X-ray to J-band separation (ΔRA, ΔDec) in arcsec for X-ray sources detected in each single observation (with a wavdetect false-positive probability detection threshold set to 10⁻⁶ and off-axis < 6′; see Sect. 2 for the details) before (red open circles) and after (blue solid circles) astrometric correction. The circles encompass 68%, 90%, and 95% of the sources before (red dashed line) and after (blue solid line) astrometric correction.