High-energy emission from jet-clump interactions in microquasars

High-mass microquasars are binary systems consisting of a massive star and an accreting compact object from which relativistic jets are launched. There is considerable observational evidence that winds of massive stars are clumpy. Individual clumps may interact with the jets in high-mass microquasars to produce outbursts of high-energy emission. Gamma-ray flares have been detected in some high-mass X-ray binaries, such as Cygnus X-1, and probably in LS 5039 and LS I+61 303. We predict the high-energy emission produced by the interaction between a jet and a clump of the stellar wind in a high-mass microquasar. Assuming a hydrodynamic scenario for the jet-clump interaction, we calculate the spectral energy distributions produced by the dominant non-thermal processes: relativistic bremsstrahlung, synchrotron and inverse Compton radiation, for leptons, and for hadrons, proton-proton collisions. Significant levels of emission in X-rays (synchrotron), high-energy gamma rays (inverse Compton), and very high-energy gamma rays (from the decay of neutral pions) are predicted, with luminosities in the different domains in the range ~ 10^{32}-10^{35} erg/s. The spectral energy distributions vary strongly depending on the specific conditions. Jet-clump interactions may be detectable at high and very high energies, and provide an explanation for the fast TeV variability found in some high-mass X-ray binary systems. Our model can help to infer information about the properties of jets and clumpy winds by means of high-sensitivity gamma-ray astronomy.

💡 Research Summary

The paper investigates the high‑energy radiation that arises when dense clumps embedded in the stellar wind of a massive star collide with the relativistic jet launched by an accreting compact object in a high‑mass microquasar (HMMQ). Using Cygnus X‑1 as a representative system, the authors adopt a binary separation of a = 3 × 10¹² cm, a stellar luminosity L★ = 10³⁹ erg s⁻¹, temperature T★ = 3 × 10⁴ K, a mass‑loss rate Ṁ★ = 3 × 10⁻⁶ M⊙ yr⁻¹ and a wind terminal velocity vw = 2.5 × 10⁸ cm s⁻¹. The wind is assumed to be highly clumped; each clump is spherical with radius Rc = 10¹⁰ cm or 10¹¹ cm, density nc = 10¹² cm⁻³, temperature Tc = 10⁴ K, and moves with the wind speed. The jet is taken to be conical with radius Rj(z) = 0.1 z (opening angle ≈ 6°), bulk velocity vj = 0.3 c (Lorentz factor ≈ 1.06), kinetic power Lkin ≈ 3 × 10³⁶ erg s⁻¹, and particle density nj ≈ 4.7 × 10⁷ cm⁻³ at the interaction height z = a/2. This yields a density contrast χ = nc/nj ≈ 2 × 10⁴, which is crucial for the dynamics.

The authors compute a series of characteristic timescales. The time for a clump to fully enter the jet is tc ≈ 2Rc/vc (≈ 80 s for Rc = 10¹⁰ cm, ≈ 800 s for Rc = 10¹¹ cm). The shock that propagates through the clump travels at vcs ≈ vj √χ, giving a clump‑crossing time tcc ≈ 2Rc/vcs (≈ 3 × 10² s–3 × 10³ s). The bow‑shock that forms in the jet material establishes itself on a much shorter timescale tbs ≈ 0.2 Rc/vjps (≪ tcc). Rayleigh‑Taylor and Kelvin‑Helmholtz instabilities develop on timescales comparable to tcc, indicating that the clump can survive long enough to transfer a substantial fraction of the jet’s kinetic energy to the shocked plasma before being disrupted.

Particle acceleration is assumed to occur at the bow‑shock via diffusive (Fermi‑I) processes. Two magnetic‑field scenarios are explored: a sub‑equipartition field Bbs ≈ 150 G (derived from 10 % of the post‑shock internal energy density) and a weaker field Bbs ≈ 1 G. The acceleration time is tacc ≈ η E/(q B c) with η ≈ (8/3)(c/vs)²; for B = 150 G, tacc ≈ 10⁻² E (E in eV), allowing electrons and protons to reach several hundred GeV within the short interaction time.

Radiative losses for electrons include synchrotron (tsyn ≈ 4.1 × 10² B⁻² E⁻¹ s), inverse‑Compton (IC) scattering on the stellar photon field (energy density uph ≈ 2.4 × 10² erg cm⁻³, with Klein‑Nishina effects above ∼ 30 GeV), and relativistic bremsstrahlung (negligible because nbs ≈ 2 × 10⁸ cm⁻³). Protons lose energy mainly through inelastic pp collisions, producing neutral pions that decay into γ‑rays. The authors calculate the steady‑state particle distributions by balancing acceleration against these losses and escape.

The resulting spectral energy distributions (SEDs) show three dominant components: (i) synchrotron emission peaking in the X‑ray band with luminosities Lsyn ≈ 10³²–10³⁴ erg s⁻¹, (ii) IC emission in the 100 MeV–GeV range with LIC ≈ 10³³–10³⁴ erg s⁻¹, and (iii) π⁰‑decay γ‑rays at TeV energies with Lπ⁰ ≈ 10³⁴–10³⁵ erg s⁻¹. The luminosities scale roughly linearly with the clump size; the larger clump (Rc = 10¹¹ cm) yields fluxes up to an order of magnitude higher than the smaller one. The flare duration is set by tcc, i.e., a few hundred to a few thousand seconds, matching the fast TeV variability observed in sources such as Cygnus X‑1, LS 5039 and LS I +61 303.

The authors argue that such jet‑clump interactions are readily detectable with current ground‑based Cherenkov telescopes (MAGIC, HESS, VERITAS) and space‑based γ‑ray instruments (Fermi‑LAT). Moreover, the model provides a diagnostic tool: the observed flare spectrum and temporal profile can be inverted to infer clump properties (size, density, filling factor) and jet parameters (magnetic field strength, kinetic power). Repeated interactions could also explain longer‑term γ‑ray variability patterns in HMMQs.

In conclusion, the paper presents a comprehensive, physically motivated framework for transient high‑energy emission in microquasars driven by the impact of wind clumps on relativistic jets. By coupling hydrodynamic timescales, shock physics, particle acceleration, and multi‑wavelength radiative processes, the authors demonstrate that jet‑clump collisions can naturally produce X‑ray, GeV, and TeV flares with luminosities 10³²–10³⁵ erg s⁻¹ on timescales of minutes to hours. This mechanism offers a plausible explanation for the rapid γ‑ray variability observed in several high‑mass X‑ray binaries and opens a pathway to probe the microphysics of clumpy stellar winds and relativistic jets through high‑sensitivity γ‑ray observations.