Chemical abundances and ionizing mechanisms in the star-forming double-ring of AM 0644-741 using MUSE data

We present the analysis of archival Very Large Telescope (VLT) Multi-Unit Spectroscopic Explorer (MUSE) observations of 179 HII regions in the star-forming double-ring collisional galaxy AM 0644-741 at 98.6 Mpc. We determined ionic abundances of He, N, O and Fe using the direct method for the brightest H II region (ID 39); we report $\log\rm{(\frac{N}{O})}=-1.3\pm0.2$ and $12+\log\rm{(\frac{O}{H})}=8.9\pm0.2$. We also find the so-called `blue-bump', broad He II $\lambda4686$, in the spectrum of this knot of massive star-formation; its luminosity being consistent with the presence of $\sim430$ Wolf-Rayet (WR) stars of the Nitrogen late-type. We determined the O abundances for 137 HII regions using the strong-line method; we report a median value of $12+\log\rm{(\frac{O}{H})}=8.5\pm0.8$. The location of three objects, including the WR complex, coincide with that of an Ultra Luminous X-ray source. Nebular He II is not detected in any H II region. We investigate the physical mechanisms responsible for the observed spectral lines using appropriate diagnostic diagrams and ionization models. We find that the H II regions are being photoionized by star clusters with ages $\sim2.5-20$ Myr and ionization potential $-3.5<$$\log\langle U\rangle$$<-3.0$. In these diagrams, a binary population is needed to reproduce the observables considered in this work.


INTRODUCTION
Ring galaxies are a class of peculiar galaxies (Arp 1966) that have apparent ring-like morphologies in optical images (Arp & Madore 1987).Nowadays, ring galaxies are understood as the outcome of a rare-type (1 in 1000) of a head-on collisional event: a satellite compact galaxy crashes through another's primary disk, and the resulting ring is the conspicuous short-lived evidence of this collision (t dyn ∼ 10 8 yr; Madore et al. 2009).Ring galaxies thus are an excellent ⋆ Email: vmagg@astro.physik.uni-potsdam.delaboratory to study the evolution of galaxies, particularly the triggering and suppression of star formation on galactic scales after such interactions (Higdon et al. 2011).In the most recent atlas of collisional ring galaxies, Madore et al. (2009) report 127 ring galaxies known so far in the local Universe, of which 108 are located in the southern hemisphere and 19 have positive declinations.However, the search for ring galaxies is far from complete and we could expect at least a similar number in the northern hemisphere.Projects like DESI Legacy Imaging Surveys (Dey et al. 2019) could help with this purpose in the near future.
In order to analyse the star-formation triggered in the rings of these systems we started a series of studies of ring-type galaxies with available integral field spectroscopy (IFS) observations.In Zaragoza-Cardiel et al. (2022) and Mayya et al. (2023) we focused on Cartwheel, the archetypal ring galaxy and the most observed and modelled galaxy of its category (e.g., Higdon 1995;Renaud et al. 2018).However, there is an even rarer and short lived collisional byproduct subclass: the "double-ringed" galaxies, which has also been predicted in numerical simulations by Lynds & Toomre (1976).Here we study the double-ringed galaxy AM 0644-741, a.k.a the Lindsay-Shapley (L-S) ring, located at a distance of 98.6 Mpc, assuming a Hubble constant H0 = 67.8km s −1 Mpc −1 , Ωm = 0.308, ΩΛ = 0.692 (NASA NED 1 ).AM 0644-741 is characterized by its striking double-ring of H ii regions and star cluster complexes noticeable in optical bands, particularly in Hα (see Fig. 1), but also in the near and far-UV, tracing recent bursts of star formation.The ring, presumably driven by a radially expanding density wave triggered by the collision of a satellite object nearly perpendicular to the plane of its disk and close to its centre (Lynds & Toomre 1976;Higdon et al. 2011), has an angular diameter of 97 arcsec, the second largest (after AM 1724-622 with 125 arcsec) reported in the Southern Catalogue of ring galaxies by Madore et al. (2009), corresponding to a physical size of ∼ 46.4 kpc, using the mentioned distance.A slightly lower value for the major-axis is reported by Higdon et al. (2011, see Tab. 1), but differences are minor.The nucleus is north of the geometric center of the elliptical ring, in the direction of the major-axis.Compared to the ring, the inner disk is distinctively more red and gas depleted, with a presumed older stellar population, given the absence of HII regions ionized by young stars.Unlike its "cousin" the Cartwheel, AM 0644-741 does not show a network of spokes in its inner disk, which is practically transparent in the referred bands.Few et al. (1982) reported that the doublering is rotating at 311 ± 19 km s −1 and is expanding at a velocity (Vexp) of 128 ± 12 km s −1 , giving a dynamical age (Rring/Vexp)∼ 175 Myr.In Tab. 1 we list the main physical parameters of AM 0644-741 collected from literature.
According to the Madore et al. (2009) atlas, every ring galaxy has a likely collider detected in optical bands.AM 0644-741 is not an exception, having at least three identified candidates: C1, C2 and C3, with a projected separation from the ring nucleus of 78, 110 and 326 arcsec, respectively, and heliocentric velocities of 7000, 6750 and 6430 km s −1 , respectively (see Tab. 1 and Fig. 5 in Madore et al. 2009).Assuming roughly the same distance as the L-S ring, this is equivalent to a separation between the galaxies of 37, 53 and 156 kpc, respectively.So far, the true collider has not yet been identified and this issue remains unresolved.Higdon & Wallin (1997) were the first to report the massive star formation distribution and the basic properties of 54 star forming regions in this galaxy; we indicate these regions in Fig. 1 (orange dashed circles) as a reference.Later, Higdon et al. (2011) studied the impact of star formation on the neutral interstellar medium (ISM).Since then, no  Fisher et al. (1995); (c) Schlafly & Finkbeiner (2011); (d) Mapelli et al. (2009, and references therein); (e) Higdon et al. (2011); (f) Higdon & Wallin (1997, and references therein); (g) Wolter et al. (2018); (h) Few et al. (1982).
comprehensive study has been carried out on this galaxy.The availability of spectrographs incorporating integral field units (IFUs) on large telescopes such as Multi Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope (VLT) (Bacon et al. 2010) allows a new in-depth study of AM 0644-741.One MUSE dataset is available on this galaxy at the seeing-limited spatial resolution of 1.161 arcsec.This dataset provides optical spectra covering a range of 4750 to 9350 Å (corresponding to a rest wavelength range of 4650 to 9250 Å, considering its redshift: z=0.022) over the entire galaxy.
MUSE datacubes of ring galaxies offers the opportunity to address several problems that are particular to the ring galaxies.The first of those is the study of metallic abundances and its radial gradient.Also, ring galaxies are known to be prolific sources of Ultra Luminous X-ray (ULX) sources (Wolter et al. 2018).MUSE data offers an opportunity to study the impact of these sources on the state of high ionization potential emission lines from [Ar iv] and He ii.X-ray sources are often postulated to be responsible of these ions (Schaerer et al. 2019).Furthermore, star-forming regions pass though the WR phase for a short term during which time the blue part of the spectrum is expected to contain the so-called 'blue-bump' (hereafter, BB), made up basically of broad emission lines such as He ii and, depending on the WR-type, with contributions of C iii-C iv or N iii-N v.However, the detection of BB is heavily metallicity dependent.All these phenomena have been addressed in the Cartwheel using the MUSE data in our previous papers (Mayya et al. 2023;Zaragoza-Cardiel et al. 2022).For example, in the Cartwheel, which has around 1/4 Z⊙, we found enrichment of O in the ring H ii regions without the corresponding enrichment in N and Fe, metals expelled by intermediate-age and low-mass stars.In the Cartwheel, we did not find signature of X-ray ionization even in H ii regions coinciding with ULXs, and those where He ii λ4686 line is detected.
We employ the available MUSE observations to con-  Higdon & Wallin (1997) are indicated in dashed orange circles (H1-H53), and the location of X-ray sources, some of them ULXs, from Wolter et al. (2018) by red circles (W1-W9) and their positional error ellipses with blue contours.The majority of H ii regions identified with MUSE are associated with a star-formation complex resolved by HST.Although ULX sources are located in the star-forming ring, its association with a cluster is not straightforward.The brightest H ii region, ID 39, is also a WR cluster coinciding with the location of the most luminous ULX (W1).See text for details.
tinue our series of studies on the star-formation triggered in the ring of this type of galaxies.Here in particular, we study the ionizing mechanisms and the chemical abundances in the star cluster complexes hosted in the H ii regions that shape the double-ringed morphology of AM 0644-741.We are interested in comparing our results in this galaxy with those obtained in the Cartwheel, to better understand the nature and evolution of ring structures in galaxies with different environments, star formation histories and metallicities in its post-collisional stage.Thanks to new spectroscopic data cubes like those of MUSE/VLT these studies are now possible.In a Hα image we constructed using the MUSE dataset (see Sec. 2) we identified 179 H ii regions in the double-ring of AM 0644-741.At the distance of the L-S ring, MUSE spectra are available at physical scales of ∼556 pc.At the spatial resolution of the Advanced Camera for Surveys (ACS) Wide Field Channel (WFC) images of the Hubble Space Telescope (HST), which are the highest resolution images available for AM 0644-741 (0.05 arcsec/pix), we can associate each MUSE-identified H ii region with a population of super star clusters, which presumably provide the ionization of the H ii regions.A colour-composite image using our MUSE Hα image and HST filters is shown in Fig. 1.All images used in this figure are astrometrized as explained in Section 2.2.However, the point spread function (PSF) of the images are not matched and correspond to the respective observed values given in the section below.
This article is structured as follows: in Sec. 2 we describe the spectroscopic dataset, the constructed catalog of H ii regions, the extraction of the spectra and measurement of the emission line fluxes; in Sec. 3 we determine the abundances of our objects; we study the ionization sources with diagnostic diagrams and models in Sec.4; our results are discussed in Sec.5; finally, a summary and our conclusions are given in Sec. 6.

VLT/MUSE observations
MUSE is a panoramic integral-field spectrograph at the 8m VLT of the European Southern Observatory (ESO)2 , operating in the optical wavelength range from ∼4750 to ∼9351 Å with a spatial sampling of 0.2 arcsec pixel −1 , a spectral sampling of 1.25 Å pixel −1 and a spectral resolution FWHM∼3 Å (Bacon et al. 2010).This spectral resolution corresponds to σ ∼40-60 km s −1 , which is not good enough to resolve the lines but sufficient to detect the strong lines to measure abundances.The public MUSE data cube of AM 0644-741 galaxy was retrieved from the ESO Science Archive Facility3 .The data cube was already flux and wavelength calibrated, ready for scientific exploitation.The data were obtained during a single observing run on November 9, 2020; the Principal Investigator (PI) is Bernd Husemann (Program ID: 106.2155); dedicating a total exposure time of =1350 s (effective time of =714.5 s) in a single observation.A sky coverage of observations of 2.1 arcmin 2 , encloses the entire star-forming ring of the AM 0644-741 galaxy, as can be seen in Fig. 1; here we show an RGB image formed by combining the HST/ACS/WFC filters in F814W, F625W and F435W as red, green and blue components, respectively; the Hα image constructed from MUSE data is used as a fourth reddish component.The MUSE images have a seeing-limited resolution of Full Width at Half Maximum (FWHM) of 1.162 arcsec, which corresponds to a spatial scale of ∼556 pc at the distance of the L-S ring galaxy.We list the main observation details in Tab. 2.

MUSE data cube and astrometry
We used the reduced 3-D data cube as a starting point in our analysis.The tool QFitsView4 (Ott 2012) was used for the extraction of images at selected wavelengths, as well as spectra of selected regions.A continuum image covering the entire spectral range of MUSE is prepared to transform MUSE images into International Celestial Reference System (ICRS) as defined by the coordinates of the point sources in the 2MASS catalogue.The Field of View (FoV) of the MUSE image of AM 0644-741 contains three 2MASS stars which is insufficient to obtain accurate solutions.We hence carried out the astrometry in two steps, first we brought the HST F814W images into ICRS using 14 2MASS stars, and then we identified 13 compact objects in the MUSE continuum image and the F814W image, which we used to find astrometric solution of the MUSE image.The astrometric accuracy of the resulting image is 0.1 arcsec.We used the iraf tasks ccmap and wregister to carry out the astrometric calibration.

Catalog
For our study in AM 0644-741 it was necessary to build a new catalog of H ii regions using the available MUSE observations.As a first step, we generated a continuum-free Hα image from the MUSE datacube using QFitsView.For achieving this, we summed fluxes in a 8.8 Å window centered on Hα at the redshifted wavelength of this galaxy subtracting a continuum 44 Å away on either side of the Hα line.
With these values we ensure that the emission line is covered by the width of the filter, taking into account the shift of the lines due to its kinematics.
Figure 2. VLT MUSE redshift-corrected spectrum of the cluster complex ID 39, WR1, located in the SW section of the ring of the AM 0644-741 galaxy (see Fig. 1).The so-called 'blue-bump' (BB) WR feature at 4686 Å, as well as the most common nebular lines of typical H ii regions, from [Fe iii] at 4658 Å to [S iii] at 9068.6 Å, are indicated.The spectrum is shown normalized to its best-fit continuum.
The continuum-subtracted Hα image (the reddish component in Fig. 1) allows the identification of H ii regions using source extractor codes such as pyhiiextractor (Lugo-Aranda et al. 2022), SExtractor (Bertin & Arnouts 1996), etc.The former code measures accurate fluxes of H ii regions, taking into account corrugated boundaries.We opted to measure fluxes by fitting a Gaussian function to line profiles on spectra extracted using circular apertures of fixed radius around the identified regions.This method ensures that the fluxes of all lines are measured over the same areas.For this reason, we used SExtractor to identify the locations of the objects for later extraction of their spectra.We identified a total of 184 regions with Hα emission in the entire FoV of this galaxy.Then, spectra were extracted with apertures of 1.162 arcsec radius, which is equivalent to 1 seeing FWHM, for all regions automatically selected.Finally, after careful inspection of the spectra, five objects were later identified to be spurious sources (which include the nucleus of the galaxy and probable background stars), ultimately resulting in a catalog of 179 H ii regions.Most of these sources are located in the double-ring of the galaxy (see Fig. 1).The spectrum of the most conspicuous H ii region in AM 0644-741 is shown in Fig. 2. The foreground Galactic extinction in the direction of AM 0644-741 is AV = 0.35 mag (Schlafly & Finkbeiner 2011).The extracted spectra were first corrected for this foreground extinction using the Galactic reddening curve of Cardelli et al. (1989).The selected regions are at least an order of magnitude brighter in surface brightness with respect to the diffuse ionized gas (DIG), implying that the contamination of the observed line ratios by the DIG is negligible.Moreover with the recent understanding that the DIG in star-forming galaxies is created due to photoionization by the photons leaking the H ii regions (Della Bruna et al. 2020;Belfiore et al. 2022), it is expected to occupy the immediate surroundings of H ii regions in the disk rather than the regions along the line of sight to H ii regions.Hence, we did not apply any correction to the observed line ratios.
AM 0644-741 has nine identified X-ray sources of which, excluding the galaxy nucleus and a background active galactic nucleus (AGN), seven were identified as ULXs by Wolter et al. (2018).The ULX sources are located in the ring of the galaxy and some of them coincide with the projected location of an H ii region hosting a star-forming complex (see Fig. 1).At least three of the ULXs in the ring are associated with a H ii region of our sample.We address the nature and probable role of the ULXs in the ionization of their host H ii regions in Sec. 4.

Measurement of line fluxes
The analysis of the ionizing mechanisms of the H ii regions in the double-ring of AM 0644-741 and the determination of their nebular abundances requires the previous determination of de-reddened flux ratios of the nebular lines relative to the flux of Hβ.Considering that our sample of H ii regions might be affected by the presence of an underlying absorption feature (e.g.Balmer lines, Hβ in particular), first we fitted their continuum with Single Stellar Population (SSP) synthesis models.We used the GIST pipeline (Bittner et al. 2019), making use of the most recent Charlot & Bruzual SSP models (Charlot & Bruzual, in preparation), to fit the continuum and the absorption lines over the entire observed wavelength range of our spectra: 4650-9250 Å, where the MUSE spectral resolution is ∼ 3 Å.Then we subtracted the fitted continuum to obtain pure nebular spectra, which is the one we used for later analysis.
Around 30 nebular lines were identified, from [Fe iii] at 4658 Å to [S iii] at 9068.6 Å, in the spectrum of the brightest H ii region in AM 0644-741, ID 39, most of which have been marked in Fig. 2.These lines were analysed using the Gaussian line fitting option of the iraf task splot.The measured line fluxes were corrected for extinction by using the obtained c(Hβ) value assuming an intrinsic Balmer-decrement ratio of Hα/Hβ = 2.86, for a case B photoionised nebula, corresponding to mean values for Te in the range 2000 K and 12000 K and ne between 100 cm −3 and 1200 cm −3 (see Osterbrock & Ferland 2006).We used the reddening curve of Cardelli et al. (1989) with RV=3.1.The resultant line fluxes and statistical errors are listed in Tab. 3 for the brightest H ii region of the sample.
Reddening-corrected fluxes for all the objects are reported in a Table as extra-material.The distribution of the visual extinction (AV) and the reddening corrected F (Hβ) is shown in Fig. 3.It can be noticed that AV tends to increase with F (Hβ).A median value of AV ∼ 0.84 mag is indicated by a dotted vertical line.The correlation between AV and F (Hβ) arises because the analyzed H ii regions adhere to a Kennicutt-Schmidt star-formation relation (Barrera-Ballesteros et al. 2020).In other words, the gas density of a star-forming region, which dictates AV through the almost constant gas-to-dust ratio, correlates with the star formation rate (SFR), which is traced by Hβ.It can be recalled that Cartwheel H ii regions do not show such a correlation (Zaragoza-Cardiel et al. 2022).The median values obtained here are lower than the corresponding values for the bright ring H ii regions in the Cartwheel but are comparable to the median AV of the fainter regions in the outer ring of the Cartwheel.

Direct Method
Temperature-sensitive lines are detected in only one (ID 39,) of the 179 H ii regions in AM 0644-741, making it possible to determine abundance using the direct method (DM) only for this region.This happens to be the brightest nebular region with log(F(Hβ)/[erg cm −2 s −1 ])= −13.567 ± 0.007 (see Fig. 3) and SNR(Hβ)= 141 (see Tab. A1) and host the only regions where a WR feature is detected (see Fig. 2) the location of this brightest H ii region also coincides with the brightest ULX (W1) reported in this galaxy (see Fig. 1).Determining the O abundance of this region is key to estimate the WR population responsible for the broad He ii λ4686 line.We address this issue in Sec.4.1.
We followed the methodology used to determine O abundances in the Cartwheel H ii regions (Zaragoza-Cardiel et al. 2022).First we determined the physical conditions of the ionized gas: electron temperature (Te) and electron density (ne).Te and ne are estimated simultaneously with PyNeb (Luridiana et al. 2015).We use the three ionization zones approximation from Garnett (1992) (1) Densities determined from [S ii]λ6717/λ6731 were used for all the three zone lines.In Tab. 4 we list our results for Te, ne, the ionic abundances of He, N, O and Fe for WR1.
In Fig. 4 we compare log ( N O ) vs. 12+log ( O H ) for the WR H ii region detected in AM 0644-741 with H ii regions in other galaxies: the prototype ring-galaxy Cartwheel (Zaragoza-Cardiel et al. 2022) and other ring galaxies (Bransford et al. 1998); with irregular galaxies (Garnett 1990); and other well known galaxies like M 101 (Kennicutt et al. 2003), M 31 (Zurita & Bresolin 2012), M 33 (Toribio San Cipriano et al. 2016) and M 81 (Magrini et al. 2017), with H ii regions of a sample of galaxies studied by Arellano-Córdova & Rodríguez (2020) and objects from the CALIFA survey (Espinosa-Ponce et al. 2020).Note that all abundances, except those from (Bransford et al. 1998) and (Espinosa-Ponce et al. 2020), are obtained using the DM.Following Zaragoza-Cardiel et al. (2022) we also indicate the schematic representation of the expected evolution of the N/O ratio for a dwarf galaxy from Garnett (1990) as a reference.The N/O ratio of WR1 is close to H ii regions in other irregular galaxies.However, the O abundance for AM 0644-741, with 12 + log ( O H ) = 8.9, is higher by as much as 0.6 dex, and is among the highest values measured using the DM.It is likely that the equation that we have used to determine temperature of the high ionization zone, obtained for low metallicity irregular galaxies, underestimates the temperature, thus slightly overestimating the abundances.Temperature calibrations for high metallicity regions are lacking (see e.g.Arellano-Córdova & Rodríguez 2020).
In Fig. 5 2016).WR1 in AM 0644-741 follows the trend of the H ii regions in these galaxies, the higher the abundance of O, the lower that of Fe.However, the measured O abundance in AM 0644-741 is a clear outlier, which as mentioned above, is likely due to the lack of reliable metallicity calibrations at the high-metallicity end.

Strong-line Method
We determined the abundances using the strong-line method (SLM) for all the H ii regions in which we could detect In order to check for any gradient, galactocentric or azimuthal, of the O abundances in the double-ring of AM 0644-741, we used a set of ellipses indicated in Fig. 6 to de- fine a galactocentric radius (R) and position angle (PA) of our catalog of H ii regions.AM 0644-741 resembles its cousin Cartwheel in the sense that the nucleus is not at the geometrical center of the star-forming elliptical ring.We hence followed the moving-centre method adopted by Marcum et al. (1992) for the Cartwheel to define the ellipses.
In this method, the center of successive ellipses is changed smoothly from the nucleus for the inner ellipses to the center of the ring of the outer ellipses.A more detailed description of this procedure is given in Zaragoza-Cardiel et al. (2022, in their Sec. 4.3).
In Fig. 7 we plot the O abundance of the H ii regions vs. the galactocentric radius.We indicate the median value of 12 + log ( O H ) = 8.52.By a linear fit to the L-S ring data points, we get a slight slope indicating a small gradient of −0.0012 ± 0.0004 dex/kpc.In comparison, the Cartwheel shows a gradient of −0.017 ± 0.0001 dex/kpc (Zaragoza-Cardiel et al. 2022) which is comparable to values found in spiral galaxies (Sánchez 2020).We find the SLM-determined O abundance of WR1 is slightly above the median value, but only by 0.05 dex.In Fig. 8 we show the O abundances vs. its position angle (PA).Here we did not find any indication of an azimuthal gradient.We list our results for each object in Tab.A1.It may be noted that the O abundance of WR1 determined from the DM is ∼ 0.3 dex higher than that determined from the SLM, which is marginally higher than the 0.2 dex error in the former method.

IONIZATION STATE OF THE H ii REGIONS
The availability of spectra covering almost the entire optical range allow us to address the ionization mechanisms of the Hα-emitting regions in the MUSE FoV.We use Xiao et al. (2018) calculations based on BPASS (Eldridge et al. 2017) and Cloudy (Ferland et al. 1998) models in standard BPT diagrams (Baldwin et al. 1981) to study the ionization sources in the double ring of AM 0644-741.We also discuss the role of the WRs and ULXs in the ionization when H ii regions are associated to these sources.

H ii region containing WR stars
WR stars are formally defined by their emission-line dominated spectra arising from their strong winds.The core-He burning objects among them, also called "classical" WR stars, represent a late stage in the evolution of massive stars,  (Bransford et al. 1998, black dots); irregular galaxies (Garnett 1990, yellow    where a considerable amount of their outer layer has been lost.Assuming single-star evolution, WR stars start their lives on the main sequence as O stars with Minit ⩾ 25 M⊙ at Z⊙ (e.g., Georgy et al. 2012;Chieffi & Limongi 2013;Chen et al. 2015).See also Massey (2003) for estimated masses (Minit ⩾ 20 M⊙) of the progenitor stars for different WR types, at different metallicities.While different assumptions about mass loss or the formation of a WR stars due to binary interaction can shift the absolute mass limits, all WR stars are so massive that they usually cannot be much older than ∼ 2 − 4 Myr when reaching the (classical) WR stage.Characterized by significant mass loss rates of Ṁ ≈ 10 −4 − 10 −5 M⊙ yr −1 , WR stars are expected to inject mechanical energy, and chemically processed material into the local ISM (see the review by Crowther 2007, and references therein).With their inherently hot temperatures, classical WR stars are major sources of hydrogen ionizing photons, while their He ii ionizing flux strongly depends on the wind strength and vanishes for more dense winds (e.g., Sander & Vink 2020;Sander et al. 2023;Sixtos et al. 2023).Given the manifold impact of WR stars on their host environment, WR stars are important engines of the cosmic matter cycle, for example in the context of ongoing star and planet formation.
For the one region where we identified a BB (ID 39 or WR1) in its spectrum, we can derive an approximate num- ber of WR stars.For this, we first measured the flux of the broad He ii λ4686 with a simple Gaussian fitting (see Fig. 9).Similar to the study of Mayya et al. (2020, in NGC 1569), the line of [Fe iii] λ4658 is also present in emission, but it is well separated from the BB, so there is no need for a de-blending procedure, which was necessary in Gómez-González et al. ( 2021).Given a distance of 98.62 Mpc, we obtain the luminosity of the He ii line, assuming it dominates the BB: L(He ii-broad)= 7.78 × 10 38 erg s −1 .We do not detect C iv λλ5801, 5812, a.k.a. the 'red-bump' (RB), ruling out a large presence of WC or WO-type stars.This also justifies our assignment of the entire fitted flux as that of the broad He ii line of L(He ii) as WC stars could contribute to the BB with a C iii λ4636 line, sometimes even exceeding the intensity of He ii.2020) in WR galaxies (defined by Conti 1991).Crowther et al. (2023) provides detailed information for the subtypes of each classification.In their Tab. 2 they report He ii luminosities for WN2-5w, WN3-7s, WN6-8, WN9-11, WN5-7h and Of/WN that go from 0.5 − 2 × 10 36 erg s −1 , with uncertainties of the same order, at MW metallicity.Given the distance of our object and the quality of our spectrum (SNR, spatial resolution), we can not provide a detailed subclassification for the WN stars in WR1, since He ii is the only broad line detected.However, if we consider the values by Crowther et al. (2023) the number of WN stars in WR1 is the exact value depending on the WN subtype which is in the range between 400 and 1500 WR stars, consistent with the value obtained using the expression from López- Sánchez & Esteban (2010).
We further estimate the number of O-type stars in the H ii regions by assuming a "typical" luminosity of L(Hβ)=4.76 × 10 36 erg s −1 emitted by O 7V stars (López-Sánchez & Esteban 2010).Considering a derived number of 6620 O-type stars in WR1, we obtain a WR/O-ratio of 0.1, which would be consistent with the time that O-type stars are expected to later spend in their WR phase, namely typically ∼ 10% of their lifetime (see Crowther 2007).and W5 (AGN a ), these objects have enough luminosities (L X > 1 × 10 39 erg s −1 ) to be considered ULX sources.

ULX sources
ULXs are point X-ray sources located off-center in their host galaxies and having X-ray luminosities LX > 3×10 39 erg s −1 , i.e. exceeding the Eddington luminosity of an accreting black hole with M• ≈ 20 M⊙ (Kaaret et al. 2017).Most likely, ULXs are binaries consisting of a massive donor star and a neutron star or a few M⊙ black hole, accreting supercritically (Poutanen et al. 2007;Stobbart et al. 2006;Gladstone et al. 2009;Sutton et al. 2013).However, stellar evolutionary models predict that some ULXs indeed may contain black holes with masses > 10 M⊙ (e.g.Finke & Razzaque 2017;Marchant et al. 2017;Hainich et al. 2018).These ULXs would represent an advanced evolutionary stage of a very massive binary star, and therefore are expected to be associated with young massive clusters.Indeed, it is not uncommon to find ULXs located in the vicinity of massive star clusters (Berghea et al. 2013;Poutanen et al. 2013;Oskinova et al. 2019).
The AM 0644-741 galaxy presents an interesting case for studies of ULXs populations.Nine X-ray sources have been detected in this galaxy (Wolter et al. 2018, see their Fig. 1).Among them, one is the nucleus of AM 0644-741, and another one is a background AGN (Heida et al. 2013) (see also Appendix B).Seven remaining X-ray sources are ULXs.Three of them (W1, W4, and W9) are located at < 1.1 arcsec in projection from star clusters and their H ii regions (WR1, 92, and 142).The other three ULXs are also located within the star-forming ring and are likely associated with nearby H ii regions.Only one ULX, W8, located in the NE section of the ring, has no obvious optical counterpart H ii region or star cluster.The projected separation of the X-ray sources to their nearest H ii regions are listed in Tab. 6.
The ULX W1 is especially interesting since its position coincides with the brightest H ii region in its host galaxy surrounding a cluster of WR stars (Figs. 2).Given the age and the mass of the associated star cluster, we tentatively suggest that W1 is powered by the accretion onto a black hole.Several ULXs have been observed in association with He iii regions (Pakull & Mirioni 2003).However, not all ULXs are associated with a nebular region (Feng & Soria 2011).For example in the Cartwheel only 10 of the 17 ULX sources have associated He ii emission.However, line ratios of commonly observed nebular lines do not show any signature of the ionization by X-ray sources (Mayya et al. 2023).No nebular He ii lines are detected in the MUSE spectra of the ULX in AM 0644-741.This implies that the presence of a ULX and large numbers of WR stars are not a sufficient condition for producing a He iii nebula as discussed recently by e.g.Schaerer et al. (2019) and Umeda et al. (2022).Given the higher than solar metallicity of AM 0644-741, the winds of the WR stars are likely too dense to provide a sufficient budget of He ii ionizing photons.Recently, Oskinova & Schaerer (2022) suggested that the lower temperature of superbubbles around lower metallicity star clusters could help to explain the observed prevalence of He iii nebulae in low-metallicity galaxies.
Another interesting source is W3, the brightest X-ray source on the FoV of AM 0644-741.Heida et al. (2013) identified this object as an AGN due to detecting [Mg ii] λ2798 and C iii] λ1909 with the VLT/FOcal Reducer and low dispersion Spectrograph (FORS2) observations.In Fig. B1 we show the MUSE spectrum extracted at the position of W3, identified as an Hα-emission region in our first SExtractor catalog.This mis-identification happened due to the [Mg ii] λ2798 line of the AGN being redshifted precisely to the wavelength of Hα, which was the criteria to construct our catalog.Additionally, we identify [O ii] λ3727 and [Ne iii] λ3869 at a similar redshift of z ∼ 1.4.Their redshifted wavelength range was not covered in previous observations.Thus, we independently confirm that W3 is a background AGN at z ∼ 1.4.On top of the wide emission line, we identify a narrow Hα absorption line at the redshift of AM 0644-741 (z∼0.022).We use BPT diagrams to check whether any of the observed lines of regions containing ULX sources require ionization from X-rays.

BPT diagrams
We use the standard diagnostic diagrams to determine the physical parameters such as the age, ionization parameter (log⟨U ⟩) and gas density (log nH) for the H ii regions in the double ring of AM 0644-741.For this purpose we use the photoionization calculations of Xiao et al. (2018) which are based on Cloudy models (Ferland et al. 2017) using single and binary population synthesis models of BPASS (Eldridge et al. 2017).We found that the observed points lie between the calculated values for metallicities Z= 0.014 and 0.020.We hence generated a new set of tables corresponding to Z= 0.017 by interpolating the fluxes of each nebular line from the Z= 0.014 and 0.020 tables.These tables were generated for both single and binary star models.
The EW (Hβ) is a parameter commonly used as an indicator of the age, whereas [O iii] λ5007/Hβ, [N ii] λ6583/Hα, and [S ii] λ6717 + 6731/Hα are sensitive to the ionization state of a starburst region.Flux ratios of the [S ii] doublet are sensitive to the ne of H ii regions.We hence compare the observed values of these quantities with the results from photoionization models.In Fig. 10, we plot the [O iii] λ5007/Hβ line ratio vs. EW (Hβ) on the left and [S ii] doublet line ratios vs [S ii] λ6717 + 6731/Hα on the right.Errors on observed quantities are plotted in both axis but is noticeable only when it is larger than the symbol size.The three H ii regions containing ULX sources, one of which is also a WR source, are shown by large red coloured symbols.
On the left figure, photoionization models are shown for single and binary models with continuous and dashed lines, respectively, at five values of logU ranging from −3.5 to −1.5 at an interval of 0.5 dex.Along each curve, age of the ionizing cluster changes from 1 Myr to 100 Myr, with the colour of the curve denoting interesting ranges of ages: 1-2.5 Myr (blue), 2.5-5 Myr (cyan), 5-10 Myr (green), 10-20 Myr (yellow) and 20-100 Myr (red).The plotted models correspond to density log nH[cm −3 ]=2.
On the right Figure, we show the binary evolutionary tracks for log nH[cm −3 ]=1.5 and 2.5.The plotted [S ii] doublet ratio becomes insensitive to density for nH ≲ 30 cm −3 , whereas the ratio decreases for densities higher than the plotted limit.The Figure illustrates that AM 0644-741 regions lie between the two plotted ranges, and hence we take a mean density of nH = 100 cm −3 .
Binary models at low ionization (−3.5 < log U < −3.0) at ages >5 Myr at ne of 100 cm −3 fit the four plotted quantities simultaneously for the majority of the regions.We derive an age of ∼6 Myr with or without binary for WR1, which is also a ULX (red asterix), whereas for the other two ULX sources, we derive ages of 10 and 25 Myr respectively for ID 92 and ID 142.Only binary models reproduce all the observed quantities for these two ULX sources.
In Fig. 11 we plot the observed H ii regions in the three standard BPT diagrams (Baldwin et al. 1981 [O i] λ6300/Hα line ratios.The same photoionization models that are used in the left panel of Fig. 10 are shown on these diagrams.In addition, we draw the maximal starburst locus of Kewley et al. (2006) in these plots.As expected, all the H ii regions are located in the star-forming zone, including those containing ULX and WRs.In fact, the location of these ULX sources does not differ from that of the rest of the H ii regions in these BPT diagrams.The X-ray photons from ULX sources are expected to ionize the neutral medium surrounding the H ii regions, creating energetic free electrons in the cold medium.These free electrons collisionally excite oxygen in the cold neutral medium, thus increasing the [O i] λ6300/Hα ratio to values above those for normal H ii regions.(Gúrpide et al. 2022).No such effect is seen, and hence the ULX sources do not contribute in any significant way to the ionization of H ii regions.It can be noticed that the same low ionization (−3.5 < log U < −3.0) binary models at ages >5 Myr and ne of 100 cm −3 that best fit the [O iii] λ5007/Hβ vs EW (Hβ) diagram also fit the plotted quantities simultaneously for the majority of the regions.
As mentioned in the beginning of this section, we have used the results of the photoionization code for Z=0.017.This value corresponds to a gas phase metallicity of 12 + log( O H ) = 8.88 for dust-free H ii regions, whereas it would be 8.65 for dust-to-metal mass ratio of ξ d =0.5 (Gutkin et al. 2016).The inferred gas phase metallicity is closer to the metallicity obtained from the DM rather than the SLM.At lower metallicities the [O iii] λ5007/Hβ line ratio requires a higher logU as compared to the [N ii] λ6583/Hα line ratio.
Single star evolutionary models in BPASS SSP code are able to reproduce the observed values only for regions whose EW(Hβ)>50 Å, which corresponds to an age of <6 Myr.At older ages, line ratios fall rapidly for single star models, whereas the ratios are marginally higher for binary star models.This trend seen in AM 0644-741 is similar to the results obtained by Xiao et al. (2018) for the sample of H ii regions used in their study.

Abundances
Until now, there has not been a comprehensive study of the chemical abundances in AM 0644-741.The first reports in this regard were made by Higdon et al. (2011), who reported an O abundance of 12 + log ( O H ) = 9.1 for three regions in the ring of AM 0644-741.The locations of their slitlets correspond to our objects identified as ID 84 (their slitlet 1); ID 44, 42, 39 and 37 (slitlet 2); and ID 9 (slitlet 3).They used EFOSC2 spectra covering the spectral range from 6200 to 7800 Å.Given the wavelength range limitations of their spectra, they obtained these values based on F([N ii])/F(Hα) and F([N ii])/F([S ii]) relations from Nagao et al. (2006).Actually, Higdon et al. (2011) observed the 3500 to 5500 Å wavelength range, but due to problems in the reduction process did not use these spectra in their analysis, which is probably the reason why they did not report the WR feature at 4686 Å in their slitlet 2, where the brightest H ii region ID 39 (WR1) is located.
Given the FoV and wavelength range covered by MUSE observations we are able to determine O abundances for 137 regions in the ring of AM 0644-741, including those covered by Higdon et al. (2011).We report a median value of 12 + log ( O H ) = 8.52, i.e. slightly subsolar.However, caution should be exercised when comparing this value obtained with the S-calibrator from Pilyugin & Grebel (2016) to those values obtained with different SLM calibrators, as differences of 0.5 dex are common.Conversions between abundances from different SLM calibrators up to the precision of less than 0.1 dex for most of the SLM calibrators do exist (Espinosa-Ponce et al. 2022).We also obtain a slight gradient of −0.0012 ± 0.0004 dex/kpc among the ellipses 7 and 11.With this estimation we were able to compare with proper ionizing models in BPT diagrams and to determine the number of WR stars in WR1.Using the DM, we obtain a supersolar value with 12 + log ( O H ) = 8.9 ± 0.2, albeit already 0.2 dex lower than previously reported by Higdon et al. (2011).

Comparison with the Cartwheel
AM 0035-335 (the Cartwheel) and AM 0644-741, are probably the most iconic and studied ring-galaxies in the literature.This is in part explained by their striking ring morphology and also their relative proximity, located at 128 Mpc and 98.6 Mpc, respectively. In Zaragoza-Cardiel et al. (2022) and Mayya et al. (2023) we started a series of studies in ring-type galaxies with available MUSE data to analyse the star-formation triggered in the ring of these peculiar of galaxies.In Zaragoza-Cardiel et al. (2022) we reported that the H ii regions in the ring of the Cartwheel have [O i] λ6300/Hα, our objects are in another zone, at the bottom left of the BPT diagrams relative to the Cartwheel regions, where the ionization parameter can be as high as log⟨U ⟩= −2.0, an order of magnitude higher than in AM 0644-741.Also, Mayya et al. (2023) report the detection of neb-ular He ii λ4686 in 32 H ii regions in the Cartwheel, with a mean I(He ii λ4686)/I(Hβ) ratio of 0.010±0.003.In contrast, we do not detect nebular He ii λ4686 in the L-S ring.Instead, we detect the broad He ii λ4686 in the spectrum of a knot of star-formation with a luminosity consistent with the presence of at least ∼430 WR stars.The non-detection of nebular He ii λ4686 in spite of the detection of a WR feature in the L-S ring is likely due to metallicity difference.At the slightly higher metallicity of L-S ring, it is expected that the atmosphere absorbs the He+ ionizing photons more efficiently than at lower metallicity of the Cartwheel.
Like the Cartwheel, AM 0644-741 contains a relatively high number of ULXs, conforming the universal scaling of the X-ray luminosity function and star formation rate in galaxies (SFR, Mineo et al. 2012).According to Wolter et al. (2018, and references therein), Cartwheel with a SFR of 20 M⊙/yr has 15 ULXs and AM 0644-741 with a SFR of 11.2 M⊙/yr has 7 ULX sources.An anti-correlation between the number of ULXs per host galaxy normalized to the SFR vs. the metallicity of the host galaxy is empirically established (Wolter et al. 2018;Lehmer et al. 2021, and references therein).The number of ULXs normalized to the SFR in this galaxy is consistent with the metallicity we report in this work.However, we do not find any evidence of additional ionization by X-ray sources in the H ii regions containing ULX sources in AM 0644-741, a result which is similar to that found by Mayya et al. (2023) for the Cartwheel H ii regions.

SUMMARY AND CONCLUDING REMARKS
We have presented an analysis of a sample of H ii regions in the star-forming double-ring of the AM 0644-741 collisional galaxy using spectra we extracted from available VLT MUSE observations.We constructed a new catalogue of 179 objects following a semi-automatic approach with the standard tool SExtractor based on the Hα emission of these sources.Until now, this is the largest sample of H ii regions analyzed in this galaxy.This sample could serve as a reference for future studies on star formation triggered in the rings of post-collisional galaxies.After a proper extraction, dereddening, correction for underlying absorption using SSP synthesis models and the flux measurement of all the emission lines present in the spectra, we investigated the chemical abundances and ionization state of these sources.Here we summarize our findings: • We determined the O abundances for 137 H ii regions using the SLM.The rest of the objects did not have all the necessary lines to determine their abundance.We report a median a median O abundance value of 12 + log (  2012, and references therein).A linear fit to the data points among the ellipses including the H ii regions of the ring indicates a slight gradient of −0.0012±0.0004dex/kpc.There is no indication of an azimuthal gradient.This information was used to select appropriate photoionization models based on the metallicity for further analysis of the physical conditions of H ii regions in this galaxy.
• We calculated ionic abundances of He, N, O and Fe using the DM for the brightest H ii region, ID 39.Only this region has all the necessary lines to determine chemical composition via this method.We find values of 12 + log ( He H ) = 10.75 ± 0.14; log ( N O ) = −1.3± 0.2; 12 + log ( O H ) = 8.9 ± 0.2 and log ( Fe O ) = −2.7 ± 0.3.We also determine other physical parameters of the H ii regions in the double-ring of this galaxy like flux, SNR and EW of Hβ, visual extinction AV and report updated radial velocities.
• We found a WR feature, the BB, in the brightest H ii region, naming it WR1.The luminosity of the observed He ii λ4686 broad line is consistent with the presence of at least ∼400 WNL WR stars in this knot of massive starformation.We have carried out a careful search for nebular He ii λ4686 in all the H ii regions of this galaxy, but do not detect any narrow He ii λ4686 in any of the analyzed regions.
• We estimate the number of O-type stars in the H ii regions assuming a typical luminosity emitted by O 7V stars.The L(Hβ) in WR1 in particular, is consistent with a number of 6620 O-type stars, giving a WR/O ratio of 0.1.This is consistent with the length of the WR phase, ∼ 10% of the lifetime of the massive star progenitor.
• We observe that the location of at least three of our objects (WR1, 92 and 142) coincide with of one of the ULX sources reported by Wolter et al. (2018) in this galaxy (W1, W4 and W9).The ULXs are related to the star-forming regions in the ring (Wolter et al. 2018).However, we encountered that the exact H ii region in our sample is not very clear for half of the ULX sources.Other three ULX sources (W2, W3 and W8) are located a projected distance > 1 arcsec from the nearest H ii regions (ID 13,158 and 113).The analysis of similar ring systems with the presence of ULXs could help to settle their nature and the role they play in the ionization of star-forming regions.However, the optical spectrum does not show line ratios characteristic of ionization by an X-ray source.
• We independently discard the ULX nature of the W3 (Wolter et al. 2018), reporting two additional lines from those reported by Heida et al. (2013) at z ∼ 1.4 by using novel spectra covering a longer wavelength range.Our result supports the AGN nature of W3.Moreover, we show that its location coincides with a star-like counterpart in optical bands using available HST images.
[O i] λ6300/Hα, we find that our H ii regions are consistent with photoionization by star clusters with ages of 2.5-20 Myr.Comparing the observed line-ratios with single and binary evolution SSP models, we estimate −3.5 <log⟨U ⟩< −2.9 and log⟨nH⟩.In three BPT diagrams, a binary population is needed to reproduce the observations.
• In this work we have compared the star-forming regions in the two collisional ring galaxies observed so far with VLT MUSE: the Cartwheel and AM 0644-741.They are similar in morphology but turn out to be different in metallicity.The Cartwheel is a relatively metal-poor galaxy (Zaragoza-Cardiel et al. 2022) with a single external ring while AM 0644-741 is a double-ring metal-rich galaxy.
• In the Cartwheel, He ii nebular has been reported by Mayya et al. (2023).In contrast, AM 0644-741 does not show any nebular He ii but broad He ii in one region.These find-ings are consistent with the metallicities determined for the two galaxies.

Figure 1 .
Figure 1.Colour-composite image of the double-ring galaxy AM 0644-741, formed using the HST/ACS/WFC images in the filters F814W, F625W and F435W as red, green and blue components, respectively; and a new Hα image constructed from MUSE data (FWHM=1.161arcsec) as a fourth reddish component.The 179 H ii regions studied here are identified by green circles of 1.162 arcsec radius (∼556 pc at D= 98.62 Mpc), which is twice the sky resolution size of MUSE.Star forming regions from Higdon & Wallin (1997) are indicated in dashed orange circles (H1-H53), and the location of X-ray sources, some of them ULXs, from Wolter et al. (2018) by red circles (W1-W9) and their positional error ellipses with blue contours.The majority of H ii regions identified with MUSE are associated with a star-formation complex resolved by HST.Although ULX sources are located in the star-forming ring, its association with a cluster is not straightforward.The brightest H ii region, ID 39, is also a WR cluster coinciding with the location of the most luminous ULX (W1).See text for details.

Figure 3 .
Figure3.Distribution of the visual extinction A V and the reddening corrected F(Hβ)  of the H ii regions in the double-ring of AM 0644-741.The average value of A V = 0.84 mag is shown by the vertical dashed line.A V tends to increase with F(Hβ).The star symbols indicates the H ii regions with a ULX counterpart(ID 39, 92 and 142).The red star represents the H ii region (ID 39) with a WR feature in its spectrum.
: Te for the low ionization zone (T low e ) was determined with [N ii](λ6548+λ6584)/λ5755; the medium ionization zone (T medium e ) with [S iii]λ6312/λ9069 and the high ionization zone ( [O iii], [N ii] and [S ii] lines at SNR> 3. As we did in the Cartwheel galaxy (see Zaragoza-Cardiel et al. 2022), we used the empirical "S-calibrator" from Pilyugin & Grebel (2016), since the strong lines used are all in the MUSE spectral range: Hβ, Hα, [O iii]λ4959+λ5007, [N ii]λ6548+λ6584 and [S ii]λ6717+λ6731.Abundances could be determined for 137 regions of the sample.

Figure 5 .
Figure 5. log ( Fe O ) vs. 12 + log ( O H ) for the WR H ii region (red circle) detected in AM 0644-741.Fe and O abundances were determined with the DM.Following Zaragoza-Cardiel et al. (2022) we compare our results with the corresponding values reported for H ii regions in other systems: Cartwheel (Zaragoza-Cardiel et al. 2022, blue dots); the Milky Way by (Rodríguez 2002, blue crosses) and Delgado-Inglada et al. (2016, red crosses) and in M 33 (Toribio San Cipriano et al. 2016, red crosses).

Figure 6 .
Figure 6.HST/ACS/WFC image in F625W filter of AM 0644-741 with the ellipses (1 − 11) used to estimate the galactocentric radius and position angle of the H ii regions in the star-forming double-ring of this galaxy.

Figure 7 .Figure 8 .
Figure 7. 12 + log ( O H ) vs. galactocentric radius (R) for the H ii regions (black points) located in the double ring of AM 0644-741.Average values for the regions amidst the ellipses defined in Fig. 6 are indicated with blue points.O abundances were determined with the SLM; the blue dashed line indicates the median value.A linear fit (blue line) to the L-S ring data points indicates a slight gradient of −0.0012 ± 0.0004 dex/kpc among the ellipses 7 and 11.The red star represents the H ii region (ID 39) with the WR feature.

Figure 9 .
Figure 9. Gaussian fit to the BB of the H ii region ID 39, WR1.The blue dashed line represents the fit to the broad WR feature, He ii λ4686, and the red dotted line the fit to the narrow nebular line.The sum is shown in black.The fitted continuum is shown by the dashed straight line.The residuals are shown at the bottom of the panel (in percent).The results are listed in Tab. 5.

Figure 10 .
Figure 10.Diagrams for the diagnostic of age and ionization state (left) and density (right) of the H ii regions in AM 0644-741 (black points with vertical error bars).Red points correspond to special H ii regions that have ULX emission (star ID 39=WR1, triangle ID 92 and circle ID 142).(left) Photoionization model results from Xiao et al. (2018) for BPASS single (continuous line) and binary (dashed line) models are plotted at Z=0.017, density log n H [cm −3 ]=2 for five values of log U , which are identified by the labels.The curves are colour-coded to denote the ages: 1-2.5 Myr blue, 2.5-5 Myr cyan, 5-10 Myr green, 10-20 Myr yellow and 20-100 Myr red.(right) Colour coding of the models is the same as on the left except that only the binary models at logU=−3.5 are shown for two densities which are indicated.Binary low ionization models (−3.5 < log U < −3.0) at ages >5 Myr at ne of 100 cm −3 fit the four plotted quantities simultaneously for the majority of the regions.
ESO Science Archive Facility, program ID: 106.2155.Observations made with the NASA/ESA Hubble Space Telescope were obtained from the data archive at the Space Telescope Science Institute.STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555.This research has made use of the NASA/IPAC Extragalactic Database (NED), which is funded by the National Aeronautics and Space Administration and operated by the California Institute of Technology.VMAGG is funded by the Deutsche Forschungsgemeinschaft (DFG -German Research Foundation), grant number 443790621.YDM thanks CONACYT (Mexico) for the research grant CB-A1-S-25070.AACS is funded by the Deutsche Forschungsgemeinschaft (DFG -German Research Foundation) in the form of an Emmy Noether Research Group -Project-ID 445674056 (SA4064/1-1, PI Sander).AACS further acknowledges supported by funding from the Federal Ministry of Education and Research (BMBF) and the Baden-Württemberg Ministry of Science as part of the Excellence Strategy of the German Federal and State Governments.

Table 3 .
De-reddened nebular line fluxes relative to Hβ=100 for the H ii region ID 39 in AM 0644-741 (see Fig.1).Its spectrum is shown in Fig.2.The complete information for all the H ii regions is given as extra material.

Table 4 .
Te, ne and He, O, N and Fe ionic abundances using the DM for ID 39 (WR1) in AM 0644-741.
) for the WR H ii region (red circle) detected in AM 0644-741.N and O abundances were determined with the DM.Following Zaragoza-Cardiel et al. (2022) we compare our results with the corresponding values reported for H ii regions in other systems: Cartwheel (Zaragoza-Cardiel et al. 2022, blue dots); ring galaxies

Table 5 .
Observed and derived parameters of WR1.

Table 6 .
X-ray sources and their luminosities reported in AM 0644-741 by Wolter et al. (2018, assuming a distance of 91.6 Mpc from NED in 2018; updated values assuming 98.62 Mpc (NED) are shown in parentheses) † and their nearest H ii region analyzed in this work † † .Except for W3 (nucleus)

Table A1 .
Catalogue of the 179 H ii regions identified in the double-ringed AM 0644-741 galaxy and determined parameters.Figure B1.MUSE spectrum of a 'false' H ii candidate in the AM 0644-741 galaxy.Three emission lines are identified at z∼1.4 and are indicated above the continuum (red line).The false Hα corresponds to [Mg ii] λ2798 (Heida et al. 2013).Although, on top of the wide emission line we do identified the narrow Hα line in absorption corresponding to the redshift of AM 0644-741 (z∼0.022).Additionally to Heida et al. (2013) we identified [O ii] λ3727 and [Ne iii] λ3869.Flux is shown normalized to 10 −20 erg cm −2 s −1 Å−1 .