A soft and transient ultraluminous X-ray source with six-hour modulation in the NGC 300 galaxy

We investigate the nature of CXOUJ005440.5 − 374320 (J0054), a peculiar bright ( ∼ 4 × 10 39 ergs − 1 ) and soft X-ray transient in the spiral galaxy NGC300 with a six-hour periodic ﬂux modulation that was detected in a 2014 Chandra observation. Subsequent observations with Chandra and XMM-Newton , as well as a large observational campaign of NGC300 and its sources performed with the Swift Neil Gehrels Observatory, showed that this source exhibits recurrent ﬂaring activity: four other outbursts were detected across ∼ 8years of monitoring. Using data from the Swift / UVOT archive and from the XMM-Newton / OM and Gaia catalogues, we determined that the source is likely associated with a bright blue optical / ultraviolet counterpart. This prompted us to perform follow-up observations with the Southern African Large Telescope in December 2019. With the multi-wavelength information at hand, we discuss several possibilities for the nature of J0054. Although none is able to account for the full range of the observed peculiar features, we found that the two most promising scenarios are a stellar-mass compact object in a binary system with a Wolf–Rayet star companion, or the recurrent tidal stripping of a stellar object trapped in a system with an intermediate-mass ( ∼ 1000 M (cid:12) ) black hole.


Introduction
The Chandra ACIS Timing Survey at the Brera And Roma astronomical observatories (CATS at BAR) is a systematic search for coherent periodic signals in Chandra/ACIS archival data in timed exposure mode.The first catalogue of new pulsators was published in Israel et al. (2016), and several sources have been studied individually (Esposito et al. 2013a(Esposito et al. ,b,c, 2015;;Bartlett et al. 2017;Sidoli et al. 2016Sidoli et al. , 2017)).Over 50 new X-ray pulsators have been discovered so far.
The spectra are available at the CDS via anonymous ftp to cdsarc.cds.unistra.fr(130.79.128.5) or via https:// cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/682/A151CXOU J005440.5-374320(hereafter J0054) was discovered in the CATS at BAR project with a large-amplitude flux modulation at a period of ∼6 h.It is seen projected in the sky inside the inner region of the NGC 300 (Fig. 1), a face-on spiral galaxy (Scd) in the Sculptor group at a Cepheid distance of 1.88 Mpc (Gieren et al. 2005, corresponding to a distance modulus of 26.4 mag).
NGC 300, due to its proximity and favourable inclination, has been the subject of many studies of its stellar populations (Bresolin et al. 2009, and references therein), star formation history (Butler et al. 2004), Wolf-Rayet (WR) stars and OB associations (Schild et al. 2003;Pietrzyński et al. 2001), planetary nebulae (Peña et al. 2012), variable stars (Pietrzyński et al. 2002; Fig. 1.NGC 300 from Swift/UVOT in the UVW2 band.The inset shows the location of J0054, which is indicated by the white arrow.X-ray contours from the Chandra detection of November 2014 are plotted in green.Mennickent et al. 2004), dust content (Helou et al. 2004;Roussel et al. 2005), X-ray sources (Read & Pietsch 2001;Carpano et al. 2005Carpano et al. , 2018;;Binder et al. 2017;Urquhart et al. 2019), supernova remnants (Blair & Long 1997;Pannuti et al. 2000;Payne et al. 2004;Gross et al. 2019), and UV emission properties (Muñoz-Mateos et al. 2007).NGC 300 has therefore been observed with a wide variety of different telescopes, and a large amount of multi-wavelength data is available.
In this work we focus on the nature of J0054.In Sect. 2 we present the datasets and the observational properties of the source, highlighting its X-ray behaviour and its optical/UV counterpart.In Sect. 3 we discuss possible scenarios for the origin of the J0054 emission, and make our concluding remarks.

Observational properties
2.1.X-ray datasets 2.1.1.Chandra J0054 fell into the Chandra field of view four times (see Table A.1).The data were reprocessed and reduced with the Chandra Interactive Analysis of Observations software package (CIAO, v.4.12;Fruscione et al. 2006) and the CALDB 4.9.0 release of the calibration files.In the first two visits the source was not detected and 3σ upper limits on its flux were obtained with the CIAO tool srcflux, following the default Bayesian approach.In the two most recent observations, the source is located at 3.7 and 6 arcmin, respectively, from the telescope aim point.The source counts were extracted from elliptical regions with semi-major and semi-minor axes of 3.2 and 2.6 arcsec for the November 2014 observation, and of 5 and 4 arcsec for the April 2020 observation, corresponding to a point spread function (PSF) fraction of about 96%.Backgrounds were estimated from source-free annular regions, centred on the source position of 10 and 20 arcsec radii.

Swift/XRT
Owing to the large monitoring campaign performed on NGC 300 and its sources, the location of J0054 was in the Swift/XRT field of view on numerous occasions (170 times by the end of 2022) over more than 15 years, but it was detected in only four visits, August 2018, January 2019, April 2020, and one last time in September 2020, as reported in Table A.1.Count rates and 3σ upper limits for all the observations in which the source was not detected were extracted using the ximage tool sosta, following the default Poissonian approach.A Bayesian approach was also A151, page 2 of 17 The inset shows the pulse profile obtained by folding the data at the best period of 5.88 ± 0.12 h.Right panel: light curve (the background is negligible).The bin time is 2500 s.
tested, and provided slightly deeper upper limits, yet still compatible with the Poissonian values.Merging all the Swift-XRT non-detections, the total exposure time amounts to ≈570 ks, but the source still could not be detected.The 3σ upper limit on the stacked observation is 8.05×10 −5 cts s −1 , corresponding to a flux limit of 2.2 × 10 −15 erg cm −2 s −1 (assuming the best-fitting model described below).

XMM-Newton
The position of J0054 was imaged with XMM-Newton seven times, as reported in Table A.1, but the source was never detected.For each observation the data were retrieved from the XMM-Newton science archive and reduced following the standard procedure.The 3σ upper limits were obtained from the EPIC-pn cameras, with the sole exception of the fourth observation, in which the source falls on EPIC-pn's border, and hence data from the merged EPIC-MOS cameras were used.The merging of the MOS cameras was performed with the sas tool merge.The 3σ upper limits were obtained with the eupper tool, from a circular region of 15 radius centred on J0054 position, with background counts extracted from a nearby free-of-sources circular region of 30 radius on the same detector chip, following the default Bayesian approach.

Short-term variability
The CATS at BAR pipeline detected the uncatalogued X-ray source J0054 in a ≈60 ks exposure carried out in November 2014 (Table A.1), and singled it out as a new X-ray pulsator with a ∼6 h flux modulation (Fig. 2).Taking into account the 16 377 independent trials, the false alarm probability was ∼7.6 × 10 −11 , which corresponds to a 6.5σ detection.After correcting for the (mild) red noise in the exposure, following Israel & Stella (1996), we evaluated the significance of the signal at 5.9σ.Due to the relatively poor statistics, the approach of using the light curve to estimate the significance of modulation is not recommended because it results in an underestimation of the real statistical level.Nonetheless, as an additional test, we compared the fit of the light curve with a constant and with a constant plus a sinusoidal component.This comparison gives an F-test probability of 5σ that the addition of the sinusoid is significant.
As a further test, we also simulated 10 5 Fourier power spectra with the same properties as that of Chandra (Poissonian noise plus an additional f −α component, where α = 0.71 ± 0.05 is inferred by fitting the power spectra distribution continuum of the original Chandra dataset), and we verified that no significant peak was detected by the used detection algorithm (which takes into account any additional non-Poissonian noise component) at frequencies shorter than 10 −3 Hz, setting a probability threshold of 10 −5 (>4.4σ) at the 5.88 h period frequency.The above numbers are consistent with the 5σ and the 5.9σ level inferred by using two different independent approaches.Correspondingly, we conclude that the signal significance is larger than >4.4σ, and likely lies in the 5-5.9σ range.
From the fit of the sinusoidal function, we derived a period of P = 5.88 ± 0.12 h, which is entirely consistent with that reported in Israel et al. (2016).The pulsed fraction, estimated from the semi-amplitude of the sinusoidal function, was 52 ± 4%.With a ν/∆ν factor of ∼10, the signal is seemingly coherent (i.e., strictly periodic), but this is something difficult to assess when only a few cycles are sampled, and thus a quasi-periodic modulation cannot be excluded.
In the last Chandra visit, no significant pulsation was detected, although the 3σ upper limit on the pulsed fraction is about 50%.In the four Swift/XRT detections, the signal-to-noise ratio was too low to carry out a meaningful timing analysis.

Long-term variability
Owing to the long-term monitoring of NGC 300, we were able to trace the J0054 X-ray variability across more than two decades (an early 1990s ROSAT upper limit is unfortunately too shallow to be relevant in this regard).J0054 had never been detected before the Chandra pointing of November 2014 (Obs.ID 16029).The closest observation is the non-detection by Chandra six months earlier, in May 2014 (Obs.ID 16028).The 3σ upper limit obtained in May 2014 implies a flux variation of at least a factor of 100.After this, J0054 was not pointed for ∼1.5 years, and when NGC 300 was observed again, it had disappeared: it is not detected in three short observations by Swift/XRT in April 2016 (although the upper limits for these observations are very shallow), nor in two longer observations by XMM-Newton at the end of the same year.J0054 reappeared in a Swift/XRT observation in late August 2018; A151, page 3 of 17 unfortunately, the upper limits around this detection are too shallow to reconstruct the detailed source behaviour.The scene was repeated in January 2019, April 2020, and September 2020.In April 2020 J0054 was detected by both Swift/XRT (Obs.ID 00095672001) and Chandra (Obs.ID 22375) less than ten days apart.After September 2020, J0054 was never detected again, possibly also due to the visits on NGC 300 growing sparser and shallower with time.Figure 3 shows the long-term light curve of J0054 in the years from approximately 2000-2023; the count-rates were converted into fluxes with the model described below.

Spectral fitting
Here we address the X-ray spectral fitting of J0054.In particular, we focus on its first detection with Chandra in November 2014, which is the dataset with the highest count statistics.
The spectra, the spectral redistribution matrix, and the ancillary response file were generated using the CIAO script specextract.The spectrum of J0054 was fed into the spectral fitting package Xspec (Arnaud 1996) version 12.12.1.Spectral channels having energies below 0.5 keV and above 7.0 keV were ignored in the fit, owing to the very low signal-to-noise ratio from J0054 (essentially all the counts are between approximately 0.7 and 1.7 keV).The spectra were grouped to have a minimum of one count per energy bin, and the C-statistic (Cash 1979) was employed (for the spectra shown in Fig. 4, further rebinning was adopted for display purposes only).
We fit a number of different simple models to the spectra, including (but not limited to) the blackbody (bbody), power-law, bremsstrahlung, Raymond-Smith plasma (Raymond & Smith 1977), hot diffuse gas (mekal; Mewe et al. 1985Mewe et al. , 1986;;Liedahl et al. 1995), collisionally ionized gas (apec, Smith et al. 2001), and accretion disc models with multi-blackbody components (diskbb; with standard colour-correction factor fixed at 1.7, Lorenzin & Zampieri 2009); all corrected for interstellar absorption (TBabs; with N H fixed to the Galactic value 9.45 × 10 20 cm −2 ; HI4PI Collaboration 2016).The abundances used are those of Wilms et al. (2000), with the photoelectric absorption cross-sections from Verner et al. (1996).While the power-law, mekal, apec, Raymond-Smith plasma, and bremsstrahlung models provided unacceptable fits (C/ν between 2 and 3, C being the value of the statistic and ν the number of degrees of freedom), both bbody and diskbb reproduced the spectrum well, and the fits improved when an extra layer of absorption and an absorption Gaussian line at 1.13 ± 0.01 keV with width fixed to 0 and normalization K = (−1.4± 0.4) × 10 −5 photons cm −2 s −1 , were added (EW = 0.077 ± 0.002 keV).The significance of the extra layer of absorption and of the Gaussian line were tested with simulations.In both instances, the Xspec routine simftest 1 returned a <0.01%probability that the data are consistent with the model without Model (1)  N H (2) C/ν (6) g.o.f. (7)  bbody 0.73 +0.16 −0.13 0.109 ± 0.006 7.0 +6.6 −2.9 × 10 −5 -1.9  the extra component.Furthermore, the statistic improvement of adding the line is ∆C = 35.1 for three degrees of freedom; even accounting for the 'look elsewhere' effect (e.g., Lyons 2008), as the absorption feature does not line up with a specific atomic transition, by correcting the obtained p-value for the dimension of the energy space (i.e., multiplying it for the ratio of the bandwidth to the average resolution: (2 keV-0.5 keV)/0.05keV ≈ 30), the line significance results to be >3.9σ.For both models, the best-fit parameters are reported in Table 1.
The bbody and diskbb models both provided similar tem- and the other left free to vary) and an absorption Gaussian line at 1.13 keV, and kept the disc inclination and spin fixed at 45 • and 0, respectively.We obtained a good fit (Table 1) for a BH with mass 1.4 +1.0 −0.4 × 10 3 M and moderate values of accretion rate ( ṁ = 0.11 +0.02 −0.01 ṁEdd , where ṁEdd indicates the maximum Eddington accretion rate) and intrinsic absorption N H = 0.9 +0.1 −0.1 × 10 22 cm −2 , where errors correspond to a variation in the statistics ∆C = 1 (1σ).We note that both the BH mass and mass accretion rate heavily correlate with the intrinsic absorption, as shown by the contour plots in Fig. 5.The value of unabsorbed X-ray luminosity (between 0.3 and 7 keV) computed with this model and assuming J0054 is located in NGC 300 amounts to 3.6 × 10 39 erg s −1 , which is in the regime of the ultraluminous X-ray sources (ULXs; e.g., Kaaret et al. 2017;Pinto & Walton 2023).
The value derived for the BH mass is affected not only by statistical uncertainties, but also by systematic ones: we assumed fixed disc inclination and spin, and of course, the estimate is model dependent.Furthermore, the slimd model does not support BH masses lighter than 1000 M , thus preventing us from fully exploring the parameter space, as highlighted by Fig. 5.In order to have an idea of these uncertainties, first of all we performed fits with different BH spin and disc inclination values: prograde rotation (a • = 0.99) and edge-on (θ = 90 • ) provided heavier masses, up to ∼10 4 M , although the maximally rotating case (a • = 0.99) provided an unacceptable fit (C/ν > 3).To explore the lighter mass regime we employed the slimbh model (Sadowski 2011;Straub et al. 2011).This was designed to describe slim accretion discs around Eddington-limited stellarmass ( 100 M ) BHs and has an upper limit for the BH mass of 1000 M , thus complementing the slimd model.The slimbh model with disc inclination fixed at 45 • provides an unacceptable fit (C/ν > 3) as the BH mass peaks at 1000 M .A faceon configuration provides an acceptable fit (C/ν = 70/85, 10% goodness of fit, i.e., the percentage of cases, out of 10 000 spectra simulated based on the model, in which the test statistic was less than that of the data) with a BH mass of ≈800 M .Finally, we note that from the diskbb model, with the corrections by A151, page 5 of 17 Lorenzin & Zampieri (2009), the mass can be estimated from 320 to 1000 M in a 90% range for the inclination (0 • -85 • ).All in all, although we can poorly constrain the BH mass, as it ranges from ∼300 to 10 4 M , the spectral results consistently indicate an IMBH.
Unfortunately, the spectra obtained in the other detections do not afford the possibility to perform meaningful spectroscopic analysis: the latest Chandra detection, in April 2020, is heavily affected by the loss of effective area of the ACIS camera below 0.7 keV, while the four Swift/XRT detections, taken individually, have a signal-to-noise ratio that is too low for a spectrum to be extracted.Nonetheless, we tentatively merged data from all four Swift/XRT detections with the ftool routine extractor and extracted a merged spectrum with xselect from a circular region of 20 arcsec radius centred on the source position.The background was extracted from a free-of-sources circular region of 1 arcmin radius at a 3 arcmin distance from the J0054 location and was likewise merged.In this way we reached a total of 32 net counts with a source fraction of the total counts evaluated at 94.3%.We then fitted the best-fitting model we obtained above simultaneously to the three spectra (Chandra from November 2014 and April 2020, and Swift/XRT from the combined datasets).We froze all parameters to the bestfit values, except for the normalizations (for the slimd model, this corresponds to the mass accretion rate).We obtained an acceptable value of the statistic (C = 119 with 145 degrees of freedom and goodness of 31%) with no Gaussian lines in the latest Chandra observation and in the merged Swift/XRT spectra and mass accretion rates equal to 0.07 and 0.09 ṁEdd , respectively.We can conclude that the emission of J0054 in the latest Chandra and in the Swift/XRT detections is compatible with that observed in the first Chandra detection, although spectral evolution or variations in the amount of intrinsic absorption cannot be assessed.Figure 4 shows the three spectra and their residuals, as well as the best-fitting model.
We found no trace of significant variability (within 1σ, roughly corresponding to half a magnitude) in any of the six bands; in particular, we found none in coincidence with the X-ray flaring activity, as shown in Fig. 6, which highlights the difference between the UVW2 AB magnitude and the 0.3-10 keV flux at the epoch of the latest flare.As no variability was detected, all observations were stacked using the ftool routine uvotimsum and fluxes were extracted using uvotsource (with flag APERCORR = curveofgrowth) from a circular region centred on the source position and with a radius of 5 arcsec.Backgrounds were estimated from a circular region of 10 arcsec radius, free of sources, at approximately 15 arcsec from the source location.The AB magnitudes from the merged Swift/UVOT observations, as well as the averaged magnitudes over the single observations, are reported in Table 2.
In order to correct the Swift/UVOT spectral energy distribution (SED) for dust extinction we adopted different strategies.The minimum possible value of the reddening is the Galactic line-of-sight value E(B − V) = 0.0108 (Schlafly & Finkbeiner 2011): in this case, the optical/UV SED would be consistent with a blackbody profile of ≈15 000 K and a luminosity of 7.5 × 10 4 L , compatible with a blue supergiant star (M V ≈ −6.5 mag).A slightly higher reddening was adopted by Gieren et al. (2004), who assumed a foreground Galactic E(B − V) = 0.025 mag (Burstein & Heiles 1984) plus a reddening E(B − V) = 0.05 mag through the halo of NGC 300.In this case, the best-fitting blackbody temperature rises to about 17 000 K and the luminosity to 10 5 L , still compatible with a single blue supergiant star (M V ≈ −6.7 mag).However, the complete absence of individual stellar lines in the observed optical spectra (see Sect. 2.5.3)makes it unlikely that the observed SED stems from a barely reddened, single blue supergiant or a (very) late-type WR star with a comparable temperature (e.g., Sander et al. 2014).
The other extreme in terms of possible extinction would be to use the N H inferred from the X-ray spectral modelling.Converted to an optical extinction A V via the empirical relation in Foight et al. (2016), this would imply A V ≈ 3.1 mag, and hence an absolute brightness M V ≈ −9.6 mag.Such a source would be too luminous to be a single star and would further be unphysically blue (B−V ≈ −1.2 mag) for any star, cluster, or blackbodylike spectrum.Thus, we can rule out such a high extinction for the optical counterpart.Assuming a physically meaningful limit of B − V −0.5 mag and U − B −1.5 mag, we can place an upper limit on the total extinction of A V 1 mag.In this case the photometry is compatible with a young stellar cluster (YSC) with an age of 4 Myr and ≈10 3 M , assuming instantaneous star formation and a Large Magellanic Cloud (LMC)-like metallicity (similar to that of NGC 300; Gazak et al. 2015;Toribio san Cipriano et al. 2016).This would correspond to a small stellar population dominated by three or four mainsequence O stars and about 12−15 B stars (see Sect. 2.5.3).

Archival data
J0054 is also present in the XMM-Newton/OM catalogue of serendipitous sources (Page et al. 2012).Our source location A151, page 6 of 17 was visited six times, as reported in Table 2. XMM-Newton/OM data are compatible with the Swift/UVOT data when one considers that, at the magnitudes of our source, discrepancies as large as 1 mag are not uncommon between Swift/UVOT and XMM-Newton/OM (see Yershov 2014 and the XMM-Newton/OM calibration report2 ).J0054 is also present in the Gaia catalogue (Gaia Collaboration 2023), with a parallax p = 0.53 ± 0.78 mas, corresponding to a distance of 1.2 +0.5 −0.4 kpc (Lindegren et al. 2021;Bailer-Jones et al. 2021).However, at a magnitude G = 20.49(G BP = 20.61 and G RP = 20.37), the source is rather faint for Gaia and the low signal-to-noise ratio parallax is probably unreliable.

SALT spectrum
Two spectra were acquired on December 2 and December 15, 2019 (Progr.ID: 2018-2-LSP-001), with the Southern African Large Telescope (SALT; Buckley et al. 2006;O'Donoghue et al. 2006), equipped with the Robert Stobie Spectrograph (RSS) (Burgh et al. 2003;Kobulnicky et al. 2003) in the long-slit (8 × 1 .5) spectroscopy mode.The PG0300 and PG0900 gratings were used for the observations with exposure times of 1800 s and 2000 s, respectively.A grating tilt of 5 • .4 was used for the PG0300 observation, which covered the wavelength range 3700-7500 Å and provided a resolving power of 250-600.For the PG0900 observation, a tilt of 15 • .125 (4200-7250 Å) was used, with a resultant resolving power of 800-1200.The position angle (PA) was 0 deg from north and the average seeing during the observations was 1 .5.
Standard spectral reduction (bias, flat-field, sky subtraction, and cosmic-ray removal) was performed using the PySALT pipeline (Crawford et al. 2010).The wavelength calibration was performed with Ar (PG0300) and Xe (PG0900) lamps, and the 1D spectrum was extracted using various tasks in IRAF.Since no spectrophotometric standard star was observed, the spectra are not calibrated in flux.
The two spectra show similar features and display strong emission lines of Balmer series and neutral He, as well as forbidden lines of [Oii], [Oiii], [Neiii], [Nii], and [Sii], with a blueward asymmetry, probably due to composite components in the emitting region, which however cannot be resolved with this resolution (see Fig. 7; the lower-resolution spectrum is shown in Fig. B.1 and the parameters of the main lines, which were derived from Gaussian fits, are given in Table B.1).
The lack of flux calibration does not allow us to measure emission line flux ratios.However, we can use the broadband SED from Swift/UVOT and the unabsorbed blackbody fit described in Sect.2.5.1, to estimate an approximate continuum flux level (assuming that it did not change substantially between the Swift and SALT observations), and then convert the measured line equivalent width (EW) to line fluxes.In particular, we used the P0900 grating spectrum from December 15, 2019, which provides the more reliable measurement of the line profiles because of its higher resolution.
We find an observed flux ratio F(H α )/F(H β ) ≈ 2.9 and F(H γ )/F(H β ) ≈ 0.47, perfectly consistent with photo-ionized gas in Hii regions (Case B recombination) without any reddening corrections apart from the line-of-sight Galactic component.Our simulations with the starburst99 code (Leitherer et al. 1999(Leitherer et al. , 2014) ) show that the EWs of H α and H β are consistent with those expected from photo-ionized gas illuminated by a YSC with the same continuum flux we observed.Both of those findings suggest that the emission lines are from an extended ionized nebula rather than from the direct stellar counterpart of the X-ray source.Moreover, the ionized gas sees the same continuum flux as we observe.If there is additional intrinsic extinction, it must be located between the X-ray source and the surrounding nebula, rather than between the source of the line emission and the A151, page 7 of 17 line-of-sight.We note that an O-type ionizing star embedded in a Hii region is not supported by the lack of absorption features of Heii andHei (McLeod et al. 2015, 2020), while only Hei in emission is observed.
If the 6 h periodicity identified in the X-ray light curve corresponds to the orbital period of a binary system, a compact WR-like donor is needed; assuming a total mass of the system of ≈30 M and a mass ratio of ≈3, the binary separation amounts to ≈5 R and the upper limit on the radius of the companion to ≈2.5 R .However, our SALT spectra do not show any explicit WR features, such as broad Heii 4686 Å emission (e.g., Dodorico et al. 1983).In addition, the lack of a number of diagnostic lines (Schild & Testor 1992) does not support a WC or a WN: Ciii, Cii, or Civ for the former and Niii 4100 Å and 4640 Å for the latter are not detected.While this could in principle be explained by a compact ('stripped') star that does not show WR-type spectral features (e.g., Götberg et al. 2018), such stars are a huge source of Heii ionizing flux (e.g., Sander & Vink 2020;Sander et al. 2023), which should result in nebular Heii emission, which is absent as well.We thus ran starburst99 simulations to test whether stellar line emission features from a WR star could be hidden in a YSC with the observed continuum brightness and the line emission from its surrounding Hii region.Assuming the same uniform extinction A V ≈ 1 mag for both the YSC and a WR star inside it, we verified that all features of a typical compact WR star would be sufficiently diluted at least for some classes of WR stars.For the WR star we used LMC models from Hainich et al. ( 2014) calculated with the PoWR (Gräfener et al. 2002;Hamann & Gräfener 2003;Sander et al. 2015) model atmosphere code and diluted to the distance of NGC 300.From our calculations we can thus conclude that the lack of observed WR emission lines in the SALT spectra does not rule out the scenario of a WR donor for the X-ray source.Moreover, an additional viable scenario is that the extinction around the X-ray binary system (including a WR donor with a dense wind) is higher than the extinction of the surrounding group of OB stars, which would further dilute or completely hide strong WR emission lines.

Discussion
J0054 is a puzzling source.It was discovered as a bright X-ray pulsator with a 6 h modulation; it shows a peculiar supersoft X-ray spectrum, and also displayed long-term variability.The available spectroscopy and photometry for the optical/UV counterpart show no hints of variability, but reveal only an Hii region.While the photometry as such could match an individual B star the strong absorption in the X-ray regime indicates that the photometry reflects an unresolved population of stars.Thus, any B star, O star, WR star, or even a whole YSC are viable options.In any case, the optical/UV and X-ray cannot be fitted simultaneously by a single blackbody or disc model, nor is it possible to intercept the optical/UV data extrapolating the model bestfitting the X-ray and vice versa (even accounting for the parameters' uncertainties), as clearly demonstrated by Fig. 8, which shows the full SED and the absorbed and de-absorbed models.This suggests that the two emissions, optical/UV and X-ray, have different origins.Here we discuss different scenarios that could explain its peculiar multi-wavelength appearance.
Projected in the sky, J0054 is seen well inside the B − R 25 radius3 of NGC 300, at only 3.4 arcmin (about 1.9 kpc) from the centre of the galaxy.In addition, the Galactic latitude is b −79 • .4,making a Galactic foreground object highly unlikely.The only piece of information that possibly suggests a foreground Galactic object is the Gaia parallax, which is, however, probably unreliable given its low S/N.In the hypothesis of a Galactic object, in view of the 6 h modulation, the pulse profile, and the flux, a cataclysmic variable (CV) is the only plausible candidate (although the X-ray spectrum discourages this interpretation and CVs are very unlikely to occur at the latitude of J0054; e.g., Drake et al. 2014).If the X-ray period traces the binary motion, for a CV in a 6 h orbit, a donor of spectral type of K7V (Knigge 2006) is expected.If we assume for it M V = 7.7, B − V = 1.3, and V − R = 1.15 (e.g., Johnson 1966;Gray & Corbally 2009), the possibility appears unlikely, since a late-type K7V would be too bright and red with respect to our source optical counterpart.In the case of weakly magnetic or non-magnetic system, the relationship between luminosity and orbital period by Warner (1987) indicates absolute magnitudes of V ≈ 4 in a high state or ≈8 while in quiescence.In general, the absolute magnitudes of such systems are always between 8 and 2 (Ramsay et al. 2017), and are therefore incompatible with the optical counterpart of J0054.
The lack of correlation between the X-ray flares and the optical/UV emission and the overall lack of significant variability at optical/UV wavelengths across years does not support a nova at later stages (Williams et al. 1994;Williams 2016) nor a supersoft source (SSS; van den Heuvel et al. 1992).A SSS scenario, on the other hand, is also discouraged by the fact that the observed X-ray and optical luminosity would require a massive WD, of about 1.2 M (Starrfield et al. 2004) and this would place J0054 at ≈50-200 kpc, which would result in an isolated intergalactic SSS, a highly unluckily occurrence.
The most natural way to explain the multi-wavelength behaviour of J0054 is probably an ultraluminous supersoft X-ray source (ULSs) scenario.ULSs can be considered as high-inclination, high-accretion-rate compact objects.Here the A151, page 8 of 17 hard X-ray photons coming from the inner regions are significantly blocked by a strong optically thick wind, which manifests itself in the form of Doppler-shifted absorption lines similar to the feature shown at 1.13 keV in Fig. 4 (Pinto & Walton 2023;Urquhart & Soria 2016).Moreover, this feature seems to be a hallmark strongly associated with the ULS population (Urquhart & Soria 2016).A well-known example is NGC 247 ULS or X-1 for which high-resolution spectra resolved the 1 keV feature into a forest of lines produced by a powerful 0.17c wind (Pinto et al. 2021); this source also exhibits modulations on timescales of a few ks (Alston et al. 2021).Here, the spectral-timing analysis would rather support the case for a heavy NS or a small stellar-mass BH accreting well beyond the Eddington limit (D'Aì et al. 2021).
J0054 also shares some spectral characteristics of M 101 ULX-1, a well-studied ULX and SSS consisting of a stellar-mass BH and a WR star (Liu et al. 2013).The only object compatible with the 6 h modulation, if it reflects the binary orbit, is a WR star (see Esposito et al. 2013aEsposito et al. , 2015;;Qiu et al. 2019 for the discussion of similar systems and candidates).As discussed in Sect.2.5.3, a WR star, isolated or belonging to a YSC, is not excluded by the optical information.For the compact object it is unsafe to rule out a neutron star only on the basis of the observed super-Eddington luminosity (e.g., Bachetti et al. 2014;Israel et al. 2017); however, a stellar-mass BH is the most likely compact object in WR binaries for evolutionary reasons (van den Heuvel et al. 2017).The two sources exhibit a highly variable (by a factor of ≈300) X-ray emission with a similar spectrum (at least in some states of M 101 ULX-1), in particular, similar temperatures and sizes, and a dip at 1.1 keV (Soria & Kong 2016;Urquhart & Soria 2016).
Finally, it is worth mentioning that the NGC 300 galaxy hosts another bright source, NGC 300 X-1, which hosts a WR star feeding a massive black hole candidate (with a dynamically inferred mass of 20 ± 4 M , although a lighter compact object cannot be completely ruled out; Laycock et al. 2015) which sometimes crosses the 10 39 erg s −1 threshold (Crowther et al. 2010;Earnshaw & Roberts 2017).
The fact that the absorption inferred from the X-ray spectrum is local to the X-ray source and does not involve the optical counterpart (as demonstrated in Sect.2.5.1)might support an outflowing wind in this scenario.However, the main problem with a ULX/ULS scenario is probably the transient nature of the source; with a compact object in such a tight orbit with a strongly winded WR star, one would always expect significant accretion.A possible solution to this would be interpreting the variability in terms of obscuration, which would likely result in spectral changes.The available data, unfortunately, are inconclusive about this matter.Finally, we note that this source is not present in any ULX/ULS catalogues (e.g., Walton et al. 2022): although its unabsorbed luminosity exceeds the 10 39 erg s −1 threshold, its observed absorbed luminosity does not.
A radically different scenario that is capable of explaining some of the features of J0054 is the partial tidal disruption of a star by an intermediate-mass BH (IMBH).Tidal disruption events (TDEs) usually occur when a star wanders too close to a supermassive BH (SMBH), and its binding self-gravity is overcome by the BH's tidal forces, which tear the star apart.Part of the stellar debris is subsequently circularized and accreted, emitting a bright electromagnetic (EM) signal, and part gets ejected (Rees 1988;Phinney 1989).TDEs, although they are bright across the whole EM spectrum, from radio to γ rays (e.g., Swift J1644, Burrows et al. 2011), in the X-ray band they usually appear as luminous supersoft transients.The X-ray spectrum suggests that the J0054 emission is linked to accretion processes, and the slimd model (specifically developed to fit slim disc emission from the tidal disruption of stellar objects by SMBHs) provides an estimate for the mass of J0054 (≈1400 M ) and places it in the IMBH class.The TDE hypothesis could also explain the observed long-term X-ray variability.As invoked for XMMU J122939.7+075333(Tiengo et al. 2022), an object sharing many characteristics with J0054 (long-term variability, very soft X-ray emission, forbidden lines in the optical counterpart), a star on a highly eccentric orbit would be stripped of its material at every pericentre passage, thus producing recurrent flares.
Assuming we spotted the TDE close to its peak luminosity, we can use the mass accretion rate and BH mass obtained from the spectral fit to derive the penetration factor, orbital eccentricity, and mass of the stripped star.To this end, we employed reasonable mass-radius relations for a white dwarf (WD) and for a main sequence star (MS)4 , coupled with the analytical formulas derived by Guillochon & Ramirez-Ruiz (2013) for the γ = 5/3 polytrope case.Figure 9 shows the possible combination of star mass and orbital eccentricity compatible with the spectral estimates of mass accretion rate and BH mass.The blue and red contours represent the results obtained for a main sequence star and a white dwarf, respectively.The width of the contours corresponds to the 5σ region.The penetration factor β, defined as the ratio between pericentre distance and tidal radius, measures how deep the star dives into the potential well of the hole.As the tidal radius r t r (M h /m ) 1/3 represents the distance at which the BH tidal forces balance the stellar self-gravity, for penetration factors β < 1 the disruption is only partial.For values of β 0.5 the mass loss of the star stops (Guillochon & Ramirez-Ruiz 2013): in Fig. 9 the grey bars cover these forbidden regions.As Fig. 9 shows, only stars with masses below one solar mass are compatible with the spectral fitting results.Furthermore, for a WD only highly eccentric orbits are permitted, with 0.94 e 0.96, while for MS stars only values of eccentricities 0.7 are permitted.In any case, for both WDs and MS stars, the passage around the BH is shallow: the dashed black line in Fig. 9 represents the values for which the penetration factor is β = 0.6.As for the case of XMMU J122939.7+075333, the amount of mass accreted at every passage is very small, about 5.5 × 10 −10 M .As pointed out by Tiengo et al. (2022), with these low values of mass getting accreted per passage, one such event can last for very long times, and XMMU J122939.7+075333 has indeed been active for more than two decades.Finally, although the available observations are sparse and often provide only shallow upper limits, the outbursts of J0054 seem to recur on a timescale of ≈5 months, which is the time interval between the two closest outbursts and cannot be ruled out by non-detections.
The TDE scenario could also explain J0054 short-term variability: the observed periodicity could be linked to disc instability in a similar way to that described by Pasham et al. (2019) for the 'text-book TDE' ASASSN-14li (Miller et al. 2015).To investigate this possibility, we can study the fundamental frequencies at the innermost stable circular orbit (ISCO) around the BH.There are three: the Keplerian orbital frequency ν φ , the vertical epicyclic frequency ν θ , and the Lense-Thirring frequency, given by the beating between these two, ν LT = ν φ −ν θ .Analytical expressions for these frequencies were derived by Kato (1990): Figure 10 shows the contours, in the BH mass-spin space, for the three described frequencies: Keplerian (in red), vertical epicyclic (in green), and Lense-Thirring (in blue) for a 47 ± 1 µHz frequency (the 5.88 ± 0.12 h modulation).The width of the contours represents the 5σ region.The shaded region shows the BH mass range identified by the spectral fit; its width corresponds to a ∆C = 1.The only frequency compatible with the mass range identified by the spectral fitting is the Lense-Thirring frequency, and only for a non-spinning BH: |a • | 4 × 10 −4 .The TDE scenario cannot account for every aspect of J0054.The absorption feature in the X-ray spectrum, around 1 keV is similar to those often observed in SSSs, both Galactic (nuclear burning WD, see e.g., Ebisawa et al. 2001) and extragalactic (ULXs, see e.g., Pinto et al. 2021); however, this feature is usually detected in sources with thick outflows rather than simple disc emission, and only at high values of mass accretion rates.Another weak point in this scenario is the involvement of a non-spinning 10 3 M IMBH.Although it has been shown that young dense clusters can nurture the seeding of IMBHs (Arca Sedda et al. 2021, and in prep.;Di Carlo et al. 2021;Rizzuto et al. 2021Rizzuto et al. , 2022;;Gonzalez et al. 2023), it seems hard for YSCs to grow IMBHs above 1000 M , unless the host YSC has a large central density (e.g., Maliszewski et al. 2022) and the tightly constrained null value of the spin would require some fine tuning for the model to work.On the other hand, the TDE scenario can provide a satisfactory explanation for the Xray spectral shape, and both the long-and short-term behaviour of J0054.

Fig. 2 .
Fig.2.Timing analysis of J0054.Left panel: Fourier power spectrum of the Chandra data of J0054.The red line indicates the local 3.5σ detection threshold adopted in the CAT at BAR project.The prominent peak well above the threshold (5.9σ) corresponds to the ∼6 h modulation of J0054.The inset shows the pulse profile obtained by folding the data at the best period of 5.88 ± 0.12 h.Right panel: light curve (the background is negligible).The bin time is 2500 s.

Fig. 3 .
Fig. 3. Long-term X-ray light curve of J0054.The magenta and green data refer to Chandra and XMM-Newton data, respectively; the downpointing arrows indicate 3σ upper limits, while the diamond markers indicate detections (with 1σ error bars).Swift/XRT detections are shown as blue diamonds, while the upper limits are indicated by down-pointing grey arrows.Count rates for the upper limits and for the Swift/XRT detections were converted to fluxes assuming the same spectral shape of the Chandra 2014 detection.Years are on the X-axis and flux in the 0.3-10 keV band is on the Y-axis.

Fig. 4 .
Fig. 4. X-ray spectra of J0054.The upper panel shows the folded spectra and best-fitting model, the lower panel shows the residuals.The data from Chandra November 2014, April 2020, and the Swift/XRT merged detections are shown as black, red, and green dots, respectively.The solid lines indicate the best-fitting slimd model.
The errors correspond to a statistic variation ∆C = 1.(1)The models are reported with their Xspec names.(2)Intrisic absorption in units of 10 22 atoms cm −2 . (3)Normalization of the model, corresponding to K = L/D 2 (with L luminosity in units of 10 39 erg s −1 and D distance of the source in units of 10 kpc) for the bbody model, K = (R 2 /D 2 ) cos θ (with the internal radius R in km and θ inclination of the disc, θ = 0 indicating face-on configuration) for the diskbb model, and K = ṁ/ ṁEdd for the slimd model. (4)BH mass in units of 10 3 M .Derived from the model normalization for the diskbb and as a fitted parameter for the slimd model, in both cases under the assumptions of the Schwarzschild metric and θ = 45 • .(5)Unabsorbed luminosity in units of 10 39 erg s −1 in the 0.3-7 keV band.(6)Value of the C-statistic divided by the degrees of freedom.(7)Goodness of the fit from Monte Carlo simulations.
peratures, kT ≈ 110−120 eV, and similar amounts of intrinsic absorption, N H ≈ (0.7-0.8) × 10 22 atoms cm −2 .The diskbb model naturally suggests a black hole (BH) as the accretor.From the fit we get an emitting region of ≈9000 km, which corresponds, under the assumption of the Schwarzschild metric and 45 • disc inclination, to a mass of about 1000 M .This model also naturally suggests the presence of an accretion disc.Since J0054 is a transient source, to investigate this possibility better, we tried a model designed to reproduce accretion discs around black holes in transient events: slimd(Wen et al. 2022).As in the previous cases, we added the two layers of absorption to the slimd model (one fixed to the Galactic value, as above,

Fig. 5 .
Fig. 5. Contour plots in the BH mass-intrinsic absorption (upper panel) and mass accretion rate-intrinsic absorption spaces (lower panel), obtained with the slimd model.The red, green, and blue contours indicate the ∆C = 1, 2, 3 levels, while the magenta dots are the best-fitting parameters.

Fig. 6 .
Fig. 6.X-ray flux (upper panel) and UVW2 AB magnitude (lower panel) evolution during the flare detected in the September 2020 Swift data.The X-ray upper limits in the single observations are reported as black arrows; the upper limits derived from the merged observations are reported as grey arrows.UVW2 magnitudes for each of the three epochs were derived by merging the single orbit exposures.

Fig. 8 .
Fig.8.Full SED of J0054.The magenta and blue diamonds show the Chandra and Swift/UVOT data, respectively.The black solid lines show the two independent best-fitting models for the two components with no absorption correction, and the dashed black lines show the de-absorbed models.For Swift/UVOT, the full markers indicate the observed flux, while the empty blue markers the de-absorbed fluxes, corrected following the different values discussed in the text (the full markers lie under the empty ones).For Chandra, the de-absorbed model was obtained by setting to 0 the amount of N H .

Fig. 9 .
Fig. 9. Orbital eccentricities and stellar mass values compatible with the BH mass and mass accretion rate obtained from the spectral fitting.The blue and red regions indicate WD and MS star cases, respectively.The width of the contours covers the 5σ regions.The barred portions of the parameter space are forbidden as they represent the regions where β < 0.5 (no disruption occurs) and the dashed lines indicate the values for which β = 0.6.

Fig. 10 .
Fig. 10.Contour plot in the BH mass-spin space of the three fundamental frequencies at ISCO for a 47 µHz frequency.The shaded region indicates the BH mass range obtained from the spectral fit.The width of the lines reflects a 5σ range.

Table 2 .
(Page et al. 2012udes from Swift/UVOT and XMM-Newton/OM.Notes.Swift/UVOT AB magnitudes from the merged observations and averaged over the single observations.XMM-Newton/OM magnitudes are from the XMM-Newton/OM catalogue(Page et al. 2012).U and UVW1 magnitudes from the 2016 XMM-Newton/OM observations have not been reported as they are affected by the 'smoke ring' feature.Quantities are reported with 1σ errors.