while the main results obtained are shown in Section \[results\] and discussed in Section \[discussion\]. Final conclusions are presented in Sect. \[conclusions\].

Through this paper we assume a $\Lambda$ CDM cosmology with parameters $H_\mathrm{0} = 73$ km s$^{-1}$ Mpc$^{-1}$, $\Omega_{\Lambda}=0.73$, and $\Omega_\mathrm{m}=0.27$.

Observations and data analysis {#observations}
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*Chandra* X-ray observations {#chandraobservations}
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The ULX N4088–X1 was observed on 2012 June 06 (Obs. ID: 14442; PI: Mezcua) with the *Chandra X-ray observatory* (Weisskopf et al. 2002). The observation was performed using the Advanced CCD Imaging Spectrometer detector (@1997AAS...190.3404G; ACIS-S) with an integration time of 19.8 ks. The data were reprocessed using CIAO version 4.5 and the corresponding calibration files, following the standard *Chandra* ACIS data analysis threads[^4]. The *chandra\_repro* reprocessing script was used to reprocess the data and generate a new level=2 event file. An image of the S3 chip (ccd\_id=7), a background image, and a PSF map that provides the size of the PSF at each pixel in the image were then produced using the tools *dmcopy*, *aconvolve*, and *mkpsfmap* and given to *wavdetect*, which performed source detection and extracted source net counts in the energy range 0.3–10 keV. The detected source count rates for all sources lying within 