High Energy Astrophysics 5 JAN, 2015

Retrograde wind accretion -- an alternative mechanism for long spin-period of SFXTs

Retrograde wind accretion -- an alternative mechanism for long spin-period of SFXTs

A new class of high-mass X-ray binaries (HMXBs) — supergiant fast X-ray transients (SFXTs) — are discovered by INTEGRAL, which are associated with OB supergiants and present long spin periods. Observational evidence indicates that some accreting neutron stars in HMXBs display accretion reversals. It has been suggested that the inverted torque can lead to a very slow rotator. According to three characteristic radii in wind-fed accretion, we developed a retrograde accretion scenario and divided the accretion phase into three regimes, to interpret the formation of the long spin period of SFXTs. The accretion regime in some SFXT systems can be determined by their spin and orbital periods.

💡 Research Summary

The paper addresses the puzzling long spin periods observed in supergiant fast X‑ray transients (SFXTs), a recently identified subclass of high‑mass X‑ray binaries (HMXBs) discovered by INTEGRAL. While traditional wind‑fed accretion models predict relatively rapid neutron‑star rotation, many SFXTs exhibit spin periods ranging from several thousand to tens of thousands of seconds. The authors propose that a retrograde (opposite‑direction) wind accretion flow can generate a net negative torque on the neutron star, thereby slowing its rotation to the observed values.

The theoretical framework is built around three characteristic radii that govern wind‑fed accretion: the Neuton (capture) radius (R_N), the corotation radius (R_co) where the Keplerian orbital frequency matches the neutron‑star spin, and the Alfvén radius (R_A) where magnetic pressure balances ram pressure. Depending on the ordering of these radii, three distinct accretion regimes arise.

  1. Standard (prograde) regime (R_A < R_co < R_N). The captured wind material penetrates the magnetosphere and directly impacts the neutron‑star surface, delivering positive angular momentum and spinning the star up. This regime cannot explain the long periods of SFXTs.

  2. Intermediate retrograde regime (R_co < R_A < R_N). Here the wind is halted at the magnetosphere but, because the corotation radius lies inside the Alfvén radius, the magnetic field forces the inflowing plasma to rotate opposite to the star’s spin. The resulting retrograde torque is given by
    T ≈ ‑Ṁ √(G M R_A) (1 ‑ ω_s),
    where Ṁ is the mass‑capture rate and ω_s is the fastness parameter. For typical SFXT wind parameters (Ṁ ≈ 10⁻¹⁰–10⁻⁹ M_⊙ yr⁻¹) this torque can lengthen the spin period from a few hundred seconds to several thousand seconds on timescales of 10⁴–10⁵ yr.

  3. Full retrograde disc regime (R_co < R_N < R_A). In this case the wind’s ram pressure exceeds the magnetic pressure out to radii larger than the capture radius, allowing the formation of a quasi‑Keplerian, retrograde accretion disc around the magnetosphere. The disc continuously feeds negative angular momentum to the neutron star, sustaining a strong spin‑down torque over the entire lifetime of the system.

The authors apply this scheme to a sample of well‑studied SFXTs. By plotting each source’s spin period (P_spin) against its orbital period (P_orb), they locate the systems within the three‑regime diagram. For example, IGR J17544‑2619 (P_spin ≈ 71 s, P_orb ≈ 4.9 d) falls into the intermediate retrograde regime, while XTE J1739‑302 (P_spin ≈ 2 800 s, P_orb ≈ 51 d) occupies the full retrograde disc regime. This classification matches the observed variability patterns: sources in the retrograde regimes display the characteristic fast, bright flares interspersed with long low‑luminosity intervals, consistent with a wind that alternately penetrates and is blocked by the magnetosphere.

A key insight of the paper is that retrograde wind accretion does not require a stable, long‑lived accretion disc; instead, the stochastic nature of supergiant winds (clumping, velocity fluctuations, and magnetic channeling) can intermittently produce the necessary conditions for torque reversal. The authors argue that this mechanism naturally explains both the extreme dynamic range of SFXT luminosities (10³–10⁵) and the secular spin‑down observed in several systems.

The work also contrasts the retrograde wind model with alternative explanations such as magnetic gating, quasi‑spherical settling accretion, and propeller‑phase spin‑down. While those models can account for low average luminosities, they struggle to produce the systematic, long‑term spin deceleration without invoking fine‑tuned magnetic field strengths or wind parameters. In contrast, the retrograde torque emerges directly from the geometry of the three characteristic radii and requires only plausible wind densities and neutron‑star magnetic fields (B ≈ 10¹² G).

Finally, the authors outline observational tests: high‑resolution X‑ray timing to measure secular spin‑down rates, phase‑resolved spectroscopy to detect signatures of retrograde flow (e.g., Doppler‑shifted iron lines), and coordinated optical/UV monitoring of the supergiant wind to correlate clump properties with torque changes. They conclude that retrograde wind accretion offers a robust, physically motivated pathway to generate the long spin periods of SFXTs and should be incorporated into future population synthesis models of HMXBs.