[Paper Review] Radiography in high mass X-ray binaries -- Micro-structure of the stellar wind through variability of the column density

I. El Mellah, V. Grinberg+3 more|arXiv (Cornell University)|Jun 29, 2020

Astrophysical Phenomena and Observations5 references4 citations

TL;DR

This paper proposes using X-ray variability in high-mass X-ray binaries as a radiographic probe to infer the micro-structure of stellar winds. By modeling the wind as radially advected clumps and analyzing the time variability of the absorbing column density, the authors show that the coherence time scale directly measures clump size, while the standard deviation of column density constrains clump mass, enabling unbiased mass-loss rate measurements without relying on intrinsic X-ray variability.

ABSTRACT

In high mass X-ray binaries (HMXBs), an accreting compact object orbits a high mass star which loses mass through a dense and inhomogeneous wind. Using the compact object as an X-ray backlight, the time variability of the absorbing column density in the wind can be exploited in order to shed light on the micro-structure of the wind and obtain unbiased stellar mass loss rates for high mass stars. We explore the impact of clumpiness on the variability of the column density with a simplified wind model. In particular, we focus on the standard deviation of the column density and the characteristic duration of enhanced absorption episodes, and compare them with analytical predictions based on the porosity length. We identified the favorable systems and orbital phases to determine the wind micro-structure. The coherence time scale of the column density is shown to be the self-crossing time of a clump in front of the compact object. We provide a recipe to get accurate measurements of the size and of the mass of the clumps, purely based on the observable time variability of the column density. The coherence time scale grants direct access to the size of the clumps while their mass can be deduced separately from the amplitude of the variability. If it is due to unaccreted passing-by clumps, the high column density variations in some HMXBs requires high mass clumps to reproduce the observed peak-to-peak amplitude and coherence time scales. These clump properties are hardly compatible with the ones derived from first principles. Alternatively, other components could contribute to the variability of the column density: larger orbital scale structures produced by a mechanism still to be identified, or a dense environment in the immediate vicinity of the accretor such as an accretion disk, an outflow or a spherical shell around the magnetosphere of the accreting neutron star.

Motivation & Objective

• To develop a radiographic method to probe the micro-structure of line-driven winds in high-mass X-ray binaries using X-ray absorption variability.
• To determine whether time variability in the absorbing column density can provide unbiased measurements of stellar mass-loss rates independent of traditional diagnostics.
• To identify favorable orbital phases and system parameters for detecting wind clump properties via X-ray light curves.
• To test the hypothesis that observed X-ray column density variations are caused by unaccreted clumps passing through the line of sight.
• To assess the compatibility of inferred clump properties with radiative-hydrodynamics simulations and observational constraints.

Proposed method

• Model the stellar wind as a collection of spherical, radially advected clumps with defined mass and radius, assuming stochastic distribution along the line of sight.
• Use the porosity length to analytically predict the standard deviation of the column density and its coherence time scale as functions of clump size, mass, and orbital geometry.
• Simulate time series of the absorbing column density $N_H$ for various orbital phases, clump parameters, and viewing angles to compare with analytical predictions.
• Relate the observed coherence time scale to the self-crossing time of a clump across the compact object's line of sight, enabling direct clump size estimation.
• Use the amplitude of $N_H$ variability (standard deviation) to infer the mass of individual clumps independently of intrinsic X-ray variability.
• Apply the model to systems with moderate luminosity and intermediate orbital inclination, focusing on phases $\phi = 0.25$ and $\phi = 0.5$ for optimal clump visibility.

Experimental results

Research questions

• RQ1 Can the time variability of the absorbing column density in high-mass X-ray binaries be used to infer the micro-structure of the stellar wind?
• RQ2 What is the physical origin of the observed coherence time scale in $N_H$ light curves, and can it be linked to clump size?
• RQ3 To what extent can the amplitude of $N_H$ variability constrain the mass of individual clumps?
• RQ4 Are the inferred clump properties (size and mass) consistent with those from radiative-hydrodynamics simulations?
• RQ5 What observational conditions (orbital phase, inclination, exposure time) maximize the detectability of clump-induced $N_H$ variability?

Key findings

• The coherence time scale of the column density variability corresponds to the self-crossing time of a single clump across the line of sight, enabling direct measurement of clump radius.
• The standard deviation of $N_H$ is proportional to $\sqrt{m_{cl}}/R_{cl}$, providing a direct constraint on the ratio of clump mass to radius.
• Clump mass can be estimated independently from the amplitude of $N_H$ variability, without relying on assumptions about intrinsic X-ray variability.
• The inferred clump sizes from coherence time scales are a few times larger than those predicted by radiative-hydrodynamics simulations, suggesting a discrepancy.
• The inferred clump masses required to produce observed peak-to-peak $N_H$ amplitudes are high, and marginally compatible with simulation results.
• Monitoring at superior conjunction ($\phi = 0.5$) can probe the onset of the clump-forming region above the stellar photosphere.