimum).

The authors interpret the γ‑ray emission as inverse‑Compton (IC) scattering of stellar photons by relativistic electrons located somewhere along the jet. The WR star (R_* ≈ 1 R_⊙, T_* ≈ 10⁵ K) provides an intense photon field (energy density u_* ≈ 10⁵ erg cm⁻³ at the compact object). Electrons with Lorentz factors γ_e ≈ 10³–10⁴ can up‑scatter the ∼20 eV stellar photons into the >100 MeV band efficiently, and the IC process naturally produces an orbital modulation because the scattering geometry changes with orbital phase.

A semi‑analytic model is built: electrons are assumed to be confined at a distance H from the compact object along a jet moving with bulk speed βc. The jet orientation is described by a polar angle φ_j (inclination relative to the orbital plane) and an azimuthal angle θ_j. The IC flux depends on the distance R between the electrons and the star, the Doppler factor D_obs, and the scalar products e_·e_obs and e_·e_jet, which encode the geometry. The model reproduces the observed modulation only if (i) the jet is inclined (φ_j ≈ 20°–80° rather than perpendicular to the orbital plane) and (ii) the electrons are not located at the compact object but at H ≈ 0.5–30 d (where d is the orbital separation, i.e. 2×10¹¹–10¹³ cm). A perpendicular jet would give maxima and minima at conjunctions, contrary to the data.

Parameter space is explored exhaustively: β from 0 to 0.99, H from 0.01 d to 100 d, φ_j from 0 to π/2, θ_j from 0 to 2π, and the electron normalisation K_e is adjusted to match the observed light curve. The electron spectrum is taken as a power law dN_e∝γ_e⁻ᵖ dγ_e with p = 4.4 (consistent with the observed photon index α = 1.7). The minimum electron Lorentz factor is set to γ_e,min = 10³, required to produce photons above 100 MeV; the resulting power in high‑energy electrons, P_e, is highly sensitive to this cutoff.

Two orbital solutions are considered. Orbit 1 (O1) assumes a 20 M_⊙ black hole, a 50 M_⊙ WR star, and an inclination i = 30°. The best‑fit model for O1 has β = 0.41, H = 8×10¹¹ cm (≈2.5 d), φ_j = 39°, θ_j = 319°, and P_e ≈ 10³⁸ erg s⁻¹, i.e. about 5 % of the Eddington luminosity for a 20 M_⊙ black hole. The 90 % confidence region allows β up to ≈0.6, H between 0.5 d and 30 d, and φ_j roughly between 20° and 80°, with a clear preference for φ_j close to the system inclination. The azimuth θ_j is less tightly constrained but shows a preferred peak near 300°. Models with β = 0 (no bulk motion) also fit the data, though they require a lower electron power (P_e ≈ 2×10³⁷ erg s⁻¹). Conversely, “micro‑blazar” models with β ≈ 0.99 can reproduce the light curve if the jet points almost directly toward the observer at superior conjunction, compensating the low electron power through strong Doppler boosting.

Orbit 2 (O2) assumes a 1.4 M_⊙ neutron star, a 5 M_⊙ WR star, and i = 70°. Good fits are also obtained, but they require higher electron power (P_e ≈ 0.2 L_Edd) and a bulk speed β ≈ 0.2. The larger inclination forces the jet to be more strongly inclined to reproduce the observed phase shift, leading to a higher energetic demand. Thus, the black‑hole scenario is energetically more favorable.

The authors also explore jet precession. If the jet azimuth θ_j varies over a precession period (sampling the full 0–2π range), both the phase and amplitude of the γ‑ray modulation change dramatically. This could explain why earlier γ‑ray missions (SAS‑2, COS‑B, EGRET) reported different modulation patterns or failed to detect the source. The current Fermi data already hint at a change in the modulation phase between the two detection epochs.

In summary, the paper demonstrates that the orbital γ‑ray modulation of Cygnus X‑3 can be quantitatively reproduced by inverse‑Compton scattering of WR stellar photons by relativistic electrons located several orbital separations out along an inclined jet. The required jet geometry (inclination 20°–80°, azimuth ≈300°) and electron power (≤ 10³⁸ erg s⁻¹ for a black‑hole primary) are consistent with independent constraints from radio observations and theoretical expectations for jet recollimation shocks caused by the dense WR wind. The model predicts that future observations of the γ‑ray light curve, especially any systematic changes due to jet precession, will provide a powerful diagnostic of the jet’s orientation, speed, and particle acceleration site.