Slow wind in the orbital plane of wind-fed high-mass X-ray binaries: multi-component wind geometry, its ubiquity, and the origin of the required radial transport

Accretion-powered X-ray pulsars in high-mass X-ray binaries (HMXBs) act as probes of the wind of their massive companion: the observed X-ray luminosity fixes the mass-capture rate, which via Bondi–Hoyle–Lyttleton accretion sets an upper limit on the wind speed in the orbital plane. Applying this to eight well-studied systems, Beskrovnaya, Ikhsanov and Kim (2025) found upper limits on the in-plane wind speed of 120–1000 km/s, a factor of 2–4 below both terminal and polar wind speeds, in Be systems and non-Be systems alike, and a lower limit of 2–12 km/s on the radial wind speed. This raises an unresolved question about massive-star wind structure: do early-type stars without the Be phenomenon eject a genuinely slower wind component in the orbital plane (a multi-component wind geometry), how ubiquitous is this component and how does it depend on orbital separation and stellar spectral type, and what physical mechanism — possibly magnetically mediated transport — supplies the angular-momentum and mass transport needed to maintain the inferred finite radial outflow speed? As of 2026 the only follow-up literature adopts a competing one-dimensional slow-acceleration reading and explicitly defers the geometry, clumping, and phase-dependence issues.

Background

A high-mass X-ray binary (HMXB) is a binary system containing a neutron star or black hole orbiting a massive (≳10 solar mass) O- or B-type companion. In the wind-fed subclass, the compact object captures gas from the line-driven stellar wind of its companion rather than through Roche-lobe overflow (Roche lobes are the gravitational equipotential lobes of the binary; the companion does not fill its lobe here). For an accreting magnetized neutron star, the accretion luminosity is $L_x \simeq \dot M_a GM_{\mathrm{ns}}/R_{\mathrm{ns}}$, so the measured X-ray luminosity directly gives the mass accretion rate $\dot M_a$. The capture rate from a wind of density $\rho_w$ moving past the neutron star at relative velocity $v_{\mathrm{rel}}$ follows the Bondi–Hoyle–Lyttleton prescription $\dot M_c = \pi r_G^2 \rho_w v_{\mathrm{rel}}$, where $r_G = 2GM_{\mathrm{ns}}/v_{\mathrm{rel}}^2$ is the Bondi (gravitational capture) radius. Since steady accretion requires $\dot M_a \le \dot M_c$, a measured $L_x$ bounds $v_{\mathrm{rel}}$ from above — the neutron star thereby becomes a probe of the wind speed in the orbital plane of the system.

The method was introduced by Delgado-Martí, Levine, Pfahl and Rappaport (2001) for the Be/X-ray binary X Persei, where the wind in the orbital plane cannot exceed about 150 km/s, far below the roughly 800 km/s wind speed inferred from ultraviolet spectral lines. This was expected for Be stars — B-type stars showing Balmer emission from a dense, slowly outflowing equatorial decretion disk whose radial speeds are a factor of 3–5 below polar wind speeds. Ikhsanov, Kim and Beskrovnaya (2024) applied the same technique to OAO 1657-415, whose Ofpe/WNL donor shows no Be phenomenon, obtaining 200–500 km/s in the orbital plane, again well below typical terminal wind speeds (about 2000 km/s for O-type stars, 500–1500 km/s for B-type supergiants; the terminal velocity $v_\infty$ is the asymptotic speed of a line-driven wind, often parameterized by the β-law $v(r) = v_\infty(1 - bR_*/r)^\beta$). Beskrovnaya, Ikhsanov and Kim (2025) extended the analysis to eight thoroughly studied persistent wind-fed pulsars (Cen X-3, 4U 1538-52, Vela X-1, OAO 1657-415, 2S 0114+650, GX 301-2, X Per, RX J0146.9+6121). For every system, the upper limit on the orbital-plane wind speed during the X-ray high state (120–1000 km/s) is a factor of 2–4 below both the terminal wind velocity and the polar-region wind speed, regardless of whether the donor exhibits the Be phenomenon. A complementary steady-accretion argument — the wind must traverse a radial distance comparable to the neutron-star Roche-lobe radius within one orbital period — sets a lower limit $v_f \simeq R_{\mathrm{L_{ns}}}/P_{\mathrm{orb}} \approx 2$–$12$ km/s on the radial wind speed in the orbital plane, a few percent of the neutron-star orbital velocity.

These results support a multi-component (slow equatorial, fast polar) structure for massive-star winds in HMXBs and constrain the mass-transfer physics of Be decretion disks: the inferred lower limit on radial speed challenges purely hydrodynamical, cool, moderately viscous disk scenarios, and the authors suggest that incorporating the stellar-wind magnetic field may be needed to explain efficient outward mass and angular-momentum transport. The analytic estimates, however, rest on simplifying assumptions — spherically symmetric wind-density scaling in the orbital plane, $v_{\mathrm{rel}} \approx v_w$, and Roche-lobe approximations for $R_{\mathrm{L_{ns}}}$ — and the X-ray luminosities of some systems (notably OAO 1657-415, with conflicting distance estimates) carry distance-driven ambiguity. Whether the slow in-plane component reflects true two-dimensional wind geometry or merely slow one-dimensional radial acceleration (for instance through X-ray photoionization suppressing line driving, since X-rays from the neutron star can quench the radiative acceleration of the wind) remains observationally undecided.

Problem Statement

Determine the structure of the winds of massive early-type stars in wind-fed high-mass X-ray binaries as probed by their accreting neutron stars. The overarching question, posed by Beskrovnaya, Ikhsanov and Kim (2025): is the wind that massive stars without the Be phenomenon eject within the orbital plane of the binary genuinely slower than the wind flowing from the polar regions (a multi-component wind geometry), or can the accretion-derived limits be explained within a one-dimensional spherical wind model with suppressed acceleration? Beyond the overarching question, the source's results raise three open issues, each of which stands independently and is not resolved by settling the others: whether the slow in-plane component (orbital-plane upper limits of order 120–1000 km/s, a factor of 2–4 below terminal/polar speeds) extends beyond the eight systems analyzed, and how it depends on orbital separation and spectral type of the donor; the radial dependence of the in-plane wind speed between the donor surface and the neutron-star orbit (the source notes the limits decrease only weakly with system size); and the physical mechanism that maintains the required radial outflow speed in the slow component — the source conjectures that incorporation of the stellar-wind magnetic field into the model may help increase the efficiency of the mass and angular-momentum transfer out from the star and thereby explain the inferred lower limit of a few percent of the neutron-star orbital velocity, which challenges purely hydrodynamical treatments of Be-star decretion disks.

References

1. Beskrovnaya, N.; Ikhsanov, N.; Kim, V. Stellar Wind Parameters of Massive Stars in Accretion-Powered High-Mass X-Ray Binary Pulsars. Galaxies 2025, 13, 37. DOI: 10.3390/galaxies13020037; arXiv:2505.02958. https://doi.org/10.3390/galaxies13020037
2. Delgado-Martí, H.; Levine, A. M.; Pfahl, E.; Rappaport, S. A. The Orbit of X Persei and Its Neutron Star Companion. The Astrophysical Journal 2001, 546, 455–468. DOI: 10.1086/318236. https://doi.org/10.1086/318236
3. Ikhsanov, N. R.; Kim, V. Yu.; Beskrovnaya, N. G. On the estimate of the stellar wind velocity of the massive component in OAO 1657-415. Publications of the Pulkovo Observatory 2024, 233, 34–38. DOI: 10.31725/0367-7966-2024-233-34-38. https://doi.org/10.31725/0367-7966-2024-233-34-38
4. Muratkhan, Z.; Khassanov, M.; Taukenova, A.; Toktarbay, S. Empirical Determination of β-Law Wind Acceleration Profiles in High-Mass X-Ray Binaries. Universe 2026, 12, 67. DOI: 10.3390/universe12030067. https://doi.org/10.3390/universe12030067
5. Muratkhan, Z.; Toktarbay, S.; Muratkhan, A.; Taukenova, A.; Azhar, N. Correlation analysis of the wind acceleration parameter in high-mass X-ray binaries. Physical Sciences and Technology 2026, 13(1–2), 94–102. DOI: 10.26577/phst20261319. https://doi.org/10.26577/phst20261319