Characterisation of the stellar wind in Cyg X-1 via modelling of colour-colour diagrams

¹ INAF-Osservatorio Astronomico di Cagliari, Via della Scienza 5, I-09047 Selargius, CA, Italy
² Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, PL-00-716 Warszawa, Poland
³ Departament de Física, EEBE, Universitat Politècnica de Catalunya, c/Eduard Maristany 16, 08019 Barcelona, Spain
⁴ Departamento de Física, Universidad de Santiago de Chile, Av. Victor Jara 3659, Santiago, Chile
⁵ Center for Interdisciplinary Research in Astrophysics and Space Exploration (CIRAS), USACH, Santiago, Chile
⁶ Institute of Astronomy, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudzidzka 5, 87-100 Toruń, Poland
⁷ European Space Agency (ESA), European Space Astronomy Centre (ESAC), Camino Bajo del Castillo s/n, 28692 Villanueva de la Cañada, Madrid, Spain
⁸ European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁹ Anton Pannekoek Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
¹⁰ Institut d’Estudis Espacials de Catalunya, c/Gran Capità 2-4, Ed. Nexus-201, 08034 Barcelona, Spain
¹¹ Dr. Karl Remeis-Observatory, University of Erlangen-Nuremberg, Sternwartstr. 7, 96049 Bamberg, Germany

^⋆ Corresponding author; eleonora.lai@inaf.it

Received: 8 June 2024
Accepted: 12 August 2024

Abstract

Context. Cygnus X-1 (Cyg X-1) is a high-mass X-ray binary where accretion onto the black hole (BH) is mediated by the stellar wind from the blue supergiant companion star HDE 226868. Due to its inclination, the system is a perfect laboratory to study the not yet well-understood stellar wind structure. In fact, depending on the position of the BH along the orbit, X-ray observations can probe different layers of the stellar wind. Deeper wind layers can be investigated at superior conjunction (i.e. null orbital phases).

Aims. We aim to characterise the stellar wind in the Cyg X-1/HDE 226868 system, analysing one passage at superior conjunction covered by XMM-Newton during the ‘Cyg X-1 Hard state Observations of a Complete Binary Orbit in X-rays’ (CHOCBOX) campaign.

Methods. To analyse the properties of the stellar wind, we computed colour-colour diagrams. Since X-ray absorption is energy-dependent, colour indices provide information on the parameters of the stellar wind, such as the column density, N_H, w, and the covering factor, f_c. We fitted colour-colour diagrams with models that include both a continuum and a stellar wind component. We used the kernel density estimation method to infer the unknown probability distribution of the data points in the colour-colour diagram, and selected the model corresponding to the highest likelihood. In order to study the temporal evolution of the wind around superior conjunction, we extracted and fitted time-resolved colour-colour diagrams.

Results. We found that the model that best describes the shape of the colour-colour diagram of Cyg X-1 at superior conjunction requires the wind to be partially ionised. The shape of the colour-colour diagram strongly varies during the analysed observation, due to concurrent changes of the mean N_H, w and the f_c of the wind. Our results suggest the existence of a linear scaling between the rapid variability amplitude of N_H, w (on timescales between 10 s and 11 ks) and its long-term variations (on timescales > 11 ks). Using the inferred best-fit values, we estimated the stellar mass loss rate to be ∼7 × 10⁻⁶ M_⊙ yr⁻¹ and the clumps to have a characteristic mass of ∼10¹⁷ g.