Modeling Forbidden Line Emission Profiles from Colliding Wind Binaries

This paper presents calculations for forbidden emission line profile shapes arising from colliding wind binaries. The main application is for systems involving a Wolf-Rayet (WR) star and an OB star companion. The WR wind is assumed to dominate the forbidden line emission. The colliding wind interaction is treated as an archimedean spiral with an inner boundary. Under the assumptions of the model, the major findings are as follows. (a) The redistribution of the WR wind as a result of the wind collision is not flux conservative but typically produces an excess of line emission; however, this excess is modest at around the 10% level. (b) Deviations from a flat-top profile shape for a spherical wind are greatest for viewing inclinations that are more nearly face-on to the orbital plane. At intermediate viewing inclinations, profiles display only mild deviations from a flat-top shape. (c) The profile shape can be used to constrain the colliding wind bow shock opening angle. (d) Structure in the line profile tends to be suppressed in binaries of shorter periods. (e) Obtaining data for multiple forbidden lines is important since different lines probe different characteristic radial scales. Our models are discussed in relation to ISO data for WR 147 and gamma Vel (WR11). The lines for WR 147 are probably not accurate enough to draw firm conclusions. For gamma Vel, individual line morphologies are broadly reproducible but not simultaneously so for the claimed wind and orbital parameters. Overall, the effort demonstrates how lines that are sensitive to the large-scale wind can help to deduce binary system properties and provide new tests of numerical simulations.

💡 Research Summary

The paper presents a semi‑analytic framework for predicting the shapes of forbidden‑line emission profiles in colliding‑wind binaries, with a focus on systems composed of a Wolf‑Rayet (WR) star and an OB companion. The authors assume that the WR wind dominates the forbidden‑line formation and that the wind–wind interaction region can be represented as an Archimedean spiral bounded on the inside by the stagnation point. Within this geometry the WR wind is redistributed by the shock, a process that is not strictly flux‑conservative; the total line flux is typically enhanced by about ten percent, a modest increase that nevertheless influences the detailed profile shape.

A key result is that the line profile morphology depends strongly on the observer’s inclination relative to the orbital plane. When the system is viewed nearly face‑on (i.e., the orbital plane is close to the line of sight), the classic flat‑top profile expected from a spherical, isotropic wind is strongly distorted: the central plateau becomes shallow and pronounced wings appear on both the blue and red sides. At intermediate inclinations the deviations are mild, and the profile remains close to a flat‑top. This inclination sensitivity provides a direct diagnostic of the orbital tilt.

The opening angle of the wind‑collision bow shock (the “cone” angle) also leaves a clear imprint. A wider opening angle means that a larger solid angle of the WR wind is intercepted and swept into the shocked region, reducing the contribution of that wind to the line emission over a broader radial range. Consequently the central part of the profile is flattened further and the wings become more prominent. By fitting observed profiles, one can therefore infer the bow‑shock opening angle and, indirectly, the momentum ratio of the two winds.

Orbital period plays a secondary but important role. Short‑period binaries have tightly wound spirals; the wind material is mixed over many turns, which tends to average out azimuthal variations and suppresses structure in the line profile, yielding an almost perfect flat‑top. In contrast, long‑period systems possess loosely wound spirals, allowing distinct density and velocity perturbations to survive and manifest as asymmetries or bumps in the profile.

The authors emphasize the value of observing multiple forbidden lines simultaneously. Different ions (e.g.,