[Paper Review] Conditions for accretion disc formation and observability of wind-accreting X-ray binaries

Ryosuke Hirai, Ilya Mandel|arXiv (Cornell University)|Aug 9, 2021

Astrophysical Phenomena and Observations108 references41 citations

TL;DR

This paper investigates the conditions for accretion disc formation in wind-fed high-mass X-ray binaries by modeling anisotropic line-driven winds in close binaries. It shows that velocity reduction due to binary tidal forces enables focused accretion streams when the donor star fills >80–90% of its Roche lobe, which is necessary for sufficient angular momentum to form discs. The study predicts a sharp transition in observability at this threshold.

ABSTRACT

We explore the effect of anisotropic wind driving on the properties of accretion onto black holes in close binaries. We specifically focus on line-driven winds, which are common in high-mass X-ray binaries. In close binary systems, the tidal force from the companion star can modify the wind structure in two different ways. One is the reduction of wind terminal velocity due to the weaker effective surface gravity. The other is the reduction in mass flux due to gravity darkening. We incorporate these effects into the so-called CAK theory in a simple way and investigate the wind flow around the accretor on the orbital scale. We find that a focused accretion stream is naturally formed when the Roche lobe filling factor is $\gtrsim0.8$-0.9, analogous to that of wind Roche lobe overflow, but only when the velocity reduction is taken into account. The formation of a stream is necessary to bring in sufficient angular momentum to form an accretion disc around the black hole. Gravity darkening effects reduce the amount of accreted angular momentum, but not enough to prevent the formation of a disc. Based on these results, we expect there to be a discrete step in the observability of high-mass X-ray binaries depending on whether the donor Roche lobe filling factor is below or above $\sim$0.8-0.9.

Motivation & Objective

• To understand the physical conditions enabling accretion disc formation in high-mass X-ray binaries (HMXBs) fed by anisotropic stellar winds.
• To investigate how tidal forces in close binaries modify wind structure, particularly wind velocity and mass flux, via reduced effective gravity and gravity darkening.
• To determine whether these modifications enable focused accretion streams and, consequently, disc formation.
• To identify a critical threshold in Roche lobe filling factor that separates observable HMXBs with discs from those without.
• To assess the implications for the observability of black hole HMXBs, especially in the context of gravitational wave progenitor systems.

Proposed method

• Adapts the CAK theory of line-driven winds to include tidal effects in close binaries, modifying wind acceleration and mass flux via effective gravity and gravity darkening.
• Incorporates velocity reduction due to the companion's tidal field into the wind structure, using a modified force multiplier approach.
• Applies gravity darkening via von Zeipel's theorem to reduce mass flux in regions of lower surface gravity, particularly near the equator.
• Uses a simplified hydrodynamic model to compute accretion rates and angular momentum flux onto the compact object across different Roche lobe filling factors.
• Compares results to the standard Bondi-Hoyle-Lyttleton model to isolate the impact of anisotropic wind effects.
• Performs numerical calculations for orbital parameters typical of known BH-HMXBs, such as Cygnus X-1, to derive observable thresholds.

Experimental results

Research questions

• RQ1 What is the minimum Roche lobe filling factor required for focused accretion stream formation in wind-fed HMXBs?
• RQ2 How do tidal forces from a binary companion alter the wind velocity and mass flux structure in line-driven winds?
• RQ3 To what extent do velocity reduction and gravity darkening affect the angular momentum accreted by a black hole?
• RQ4 Can anisotropic wind effects alone explain the observed presence of accretion discs in systems like Cygnus X-1?
• RQ5 Is there a sharp transition in the observability of HMXBs based on the Roche lobe filling factor due to disc formation?

Key findings

• A focused accretion stream forms naturally when the Roche lobe filling factor exceeds approximately 0.8–0.9, driven primarily by velocity reduction in the tidal field.
• The formation of such a stream is essential for delivering sufficient angular momentum to form an accretion disc around the black hole.
• Gravity darkening reduces the accreted angular momentum but not enough to prevent disc formation when the filling factor is above the threshold.
• The total accreted mass remains similar to the standard Bondi-Hoyle-Lyttleton model when both velocity reduction and gravity darkening are included.
• Systems with Roche lobe filling factors below ~0.8 are unlikely to host accretion discs, implying a discrete transition in observability for HMXBs.
• The model predicts prograde accretion in observable systems, contrary to the retrograde accretion expected in standard wind-fed models.