Properties of intra-cluster low-mass X-ray binaries in Fornax globular clusters

Aims. We present a study of the intra-cluster population of low-mass X-ray binaries (LMXB) residing in globular clusters (GC) in the central 1 deg2 of the Fornax galaxy cluster. Differently from previous studies, which were restricted to the innermost regions of individual galaxies, this work is aimed at comparing the properties of the intra-cluster population of GC-LMXBs with those of the host galaxy. Methods. The data used in this work are a combination of the VLT Survey Telescope (VST) and Chandra observations. We performed a cross-match between the optical and the X-ray catalogue in order to identify the LMXBs residing in GCs. We divided the GC-LMXBs into host-galaxy and intra-cluster objects based on their distance from the nearest galaxy in terms of effective radius (Reff). We found 82 intra-cluster GC-LMXBs and 86 objects that are hosted in galaxies. As the formation of LMXBs also depends on the host GC colour, we performed a Gaussian mixture model to divide the population into red and blue GCs. Results. As has been found for the innermost regions of galaxies, LMXBs tend to form in red and bright GCs in intra-cluster space as well. We find, however, that the likelihood of a red GC to host an LMXB decreases with galactocentric distance, but it remains approximately constant for the blue GC population. Investigating the X-ray properties of the LMXBs residing in GCs, we find a difference in the X-ray luminosity function between the intra-cluster and host-galaxy sample: both follow a power-law down to ∼8.5 × 1037 erg s−1, which is consistent with field LMXBs for the intra-cluster sample, while the latter agree with previous estimates for LMXBs in GCs. We observe a deficiency of bright LMXBs in blue intra-cluster GCs, however. This might indicate a lack of black hole binaries in metal-poor systems. We further investigated the spectral properties of the GC-LMXBs through their hardness-ratio. We detect a tentative difference in the hardness ratio of two populations, where the intra-cluster GC-LMXBs appear to have harder spectra than the host-galaxy objects. We find the same trend when we compare red and blue GC-LMXBs: the spectra of the blue sample are harder spectra than those of the red sample. This result could suggest a relation between the spectral properties of LMXBs and the host GC colour and therefore its metallicity. We discuss the possibilities of spatial biases due to uncertainties in the X-ray spectral response correction and due to contamination by background active galactic nuclei.