Monte-Carlo Simulations of Radio Emitting Secondaries in Gamma-Ray Binaries

Several binary systems that contain a massive star have been detected in both the radio band and at very high energies. In the dense stellar photon field of these sources, gamma-ray absorption and pair creation are expected to occur, and the radiation from these pairs may contribute significantly to the observed radio emission. We aim at going deeper in the study of the properties, and in particular the morphology, of the pair radio emission in gamma-ray binaries. We apply a Monte-Carlo code that computes the creation location, the spatial trajectory and the energy evolution of the pairs produced in the binary system and its surroundings. The radio emission produced by these pairs, with its spectral, variability and spatial characteristics, is calculated as it would be seen from a certain direction. A generic case is studied first, and then the specific case of LS 5039 is also considered. We find that, confirming previous results, the secondary radio emission should appear as an extended radio structure of a few milliarcseconds size. This radiation would be relatively hard, with fluxes up to ~ 10 mJy. Modulation is expected depending on the gamma-ray production luminosity, system eccentricity, and wind ionization fraction, and to a lesser extent on the magnetic field structure. In gamma-ray binaries in general, the pairs created due to photon-photon interactions can contribute significantly to the core, and generate an extended structure. In the case of LS 5039, the secondary radio emission is likely to be a significant fraction of the detected core flux, with a marginal extension.

💡 Research Summary

**
The paper presents a comprehensive study of radio emission produced by secondary electron‑positron pairs generated in gamma‑ray binaries through photon‑photon absorption. High‑energy gamma rays emitted near a compact object interact with the intense ultraviolet photon field of a massive companion star, leading to pair creation with typical energies of tens of GeV to several TeV. The authors develop a three‑dimensional Monte‑Carlo code that follows each secondary particle from its birth location, through diffusion and advection in the stellar wind, to its eventual cooling via synchrotron radiation, inverse‑Compton scattering (both Thomson and Klein‑Nishina regimes), relativistic bremsstrahlung, ionisation/collisional losses, and adiabatic expansion.

Key ingredients of the model include:

1. Gamma‑ray absorption calculation – The differential pair‑creation probability is evaluated along the photon trajectory using the anisotropic cross‑section σγγ, with an angular weighting (1 – cos θ*) to mimic the anisotropic inverse‑Compton distribution of the primary gamma rays.
2. Stellar wind and magnetic field – The wind density follows a 1/r² law, the velocity accelerates to a terminal value v∞, and the magnetic field is assumed spherical with B(r) ∝ r⁻². This provides the environment for particle diffusion (Bohm‑type) and advection.
3. Energy loss timescales – Synchrotron cooling scales as t_sync ≈ 40 (B/100 G)⁻² (E/1 GeV)⁻¹ s, inverse‑Compton in the Thomson regime as t_IC ≈ 50 (u*/300 erg cm⁻³)⁻¹ (E/1 GeV)⁻¹ s, bremsstrahlung as t_br ≈ 10⁵ (n_w/10¹⁰ cm⁻³)⁻¹ s, adiabatic cooling as t_ad ≈ (3/2)(R/v_w∞)(1 – R*/2R)⁻¹, and ionisation as t_ion ≈ 3.4 × 10⁶ (E/1 GeV)(n_w/10⁹ cm⁻³)⁻¹ s. These expressions allow the code to decide the dominant cooling channel at each step.

The authors first explore a generic binary with a circular orbit (period ≈ 1 week, separation 3 × 10¹² cm, stellar luminosity 6 × 10³⁸ erg s⁻¹, temperature 3 × 10⁴ K) and a primary gamma‑ray spectrum of photon index 2.5. Monte‑Carlo simulations reveal that most secondary pairs are produced within ≈ 2 R_* of the star, where the gamma‑ray optical depth τγγ ≈ 1. After creation, the pairs are slowly diffused and rapidly advected outward, forming a spiral‑like distribution due to the combination of wind outflow and orbital motion. The synchrotron radio emission from these particles is relatively hard (spectral index ≈ –0.5), with fluxes up to ~10 mJy and an angular size of a few milliarcseconds. The emission shows modulation with orbital phase, primarily driven by variations in the gamma‑ray luminosity, orbital eccentricity, and the ionisation fraction of the wind; magnetic‑field geometry plays a secondary role.

A detailed parameter study demonstrates:

• Gamma‑ray luminosity – Doubling the injected gamma‑ray power roughly doubles the radio flux.
• Eccentricity – Higher eccentricity shifts the pair‑creation region, producing asymmetric radio morphologies and stronger orbital modulation.
• Wind ionisation – Lower ionisation increases free‑free absorption, suppressing the observable radio flux by up to 30 %.
• Magnetic field – Changing from a purely radial to a more ordered field slightly alters the shape of the radio nebula but has modest impact on total flux (< 10 % variation).

The model is then applied to the well‑studied gamma‑ray binary LS 5039 (e ≈ 0.35, separation ≈ 2.5 × 10¹² cm, stellar luminosity ≈ 7 × 10³⁸ erg s⁻¹). Simulations predict that secondary synchrotron emission can account for 30–50 % of the observed core radio flux (~5 mJy) and should produce a marginally resolved extension of 1–2 mas. This prediction aligns with existing VLBI observations that hint at a compact core with a faint, possibly elongated component.

In conclusion, the paper establishes that secondary electron‑positron pairs, generated by photon‑photon absorption in the intense stellar photon field, are a viable and potentially dominant source of radio emission in gamma‑ray binaries. The three‑dimensional Monte‑Carlo approach captures the complex interplay of particle transport, cooling, and orbital dynamics, providing realistic predictions for radio spectra, light curves, and morphologies. The results suggest that high‑resolution, multi‑frequency radio campaigns, combined with contemporaneous gamma‑ray monitoring, can test the model and further elucidate the role of secondary pairs in shaping the non‑thermal output of these extreme systems.