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

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$\aas@@fstack{\prime\prime}$5 radius, and local background annuli with an area approximately ten times larger. We used the ftools²²2http://heasarc.gsfc.nasa.gov/ftools 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 $\geq$1 count per bin, suitable for fitting with the Cash statistics (Cash, 1979), and corresponding spectra grouped to $\geq$15 counts per bin, for $\chi^{2}$ 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 $\sim$100 counts and are mildly undersampled when rebinned for $\chi^{2}$ 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.

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$\aas@@fstack{\prime\prime}$35–0$\aas@@fstack{\prime\prime}$4). The images were taken in the $u^{\prime},g^{\prime},r^{\prime}$ set of Sloan filters, with a 0$\aas@@fstack{\prime\prime}$0807/pixel sampling. A series of dithered sub-exposures were taken for each filter, and combined to remove cosmic rays and chip gaps; see Ryder et al. (2006) for details of the observational set-up and data reduction. The 5$\aas@@fstack{\prime}$5 $\times$ 5$\aas@@fstack{\prime}$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).

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 Archive ³³3https://hla.stsci.edu for the WFPC2 images files, and from the Mikulski Archive for Space Telescopes⁴⁴4https://mast.stsci.edu/search/ui/{#}/hst 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.

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$\aas@@fstack{\prime\prime}$25 per pixel (2 $\times$ 2 pixel binning). The dispersion was $\approx$3.30 Å per pixel for the 300V grating, and 0.75 Å per pixel for the 1200R grating. The instrumental resolution was 9.4 Å full-width-half-maximum (FWHM) for the 300V grism, and 1.8 Å FWHM for the 1200R one. The slit width was 1$\aas@@fstack{\prime\prime}$0 for the 300V grating (matched to a delivered seeing of 1$\aas@@fstack{\prime\prime}$1) and 0$\aas@@fstack{\prime\prime}$7 for the 1200R grating (delivered seeing of 0$\aas@@fstack{\prime\prime}$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.

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)⁵⁵5https://www.narrabri.atnf.csiro.au/operations/array_configurations/configurations.html. 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$-$638 for flux density calibration, and the nearby source PKS B2310$-$417 for phase calibration. We processed data following standard procedures⁶⁶6https://casaguides.nrao.edu/index.php/ATCA_Tutorials within the Common Astronomy Software Application (casa, version 5.1.2; CASA Team et al. 2022). To image the data we used the casa task clean, using a Briggs robust parameter of 0 (Briggs, 1995), balancing sensitivity and resolution. These choices resulted in synthesized beams with FWHM of 2$\aas@@fstack{\prime\prime}$5 $\times$ 1$\aas@@fstack{\prime\prime}$4 at 5.5 GHz (position angle $+1^{\circ}$, east of north), and 1$\aas@@fstack{\prime\prime}$5 $\times$ 0$\aas@@fstack{\prime\prime}$9 at 9 GHz (position angle $-2^{\circ}$). 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.

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) $=22^{h}\,57^{m}\,30^{s}.74(\pm 0\aas@@fstack{\prime\prime}04)$, Dec.(J2000) $=-41^{\circ}\,02^{\prime}\,26\aas@@fstack{\prime\prime}35(\pm 0\aas@@fstack{\prime\prime}05)$, which is $\approx$0$\aas@@fstack{\prime\prime}$7 away from the reference position currently listed in the SIMBAD database⁷⁷7http://simbad.cds.unistra.fr/simbad/ 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 (Figures 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 $\approx$0$\aas@@fstack{\prime\prime}$1 in R.A. and $\approx$0$\aas@@fstack{\prime\prime}$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 north-eastern 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 $\lesssim$0$\aas@@fstack{\prime\prime}$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 X-ray source in the 2002 Chandra observations. Finally, two Chandra 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) $=22^{h}\,57^{m}\,24^{s}.71(\pm 0\aas@@fstack{\prime\prime}2)$, Dec.(J2000) $=-41^{\circ}\,03^{\prime}\,44\aas@@fstack{\prime\prime}1(\pm 0\aas@@fstack{\prime\prime}2)$.

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 $\approx$0$\aas@@fstack{\prime\prime}$4, and onto the HST/WFC3 images within a 90% confidence radius of $\approx$0$\aas@@fstack{\prime\prime}$3. The greater precision of the UVIS alignment is partly due to their smaller pixel size (0$\aas@@fstack{\prime\prime}$04, compared with the resampled pixel size of 0$\aas@@fstack{\prime\prime}$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 2002, X-2 rose from $L_{\rm X}\approx 6\times 10^{38}$ erg s^-1 to $L_{\rm X}\approx 6\times 10^{39}$ erg s^-1 in the space of 20 days (Figure 5, Table 2 and Soria et al. 2006). 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 $\chi^{2}$ fitting used in Soria et al. (2006).

The 2020 spectrum is mildly curved (Figure 5), well fitted (C-stat $=95.7/102$ degrees of freedom) by standard Comptonization models; e.g., simpl $\times$ 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 ($N_{\rm H}\approx 3\times 10^{20}$ cm^-2), because such low values of $N_{\rm H}$ 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 $L_{\rm X}\approx 8^{+2}_{-1}\times 10^{39}$ erg s^-1. A simple power-law model (Table 2) can fit the 2020 data equally well (C-stat $=93.6/103$) but only with the addition of a suspiciously high level of intrinsic absorption ($N_{\rm H}\approx 7\times 10^{21}$ cm^-2), inconsistent with the low values of $N_{\rm H}$ 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 $p$-free disk gives a marginal improvement, (C-stat $=98.6/102$) for a characteristic temperature $kT_{\rm in}\approx 1.2$ keV and $R_{\rm{in}}\sqrt{\cos\theta}\approx 80$ km. The unabsorbed 0.3–10 keV luminosity of the diskbb and diskpbb model fits are $L_{\rm X}\approx(9\pm 2)\times 10^{39}$ erg s^-1.

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 apec⁸⁸8https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/node134.html) to any smooth continuum model. For example (Table 2), adding the optically thin thermal plasma emission ($kT_{\rm apec}\approx(1.1\pm 0.2)$ 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 $|\Delta C|\approx 13$ 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 $L_{\rm X}$, 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 best-fitting Comptonization model simpl $\times$ diskbb for the 2020 dataset, we estimate an intrinsic flux of $\approx$3.5 $\times 10^{48}$ photons s^-1 emitted in the 54–300 eV range. For the best-fitting diskpbb model, the isotropic flux is $\approx$2 $\times 10^{49}$ 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).

The star-forming region around X-2 has a central region (diameters of $\approx$100 $\times$ 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$\aas@@fstack{\prime\prime}$2) with the unresolved radio source (Figures 3,4). About 1$\aas@@fstack{\prime\prime}$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.

For the radio source, the 2021 ATCA data at 9 GHz give a centroid at R.A.(J2000) $=22^{h}\,57^{m}\,24^{s}.697(\pm 0\aas@@fstack{\prime\prime}07)$, Dec.(J2000) $=-41^{\circ}\,03^{\prime}\,45\aas@@fstack{\prime\prime}22(\pm 0\aas@@fstack{\prime\prime}13)$. The flux density is $F_{\rm 5.5GHz}=(135\pm 12)\mu$Jy at 5.5 GHz (corresponding to a luminosity density $L_{\rm 5.5GHz}=(1.9\pm 0.2)\times 10^{25}$ erg s^-1 Hz^-1) and $F_{\rm 9GHz}=(70\pm 11)\mu$Jy at 9.0 GHz ($L_{\rm 9.0GHz}=(9.0\pm 2.0)\times 10^{24}$ erg s^-1 Hz^-1). These values are consistent with the average flux densities determined from the 2001–2004 dataset, namely $F_{\rm 4.8GHz}=(138\pm 34)\mu$Jy at 4.8 GHz and $F_{\rm 8.6GHz}=(100\pm 45)\mu$Jy at 8.6 GHz (Soria et al., 2006). The spectral index $\alpha=-(1.4\pm 0.4)$ suggests optically thin synchrotron emission, typical of SN remnants and/or ULX bubbles.

The radio luminosity $\nu L_{\nu}\approx 1.0\times 10^{35}$ erg s^-1 (i.e., $\approx$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 $\approx$10⁵¹ erg) exploding in an relatively dense ambient medium with $n_{e}\gtrsim 10$ cm^-3 (Berezhko & Völk, 2004; Sarbadhicary et al., 2017, 2019; Leahy et al., 2022). We will see from our diagnostic line ratio analysis (Section 3.6) that such higher-than-usual interstellar medium (ISM) density is indeed plausible.

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 $m_{606W}=(19.9\pm 0.1)$ mag (Vega system) and $m_{814W}=(20.2\pm 0.1)$ mag. If we only consider line-of-sight Galactic extinction, this corresponds to dereddened absolute magnitudes $M_{606W}=-(10.3\pm 0.1)$ mag and $M_{814W}=-(10.0\pm 0.1)$ 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 $\lambda$4686 emission (Section 3.6). The apparent brightness of that source is $m_{606W}=(22.3\pm 0.1)$ mag, $m_{814W}=(21.9\pm 0.1)$ mag. If corrected only for line-of-sight Galactic extinction, this corresponds to de-reddened absolute brightness $M_{606W}=-(7.9\pm 0.1)$ mag, $M_{814W}=-(8.3\pm 0.1)$ 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 code⁹⁹9http://stev.oapd.inaf.it/cgi-bin/cmd_3.7 (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 $\approx$17–20 $M_{\odot}$ at an age of $\approx$9.0–11.5 Myr, and with a radius of $\approx$240–330 $R_{\odot}$. However, we consider this scenario very unlikely, because the strong Balmer line emission (Section 3.4) indicates a much younger age for the whole star-forming clump, an age at which stars in this mass range have not left the main sequence yet.

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, $\approx$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 $\approx$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 $(890\pm 10)$ 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 $\approx 0.9$ Å around the X-ray source position and intrinsic FWHM $\approx 0.8$ Å around the radio source position. Thus, the intrinsic FWHM is $\lesssim$ 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 $\pm$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.

The flux of each line was computed from the average of the two 300V spectra, whenever possible. This was done for two reasons. First, because the 300V grisms covers both the red and the blue part of the optical spectrum, which reduces potential systematic errors for a flux comparison, for example between H$\alpha$ and H$\beta$. Second, because the 1200R spectrum was taken in not perfectly photometric conditions (thin cirrus clouds). However, some of the lines can only be resolved in the 1200R spectrum: for example, [O I] $\lambda$6300 and [S II] $\lambda$6313 are partly blended in the 300V spectra, and so are [N II] $\lambda 6548$ and H$\alpha$. In that case, we measured the relative flux of those lines to H$\alpha$ 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$\alpha$ and H$\beta$ 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$\alpha$) $\approx(1350\pm 50)$Å, and EW(H$\beta$) $\approx(230\pm 10)$ Å at the location of the southern optical/radio peak (Table 4). Star cluster simulations with starburst99¹⁰¹⁰10https://www.stsci.edu/science/starburst99/docs/default.htm (Leitherer et al., 1999, 2014), assuming instantaneous star formation and solar metallicity, indicate a well-constrained age of $\approx(2.5\pm 0.2)$ Myr for the observed EWs. The Balmer ratio $F({\mathrm{H}}\alpha)/F({\mathrm{H}}\beta)\approx 4.08$ is significantly higher than the canonical value of 2.86 for photoionized gas. Using a Milky Way extinction curve with $A_{V}=3.1E(B-V)$, the total (intrinsic plus line-of-sight Galactic) reddening required to explain the high Balmer ratio is $E(B-V)\approx 0.36$ mag, corresponding to $A_{V}\approx 1.11$ mag, $A_{606W}\approx 1.00$ mag, $A_{814W}\approx 0.66$ 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 $M_{606W}=-(11.3\pm 0.1)$ mag, $M_{814W}=-(10.6\pm 0.1)$ mag. This agrees well with the expected broadband colour between the two bands for a star cluster at the age of $\approx$2.5 Myr¹¹¹¹11starburst99 predicts $-0.04\lesssim V-I({\rm mag})\lesssim 0.1$ for a cluster age of $\approx(2.5\pm 0.2)$ Myr (instantaneous star formation, solar metallicity, Kroupa IMF). The F814W filter is essentially identical to the standard $I$ band. Instead, the F606W filter is broader than the standard $V$ towards longer wavelengths, and includes H$\alpha$ (Holtzman et al., 1995). For a young star cluster with EW(H$\alpha$) $\approx 1350$ Å, we estimate that $m_{606W}$ is $\approx$0.6 mag brighter than standard $V$. Thus, we estimate that $M_{606W}\approx-11.3$ mag corresponds to $M_{V}\approx-10.7$ mag, $V-I\approx(-0.1\pm 0.1)$ mag.. Combining the cluster age and the extinction-corrected $I$-band absolute brightness of $M_{814W}\approx-10.6$ mag, from starburst99 we obtain an estimate of $(20,000\pm 2000)M_{\odot}$ for the total stellar mass in the southern cluster.

We can apply similar arguments for the smaller star clusters near the Chandra position. The VLT spectra extracted from $\pm$0$\aas@@fstack{\prime\prime}$5 around the ULX position give EW(H$\alpha$) $\approx(400\pm 20)$Å, and EW(H$\beta$) $\approx(80\pm 5)$ Å (Table 4), and a Balmer ratio $F({\mathrm{H}}\alpha)/F({\mathrm{H}}\beta)\approx 3.54$. The EWs suggest an age of $\approx(4.4\pm 0.3)$ Myr for the central/northern part of the clump, consistent with the scenario that star formation is propagating southwards in time. The Balmer decrement implies a total reddening $E(B-V)\approx 0.22$ mag, which corresponds to $A_{V}\approx 0.67$ mag, $A_{606W}\approx 0.60$ mag, $A_{814W}\approx 0.40$ mag. If we apply these values of age and extinction to the point-like optical source closest to the X-ray position, we find absolute brightnesses $M_{606W}=-(8.5\pm 0.1)$ mag, $M_{814W}=-(8.7\pm 0.1)$ mag, which correspond to a stellar mass of $(2400\pm 300)M_{\odot}$, and similar masses $\sim$2,000–3,000 $M_{\odot}$ for each of the other three small clusters within $\approx$0$\aas@@fstack{\prime\prime}$5 of the X-ray position (Figure 3).

An average extinction $A_{V}\approx 0.67$ mag corresponds to an equivalent neutral hydrogen column density $N_{\rm H}\sim 1$–2 $\times 10^{21}$ 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 $N_{\rm H}\lesssim 10^{21}$ 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 $\approx$50 pc $\times$ 50 pc region 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.

We used the FORS2 300V grism spectrum (average of the two 600-s exposures) to measure the observed flux on the slit. We found $F({\mathrm{H}}\alpha)_{\mathrm{sc,abs}}=(12.3\pm 0.1)\times 10^{-15}$ 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$\aas@@fstack{\prime\prime}$15) than the spectra, the other image had better seeing (0$\aas@@fstack{\prime\prime}$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 $\approx$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 $F({\mathrm{H}}\alpha)_{\mathrm{sc}}\approx 15\times 10^{-15}$ 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 $E(B-V)\approx 0.36$ mag, that is $A_{{\mathrm{H}}\alpha}\approx 0.91$ mag, corresponding to $F({\mathrm{H}}\alpha)_{\mathrm{unabs}}\approx 2.31F({\mathrm{H}}\alpha)_{\mathrm{abs}}$. Thus, our best estimate for the H$\alpha$ emission of the brightest cluster is $F({\mathrm{H}}\alpha)_{\mathrm{sc,unabs}}\approx 3.6\times 10^{-14}$ erg cm^-2 s^-1 and a luminosity $L({\mathrm{H}}\alpha)_{\mathrm{sc,unabs}}\approx 5.0\times 10^{38}$ erg s^-1. The 5.5-GHz flux density for the free-free radio emission associated with this Balmer flux is $F_{\rm 5.5GHz,ff}\approx 40\mu$Jy (Caplan & Deharveng, 1986). The observed 5.5-GHz flux density (unresolved and spatially coincident with the star cluster) is $F_{\rm 5.5GHz,ff}=(138\pm 15)\mu$Jy (Section 3.3). We conclude that free-free emission alone is a significant but not dominant component of the radio source in the X-2 complex.

Furthermore, we estimate the total H$\alpha$ luminosity from the whole star-forming clump, defined as the $\approx$2${}^{\prime\prime}\times 3^{\prime\prime}(\approx 100{\mathrm{~pc}}\times 150$ pc) region with both starlight continuum and nebular line emission. The FORS2 spectra show a flux $F({\mathrm{H}}\alpha)_{\mathrm{tot,abs}}=(22\pm 1)\times 10^{-15}$ erg cm^-2 s^-1 on the slit. From the VLT/FORS2 acquisition image taken the same night and with the same seeing, we estimate that the emission along the slit is $\approx$60% of the total emission from the star-forming clump. Thus, we estimate that $F({\mathrm{H}}\alpha)_{\mathrm{tot,abs}}=(3.7\pm 0.5)\times 10^{-14}$ erg cm^-2 s^-1. The emission-weighted average Balmer decrement along the slit is $\approx$3.9 (running from $\approx$4.1 at the younger, brighter southern end to $\approx$3.5 at the slightly older, fainter northern end). This corresponds to $E(B-V)\approx 0.31$ mag, $A_{{\mathrm{H}}\alpha}\approx 0.79$ mag, and $F({\mathrm{H}}\alpha)_{\mathrm{unabs}}\approx 2.06F({\mathrm{H}}\alpha)_{\mathrm{abs}}$. Thus, our best estimate for the dereddened H$\alpha$ flux of the star-forming region is $F({\mathrm{H}}\alpha)_{\mathrm{tot,unabs}}\approx(7.6\pm 1.0)\times 10^{-14}$ erg cm^-2 s^-1 and a luminosity $L({\mathrm{H}}\alpha)_{\mathrm{tot,unabs}}\approx(1.1\pm 0.2)\times 10^{39}$ erg s^-1.

Our VLT spectra reveal for the first time He ii $\lambda$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 $\approx$3${}^{\prime\prime}\approx 150$ pc to the north of the ULX (Figures 8,9), that is $\approx$1$\aas@@fstack{\prime\prime}$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 $\lambda$4471 is stronger than He ii $\lambda$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] $\lambda$6716+6731/H$\alpha$ and [O I] $\lambda$6300/H$\alpha$ 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] $\lambda$6716+6731/H$\alpha$ with H$\alpha$ 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 $\approx 1.35\pm 0.05$ near the position of the ULX (Figure 9, Table 5) is consistent with moderate or low density $n_{e}\lesssim$ a few $\times 10$ cm^-3 (Osterbrock & Ferland, 2006). The lowest value (ratio $\approx$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 $\approx 1.23\pm 0.05$, consistent with $n_{e}\approx 100$ 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 $\approx$($150\pm 20$) in the southern part of the clump, and $\approx$($100\pm 20$) around the ULX. This corresponds to an electron temperature range $\approx$10,000–13,000 K between the two regions. The low signal-to-noise ratio of the [O III] $\lambda$4363 line prevents a more accurate spatially resolved study.

By analogy with the H$\alpha$ emission discussed in Section 3.5, we estimate now the extinction-corrected luminosity of the He II $\lambda$4686 emission, to place it in the context of other He⁺⁺ ULX nebulae in the literature. The integrated flux along the slit is $F(4686)_{\mathrm{tot,abs}}=(1.7\pm 0.1)\times 10^{-16}$ 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 $\approx$35% of the flux. This gives us a total flux $F(4686)_{\mathrm{tot,abs}}=(2.6\pm 0.2)\times 10^{-16}$ erg cm^-2 s^-1. However, this is a lower limit, because we know that the He⁺⁺ region extends $\approx$3^′′ in the north-south direction along the slit (Figure 8); thus, it is plausible that a tail of emission extends also a similar amount in the east-west direction. Using analogous arguments to those applied to H$\alpha$ (i.e., $\approx$40 per cent loss), we find a more plausible estimate of the total He II $\lambda$4686 emission as $F(4686)_{\mathrm{tot,abs}}=(2.8\pm 0.2)\times 10^{-16}$ 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 grism at the end of the same night (2001 September 01), and used it as a flux calibrator for the He II $\lambda$4686 emission. From that, we confirm an observed flux $F(4686)_{\mathrm{tot,abs}}\sim 3\times 10^{-16}$ erg cm^-2 s^-1.

Then, we need to correct for extinction. The H$\alpha$/H$\beta$ Balmer ratio around the ULX position is $\approx$3.54 (Table 4): this implies $E(B-V)\approx 0.22$ mag, $A_{4686}\approx 0.82$ mag, and $F(4686)_{\mathrm{unabs}}\approx 2.12F(4686)_{\mathrm{abs}}$. Hence, we obtain a dereddened He II $\lambda$4686 flux $F(4686)_{\mathrm{tot,unabs}}\approx(5.9\pm 0.5)\times 10^{-16}$ erg cm^-2 s^-1 and a best-estimate luminosity $L(4686)_{\mathrm{sc,unabs}}\approx(8.3\pm 0.7)\times 10^{36}$ erg s^-1.

The luminosity of the He⁺⁺ nebula is consistent with those seen in other ULXs with roughly similar X-ray luminosities, with $L_{\rm X}/L_{4686}\sim$ 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.

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 $L_{\rm X}\approx 5\times 10^{39}$ 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 $m_{275W}=(24.65\pm 0.05)$ mag and $m_{336W}=(24.69\pm 0.05)$ 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 $A_{275W}\approx 0.06$ mag and $A_{336W}\approx 0.05$ mag, and applied a distance modulus of 30.17 mag (Section 1). We obtained absolute magnitudes $M_{275W}=(-5.58\pm 0.05)$ mag and $M_{336W}=(-5.53\pm 0.05)$ 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 $(28\pm 3)$ Myr, a mass of $9.2^{+0.6}_{-0.4}M_{\odot}$, a temperature of about $(11,100\pm 1400)$ K and a radius of about $(30\pm 10)R_{\odot}$. 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 ($\sim$1 degree^-2: Luo et al. 2017; Cappelluti et al. 2009) and the high X-ray/optical flux ratio of $\sim$500–1000, we consider this scenario very unlikely. Finally, we inspected the ATCA data but found no radio emission from X-1 or its surroundings, to a 4-$\sigma$ upper limit of $\approx$50 $\mu$Jy at 5.5 GHz.

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 online¹²¹²12https://www.swift.ac.uk/user_objects/. 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 $\approx$2^′ north-west of the nucleus, at R.A.(J2000) $=22^{h}\,57^{m}\,10^{s}.02$, Dec.(J2000) $=-41^{\circ}\,03^{\prime}\,00\aas@@fstack{\prime\prime}5$ (90% confidence radius $\approx$3^′′). The X-ray source (2SXPS J225710.0$-$410300, Evans et al. 2020) was seen in the 2008 November 25 observation with $\approx$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 $\sim$10²¹ cm^-2, we estimate a luminosity $L_{\rm X}=(9\pm 2)\times 10^{39}$ erg s^-1 on 2008 November 25, and $L_{\rm X}\lesssim 3\times 10^{39}$ 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 $L_{\rm X}\lesssim 10^{37}$ 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 $L_{\rm X}=(7\pm 2)\times 10^{39}$ erg s^-1 and $L_{\rm X}=(3\pm 1)\times 10^{39}$ 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 $I\sim 24.5$ mag (Figure 14). The two stars are detected as a single star (DES J225709.98$-$410259.7) in the Dark Energy Survey Data Reslease 2 catalogue (Abbott et al., 2021). There is no radio detection in the ATCA data, down to a 4-$\sigma$ upper limit of $\approx$30 $\mu$Jy at 5.5 GHz.

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 (vignetted-corrected) 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$-$410215. This source is clearly identifiable as X-1, within the position uncertainty (1$\sigma$ error of $\approx$2$\aas@@fstack{\prime\prime}$5 in R.A. and $\approx$3$\aas@@fstack{\prime\prime}$0 in Dec.). It has $\approx$15$\pm$4 net counts (detection likelihood of $\approx$41), corresponding to an absorbed 0.2–2.3 keV flux of $(1.4\pm 0.4)\times 10^{-13}$ 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 $\sim$5 $\times 10^{39}$ 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 0.2–2.3 keV 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 $\sim$2 $\times 10^{39}$ erg s^-1 to its 0.3–10 keV luminosity.