[Paper Review] The Evolution of Binaries under the Influence of Radiation-Driven Winds from a Stellar Companion

Sophie L. Schrøder, Morgan MacLeod+5 more|arXiv (Cornell University)|Jul 20, 2021

Stellar, planetary, and galactic studies10 citations

TL;DR

This study uses 3D hydrodynamical simulations to investigate how radiation-driven winds from a massive stellar companion influence orbital evolution in binary systems. It finds that wind velocity and mass ratio are the dominant factors: low wind-to-orbital velocity ratios and high mass ratios lead to strong angular momentum loss and orbital shrinkage, while wider binaries with lighter companions experience orbital widening. A simple analytic formula based on wind velocity and mass ratio accurately predicts orbital evolution, validated through simulations of high-mass X-ray binaries like Vela X-1 and Cygnus X-1.

ABSTRACT

Interacting binaries are of general interest as laboratories for investigating the physics of accretion, which gives rise to the bulk of high-energy radiation in the Galaxy. They allow us to probe stellar evolution processes that cannot be studied in single stars. Understanding the orbital evolution of binaries is essential in order to model the formation of compact binaries. Here we focus our attention on studying orbital evolution driven by angular momentum loss through stellar winds in massive binaries. We run a suite of hydrodynamical simulations of binary stars hosting one mass losing star with varying wind velocity, mass ratio, wind velocity profile and adiabatic index, and compare our results to analytic estimates for drag and angular momentum loss. We find that, at leading order, orbital evolution is determined by the wind velocity and the binary mass ratio. Small ratios of wind to orbital velocities and large accreting companion masses result in high angular momentum loss and a shrinking of the orbit. For wider binaries and binaries hosting lighter mass-capturing companions, the wind mass-loss becomes more symmetric, which results in a widening of the orbit. We present a simple analytic formula that can accurately account for angular momentum losses and changes in the orbit, which depends on the wind velocity and mass ratio. As an example of our formalism, we compare the effects of tides and winds in driving the orbital evolution of high mass X-ray binaries, focusing on Vela X-1 and Cygnus X-1 as examples.

Motivation & Objective

• To understand how radiation-driven winds from a massive stellar companion affect the orbital evolution of binary systems.
• To determine the dominant physical parameters—such as wind velocity, mass ratio, and wind profile—that govern angular momentum loss in binaries.
• To develop and validate a simple analytic formula for predicting orbital evolution driven by wind-induced drag.
• To compare the relative effects of winds and tides in shaping the evolution of high-mass X-ray binaries, using Vela X-1 and Cygnus X-1 as case studies.

Proposed method

• Conducting 3D hydrodynamical simulations of binary systems with one mass-losing star and a compact companion, using a β-law wind profile with β = 0.5 for computational tractability.
• Varying wind terminal velocity, wind velocity at binary separation, mass ratio (q), and adiabatic index (γ_ad) to isolate key drivers of angular momentum loss.
• Using gravitational softening and adaptive mesh refinement (AMR) to control numerical resolution and avoid singularities near the companion.
• Measuring drag forces and angular momentum loss via the drag efficiency parameter γ_drag, derived from the ratio of momentum transfer to wind momentum flux.
• Comparing simulation results to analytic estimates of wind drag and torque, particularly focusing on the dependence on wind velocity and mass ratio.
• Validating the model against observed high-mass X-ray binaries, including Vela X-1 and Cygnus X-1, to assess the relative importance of wind-driven evolution versus tidal effects.

Experimental results

Research questions

• RQ1 How does the wind velocity relative to orbital velocity influence orbital shrinkage or widening in massive binaries?
• RQ2 What is the role of the mass ratio between the accreting companion and the wind donor in determining angular momentum loss?
• RQ3 How do variations in the wind acceleration profile (e.g., β-law) and equation of state (γ_ad) affect the structure of the wind wake and drag forces?
• RQ4 Can a simple analytic formula based on wind velocity and mass ratio accurately predict orbital evolution in wind-driven binaries?
• RQ5 How do wind-driven effects compare to tidal forces in shaping the orbital evolution of high-mass X-ray binaries like Vela X-1 and Cygnus X-1?

Key findings

• Orbital shrinkage occurs when the wind-to-orbital velocity ratio is small and the mass ratio is high, due to strong angular momentum loss from asymmetric wind drag.
• For wider binaries or systems with lighter accreting companions, wind mass-loss becomes more symmetric, leading to orbital widening due to net momentum transfer.
• The drag efficiency γ_drag varies by a factor of approximately 2.5 across different adiabatic indices (γ_ad = 1.1 to 5/3), with lower γ_ad producing more compressible, clumpier flows and higher drag.
• Numerical resolution tests show that γ_drag is robust to changes in softening radius (r_soft) and AMR levels, with variations within ±5% across tested parameters.
• The simulations confirm that wind velocity and mass ratio are the dominant factors in orbital evolution, with other parameters like wind profile and γ_ad playing secondary roles.
• A simple analytic formula based on wind velocity and mass ratio accurately captures the observed orbital evolution, enabling predictive modeling of compact binary formation pathways.