11institutetext: Departamento de Física de la Tierra y Astrofísica, Instituto
de Física de Partículas y del Cosmos, IPARCOS. Universidad Complutense de
Madrid (UCM), E-28040, Madrid, Spain 11email<EMAIL_ADDRESS>22institutetext:
Institute of Theoretical Physics and Astronomy, Vilnius University, Sauletekio
av. 3, 10257, Vilnius, Lithuania 33institutetext: Main Astronomical
Observatory, National Academy of Sciences of Ukraine, 27 Akademika Zabolotnoho
St, 03680, Kiev, Ukraine 44institutetext: Instituto Nacional de Astrofísica,
Óptica y Electrónica (INAOE), Luis E. Erro 1, Tonantzintla, Puebla, C.P.
72840, México 55institutetext: Consejo Nacional de Ciencia y Tecnología, Av.
Insurgentes Sur 1582, 03940, Ciudad de México, Mexico 66institutetext: Faculty
of Physics, Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679 Munich,
Germany 77institutetext: School of Physical Sciences and Centre for
Astrophysics & Relativity, Dublin City University, Glasnevin, D09 W6Y4,
Ireland 88institutetext: Universidad de Buenos Aires, Facultad de Ciencias
Exactas y Naturales y Ciclo Básico Común. Buenos Aires, Argentina
99institutetext: CONICET-Universidad de Buenos Aires, Instituto de Astronomía
y Física del Espacio (IAFE). Buenos Aires, Argentina 1010institutetext: Max
Planck Institute for Astronomy, Königstuhl 17, 69117, Heidelberg, Germany
1111institutetext: Instituto de Astronomía, Universidad Nacional Autonoma de
México, Apartado Postal 70-264, CP 04510 México, CDMX, México

# Metal-THINGS: The association and optical characterization of SNRs with H i
holes in NGC 6946

M. A. Lara-López 11 L. S. Pilyugin 2233 J. Zaragoza-Cardiel 4455 I. A.
Zinchenko 6633 O. López-Cruz 44 S. P. O’Sullivan 77 M. E. De Rossi 8899 S. Dib
1010 L. E. Garduño 44 M. Rosado 1111 M. Sánchez-Cruces 1111 M. Valerdi 44

(Received TBD; accepted TBD)

###### Abstract

Context.  NGC 6946, also known as the ‘Fireworks’ galaxy, is an unusual galaxy
that hosts a total of 225 supernova remnant (SNR) candidates, including 147
optically identified with high [S ii]/H$\alpha$ line ratios. In addition, this
galaxy shows prominent H i holes, which were analyzed in previous studies.
Indeed, the connection between SNRs and H i holes together with their physical
implications in the surrounding gas is worth of attention.

Aims.  This paper explores the connection between the SNRs and the H i holes,
including an analysis of their physical link to observational optical
properties inside and around the rims of the holes, using new integral field
unit (IFU) data from the Metal-THINGS survey.

Methods. We present an analysis combining previously identified H i holes,
SNRs candidates, and new integral field unit (IFU) data from Metal-THINGS of
the spiral galaxy NGC 6946, which has an unusually high supernova rate. We
analyze the distributions of the oxygen abundance, star formation rate surface
density, extinction, ionization, diffuse ionized gas, and the Baldwin-
Phillips-Terlevich classification throughout the galaxy.

Results.  By analyzing in detail the optical properties of the 121 previously
identify H i holes in NGC 6946, we find that the SNRs are concentrated at the
rims of the H i holes. Furthermore, our IFU data shows that the star formation
rate and extinction are enhanced at the rims of the holes. To a lesser degree,
the oxygen abundance and ionization parameter show hints of enhancement on the
rims of the holes. Altogether, this provides evidence of induced star
formation taking place at the rims of the holes, whose origin can be explained
by the expansion of superbubbles created by multiple supernova explosions in
large stellar clusters dozens of Myr ago.

###### Key Words.:

galaxies: spiral – galaxies: abundances – galaxies: ISM

##  1 Introduction

NGC 6946, also known as the ”Fireworks galaxy” due to its high number of
supernovae (SNe), is a nearly face-on galaxy, with a reported inclination
angle between $\sim$38$\degr$ (Carignan et al., 1990; Boomsma et al., 2008),
and $\sim$32$\degr$ (Bonnarel et al., 1988; de Blok et al., 2008).

Morphologically, NGC 6946 is a late-type SABcd galaxy (de Vaucouleurs et al.,
1991) and hosts well-defined multiple spiral arms and three bars (e.g.,
Elmegreen et al., 1998; Schinnerer et al., 2006; Fathi et al., 2009; Romeo &
Fathi, 2015). Deep H i observations reveal the existence of regular and
prominent spiral arms in the outer gaseous disc, well outside the optical disc
(Boomsma et al., 2008; Bertin & Amorisco, 2010). In addition, NGC 6946 is an
isolated galaxy located in the nearby void (Sharina et al., 1997), although
the presence of tidal encounters and minor mergers cannot be discarded
(Boomsma et al., 2008)

Due to its intriguing nature, NGC 6946 has been mapped at multiple
wavelengths. For example, in the 21 cm atomic hydrogen emission line (e.g.,
Rogstad & Shostak, 1972; Carignan et al., 1990; Boomsma, 2007; de Blok et al.,
2008), in H$\alpha$ emission of the ionized hydrogen (e.g., Bonnarel et al.,
1988; Blais-Ouellette et al., 2004; Daigle et al., 2006), in the molecular
(CO) emission lines (e.g., Walsh et al., 2002; Leroy et al., 2009; Helfer et
al., 2003; Romeo & Fathi, 2015), with the Hubble Space Telescope (HST)
(Larsen, 2004), and as part of large surveys, such as the Key Insights on
Nearby Galaxies: a Far-Infrared Survey with Herschel (KINGFISH, Kennicutt et
al., 2011), and the Spitzer Infrared Nearby Galaxies Survey (SINGS, Moustakas
et al., 2010), among others.

In particular, NGC 6946 is part of the H i Nearby Galaxy Survey (THINGS)
survey (Walter et al., 2008), which observed 34 large, nearby galaxies with
the Very Large Array (VLA), obtaining high spatial and spectral resolution H i
data. Therefore, the distribution of properties (surface mass density,
velocity dispersion, and rotation velocity) of the atomic gas across the disc
are available for this galaxy.

NGC 6946 is the most extreme known example of a galaxy with a high supernova
rate. Ten supernova events have been observed since 1917 (Eldridge & Xiao,
2019). A large number of supernova remnants (SNR) and candidates have been
identified in NGC 6946 in different ways (Matonick & Fesen, 1997; Long et al.,
2019, 2020). Recently, a large optical search of SNR was performed by Long et
al. (2019) using the WIYN telescope (Kitt Peak National Observatory). A total
of 225 SNR candidates were found by Long et al. (2020) using optical and IR
data, including 147 SNRs identified as optical nebulae with high [S
ii/H$\alpha$] line ratios (Long et al., 2019).

One prominent feature detectable with H i observations is the existence of H i
holes (Brinks & Bajaja, 1986). Boomsma (2007) and Boomsma et al. (2008)
studied the distribution and kinematics of the neutral gas in NGC 6946 at
21-cm with the Westerbork Synthesis Radio Telescope. They detected high-
velocity H i gas and found 121 H i holes, most of which are located in the
inner regions where the gas density and the star formation rate are higher.
The sizes of the H i holes are up to 3 kpc diameter, while their ages are in
the range of 1 to 6$\times$107 yr.111Boomsma (2007) and Boomsma et al. (2008)
adopt a distance of 6 Mpc to NGC 6946, while recent distance estimates using
the tip of the red giant branch result in a value of around 7.8 Mpc (Anand et
al., 2018; Murphy et al., 2018). This implies that the sizes and ages of the H
i holes can be underestimated by around thirty per cent. Boomsma (2007) and
Boomsma et al. (2008) conclude that stellar feedback (galactic fountain) is
probably at the origin of most of the high-velocity gas and H i holes (see
also Dib et al., 2021). That is, that the most likely mechanism for producing
H i holes is the expansion (and blow-up) of superbubbles created by multiple
supernova explosions around large stellar clusters.

The number of holes in NGC 6946 and their sizes is still debatable. A later
study by Bagetakos et al. (2011) found only 56 holes, although with an
excellent agreement for the holes larger than 700 pc in comparison with
Boomsma et al. (2008). Part of the disagreement can be attributed to the
different resolution limit of each study. Moreover, both studies rely on a ”by
eye” identification of the H i holes, which is less quantifiable and prone to
human error.

We observed NGC 6946 as part of the Metal-THINGS survey with integral field
unit (IFU) spectroscopy. A mosaic was built with a collection of 12 pointings,
which is, to the best of our knowledge, the largest collection of optical
spectra of this galaxy to date. Our aim is to characterize the optical
properties of this galaxy such as the oxygen abundance gradient and the SFR,
as well as to characterise the SNRs and their possible effect on the
aforementioned properties. Due to the starburst nature of this galaxy, we
search as well for relations between the observed H i holes, SNRs, and star
formation rate (SFR) enhancements. Throughout this paper, we use the most
recent distance estimate using the tip of the red giant branch of 7.8 Mpc
(Anand et al., 2018; Murphy et al., 2018).

This paper is organized as follows. The observations are described in Section
2. In Section 3, we determine the oxygen abundance, SFR surface density,
ionization parameter and color excess in NGC 6946. In Section 4, our results
are presented, and Section 5 provides a Summary and Conclusions.

##  2 Observations

The Metal-THINGS survey is a large program focussed on obtaining IFU
spectroscopy of a unique sample of nearby galaxies with complementary imaging
and spectroscopic mapping at multiple wavelengths. Our sample of galaxies is
based on the THINGS survey (Walter et al., 2008), which observed 34 large,
nearby radio galaxies with the Very Large Array (VLA), providing high spatial
and spectral resolution H i data.

The Metal-THINGS survey is obtaining IFU data using the 2.7m Harlan Schmidt
telescope at McDonald Observatory, with the George Mitchel spectrograph (GMS,
formerly known as VIRUS-P, Hill et al., 2008). GMS is a square array of 100
$\times$ 102 arcsec. The IFU consists of 246 fibers arranged in a fixed
pattern, where each fiber has a 4.2 arcsec diameter. Every pointing is
observed with 3 dither positions to ensure a 90$\%$ surface coverage (see Fig.
1 of Blanc et al., 2009). Due to the extended nature of our galaxies, sky
exposures are taken off-source for sky subtraction purposes during the
reduction process.

NGC 6946 was observed as part of the Metal-THINGS survey (Lara-López et al.,
2021) through a red setup covering the wavelength range from 4400 to 6800 Å,
with the low resolution grid (VP1), which provides a spectral resolution of
$\sim$5 Å FWHM. The wavelength range of the red setup allows us to measure the
strongest emission lines: H$\beta$, [OIII]$\lambda\lambda$4959, 5007,
[OI]$\lambda$6300, H$\alpha$, [NII]$\lambda$6584, [SII]$\lambda\lambda$6716,
6731.

Our observing procedure consists on 15 mins exposure per dither, followed by a
sky exposure, and repetition of the process until 45 mins are reached per
dither, per pointing. A calibration star was observed every night using 6
dither positions to ensure a 99$\%$ flux coverage. Calibration lamps (Neon $+$
Argon for the red setup) were observed at the beginning and end of every night
to wavelength calibrate the spectra.

NGC 6946 was observed using GMS in June 2018, October 2018, October 2020, and
June 2021. The average seeing during the observations was 1.5 arcsecs. A total
of 12 pointings were observed to form the mosaic shown in Fig 1. The whole
mosaic has a total of 8,856 individual spectra. The astrometry was set by
using all the fibers of individual pointings and their relative positions
within each. First, we created a tridimensional cube associating each fiber to
its relative spatial position in the pixel (x,y) plane and convolving by a
gaussian with a FWHM of 4$\aas@@fstack{\prime\prime}$2 (the diameter of the
fiber) at each wavelength. Next, from the spectral-dimension collapsed image
we identified several stars and used the same star positions from 2MASS images
to set an absolute astrometry for each pointing. We repeated this process for
each pointing to create the mosaic of Fig 1. Even though our initial pointings
were aligned next to each other, since the observing runs spread over several
years, we attribute the observed shifts to variations in the instrumentation
setups.

The galaxy NGC 6946 is at a distance of about 7.8 Mpc (Anand et al., 2018;
Murphy et al., 2018) which gives a scale of 37.8 pc/$\arcsec$, so that each
4$\aas@@fstack{\prime\prime}$2 fiber in the IFU corresponds to $\sim$158.8 pc.
The optical radius of NGC 6946 ($R_{25}$ = 344.45 arcsec) is taken from the
NASA/IPAC Extragalactic Database (ned)222The NASA/IPAC Extragalactic Database
(ned) is operated by the Jet Populsion Laboratory, California Institute of
Technology, under contract with the National Aeronautics and Space
Administration. http://ned.ipac.caltech.edu/ . With the adopted distance, this
gives an optical radius of $R_{25}$ = 13.02 kpc.

The basic data reduction including bias subtraction, flat frame correction and
wavelength calibration, was performed using P3D 333https://p3d.sourceforge.io.
The sky subtraction and the combination of dithers was performed using our own
routines in Python. Flux calibration was performed following Cairós et al.
(2012) using 6 dither positions, ensuring 99$\%$ coverage. Next, we used IRAF
(Tody, 1986) to create a flux calibration function using the packages standard
and sensfunc.

The stellar continuum of all flux-calibrated spectra was fitted using
STARLIGHT (Cid Fernandes et al., 2005; Mateus et al., 2006; Asari et al.,
2007). Briefly, we used 45 simple stellar population (SSP) models from the
evolutionary synthesis models of Bruzual & Charlot (2003) with ages from 1 Myr
up to 13 Gyr and metallicities Z=0.005, 0.02 and 0.05. The reddening law of
Cardelli et al. (1989) was adopted, assuming Rv=3.1. Next, the fitted
continuum was subtracted from the spectra, and the emission lines were
measured using Gaussian line-profile fittings. It should be noted that only
those fiber spectra where all the used lines were measured with a signal-to-
noise ratio S/N $>3$ were considered. For a more detailed description, see
Zinchenko et al. (2016).

In this paper we are using the individual spectra of the fibers, which are
independent of each other. This is in contrast to the spaxel spectra in
surveys such as the Mapping Nearby Galaxies at Apache Point Observatory survey
(MaNGA), where the point spread function (PSF) is estimated to have a FWHM of
2.5$\arcsec$ (Bundy et al., 2015; Belfiore et al., 2017). Our IFU spectroscopy
and derived astrometry provide the possibility to construct the maps of the
oxygen abundance (and other characteristics) in the disc and to investigate
the global and local properties of the abundance distribution (Lara-López et
al., 2021).

##  3 Physical properties of NGC 6946

Figure 1:  Observed 12 pointings superimposed on the NGC 6946 image. Each
individual box corresponds to the field of view of the George Mitchel
spectrograph (GMS, formerly known as VIRUS-P).

The geometrical parameters of the galaxy (location of the center of the
galaxy, the position angle of the major axis and the inclination angle) are
needed to determine the galactocentric distances of the fibers.

In this paper, we use the position of the center obtained by Trachternach et
al. (2008) (RA = 20h 34m 52$\aas@@fstack{s}$2 and DEC = +60$\degr$ 09$\arcmin$
14$\aas@@fstack{\prime\prime}$4), and the position angle of the major
kinematic axis (PA = 242$\aas@@fstack{\circ}$7) and the inclination angle ($i$
= 32$\aas@@fstack{\circ}$6) obtained by de Blok et al. (2008).

The stellar mass estimates for this galaxy show an appreciable spread. At the
distance of 5.9 Mpc, using data from the Spitzer Infrared Nearby Galaxies
Survey, de Blok et al. (2008) found the mass value to be within the range
log(M⋆/M☉) $\sim$ 10.58 – 10.77. On the other hand, Jarrett et al. (2019)
found a value of log(M⋆/M☉)= 10.26 using the mid-infrared luminosity from the
Wide-field Infrared Survey Explorer (WISE). NGC 6946 does not show a classical
bulge but has a tiny pseudobulge, and there is no evidence that this galaxy
hosts an AGN (Kormendy et al., 2010).

###  3.1 Diffuse ionized gas

Figure 2: Identification of DIG based on the extinction corrected H$\alpha$
flux and ${\rm C}_{\rm H\,{\textsc{ii}}}$. The dashed and dotted horizontal
lines show the median [S ii]/H$\alpha$ for the 100 brightest and 100 dimmest
fibers, respectively. The vertical solid line shows the value of log($f_{0}$).
The red solid line shows the fit of Eq. 2 to our data.

The diffuse ionized gas (DIG), also known as the warm ionized medium (WIM), is
a warm ($\sim$104 K), low density ($\sim$10-1cm-3 ) gas phase found in the
interstellar medium of galaxies (Reynolds, 1984). DIG is an important
component in star-forming galaxies, and its contribution to emission line
fluxes can affect and impact the interpretation of measured metallicities,
ionization, and BPT diagrams (Baldwin, Phillips, Terlevich, 1981) in galaxies.
Several approaches have been proposed for the identification of DIG using IFU
spectroscopy (e.g. Poetrodjojo et al., 2019; Kaplan et al., 2016).

To determine the fraction of flux originating from H ii regions and from the
DIG (named C${}_{\rm H\,{\textsc{ii}}}$), we use the method first proposed by
Blanc et al. (2009), and further developed by Kaplan et al. (2016). This
method relies on the assumption that the brightest fiber fluxes are dominated
by H ii emission, while the dimmest ones are dominated by DIG emission.
Following Kaplan et al. (2016), we first estimate the characteristic value of
[S ii]/H$\alpha$ in the brightest fibers for H ii regions ([S
ii]/H$\alpha$)${}_{\rm H\,{\textsc{ii}}}$, and in the dimmest ones for DIG ([S
ii]/H$\alpha$)DIG. Only fibers with a S/N $>$ 3 in H$\alpha$, H$\beta$, and [S
ii] are included in this analysis.

Then, in each fiber, we make an initial guess for C${}_{\rm
H\,{\textsc{ii}}}$:

${\rm C}_{\rm H\,{\textsc{ii}}}=\frac{[\rm S\,{\textsc{ii}}]/\rm H\alpha-([\rm
S\,{\textsc{ii}}]/\rm H\alpha)_{\rm\scriptscriptstyle DIG}}{([\rm
S\,{\textsc{ii}}]/\rm H\alpha)_{\rm\scriptsize H\,{\textsc{ii}}}-([\rm
S\,{\textsc{ii}}]/\rm H\alpha)_{\rm\scriptscriptstyle DIG}}$ (1)

Next, by using the initial estimate of ${\rm C}_{\rm H\,{\textsc{ii}}}$ and
the extinction corrected $f({\rm H{\alpha}})$, we fit the data for $f_{0}$ and
$\beta$ in the following expression:

${\rm C}_{\rm
H\,{\textsc{ii}}}=1-\left({\frac{{f_{0}}}{f{\rm(H{\alpha})}}}\right)^{\beta}$
(2)

obtaining $f_{0}$ = 2.56 $\pm$ 0.12, and $\beta$= 0.427 $\pm$ 0.007, shown by
the red solid line in Fig. 2. A final value for ${\rm C}_{\rm
H\,{\textsc{ii}}}$ is provided by Eq. 2 using the best-fit coefficients.

While all regions where H$\alpha$corr $<$ $f_{0}$ are 100$\%$ DIG dominated, a
somewhat arbitrary threshold in ${\rm C}_{\rm H\,{\textsc{ii}}}$ is needed to
select the DIG, which is based on the dimmest fluxes in the observed sample.
In this paper, we define fibers with ${\rm C}_{\rm H\,{\textsc{ii}}}$ $<$ 0.4
as dominated by DIG, which are flagged in the rest of our analysis. In Fig. 3,
we show the fibers identified as DIG in small black circles, which corresponds
to 9.2$\%$ of the analyzed sample.

###  3.2 BPT classification

Figure 3: Top panel: map of the BPT classification, color-coded as indicated
in the label. Bottom Panel: BPT diagram for the individual fibers with SF-like
spectra (blue symbols), Composite (green symbols), and AGN-like (red symbols).
The black solid and red dashed curves are the demarcation lines between SF and
AGN regions defined by Kauffmann et al. (2003) and Kewley et al. (2001),
respectively. The ellipses in the top panel indicate the H i holes (see §4.2),
while the small black circles denote regions dominated by DIG.

The measured emission line fluxes of each fiber spectra are corrected for the
interstellar reddening using the reddening law from Cardelli et al. (1989)
with $R_{V}$ = 3.1. The value of the interstellar reddening is estimated
through the comparison between the measured and the theoretical
H$\alpha$/H$\beta$ ratio (that is, using the standard value of
H$\alpha$/H$\beta$ = 2.86). When the measured value of H$\alpha$/H$\beta$ is
lower than 2.86, the reddening is assumed to be zero. We adopted $C_{{\rm
H}{\beta}}=0.47A_{V}$ (Lee et al., 2005).

We classify every spectra using its location in the [N
ii]$\lambda$6584/H$\alpha$ versus [O iii]$\lambda$5007/H$\beta$ line ratio
diagram suggested by Baldwin, Phillips, Terlevich (1981, BPT diagram), The NGC
6946 map and BPT classification is shown in Fig. 3. As in our previous studies
(Zinchenko et al., 2019; Pilyugin et al., 2020a, b, 2021a, 2021b; Lara-López
et al., 2013), the spectra located to the left (below) the demarcation line
from Kauffmann et al. (2003) (blue symbols in the two panels of Fig. 3) are
referred to as the SF-like or H ii region-like spectra. Those located to the
right (above) the demarcation line from Kewley et al. (2001) (red symbols in
Fig. 3) are referred to as the AGN-like spectra. The spectra located between
those demarcation lines are Composite, or intermediate spectra (green symbols
in Fig. 3). In both panels of Fig. 3, the black circles denote regions
dominated by DIG.

###  3.3 Oxygen abundance and Ionization parameter

Here we estimate the oxygen abundance for the fibers classified as H ii
region-like by the BPT. The oxygen lines [O ii]$\lambda$3726 and $\lambda$3729
are beyond the spectral range of our red GMS spectra. Hence, the calibrations
which involve those lines cannot be used for abundance determinations with our
current data. From the plethora of available methods, we use the three-
dimensional S calibration O/H = $f$($N2,S2,R3/S2$) from Pilyugin & Grebel
(2016). The advantage of 3D calibrations for the abundance determinations in
comparison to 1D calibrations is discussed in Pilyugin et al. (2018). The S
calibration consists of an upper (high metallicity) and lower (low
metallicity) branches. The transition from the upper to lower branch occurs at
log $N_{2}$ $\approx-0.6$. The corresponding calibration relation for the
upper branch (log$N_{2}$ $>$ –0.6) is

$\displaystyle\begin{array}[]{lll}{\rm(O/H)}^{*}_{S,U}&=&8.424+0.030\,\log(R_{3}/S_{2})+0.751\,\log
N_{2}\\\ &+&(-0.349+0.182\,\log(R_{3}/S_{2})+0.508\log N_{2})\\\ &\times&\log
S_{2},\\\ \end{array}$ (6)

where we use the notation (O/H)${}^{*}_{S,U}$ = 12 +log(O/H)S,U for a compact
way. The calibration for the lower branch (log$N_{2}$ $<$ –0.6) is

$\displaystyle\begin{array}[]{lll}{\rm(O/H)}^{*}_{S,L}&=&8.072+0.789\,\log(R_{3}/S_{2})+0.726\,\log
N_{2}\\\ &+&(1.069-0.170\,\log(R_{3}/S_{2})+0.022\log N_{2})\\\ &\times&\log
S_{2}\\\ \end{array}$ (10)

where (O/H)${}^{*}_{S,L}$ = 12$+$log (O/H)S,L.

Since the [O iii]$\lambda$5007 and $\lambda$4959 lines originate from
transitions from the same energy level, their flux ratio is defined only by
the transition probability ratio, which is close to 3 (Storey & Zeippen,
2000). The line measurement of the stronger line [O iii]$\lambda$5007 is
usually more precise than that for the weaker line [O iii]$\lambda$4959\.
Therefore, we estimated the value of $R_{3}$ as $R_{3}=1.33$ [O
iii]$\lambda$5007/H$\beta$. Similarly, we estimated the value of $N_{2}$ as
$N_{2}=1.33$ [N ii]$\lambda$6584/H$\beta$. The metallicity gradient and map,
will be further analyzed in $\S\,\ref{SecSuperNova}$ and
$\S\,\ref{SecHolesMaps}$, respectively.

The ionization parameter is defined as $U=Q_{\rm ion}/4\pi R^{2}_{\rm in}nc$,
where $Q_{\rm ion}$ is the number of hydrogen ionizing photons emitted per
second by the ionizing source, $R_{\rm in}$ is the distance from the
ionization source to the inner surface of the ionized gas cloud, $n$ is the
particle density, and $c$ is the speed of light. We estimate the ionization
parameter following the prescription of Dors et al. (2017):

${{\rm log\,(U)_{D}}}=c\times S2+d$ (11)

where S2 = log([S ii]$\lambda\lambda$ 6717,31 / H$\alpha$),
$c=-0.26\times(Z/Z_{\sun})-1.54$, and
$d=-3.69\times(Z/Z_{\sun})^{2}+5.11\times(Z/Z_{\sun})$ -5.26. For the oxygen
abundance of the Sun, we use Z☉=8.69 (Amarsi et al., 2018). Since the oxygen
abundance is needed for the ionization parameter estimation, the final sample
is the same (4154 fibers). The resulting ionization will be analyzed in §4.3.

###  3.4 Star formation rates and color excess

In this section, we estimate the SFRs and color excess that will be further
analyzed in detail in §4.3.

The resolved SFR is estimated using the H$\alpha$ prescription of Kennicutt et
al. (2009) (see also the review of Calzetti, 2013), which uses an Kroupa
(2001) initial mass function (IMF).

${{\rm SFR[Myr^{-1}]}}=5.5\times 10^{-42}L_{\rm corr}({\rm H}\alpha_{\rm
corr})\ {\rm ergs^{-1}}$ (12)

where ${\rm H}\alpha_{\rm corr}$ is the H$\alpha$ flux corrected by
extinction. The estimated SFRs are then converted to SFR surface densities
($\sum_{\rm SFR}$) by dividing them by the area on the sky of the 4.2”
diameter fiber. The SFR was measured only in fibers whose spectra are
classified as SF or Composite in the BPT diagram, and have a S/N $>$ 3 in
H$\alpha$ and H$\beta$. The final SFR sample used is formed by 4972 fiber
spectra.

Finally, as an indicator of the dust content, we estimated the color excess
E(B-V) (e.g. Calzetti et al., 1996). For its estimation, different ratios from
Hydrogen recombination lines can be used. For our sample, we are using
H$\alpha$ and H$\beta$, and the prescription of Calzetti et al. (1994) in the
following:

${\rm E\,(B-V)}_{\rm gas}={\frac{{\rm log}({\rm R}_{\rm obs}/{\rm R}_{\rm
int})\;}{0.4\,[\,k(\lambda_{{\rm H}\alpha})-k(\lambda_{{\rm H}\beta})\,]}}$
(13)

where the observed radio ${\rm R}_{\rm obs}$ is the Balmer decrement
(H$\alpha$/H$\beta$), and the intrinsic ratio ${\rm R}_{\rm int}$ is 2.86,
taking a case B recombination (Osterbrock, 1989). Finally, $k(\lambda)$
corresponds to the dust extinction curve, in this case, we use Calzetti et al.
(2000), which is based on a set of starburst galaxies, appropriate for this
analysis. The color excess was estimated using the same exclusion criteria as
for the SFR.

##  4 Results

###  4.1 Oxygen abundance gradient and Supernova remnants

Figure 4: Radial distribution of the oxygen abundance. The grey points denote
the oxygen abundance of the individual fibers. The solid line is the best fit
to the data. The green points mark the fibers hosting SNRs, while the magenta
points correspond to the neighboring fibers to the SNRs positions.

NGC 6946 is the most extreme example of a galaxy with a high supernova rate,
with ten supernova events since 1917 (Eldridge & Xiao, 2019). A large number
of SNR and candidates have been identified in NGC 6946 in different ways
(e.g., Matonick & Fesen, 1997; Lacey et al., 1997; Lacey & Duric, 2001;
Bruursema et al., 2014; Long et al., 2019, 2020), amounting to a total of 225
SNR candidates. In this section, we explore whether the oxygen abundance is
affected in the immediate environment of the SNR.

To this aim, first we estimate the oxygen abundance gradient for the whole
galaxy. The gas metallicity estimated through strong emission lines give
important clues on the physical properties of the ISM and formation and growth
of galaxies. Negative gas metallicity gradients are widely found in late-type
galaxies in the local universe (e.g., Zaritsky, Kennicutt & Huchra, 1994;
Pilyugin et al., 2004; Moustakas et al., 2010; Pilyugin et al., 2014; Belfiore
et al., 2017; Lara-López et al., 2022). Such negative gradients are consistent
with an inside-out growth scenario of the discs (e.g. White & Frenk, 1991; Mo,
Mao, & White, 1998).

The gradient O/H = $f(R)$ is approximated by a linear relation of the type
12+log(O/H) = 12+log(O/H)0 \+ grad $\times$ $R_{g}$, where 12+log(O/H)0 is the
oxygen abundance at the center of the galaxy, grad is the gradient in units of
dex/R25, and Rg is the radius normalised to the optical radius of the galaxy
R25. We find the following expression for the SF fibers in the disk of NGC
6946:

$12+\log{\rm(O/H)}=8.603(\pm 0.002)-0.1938(\pm 0.0037)\times R_{g}$ (14)

The mean value of the scatter around this relation is 0.0429 dex. The solid
line of Fig. 4 shows the obtained relation. In comparison with other galaxies,
and considering NGC 6946 has a stellar mass of 1010.26 M⊙(Jarrett et al.,
2019), our measured gradient is in agreement with galaxies of similar stellar
masses from Kreckel et al. (2019) and Zinchenko et al. (2021). A more detailed
analysis on the metallicity gradients of Metal-THINGS galaxies will be
presented in Lara-López et al. (in preparation).

Next, to explore the effect of the SNRs on their enviroment, we obtain the
fibers overlapping (hosting) with SNRs from the condition that the separation
between the center of the fiber and the SNR is less than the fiber radius
($r_{fiber}$ = 2.1 arcsecs), otherwise a fraction of the SNR would be beyond
the field of the host fiber. Moreover, the uncertainty in the coordinates of
the fibers is around one arcsec and could be larger for some pointings. This
can result in the incorrect identification of some fibers hosting SNRs. To
take this possibility into account, we also obtain a “neighboring” fiber(s)
for each SNR from the condition that the separation between the SNR and the
center of the fiber is larger than $r_{fiber}$, and lower than $r_{fiber}$ \+
2 arcsecs. Thus, the SNR could make a contribution to the radiation in the
host or neighbouring fiber, or even both, if the SNR is located in between
them.

Most of host fibers are located in the SF region of the BPT diagram. Hence,
this provides evidence that the contribution of the SNR radiation to the fiber
spectra is not significant. Since the majority of the host and neighboring
fibers show H ii like spectra, their oxygen abundances are determined through
the $S$ calibration as indicated in $\S\,\ref{OxygenAbundanceMeasure}$. The
fibers hosting SNRs are indicated as green points in Fig. 4, while the magenta
points denote the neighboring fibers. It can be appreciated that there is no
systematic difference or shift between the oxygen abundance of the fibers
hosting SNRs and the rest of the fibers.

Altogether, we find no appreciable difference in the properties of the gas
(BPT type and abundance) in fibers hosting SNRs in comparison with the rest.
This suggests that the radiation of SNRs makes a small contribution to the
radiation in the fiber field.

###  4.2 On the relation between SNR and H i holes

Figure 5:  H i holes and supernova remnants in the galaxy NGC 6946. The sizes
and orientations of H i holes are indicated by the black solid ellipses. The
green points show the positions of the SNRs. The dashed blue ellipse denotes
the optical radius of the galaxy, the plus sign marks the position of the
center, and the dashed line denotes the position of the major axis.

Figure 6:  Histogram of the difference between the SNR distance to the closest
H i hole center, and the H i hole rim distance to the hole center (in the line
from the center to the SNR).

Figure 7:  Left: H i holes (black solid ellipses) superimposed on the
log($\sum$SFR) map of NGC 6946. The small black circles indicate DIG dominated
fibers. Right: Histogram of the differences $\Delta$ log($\sum$SFR) $=$
log($\sum$$\widehat{{}_{\rm SFR_{rim}}}$) $-$ log($\sum$$\widehat{{}_{\rm
SFR_{hole}}}$), see text for details.

Figure 8:  Left: H i holes (black solid ellipses) superimposed on the E(B-V)
map of NGC 6946. The small green circles indicate DIG dominated fibers. Right:
Histogram of the differences $\Delta$ ${\rm E(B-V)}$ $=$ $\widehat{\rm
E(B-V)}$rim $-$ $\widehat{\rm E(B-V)}$hole, see text for details.

Figure 9:  Left: H i holes (black solid ellipses) superimposed on the
12+log(O/H) map of NGC 6946. The small green circles indicate DIG dominated
fibers. Right: Histogram of the differences $\Delta$ ${\rm 12+log(O/H)}$ $=$
$\widehat{\rm 12+log(O/H)}$rim $-$ $\widehat{\rm 12+log(O/H)}$hole, see text
for details.

Figure 10:  Left: H i holes (black solid ellipses) superimposed on the log(U)
map of NGC 6946. The small green circles indicate DIG dominated fibers. Right:
Histogram of the differences $\Delta$ ${\rm log(U)}$ $=$ $\widehat{\rm
log(U)}$rim $-$ $\widehat{\rm log(U)}$hole, see text for details.

As indicated in the introduction, Boomsma (2007) and Boomsma et al. (2008)
identified and characterised 121 H i holes, most of which are located in the
inner regions where the gas density and the star formation rate are higher.
The origin of these H i holes is analyzed in detail in Boomsma et al. (2008).
In general, they found that smaller holes up to 1 kpc in size, are more likely
to be caused by SN feedback. However, it is still a puzzle that many H i holes
in NGC 6946 are observed without progenitor remnants. Also, they observed high
velocity H i gas, that is likely produced by the blown-out (into the halo) of
the superbubbles that produce the holes in the disk, in agreement with the
galactic fountain model (Collins et al., 2002). In addition, larger holes
could be a blend of a number of smaller ones, or even be caused by the
combination of thermal and gravitational instability (Dib & Burkert, 2005).
Since the likely origin for most of these H i holes is related to superbubbles
created by multiple supernovae explosions, in this section, we explore such
connection.

In Fig. 5 we show the distribution of H i holes and recent supernovae remnants
across the image of NGC 6946. The sizes and orientations of the H i holes are
indicated by the black solid ellipses, while the green points show the
positions of the SNRs. For this study, we use the sample of SNR candidates
from Long et al. (2019), who identified 147 candidates, using narrowband
images, based on their elevated [S ii]$\lambda\lambda$6716+6731/H$\alpha$
ratios (Mathewson & Clarke, 1973).

Inspection of Fig. 5 suggests that recent SNRs tend to avoid the H i holes, in
fact, SNRs are mostly distributed in the rims of the H i holes. To quantify
this effect, we estimated two distances: (a) the distance from the SNR to the
closest H i hole center (RSNR), and (b) the distance from the H i hole center
to the rim of the hole in the direction of the SNR (Rrim). A histogram of the
differences between distances (a) and (b) is shown in Fig. 6. Every SNR is
counted only once, and with respect to the closest hole center. The peak
around zero in this histogram indicates an excess of SNRs coincident with the
rims of the H i holes. The skewness of the histogram towards positive
differences highlights that only few SNRs lie within the H i holes. Since the
inclination angle of NGC 6946 is $\sim$32.6$\degr$ (Bonnarel et al., 1988; de
Blok et al., 2008), projection effects could in principle alter the
distribution of the histogram in Fig. 6. However, we estimate a maximum
$\sim$15 % correction in the obtained distances.

On the other hand, the H i holes are not related to the BPT classification of
the individual fibers. Instead, different BPT classifications take place
within and outside the H i holes, as shown in Fig. 3. Also, the same figure
shows that the DIG does not tend to dominate regions inside the holes, with
only a $\sim$10$\%$ of DIG residing within the holes.

###  4.3 The physical properties of H i holes and rims

The excess of SNRs associated with the H i holes rims is evidence that the
induced star formation takes place in the shells of some superbubbles created
by multiple supernova explosions at their centres dozens of Myr ago. Figure 7
(left) shows the log($\sum$SFR) map of NGC 6946 together with the H i holes
superimposed. A close examination of this map suggests that the $\sum$SFR tend
to increase towards the H i hole rims. To examine this effect we estimated two
$\sum$SFR for the whole sample, (i) the median star formation surface density
inside each hole $\sum$$\widehat{{}_{\rm SFR_{hole}}}$, which corresponds to
the median values of the fibers from the center of the hole to up to 79% of
the distance from the center to the edge of the ellipse that define each hole,
and (ii) the median for the holes rims $\sum$$\widehat{{}_{\rm SFR_{rim}}}$,
which corresponds to the median value of the fibers within 80% to 130% of the
distance from the center to the edge of the ellipse of each hole. The same
selection of fibers inside the holes and in the rims is followed in the next
sections, although the number of holes analyzed will slightly change due to
the different number of fibers used. The use of different distances to define
center and rim fibers do not change our results drastically.

The difference $\Delta$ log($\sum$SFR) $=$ log($\sum$$\widehat{{}_{\rm
SFR_{rim}}}$) $-$ log($\sum$$\widehat{{}_{\rm SFR_{hole}}}$) is estimated only
when more than 8 fibers are available in both, inside and in the rims of each
hole, giving us a total of 31 holes. The histogram of these differences is
shown in Figure 7 (right), where it is clear that the histogram is skewed
towards larger differences. From our sample, $\sim$67.7$\%$ of the holes show
an enhanced $\sum$SFR in their rims. To further quantify the degree of
difference between rims and holes, we estimated a paired t-test, and obtained
a t = 2.85, and a p-value = 0.007, meaning that there is a 0.7$\%$ probability
that our result happened by chance, hence we can reject the null hypothesis.
When we discard the fibers previously identified as DIG (small circles in Fig.
7) and perform the same exercise, our sample is reduced to 28 holes, while the
SFR enhancement in the rims holds, with $\sim$64 $\%$ of the difference
showing a $\Delta$ log($\sum$SFR) $>$ 0.

Following the same methodology, we analyzed the color excess E(B-V) as an
indicator of dust extinction. We use the same sample used for the SFRs. The
obtained E(B-V) map is shown in Fig. 8 (left). We analyze the color excess
inside the holes and in the rims for 31 holes. The histogram of the difference
$\Delta$ E(B-V) $=$ $\widehat{\rm E(B-V)}$rim $-$ $\widehat{\rm E(B-V)}$hole,
is shown in Fig. 8 (right). The color excess histogram indicates a skewness
towards higher values in the rims, with a total of $\sim$61$\%$ of holes
showing a higher color excess in their rims. We run a paired t-test, and
obtained a t = 2.17, and a p-value = 0.03, hence, our data suggest higher dust
extinction on the hole’s rims. If fibers identified as DIG are not considered,
the percentage of $\Delta$ E(B-V) $>0$ remains at $\sim$61$\%$.

We did the same exercise for the oxygen abundance and ionization parameter.
Since the oxygen abundance and ionization parameter have the most restrictive
criteria, we were able to analyze only 29 holes. The map of 12+log(O/H) is
shown in Fig. 9 (left), while its respective histogram of the difference
$\Delta$ 12+log(O/H) $=$ $\widehat{\rm 12+log(O/H)}$rim $-$ $\widehat{\rm
12+log(O/H)}$hole in Fig. 9 (right). The histogram indicates a minor shift
towards higher abundances, with $\sim$58.6$\%$ of our data showing higher
differences. The paired t-test indicate a t = 1.45, and a p-value = 0.16.
Hence, the difference in oxygen abundance between holes and rims is minor. Our
results do not change when we exclude DIG dominated fibers (green circles in
Fig. 9).

Similarly, the ionization parameter is displayed in Fig. 10 (left), while its
respective histogram of the difference $\Delta$ log(U) $=$ $\widehat{\rm
log(U)}$rim $-$ $\widehat{\rm log(U)}$hole, is shown in Fig. 10 (right). The
t-test indicate that we cannot reject the null hypothesis with t = 0.72,
p-value = 0.48. Hence, we conclude that there is not a statistically
significant difference in the ionization parameter between holes and rims.
However, the histogram is skewed towards higher ionization parameter
differences, with $\sim$66$\%$ of the holes showing positive differences.

From our statistical analysis, both the t-test and the skewness in the
histogram show that the SFR has the strongest difference between the holes and
the rims. To a lesser degree, E(B-V) shows as well a clear enhancement on the
rims. On the other hand, the t-tests do not show a statistical significant
difference between the chemical abundance and the ionization. However, both
show a skewness in their histogram towards positive differences, specially
higher for the ionization, with a $\sim$66$\%$ of the holes showing an
enhancement on the rims.

##  5 Discussion

In this section we discuss the physical implications of the overabundance of
SNRs in the rims of the H i holes. As indicated in Section 4.3, a remarkable
feature in NGC 6946 is the existence and classification of 121 H i holes
(Boomsma et al., 2008). Our data indicate an overabundance of SNRs located
around the rims of the H i holes (Fig. 6). The H i holes in NGC 6946 were
analyzed in detail by Boomsma et al. (2008), and they concluded that the
creation of some of the holes can be attributed to the expansion of
superbubbles generated by multiple SN explosions (e.g., Dib et al., 2006;
Bagetakos et al., 2011; Dib et al., 2021). In addition, they found that
stellar feedback in the form of a galactic fountain is probably the origin of
some of the H i holes. This is in agreement with the lack of bright emission
at multiple wavelengths inside the holes, suggesting that the H i holes are
already devoid of gas, which could also explain the lack of SNRs located
inside the holes.

As shown in Section 4.3, we observe a clear enhancement in SFR and dust
extinction on the hole’s rims, and to a minor degree, the gas metallicity and
ionization parameter. The star formation is a complex process that is affected
by internal and external mechanisms, as well as the aforementioned properties
to different degrees. For instance, since the existence of dust in galaxies
affects the star-formation activity, it is not surprising that the observed
enhancement in SFR is accompanied by a higher dust extinction in the hole’s
rims. Indeed, it has been shown that dust grains increase the molecular
formation rate by two orders of magnitude compared to the case without dust
(Hollenbach & McKee, 1979), drastically enhancing the star formation activity
(e.g., Asano et al., 2013). Hence, it makes sense that bursts of star
formation are associated with areas of high dust extinction.

Furthermore, the excess dust we observe in the hole’s rims is likely produced
by the SNRs. It is known that SNe are very efficient dust producers (mainly
core-collapse Type II-P, i.e., there is a plateau in their light curve), as
well as dust destroyers (i.e., the pressure of the ISM gas that is shocked by
the expanding SNe blast wave generates a reverse shock that propagate through
the expanding ejecta, partially destroying the newly formed dust, Bianchi &
Schneider, 2007; Marassi et al., 2019). The composition and size of grains
formed in the SN ejecta that survive the subsequent passage of the reverse
shock is still an open question. Recent models suggest that only between 1 to
8$\%$ of the observed dust mass produced by SNe will survive and contribute to
the ISM (e.g., Bocchio et al., 2016; Sarangi, Matsuura, & Micelotta, 2018).
Taking into account the cumulative effect of the high number of SNR in NGC
6946, it is not surprising we observe a higher dust extinction in the rims of
the holes.

On the other hand, the ionization parameter in the rims of the holes shows
only a small difference with respect to the holes, although $\sim$66$\%$ of
the rim’s show higher values. The ionization parameter directly reflects the
ratio of radiation to gas pressure, or the interaction between the ionizing
source and ionizing gas. Therefore, the ionization parameter increases with
the luminosity of the stellar population and the hardness of the ionizing
radiation field.

It has also been suggested that high ionization parameters are the result of
high SFRs, which lead to a larger reservoir of ionizing photons (e.g.,
Hainline et al., 2009; Kewley et al., 2013). This would be in agreement with
the observed enhancement in SFR in the rims of the holes. Hence, the observed
difference is likely a result of the enhanced SFR taking place. Another
possible effect at play is the dust absorption. On galactic scales, Yeh &
Matzner (2012) suggest that the ionization parameter can be suppressed by
selective dust absorption of ionizing photons in the regions where U is
highest, decreasing the observed ionization parameter. This suggests that the
ionization parameter we observe could be higher.

Finally, we observe only a minor increase in the oxygen abundance in the rims
of the holes. Considering that the chemical enrichment produced by the SNe
will be mixed into an already enriched ISM (12+log(O/H) $\sim$ 8.5, see Fig.
4), the cumulative effect of the SNe on the ISM metallicity is expected to be
small and within the errors.

##  6 Conclusions

In this paper, we analyze the spiral galaxy NGC 6946, also known as the
Fireworks galaxy due to its extremely high number of SNRs. We link the high
number of SNRs with H i holes in NGC 6946, and analyze their optical
properties such as the oxygen abundance, SFR surface density, ionization
parameter, and the BPT classification. This work relies on the combination of
the SNR candidates of Long et al. (2019), the H i holes catalog of Boomsma et
al. (2008), and the GMS IFU spectroscopy of Metal-THINGS for NGC 6946. Our
findings can be summarized as follows.

-The oxygen abundance of fibers hosting SNRs are in agreement with the rest of our data and follow the general tendency of the metallicity gradient of fibers not hosting SNRs. Altogether, this suggests that SNRs do not contribute significantly to the radiation of the fibers.

\- Our data indicate an overabundance of SNRs located around the rims of the H
i holes (Fig. 6). This is in agreement with the lack of bright emission at
multiple wavelengths inside the holes, suggesting that the H i holes are
already devoid of gas, which also could explain the lack of SNRs located
inside the holes.

\- The overabundance of SNRs in the H i hole rims indicates an enhanced star
formation in the very recent past in those regions. Indeed, our IFU data shows
a higher star formation rate on the rims compared to within the H i holes (see
Fig. 7). This is connected with the overabundance of SNRs, in the sense that
expanding shells would compress the surrounding gas and trigger the formation
of a new generation of stars. Supporting this effect, our data indicates that
the dust extinction is also higher in the rims. Indeed, this result is
expected since dust grains increase the molecular formation and enhance the
SFR.

\- Our analysis provides a hint of an enhanced ionization parameter in the
rims for 66$\%$ of the analyzed holes, although this is not statistically
significant according to the paired t-test (p-value of 0.48). Additionally,
our analysis shows only a marginal chemical enrichment, with $\sim$58.6$\%$ of
holes showing a higher oxygen abundance in the rims.

Altogether, our data supports a picture in which multiple SN explosions
occurred dozens of Myrs ago, producing the H i holes, and compressing the gas
and inducing star formation in the rims of the H i holes.

###### Acknowledgements.

We thank Dr T.A. Oosterloo for providing us with the H i holes catalog. Our
team acknowledges funding from the International Space Science Institute
(ISSI) for collaboration meetings. L.S.P acknowledges support in frame of the
program “Support for the development of priority fields of scientific
research” of the NAS of Ukraine (“ActivPhys”, 2022-2023). M.A.L.L. acknowledge
support from the Spanish grant PID2021-123417OB-I00. M. R. acknowledges
support from the grants CONACYT CF-86367; CY-253085, and DGAPA-PAPIIT (UNAM)
IN 109919. O.L.C acknowledges travel support from INAOE and Sistema Nacional
de Investigadores (SNI). This research has made use of the NASA/IPAC
Extragalactic Database, which is funded by the National Aeronautics and Space
Administration and operated by the California Institute of Technology. We
acknowledge the usage of the HyperLeda database (http://leda.univ-lyon1.fr).

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