[Paper Review] Modelling light curves of binary systems: accounting for extended winds

É. A. Antokhina, I. I. Antokhin+1 more|arXiv (Cornell University)|Mar 26, 2013

Material Science and Thermodynamics4 citations

TL;DR

This paper presents a refined light curve model for eclipsing binary systems that incorporates extended stellar winds using a flexible velocity law (e.g., β-law) and electron scattering opacity. Simulations show that wind absorption significantly alters light curve depths and widths—particularly increasing secondary minimum depth when the wind-embedded star transits—demonstrating that neglecting winds leads to overestimated stellar radii, especially for Wolf-Rayet stars.

ABSTRACT

We suggest a simple synthesis model of an eclipsing binary system which includes one component with strong stellar wind. Numerical simulations show that the shape of the light curve (and in particularly the widths of the minima) strongly depends on wind parameters. Wind effects are crucial in modelling light curves of binaries including e.g., WR stars.

Motivation & Objective

• To address the discrepancy between observed large radii of Wolf-Rayet stars in eclipsing binaries and theoretical expectations based on mass loss.
• To improve light curve modeling by accounting for extended, accelerating stellar winds instead of assuming thin atmospheres.
• To quantify how wind parameters affect light curve morphology, particularly minimum depths and widths.
• To demonstrate that wind absorption must be included to avoid systematic overestimation of stellar radii in binary light curve analysis.

Proposed method

• Adopts the Roche model for both stars in a binary, with one component embedded in a spherically symmetric, homogeneous wind.
• Uses a parametric velocity law, such as the β-law: v(r) = v∞(1 - r*/r)^β, to model accelerating winds.
• Calculates optical depth via electron scattering using τ(p,z₀) = ∫ε(z)dz, with opacity ε(r) = zₑσₜṀ/(4πmₚv(r)r²).
• Integrates flux from each surface element of the Roche lobe, accounting for eclipses and wind absorption.
• Fixes wind parameters (Ṁ, V∞, β, zₑ) individually while varying them to isolate their effects on light curve shape.
• Uses effective temperature, gravity darkening, limb darkening, and bolometric albedo to model stellar emission.

Experimental results

Research questions

• RQ1 How does the presence of an extended stellar wind affect the depth and width of eclipses in binary light curves?
• RQ2 To what extent do wind parameters such as mass loss rate, terminal velocity, and velocity law index alter the observed light curve morphology?
• RQ3 Can accounting for wind absorption reconcile observed large radii of Wolf-Rayet stars with theoretical predictions?
• RQ4 What is the degeneracy structure between wind parameters in light curve fitting, and can they be independently constrained?

Key findings

• The depth of the secondary minimum increases significantly when the wind-embedded star transits, while the primary minimum depth decreases, due to enhanced wind absorption.
• The width of the minima is strongly sensitive to wind parameters, especially mass loss rate and terminal velocity, which directly affect the optical depth.
• A mass loss rate of 2×10⁻⁵ M☉/yr with V∞ = 2000 km/s and β = 0.5 produces measurable distortions in light curve shape, even in detached systems.
• The simulations confirm that neglecting wind absorption leads to overestimated stellar radii, particularly for Wolf-Rayet stars in eclipsing binaries.
• Degeneracy exists between wind parameters, but independent constraints (e.g., from UV spectra for V∞, radio data for Ṁ) can break it in practice.
• The model shows that wind effects are crucial for accurate radii and temperature determination in binary light curve analysis.