Implication of the striped pulsar wind model for gamma-ray binaries

(abridged) Gamma-ray binaries are massive stars with compact object companions that are observed to emit most of their energy in the gamma-ray range. One of these binaries is known to contain a radio pulsar, PSR B1259-63. Synchrotron and inverse Compton emission from particles accelerated beyond the light cylinder in striped pulsar winds has been proposed to explain the X-ray to high energy (HE, $>$ 100 MeV) gamma-ray emission from isolated pulsars. This pulsar model extends naturally to binary environments, where seed photons for inverse Compton scattering are provided by the companion star. Here, we investigate the possibility of gamma-ray emission from PSR B1259-63 in the framework of the striped pulsar wind model. The orbital geometry of PSR B1259-63 is well constrained by observations and the double radio pulse suggests an almost orthogonal rotator so that the solid angle covered by the striped region is close to $4\pi$. We calculate the orbital and rotational phase-resolved spectral variability and light-curves to expect.

💡 Research Summary

The paper investigates whether the striped pulsar wind model can account for the high‑energy (HE, >100 MeV) gamma‑ray emission observed from the binary system PSR B1259‑63/SS 2883. In the striped wind scenario, the pulsar’s oblique rotator geometry (magnetic axis nearly orthogonal to the spin axis) creates a current sheet that spirals outward in a split‑monopole magnetic field. Inside the sheet the plasma is hot, weakly magnetised and populated by relativistic electron‑positron pairs with a power‑law energy distribution; outside the sheet the plasma is cold and strongly magnetised. The sheet’s thickness (Δφ) and the density contrast between sheet and ambient plasma (N/N₀) control the emissivity.

When the observer’s line of sight cuts through the sheet (|π/2 − ζ| ≲ χ), relativistic aberration and Doppler boosting produce two narrow gamma‑ray pulses per rotation, separated by a phase given by arccos(cot χ cot ζ). For an almost orthogonal rotator (χ≈90°) the pulses are roughly 180° apart, matching the double‑peaked radio profile of PSR B1259‑63. The particles radiate synchrotron X‑rays and, crucially for this work, inverse‑Compton (IC) scatter photons from the massive companion star. Because the companion is a luminous Be star (L_≈10³¹ W, T_≈2.7×10⁴ K) the stellar photon field provides a dense, anisotropic seed for IC scattering. The photon density at the pulsar varies by a factor ≈200 between periastron (d≈10¹¹ m) and apastron (d≈10¹² m), and the scattering angle changes from ~54° to ~126°, strongly modulating the IC output.

The authors model the IC emission by integrating the emissivity over the first few stripes, assuming the wind expands radially with a constant bulk Lorentz factor Γ_v and that the particle density falls off faster than r⁻² due to adiabatic cooling (effectively r^{−2(p+2)/3}). They adopt a power‑law index p≈2–3, a minimum Lorentz factor γ_min≈10⁴ and a maximum γ_max set by the observed spectral cutoff (a few GeV). The light‑cylinder particle density is constrained to n_L≈7×10¹⁵ m⁻³, which yields a sheet density contrast of order 10⁴.

The calculated phase‑resolved spectra show that near periastron the IC component peaks at ≈100 MeV–few GeV with a photon index ≈2 and a flux ≈10⁻⁷ ph cm⁻² s⁻¹, in excellent agreement with the first Fermi‑LAT detection (mid‑December 2010). The model predicts that the emission originates predominantly at radii >10³ r_L; at these distances the IC scattering occurs partly in the Klein‑Nishina regime, producing the observed spectral shape.

A second, brighter flare observed about a month after periastron, with a softer spectrum (photon index ≈3) and flux ≈10⁻⁶ ph cm⁻² s⁻¹, can be explained by additional seed photons supplied by the trailing pulsar wind nebula or by re‑energised stellar photons scattered off particles that have traveled farther downstream. The model naturally accounts for the lack of detected pulsations: the line of sight only intermittently intersects the thin current sheet, and the pulsed component is diluted by the broader, unpulsed IC emission from the ambient wind.

The paper extends the discussion to other gamma‑ray binaries such as LS 5039 and LS I +61° 303. In those systems the orbital geometry and observer inclination determine whether the line of sight crosses the striped region. When it does, HE gamma‑ray light curves show orbital modulation and spectra reminiscent of isolated pulsars (hard power‑law with exponential cutoff). Conversely, for systems like HESS J0632+057, where the line of sight never intersects the sheet, the model predicts very faint or absent HE emission, consistent with observations.

Overall, the striped pulsar wind model provides a unified framework that (i) links the pulsar’s magnetospheric geometry to observable gamma‑ray pulsations, (ii) incorporates the companion’s luminous photon field to produce strong orbital modulation of the IC component, and (iii) explains the timing and spectral properties of the HE flares seen by Fermi‑LAT. The authors emphasize that key parameters—sheet thickness, particle spectral index, and light‑cylinder density—are directly testable with simultaneous multi‑wavelength campaigns (radio, X‑ray, VHE) and future facilities such as CTA. Precise measurements of pulse phase, spectral cutoffs, and orbital light‑curve shapes will allow stringent constraints on the striped wind physics and on the role of pulsar winds in gamma‑ray binaries.