#  Detection of He++ ion in the star-forming ring of the Cartwheel using MUSE
data and ionizing mechanisms

Y. D. Mayya${}^{1\href https://orcid.org/0000-0002-4677-0516{}}$, A.
Plat${}^{2\href https://orcid.org/0000-0003-0390-0656{}}$, V. M. A. Gómez-
González${}^{3\href https://orcid.org/0000-0001-8252-6548{}}$, J. Zaragoza-
Cardiel${}^{1,4\href https://orcid.org/0000-0001-8216-9800{}}$, S.
Charlot${}^{5\href https://orcid.org/0000-0003-3458-2275{}}$ and G.
Bruzual${}^{6\href https://orcid.org/0000-0002-6971-5755{}}$
1Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro 1,
Tonantzintla 72840, Puebla, Mexico
2Steward Observatory, 933 N. Cherry Avenue, University of Arizona, Tucson, AZ
85721, USA
3Institute for Physics and Astronomy, Universität Potsdam, Karl-Liebknecht-
Str. 24/25, D-14476 Potsdam, Germany
4Consejo Nacional de Ciencia y Tecnología, Av. Insurgentes Sur 1582, 03940,
Mexico City, Mexico
5Sorbonne Université, CNRS, UMR7095, Institut d’Astrophysique de Paris,
F-75014, Paris, France
6Instituto de Radioastronomía y Astrofísica, UNAM Campus Morelia, Apartado
postal 3-72, 58090 Morelia, Michoacán, Mexico
Email<EMAIL_ADDRESS>
###### Abstract

We here report the detection of the nebular He ii $\lambda 4686$ line in 32 H
ii regions in the metal-poor collisional ring galaxy Cartwheel using the
Multi-Unit Spectroscopic Explorer (MUSE) dataset. The measured I(He ii
$\lambda 4686$)/I(H$\beta$) ratio varies from 0.004 to 0.07, with a mean value
of 0.010$\pm$0.003. Ten of these 32 H ii regions are coincident with the
location of an Ultra Luminous X-ray (ULX) source. We used the flux ratios of
important diagnostic lines and results of photoionization by Simple Stellar
Populations (SSPs) to investigate the likely physical mechanisms responsible
for the ionization of He+. We find that the majority of the regions (27) are
consistent with photoionization by star clusters in their Wolf-Rayet (WR)
phase with initial ionization parameter $-3.5<$$\log\langle U\rangle$$<-2.0$.
Blue Bump (BB), the characteristic feature of the WR stars, however, is not
detected in any of the spectra. We demonstrate that this non-detection is due
to the relatively low equivalent width (EW) of the BB in metal-poor SSPs, in
spite of containing sufficient number of WR stars to reproduce the observed
I(He ii $\lambda 4686$)/I(H$\beta$) ratio of $\leq$1.5% at the Cartwheel
metallicity of Z=0.004. The H ii regions in the WR phase that are coincident
with a ULX source do not show line ratios characteristic of ionization by
X-ray sources. However, the ULX sources may have a role to play in the
ionization of He+ in two (#99, 144) of the five regions that are not in the WR
phase. Ionization by radiative shocks along with the presence of channels for
the selective leakage of ionizing photons are the likely scenarios in #17 and
#148, the two regions with the highest observed I(He ii $\lambda
4686$)/I(H$\beta$) ratio.

###### keywords:

galaxies: star clusters – galaxies: individual (ESO 350-G040 or Cartwheel)

##  1 Introduction

Ionization of He+ requires environments that generate energies in excess of
54.4 eV. Detection of the He ii $\lambda 4686$ nebular line in star-forming
galaxies suggests that processes related to star formation are able to create
such environments. Photoionization by hard ultraviolet photons emanating from
Wolf–Rayet (WR) stars is the front-runner among these processes (Schaerer,
1996). Simple stellar population (SSP) models incorporating the state-of-the-
art developments in massive star evolution and modeling of the wind-dominated
atmospheres of O-type and WR stars are able to explain the observed I(He ii
$\lambda 4686$)/I(H$\beta$) intensity ratios (He ii $\lambda 4686$/H$\beta$
for short) in at least some star-forming galaxies (Plat et al., 2019). These
models predict a maximum value of He ii $\lambda 4686$/H$\beta$=0.01 during
the WR phase ($\sim$3–5 Myr) for metallicities $Z\geq$0.004, with a decrease
of this ratio at lower metallicities (see Mayya et al., 2020, and references
therein). The observed values of the He ii $\lambda 4686$/H$\beta$ ratio in
metal-poor galaxies often are found to be above 0.01 (Shirazi & Brinchmann,
2012; Kehrig et al., 2015, 2018; Schaerer, Fragos & Izotov, 2019). The SSP
models of Eldridge et al. (2017) involving binary stars help to alleviate the
problem to some extent, but explaining the presence of He++ ion in high
H$\beta$ equivalent width (EW) systems (burst ages $<$3 Myr) remains a
challenge. This has forced exploration of alternative mechanisms of
ionization. Plat et al. (2019) carried out an exhaustive analysis of the
physical mechanisms that can produce the observed ratio of He ii $\lambda
4686$/H$\beta$. They find the need for one or more of the following processes
at work in order to produce the observed high values: (1) the presence of
stars significantly more massive than 100 M⊙; (2) extremely high ionization
parameter, $\log(U)>-1$; (3) hard radiation from binary stars (in particular,
X-ray binaries); (4) ionization of He+ by radiative shocks; and/or (5)
ionization of He+ by an active galactic nucleus (AGN), if and when present.

Over the last decade or so, it has been possible to obtain reliable fluxes of
the relatively weak He ii $\lambda 4686$ line for a large sample of objects,
thanks to dedicated spectroscopic surveys such as Sloan Digital Sky Survey
(SDSS). Given that the often-used nebular diagnostic lines (see e.g. Pérez-
Montero, 2017) are much brighter than the He ii $\lambda 4686$ line, the
available dataset has also allowed accurate determination of nebular metallic
abundances. Dataset obtained from these large surveys are the ones often used
to confront with the predictions of SSP models (e.g. Plat et al., 2019;
Schaerer, Fragos & Izotov, 2019). These data typically sample zones that span
several kiloparsecs in size, centered on the nucleus of the galaxy. Though the
diagnostic lines (Baldwin, Phillips, & Terlevich, 1981) allow the rejection of
spectra dominated by an AGN at least at high enough metallicities ($Z>$0.008;
see Feltre, Charlot, & Gutkin, 2016), the presence of a weak AGN in a spectrum
dominated by a starburst component cannot be ruled out. Over the large spatial
scales sampled in these studies, several of the above mentioned five physical
mechanisms are likely to be at work, thus inhibiting discerning the relative
importance of each mechanism. Data on smaller scales, ideally of selected
regions in nearby galaxies, are required so as to explore the role of each of
the above-listed mechanisms in increasing the He ii $\lambda 4686$/H$\beta$
ratio above the canonical values predicted by the SSP models.

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) and MEGARA on the Gran Telescopio
Canarias (GTC) (Gil de Paz et al., 2018) is allowing such studies possible in
recent years. Kehrig et al. (2015) and Kehrig et al. (2018) used MUSE data to
spatially map the He ii $\lambda 4686$ line in two of the most metal-poor
galaxies: I Zw 18 and SBS 0335 $-$ 052E, finding that the observed He+
ionization cannot be explained by the WR stars present in these galaxies.
Recently, Mayya et al. (2020) used MEGARA to map the central starburst cluster
of NGC 1569, a galaxy with the oxygen abundance similar to that of the Large
Magellanic Cloud (LMC), finding that the WR stars in the starburst cluster are
able to completely explain the observed ionization. Data on regions where
hydrogen ionization is dominated by photons from massive stars of metallicity
below that of the LMC are needed to address the sources of He+ ionization in
distant metal-poor galaxies. The collisional-ring galaxy Cartwheel provides
such a laboratory, as explained below.

The Cartwheel is considered as the archetype of the class of collisional ring
galaxies (Appleton & Struck-Marcel, 1996; Struck, 2010). Ring galaxies are
characterized by a ring that harbours a chain of star forming knots. The star
formation in the ring is believed to be triggered by a radially expanding
density wave that was formed as a result of a compact galaxy plunging through
a massive gas-rich disk galaxy close to its center and almost perpendicular to
it (Lynds & Toomre, 1976). Higdon (1995) found that the H$\alpha$ emission in
the Cartwheel, a tracer of current star formation, is distributed along a ring
as predicted by the collisional scenario of the formation of ring galaxies.
MUSE dataset is available on this galaxy at the seeing-limited spatial
resolution of $\sim$0.6 arcsec. This dataset provides optical spectra covering
a rest wavelength range of $\sim$4600 to 9100 Å over the entire galaxy. On the
H$\alpha$ image constructed using this dataset, we have identified more than
200 individual H ii regions in and around the ring. A colour-composite image
formed using this H$\alpha$ image is shown in Figure 1. At the distance of the
Cartwheel (128 Mpc using the Hubble constant of 71 km s-1 Mpc-1), MUSE spectra
are available at physical scales of $\sim$370 pc, which is an order of
magnitude better as compared to the typical size scale where He ii $\lambda
4686$ is detected in metal-poor galaxies. At the spatial resolution of the
Wide Field and Planetary Camera 2 (WFPC2) images of the Hubble Space Telescope
(HST), which are the highest resolution images ($\sim$0.2 arcsec=125 pc)
available for this galaxy, we can associate each MUSE-identified H ii region
with a population of super star clusters (SSCs), which provide the ionization
of the H ii regions. Fosbury & Hawarden (1977) have measured an oxygen
abundance of 12+log(O/H)$\sim$8.0, corresponding roughly to $Z\sim 0.003$ (see
Table 2 of Gutkin et al., 2016), a value at which the observed He ii $\lambda
4686$/H$\beta$ ratio in galaxy samples is higher than that predicted by most
of the SSPs. The wide spectral coverage of MUSE data allowed the flux
measurement of nebular lines useful to study the ionization state of the H ii
regions using the standard line ratio diagrams (Baldwin, Phillips, &
Terlevich, 1981, hereafter BPT). We used this new dataset to measure an
average oxygen abundance for the ring regions of
12+log(O/H)$\sim$8.19$\pm$0.15 (Zaragoza-Cardiel et al., 2022), which is
marginally higher than the value reported by Fosbury & Hawarden (1977) for
three of the brightest H ii regions.

Figure 1: Colour-composite HST/WFPC2 and VLT/MUSE image of the Cartwheel
galaxy. The RGB image is formed using the HST/WFPC2 filters (PSF=0.2 arcsec)
in F814W, pseudo-green and F450W as red, green and blue components,
respectively; the H$\alpha$ image is constructed from MUSE data (PSF=0.6
arcsec) as a fourth reddish component. The H ii regions in the ring are
identified by numbers and shown by green circles of 0.6 arcsec radius, which
corresponds to 370 pc at the distance of the Cartwheel.

An additional aspect that makes the Cartwheel a good candidate for
understanding the He ii ionization problem is the presence of more than 15
ultra-luminous X-ray sources (ULXs) in its star-forming ring (Gao et al.,
2003; Wolter & Trinchieri, 2004). In fact the Cartwheel is the record holder
for the maximum number of ULX sources in a single galaxy (Wolter, Fruscione &
Mapelli, 2018). The ULX emission is believed to be originating in high-mass
X-ray binaries (HMXBs), with the compact object most likely an intermediate-
mass black hole (IMBH) (Mapelli et al., 2010; Wolter, Fruscione & Mapelli,
2018). The presence of these sources allows us to explore the role of HMXBs in
the He+ ionization in regions where massive stars contribute to the ionization
of hydrogen and other ions of ionization potential much lower than 54.4 eV.

In Section 2, we describe the dataset, extraction of individual spectrum, and
details of measurement of line fluxes. The analysis of nebular line ratios is
described in Section 3. A detailed discussion of results on the He+ ionization
in each star-forming complex is carried out in Section 4. Our conclusions are
given in Section 5.

Table 1: Cartwheel H ii regions with He ii $\lambda 4686$ nebular emission
line.

ID |  |  H$\beta$ |  |  He ii |  | O and WR stars | Cont
---|---|---|---|---|---|---|---
H ii | Higdon | ULX |  |  log f(H$\beta$) | SNR | EW |  log M∗ |  |  log Q(He+) |  I(He ii)/I(H$\beta$) |  | $N_{\rm O7V}$ |  EWBB | $N_{\rm WNL}$ | $N_{\rm WR}$ | SNR
|  |  |  |  [erg cm-2 s-1] |  | [Å] |  M⊙ |  |  ph s-1 |  $\times$100 |  |  |  3$\sigma$ | C&B | C&B |
(1) | (2) | (3) |  | (4) | (5) | (6) | (7) |  | (8) | (9) |  | (10) | (11) | (12) | (13) | (14)
10 | H1 | — |  | $-15.082\pm 0.009$ | 109.9 | 57.2 | 4.84 |  | 49.29 | $1.186\pm 0.326$ |  | 341 | 6.07 | 2 | 7 | 17.9
16 | H3 | G18 |  | $-14.672\pm 0.005$ | 183.5 | 71.7 | 5.25 |  | 49.56 | $0.845\pm 0.196$ |  | 876 | 3.28 | 7 | 19 | 34.1
17 | H4 | — |  | $-15.533\pm 0.014$ | 70.7 | 29.6 | 4.39 |  | 49.19 | $2.666\pm 0.784$ |  | 120 | 5.07 | 1 | 2 | 21.9
20 | H5 | — |  | $-14.841\pm 0.005$ | 204.6 | 63.7 | 5.08 |  | 49.55 | $1.232\pm 0.168$ |  | 594 | 2.77 | 4 | 13 | 38.3
60 | H6 | — |  | $-14.808\pm 0.006$ | 165.3 | 154.4 | 5.11 |  | 49.43 | $0.861\pm 0.160$ |  | 640 | 7.22 | 5 | 14 | 14.7
75 | H10 | G19/W23 |  | $-14.512\pm 0.003$ | 287.3 | 90.5 | 5.41 |  | 49.68 | $0.775\pm 0.151$ |  | 1267 | 3.48 | 10 | 28 | 34.0
81 | H12 | — |  | $-14.366\pm 0.003$ | 363.8 | 159.6 | 5.55 |  | 50.03 | $1.256\pm 0.098$ |  | 1773 | 3.43 | 14 | 39 | 30.2
84 | H14 | — |  | $-14.364\pm 0.002$ | 408.3 | 120.7 | 5.56 |  | 49.91 | $0.936\pm 0.110$ |  | 1781 | 2.93 | 14 | 39 | 35.4
85 | H14 | G17/W7 |  | $-14.517\pm 0.003$ | 303.4 | 79.8 | 5.40 |  | 49.87 | $1.221\pm 0.149$ |  | 1252 | 2.66 | 10 | 27 | 38.3
86 | H14 | — |  | $-14.994\pm 0.005$ | 195.7 | 77.8 | 4.93 |  | 49.12 | $0.648\pm 0.195$ |  | 417 | 4.91 | 3 | 9 | 21.7
90 | H15 | — |  | $-14.339\pm 0.003$ | 338.4 | 126.8 | 5.58 |  | 49.80 | $0.686\pm 0.101$ |  | 1887 | 3.04 | 15 | 41 | 33.2
91 | H15 | G14 |  | $-14.756\pm 0.006$ | 170.9 | 49.4 | 5.16 |  | 49.55 | $1.008\pm 0.207$ |  | 722 | 2.14 | 6 | 15 | 46.0
92 | H15 | — |  | $-14.808\pm 0.005$ | 194.1 | 66.4 | 5.11 |  | 49.42 | $0.854\pm 0.195$ |  | 640 | 3.15 | 5 | 14 | 31.0
97 | H17 | — |  | $-14.984\pm 0.007$ | 136.5 | 68.8 | 4.94 |  | 49.18 | $0.733\pm 0.161$ |  | 427 | 3.13 | 3 | 9 | 35.6
98 | H17 | — |  | $-14.887\pm 0.006$ | 163.3 | 72.9 | 5.03 |  | 49.17 | $0.565\pm 0.171$ |  | 534 | 3.70 | 4 | 11 | 27.6
99 | H17 | G12/W24 |  | $-13.575\pm 0.001$ | 1055.0 | 282.6 | 6.35 |  | 50.55 | $0.664\pm 0.052$ |  | 10960 | 2.78 | 92 | 242 | 35.2
100 | H17 | — |  | $-14.721\pm 0.005$ | 221.9 | 69.9 | 5.20 |  | 49.42 | $0.694\pm 0.159$ |  | 783 | 2.68 | 6 | 17 | 39.2
105 | H19 | — |  | $-14.824\pm 0.006$ | 171.0 | 61.4 | 5.10 |  | 49.31 | $0.676\pm 0.162$ |  | 617 | 2.63 | 5 | 13 | 42.0
106 | H19 | — |  | $-14.563\pm 0.004$ | 241.5 | 81.3 | 5.36 |  | 49.57 | $0.683\pm 0.161$ |  | 1126 | 2.99 | 9 | 24 | 34.2
108 | H21 | — |  | $-15.148\pm 0.009$ | 116.2 | 52.5 | 4.77 |  | 49.32 | $1.461\pm 0.323$ |  | 292 | 4.66 | 2 | 6 | 21.8
111 | H20 | G11/W10 |  | $-14.894\pm 0.007$ | 152.5 | 34.9 | 5.03 |  | 49.43 | $1.066\pm 0.240$ |  | 525 | 2.38 | 4 | 11 | 47.5
112 | H22 | — |  | $-14.493\pm 0.004$ | 271.0 | 219.4 | 5.43 |  | 49.37 | $0.361\pm 0.107$ |  | 1323 | 5.50 | 11 | 29 | 22.5
113 | H22 | — |  | $-15.201\pm 0.009$ | 109.4 | 46.1 | 4.72 |  | 49.02 | $0.831\pm 0.213$ |  | 259 | 4.07 | 2 | 5 | 26.4
116 | H23 | — |  | $-14.614\pm 0.004$ | 259.1 | 93.4 | 5.31 |  | 49.81 | $1.341\pm 0.153$ |  | 1001 | 3.14 | 8 | 22 | 34.1
118 | H23 | G8 |  | $-14.432\pm 0.003$ | 360.0 | 123.3 | 5.49 |  | 49.71 | $0.686\pm 0.126$ |  | 1523 | 3.24 | 12 | 33 | 35.1
119 | H24 | G6/W14 |  | $-14.498\pm 0.006$ | 170.1 | 60.6 | 5.42 |  | 49.83 | $1.053\pm 0.184$ |  | 1308 | 2.61 | 11 | 28 | 39.1
120 | H24 | — |  | $-14.679\pm 0.007$ | 152.4 | 51.0 | 5.24 |  | 49.60 | $0.951\pm 0.251$ |  | 862 | 2.98 | 7 | 19 | 36.5
121 | H24 | — |  | $-14.983\pm 0.011$ | 91.3 | 69.8 | 4.94 |  | 49.28 | $0.908\pm 0.239$ |  | 428 | 5.69 | 3 | 9 | 18.4
141 | H26 | — |  | $-14.700\pm 0.005$ | 188.6 | 37.4 | 5.22 |  | 49.56 | $0.918\pm 0.223$ |  | 821 | 2.11 | 6 | 18 | 54.6
144 | H26 | G2/W17 |  | $-15.036\pm 0.007$ | 134.8 | 38.0 | 4.88 |  | 49.61 | $2.223\pm 0.322$ |  | 379 | 3.01 | 3 | 8 | 34.8
148 | — | — |  | $-15.785\pm 0.021$ | 46.8 | 21.8 | 4.14 |  | 49.31 | $6.283\pm 1.599$ |  | 67 | 7.90 | 0 | 1 | 13.8
213 | H29 | G9/W12 |  | $-14.907\pm 0.006$ | 164.5 | 88.9 | 5.01 |  | 49.20 | $0.644\pm 0.196$ |  | 510 | 4.53 | 4 | 11 | 24.4

(1) H ii region identification number used in this work, (2) H ii complex
number from Higdon (1995), (3) ULX sources associated to the H ii region,
(4-7) Measured and derived quantities using H$\beta$ nebular line, where
stellar mass in column 7 is derived assuming a Lyman continuum photons rate of
4.94$\times 10^{46}$ using C&B model corresponding to an age of 3.4 Myr for
the ionizing cluster, (8) He+ ionizing photon rate determined from the
observed He ii $\lambda 4686$ flux for a Case B H ii region, (9) 100$\times$
the intensity of He ii $\lambda 4686$ line with respect to that of H$\beta$,
(10) Equivalent number of O7V stars derived assuming a typical H$\beta$
luminosity of 4.76$\times 10^{36}$ erg s-1 for an O7V star from López-Sánchez
& Esteban (2010), (11) Upper limit for the equivalent width of the BB from WNL
type inferred as the 3$\sigma$ flux of a broad (FWHM=20 Å) BB divided by the
underlying continuum flux, (12-13) The number of WNL and total WR stars
expected in C&B models during the WR phase for the cluster mass in column 7,
(14) SNR of the continuum adjacent to the BB bump.

##  2 The sample of He++ nebulae and the control sample of bright H ii regions

###  2.1 The H ii region parent sample

Given that the ionization potential of hydrogen is four times lower as
compared to the second ionization potential of helium, the He++ nebulae are
expected to be a subset of the ionized nebulae. The outer ring of the
Cartwheel is currently experiencing an intense burst of star formation. Higdon
(1995) found that the H$\alpha$ emission, a tracer of current star formation,
is predominantly confined to 29 ionized complexes in the outer ring. As a
first step, we used the MUSE datacube to obtain a narrow-band image at the
red-shifted wavelength of the H$\alpha$ line to locate ionized regions at the
resolution of MUSE (FWHM=0.6 arcsec$\sim$370 pc), which is $\sim$3 times
better as compared to the image used by Higdon (1995). In Figure 1, we show an
RGB image formed by combining the HST/WFPC2 filters in F814W, pseudo-green and
F450W as red, green and blue components, respectively; the H$\alpha$ image
constructed from MUSE data is used as a fourth reddish component. We
identified visually 221 prominent H$\alpha$-emitting knots in the ring or near
to it on the MUSE image, which are shown by numbers in this image. At the
resolution of the HST/WFPC2 images, most of the H$\alpha$-emitting knots are
associated with one or more compact clusters, which are the most likely
ionizing sources of the nebulae. Thus, the selected regions are star-forming
complexes spread over the entire extracted area. However, at the spatial
resolution offered by MUSE, each complex is basically a compact unresolved
knot. We hence used a uniform aperture of 0.6 arcsec radius to extract
spectrum of each region. We note that the H$\alpha$ surface brightness in the
outer ring is 10 to 100 times brighter than the typical cut-off surface
brightness of 2$\times 10^{-17}$ erg cm-2 s-1 arcsec-2 for the Diffuse Ionized
Gas (DIG) (see e.g. Belfiore et al., 2022), and hence the DIG contribution to
the flux ratios of lines in the extracted spectra can be ignored.

We did not attempt to subtract the disk spectrum from the extracted spectra as
it is non-trivial to locate a region for extraction of the local disk spectrum
in a galaxy such as the Cartwheel because of its peculiar morphology and star
formation history. Thus the extracted spectra contain contributions from any
pre-collisional, as well as from all post-collisional, populations in the
extracted area. From an analysis of stellar populations in the extracted
spectra, Zaragoza-Cardiel et al. (2022) concluded that the spectra lack
absorption features characteristics of disk stellar populations. This is
understandable because the pre-collsional disk is around a factor of five
fainter than the ring (Marcum, Appleton & Higdon, 1992; Higdon, 1995), and
hence the extracted spectra are dominated by contribution from all populations
formed after the collision around 100 Myr ago (Renaud et al., 2018). The
extracted spectra, however, could contain contribution from non-ionizing
populations formed over the last 100 Myr. Such a population will not
contribute to the measured emission line fluxes, but will make the observed
values of emission-line EWs lower that that expected for a single burst young
population. We will take this into account while we carry out a detailed
comparison of the observed EWs with that predicted from population synthesis
models in Sec.4.

Figure 2: The He ii $\lambda 4686$/H$\beta$ ratio as a function of
SNR(H$\beta$) for the Cartwheel H ii regions. Detections and the 3-$\sigma$
upper limits for the He ii $\lambda 4686$ line are shown by blue circles and
red triangles, respectively. All detections are tagged by their identification
numbers. The inclined dotted line denotes the lowest He ii $\lambda
4686$/H$\beta$ ratio that can be detected at 3-$\sigma$ for H ii regions
having EW(H$\beta$)=125 Å. See text for details.

###  2.2 The He++ nebular sample

We measured fluxes of all major nebular lines in all the extracted spectra. We
used the Gaussian profile fitting routine of the splot task in iraf111 IRAF is
distributed by the National Optical Astronomy Observatories, which are
operated by the Association of Universities for Research in Astronomy, Inc.,
under cooperative agreement with the National Science Foundation. for this
purpose. The measured line fluxes are free from the underlying continuum. We
fitted each extracted spectrum with a Gaussian profile at the redshifted
wavelengths of a list of nebular lines commonly reported in extragalactic H ii
regions, including the He ii $\lambda 4686$ line. The output quantities of the
Gaussian fitting task that we used here are: line flux, FWHM and EW. We
measured the root mean square (rms) noise at feature-less parts of the
continuum adjacent to the measured line, which we used to determine the
signal-to-noise ratio (SNR) of the measured line. An emission line is deemed
detected if the fitted FWHM is comparable to that of the H$\beta$ line (2.5 Å)
and that the integrated line flux has a SNR$\geq$3\. Using these line fluxes,
we constructed two sub-samples: (1) a sub-sample of 87 bright H ii regions
defined as those with SNR$>$40 in the H$\beta$ line, and (2) a sub-sample of
32 He ii nebulae defined as those where the He ii $\lambda 4686$ nebular line
is detected. As expected, the latter sample is a subset of the former. The
bright H ii region sample is used as a control sample to understand the
physical conditions that favour the detection of the He ii $\lambda 4686$ line
in ionized regions.

The criterion that the FWHM of a line should be comparable to that of the
H$\beta$ emission line ensures that the detected line is of nebular origin.
Nevertheless, the spectra of the He ii nebulae were visually inspected for the
possible presence of an underlying broad He ii $\lambda 4686$ emission
feature, commonly referred to as the ’blue bump’ (BB), from WR stars. None of
the spectra showed this feature, and hence any contribution of the WR bump to
the measured nebular He ii $\lambda 4686$ fluxes can be ignored.

The He ii nebular sample222Fluxes of all measured lines for the entire sample
of H ii regions are presented in companion paper by Zaragoza-Cardiel et al.
(2022), which deals with the nebular elemental abundances. The ratios of
fluxes of lines used in this work are given in a Supplementary Electronic
Table. is listed in Table 1. In column 2, we list the cross identification of
our sources with the H ii complexes of Higdon (1995). In other columns, we
give the basic measured quantities of these regions such as the flux, SNR and
EW of the H$\beta$ line (columns 4, 5 and 6, respectively), and the He ii
$\lambda 4686$ intensity normalized to I(H$\beta$) and multiplied by 100,
along with error (column 9). The error in measured flux ($\sigma_{\rm l}$) of
each line is calculated using the expression (Tresse et al., 1999):,

$\sigma_{\rm l}=\sigma_{\rm c}D\sqrt{(2N_{\rm pix}+\frac{EW}{D})},$ (1)

where $D$ is the spectral dispersion in Å per pixel (1.25 for MUSE),
$\sigma_{\rm c}$ is the mean standard deviation per pixel of the continuum,
which is measured in a line-free part of the continuum adjacent to each line,
$N_{\rm pix}$ is the number of pixels covered by the line, which is equated to
the FWHM of the fitted Gaussian profile. In all these 32 regions, the H$\beta$
flux has SNR$>$50, with a median SNR of 176. The He ii $\lambda 4686$ line is
detected at SNR=3–15.

Detection of a line depends on the SNR of the spectrum. In Figure 2, we show
the He ii $\lambda 4686$/H$\beta$ ratio for all the H ii regions with
SNR(H$\beta$)$\geq$40\. Detections are shown in blue solid circles, whereas
the upper limits, defined as 3-$\sigma$ fluxes where $\sigma$ is calculated
using the error equation 1 with $N_{\rm pix}$=FWHM(H$\beta$), are shown by red
inverted triangles. As a reference, we show by the dotted line the minimum
value of He ii $\lambda 4686$/H$\beta$ ratio that a region should have so that
the He ii $\lambda 4686$ line is detected, given the SNR of H$\beta$ in its
spectra. The intercept of this line depends slightly on EW(H$\beta$), with the
plotted line corresponding to EW(H$\beta$)=125 Å. The line would shift upwards
(downwards) by $\sim$0.005 for regions with EWs a factor of two lower
(higher). Our sample of He ii nebulae has a mean value of I(He ii $\lambda
4686$)/I(H$\beta$)=0.010$\pm$0.003, with the lowest and highest ratios being
0.004 (#112) and 0.07 (#148). We can expect He ii line detection only in H ii
regions with SNR(H$\beta$)$>$100, if their He ii $\lambda 4686$/H$\beta$ ratio
is close or higher than the mean value of the sample. Conversely, the
detection of He ii $\lambda 4686$ line would require abnormally high ratio of
He ii $\lambda 4686$/H$\beta$ in regions with SNR(H$\beta$)$<$100, such as the
case in #148 and #17. As expected, the He ii $\lambda 4686$ line is detected
in all MUSE spectra with SNR(H$\beta$)$\geq$200 (12 regions). For regions
having 100$<$SNR(H$\beta$)$<$200, the He ii $\lambda 4686$ line is detected in
$\sim$59 per cent (17 of 29) of the H ii regions.

Figure 3: The VLT/MUSE rest-frame spectra in the blue part of three
representative H ii regions #99, #112 and #148 in the Cartwheel. Each spectrum
is shown normalized to the best fit continuum spectrum and displaced
vertically for clarity sake. The nebular lines in the plotted spectral range
are indicated. In the three spectra, the He ii $\lambda 4686$ line is detected
at SNR=12, 3.3, and 3.6 (from top to bottom), with the bottom two spectra
illustrating detections just above our chosen 3-$\sigma$ detection limit. In
addition, all detections have line widths comparable to that of the typical
line spread function. We mark by a cross a spurious feature at $\lambda$=4810
Å in the bottom-most spectrum, which is narrower than the typical line spread
function.

In Figure 3 we show the blue part of the MUSE spectrum for three
representative H ii regions where the He ii $\lambda 4686$ line is detected.
The regions selected for illustrations are: #99, the brightest H ii region in
the Cartwheel, #112 and #148, the H ii regions with the lowest and the highest
He ii $\lambda 4686$/H$\beta$ values, respectively. The He ii $\lambda 4686$
and other nebular lines in the plotted range are indicated.

Figure 4: Zoomed view of Figure 1 to facilitate visualization of the ionizing
clusters associated with the MUSE-detected H ii regions (small circles) at the
HST resolution. Top and bottom images correspond to northern and southern part
of the ring, respectively, whereas the middle row contains 2 subimages each of
the eastern and western ring. Thirty two H ii regions with well-detected He ii
$\lambda 4686$ nebular line are distinguished by cyan coloured circles, with
the rest of the H ii regions identified by dashed green circles. ULX sources
are identified by red circles. The 29 H ii complexes defined by Higdon (1995)
are shown by big orange circles identified by labels H1 to H29. The
orientation of all sub-images are the same as in Figure 1, and small circles
in all images have a radius of 0.6 arcsec. In general, He ii $\lambda
4686$-emitting regions are among the brightest H ii regions. However, there
are fainter H ii regions (e.g. #10, #148) with He ii $\lambda 4686$ emission.
See text for details.

###  2.3 Association of He++ nebulae to Star Clusters

We use the astrometrized HST images in the F450W and F814W filters to look for
a spatial association between the He++ nebulae and star clusters. In Figure 4,
we present a close-up view of the entire ring with the intention of showing
the cluster(s) associated to He++ nebulae. The HST images reveal the presence
of at least one ionizing cluster inside the aperture used to extract the MUSE
spectrum in all the 32 He++ nebulae. This association suggests that
photoionization from stars in young clusters, or alternatively any process
related to young clusters, is mainly responsible for the ionization of He+.

Figure 5:  Evolutionary behaviour of the emission EWs of H$\beta$ (top) and
the nebular He ii $\lambda 4686$ (bottom) for C&B SSPs (single-stars) with
$M_{\rm up}$=100 M⊙ (black solid line) and 300 M⊙ (yellow dashed line) and
BPASS (binary-stars). See text for details.  Figure 6:  Evolutionary behaviour
of nebular He ii $\lambda 4686$/H$\beta$ ratio for C&B (single-star) and BPASS
(binary-star) SSPs. See text for details.  Figure 7:  Evolution of cluster
quantities during the WR phase in the C&B SSP model at Z=0.004. The top panel
shows the number of different types of WR stars, while the bottom panel shows
the ionizing photon rates of H0 and He+ (left axis) and the EW of the Blue
Bump (solid blue line and the right axis). In both the plots, solid lines
correspond to the default model of $M_{\rm u}$=100 M⊙ used in this work,
whereas the dotted lines that extend to ages $<$3 Myr correspond to $M_{\rm
u}$=300 M⊙. In the top panel, the number of different WR subtypes are shown by
dashed and dotted lines for $M_{\rm u}$=100 and 300 M⊙, respectively.

The star forming complexes defined by Higdon (1995), after correcting for
offsets in their coordinates with respect to our MUSE H$\alpha$ image, are
also marked in Figure 4. The radius of the circles used to identify the H ii
regions and H ii complexes indicates the FWHM of the point spread function
(PSF) of the corresponding observations. With the exception of one source
(#148), all are associated with these complexes. In general, these complexes
contain multiple H ii regions and stellar clusters. However, only 18 of the
complexes are associated with a He++ nebula, with a few of the complexes
containing multiple knots of He++ emission. H17 in the southern quadrant of
the ring, the brightest complex, contains as much as four knots of He++
emission.

###  2.4 The He ii $\lambda 4686$ nebular line in the SSP models

Photoionization from massive stars is the dominant source of ionization in H
ii regions. Massive stars with zero-age main-sequence mass
$M_{\mathrm{ZAMS}}\gtrsim 25$ M⊙ go through the WR phase during their post-
main sequence evolution (see Crowther, 2007, and references therein). WR stars
are the hottest stars in coeval young clusters whose surface temperature
reaches in excess of 105 K, hot enough to doubly ionize helium. The exact age
and duration at which WR stars appear in a coeval population depends on the
metallicity, the upper cut-off mass ($M_{\rm u}$) of the Initial Mass Function
(IMF), and also the inclusion or not of binary star populations in the SSP
models used. In this work, we used the latest version of Bruzual & Charlot
(2003) SSP models (Charlot & Bruzual in-preparation, hereafter C&B; see also
Plat et al. (2019) for details) for single stars corresponding to Z=0.004, the
metallicity in the SSP models closest to that of the Cartwheel. These updated
models have incorporated the theoretical spectra from Potsdam Wolf-Rayet
(PoWR) model library (see references in Todt et al., 2015) and the stellar
evolutionary tracks from Chen et al. (2015) that were computed with the parsec
code of Bressan et al. (2012). Tracks for Very Massive Stars up to initial
masses of 600 M⊙ are available in this code. We here use the SSP models
adopting a Chabrier (2003) IMF with lower cut-off mass of $M_{\rm l}$=0.1 M⊙.
We present the model results for two values of upper cut-off mass: $M_{\rm
u}$=100 M⊙ and $M_{\rm u}$=300 M⊙. We investigate the effect of including
binary star processes (such as envelope stripping and chemical homogenisation)
using the BPASS v2.2.1 stellar population models (Stanway & Eldridge, 2018).
The models are computed for a zero-age volume-average ionization parameter
$\log\langle U\rangle$ =$-2$ (see Section 4 for details).

In Figures 5 and 6, we show the evolutionary behaviour of the EWs for the
H$\beta$ and He ii $\lambda 4686$ nebular lines, and the intensity ratio, I(He
ii $\lambda 4686$)/I(H$\beta$). For C&B models, we show the results for two
values of $M_{\rm u}$, 100 and 300 M⊙, whereas the binary models are shown
only for $M_{\rm u}$=300 M⊙. The nebular EW(H$\beta$) steadily decreases with
age as massive stars die in a coeval population. On the other hand, the
nebular EW(He ii $\lambda 4686$) shows a second peak after the initial steady
decrease, with the value of this second peak, which corresponds to the WR
phase, higher than the values at the pre-WR phase for the C&B models. The
log(I(He ii $\lambda 4686$)/I(H$\beta$)) has values between $-$3.5 to $-$2.7
when all stars are in the main sequence. However, the highest value is reached
during the WR phase of single star evolutionary models, which happens between
2.3 to 4.0 Myr with $M_{\rm u}$=300 M⊙, and between 3.2 to 4.0 Myr with
$M_{\rm u}$=100 M⊙. In C&B models, the highest value is close to $-1.8$ for
both the values of $M_{\rm u}$, dropping steeply to values below $-5$ at 4
Myr. The evolutionary trend is notably different in BPASS binary models: the
highest values are reached during the main sequence phase, thereafter the
value remaining between $-$3.5 and $-$3 to ages even beyond 30 Myr.
Unfortunately, the highest value of I(He ii $\lambda 4686$)/I(H$\beta$) ratio
differs in different publicly available SSP models, with the value depending
on the details of the stellar evolutionary and atmospheric models used as
illustrated in Mayya et al. (2020). The mean value of I(He ii $\lambda
4686$)/I(H$\beta$)=0.0094$\pm$0.0025 for our sample regions is in good
agreement with the expected value for ionization from WR stars in C&B models,
whereas it is higher than the peak value reached in BPASS models. The
systematically low value of this ratio during the WR phase in BPASS single
star and binary star models limits the use of BPASS models, as of now, for a
robust discussion of WR stars as ionizing source in our He ii nebula. We hence
draw conclusions regarding the source of ionization of He+ using the C&B SSP
models, and make use of the BPASS models only to discuss qualitative changes
in our C&B-based results, if the Cartwheel clusters contain binaries in
significant numbers.

In Figure 7, we show the expected number of WR stars of different sub-types
during the WR phase (top panel), the ionizing photons rates Q(H0) and Q(He+),
as well as the expected EW of the BB (bottom panel) for the Z=0.004 C&B SSP.
Note that these numbers do not take into account the presence of WR-like
stripped (or spun-up) binary stars, which are capable of ionizing He+, but do
not show strong blue bumps (see e.g. Götberg et al., 2018). In this figure,
all quantities except EW(BB) depend on the cluster mass. We scaled all
calculated values to a cluster mass of $10^{6}$ M⊙. In order to calculate the
model EW(BB), we obtained the flux in the BB, and the underlying continuum.
The bump flux is obtained by integrating the model spectra of pure WR stars
between 4570 Å and 4740 Å. The underlying continuum flux is obtained as a mean
of continuum fluxes at the blue and red part of the BB. The blue and red
continua are obtained over 50 Å width filters centered at 4525 Å and 4905 Å,
respectively.

Both the $M_{\rm u}$=100 M⊙ and 300 M⊙ models have a total number of $\sim$100
WR stars/$10^{6}$ M⊙ of stellar mass at any time during the WR phase. The WC
and WNL stars are the two main types expected up to around 3.6 Myr, after
which WNL type is the dominant type with some contribution from WNE type.
However, as illustrated earlier, the WR phase begins earlier for higher
$M_{\rm u}$, which leads to earlier availability of the He+ ionizing photons
for $M_{\rm u}$=300 M⊙ models. It can be noticed from the figure that the
Q(He+) increases by more than two orders of magnitudes when the WR stars start
appearing in the cluster, whereas the Q(H0) continues its steady decrease that
started at the end of the pre-WR phase into the WR phase. Unlike Q(He+) and
Q(H0), whose maximum values do not depend on the chosen $M_{\rm u}$ of the
IMF, the maximum value of the EW(BB) is very sensitive to the choice of
$M_{\rm u}$. The maximum value reached for $M_{\rm u}$=100 M⊙ is 1.2 Å at 3.6
Myr, whereas it is as high as 10 Å for the $M_{\rm u}$=300 M⊙ models. The
evolutionary behaviours for $M_{\rm u}$=300 M⊙ and 100 M⊙ are
indistinguishable for ages greater than 3.4 Myr.

###  2.5 Ionizing photon rates and cluster masses

We used the observed luminosity in the H$\beta$ recombination line,
L(H$\beta$), to estimate the equivalent number of O7V stars using a typical
luminosity of an O7V star of 4.76$\times 10^{36}$ erg s-1 from López-Sánchez &
Esteban (2010). We also calculated the H0 and He+ ionizing photon rates, Q(H0)
and Q(He+), respectively, for a Case B photoionized nebula using the basic
equations for photoionized nebulae (Osterbrock & Ferland, 2006; Mayya et al.,
2020). We then calculated the stellar mass in the cluster that is ionizing
each region, using:

$\frac{M_{\ast}}{\rm M_{\odot}}=\frac{{\rm Q(H}^{0})}{{{\rm Q(H}^{0})_{\rm
SSP}}},$ (2)

where ${{\rm Q(H}^{0})_{\rm SSP}}=4.94\times 10^{46}~{}{\rm
photon~{}s^{-1}}$M⊙-1 is the H0 ionizing photon rate for the Z=0.004 SSP in
the C&B models for the characteristic age in the WR phase of 3.4 Myr. The
masses would be around a factor of two lower, or higher, for the clusters that
are in the pre- or post-WR phases, respectively. The derived values of N(O7V),
M∗, and Q(He+) are given in columns 10, 7 and 8, respectively, of Table 1.

###  2.6 Potential ionizing sources of He++ nebulae

####  2.6.1 Wolf-Rayet stars

From Figure 6, it is apparent that the WR stars are the most likely sources of
ionization of He+ in majority of our H ii regions. However, as commented
earlier in this section, none of the spectra showed the BB (neither other WR
features; see e.g. Gómez-González et al. 2021). In order to understand this
apparent contradiction, we estimated an upper limit on the EW of the BB, using
the noise measurement in the continuum adjacent to the expected BB and
assuming a Gaussian profile of FWHM=20 Å for the BB (see e.g. Gómez-González
et al., 2020). The resulting EWs are given in column 11 of Table 1. In the
table, we also give the theoretically expected number of WNL-type and all WR
stars in each region, assuming a uniform age of 3.4 Myr. The expected number
of WR stars is as high as 242 for region#99, and in the 30–40 range for four
other regions (#90, 81, 84, 118). In rest of the regions the expected numbers
are less than 30.

Figure 8:  Observational upper limits (inverted triangles) on the EW(BB)
plotted against the He ii $\lambda 4686$/H$\beta$ ratio for Cartwheel H ii
regions with He ii $\lambda 4686$ line detections. The expected values during
the WR phase from the C&B SSP model for two upper cut-off masses are shown. In
the presence of massive stars of 300 M⊙ the EW(BB) reaches values as high as
10 Å for a brief period around 2.5 Myr, whereas the EW(BB) stays lower than
1.5 Å when $M_{\rm u}$=100 M⊙, which is at least a factor of two lower than
the detection threshold as indicated by the 3-$\sigma$ upper limits. H ii
regions with extreme values of He ii $\lambda 4686$/H$\beta$ ratio are
identified with their numbers. See text for details.

The observed upper limits on the EW(BB) are compared with those expected in
the C&B models in the EW(BB) vs He ii $\lambda 4686$/H$\beta$ plane in Figure
8. As discussed earlier, the theoretically expected EW(BB) reaches a maximum
value of only 1.2 Å for $M_{\rm u}=100$ M⊙, whereas it could be as high as 10
Å for $M_{\rm u}=300$ M⊙. The observational detection upper limits on the
EW(BB) are higher by factors of 2 to 6 as compared to the theoretical values
in the absence of Very Massive (mass$>$100 M⊙) Stars. This illustrates that
the absence of the blue bump does not necessarily imply the absence of WR
stars. At the metallicity of the Cartwheel H ii regions, WR stars in numbers
sufficient to doubly ionize helium could be present even when the
characteristic broad BB is not detected. This could be the case not only in
the Cartwheel regions, but in general in all metal-poor systems that show He
ii $\lambda 4686$ nebular line (e.g. Shirazi & Brinchmann, 2012).

It is interesting to note that we would have been able to detect the BB when
Very Massive Stars in clusters, if present, go through the WR phase. It can be
inferred from Figure 7, that the $M_{\rm u}$=300 M⊙ models provide He+
ionizing photons for double the duration as compared to the $M_{\rm u}$=100 M⊙
models. This implies that if all the He ii $\lambda 4686$-detected H ii
regions had an IMF with $M_{\rm u}$=300 M⊙, the BB would have been at the
detectable level in 50% of the cases. The non-detection of the BB in all
regions points to the absence of $M_{\rm u}>$100 M⊙ stars in H ii regions of
the Cartwheel.

Given that our He ii $\lambda 4686$-line detection criteria are tuned to
detect nebular (narrow) lines, there exists a possibility that we
inadvertently excluded possible WR sources in spectra where we did not detect
the He ii $\lambda 4686$ narrow line. In order to verify this possibility, we
analyzed the output results of the Gaussian-fitting for all the regions to
look for a broad He ii $\lambda 4686$ component with SNR$\geq$3\. None of the
spectra showed evidence for it. If stars more massive than 100 M⊙ were common,
the BB should have been present at detectable levels in at least a few of the
80 H$\beta$-bright regions. In fact, none of the spectra of our original
sample of 221 H ii regions showed the BB. Such a non-detection reinforces the
inference drawn from the He ii $\lambda 4686$-detected regions that the upper
mass cut-off of the IMF rarely exceeds 100 M⊙ in H ii regions.

In summary, WR stars are viable sources of He+ ionization in He ii $\lambda
4686$-detected regions of the Cartwheel, in spite of the non-detection of the
BB. In rest of this paper, we use photoionization models to investigate
whether the intensity ratios of bright nebular lines support the scenario of
WR stars as the only source of ionization in majority of the regions. Four
regions with extreme He ii $\lambda 4686$/H$\beta$ ratio (identified in Figure
8), possibly require alternative sources of ionization, which are also
investigated in the paper.

####  2.6.2 Main sequence stars

The bulk of the ionization of hydrogen in H ii regions is provided by star
clusters in their early phase when massive O stars are in the main sequence
(MS). Some of these stars are hot enough to doubly ionize helium. The emission
EW(H$\beta$) is maximum during this early phase having values larger than 500
Å. The highest values of He ii $\lambda 4686$/H$\beta$ during this phase are
0.002 and 0.001, respectively in C&B and BPASS models, both with $M_{\rm
u}$=300 M⊙. It can be inferred from Figure 2 that we require SNR above 400 to
detect He ii $\lambda 4686$ line ionized by the MS stars. There are 5 regions
with SNR$>$330, all of which have He ii $\lambda 4686$/H$\beta$$>$0.006, i.e.
at least a factor of three higher than the MS values. On the other hand, the
region with the lowest value of He ii $\lambda 4686$/H$\beta$ is #112, which
is around twice the MS value. Stripped binary stars, which are not taken into
account in the C&B and BPASS models, may have a role in increasing the He ii
$\lambda 4686$/H$\beta$ above the calculated values. The MS phase is
characterized by high EW(H$\beta$). We analyse all regions in He ii $\lambda
4686$/H$\beta$ vs EW(H$\beta$) plane to address this issue in Sec. 3.

Table 2: Cartwheel H ii regions nearest to an ULX source. H ii ID | Higdon | Gao |  | Wolter |  He++
---|---|---|---|---|---
|  | ID | offset |  | ID | offset |  log LX |
|  |  | [arcsec] |  |  | [arcsec] |  erg s-1 |
(1) | (2) | (3) | (4) |  | (5) | (6) | (7) | (8)
13 | H2 | — | — |  | W21 | 0.61 | 38.70 | no
16 | H3 | G18 | 0.84 |  | — | — | — | yes
49 | — | — | — |  | W18 | 0.29 |  | no
75 | H10 | G19 | 0.65 |  | W23 | 0.33 | 38.78 | yes
85 | H14 | G17 | 0.16 |  | W7 | 0.42 | 39.70 | yes
88 | — | G15 | 0.12 |  | W8 | 0.52 | 39.18 | no
91 | H15 | G14 | 0.44 |  | — | — | — | yes
99 | H17 | G12 | 0.77 |  | W24 | 2.39 | 38.57 | yes
111 | H20 | G11 | 2.17 |  | W10 | 1.75 | 40.44 | yes
117 | — | G7 | 1.33 |  | W13 | 1.21 |  | no
118 | H23 | G8 | 0.24 |  | — | — | — | yes
119 | H24 | G6 | 0.56 |  | W14 | 1.28 | 39.88 | yes
125 | — | G5 | 0.65 |  | W15 | 1.42 | 39.06 | no
144 | H26 | G2 | 0.50 |  | W17 | 0.70 | 39.92 | yes
146 | — | G3 | 1.74 |  | W16 | 2.32 | 39.83 | no
155 | — | G4 | 0.41 |  | — | — | — | no
213 | H29 | G9 | 0.81 |  | W12 | 0.72 | 39.49 | yes

####  2.6.3 Ultra-luminous X-ray sources

Pointlike non-nuclear X-ray sources with isotropic bolometric luminosity in
the the 0.5–10 keV band ($L_{\rm X}$) exceeding 3$\times 10^{39}$ erg s-1are
referred to as ULX sources. Gao et al. (2003) and Wolter & Trinchieri (2004)
analyzed the Chandra/Acis data of Cartwheel finding 31 and 24 ULX sources,
respectively, in the FoV of the Cartwheel, the majority of them coinciding
with the star-forming ring of the Cartwheel. The most luminous of these
sources (#11 in Gao et al. 2003 and #10 in Wolter & Trinchieri 2004) has
$L_{\rm X}>10^{41}$ erg s-1, thus satisfying the criterion to be called as a
hyperluminous X-ray source (HLX). However, a one-to-one correspondence with an
optical knot in the ring was poor in both the studies, with offsets between
the H ii complexes defined by Higdon (1995) and the ULX coordinates, generally
exceeding the 1 arcsec beam of the Chandra/Acis observations, even after
correcting for zeropoint offsets in the respective coordinate systems. The
reason for these large offsets is that there is more than one star cluster
within the seeing-limited resolution of $\sim$1.7 arcsec (1 kpc) of the
H$\alpha$ image of Higdon (1995), with the coordinates referring to that of
the brightest H ii region in the complex, which is not necessarily the ULX
source. The astrometrically calibrated MUSE and HST dataset that we use in
this study offers $\sim$3 and 8 times better spatial resolutions,
respectively, as compared to the H$\alpha$ image of Higdon (1995), which
allows us to improve upon the identification of the optical counterpart of the
ULX sources.

In Figure 4, we mark the positions of ULX/HLX sources by red circles overlaid
on the HST image. Fourteen of the 17 X-ray sources coincide with the position
of an H ii region to better than an arcsec, the beam of the X-ray
observations. The H ii region closest to a ULX/HLX source is identified in
Table 2, where we also give the offsets for each source from the coordinates
reported by Gao et al. (2003) and Wolter & Trinchieri (2004). It is worth
noting that given the high density of H ii regions in the ring, more than one
H ii region can be associated for sources with offsets exceeding an arcsec.
The offsets are systematically smaller for Gao et al. (2003) coordinates.
Source #111, the identified counterpart of the HLX source (G11) is outside the
Chandra/Acis beam, suggesting that the identification is likely to be wrong,
and that the source may be associated to a non-H$\alpha$-emitting object. In
order to identify such a candidate, we looked for any stellar knot in the HST
images. We find a faint red knot at the edge of the Chandra/Acis beam, which
could be a likely counterpart of the HLX source (see the region G11 in the
figure). A He++ nebula is present within the beam of the X-ray observations
for ten and seven ULX sources identified by Gao et al. (2003) and Wolter &
Trinchieri (2004), respectively (see the last column of the table). We analyse
below the possible role of X-rays from the ULX sources in the ionization of
He+.

Schaerer, Fragos & Izotov (2019) found that the observed He ii $\lambda
4686$/H$\beta$ ratio in metal-poor galaxies can be explained if the bulk of
the He+ ionizing photons is emitted by HMXBs, whose numbers are found to
increase with decreasing metallicity. They obtained an empirical relation
between Q(He+) and the X-ray luminosity, ${\rm L_{X}}$, suggesting an almost
constant ratio $q={\rm Q(He^{+})/L_{X}}=2\times 10^{10}$ photon erg-1, with
extreme values of $q$ being 1–3$\times 10^{10}$ photon erg-1. Plat et al.
(2019) warned that this process is not efficient at EW(H$\beta$)$>$200 Å, as
these systems are too young to form compact objects (neutron stars and stellar
mass black holes) necessary for the existence of HMXBs. Only two Cartwheel He
ii-emitting regions have EW(H$\beta$)$>$200 Å, and hence ionization of He+ by
ULX sources is a possibility in majority of the He ii-emitting regions with an
associated ULX source.

Figure 9:  Analysis of the possibility of ionization of He+ by the ULX sources
associated with the H ii regions of Cartwheel in He ii $\lambda 4686$/H$\beta$
ratio vs. $q={\rm Q(He^{+})/L_{X}}$ plane. Circles are detections, and
inverted triangles are 3-$\sigma$ upper limits on He ii $\lambda 4686$
detection. Regions in which The range of values for this ratio proposed by
Schaerer, Fragos & Izotov (2019) is shown by the vertical hatched area. The
points are annotated with the optically identified H ii region numbers
associated with each ULX source (see Table 1).  Figure 10: Relation between
the He ii $\lambda 4686$/H$\beta$ ratio and EW(H$\beta$) for the Cartwheel H
ii regions: circles are detections whereas triangles are 3-$\sigma$ upper
limits. Filled symbols correspond to H ii regions associated to ULX sources.
The radius of the circle is proportional to its log(He ii $\lambda
4686$/H$\beta$) ratio. All H ii regions where the He ii $\lambda 4686$ line is
detected as well as those without He ii detection, but with 3-$\sigma$ upper
limits of He ii $\lambda 4686$/H$\beta$$<$0.06 are identified by their H ii
region number.

The presence of an ULX source in 17 of the Cartwheel H ii regions allows us to
calculate the value of $q$ directly for these regions. For this purpose, we
use the Q(He+) for each region in column 8 of Table 1 and the ${\rm L_{X}}$ of
column 7 of Table 2, which was taken from Wolter & Trinchieri (2004). In
Figure 9, we plot the He ii $\lambda 4686$/H$\beta$ ratio against the $q$
values for the 11 sources for which we have well-determined values of ${\rm
L_{X}}$. The He ii $\lambda 4686$ line is detected in seven of these sources,
with the remaining four only having an upper limit for the detection of the He
ii $\lambda 4686$ line. We find a dispersion of more than 2 orders of
magnitudes in the value of $q$ for the individual H ii regions in the
Cartwheel, with only one of these regions having $q$ in the range found by
Schaerer, Fragos & Izotov (2019). This large variation in the $q$ value
suggests that the X-rays cannot be the unique source of ionization in these
sources. It is likely that not all ULX sources in the Cartwheel are HMXBs, and
instead the X-ray luminosity may be originating in supernova (SN) remnants.
Wolter, Fruscione & Mapelli (2018) discuss them as HMXBs, whereas in the
original detection papers (Gao et al., 2003; Wolter & Trinchieri, 2004), such
a possibility was firmly established for the only HLX source (#111) in the
Cartwheel. The $q$-value obtained for this source is more than an order of
magnitude lower than the value proposed by Schaerer, Fragos & Izotov (2019).
We analyse the fluxes of lines from high ionization levels such as [Ar iv] to
address the role of X-ray ionization in each of the H ii regions associated
with an ULX source.

Figure 11: (left) [O iii] $\lambda 5007$/H$\beta$ ratio vs. EW(H$\beta$);
(right) He ii $\lambda 4686$/H$\beta$ vs. [O iii] $\lambda 5007$/H$\beta$
ratio, plotted against each other. Symbols have the same meaning as in Figure
10.

##  3 Analysis of nebular line ratios

The wealth of spatial and spectroscopic information contained in the MUSE data
of the Cartwheel offers us a great opportunity to comprehensively address the
nature of ionizing sources based on the ionization state of the nebulae.
Specifically, the data allow us to study whether the H ii regions containing
the He ii $\lambda 4686$ line show any difference with respect to our control
sample of 87 H ii regions in the same galaxy, in any of the diagnostic line
ratios commonly used in ionized nebulae (Baldwin, Phillips, & Terlevich,
1981).

In this section, we discuss the general trends seen in different line ratio
diagrams. We also discuss the possible role of ULX sources in the ionization
of He+. In Sec.4, we compare the observed trends with that expected from
different theoretical scenarios of ionization of He+.

###  3.1 He ii $\lambda 4686$/H$\beta$, [O iii] $\lambda 5007$/H$\beta$ and
EW(H$\beta$)

Figure 12:  Cartwheel H ii regions in BPT diagrams following the same symbol
convention as in Figure 10; (upper left) [O iii] $\lambda 5007$/H$\beta$ vs.
[N ii] $\lambda 6583$/H$\alpha$ ratio; (upper right) [O iii] $\lambda
5007$/H$\beta$ vs. [S ii] $\lambda 6717+6731$/H$\alpha$ ratio; (bottom left)
[O iii] $\lambda 5007$/H$\beta$ vs. [O i] $\lambda 6300$/H$\alpha$ ratio;
(bottom right) [O iii] $\lambda 5007$/H$\beta$ vs. [O i] $\lambda 6300$/[O
iii] $\lambda 5007$ ratio. See text for details.  Figure 13: The He ii
$\lambda 4686$/H$\beta$ ratio plotted against the shock-sensitive [O i]
$\lambda 6300$/[O iii] $\lambda 5007$ line ratio. The meaning of the symbols
are the same as in Figure 10.

We start our analysis of the diagnostic line ratios by plotting in Figure 10
the He ii $\lambda 4686$/H$\beta$ ratio versus EW(H$\beta$), which is a
standard indicator of age of stellar populations during their early nebular
phase, as illustrated in Figure 5. In this and all the upcoming figures, we
distinguish H ii regions with and without the detection of the He ii $\lambda
4686$ nebular line by circles and inverted triangles, respectively. Filled
symbols show the H ii regions that have an associated ULX. Error bars are
shown only when the errors are significantly larger than the symbol size. H ii
regions with detected He ii $\lambda 4686$ line are annotated with their
number designation from Table 1. Care is taken to avoid superposition of the
annotations, but it was not always possible due to the crowding of points in
some of the plots.

Figure 10 shows that the He ii $\lambda 4686$ line is detected in seven of the
12 H ii regions with EW(H$\beta$)$>$100 Å. Among the high EW(H$\beta$) regions
without He ii $\lambda 4686$ detection, region#96 is identified in the plot.
This region lies slightly outside the ring in the bright southern arc (see
Figure 4). The H ii regions with lower emission EW(H$\beta$) have, in general,
fainter nebular lines making the detection of the faint He ii $\lambda 4686$
line dependent of the SNR of each spectra (see Figure 2). Three regions (#144,
#17 and #148) standout in the diagram, as they are among the regions with the
lowest EW(H$\beta$), but having the highest values of He ii $\lambda
4686$/H$\beta$ ratio. In fact, these three regions exemplify a tendency for
the upper boundary of the He ii $\lambda 4686$/H$\beta$ ratio to increase with
decreasing EW(H$\beta$).

We show the [O iii] $\lambda 5007$/H$\beta$ ratio against EW(H$\beta$) on the
left panel of the Figure 11. The [O iii] $\lambda 5007$/H$\beta$ ratio is a
well-known indicator of the ionization state of an H ii region, with high
ionization regions having a higher value of the ratio. We clarify that the
error bars on the ratio are negligibly small, including for those regions
without the He ii $\lambda 4686$ detection (inverted triangles). Note that the
higher EW(H$\beta$) regions have higher [O iii] $\lambda 5007$/H$\beta$ ratio,
independent of whether the He ii $\lambda 4686$ line is detected or not, with
region #99 (the brightest H ii region) and #148 (H ii region with the highest
He ii $\lambda 4686$/H$\beta$ ratio) lying at the extreme ends of the relation
shown by the rest of the regions. The region #111 stands out from the relation
for having a too high ionization for its observed low EW(H$\beta$). We recall
that this source is the H ii region nearest to the HLX source. However, its
association with the HLX source is doubtful as discussed in Sec. 2.6.3.
Dilution of EW(H$\beta$) from a non-ionizing cluster inside the aperture used
for extracting the spectrum is the most likely reason for this region to
displace from the observed correlation. This is supported by a visual
examination of the HST images of this region, which reveals two sources, with
the source brighter in the F814W image the likely non-ionizing cluster.

In the right panel, we show the He ii $\lambda 4686$/H$\beta$ ratio against
the [O iii] $\lambda 5007$/H$\beta$ ratio. As expected, He ii $\lambda
4686$-line detection is more frequent in high ionization H ii regions as
compared to relatively low ionization regions — it is detected in as much as
75 per cent (15 out of 21) of the high ionization regions (log([O iii]
$\lambda 5007$/H$\beta$)$>$0.60). Surprisingly, low ionization H ii regions
(log([O iii] $\lambda 5007$/H$\beta$)$<$0.40) have a non-zero detection
frequency (10 per cent; two out of 20). The increasing tendency for the upper
boundary of He ii $\lambda 4686$/H$\beta$ value with decreasing EW(H$\beta$)
is also manifested in the He ii $\lambda 4686$/H$\beta$ vs [O iii] $\lambda
5007$/H$\beta$ plot, with #99 and #148 marking the endpoints of this tendency.

###  3.2 Location of He ii-emitting H ii regions in diagnostic diagrams

In order to understand the sources of ionization of He+ in H ii regions of
Cartwheel, we show in Figure 12 all our regions in the most commonly used BPT
diagrams (Baldwin, Phillips, & Terlevich, 1981). In the first three plots (top
two and the bottom left), we use lines of low ionization potential in the
x-axis, whereas the y-axis contains [O iii] $\lambda 5007$ line, which as
discussed before originates in the high ionization zone. The H ii regions lie
along a sequence wherein the ratios of [N ii] $\lambda 6583$/H$\alpha$, [S ii]
$\lambda 6717+6731$/H$\alpha$ and [O i] $\lambda 6300$/H$\alpha$,
systematically increase as the [O iii] $\lambda 5007$/H$\beta$ ratio
decreases. The fraction of He ii-emitting regions decreases along the sequence
from top-left to bottom-right. In the bottom right panel, we show line ratios
that maximize the values for high ionization regions on the y-axis and low
ionization regions on the x-axis. In this plot, the relation is much tighter
than in other plots with the He ii-emitting regions having the lowest value of
[O i] $\lambda 6300$/[O iii] $\lambda 5007$ ratio for any fixed [O iii]
$\lambda 5007$/[O ii] $\lambda 7325$ value.

In order to investigate the possible presence of shock ionization/excitation
in H ii regions having He ii $\lambda 4686$ lines, in Figure 13 we plot the He
ii $\lambda 4686$/H$\beta$ against [O i] $\lambda 6300$/[O iii] $\lambda 5007$
ratio, which is sensitive to the presence of shocks (see e.g. Figure 15 in
Plat et al., 2019). The four regions with the highest values of He ii $\lambda
4686$/H$\beta$ (#148, 17, 144 and 108) are indeed among the H ii regions with
the highest values of the shock-sensitive ratios.

The regions ionized by the ULX sources are expected to have [O iii] $\lambda
5007$/H$\beta$$>5$ and [O i] $\lambda 6300$/H$\alpha$$>$0.1, occupying the
transition region between the Active Galactic Nuclei (AGNs) and Low-Ionization
narrow-emission line regions (LINERs) in the BPT diagrams (Gúrpide et al.,
2022). None of the ULX sources in the Cartwheel occupy these zones, suggesting
that the ULX sources have very limited role, if any, in the ionization of the
nebula with which the ULX source is positionally coincident.

##  4 Discussion

We now investigate the source of He+ ionization in the Cartwheel using the
trajectory of theoretical models of ionization in various diagnostic diagrams
using the theoretical line ratios calculated by Plat et al. (2019). In
particular, we use the diagnostic diagrams involving [O iii] $\lambda
5007$/H$\beta$ ratio plotted against [N ii] $\lambda 6583$/H$\alpha$ and the
EW(H$\beta$), [O iii] $\lambda 5007$/[O ii] $\lambda 7325$ vs. [O i] $\lambda
6300$/[O iii] $\lambda 5007$, He ii $\lambda 4686$/H$\beta$ vs. EW(H$\beta$),
He ii $\lambda 4686$/H$\beta$ vs [O i] $\lambda 6300$/[O iii] $\lambda 5007$
and [O iii] $\lambda 5007$/[O ii] $\lambda 7325$ vs [Ar iv] $\lambda
4711+4740$/[Ar iii] $\lambda 7135$. These diagrams are chosen because they are
sensitive to the different mechanisms of ionization explored in this work.

###  4.1 Calculation of theoretical nebular line ratios

We consider two sources of ionization: photoionization, which is the most
dominant source of ionization in H ii regions, and ionization by radiative
shocks. Photoionization by stellar clusters with and without binaries is
considered. Since the objects under study are H ii regions, the ionizing
source is better modelled as a single age cluster (SSP), rather than a
population of stars formed over a long period of time. We hence consider only
SSP models. However, the dilution of EW(H$\beta$) caused by the presence of
any non-ionizing source (e.g. an underlying old stellar population) inside the
aperture used for extraction is taken into account.

The emission line fluxes from an H ii region are computed with CLOUDY v17.02
(Ferland et al., 2017) following the approach of Gutkin et al. (2016). We use
C&B for single star models and BPASS v2.2.1 for binary population models. The
stellar and interstellar medium (ISM) metallicity is set to $Z=0.003$, which
corresponds to the gas phase oxygen abundance of $12+\log{\rm(O/H)}_{\rm
gas}\approx 8$ for the dust-to-metal mass ratio, $\xi_{d}$=0.3 (the solar
value is 0.36) following Gutkin et al. (2016). The ISM is considered to be of
uniform hydrogen density of $n_{\rm H}=10^{2}\,$cm-3, which along with the
rate of ionizing photons and filling factor sets the ionization parameter $U$.
Models are parametrized in terms of the zero-age volume-averaged ionization
parameter $\langle U\rangle$, which is varied by varying the filling factor,
see Gutkin et al. (2016) for details. We note that the values of
$12+\log{\rm(O/H)}_{\rm gas}$, $\log{\rm(N/O)}_{\rm gas}$ and $n_{\rm e}$ used
here are based on the mean values derived using the same MUSE dataset for the
Cartwheel ring H ii regions in a companion paper (Zaragoza-Cardiel et al.,
2022).

The H ii regions are assumed to be ionization-bounded, but contain dust grains
that compete with gas in the absorption of ionizing photons. We also discuss
the effect on the line ratios if the H ii regions are density bounded, i.e.
when the size of the H ii region is limited by the gas density, rather than
the ionizing photon rate. We account for the possible presence of holes or
cavities in the H ii regions by means of an escape fraction of ionization
photons. In addition to these two escape geometries, we follow the approach of
Ramambason et al. (2020) and compute two-zone models, combining a low and high
ionization parameter component. These two zones are either both ionization
bounded, or one of them is density bounded.

The emission from fast radiative shocks is added using the models of Alarie &
Morisset (2019)333The ISM metallicity in the shock models corresponds to the
SMC metallicity, which is slightly lower than that used for our H ii regions.
The nitrogen to oxygen abundance ratio is also lower in these models as
compared to that used in our H ii region models. for the full set of shock
velocities (100 to 1000 km s-1) available in these models. A pre-shock density
of $10^{2}\,$cm-3 and transverse magnetic field strength $B=1\mu G$, which are
typical values for the diffuse ISM in galaxies, are used. The calculated line
ratios depend weakly on these fixed values, as compared to the variation in
shock velocities. The effects of shocks are added at representative ages,
which allows us to illustrate the effect of shocks on line ratios as the
cluster evolves.

Figure 14: Theoretical models superposed on the observed points of the
Cartwheel in the line ratio diagnostic diagrams illustrated in Figure 12. Top
panels: C&B model sequences, formed by varying the initial $\log\langle
U\rangle$ from $-1$ to $-4$, at 0, 3 and 4 Myr (solid yellow lines). The
evolutionary tracks at $\log\langle U\rangle$=$-2$, $-2.5$ and $-3$ are shown
by black dashed lines. Effect of regions being density-bounded (solid green
lines at $\log\langle U\rangle$=$-2.5$), two-zone escape (red lines joining
$\log\langle U\rangle$=$-1$ and $-3.5$ at 3 Myr), and shock models (purple
tracks at 4 Myr and $\log\langle U\rangle$=$-2.5$) are illustrated at selected
locations in the diagrams. The numbers along the two-zone model sequences
correspond to the fractional contribution to the H$\beta$ flux from the high
$\log\langle U\rangle$ zone, and the numbers in the shock models correspond to
shock velocities that range from 100 to 1000 km s-1. Bottom panels: BPASS
binary SSP age sequences for two values of initial $\log\langle U\rangle$. See
the inset for identification of various lines and symbols, and Sec. 4.2 for
more details of the models used in these plots.

###  4.2 The line ratio sequence from photoionization models

In Figures 14 and 15, we overplot tracks for photoionization models for
different initial $\log\langle U\rangle$ values using C&B SSP models without
binary stars, and BPASS models with binary stars. The ratios for leaky H ii
regions, as well as for H ii regions experiencing radiative shocks are also
explored. Additionally, the effect of an underlying old population is
illustrated. We also explored the effect of binaries using BPASS models. We
refer the reader to Plat et al. (2019) for a detailed illustration of the
sensitivities of the explored parameters on the commonly observed optical and
ultraviolet line ratios. In different plots, we plot sequences of age, or
$\log\langle U\rangle$ or shock velocities, depending on the sensitivity of
the plotted quantities on the models. These are explained in annotations and
legends of the corresponding figures.

The cluster evolution is followed up to 50 Myr with three epochs (0, 3, and 4
Myr) marked with differently shaped symbols (in some of the plots, the plotted
range covers only the trajectory around 3–4 Myr). The initial $\log\langle
U\rangle$ between $-1$ and $-4$ are explored. In shock models, shocks are
assumed to provide 25 per cent of the observed H$\beta$ flux. The sequences
are formed for shock velocities between 100 to 1000 km s-1. High velocity
shocks are expected in H ii regions following the explosion of SN, which start
occurring at an SSP age of $\sim$4 Myr. Hence, the shock component is added to
the 4 Myr H ii region emission with $\log\langle U\rangle=-2.5$. These are
shown in Figures 14, 16 and 17 by purple lines. In models involving escape of
ionizing photons, the sequence is formed by varying the fraction of Lyman
continuum (LyC) photons escaping the H ii regions. In two-zone models, the
sequence is formed by varying the fractional contribution to the H$\beta$ flux
from the high $\log\langle U\rangle$ zone. These are shown in Figures 14, 16
(right) and 17 with red lines marked with dots for increase of the escape
fraction between 0.1 and 0.9.

We now discuss the results on the ionization mechanisms suggested by the
models based on the comparison of the locus of model parameters with
observations, in selected line-ratio diagrams. We first discuss the results
based on C&B models without binary stars, and at the end, comment on the
effect of having binary stars in the SSPs.

Effect of $\log\langle U\rangle$: The density of the ISM surrounding the
cluster, the rate of ionizing photons, and the volume filling factor of the
ionized gas fix the initial $\log\langle U\rangle$ of the models. In the top-
left panel of Figure 14, it can be seen that the observed sequence of [O iii]
$\lambda 5007$/H$\beta$ values can be understood as due to a dispersion in the
initial $\log\langle U\rangle$ values, with the ionizing clusters in almost
all of the H ii regions having ages between 3 and 4 Myr in C&B models. The
observed range of line ratios is covered by the models with $\log\langle
U\rangle$=$-1.5$ to $-3.0$, with the small variations in the age being
responsible for the observed spread in the direction perpendicular to the
sequence. The observed sequence in the [O iii] $\lambda 5007$/[O ii] $\lambda
7325$ vs [O i] $\lambda 6300$/[O iii] $\lambda 5007$ plane (top-right) is also
consistent as a sequence of initial $\log\langle U\rangle$. However, the
inferred age from this diagram is $\sim$0 Myr, rather than 3–4 Myr inferred
from the [O iii] $\lambda 5007$/H$\beta$ vs [N ii] $\lambda 6583$/H$\alpha$
diagram. The latter diagram is sensitive to the selective escape of photons
from either the low or the high ionization zones as will be discussed in the
two-zone models below.

Effect of dust in H ii regions: All our models include dust inside the H ii
regions. The quantity of dust is parametrized by the dust-to-metal mass ratio
$\xi_{\rm{d}}$. The dust competes with gas in the absorption of ionization
photons following the scheme proposed by Bottorff et al. (1998). Hence the
number of ionizing photons absorbed by hydrogen, and all properties that
depend on the ionizing photon flux, predicted by our models is lower than
those predicted for dust-free ionization-bounded models. The optical depth of
ionizing photons arising from dust is proportional to the total hydrogen
column density, which is proportional to the ionization parameter. So as the
ionization parameter increases, so does the absorption of ionizing photons by
dust rather than hydrogen. This effect can be noticed in Figures 15 and 16,
where the EW(H$\beta$) decreases with $\log\langle U\rangle$ at a fixed age
(see also Erb et al., 2010; Plat et al., 2019).

Effect of upper cut-off mass of the IMF: The SSPs we used for the calculation
of nebular quantities correspond to $M_{\rm u}$=300 M⊙. The non-detection of
BB (see Sec. 2.6.1) in our spectra suggests the absence of stars more massive
than 100 M⊙ in Cartwheel H ii regions. However, the results for $M_{\rm
u}$=100 M⊙ are identical to that for $M_{\rm u}$=300 M⊙ after 3.2 Myr, as can
be inferred from Figures 7 and 8. The expected values of He ii $\lambda
4686$/H$\beta$ before and during the WR phase with $M_{\rm u}$=300 M⊙ is only
marginally higher than that for $M_{\rm u}$=100 M⊙. Thus, the results
presented here are not sensitive to the choice of upper cut-off mass as long
as the SSP contains hot massive-stars that go through the WR phase ($M_{\rm
u}>$25 M⊙).

Effect of cluster evolution: The rate of ionizing photons emanating from a
cluster starts decreasing when the most massive stars, also the hottest and
the most luminous, end their main sequence life time. For clusters with the
highest mass $\sim$100 M⊙, this starts happening at $\sim$3 Myr at Z=0.003,
the metallicity corresponding to the Cartwheel. This decreases $\log\langle
U\rangle$ by $\sim$0.6 dex over the first 10 Myr, which leads to a gradual
decrease of the high ionization line intensity ratios such as [O iii] $\lambda
5007$/H$\beta$. The EW(H$\beta$) decreases slowly in the first 3 Myr reaching
values $\sim$200 Å at 3 Myr, beyond which it drastically drops by more than an
order of magnitude in $\sim$10 Myr. The decrease of $\log\langle U\rangle$ and
the EW(H$\beta$) with age leads to a decrease of [O iii] $\lambda
5007$/H$\beta$ ratio as the EW(H$\beta$) decreases.

The evolutionary track in C&B models for a given initial $\log\langle
U\rangle$ in Figure 15 follows the observed relation for clusters younger than
$\sim$4 Myr beyond which the model-predicted [O iii] $\lambda 5007$/H$\beta$
ratio is much smaller than that expected from the observed relation.
Consequently, H ii regions with EW(H$\beta$)$<$50 Å are not expected to have
detectable levels of the [O iii] $\lambda 5007$ line emission. The continuity
of the observed sequence in this diagram for the whole range of EW(H$\beta$)
suggests that the Cartwheel H ii regions are indeed ionized by clusters
younger than 4 Myr, and some physical effect is responsible for lowering the
observed values of EW(H$\beta$) compared to that predicted in the SSP models
we used. The ionization sequence in Figure 14 also implies that all our H ii
regions are younger than 4 Myr. Escape of ionizing photons, presence of
density-bounded H ii regions, presence of an older underlying population, are
some of the physical processes that we have explored in this work to explain
the decrease of EW(H$\beta$) without the corresponding decrease in [O iii]
$\lambda 5007$/H$\beta$ ratio.

Figure 15:  Comparison of the observed values for the Cartwheel H ii regions
(circles and small inverted triangles; see caption of Figure 10 for their
meaning) with theoretical models. Trajectory of evolutionary tracks for
evolving stellar populations at two values of initial $\log\langle
U\rangle$=$-1.5$ and $-2.5$ are shown (dashed black lines) with the points on
the two tracks at selected ages joined by yellow lines. The left panel shows
the C&B SSP tracks without binaries, where we also show the effect of escape
of ionizing photons for two escape geometries (holes and density bounded) at
ages 3 and 4 Myr, and the effect of adding a non-ionizing cluster of 10 Myr
that is 1 and 10 times more massive than the ionizing cluster. In the right
panel, we show the BPASS SSP models including binary stars.

Effect of an older population: H ii regions often contain a population other
than that is ionizing the surrounding gas inside the aperture used for
spectral extraction(e.g. Charlot & Fall, 1993; Mayya & Prabhu, 1996). The non-
ionizing population could be a cluster older than the ionizing cluster, or it
could be the underlying disk population. Given the recent star formation
history of the Cartwheel, it is likely that the apertures used for spectral
extraction (740 pc diameter) contain non-ionizing clusters of $\sim$10 Myr or
slightly older. Results from the recent numerical simulation of the wave
propagation in the Cartwheel by Renaud et al. (2018) support the existence of
a spread of this order in the ages of clusters in the outer ring. Multiple
clusters within the extracted apertures can be directly seen in Figure 4 at
the spatial resolution of the HST images. The presence of such a cluster would
decrease the EW(H$\beta$) without affecting the line ratios, and hence would
move the points horizontally in Figure 15. The EW(H$\beta$) would be affected
by a larger amount for larger mass of the non-ionizing cluster. In the left
panel, we show the effect of a non-ionizing cluster of 10 Myr age for two
values of relative masses: (1) equal masses, and (2) the non-ionizing cluster
10 times more massive than the ionizing cluster. This effect is shown by
crosses placed at 3 and 4 Myr of age for the ionizing cluster. A part of the
observed horizontal spread could be due to the presence of different amounts
of mass in old stellar clusters inside the apertures used for extraction.

Effect of escape of ionizing photons: We have assumed that all the ionizing
photons that are emitted by the clusters are either used in the ionization, or
absorbed by internal dust. However, there are 2 geometries by which ionizing
photons can escape the nebula without getting absorbed by gas and dust: (1)
escape through holes, and (2) escape through density-bounded zones. The former
case results in the decrease of the intensity of all lines, hence a decrease
in the EW(H$\beta$), without changing the line ratios. Thus, the escape of
ionizing photons through holes would move the points horizontally in Figure
15, producing an effect indistinguishable from the presence of a non-ionizing
population discussed above. The second case is discussed below.

Density bounded models: H ii regions have an ionization structure with the
lines of high ionization (e.g. [O iii] $\lambda 5007$) originating in zones
closer to the ionizing cluster as compared to the lines of low ionization
(e.g. [N ii]$\lambda$6583). In density-bounded H ii regions, the ionizing
photons are lost due to insufficient amount of gas to trap all the ionizing
photons. Such regions would have a reduced intensity of low-ionization lines
and EW(H$\beta$) as compared to the values for ionization-bounded regions.
This would lead to an increase of [O iii] $\lambda 5007$/H$\beta$ as
EW(H$\beta$) decreases, which is just the opposite of what is observed in
Figure 15. Hence, density-bounded models cannot explain the continuation of
the sequence to low EW(H$\beta$). Furthermore, the observed sequence in [O
iii] $\lambda 5007$/[O ii] $\lambda 7325$ vs [O i] $\lambda 6300$/[O iii]
$\lambda 5007$ ratio is not consistent with density-bounded models.

Two-zone escape models: In order to reproduce the observed large range of [O
i] $\lambda 6300$/[O iii] $\lambda 5007$ ratios in LyC galaxies, Ramambason et
al. (2020) proposed a model wherein the nebulae loose ionizing photons
selectively from the high-$U$ or low-$U$ zones. Such a configuration is
naturally expected if the ISM around the clusters is non-uniform, and contains
dense clumps and filaments. Results for two-zone models are calculated by
combining the spectrum of a high initial $\log\langle U\rangle$ nebula with a
second spectrum of a low initial $\log\langle U\rangle$ nebula, with the
relative luminosity of the H$\beta$ lines in the two spectra used as a free
parameter. This free parameter, $\omega$, varies between 0 and 1, which is
defined as the fractional contribution of the high $\log\langle U\rangle$
spectrum to the total H$\beta$ luminosity. Thus, $\omega$=1 corresponds to a
nebula containing only high ionization zone and $\omega$=0 corresponds to a
nebula containing only low ionization zone. The ionization-bounded or density-
bounded status of the two zones are independent of each other. In Figure 14
(right), we show the locus of these models by red lines for three cases, all
corresponding to 3 Myr age clusters with initial $\log\langle U\rangle$=$-1$
and $\log\langle U\rangle$=$-3.5$ for the high and low ionization zones,
respectively. The 3 cases are: (1) both the zones are ionization-bounded
(solid line), (2) combination of an ionization-bounded low $\log\langle
U\rangle$ zone, with a density bounded high $\log\langle U\rangle$ zone with
an escape fraction, $f_{\rm esc}\sim 30$ percent (dashed line), and (3)
combination of an ionization-bounded high $\log\langle U\rangle$ zone, with a
density bounded low $\log\langle U\rangle$ zone with $f_{\rm esc}\sim 10$
percent (dotted line). Values for the free parameters are chosen that best
illustrate the observed trends in Figure 14 (right). C&B ionization-bounded
models (yellow lines) even for the youngest age lie slightly to the left of
the observed points in this figure. The tracks for ages of 3 and 4 Myr are
further away from the observed points. On the other hand, the two zone escape
models are able to explain the dataset for cluster ages of 3 Myr — most of the
observed points lie between the dashed red lines (3 Myr track with selective
escape of ionization photons from high $\log\langle U\rangle$ zone) and the
yellow line for the 3 Myr track (ionization bounded regions without any
escape). Thus, with two-zone models, it is possible to obtain consistent ages
of $\sim$3–4 Myr for the majority of the H ii regions in the Cartwheel, from
both the diagnostic diagrams in Figure 14.

Shocks: Some of the H ii regions, though principally photoionized by the
stars, can also experience shocks, especially during the post-main sequence
evolution and the death of massive stars. In order to illustrate the effect of
shocks in the line ratio diagrams, shock models of Alarie & Morisset (2019)
are added to the evolutionary track of SSP models at one particular epoch (4
Myr) with $\log\langle U\rangle=-2.5$. The shocks are parametrized by 3
parameters: the percentage of energy in shocks compared to photoionization
energy to ionize hydrogen, the velocity of the shock and the shock age. We
used their grid of truncated shock models. We here plot models where 25
percent of the total H$\beta$ flux is provided through shocks for various
values of shock velocities. At each velocity, we plot the ratios as the shock
propagates into the ISM. Increasing the shock velocity increases the line
ratios involving high ionization, whereas the low ionization lines become
stronger as the shock propagates. The effect of shocks on the line ratios can
be best seen in the [O iii] $\lambda 5007$/[O ii] $\lambda 7325$ vs. [O i]
$\lambda 6300$/[O iii] $\lambda 5007$ diagram of Figure 14 (top right panel).
High velocity shocks tend to move the points to the right, mostly occupied by
H ii regions not showing He ii $\lambda 4686$ line. Among the regions with He
ii $\lambda 4686$ emission, shocks could be important in low-ionization H ii
regions such as #148. On the other hand, shocks have very little effect in the
[O iii] $\lambda 5007$/H$\beta$ vs [N ii] $\lambda 6583$/H$\alpha$ plot (top
left panel), and no effect on the EW(H$\beta$).

Figure 16:  (left) He ii $\lambda 4686$/H$\beta$ vs. EW(H$\beta$); (right) He
ii $\lambda 4686$/H$\beta$ vs. [O i] $\lambda 6300$/[O iii] $\lambda 5007$
ratio. See the guide to the lines and symbols in the box below the graphs and
the text in the beginning of Sec. 4.2 for the explanation of parameters for
the shock and 2 zone ionization models, and see caption of Figure 10 for the
meaning of symbols for the observed points (circles and small inverted
triangles).

Cluster evolution with binaries: We now discuss the effect of binary
population on the results obtained from C&B models. For this purpose, we use
the BPASS binary models plotted in the bottom panels of Figures 14, and right
panel of Figure 15. The result that the observed sequence of points is a
sequence in $\log\langle U\rangle$ holds even after including binary stars in
the SSPs. Star clusters containing binary stars produce the ionizing photons
over an extended period of time ($>$15 Myr) as compared to the evolution
without binaries. This causes both the [O iii] $\lambda 5007$/H$\beta$ and the
EW(H$\beta$) to decrease more slowly with evolution as compared to the
evolution of clusters without binary stars. The evolutionary locus and
$\log\langle U\rangle$ sequences in binary models are almost parallel in
Figure 15, both following the ionization sequences seen in these diagrams.
Thus, under the binary models, Cartwheel H ii regions could have an age range
between 0 and 15 Myr and $\log\langle U\rangle$ range between $-1.5$ to
$-3.5$. However, at ages as late as 15 Myr, the EW(He ii $\lambda 4686$)
decreases by more than an order of magnitude (see Figure 5). Hence, it is
highly unlikely that the He ii $\lambda 4686$ detections correspond to the
faint late phase, rather than the luminous early phase.

Thus, the inclusion of binary models does not qualitatively change the
conclusions arrived from using C&B models, which do not take into account the
possible presence of binary stars.

###  4.3 On the ionization state of Cartwheel H ii regions

The observed range of line ratios in the H ii regions of the Cartwheel
corresponds to photoionization by young clusters (age$\sim$3–4 Myr in C&B
models or 3–15 Myr in BPASS binary models) with initial H ii-averaged
ionization parameter $\log\langle U\rangle$ lying between $-1.5$ to $-3.5$.
The [O iii] $\lambda 5007$/H$\beta$ ratio, which is a direct measure of the
degree of ionization of an H ii region, is correlated with EW(H$\beta$) over
the entire observed range of both the quantities. This correlation suggests a
systematic decrease of the [O iii] $\lambda 5007$/H$\beta$ ratio, or
equivalently $\log\langle U\rangle$, with age. For the ionization-bounded
models that we have used, $\log\langle U\rangle$ decreases only by 0.6 dex or
alternatively [O iii] $\lambda 5007$/H$\beta$ by 0.2 dex in 4 Myr in C&B SSP
models and 0.1 dex in 15 Myr in BPASS binary SSP models. The amount of change
of this ratio in SSP models depends on the metallicity, with the values in our
models being consistent with the values obtained by Stasinska & Leitherer
(1996) for the Cartwheel metallicity. Thus, an age-dependent process of
softening of $\log\langle U\rangle$ is required in order to interpret the
observed correlation between [O iii] $\lambda 5007$/H$\beta$ and EW(H$\beta$)
primarily as an age sequence.

Kim, Kim & Ostriker (2019) found that the fraction of the escape of the
ionizing photons systematically increases with age of the cluster due to the
increased amount of feedback with age. The escape of ionizing photons has been
long suspected to be one of the reasons for the low EW(H$\beta$) of H ii
regions (e.g. Mayya & Prabhu, 1996). Castellanos, Diáz & Tenorio-Tagle (2002)
determined escape fraction between 0.1–0.7 for three H ii regions they
analysed. The mechanical energy feedback to the ambient ISM can also decrease
$\log\langle U\rangle$ due to the decrease in the density following the
feedback-driven expansion of the H ii regions. Martín-Manjón et al. (2010)
found that this effect can decrease $\log\langle U\rangle$ by as much as 3 dex
at the Cartwheel metallicity. All these suggest that the evolution-dependent
feedback is driving the observed correlation through the escape of ionizing
photons and the decrease in the ISM density. Thus, statistically, the high
excitation regions are systematically younger than the low excitation regions.

We also investigated the effect of radiative shocks in H ii regions primarily
photoionized by clusters as described in Sec. 4.2 above. High velocity shocks
tend to increase the line ratios involving low ionization ions such as the [O
i] $\lambda 6300$ line (e.g. Stasinska et al., 2015), which would move the
points to the right of the ionization sequence in the right panels of Figure
14. A tendency of broadening of the sequence in this diagram for low-
ionization H ii regions is seen, suggesting a possible presence of shocks in
some low $\log\langle U\rangle$, which are relatively older, H ii regions.

###  4.4 The ionizing source of He+ in the Cartwheel H ii regions

Having addressed the ionization mechanism and physical processes prevalent in
the Cartwheel H ii regions, we now investigate whether the same physical
mechanisms account for the observed He ii $\lambda 4686$/H$\beta$ ratio. We
have chosen two plots to verify this: He ii $\lambda 4686$/H$\beta$ vs
EW(H$\beta$) and He ii $\lambda 4686$/H$\beta$ vs [O i] $\lambda 6300$/[O iii]
$\lambda 5007$. These are shown in Figure 16 for the chosen theoretical tracks
from C&B models, along with special scenarios discussed in the paragraphs
above. We do not show the plots with BPASS binary models, as the He ii
$\lambda 4686$/H$\beta$ ratios produced by these models are systematically
lower than the observed values as illustrated in Figure 6.

####  4.4.1 He++ nebulae photoionized by WR stars

The majority of He ii $\lambda 4686$-emitting regions fall between the tracks
corresponding to ionization-bounded H ii regions photoionized by clusters of
age between 3 and 4 Myr. This age range corresponds to the WR-phase in C&B
models, as can be inferred from Figure 6.

Escape of ionizing photons through holes, and/or the presence of non-ionizing
population: The $\log\langle U\rangle$ values inferred for each region using
the He ii $\lambda 4686$/H$\beta$ vs EW(H$\beta$) are systematically higher by
around 1 dex as compared to that inferred from the He ii $\lambda
4686$/H$\beta$ vs [O i] $\lambda 6300$/[O iii] $\lambda 5007$ plot. This can
be explained as due to the escape of ionizing photons through holes, and/or
the presence of a spatially close older cluster in majority of the Cartwheel H
ii regions, both of which displace the tracks horizontally without changing
the flux ratios of the nebular lines. This inference is consistent with the
observed correlation between [O iii] $\lambda 5007$/H$\beta$ ratio and
EW(H$\beta$).

Is the ionization by WR stars the only way to explain all the observed line
ratios. Is the source of ionization of He+ the same as that of other ions? In
order to address these questions, we here summarize the results from other
scenarios that we have explored.

Density-bounded models: The loci of density-bounded H ii regions in the line
ratio diagrams are shown by green solid lines in the two panels of Figure 16
for C&B models of initial $\log\langle U\rangle$=$-2.5$. The length of the
plotted lines correspond to 50 percent of the ionizing photons escaping the
nebula from the density bounded zones. The locations of the observed points,
with the exception of regions #144, #17 and #148, can be reconciled with this
scenario, but for a lower initial $\log\langle U\rangle$ value, as compared to
the ionization-bounded case. However, the observed ionization sequences (see
Figure 15) are not consistent with a low value of $\log\langle U\rangle$.
Thus, we rule out the possibility that the majority of the Cartwheel H ii
regions are density-bounded with a low initial $\log\langle U\rangle$.

Role of radiative shocks and two-zone escape models: In Figure 16, the
radiative shocks and two-zone escape models are plotted for a 3 Myr old
ionizing cluster in the right panel, with the aim of covering the observed
ratios of regions #144, #17 and #148. It can be inferred from the plot that
these scenarios, especially with escape from high $\log\langle U\rangle$ zone
(dashed red line) would cover the observed range of values for the majority of
the regions if the ionizing cluster is $\sim$4 Myr old. In fact, we have
considered such a possibility to explain the behaviour of points in the right
panel of Figure 16. However, these scenarios produce higher than the observed
values of [Ar iv] $\lambda 4711+4740$/[Ar iii] $\lambda 7135$ line ratio, as
will be discussed later in this section. Thus, we do not find it necessary to
look beyond the WR stars to explain the observed He++ nebulae. In summary, the
majority of the He++ nebulae in the Cartwheel are photoionized by WR stars,
with the H ii regions enclosing the He++ nebulae. Different observed
quantities can be consistently explained with $\sim$50 percent of the hydrogen
ionizing photons escaping through holes, and/or the presence of older non-
ionizing populations inside the aperture used for extraction.

####  4.4.2 He++ nebulae requiring alternative sources of ionization

Exceptions to the above scenario are five H ii regions that standout from the
main group. Two (#99 & #112) are at the high-EW(H$\beta$) end, and the other
three (#144, #17 & #148) are among the lowest EW(H$\beta$) H ii regions.

Ionization by ULX source and stripped binary stars: The two high-EW(H$\beta$)
regions also have the highest [O iii] $\lambda 5007$/H$\beta$ ratio and the
lowest [O i] $\lambda 6300$/[O iii] $\lambda 5007$ ratio, all indicating that
these regions have the highest ionization parameter, and the youngest of the
sample regions. We infer $\log\langle U\rangle$$\sim-$2.0 and an age
corresponding to the pre-WR phase, suggesting that the hot main-sequence stars
are the most likely sources of He+ ionization in these two sources.

Region #99 is the brightest, and the most massive H ii region in the Cartwheel
with an estimated number of more than 11,000 O stars, assuming O stars are the
sole sources of ionization of hydrogen. This region is associated with an ULX
source, and hence we discuss here the possible role of this ULX source in the
ionization of He+. The observed [O iii] $\lambda 5007$/H$\beta$ is high enough
as expected for the ionization by the hard radiation from a ULX source.
However, the observed [O i] $\lambda 6300$/H$\alpha$ ratio for this regions is
significantly lower than that expected for the ionization by a ULX source
(Gúrpide et al., 2022), and hence ULX cannot be the sole or principal source
of ionization of this region. The line ratio diagrams presented suggest that
the photoionization by the main-sequence stars is a viable source of
ionization. The ULX may provide additional photons for the ionization of He+.
The observed EW(H$\beta$), which in spite of being the highest among the
sample regions, is still more than a factor of two lower than that expected
for single burst of age$<$3 Myr, suggests the presence of underlying non-
ionizing populations. It is likely that the star formation in the region is
proceeding for more than 3 Myr or that it had a star formation event in the
recent past. These slightly evolved stars had enough time to form HMXBs that
are generating the X-rays emitted by the ULX source (Plat et al., 2019).

Region #112 has the lowest value of He ii $\lambda 4686$/H$\beta$ among the
regions studied here, with a value intermediate between that of main-sequence
and WR phases. Like in the case of #99, all line ratio diagrams presented here
suggest ionization of He+ by main sequence stars.

Figure 17:  [O iii] $\lambda 5007$/[O ii] $\lambda 7325$ vs. [Ar iv] $\lambda
4711+4740$/[Ar iii] $\lambda 7135$ ratio. [Ar iv] lines are detected only in
the regions indicated by the black circles, with error bars. All red coloured
symbols (circles and triangles) are 3-$\sigma$ upper limits on the [Ar iv]
$\lambda 4711+4740$/[Ar iii] $\lambda 7135$ ratio. The box below the plot
contains a guide to the models plotted. See text for details.

Regions affected by radiative shocks and/or two-zone escape models: We now
discuss the ionization mechanism of He+ in regions #148, #17 and #144, the
three low-EW(H$\beta$) regions with the highest ratio of He ii $\lambda
4686$/H$\beta$. These three regions are at the low $\log\langle U\rangle$ end
of the ionization sequence. The He ii $\lambda 4686$/H$\beta$ ratios predicted
by the traditional ionization-bounded case and photoionized by stellar
radiation are much lower at these low $\log\langle U\rangle$ values as
compared to the observed values for these three regions. Two of the various
processes we have explored produce the observed high He ii $\lambda
4686$/H$\beta$ ratios at low $\log\langle U\rangle$ values. These are (1)
radiative shock contribution, and (2) two-zone escape models with $\sim$50
percent escape from the high $\log\langle U\rangle$ zone. Regions #144, #17
and #148, in that order, lie on a sequence of increasing shock velocities with
shock velocities in the 100–1000 km s-1 range, with the He ii $\lambda
4686$/H$\beta$ value of #148 only produced by shock models. The two-zone
escape models can also explain their location in the plots. Their low
EW(H$\beta$) and low $\log\langle U\rangle$ suggest that these three regions
are more evolved than the rest of the regions, and are likely to be in the
post-WR phase. We hence favour shock ionization associated with SN explosions
as the most likely causes of the observed high values of He ii $\lambda
4686$/H$\beta$ ratio. SN explosions can also create escape routes for ionizing
photons from the high $\log\langle U\rangle$ zone, and hence shocks and two-
zone escape scenarios could be co-existing. Region #144 is associated with a
ULX source whose X-ray luminosity is high enough to contribute to He+
ionization. Thus, X-ray ionization could also be prevalent in #144.

Stasinska et al. (2015) has advocated the use of the [Ar iv] $\lambda
4711+4740$/[Ar iii] $\lambda 7135$ ratios to test the hardness of the ionizing
spectrum, especially for the He ii $\lambda 4686$-emitting regions. Ar++ has
an ionization potential of 40.7 ev and hence the collisionally excited [Ar iv]
lines are expected to be present in He ii $\lambda 4686$-emitting regions. The
[Ar iv]$\lambda\lambda$4711,4740 doublet is relatively faint. Nevertheless,
the doublet is detected at more than 3$\sigma$ levels in 14 of the 32 He ii
$\lambda 4686$-emitting regions. In Figure 17, we plot the [O iii] $\lambda
5007$/[O ii] $\lambda 7325$ ratios against the [Ar iv] $\lambda 4711+4740$/[Ar
iii] $\lambda 7135$ line ratio. For photoionized nebulae, the locus of points
in this diagram is mainly governed by $\log\langle U\rangle$, with the
observed points lying between $-3.0<$$\log\langle U\rangle$$<-2.0$. Spectral
evolution in the age range 0–4 Myr introduces small spread in the direction
perpendicular to the sequence formed by ranges of initial $\log\langle
U\rangle$. On the other hand, the presence of radiative shocks and/or
selective escape of photons from low or high $\log\langle U\rangle$ zones
moves the points to the right (i.e. higher [Ar iv] $\lambda 4711+4740$/[Ar
iii] $\lambda 7135$ ratios). Thus, this figure is useful to discriminate the
purely photoionized models from the photoionized+shock models, or the models
involving selective escape of photons. Unfortunately the last two cases follow
similar trajectories in the diagram, and hence cannot be distinguished.

The main-group of the He ii $\lambda 4686$-emitting regions in which [Ar iv]
lines have been detected lie along the photoionization sequence by the SSP
models, and more importantly, are not consistent with the presence of shocks
and/or two-zone escape scenarios, independent of the age of the ionizing
clusters. Thus, this diagram helps us to break the degeneracy seen in Figure
16. Region #99 lies clearly to the right of the photoionization sequence,
reiterating that the hard radiation from the ULX source plays a role in the
ionization of ions that have higher than 40 eV of ionization potential. The
second region in which we cannot rule out ionization by the ULX source is
#144. The [Ar iv] lines are not detected in this region, but the upper limit
on the [Ar iv] $\lambda 4711+4740$/[Ar iii] $\lambda 7135$ ratio is slightly
to the right of the photoionization sequence by the SSP models. Unfortunately,
we have only upper limits on the detection of the [Ar iv] lines in the
remaining two interesting regions #148 and #17. The observed upper limits in
#148 and #17 are consistent with the presence of shocks and/or two-zone escape
scenarios.

###  4.5 Regions with non-detection of He ii$\lambda$ 4686 line

We here carry out an analysis on the nature of the H ii regions where the He
ii $\lambda 4686$ line could not be detected at the 3-$\sigma$ confidence
level. Given that the WR stars are the principal sources of He+ ionizing
photons in our sample regions, and that the WR stars appear only for a short
duration in an SSP, this fraction is expected to be a function of age. The
EW(H$\beta$) is an excellent proxy for age in young stellar systems (see
Figures 5), and hence we analyse the detection fraction as a function of
EW(H$\beta$). From the analysis of Figures 15 and 16, we arrived at the
conclusion that quantitatively the observed values of EW(H$\beta$) are
systematically smaller as compared to the values expected for ionization-
bounded H ii regions using C&B models. Continuum contribution from a non-
ionizing population and the escape of ionizing photons from the nebula are two
principal mechanisms that lead to a decrease in EW(H$\beta$) from those
expected for ionization-bounded H ii regions ionized by a single-age
population. The factor by which the EW(H$\beta$) is reduced may vary from
region to region. For the sake of using EW(H$\beta$) as a proxy for age, we
assume a reduction factor anywhere between 0 and 50% for the sample regions.

In Figure 18, we show the fraction of H ii regions detected as a function of
the observed EW(H$\beta$). The theoretically expected range of EW(H$\beta$)
during the WR phase is shown by the shaded area, which takes into account the
reduction of EW(H$\beta$) by 0 to 50% during the WR phase. The distribution of
observed EW(H$\beta$) for the whole sample (dotted histogram), and the sample
of regions where we have achieved a 3-$\sigma$ sensitivity to detect the He ii
$\lambda 4686$ line if they had He ii $\lambda 4686$/H$\beta$$\geq$0.01
(dashed histogram), are shown. For the whole sample (black line), the
detection fraction decreases with decreasing EW(H$\beta$). For the subset of H
ii regions (red line) that have SNRs sufficient to detect the He ii $\lambda
4686$ line for typical values during WR phase (He ii $\lambda
4686$/H$\beta$$\geq$0.01), the detection fraction peaks at
EW(H$\beta$)$\sim$60 Å. The peak value reaches as high as 90%. The
EW(H$\beta$) at the peak value corresponds to that during the WR phase. This
suggests that our dataset is sensitive enough to detect almost all ($\sim$90%)
He++ nebulae ionized by the WR stars. Before the onset of the WR phase (at the
high EW(H$\beta$)-end), the detection fraction is nonzero. The He ii $\lambda
4686$ line is detected in two of the three H ii regions, indicating that the
He ii $\lambda 4686$/H$\beta$ ratio might be higher than the values predicted
in the current SSPs during the main sequence phase of stars. The ULX is the
likely source of additional ionization in one of these (#99), whereas stripped
binary stars, which are not included in the C&B models, could be the possible
source of the weak ionization in the other (#112).

The rest of the non-detections (26) corresponds to low-EW(H$\beta$) regions.
In the C&B models, these regions correspond to the post-WR phase. However, the
inclusion of the binary channel for the formation of WR stars in the BPASS
models extends the duration of WR phase to these low EW(H$\beta$) values, with
the expected ratio of He ii $\lambda 4686$/H$\beta$ lower than that during the
WR phase in C&B models. Unfortunately, we do not reach the sensitivity to
detect the He ii $\lambda 4686$ line with He ii $\lambda 4686$/H$\beta$$<$0.01
for regions with EW(H$\beta$)$<40$ Å regions, and hence the non-detection of
the He ii $\lambda 4686$ line could be due to the absence of He++ ions in
these regions, or that we do not reach the sensitivity level required to
detect weak ionization from the WR stars formed through the binary channel.

In general, the H ii regions with He ii $\lambda 4686$-line detection have
higher ionization parameter as compared to the H ii regions without the He ii
$\lambda 4686$-line detection, at each EW(H$\beta$) bin.

The location of H ii regions with non-detection of He ii $\lambda 4686$ line
in Figure 17 suggests shock and/or two-zone escape scenarios are more
prevalent in these regions as compared to the He ii $\lambda 4686$-emitting
main-group H ii regions. These processes are strong enough to increase the He
ii $\lambda 4686$ lines above the detectable limits in only three cases (#144,
#17 and #148).

Figure 18:  Fraction of H ii regions with detection of the He ii $\lambda
4686$-line as a function of the EW(H$\beta$) for the whole sample (black solid
line) and a sample of H ii regions that had sensitivity to detect the He ii
$\lambda 4686$ line if He ii $\lambda 4686$/H$\beta$$\geq$0.01 (red solid
line). The distribution of the EW(H$\beta$) for the whole sample (dotted
histogram) and a sample of H ii regions that had sensitivity to detect the He
ii $\lambda 4686$ line if He ii $\lambda 4686$/H$\beta$$\geq$0.01 (dashed
histogram) are also plotted, with the right axis showing the numbers. For
reference, we also show the range of EW(H$\beta$) when the number of WR stars
in the C&B $M_{\rm u}=100$ M⊙ models is non-zero, for an ionization-bounded H
ii region (the shaded area). The error on the derived fractions for the whole
sample is shown, which is based on the square-root of the number of H ii
regions in each bin (the sizes of the error bars on the red line are similar
and hence we omit them for the sake of clarity of the figure).

##  5 Conclusions

We have carried out a search for He ii $\lambda 4686$ nebular line in the
Cartwheel H ii regions using the VLT/MUSE datacube. We detect the He ii
$\lambda 4686$ line in 32 H ii regions, with a mean value of He ii $\lambda
4686$/H$\beta$=0.010$\pm$0.003. All the detections are situated in the star-
forming ring of the Cartwheel, with ten of these sources coinciding with the
location of a ULX source. We use commonly used diagnostic line ratios to
compare the ionization properties of H ii regions with and without the
detection of the He ii $\lambda 4686$ line. The He ii $\lambda 4686$ line-
emitting regions with and without the ULX sources, in general, show similar
ionization properties in the diagnostic diagrams. Hence, the ULX sources are
not the principal suppliers of ionizing photons in all the H ii regions
containing ULX sources. Analysis of the diagnostic diagrams using C&B SSPs
suggests that the majority (27) of the detections correspond to H ii regions
in their WR phase, with two and three detections corresponding to H ii regions
in their pre-WR and post-WR phases, respectively. However, the characteristic
BB indicating the presence of WR stars is not detected in our sample regions.
We illustrate that this non-detection is due to the relatively low EWs of the
BB in SSPs for IMFs with $M_{\rm u}\leq$100 M⊙ at the metallicity of the
Cartwheel, even when the SSPs have sufficient number of WR stars to provide
the ionization of He+. We suggest that main sequence stars are the major
contributors to ionization in the two pre-WR H ii regions, with an additional
contribution from other hard sources. In region#99, this additional
contribution most likely comes from the ULX source. On the other hand, the
three H ii regions in the post-WR phase may be either ionized by radiative
shocks or their H ii regions are leaky. We find a correlation between [O iii]
$\lambda 5007$/H$\beta$ and EW(H$\beta$), which requires a more rapid
softening of the ionization parameter $\log\langle U\rangle$ than that
considered in C&B SSP models. This rapid softening can be naturally explained
if the H ii regions expand as the cluster evolves due to the feedback from
massive stars. The detection frequency of the He ii $\lambda 4686$ line
reaches values as high as 90% for H ii regions that have EW(H$\beta$)=40–70 Å.
These values of EW(H$\beta$) correspond to late stages of the WR phase in the
C&B models. Our dataset lacks sensitivity to detect the He ii $\lambda 4686$
line from H ii regions with EW(H$\beta$)$<$40 Å, when WR stars formed from the
binary channel are expected to dominate the ionization of He+.

## Acknowledgements

We thank an anonymous referee for many thoughtful comments that improved the
paper. We also thank Gerardo Ramos-Larios who helped us in preparing the
images appearing in Figures 1 and 4, and CONACyT for the research grant
CB-A1-S-25070 (YDM). This work is based on data obtained from the ESO Science
Archive Facility, program ID: 60.A-9333. 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.

## Data availability

The fluxes of principal emission lines used in this work are available in the
article and in its online supplementary material. The reduced fits files on
which these data are based will be shared on reasonable request to the first
author. The ESO datacubes are in the public domain. The link and observation
ID are available in the article.

## References

  * Alarie & Morisset (2019) Alarie A., Morisset C. 2019, RMxAA, 55, 377
  * Appleton & Struck-Marcel (1996) Appleton, P. N. & Struck-Marcel, C. 2010, Fundamentals Cosmic Phys., 16, 111
  * Baldwin, Phillips, & Terlevich (1981) Baldwin J. A., Phillips M. M., Terlevich R. 1981, PASP, 93, 5
  * Bacon et al. (2010) Bacon, R. et al. 2010, Proc. SPIE, 7735, 773508
  * Belfiore et al. (2022) Belfiore, F., Sontoro, F., Groves, B. et al. 2022, A&A, 659, 26
  * Bottorff et al. (1998) Bottorff M., Lamothe J., Momjian E., Verner E., Vinković D., Ferland G., 1998, PASP, 110, 1040
  * Bressan et al. (2012) Bressan, A., Marigo, P., Girardi, L. et al. 2012, MNRAS, 427, 127
  * Bruzual & Charlot (2003) Bruzual, A. G., Charlot, S. 2003, MNRAS, 344, 1000
  * Castellanos, Diáz & Tenorio-Tagle (2002) Castellanos, M., Diáz, A. I., Tenorio-Tagle, G. 2002, ApJ, 579, L79
  * Chabrier (2003) Chabrier, G. 2003, PASP, 115, 763
  * Charlot & Fall (1993) Charlot S., Fall S. M. 1993, ApJ, 415, 580
  * Chen et al. (2015) Chen, Y., Bressan, A., Girardi, L., et al. 2015, MNRAS 452, 1068
  * Crowther (2007) Crowther, P. A. 2007, ARA&A, 45, 177
  * Eldridge et al. (2017) Eldridge, J. J., Stanway, E. R., Xiao, L. et al. 2017, PASA, 34, e058
  * Erb et al. (2010) Erb, D. K., Pettini M., Shapley A. E., Steidel C. C.. Law D. R., Reddy N. A., 2010, ApJ, 719, 2
  * Feltre, Charlot, & Gutkin (2016) Feltre A., Charlot S., Gutkin J. 2016, MNRAS, 456, 3354
  * Ferland et al. (2017) Ferland G. J., Chatzikos M., Guzmán F., et al. 2017, RMxAA, 53, 385
  * Fosbury & Hawarden (1977) Fosbury, R. A. E. & Hawarden, T. G. 1977, MNRAS, 178, 473
  * Gao et al. (2003) Gao, Yu, Wang, Q. Daniel, Appleton, P. N. & Lucas, Ray A. 2003, ApJ, 596, L171
  * Gil de Paz et al. (2018) Gil de Paz, A., Carrasco, E., Gallego, J. et al. 2018, SPIE, 1070217, SPIE10702
  * Götberg et al. (2018) Götberg Y., de Mink S. E., Groh J. H., Kupfer T., Crowther P. A., Zapartas E., Renzo M. 2018, A&A, 615, A78.
  * Gómez-González et al. (2020) Gómez-González, V.M.A., et al. 2020, MNRAS, 493, 3879
  * Gómez-González et al. (2021) Gómez-González, V.M.A., et al. 2021, MNRAS, 500, 2076
  * Gúrpide et al. (2022) Gúrpide A., Parra M., Godet O., Contini T., Olive J.-F., 2022, A&A, 666, A100
  * Gutkin et al. (2016) Gutkin J., Charlot S. & Bruzual, G. 2016, MNRAS, 462, 1757
  * Higdon (1995) Higdon, J. L. 1995, ApJ, 455, 524
  * Kehrig et al. (2015) Kehrig, C., Vílchez, J. M., Pérez-Montero, E. et al. 2015, ApJ, 80, L28
  * Kehrig et al. (2018) Kehrig, C., Vílchez, J. M., Guerrero, M. A. et al. 2018, MNRAS, 480, 1081
  * Kim, Kim & Ostriker (2019) Kim, Jeong-Gyu, Kim, Woong-Tae, Ostriker, Eve C. 2019, ApJ, 883, 102
  * López-Sánchez & Esteban (2010) López-Sánchez Á. R., Esteban C. 2010, A&A, 516, A104
  * Lynds & Toomre (1976) Lynds, R. & Toomre, A. 1976, ApJ, 209, 382
  * Marcum, Appleton & Higdon (1992) Marcum, P.M, Appleton, P.N, & Higdon, J. L. 1992, ApJ, 399, 57
  * Martín-Manjón et al. (2010) Martín-Manjón, M. L., García-Vargas, M. L., Mollá, M., Díaz, A. I. 2010, MNRAS, 403, 2012
  * Mapelli et al. (2010) Mapelli, M., Ripamonti, E., Zampieri, L., Colpi, M. & Bressan, A. 2010, MNRAS, 408, 234
  * Mayya & Prabhu (1996) Mayya Y. D., Prabhu T. P. 1996, AJ, 111, 1252
  * Mayya et al. (2020) Mayya, Y. D., Carrasco, E., Gómez-González, V. M. A. et al. 2020, MNRAS, 498, 1496
  * Osterbrock & Ferland (2006) Osterbrock, D. E. & Ferland, G. J. 2006, in Astrophysics of Gaseous Nebulae and Active Galactic Nuclei (CA: University Science Books)
  * Pérez-Montero (2017) Pérez-Montero, E. 2017, PASP, 129, 043001
  * Plat et al. (2019) Plat, A., Charlot, S., Bruzual, G., et al. 2019, MNRAS, 490, 978
  * Ramambason et al. (2020) Ramambason L., Schaerer D., Stasińska G., et al., 2020, A&A, 644, A21
  * Renaud et al. (2018) Renaud F., Athanassoula E., Amram P., et al. 2018, MNRAS, 473, 585
  * Schaerer (1996) Schaerer, D., 1996, ApJ, 467, L17
  * Schaerer, Fragos & Izotov (2019) Schaerer D., Fragos T., Izotov Y. I., 2019 A&A, 622, L10
  * Shirazi & Brinchmann (2012) Shirazi, M. & Brinchmann, J. 2012, MNRAS, 421, 1043
  * Stasinska & Leitherer (1996) Stasińska G., Leitherer, C. 1996, ApJSS, 107, 661
  * Stasinska et al. (2015) Stasińska G., Izotov Yu., Morisset, C., Guseva, N. 2015, A&A, 576, A83
  * Stanway & Eldridge (2018) Stanway E. R., Eldridge J. J. 2018, MNRAS, 479, 75
  * Struck (2010) Struck, C. 2010 MNRAS, 403, 1516
  * Todt et al. (2015) Todt, H., Sander, A., Hainich, R. et al. 2015, A&A, 579, A75
  * Tresse et al. (1999) Tresse, L., Maddox, S., Loveday, J. & Singleton, C. 1999, MNRAS, 310, 262
  * Wolter & Trinchieri (2004) Wolter, A. & Trinchieri, G. 2004, A&A, 426, 787
  * Wolter, Fruscione & Mapelli (2018) Wolter, A., Fruscione, A. & Mapelli, M. 2018, ApJ, 863, 43
  * Zaragoza-Cardiel et al. (2022) Zaragoza-Cardiel J., Gómez-González V. M. A., Mayya D., Ramos-Larios G., 2022, MNRAS, 514, 1689