A multiband look at ultraluminous X-ray sources in NGC 7424

We studied the multiband properties of two ultraluminous X-ray sources (2CXO J225728.9-410211 = X-1 and 2CXO J225724.7-410343 = X-2) and their surroundings, in the spiral galaxy NGC 7424. Both sources have approached X-ray luminosities L_{X} ~ 10^{40} erg/s at some epochs. Thanks to a more accurate astrometric solution (based on Australia Telescope Compact Array and Gaia data), we identified the point-like optical counterpart of X-1, which looks like an isolated B8 supergiant (M ~ 9 Msun, age ~ 30 Myr). Instead, X-2 is in a star-forming region (size of about 100 pc x 150 pc), near young clusters and ionized gas. Very Large Telescope long-slit spectra show a spatially extended region of HeII 4686 emission around the X-ray position, displaced by about 50 pc from the brightest star cluster, which corresponds to the peak of lower-ionization line emission. We interpret the HeII 4686 emission as a signature of X-ray photo-ionization from the ULX, while the other optical lines are consistent with UV ionization in an ordinary HeII region. The luminosity of this He^{++} nebula puts it in the same class as other classical photo-ionized ULX nebulae such as those around Holmberg II X-1 and NGC 5408 X-1. We locate a strong (5.5-GHz luminosity nu L_{nu} ~ 10^{35} erg/s), steep-spectrum, unresolved radio source at the peak of the low-ionization lines, and discuss alternative physical scenarios for the radio emission. Finally, we use WISE data to obtain an independent estimate of the reddening of the star-forming clump around X-2.


INTRODUCTION
X-ray and multiband studies of the most luminous off-nuclear sources in nearby galaxies (ultraluminous X-ray sources, ULXs; see reviews by Pinto & Walton 2023;King et al. 2023;Kaaret et al. 2017;Feng & Soria 2011) have proved that such sources are usually powered by accretion onto stellar-mass compact objects.In most cases, they are fed by a high mass donor star (i.e., they are high mass X-ray binaries) and can reach X-ray luminosities in excess of 10 40 erg s −1 , well above their critical Eddington limit (supercritical accretion regime).Investigating super-critical stellar-mass sources in the local universe helps our modelling of accretion and feedback properties in this accretion regime at all scales, including for example in the early phases of supermassive black hole growth (e.g., King & Pounds 2015;Tombesi et al. 2015;Volonteri et al. 2015;Parker et al. 2017).
★ Email: roberto.soria@inaf.it(RS) One of the distinguishing properties of super-critical accretion is the strong effect such sources have on the surrounding medium, particularly as the most powerful sources tend to be located in gasrich, young stellar environments.X-ray photo-ionization effects are expected because of their high luminosity and long mean-free-path of their X-ray photons.It was also speculated that ULXs may have played a role in cosmic re-ionization (e.g., Mirabel et al. 2011;Fragos et al. 2013;Madau & Fragos 2017;Douna et al. 2018), at least for the pre-heating of the intergalactic medium and the formation of extended partially ionized zones (e.g., Jeon et al. 2014;Knevitt et al. 2014;Xu et al. 2014).Moreover, super-critical sources produce strong radiatively-driven outflows (e.g., King & Pounds 2003;Poutanen et al. 2007;Dotan & Shaviv 2011;Kosec et al. 2018;Pinto & Kosec 2023).Magneto-hydrodynamical simulations (e.g., Ohsuga & Mineshige 2011;Kawashima et al. 2012;Jiang et al. 2014;Ogawa et al. 2017;Narayan et al. 2017;Kitaki et al. 2021) show that the massive wind from a geometrically thick disk produce a lower-density polar funnel, inside which a collimated jet  ′ , blue =  ′ ), with Chandra/ACIS-S contours of the brightest X-ray sources (0.3-7 keV band) overplotted in green.We have also labelled the location of a strong, persistent radio source (R-1) without any X-ray counterpart.
may also be launched.Theoretical studies show (Poutanen et al. 2007;Yoshioka et al. 2022) that the kinetic power of the super-Eddington outflows can reach ∼10-30% of the radiative luminosity, and possibly even exceed the radiative luminosity for accretion rates in excess of about 40 times the critical limit (Kitaki et al. 2021).This is supported by observational discoveries of large (diameters of ∼100-300 pc) shock-ionized bubbles around several ULXs, inflated by mechanical powers of ∼10 39 -10 40 erg s −1 (Pakull & Mirioni 2002;Pakull et al. 2010;Cseh et al. 2012;Soria et al. 2021;Gúrpide et al. 2022;Zhou et al. 2023).In summary, by studying the gas and stellar environment around a ULX, we constrain the age and activity phase of the super-Eddington source, and its ionizing effect on the surrounding gas.
In this paper, we investigate two ULXs in the grand-design, face-on spiral galaxy NGC 7424 (Figure 1), with morphological classification SABcd.In the absence of Cepheid distances to this galaxy, we adopt the average between the Hubble Flow distance (10.1 Mpc) and the Tully-Fisher distance (11.5 Mpc), both listed in the NASA/IPAC Extragalactic Database (NED) 1 ; thus, we take  = 10.8Mpc (distance modulus 30.17 mag, scale of 52 pc arcsec −1 ).The star formation rate is ≈0.2-0.3  ⊙ yr −1 (Larsen 2002;Iglesias-Páramo et al. 2006, accounting for the slightly lower distance assumed here).NGC 7424 was host to the Type-IIb supernova SN 2001ig; some of the observational datasets used for this work were originally collected for a study of that SN.We will report on the evolution of SN 2001ig in a separate paper, and focus here instead on the ULXs and their environments.

Chandra
NGC 7424 was observed with the Advanced CCD Imaging Spectrometer (ACIS) camera on board the Chandra X-ray Observatory three times (Table 1): on 2002 May 21 and June 11, and on 2020 December 2 (ObsIDs 3495, 3496, 23572 respectively).The sources of interest for this work were located on the S3 chip.The live time was 23 ks, 24 ks and 5 ks for the three observations.We retrieved the data from the public archives, and reprocessed them with the Chandra Interactive Analysis of Observations (ciao) version 4.15 (Fruscione et al. 2006), with calibration database version 4.9.8.Specifically, we created new level-2 event files with the ciao task chandra_repro.We used merge_obs to create stacked event files and images, and dmcopy for energy filtering.Point-like sources were identified and located with wavdetect, in the images from each observation.
We used specextract to create spectra and associated response and ancillary response files ("correctpsf" parameter set to yes) for the two ULXs.We chose source extraction circles of 2. ′′ 5 radius, and local background annuli with an area approximately ten times larger.We used the ftools2 package (Blackburn 1995; Nasa High Energy Astrophysics Science Archive Research Center (Heasarc) 2014) from NASA's High Energy Astrophysics Science Archive Research Center (HEASARC) for further data analysis.We regrouped the spectra to a minimum number of counts per bin with ftools's grppha task.In particular, we created spectra with ≥1 count per bin, suitable for fitting with the Cash statistics (Cash 1979), and corresponding spectra grouped to ≥15 counts per bin, for  2 fitting.
We modelled the X-ray spectra over the 0.3-8 keV band with XSPEC version 12.12.1 (Arnaud 1996), with standard models suitable to accreting compact objects.The spectra for some of the observations (e.g., X-2 in ObsIDs 3495 and 23573) only have ∼100 counts and are mildly undersampled when rebinned for  2 fitting; therefore, for consistency, we report the modelling results obtained with the Cash statistics for all spectra, unless explicitly mentioned.Observed fluxes and unabsorbed luminosities were calculated with the cflux convolution model.

Gemini
NGC 7424 was imaged with the Gemini Multi-Object Spectrograph (GMOS) on the Gemini South telescope, on 2004 September 14 (Ryder et al. 2006, Program ID GS-2004B-Q-6).Conditions were not photometric (thin cirrus clouds) but the seeing was exceptionally good (0. ′′ 35-0.′′ 4).The images were taken in the  ′ ,  ′ ,  ′ set of Sloan filters, with a 0. ′′ 0807/pixel sampling.A series of dithered sub-exposures were taken for each filter, and combined to remove cosmic rays and chip gaps; see Ryder et al. (2006) for details of the observational set-up and data reduction.The 5. ′ 5 × 5. ′ 5 field of view of GMOS covers most of the star-forming disk of NGC 7424 and is well suited for a search of the optical counterparts to the Chandra sources (Figure 1).

Hubble Space Telescope (HST)
For the imaging study of our main target of interest, the optical nebula around X-2, we used an HST Wide Field Planetary Camera 2 (WFPC2) image in the F606W filter, taken on 1994 July 16 (exposure time 160 s), and a WFPC2 image in the F814W filter taken on 2001 June 1 (exposure time 640 s).To image the star-forming complex around the bright radio source R1 (S.Cheng et al.,in prep.), in the southern half of the galaxy, we used a different set of WFPC2 images, taken on 2001 July 7, in the F450W filter (460-s exposure) and in the F814W filter (460-s exposure).The latter pair of WFPC2 images do not cover the X-2 field.For a search of the optical counterpart of X-1, we used two Wide Field Camera 3 (WFC3) UVIS images, taken on 2016 April 28 (Ryder et al. 2018): in the F275W (8694-s exposure) and in F336W (2920-s exposure).The field of view of those WFC3/UVIS images includes also the counterpart of SN 2001ig but not the field around X-2.
We downloaded the drizzled, calibrated data from the Hubble Legacy Archive3 for the WFPC2 images files, and from the Mikulski Archive for Space Telescopes4 for the WFC3 ones.We used ds9 imaging tools to determine the centroids of bright point-like sources and improve the astrometric solution (Section 3.1), and, subsequently, for direct comparisons of X-ray, optical and radio positions of our targets of interest.

Very Large Telescope (VLT)
We observed the X-2 nebula with the FOcal Reducer and low dispersion Spectrograh 2 (FORS2) on the VLT of the European Southern Observatory, on 2011 September 1, from MJD 55805.09 to MJD 55805.11(corresponding to UT time between about 02:05 and 02:40) (Table 1).Specifically, we took two spectra with the 300V grating (covering 3300 Å to 9500 Å) and one spectrum with the 1200R grating (covering 5750 Å to 7310 Å), and an acquisition image before each choice of grating (Table 1).In the spatial direction, the scale was 0. ′′ 25 per pixel (2 × 2 pixel binning).The dispersion was ≈3.30Å per pixel for the 300V grating, and 0.75 Å per pixel for the 1200R grating.The instrumental resolution was 9.4 Å full-width-half-maximum (FWHM) for the 300V grism, and 1.8 Å FWHM for the 1200R one.The slit width was 1. ′′ 0 for the 300V grating (matched to a delivered seeing of 1. ′′ 1) and 0. ′′ 7 for the 1200R grating (delivered seeing of 0. ′′ 9).In both cases, the slit was oriented north to south, passing roughly through the middle of the X-2 nebula.
Spectra were corrected for bias, flat-fielded and calibrated in wavelength and flux using the EsoReflex FORS package (Freudling et al. 2013) version 5.6.5.Flux calibration was derived from the spectrophotometric standard LTT7379.We used software from both the Munich Image Data Analysis System (midas: Warmels 1992) (in particular, the integrate/line task) and from the Image Reduction and Analysis Facility (iraf) Version 2.16.In particular, we used the iraf splot sub-package to determine central wavelengths of the emission lines, their equivalent widths (EWs), FWHM, and fluxes.

Australia Telescope Compact Array (ATCA)
We observed NGC 7424 with the ATCA on 2021 April 10-13 (Table 1), under project code C3421.The aimpoint was near the position of X-2.The array was in its most extended 6 km configuration (6D)5 .The data were recorded simultaneously at central frequencies of 5.5 and 9.0 GHz, with a bandwidth of 2 GHz at each frequency.The total observing time on source was 21 hr.We used the primary ATCA calibrator PKS B1934−638 for flux density calibration, and the nearby source PKS B2310−417 for phase calibration.We processed data following standard procedures6 within the Common Astronomy Software Application (casa, version 5.1.2;CASA Team et al. 2022).To image the data we used the casa task clean, using a Briggs robust parameter of 0 (Briggs 1995), balancing sensitivity and resolution.These choices resulted in synthesized beams with FWHM of 2. ′′ 5 × 1. ′′ 4 at 5.5 GHz (position angle +1 • , east of north), and 1. ′′ 5 × 0. ′′ 9 at 9 GHz (position angle −2 • ).To determine the centroids of our sources of interest, we used the casa task imfit, fitting a 2-D Gaussian with a FWHM fixed to the parameters of the synthesized beam.

Astrometric alignment
In addition to the use of new observations not available at the time, our multiband study improves on the results of Soria et al. (2006) because of a more accurate astrometric alignment between X-ray, optical and radio images.The two main reasons for this improvement are: i) an astrometric calibration based on the Gaia results (Gaia Collaboration et al. 2023); ii) a new ATCA observation with higher sensitivity and more uniform coverage of the uv plane.In particular, the new 9-GHz ATCA images were not hampered by the side lobes that affected the 2001-2004 ATCA dataset, and provided a more precise and accurate reference position of SN 2001ig.Since this object is detected as a point-like source in Chandra, HST, Gemini and ATCA, it provides a useful anchor for relative astrometry between X-ray, optical and radio bands.We determined a radio position of SN 2001ig of R.A.(J2000) = 22 ℎ 57  30  .74(±0.′′ 04), Dec.(J2000) = −41 • 02 ′ 26.′′ 35(±0.′′ 05), which is ≈0.′′ 7 away from the reference position currently listed in the SIMBAD database7 and in most SN catalogues in the literature.This revised position (unlike the old one) is perfectly consistent with the alignment of the Chandra and Gemini images onto the Gaia reference frame.This also enables a more precise localization of X-2 inside its associated star-forming complex and nebula (Fig- Contours are defined as 2 /2 times the local rms noise level.For the 9 GHz map, the two plotted contours correspond to 40 Jy (4) and 57 Jy (5.7).For the 5.5 GHz map, the three plotted contours correspond to 60 Jy (4), 85 Jy (5.7) and 120 Jy (8).The Chandra position of X-2 is overplotted as a green circle.North is up, East to the left.ures 2-4), and a more fruitful search for the optical counterpart of X-1 (Section 3.8).
The first step was the alignment of the Gemini images.We selected eight Gaia sources with a bright, point-like, isolated, not saturated Gemini counterpart, as well as the radio position of SN 2001ig.We calculated the average R.A. and Dec. offsets of those nine sources, and their scatter.We corrected the Gemini astrometry (simple translation) with standard iraf imcoords tasks.After the re-alignment, we verified that the residual root-mean-square scatter of the Gemini positions with respect to the Gaia frame was ≈0.′′ 1 in R.A. and ≈0.′′ 1 in Dec.
The second step was the alignment of the HST/WFPC2 and WFC3 images.For the WFPC2 fields that cover X-2 and the northeastern sector of the galaxy, there are eight Gaia sources that appear point-like and unsaturated in the Wide Field chips of the WFPC2 F814W image, and six useful Gaia/WFPC2 associations in the F606W image.For the other pair of WFPC2 images, which cover R1 and the southern spiral arm, we found ten associations with Gaia sources.For the WFC3/UVIS fields, we found seven useful associations in both the F275W and F336W images.For each HST image, we applied a simple coordinate translation to align to the Gaia frame.In addition, as a secondary calibrator, we checked the revised HST astrometry with the help of several other sources without a Gaia identification but with a bright point-like appearance in both Gemini and HST.We verified that after our astrometric improvement, there is no systemic offset between HST and Gemini positions (only random scatter within ≲0.′′ 2).
Third, we improved the Chandra astrometry, starting from the two longer observations.There are three associations of point-like X-ray sources with Gaia sources.A fourth reference point comes from the radio position of SN 2001ig, which is also detected as an Xray source in the 2002 Chandra observations.Finally, two Chandra  2).The spectra were fitted with the Cash statistics.The datapoints were rebinned to a minimum signal to noise ratio of 2.7 for plotting purposes only.Bottom panel: unfolded spectra corresponding to the same three observations.sources have Gemini counterparts.We determined the observed centroids of the Chandra sources with the ciao task wavdetect.Then, we corrected the Chandra coordinates with the tasks wcs_match and wcs_update.We did so first using only the three Gaia and one ATCA associations; then, including also the two Gemini associations.We obtained the same result.We also verified that there is no need to include rotation and scaling corrections, as they do not improve the alignment compared with a simple translation.The third, shorter Chandra observation was aligned to the coordinates of the first two observations, based on the brightest X-ray sources visible in all three looks.For the main target of our study, the X-2 ULX, we obtain a refined position of R.A.(J2000) = 22 ℎ 57  24  .71(±0.′′ 2), Dec.(J2000) = −41 • 03 ′ 44.′′ 1(±0.′′ 2).
Taking into account the residual random scatter in the X-ray and optical positions (combined in quadrature), we estimate that we can locate the position of the brightest X-ray sources onto the HST/WFPC2 and Gemini images within a 90% confidence radius of ≈0.′′ 4, and onto the HST/WFC3 images within a 90% confidence radius of ≈0.′′ 3. The greater precision of the UVIS alignment is partly due to their smaller pixel size (0. ′′ 04, compared with the resampled pixel size of 0. ′′ 1 for the WFPC2 images), and partly to the fact that the UVIS field include the optical counterpart of SN 2001ig, whose radio coordinates are now well-determined from the ATCA maps.
In the 2020 Chandra data, it is seen again in an ultraluminous state.We fitted the new spectrum with the C statistics, because of the limited number of counts (caused by a short exposure time and a sharp decline in ACIS sensitivity since 2002).For consistency, we also refitted the two spectra from 2002 with the C statistics, which for a high number of counts give identical results to the  2 fitting used in Soria et al. (2006).The 2020 spectrum is mildly curved (Figure 5), well fitted (C- 28.5 +39.8 −13.9 :  dbb = ( in / 10 ) 2 cos , where  in is the apparent inner disk radius in km,  10 the distance to the source in units of 10 kpc (here,  10 = 1080), and  is our viewing angle ( = 0 is face-on).
:  in ≈ 1.19 in for a standard disk (Kubota et al. 1998).
: observed fluxes in the 0.3-10 keV band  : isotropic unabsorbed luminosities in the 0.3-10 keV band, defined as 4  2 times the de-absorbed fluxes.
: units of 10 −5 photons keV −1 cm −2 s −1 at 1 keV.stat = 95.7/102degrees of freedom) by standard Comptonization models; e.g., simpl × diskbb (Table 2), based on the Comptonization model of Steiner et al. (2009) applied to a seed disk-blackbody spectrum.For this fit, we froze the value of the intrinsic column density in the 2020 dataset to the best-fitting value obtained in the 2002 spectra ( H ≈ 3 × 10 20 cm −2 ), because such low values of  H are essentially unconstrained with the current low sensitivity of ACIS below 0.8 keV.The unabsorbed isotropic 0.3-10 keV luminosity for the Comptonization model is  X ≈ 8 +2 −1 × 10 39 erg s −1 .A simple power-law model (Table 2) can fit the 2020 data equally For the 2002 June 11 dataset, we confirm (in agreement with what was reported by Soria et al. 2006) that the fit is significantly improved with the addition of a thermal plasma component (modelled in xspec with apec8 ) to any smooth continuum model.For example (Table 2), adding the optically thin thermal plasma emission ( apec ≈ (1.1 ± 0.2) keV) to an absorbed power-law model brings the C statistics from 242.5 over 265 degrees of freedom, down to 229.0 over 263 degrees of freedom: an improvement significant to the 99% confidence limit (simftest in xspec).Similar improvements of |Δ | ≈ 13 are also obtained when an apec component is added to a Comptonization model.The presence of emission line residuals in the 2002 June 11 spectrum, at high  X , can be interpreted as typical evidence of ULX outflows (Middleton et al. 2015b;Pinto et al. 2016;Kosec et al. 2018).In 2020, the X-ray luminosity was even higher, but unfortunately the exposure time was shorter and ACIS has lost too much sensitivity below 1 keV (Figure 5), so that we cannot test the significance of an additional apec component in that epoch.
In summary, the 2020 Chandra observations show that the X-2 ULX remains very bright-in fact, more luminous than in 2002.This supports the hypothesis that X-2 provides an abundant supply for ionizing photons for the surrounding nebula.Extrapolating the bestfitting Comptonization model simpl × diskbb for the 2020 dataset, we estimate an intrinsic flux of ≈3.5 ×10 48 photons s −1 emitted in the 54-300 eV range.For the best-fitting diskpbb model, the isotropic flux is ≈2 ×10 49 photons s −1 in the same energy range.The average luminosity and ioinizing flux over all three Chandra observations is of course lower, because of the lower state seen in 2002 May 21 (Table 2).

Morphology of the star-forming complex around X-2
The star-forming region around X-2 has a central region (diameters of ≈100 × 150 pc) with bright continuum emission from young stars and star clusters (Gemini and HST images, Figures 2,3) together with strong line emission.In addition, line-emitting gas without significant broadband emission extends at least another 200 pc to the north and 100 pc to the south of the starlight-dominated region (compare the north-south extent of continuum and line emission in Figures 6,7).
In the continuum-dominated regions, two specific location stand out for their multiband properties.Near the southern part of the complex, we find the brightest star cluster, coincident (within a 90% confidence limit of 0. ′′ 2) with the unresolved radio source (Figures 3,4).About 1. ′′ 1 north of the radio source, in the central/upper part of the star-forming complex, it is the location of the X-2 ULX.There is at least one point-like optical source (a candidate star cluster) within the Chandra error circle, which must be considered the best candidate optical counterpart of the ULX, but nothing outstanding compared with other young star clusters in the surroundings.It was already noted by Soria et al. (2006) that X-ray and radio positions appeared to be different; now we can confirm that result, with the help of the 2021 ATCA observations and a more accurate multi-instrument astrometric alignment.Moreover, we have now ascertained that the radio source coincides with the optically brightest star cluster.
The radio luminosity   ≈ 1.0×10 35 erg s −1 (i.e., ≈2.5 times more luminous than Cas A) is near the upper end of the observed radio luminosity function for SNRs in nearby galaxies (Chomiuk & Wilcots 2009;Thompson et al. 2009).Models of SNR radio luminosity evolution suggest that such high values can be reached for a normal SN (explosion energy ≈10 51 erg) exploding in an relatively dense ambient medium with   ≳ 10 cm −3 (Berezhko & The Y axis represents the spatial direction from north to south, with a dispersion of 0. ′′ 25 per pixel.The X axis is the wavelength direction, with a spectral dispersion of 0.75 Å per pixel, and a resolution of 1.8 Å FWHM.Bottom panel: zoomed-in view around the H-[N ii] complex.The green marker indicates the spatial location of the X-ray source (corresponding to the peak He ii  4686 emission); the blue marker corresponds to the location of the unresolved radio source.
The bright star cluster coincident with the radio source is the peak both of the continuum and of the Balmer line emission.From the HST/WFPC2 images, we obtain an apparent brightness of  606 = (19.9±0.1)mag (Vega system) and  814 = (20.2±0.1)mag.If we only consider line-of-sight Galactic extinction, this corresponds to dereddened absolute magnitudes  606 = −(10.3± 0.1) mag and  814 = −(10.0± 0.1) mag.However, our analysis of the Balmer decrement in the VLT spectra suggest a higher intrinsic reddening, as we shall discuss later (Section 3.4).
Moving now our attention to the upper part of the star-forming complex, near the location of the X-ray source, we see in the HST/WFPC2 images several optical peaks, candidate (small) star clusters, standing out from an unresolved, bright background (Figures 3,4).Only one of those sources is fully inside the Chandra error circle, and is consistent with the peak of the He ii 4686 emission (Section 3.6).The apparent brightness of that source is  606 = (22.3± 0.1) mag,  814 = (21.9± 0.1) mag.If corrected only for line-of-sight Galactic extinction, this corresponds to de-reddened absolute brightness  606 = −(7.9± 0.1) mag,  814 = −(8.3± 0.1) mag.However, we will discuss how also in this case, the Balmer decrement measured in the VLT spectra suggests additional intrinsic reddening.
None of the individual optical sources in the northern part of the bright complex (inside or at the edge of the Chandra error circle for the ULX) is spatially resolved.From the broadband continuum brightness and colours alone, we cannot completely rule out that they are individual supergiant stars rather than small star clusters.For example, using the Padova isochrones computed with the parsec code9 (Bressan et al. 2012), we find that the optical source closest to the Chandra position is also consistent with a yellow supergiant with initial mass in the range of ≈17-20  ⊙ at an age of ≈9.0-11.5 Myr, and with a radius of ≈240-330  ⊙ .However, we consider this scenario very unlikely, because the strong Balmer line emission (Section 3.4) indicates a much younger age for the whole starforming clump, an age at which stars in this mass range have not left the main sequence yet.

Star formation properties near X-2 from the VLT spectra
For a better understanding of the star formation properties of this clump, we turn to the VLT/FORS2 spectra.Following up on the arguments discussed in Section 3.3, we identified two characteristic regions: one around the southern star cluster and radio source, and the other around the Chandra source, ≈1 ′′ to the north.Thus, we defined two extraction regions along the slit (both for the 300V and 1200R grisms), centred on the two positions, and with a spatial extent of 4 pixels ≈1 ′′ .In Table 3, we summarize the main properties of the lines detected in the two regions.This is more informative than the average properties over the whole complex, as we are looking for differences between the two positions.
We do not find significant velocity differences between northern and southern section in any of the lines.Thus, in Table 3 we report the average central wavelength of each line measured from the spectrum of the whole complex.The average recession speed is of (890 ± 10) km s −1 .This redshift is in excellent agreement with the expected value at the location of X-2, derived from the neutral hydrogen maps of Sorgho et al. (2019) and Sardone et al. (2021).
We selected the five strongest lines in the 1200R spectra to constrain line broadening, comparing their observed FWHMs from the X-2 region with those of sky lines.We obtain a marginally significant result of a mean intrinsic FWHM ≈ 0.9 Å around the X-ray source position and intrinsic FWHM ≈ 0.8 Å around the radio source position.Thus, the intrinsic FWHM is ≲ 40 km s −1 , a plausible value considering thermal broadening and turbulent motion of the gas in an H ii region.Moreover, we did double Gaussian fits of the strongest lines to test for the presence of a secondary, broader component in addition to the main narrow component.We found that the line profile in the radio source region does hint at the presence of broader wings extending up to ±120 km s −1 from the central position.This is consistent with a shock ionization component associated with that non-thermal radio emitting region.The flux in the broader component is only a few percent of the total line flux.We would need higher dispersion spectra to investigate that further.No such broad component was found for the region around the x-ray source.We also did not find any evidence of P-Cygni profiles (signature of strong outflows) in the Balmer lines.

Line
lines to H in the 1200R spectrum, and then converted those values to absolute fluxes based on the 300V measurements.
In this Section, and in Section 3.5, we focus on the properties of the Balmer lines.Properties of other lines will be discussed in Sections 3.6 and 3.7.For very young star clusters, the observed H and H EWs and flux ratio (Balmer decrement) are a much better proxy for age and intrinsic reddening than the broadband continuum.From the VLT spectra, we determine EW(H) ≈ (1350 ± 50)Å, and EW(H) ≈ (230 ± 10) Å at the location of the southern optical/radio peak (Table 4).Star cluster simulations with starburst99 10 (Leitherer et al. 1999(Leitherer et al. , 2014)), assuming instantaneous star formation and solar metallicity, indicate a wellconstrained age of ≈ (2.5 ± 0.2) Myr for the observed EWs.The Balmer ratio  (H)/ (H) ≈ 4.08 is significantly higher than the canonical value of 2.86 for photoionized gas.Using a Milky Way extinction curve with   = 3.1 ( − ), the total (intrinsic plus line-of-sight Galactic) reddening required to explain the high Balmer ratio is  ( − ) ≈ 0.36 mag, corresponding to   ≈ 1.11 mag,  606 ≈ 1.00 mag,  814 ≈ 0.66 mag.Subtracting this extinction from the observed values of optical brightness (Section 3.3), we obtain our best estimate for the de-reddened absolute brightness  606 = −(11.3± 0.1) mag,  814 = −(10.6± 0.1) mag.This agrees well with the expected broadband colour between the two bands for a star cluster at the age of ≈2.5 Myr 11 .Combining the cluster age and the extinction-corrected -band absolute brightness of  814 ≈ −10.6 mag, from starburst99 we obtain an estimate of (20, 000 ± 2000)  ⊙ for the total stellar mass in the southern cluster.
An average extinction   ≈ 0.67 mag corresponds to an equivalent neutral hydrogen column density  H ∼ 1-2 ×10 21 cm −2 , depending on the choice of conversion factor in the literature (Foight et al. 2016;Willingale et al. 2013;Watson 2011;Güver & Özel 2009).This is marginally higher than the total values of  H ≲ 10 21 cm −2 fitted to the Chandra spectra in the most reliable Comptonization or disk-blackbody models (Table 2).However, the optical extinction is an average value over a projected ≈50 pc × 50 pc region 10 https://www.stsci.edu/science/starburst99/docs/default.htm 11starburst99 predicts −0.04 ≲  −  (mag) ≲ 0.1 for a cluster age of ≈ (2.5 ± 0.2) Myr (instantaneous star formation, solar metallicity, Kroupa IMF).The F814W filter is essentially identical to the standard  band.Instead, the F606W filter is broader than the standard  towards longer wavelengths, and includes H (Holtzman et al. 1995).For a young star cluster with EW(H) ≈ 1350 Å, we estimate that  606 is ≈0.6 mag brighter than standard .Thus, we estimate that  606 ≈ −11.3 mag corresponds to   ≈ −10.7 mag,  −  ≈ (−0.1 ± 0.1) mag. .Spatial of a few diagnostic lines, along the slit in the north-south direction (south is left and north is right, along the X axis).The reference position (Δ = 0) on the X axis corresponds to the peak of the low-ionization lines (also coincident with the radio source).The peak of the He ii  4686 emission corresponds to the location of the ULX.The dotted vertical lines correspond to the extent of the continuum emission from the star-forming complex.The magenta dashed vertical lines represent the 90% confidence limits for the position of the ULX.
around the X-ray source.The latter may be in a lower-density cavity (perhaps because the gas is ionized by the ULX itself), or may be located on the near side of the ionized nebula rather than inside one of the small star clusters.

Total H𝛼 emission around X-2
We used the FORS2 300V grism spectrum (average of the two 600s exposures) to measure the observed flux on the slit.We found  (H) sc,abs = (12.3± 0.1) × 10 −15 erg cm −2 s −1 on the 1 ′′ slit around the southern star cluster, coincident with the radio detection.
Because the seeing is approximately the same as the slit width, we need to take into account that a fraction of light from the cluster does not fall on the slit.We estimated this fraction by inspecting the acquisition images taken before and after the two 300V spectra, and determining the fraction of emission from bright, isolated stars that falls within a 1 ′′ -wide rectangular box.One of the two acquisition images was taken in slightly worse seeing conditions (1. ′′ 15) than the spectra, the other image had better seeing (0. ′′ 65); thus we took a weighted average of the two estimates.We also verified the result by blurring the HST/WFPC2 image in the F606W filter to simulate the ground-based seeing.We obtain that ≈35% of the light from isolated point-like sources is lost off the slit in the 300V spectra.However, in the case of the slit extraction around the southern star cluster, this loss is partly compensated by the additional emission from the star-forming complex east and west of the slit that ends up into the slit.Taking both effects into account, we estimate the total absorbed flux from the star cluster is  (H) sc ≈ 15 × 10 −15 erg cm −2 s −1 .Next, we need to correct for dust reddening.As mentioned earlier (Section 3.4), the Balmer decrement of 4.08 at the position of the star cluster suggests  ( − ) ≈ 0.36 mag, that is  H ≈ 0.91 mag, corresponding to  (H) unabs ≈ 2.31 (H) abs .Thus, our best estimate for the H emission of the brightest cluster is  (H) sc,unabs ≈ 3.6 × 10 −14 erg cm −2 s −1 and a luminosity The magenta dashed vertical lines represent the 90% confidence limits for the position of the ULX.The dotted vertical lines correspond to the extent of the continuum emission from the star-forming complex.The line-emitting nebula extends a further ≈1 ′′ south of the continuum-emitting region, and at least ≈3 ′′ north of it.The nebular emission within the star-forming region (between the dotted lines) is consistent with an H 2 region.The higher [S ii]/H and [O i]/H ratios in the optically thin gas north of the ULX may be explained by the lower intensity of ionizing photons away from the southern star cluster.

He II emission near X-2 and other line diagnostics
Our VLT spectra reveal for the first time He ii 4686 emission peaking around the Chandra position for X-2 (Figure 8, Table 4).This is strongly indicative of X-ray photo-ionization near the ULX, while the rest of the star-forming complex is consistent with a normal H ii region (UV photo-ionized by OB stars).The He ++ emission extends ≈3 ′′ ≈ 150 pc to the north of the ULX (Figures 8,9), that is ≈1.′′ 5 into the purely nebular region, but is much weaker or undetected to the south of the ULX, towards the peak Balmer emission and radio source.A comparison between the two spectra extracted around the position of the radio source and around the position of the ULX show (Figure 10, Table 4) that He i 4471 is stronger than He ii 4686 in the former, and weaker in the latter.
Apart from the He lines, other emission lines do not show any dramatic difference at the ULX location compared with the southern cluster (Figures 10,11).Low-ionization line ratios [S II] 6716+6731/H and [O I] 6300/H are low (Figure 9), consistent with a normal H II region, across all the nebula.Both ratios have a minimum at the position of the southern star cluster and increase away from the main source of ionization.We suggest that this is due to a larger fraction of O and S being more ionized at the denser, brighter southern end of the star-forming clump.An inverse correlation of [S II] 6716+6731/H with H intensity and electron density is seen also in the Galactic disk (e.g., Hill et al. 2014).
The density diagnostic ratio [S II] 6716/6731 ≈ 1.35 ± 0.05 near the position of the ULX (Figure 9, Table 5) is consistent with moderate or low density   ≲ a few ×10 cm −3 (Osterbrock & Ferland 2006).The lowest value (ratio ≈1.4) is exactly at the ULX position, a possible indication of a lower-density or higher ionization cavity around the X-ray source.A marginally significant density increase is found instead at the southern location, where [S II] 6716/6731 ≈ 1.23 ± 0.05, consistent with   ≈ 100 cm −3 .If the steep-spectrum radio source is a young SNR, the enhanced ISM density in that region may explain its high luminosity.
The temperature diagnostic ratio [O III] (4959+5007)/4363 is ≈(150 ± 20) in the southern part of the clump, and ≈(100 ± 20) around the ULX.This corresponds to an electron temperature range ≈10,000-13,000 K between the two regions.The low signal-tonoise ratio of the [O III] 4363 line prevents a more accurate spatially resolved study.

Dereddened luminosity of the He ++ nebula
By analogy with the H emission discussed in Section 3.5, we estimate now the extinction-corrected luminosity of the He II 4686 emission, to place it in the context of other He ++ ULX nebulae in the literature.The integrated flux along the slit is  (4686) tot,abs = (1.7 ± 0.1) × 10 −16 erg cm −2 s −1 .We then need to estimate the fraction of emission lost outside the slit.As discussed before, for a point-like emission source centred in the middle of the slit, we would lose ≈35% of the flux.This gives us a total flux  (4686) tot,abs = (2.6 ± 0.2) × 10 −16 erg cm −2 s −1 .However, this is a lower limit, because we know that the He ++ region extends ≈3 ′′ in the northsouth direction along the slit (Figure 8); thus, it is plausible that a tail of emission extends also a similar amount in the east-west direction.Using analogous arguments to those applied to H (i.e., ≈40 per cent loss), we find a more plausible estimate of the total He II 4686 emission as  (4686) tot,abs = (2.8 ± 0.2) × 10 −16 erg cm −2 s −1 .As a further check, we analyzed a spectrum of a well-calibrated Wolf-Rayet star (WR9 in the Small Magellanic Cloud: Crowther & Hadfield 2006;Massey et al. 2003) taken with the FORS2 300V Table 5. Best-fitting parameters of the Chandra/ACIS-S spectra of X-1, fitted with the Cash statistics.Uncertainties for one interesting parameter are reported at the confidence interval of Δ = ±2.70:this is asymptotically equivalent to the 90% confidence interval in the  2 statistics.The Galactic absorption is fixed at  H,Gal = 8.6 × 10 19 cm −2 .3.55 +1.17 −1.17  3).The spectra were fitted with the Cash statistics.The datapoints were rebinned to a minimum signal to noise ratio of 2.7 for plotting purposes only.
The luminosity of the He ++ nebula is consistent with those seen in other ULXs with roughly similar X-ray luminosities, with  X / 4686 ∼ a few 10 −4 (Table 4).In fact, it is a factor of 3 more luminous and more extended than the prototypical He ++ nebula around the ULX in the Holmberg II galaxy, and several times more luminous that the X-ray photo-ionized nebula around NGC 5408 X-1.There is only one blue star inside the 90% error radius of the X-ray position (radius of 0. ′′ 3).Its brightness and colour are consistent with a B8 supergiant with a mass ∼9  ⊙ at an age of ∼30 Myr.

Multiband properties of the X-1 ULX
Although the main focus of our study was the X-2 ULX and its environment, we also provide an update on two other ULXs in this galaxy.X-1 (Soria et al. 2006) remained in an ultraluminous regime in the 2020 Chandra observation, at  X ≈ 5 × 10 39 erg s −1 (Table 5), similar to the value measured in 2002 May but a a factor of two lower than in 2002 June.No significant deviation from a simple power law (Figure 12) was recorded in any of the three spectra.
The field around X-1 is included in two deep HST/WFC3-UVIS observations from 2016 (Table 1), but not in the earlier WFPC2 observations.There is only one point-like optical source inside the Chandra error circle of the ULX position (Figure 13).We measured apparent brightness  275 = (24.65 ± 0.05) mag and  336 = (24.69± 0.05) mag (both values are in the Vegamag system).We then corrected the observed values for a line- of-sight Galactic extinction (taken from NED) of  275 ≈ 0.06 mag and  336 ≈ 0.05 mag, and applied a distance modulus of 30.17 mag (Section 1).We obtained absolute magnitudes  275 = (−5.58± 0.05) mag and  336 = (−5.53± 0.05) mag.
We used the Padova isochrones (Bressan et al. 2012) to estimate the properties of a single solar-metallicity star with such colours.It is consistent (approximately 90 per cent confidence level) with a blue supergiant of age (28 ± 3) Myr, a mass of 9.2 +0.6 −0.4  ⊙ , a temperature of about (11, 100 ± 1400) K and a radius of about (30 ± 10) ⊙ .However, there is an ongoing debate (e.g., Tao et al. 2011;Gladstone et al. 2013) on whether blue optical counterparts of ULXs are their donor stars, or the emission from the irradiated outer disk (which for plausible orbital parameters has similar size and temperature as a B supergiant), or a mix of the two components.From only two near-UV bands, we cannot discriminate between the two possibilities.We cannot also definitively rule out the possibility that the point source is a background quasar.However, considering the rarity of background sources at the observed X-ray flux (∼1 degree −2 : Luo et al. 2017;Cappelluti et al. 2009) and the high Xray/optical flux ratio of ∼500-1000, we consider this scenario very unlikely.Finally, we inspected the ATCA data but found no radio emission from X-1 or its surroundings, to a 4- upper limit of ≈50 Jy at 5.5 GHz.

Another transient ULX found with Swift
The Niels Gehrels Swift Observatory observed NGC 7424 twice, with snapshot observations: on 2008 July 23 (698-s exposure time for the X-Ray Telescope, XRT) and on 2008 November 25 (2093 s).We retrieved the data from NASA's Heasarc public archive, and estimated count rates and fluxes of the detected sources using standard data analysis tools for Swift/XRT available online 12 .We also compared the results of our re-analysis with those reported in the 2SXPS Catalogue of Swift X-ray Telescope Point Sources (Evans et al. 2020) and found them consistent.The most important result of the Swift/XRT data is the discovery of a transient ULX ≈2 ′ north-west of the nucleus, at R.A.(J2000) = 22 ℎ 57  10  .02, 12https://www.swift.ac.uk/user_objects/Dec.(J2000) = −41 • 03 ′ 00.′′ 5 (90% confidence radius ≈3 ′′ ).The Xray source (2SXPS J225710.0−410300,Evans et al. 2020) was seen in the 2008 November 25 observation with ≈19 net counts in the 0.3-10 keV band, but was not detected on 2008 July 23.Given the small number of counts, it is impossible to do any spectral analysis; however, with simple assumptions of a power-law spectrum, and column density ∼10 21 cm −2 , we estimate a luminosity  X = (9 ± 2) × 10 39 erg s −1 on 2008 November 25, and  X ≲ 3 × 10 39 erg s −1 on 2008 July 23 (using the 90% confidence limits of Kraft et al. 1991).2SXPS J225710.0−410300 was not detected in any of the three Chandra observations; we estimate an upper limit to its luminosity in 2002 of  X ≲ 10 37 erg s −1 , from a stack of the ObsID 3495 and 3496 datasets.X-1 and X-2 are visible in both Swift/XRT observations, with unabsorbed luminosities (averaged over the two XRT datasets) of  X = (7±2)×10 39 erg s −1 and  X = (3±1)×10 39 erg s −1 , respectively.2SXPS J225710.0−410300 is outside the field of view of all HST observations of NGC 7424.However, it is in the field of view of the Gemini GMOS images.There are two faint, red stars near the centre of the XRT error circle, both of them with apparent brightness  ∼ 24.5 mag (Figure 14).The two stars are detected as a single star (DES J225709.98−410259.7) in the Dark Energy Survey Data Reslease 2 catalogue (Abbott et al. 2021).There is no radio detection in the ATCA data, down to a 4- upper limit of ≈30 Jy at 5.5 GHz.

eROSITA detection of X-1 but not X-2
The field of NGC 7424 was observed by the eROSITA telescope array on the Spektrum Roentgen Gamma (SRG) satellite (Predehl et al. 2021), on 2020 May 15 (MJD 58984), for a net (vignettedcorrected) exposure time of 101 s.The recently released eRASS1 catalogue (Merloni et al. 2024) and associated sky maps show only one detected source in the galaxy, catalogued as 1eRASS J225728.6−410215.This source is clearly identifiable as X-1, within the position uncertainty (1 error of ≈2.′′ 5 in R.A. and ≈3.′′ 0 in Dec.).It has ≈15±4 net counts (detection likelihood of ≈41), corresponding to an absorbed 0.2-2.3keV flux of (1.4 ± 0.4) × 10 −13 erg cm −2 s −1 .This is the same flux observed in the Chandra observations of 2002 May and 2020 December, in the same band.Assuming a similar power-law model as in Table 5, we conclude that X-1 was at a 0.3-10 keV luminosity of ∼5 ×10 39 erg s −1 during the eROSITA observation.By contrast, X-2 was not detected by eROSITA.From an inspection of the sky map, we estimate that its 0.2-2.3keV flux in 2020 May must have been at least 4 times lower than observed in 2020 December, and we place a rough upper limit of ∼2 ×10 39 erg s −1 to its 0.3-10 keV luminosity.

A MULTIBAND LOOK AT STAR FORMATION IN NGC 7424
For a better understanding of the different star-forming properties of the environment around the X-1 and X-2 ULXs, we used archival data from three different bands: i) the Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) for the mid-IR; ii) a continuumsubtracted H image from the 1.5-m telescope at the Cerro Tololo Inter-American Observatory (CTIO); iii) GALEX near-UV and far-UV images.WISE has four channels: W1 (3.4 m), W2 (4.6 m), W3 (12 m) and W4 (22 m).Three-color images of {W1,W3,W4} show three outstanding red clumps along the spiral arms (Figure Table 6.Selected properties of the three main star-forming regions in the spiral arms of NGC 7424, identified from WISE images.The three regions have been labelled as in Figure 15, for simplicity.For each of the three young stellar complexes, we list its mid-IR brightness in the four WISE channels (Vegamag units), its brightest X-ray source (with its indicative X-ray luminosity from Chandra), its brightest radio source (with 5.5 GHz and 9.0 GHz flux densities from the ATCA), and its star-formation rate (from WISE W3 and W4).15).The data suggest that star formation is mostly concentrated in those three clumps.(Recall that in mid-IR images, redder colours indicate dusty star-forming regions, while bluer colours map the old stellar population).One of the three clumps corresponds to the star-forming complex around X-2 that we have analyzed in details in this work.Another clump corresponds to the brightest star cluster in NGC 7424 (Larsen 2002) and the brightest radio source (R-1) identified by Soria et al. (2006).The third clump, symmetrically located about 2 ′ north-west of the nucleus, is resolved into a group of several young clusters and OB associations at the end of a spiral arm; it includes a fairly bright radio source, and a sub-Eddington X-ray binary, but no ULXs.For short-hand notation, we have arbitrarily labelled the clumps "X-2", "R-1" and "C" in the three panels of Figure 15.The main properties of the three clumps are summarized in Table 6.Disk fragmentation into star-forming clumps is typically observed in high-redshift spirals (e.g., Elmegreen et al. 2007;Dekel et al. 2009;Cava et al. 2018) but is also sometimes seen in nearby galactic disks (e.g., Fisher et al. 2017;Inoue & Yoshida 2018;Larson et al. 2020;Dickinson et al. 2022).
The luminosity in the WISE W3 and W4 bands is a proxy for the total IR luminosity, and, hence, for the SFR.Using the observed brightness of the three clumps from the AllWISE catalog (Cutri et al. 2021), and the scaling of Cluver et al. (2017), we find typical SFRs of a few 10 −2  ⊙ yr −1 for each of the three clumps (Table 6).The most active one is R-1, as also suggested by the optical brightness of the associated young star cluster (Larsen 2002).All three clumps have W2−W3 colours ≈5 mag, which is typical of starburst galaxies (or starburst regions inside galaxies) and luminous infrared galaxies (e.g., the classic diagram of Wright et al. 2010).None of the three clumps stands out in the H and (especially) UV images, for the same reason why they do stand out in the WISE images: because dust removes photons from optical/UV bands and re-emits them in the mid-IR and far-IR.A more detailed analysis of the starformation properties of NGC 7424 will be presented in a followup work currently in preparation, together with a comprehensive study of the radio sources (SNRs and H II regions) detected in our ATCA observations.Here, we only use the multiband data as an independent check for some of the luminosity estimates presented in Section 3.5.
The H image 13 was taken from the 1.5-m CTIO telescope on 2000 September 16, with an exposure time of 1800 s; the 6568/28 filter was used for the narrow-band image, and an R-band image was 13 Downloaded from NED.
used for continuum subtraction.The filter has a pivot wavelength  = 6575.51Å, a Gaussian-equivalent FWHM of 36.1 Å, and a rectangular equivalent bandpass of 31.2Å.Given the narrow width of the filter and the flux ratios measured in our VLT spectra, we estimate that the contamination of the [N II] lines is only around 5% of the total flux in the band.We extracted the apparent flux from the region around the X-2 ULX, not including the nebular-only region to the north.We estimate an observed flux  (H) tot,abs = (4.0 ± 0.5) × 10 −14 erg cm −2 s −1 , which compares well with our previous estimate of  (H) tot,abs = (3.7 ± 0.5) × 10 −14 erg cm −2 s −1 based on the long-slit VLT spectra.
Next, we converted the WISE W4 magnitude into a flux density for the X-2 clump, following the prescriptions of Wright et al. (2010)  14 .We obtained a flux density  ,22m ≈ 14.7Jy, a corresponding monochromatic flux  22m ≈ 2.1 × 10 −12 erg cm −2 s −1 , and a luminosity  22m ≈ 2.9 × 10 40 erg s −1 .We then used the recipe of Kennicutt et al. (2009) to derive extinction-corrected H luminosities:  (H) unabs ≈  (H) abs + 0.02 24m .We approximated the Spitzer/MIPS 24-m luminosity (used to calibrate the Kennicutt relation) with the WISE 22-m luminosity, which introduces only errors of a few per cent, negligible for the purpose of this simple exercise.The result is a  (H) unabs ≈ (1.1 ± 0.1) × 10 39 erg s −1 ≈ 2.2 (H) abs .This is in good agreement with the independent estimate of Section 3.5 based on the Balmer decrement.It converts to a reddening  ( − ) ≈ 0.33 mag.

SUMMARY AND CONCLUSIONS
We took a second look at the two persistent ULXs in the face-on spiral NGC 7424, two decades after their discovery.We showed that X-1 is located in a low density region, along a spiral arm but away from currently star-forming regions.We identified a blue, point-like optical counterpart.If this optical source is the donor star (rather than the irradiated accretion disk), it is consistent with a blue supergiant with an age ≈28 Myr.In this case, this ULX belongs to the same ULX class as, for example, NGC 7793 P13 (Motch et al. 2014).
X-1 has been found in a bright state in all X-ray observations (three Chandra, two Swift and one SRG/eROSITA observations) over a span of 20 years, at  X ≈ 5-9 × 10 39 erg s −1 , with no obvious spectral state transitions.By contrast, X-2 has more unusual properties.It is located in one of the three most active star-forming clumps in the whole galactic disk, a region with a size of ≈100 pc × 150 pc, populated by young star clusters.Our VLT spectroscopic study shows strong line emission from a UV-photoionized H II region, as expected, but also strong nebular He II 4686 emission from the location around the X-ray source-not from the brightest and youngest part of the star-forming clump, which is located ≈50 pc south of the ULX.
A second point of interest of NGC 7424 X-2 is that the system has a younger age than most other ULXs.From the Balmer emission lines, we estimate an age of (4.4 ± 0.3) Myr for the stellar population around the ULX.The stellar progenitor of the ULX must have collapsed after less than this age.This implies a progenitor mass  ≳ 47 ⊙ (from the Padova isochrones at solar metallicity, Bressan et al. 2012).It does not, however, imply that the compact object is a black hole.The example of a neutron star found in the young Galactic cluster Westerlund 1 (age ≲5 Myr) suggests that binary evolution can lead to a supernova and neutron star formation even from progenitors above 40  ⊙ (Schneider et al. 2021;Belczynski & Taam 2008).With such a young age, the donor star of X-2 cannot be a blue supergiant (unlike the X-1 donor), and is instead either a main-sequence O star or a Wolf-Rayet.
A third interesting feature of X-2 is that it was seen once in a lower-luminosity state ( X ≈ 6 × 10 38 erg s −1 ), with a hard power-law-like spectrum in Chandra's 0.5-7 keV band.A simple assumption that this property corresponds to the bright end of the hard state of an accreting black hole ( X ≲ 0.1 Edd ) would imply a black hole mass ≳50  ⊙ .On the other hand, super-critical accretion onto strongly magnetized (young) neutron stars also produces a hard spectrum, from fan-beam emission in the accretion column.The softening of the source with brightness in the subsequent two Chandra observations may be explained by a higher contribution from the inner disk and a denser disk outflow along our line of sight, as the accretion rate increased (Gúrpide et al. 2021b,a).
A fourth interesting property of X-2, or at least of the environment around X-2, is the presence of a strong (2.5 times the luminosity of Cas A at 5.5 GHz), unresolved radio source at the southern end of the star-forming clump.Based on the observed Balmer emission, we argued that free-free emission from gas in the main star cluster is expected to contribute a non-negligible component, but cannot be the dominant process.The steep spectrum suggests a dominant optically-thin synchrotron component.It could be a young (age ≲1000 yr) SNR, completely unrelated to the ULX; however, the massive star cluster is too young (age <3 Myr) to have a substantial SN rate.Or it could be the radio hot spot/radio lobe of a jet powered by the ULX.This would be analogous to the jets in NGC 7793 S26 (Soria et al. 2010) and in NGC 6946 X-1 (T.Beuchert et al., in prep.),where the peak radio synchrotron emission is displaced from the compact object.The non-detection of a symmetrically placed radio lobe north of NGC 7424 X-2 could be explained by the much lower ISM density in that region.
If the non-thermal radio source is caused by shocks from a ULX jet, we expect the presence of broad optical emission lines from shocked-ionized gas.The H luminosity expected from the shocked gas, for typical ULX bubble parameters, is  (H) ≈ 2.2-2.5×10−3  jet (Allen et al. 2008).If we assume  jet ≈  X ≈ 7×10 39 erg s −1 , the shock-ionized component of the Balmer emission is only ≈10% of the Balmer luminosity from the star cluster (Section 3.5).This weaker component is consistent with the broader wings marginally detected in the strongest lines (Section 3.4).An objection to the ULX jet scenario is that two strong radio sources are also associated with the other two main starburst clumps in NGC 7424, although they do not contain currently active ULXs.In summary, we do not have enough information to rule out any of those scenarios for the origin of this intriguing radio source near X-2.We are planning deeper ATCA observations in 2024 to put a stronger constraint to the spatial extent and spectral index, and to look for possible northern radio lobe.

Figure 2 .
Figure 2. Left panel: zoomed-in true-colour view of the field around X-2, from the Gemini-South GMOS images in the  ′ (blue),  ′ (green) and  ′ (red) filters.Middle panel: GMOS image in the  ′ filter.Right panel: GMOS image in the  ′ filter.In all panels, we have overplotted the location of interesting multiband associations.The green circle (1) is the 90% confidence limit (radius of 0. ′′ 4) of the Chandra position of the ULX X-2.The cyan box (2) is the spatial location along the VLT slit corresponding to the peak in He ii 4686 emission; size of the box: 1 ′′ × 0. ′′ 25.The red box (3) corresponds to the peak of the low-ionization lines (H , H , [S ii]6716,6731 and several He i lines).The blue circle (4) is the 90% confidence limit (radius of 0. ′′ 2) of the centroid position of the strong, unresolved radio source detected by the ATCA.

Figure 3 .
Figure 3. Top panel: HST/WFPC2 image of the X-2 field, in the F606W filter.Bottom panel: HST/WFPC2 image in the F814W filter.In both panels, the meaning of the four overplotted regions is the same as in Figure 2.

Figure 4 .
Figure 4. ATCA flux density contours overplotted on the HST/WFPC2 F814W image.Cyan contours are for 9 GHz, yellow contours for 5.5 GHz.Contours are defined as 2 /2 times the local rms noise level.For the 9 GHz map, the two plotted contours correspond to 40 Jy (4) and 57 Jy (5.7).For the 5.5 GHz map, the three plotted contours correspond to 60 Jy (4), 85 Jy (5.7) and 120 Jy (8).The Chandra position of X-2 is overplotted as a green circle.North is up, East to the left.

Figure 5 .
Figure 5. Top panel: datapoints and data/model ratios for the Chandra/ACIS spectrum of X-2. Green is for ObsID 3495, blue for ObsID 3496 and red for ObsID 23572.The model is an absorbed Comptonization model (tbabs × tbabs × simpl × diskbb) (Table2).The spectra were fitted with the Cash well (C-stat = 93.6/103)but only with the addition of a suspiciously high level of intrinsic absorption ( H ≈ 7 × 10 21 cm −2 ), inconsistent with the low values of  H found in the much deeper 2002 observations.An absorbed diskbb model provides a worse fit (C-stat = 101.3/103)than a power law or a Comptonization model, because it has too much spectral curvature.A -free disk gives a marginal improvement, (C-stat = 98.6/102) for a characteristic temperature  in ≈ 1.2 keV and  in √ cos  ≈ 80 km.The unabsorbed 0.3-10 keV luminosity of the diskbb and diskpbb model fits are  X ≈ (9 ± 2) × 10 39 erg s −1 .

Figure 6 .
Figure 6.Top panel: portion of the VLT/FORS2 2D spectrum of the nebula and star-forming region around X-2, taken with VLT/FORS2, 300V grism.The Y axis represents the spatial direction (slit running from north to south), with a dispersion of 0. ′′ 25 per pixel.The X axis is the wavelength direction, with a spectral dispersion of 3.3 Å per pixel and instrumental resolution of 9.4 Å FWHM.The image highlights the different location of the lowerionization lines emission (closer to the southern part of the star-forming region) compared with the He ii  4686 emission (closer to the northern part).Bottom panel: zoomed-in view of the same spectrum, around the H-[O iii] complex, displayed with the different color scale, to show that all three lines peak on the southern end of the star-forming region.The vertical marker (4 pixels ≈ 1. ′′ 0) represents the spacial displacement between the peak of the He ii  4686 line and the peak of the other lines.

Figure 7 .
Figure 7. Top panel: portion of the VLT/FORS2 2D spectrum of the nebula and star-forming region around X-2, taken with VLT/FORS2, 1200R grating.The Y axis represents the spatial direction from north to south, with a dispersion of 0. ′′ 25 per pixel.The X axis is the wavelength direction, with a spectral dispersion of 0.75 Å per pixel, and a resolution of 1.8 Å FWHM.Bottom panel: zoomed-in view around the H-[N ii] complex.The green marker indicates the spatial location of the X-ray source (corresponding to the peak He ii  4686 emission); the blue marker corresponds to the location of the unresolved radio source.
Figure8.Spatial of a few diagnostic lines, along the slit in the north-south direction (south is left and north is right, along the X axis).The reference position (Δ = 0) on the X axis corresponds to the peak of the low-ionization lines (also coincident with the radio source).The peak of the He ii  4686 emission corresponds to the location of the ULX.The dotted vertical lines correspond to the extent of the continuum emission from the star-forming complex.The magenta dashed vertical lines represent the 90% confidence limits for the position of the ULX.

Figure 9 .
Figure9.Both panels show a selection of line ratios of a few diagnostic lines, plotted along the north-south spatial direction.As in Figure8, the Δ = 0 position on the X axis corresponds to the peak of the low-ionization lines.The magenta dashed vertical lines represent the 90% confidence limits for the position of the ULX.The dotted vertical lines correspond to the extent of the continuum emission from the star-forming complex.The line-emitting nebula extends a further ≈1 ′′ south of the continuum-emitting region, and at least ≈3 ′′ north of it.The nebular emission within the star-forming region (between the dotted lines) is consistent with an H 2 region.The higher [S ii]/H and [O i]/H ratios in the optically thin gas north of the ULX may be explained by the lower intensity of ionizing photons away from the southern star cluster.

Figure 10 .
Figure10.Top panel: blue section of the VLT/FORS2 300V spectrum of the northern part of the star-forming complex, with a spatial extent of Δ = 0. ′′ 5 around the Chandra position of X-2.The dispersion is 3.3 Å per pixel.The instrumental resolution is 9.4 Å FWHM.Middle panel: the same section of the VLT/FORS2 300V spectrum, for the southern part of the star-forming complex, with a spatial extent of Δ = 0. ′′ 5 around the peak of the low-ionization lines.Bottom panel: zoomed-in view of the two spectra shown in the top and middle panel, to highlight the stronger contribution of He ii compared with He i around the X-ray location (red histogram), and the absence of He ii in the bottom part of the nebula (blue histogram).

Figure 11 .
Figure11.Top panel: VLT/FORS2 1200R spectrum of the northern part of the star-forming complex, with a spatial extent of Δ = 0. ′′ 5 around the Chandra position of X-2.The spectral dispersion is 0.74 Å per pixel.Middle panel: VLT/FORS2 1200R spectrum, for the southern part of the star-forming complex, with a spatial extent of Δ = 0. ′′ 5 around the peak of the low-ionization lines.Bottom panel: zoomed-in view of the two spectra shown in the top and middle panel (red and blue histograms, respectively).

Figure 12 .
Figure12.Datapoints and data/model ratios for the Chandra/ACIS spectrum of X-1. Green is for ObsID 3495, blue for ObsID 3496 and red for ObsID 23572.The model is an absorbed powerlaw (Table3).The spectra were fitted with the Cash statistics.The datapoints were rebinned to a minimum signal to noise ratio of 2.7 for plotting purposes only.

Figure 13 .
Figure 13.UV counterpart of the X-1 ULX (HST/WFC3 F275W image).There is only one blue star inside the 90% error radius of the X-ray position (radius of 0. ′′ 3).Its brightness and colour are consistent with a B8 supergiant with a mass ∼9  ⊙ at an age of ∼30 Myr.

Figure 15 .
Figure 15.Top panel: mid-IR three-colour image: red = WISE W4 band (22 m), green = W3 (12 m), blue = W1 (3.4 m).The three dusty star-forming clumps in the spiral arms have been arbitrarily labeled for convenience (see also Table 6).For comparison, we also marked the position of the galactic nucleus, of SN 2001ig, and of the X-1 ULX.The bluer colour of the nuclear region and the bar indicates an older population and weaker star formation in that region.Middle panel: continuum-subtracted H image from the 1.5-m CTIO telescope.Bottom panel: GALEX far-UV image.

Table 1 .
Log of the Chandra, HST, VLT and ATCA observations used for this study.

Table 2 .
Best-fitting parameters of the Chandra/ACIS-S spectra of X-2, fitted with the Cash statistics.Uncertainties for one interesting parameter are reported at the confidence interval of Δ = ±2.70:this is asymptotically equivalent to the 90% confidence interval in the  2 statistics.The Galactic absorption is fixed at  H,Gal = 8.6 × 10 19 cm −2 .

Table 4 .
Comparison of He ii 4686 and X-ray luminosities in a sample of nearby ULX associated with proven or candidate photo-ionized nebulae.
Cluver et al. (2017)e identification of the three off-nuclear star-forming regions;  : peak unabsorbed 0.5-7 keV luminosity during the two longer Chandra observations of 2002;  : average of the SFRs derived from W3 and W4, using the relations ofCluver et al. (2017).