EWOCS-II: X-ray properties of the Wolf-Rayet stars in the young Galactic super star cluster Westerlund 1

Context. Wolf-Rayet (WR) stars are massive evolved stars that exhibit particularly fast and dense stellar winds. Although they constitute a very short phase near the end of a massive star's life, they play a crucial role in the evolution of massive stars and have a substantial impact on their surrounding environment. Aims. We present the most comprehensive and deepest X-ray study to date of the properties of the richest Wolf-Rayet population observed in a single stellar cluster, Westerlund 1 (Wd1). By examining the X-ray signatures of WR stars, we aim to shed light on the hottest plasma in their stellar winds and gain insights into whether they exist as single stars or within binary systems. Methods. This work is based on 36 Chandra observations obtained from the "Extended Westerlund 1 and 2 Open Clusters Survey" (EWOCS) project, plus 8 archival Chandra observations. The overall exposure depth Ms) and baseline of the EWOCS observations extending over more than one year enable us to perform a detailed photometric, colour, and spectral analysis, as well as to search for short- and long-term periodicity. Results. In X-rays, we detect 20 out of the 24 known Wolf-Rayet stars in Wd1 down to an observed luminosity of similar to 7 x 10(29) erg s(-1) (assuming a distance of 4.23 kpc to Wd1), with 8 WR stars being detected in X-rays for the first time. Nine stars show clear evidence of variability over the year-long baseline, with clear signs of periodicity. The X-ray colours and spectral analysis reveal that the vast majority of the WR stars are hard X-ray sources (kT >= 2.0 keV). The Fe XXV emission line at similar to 6.7 keV, which commonly originates from the wind-wind collision zone in binary systems, is detected for the first time in the spectra of 17 WR stars in Wd1. In addition the similar to 6.4 keV fluorescent line is observed in the spectra of three stars, which are among the very few massive stars exhibiting this line, indicating that dense cold material coexists with the hot gas in these systems. Overall, our X-ray results alone suggest a very high binary fraction (>= 80%) for the WR star population in Wd1. When combining our results with properties of the WR population from other wavelengths, we estimate a binary fraction of >= 92%, which could even reach unity. This suggests that either all the most massive stars are found in binary systems within Wd1, or that binarity is essential for the formation of such a rich population of WR stars.