11institutetext:  Obserwatorium Astronomiczne Uniwersytetu Jagiellońskiego,
ul. Orla 171, 30-244 Kraków, Poland,
11email<EMAIL_ADDRESS>22institutetext: Max-Planck-Institut für
Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany 33institutetext:
Instytut Astronomii, Wydział Fizyki, Astronomii i Informatyki Stosowanej,
Uniwersytet Mikołaja Kopernika, ul. Grudziadzka 5/7, 87-100, Toruń, Poland
44institutetext: European Space Agency, European Space Astronomy Centre
(ESA/ESAC), Camino Bajo del Castillo s/n, 28692 Villanueva de la Cañada,
Madrid, Spain 55institutetext: Ruhr University Bochum, Faculty of Physics and
Astronomy, Astronomical Institute, 44780 Bochum, Germany

# Hot magnetic halo of NGC 628 (M 74) ††thanks: Based on observations obtained
with XMM-Newton, an ESA science mission with instruments and contributions
directly funded by ESA Member States and NASA

M. Weżgowiec 11 R. Beck 22 M. Hanasz 33 M. Soida 11 M. Ehle 44 R.-J. Dettmar
55 M. Urbanik 11

(Received; accepted date)

###### Abstract

Context.  In several spiral galaxies that are observed face-on, large-scale
ordered magnetic fields (the so-called magnetic arms) were found. One of the
explanations was the action of the magnetic reconnection, which leads to a
higher ordering of the magnetic fields. Because it simultaneously converts the
energy of the magnetic fields into thermal energy of the surroundings,
magnetic reconnection has been considered as a heating mechanism of the
interstellar medium for many years. Until recently, no clear observational
evidence for this phenomenon was found.

Aims.  We search for possible signatures of gas heating by magnetic
reconnection effects in the radio and X-ray data for the face-on spiral galaxy
NGC 628 (M 74), which presents pronounced magnetic arms and evidence for
vertical magnetic fields.

Methods.  The strengths and energy densities of the magnetic field in the
spiral and magnetic arms were derived, as were the temperatures and thermal
energy densities of the hot gas, for the disk and halo emission.

Results.  In the regions of magnetic arms, higher order and lower energy
density of the magnetic field is found than in the stellar spiral arms. The
global temperature of the hot gas is roughly constant throughout the disk.

Conclusions.  The comparison of the findings with those obtained for the
starburst galaxy M 83 suggests that magnetic reconnection heating may be
present in the halo of NGC 628. The joint analysis of the properties of the
magnetic fields and the hot gas in NGC 628 also provided clues for possible
tidal interaction with the companion galaxy.

###### Key Words.:

galaxies: individual: NGC 628 – galaxies: ISM – galaxies: spiral – galaxies:
magnetic fields – magnetic reconnection

††offprints: M. Weżgowiec

##  1 Introduction

The past decades of radio observations, including sensitive polarimetry at
higher frequencies, have increasingly provided evidence that the dynamics of
the interstellar medium (ISM) is controlled by the magnetic field (see e.g.
the review by Beck, 2004). Although radio emission, both thermal and non-
thermal, is mainly associated with the star-forming galactic arms, polarised
emission from the large-scale ordered magnetic fields in some galaxies was
found between the spiral arms (e.g. Beck, 2007). To date, no widely accepted
theory exists that would explain the origin of these magnetic arms (Beck,
2015). One of the proposed mechanisms is magnetic reconnection, which converts
energy that is stored in the magnetic field into thermal energy of the
surrounding gas (Hanasz & Lesch, 1998). Because reconnection occurs in tangled
magnetic fields, the removal of this component would lead to a higher
contribution from the ordered component to the total magnetic fields.

To test this hypothesis, we analysed the radio and X-ray data for the grand-
design spiral galaxy NGC 6946 (Weżgowiec et al., 2016), in which magnetic arms
are present (Beck, 2007). The comparison of the properties of the hot gas and
the magnetic fields in the spiral arms and the inter-arm regions showed a
slight increase in the temperature of the hot gas (and the corresponding
thermal energy) in the inter-arm regions that was accompanied by lower energy
densities and by a higher order of the magnetic fields (Weżgowiec et al.,
2016). To follow-up our analyses, we studied another grand-design spiral
galaxy, M 83, which also presents ordered magnetic fields between the stellar
spiral arms (Frick et al., 2016). Although the effects that were found in NGC
6946 could not be confirmed in M 83 at a high level of significance, the deep
X-ray data allowed us to obtain reliable information about the halo gas.
Together with the properties of the magnetic fields derived from the radio
data, this in turn provided clues that reconnection heating might also occur
in the halo of M 83 (Weżgowiec et al., 2020). The possibility that magnetic
reconnection might occur in galactic haloes has been theoretically discussed
already by Kahn & Brett (1993), and a number of subsequent papers considered
it as a source of heating (e.g. Zimmer et al., 1996; Tanuma et al., 2003).

In this paper we present an analysis of radio and X-ray data for the spiral
galaxy NGC 628 in search for signs of reconnection heating. This face-on
galaxy shows both pronounced magnetic arms and substantial clues for the
existence of vertical magnetic fields (Mulcahy et al., 2017).

NGC 628 (M74) is a large grand-design spiral galaxy that presents broad and
extended stellar arms. Although it resides within a small group of galaxies
(Auld et al., 2006), the studies by Kamphuis & Briggs (1992) suggest that NGC
628 did not interact with its companions within the past 1 Gyr. This allows
NGC 628 to be regarded as an isolated galaxy. Although a significant number of
H i holes were found in this galaxy (Bagetakos et al., 2011), which suggests a
vivid star formation, the rate of this star formation remains at a moderate
level of 0.68 M☉ yr-1 (Kennicutt et al., 2011). This might be explained by the
findings of Marcum et al. (2001), who argued that NGC 628 has experienced an
increased star formation activity over the last 500 Myr that now decreases
rapidly. The basic physical properties of NGC 628 are presented in Table 1.

Table 1: Basic astronomical properties of NGC 628

Morphological type aa$a$Taken from de Vaucouleurs et al. (1991). | SAc
---|---
Inclination | 7°
Diameter D25 | 10′
R.A.2000 | 01h36m42s
Dec2000 | +15°47′01″
Distancebb$b$Karachentsev et al. (2004). | 7.3 Mpc
Column density $N_{\rm H}$cc$c$Weighted average value after the HI4PI survey; HI4PI Collaboration et al. (2016). | 4.73$\times$1020 cm-2
111 All data except for type, distance, and column density are taken from
HYPERLEDA database – http://leda.univ-lyon1.fr – see Makarov et al. (2014).

The radio emission from NGC 628 has been studied by Mulcahy et al. (2017), who
analysed sensitive single-dish observations obtained with the 100 m Effelsberg
radio telescope, as well as deep S-band (3 GHz) Karl G. Jansky Very Large
Array (VLA) observations in the compact C and D configurations. They found
little radio emission in the central region of the galaxy, which likely
results from a low abundance of the massive O stars that eventually supply the
cosmic-ray electrons to the interstellar medium. Consequently, the authors
derived the typical strengths of the magnetic fields in NGC 628 (of the order
of 9 $\mu$G). The observations also showed that NGC 628 possesses pronounced
magnetic arms between the stellar spiral arms of the galaxy, similar to those
found in NGC 6946 (Beck, 2015). A strongly polarised feature in the northern
part of the disk was especially interesting. It is not associated with any of
the star-forming regions. Furthermore, sensitive Faraday rotation data allowed
detecting signs of possible Parker loops, rising from the eastern spiral arm
above the disk and into the halo, as well as a significant feature in Faraday
depth that coincides with one of the many H i holes in NGC 628, also
suggesting that enhanced vertical magnetic fields are present in the halo of
this galaxy.

NGC 628 has been observed three times with the XMM-Newton X-ray space
telescope (Jansen et al., 2001). The details of the observations are listed in
Table 2. The results of observations 0154350101 and 0154350201 have been
published in a number of papers, most of which focused on the populations of
discrete sources (e.g. Sonbaş et al., 2010; Walton et al., 2011; Lin et al.,
2012; Earnshaw et al., 2019), and only Owen & Warwick (2009) performed the
analysis of the diffuse X-ray emission from NGC 628, along with several other
face-on galaxies. This study, however, aimed at the global properties of the
galaxies. In this paper, we add new observations, performed by the authors in
January 2021, and take advantage of the increased sensitivity of the entire
X-ray data for NGC 628. Our findings are compared to the results obtained by
Owen & Warwick (2009) below.

We analyse new X-ray observations of NGC 628 and focus on the diffuse emission
from the hot gas. Its properties in different areas of the galaxy are then
compared to the properties of the magnetic fields inferred from the radio data
presented by Mulcahy et al. (2017). The comparison is performed to search for
signs of magnetic reconnection, such as those reported for NGC 6946 (Weżgowiec
et al., 2016) and M 83 (Weżgowiec et al., 2020). The spectral analysis of the
hot gas can also give an insight into the properties of the halo gas, which
might help to confirm the detection of the vertical magnetic fields (Mulcahy
et al., 2017).

##  2 Observations and data reduction

###  2.1 Radio observations

The radio data at S band (3 GHz) presented in this paper were already
thoroughly analysed by Mulcahy et al. (2017). For the purpose of this paper,
we re-reduced these data following the calibrations performed by the authors,
but focusing only on the data observed in the most compact D configuration,
which provide high sensitivity to large-scale emission and ensure a resolution
that matches that of the X-ray data best. The maps obtained in the cleaning
process were restored with an elliptical beam of 26$\arcsec\times$22$\arcsec$
and were later smoothed with a Gaussian beam to the resolution of 30$\arcsec$.

###  2.2 X-ray observations

To process all data from the observations listed in Table 2, we used the SAS
19.0.0 package (Gabriel et al., 2004) and its standard procedures that allowed
us to produce event lists for all three detectors of the European Photon
Imaging Camera (EPIC). From these lists, we excluded data that were acquired
during periods of an increased level of the high-energy background radiation.
This step is necessary to allow a reliable analysis of the diffuse X-ray
emission. To identify these periods, we created light curves and selected for
further analysis only those observation times during which the level of the
high-flaring background was below a standard thresholds of 0.35 cts/s and 0.4
cts/s for the EPIC-MOS (Turner et al., 2001) and the EPIC-pn (Strüder et al.,
2001) cameras, respectively.

Table 2: Characteristics of the X-ray observations of NGC 628

Obs ID | EPIC-pn | EPIC-pn | total | clean
---|---|---|---|---
| filter | obs. mode | time [ks] | time [ks]
0154350101 | T | FF | 34.3 | 28.9
0154350201 | T | FF | 23.0 | 23.0
0864270101 | T | FF | 107.7 | 34.5
222 T - thin; FF - full frame.

Next, we checked the filtered event lists for possible soft proton flare
contamination using the method developed by De Luca & Molendi (2004) that is
implemented in the script333https://www.cosmos.esa.int/web/xmm-newton/epic-
scripts#flare provided by the authors. The event lists of all three
observations were found to be free from soft proton contamination.

For each of the filtered event lists, images and exposure maps (without
vignetting correction) were produced. This was done with the help of the
images script444https://www.cosmos.esa.int/web/xmm-newton/images. In the data
selection needed to create the images, we used only events with FLAG=0 and
PATTERN$\leq$4 (EPIC-pn) or FLAG=0 and PATTERN$\leq$12 (EPIC-MOS). This
ensured best-quality data, which are required to analyse the diffuse X-ray
emission. The images were produced in four energy bands, that is, 0.2-1 keV,
1-2 keV, 2-4.5 keV, and 4.5-12 keV, which cover the entire energy range of the
XMM-Newton EPIC cameras. This was needed to effectively detect the point
sources within the galactic disk, whose emission was later excluded from the
regions prepared for the spectral analysis. The two lower energy bands, that
is, 0.2-1 keV and 1-2 keV, were also used to create a hardness ratio map that
helps to trace a relative change in the amounts of cooler and hotter gas
throughout the disk. These steps were performed for each of the three
observations. Next, the corresponding images and exposure maps were combined
into final EPIC images using the SAS task emosaic. The combined images were
adaptively smoothed with a maximum smoothing scale of 30$\arcsec$ and a
signal-to-noise ratio of 30. To allow a precise creation of the hardness ratio
map, the map in the medium energy band (1-2 keV) was smoothed using the same
scales as were calculated for the soft energy band (0.2-1 keV) with the
asmooth task.

The source detection described above was performed with the SAS meta-task
edetect_stack, which simultaneously uses event lists from all observations to
maximise the sensitivity of the conducted search. The detected sources were
excluded from the spectral regions that were prepared to analyse the diffuse
X-ray emission from the hot gas. The size of the removed area was selected
individually for each source so that only the brightest emission was excluded.
This approach was desirable because the exclusion within the area of the full
point spread function (PSF) of the instrument could lead to an unnecessary
removal of the already faint diffuse emission. To account for these smaller
areas, a power-law component was added to the model fitted to the resulting
spectrum. This component was still needed to account for any possible emission
from unresolved point sources that also contributes to the X-ray sky
background.

In the next step, spectra from all regions were extracted with the use of the
same flag and pattern selection as when the images were created. For the
extracted spectra, response matrices and effective area files were created.
Because the sizes of all regions are much larger than the PSF, a detector map
(image in detector coordinates) was also used.

For the available observations of NGC 628, a proper modelling of the
background is very difficult. The significant angular size of the galaxy means
that most of the sensitive part of the field of view is covered. Owen &
Warwick (2009) used the local background, which also included the detector
contribution. We note here that their work focused on the analysis of the
global spectrum of the entire emission from the galactic disk. In this case,
the background measured in the annular region outside of the source region can
be justified. In this work, however, we analyse individual regions within the
galactic disk, most of which show a very low surface brightness. Due to the
limited sensitivity of the available observations and the resulting low
surface brightness of the emission in the studied regions, the use of the
blank-sky background (Carter & Read, 2007) led to its oversubtraction. This
could be caused by increased background emission coming from either
observations with lower column density than that in the direction NGC 628
(Table 1) or from observations with a stronger detector contribution, likely
those distant in time from the ones that we used. The low surface brightness
of most of our regions suggests that the contribution from the detector
background probably is much more significant. Therefore, we decided to account
for the detector background only, using the filter wheel closed (FWC)
data555https://www.cosmos.esa.int/web/xmm-newton/filter-closed, but only from
those observations that were performed close in time to the ones that we use.
The FWC event lists were then filtered in the same way as the source event
lists, and the background spectra were extracted using the same regions as in
the extraction of the source spectra.

In the final step, the corresponding spectral products, source and background
spectra, response matrices, and effective area files were combined (SAS task
epicspeccombine). The obtained background-subtracted spectra were binned to
reach 25 counts per energy bin, which proved to be effective in a wide range
of sensitivities (Weżgowiec et al., 2016, 2020). The spectra were then fitted
using xspec12 (Arnaud, 1996) and the models described in Sect. 3.3.

For the overlays, we also used the UV image observed with the XMM-Newton
Optical Monitor and the UVW1 filter from the most recent observations (ObsID
0864270101). The data were reduced with the standard pipeline procedure (sas
meta-task omichain).

##  3 Results

The radio data that we show in this paper were already presented by Mulcahy et
al. (2017). Nevertheless, we used the D-configuration data only, which result
in high sensitivity to extended structures, especially of faint polarised
emission, which is crucial for our study. In Sect. 3.1 we therefore briefly
present our maps with special attention to the features revealed by the more
sensitive larger beam. In Sects. 3.2 and 3.3 we present the maps of the X-ray
emission and its spectral properties, respectively. For the overlays, we used
the H$\alpha$ map of NGC 628 from the SIRTF Nearby Galaxy Survey (SINGS;
Kennicutt et al., 2003).

###  3.1 Radio emission

The map of the total radio intensity (Fig. 1, left) shows a larger extent of
the emission than of the star-forming disk, with a significant extension
towards the north. The lines of the magnetic fields follow the spiral
structure of the galaxy, although they seem to be phase-shifted and filling
the inter-arm space. This is especially visible in the right panel of Fig. 1,
where the contours of the polarised radio emission are presented together with
the magnetic field vectors with their lengths proportional to the degree of
polarisation. The lower resolution of this map compared to that of Mulcahy et
al. (2017) allowed us to reveal that the western magnetic arm extends far to
the north of the galaxy and turns eastward. The larger beam also recovered
more polarised emission in the central part of the galaxy, but it is still
strongest in its outer parts. Nevertheless, the total and polarised radio
fluxes agree within the uncertainties when C+D and D array maps are compared
(Table 3).

Table 3: S-band total radio flux densities (in mJy) of M 74

Map | C+D arrayaa$a$measured in the maps from Mulcahy et al. (2017). | D arraybb$b$this paper.
---|---|---
Total intensity | 120$\pm$6 | 119$\pm$6
Polarised intensity | 16$\pm$1 | 17$\pm$1
666

Furthermore, east and north of the galactic centre, local maxima of the
polarised emission are visible that do not correspond to any star-forming
region. The northern maximum was already investigated by Mulcahy et al.
(2017), who found an exceptionally strong and ordered magnetic field in this
position that may be compressed by an expanding super-bubble.

Figure 1:  Map of the total (left) and polarised (right) radio intensity at 3
GHz ($\lambda$ 10 cm) of NGC 628 overlaid on an H$\alpha$ and XMM-Newton
Optical Monitor in UVW1 filter map, respectively. The contour levels are 3, 5,
8, 16, 32, 64, 128, 256, and 512 $\times$ 24 $\mu$Jy (left) or 10 $\mu$Jy
(right). The lines show the orientation of the magnetic fields, and their
lengths of 1′are proportional to the polarised intensity of 150 $\mu$Jy (left)
or to a degree of polarisation of 36% (right). The angular resolution is
30$\arcsec$.

###  3.2 Distribution of the X-ray emission

The X-ray emission from the hot gas is relatively faint and is mainly limited
to the star-forming disk of NGC 628 (Fig. 2). The diffuse emission is visible
at a level not greater than 8$\sigma$ in the central part of the disk in the
soft-band (0.2-1 keV) image (Fig. 2, left) or 3-5$\sigma$ in the medium-band
(1-2 keV) image (Fig. 2). The hardness ratio (HR) map (Fig. 3) shows that the
softest emission comes from the central part of the disk, which matches the
brightest emission visible in the soft-band image (Fig. 2, left) very well.
The harder emission in the outer parts of the disk can be associated with the
hotter gas, possibly in the area of the magnetic arms. The overall low level
of the X-ray emission, with its softest part mainly coming from the central
disk, agrees with the relatively low level of star formation in NGC 628 and
with the scenario that the star-forming activity has decreased over the last
several hundred million years, which is a cooling time of the hot medium at
temperatures of 0.3-0.6 keV (e.g. Weżgowiec et al., 2020).

Figure 2:  Map of the soft X-ray emission from NGC 628 in the 0.2 - 1 keV band
overlaid on an H$\alpha$ image (left). The contours are 3, 5, 8, 16, 32, 64,
128, and 256 $\times$ rms. The map is adaptively smoothed with the largest
scale of 30$\arcsec$. Right: Map of the medium X-ray emission from NGC 628 in
the 1 - 2 keV band overlaid on a UVW1 image. The contours are 3, 5, 8, 16, 32,
64, 128, and 256 $\times$ rms. The map is adaptively smoothed with the largest
scale of 30$\arcsec$.

Figure 3: Map of the hardness ratio of the medium and soft X-ray emission from
NGC 628 (Fig. 2), overlaid with lines of the magnetic field proportional to
the degree of polarisation. The map is truncated at the 3$\sigma$ level of the
soft X-ray emission map.

###  3.3 Spectral analysis of the X-ray emission

Similar to our previous study (Weżgowiec et al., 2016, 2020), we investigated
the properties of the hot gas in all regions that are prominent in the radio
maps, that is, magnetic arms (highly polarised inter-arm regions) and spiral
arms, as well as the halo above them. The region selection was performed with
the use of the polarised intensity map (right panel of Fig. 1) and the
H$\alpha$ map, tracing the ordered magnetic fields and star-forming regions,
respectively. All regions are presented in Fig. 4 and Table 4. In addition to
the areas corresponding to the spiral arms (S) and the inter-arm spaces (I),
we also selected other interesting regions of the galaxy that are associated
with the largest H II complexes (B1) or the bright polarised radio ridges
(R1-R3). As mentioned in Sect. 2.2, all detected X-ray point sources were
excluded from all regions. Additionally, an area of the strong polarised radio
source (NVSS J013657+154422) was excluded from region I1 (red circle in Fig.
4).

Figure 4:  Regions of diffuse X-ray emission from NGC 628 (see text for a detailed description) overlaid on the H$\alpha$ map (left) and on the polarised radio intensity at 3 GHz (right). The region of the polarised radio source that we excluded from the analysis is marked with the red circle.  Table 4: Regions of NGC 628 that were used for the spectral analysis. Region name | Region description
---|---
B1 | large H II region north of centre
I1 | eastern magnetic arm
I2 | southern magnetic arm
I3 | south-central magnetic arm
I4 | western magnetic arm
R1 | polarised feature within I1 (north)
R2 | polarised feature within I1 (south)
R3 | polarised feature north of centre
S1 | eastern spiral arm
S2 | western spiral arm

Following the extraction of spectra and the background subtraction described
in Sect. 2.2, we performed spectral analysis for all regions to investigate
the properties of the hot gas. Due to the slight contribution from the
detector Al-K$\alpha$ line at 1.5 keV, which is still visible in some of the
spectra, the energy range 1.4-1.6 keV was excluded prior to the model fitting
for the best results. Despite the limited sensitivity of the X-ray data for
NGC 628, the spectra extracted from the regions of spiral arms (S1 and S2), as
well as the large H ii complex B1, were fitted with two thermal component
models that account separately for the disk and the halo X-ray emission. The
remaining inter-arm regions were fitted with only one thermal component to
model the entire emission from the hot gas. The thermal component used in our
models is described by the mekal model (Mewe et al., 1985; Kaastra, 1992) of
thermal bremsstrahlung with additional emission lines. In all models, we also
used a power-law component to account for the unresolved point sources and for
the residual emission from the sources that were removed from the spectral
regions (see Sect. 2.2). This additional component was not constrained in the
case of the two-temperature model fitted to the spectrum from region B1,
however. The absorption by the neutral hydrogen in our Galaxy is accounted for
by the wabs model with a fixed value of the column density (Table 2).

For the model fit to the S2 spiral arm region, the lower temperature of the
two thermal components was fitted at the lower limit allowed by xspec12 (kT =
0.08 keV). Therefore, the real temperature of the hot gas can be lower. We
also assumed symmetric uncertainties for this measurement because xspec12 does
not allow for values lower than 0.08 keV (see Table 5). The higher temperature
in the same model fit was similar to that obtained for the inter-arm regions,
for which a model with a single thermal component was fitted (Table 5). In our
analysis of the very sensitive X-ray data for M 83 (Weżgowiec et al., 2020),
we found that the halo emission can be described with two thermal components
with temperatures of $\sim$0.1 and $\sim$0.3 keV. Taking this into account, it
is likely that both thermal components in the model fit to region S2 refer to
the halo and that the emission from the hotter gas in the disk is not directly
detected in this moderately sensitive spectrum. Nevertheless, a relatively
flat photon index of the power-law component in this model suggests that in
fact only one thermal component is sufficient to model the spectrum of the
emission from the spiral arm S2 (see Table 5). This is because in a low-
sensitivity spectrum, the emission at higher energies is likely to be
attributed either to the thermal or the power-law model component. This mixing
of these two model components was described in Weżgowiec et al. (2016). The
fact that for the spectrum from region B1 it was impossible to use the
additional power-law component can also be due to this ambiguity, especially
that the higher temperature is surprisingly high, even for hot disk gas, and
at the same time, its uncertainty reaches 70%. The single thermal component
model for the spectrum from B1 does allow for a constrained power-law
component, but its uncertainty is relatively high, which only confirms the
ambiguity mentioned before. Therefore, we argue that the contribution from the
hot gas in the disk should be present in the spectrum from this bright star-
forming region and only the sensitivity of the spectrum does not allow us to
fit a model that includes both the second thermal and the power-law components
simultaneously. Having this in mind, in the further analyses presented in this
paper, we use the single thermal component model.

Only for the spectrum of the more pronounced spiral arm S1, which has
significantly higher net counts and surface brightness than that for the
spiral arm S2 (see Table 5), was it possible to obtain a well-constrained
model with two thermal components. Its temperatures of 0.20$\pm$0.02 and
0.77$\pm$0.17 keV suggest a direct detection of the disk emission, being
associated with the hotter component. For this spectrum, which is still
moderately sensitive, it should still be possible to associate only one
thermal component with the entire emission from the diffuse X-ray gas, whose
parameters should be similar to those derived from the two thermal component
model. We performed this test and found that in the single thermal component
model, the global temperature is the average (weighted by normalisation) of
the temperatures from the two thermal component model, and additionally, its
power-law component is much better constrained than that in the two thermal
component model. Consequently, the derived fluxes have lower uncertainties
(see Table 6), which results in better-constrained parameters of the hot gas.
Taking this into account, we decided to use the single thermal component model
also for the spectrum from region S1. Therefore, in the following discussions
of the properties of the hot gas for all regions, including the star-forming
regions B1, S1, and S2, we use the single thermal component model fits to
calculate the hot gas parameters. The parameters of the fitted models are
presented in Table 5, and the derived fluxes are listed in Table 6. The two
thermal component models are marked in both tables with italics. The plots of
the fitted (single thermal component) models with residuals are presented in
Figs. 5–7. The lowest sensitivity of the spectra was obtained for the regions
of the polarised ridges R1, R2, and R3. As shown in Table 5, only for region
R1 was it possible to obtain a constrained model fit.

Table 5:  Model-fit parameters for the regions studied in NGC 628. Region | Model | kT1 | kT2 | Photon | $\chi_{\rm red}^{2}$ | Net | Net cts
---|---|---|---|---|---|---|---
| type | [keV] | [keV] | Index |  | cts | /sqarcmin
B1 | wabs(mekal+power law) | 0.23${}^{+0.03}_{-0.02}$ | – | 2.22${}^{+0.74}_{-1.12}$ | 0.91 | 1649 | 1994
B1 | wabs(mekal+mekal) | 0.22${}^{+0.02}_{-0.03}$ | 1.03${}^{+0.75}_{-0.31}$ | – | 0.82 | 1649 | 1994
I1 | wabs(mekal+power law) | 0.20$\pm$0.01 | – | 1.39${}^{+0.32}_{-0.31}$ | 1.01 | 6164 | 738
I2 | wabs(mekal+power law) | 0.18${}^{+0.04}_{-0.06}$ | – | 1.74${}^{+0.56}_{-0.60}$ | 1.37 | 2134 | 738
I3 | wabs(mekal+power law) | 0.20$\pm$0.02 | – | 1.76${}^{+0.74}_{-0.72}$ | 1.15 | 2775 | 960
I4 | wabs(mekal+power law) | 0.16${}^{+0.03}_{-0.04}$ | – | 2.22${}^{+0.41}_{-0.46}$ | 1.04 | 3775 | 705
R1 | wabs(mekal+power law) | 0.21${}^{+0.03}_{-0.04}$ | – | 1.27${}^{+0.63}_{-0.64}$ | 1.06 | 982 | 798
S1 | wabs(mekal+power law) | 0.23$\pm$0.01 | – | 2.18${}^{+0.28}_{-0.33}$ | 1.04 | 7996 | 1985
S1 | wabs(mekal+mekal+power law) | 0.20$\pm$0.02 | 0.77$\pm$0.17 | 1.63${}^{+0.62}_{-1.04}$ | 1.11 | 7996 | 1985
S2 | wabs(mekal+power law) | 0.21$\pm$0.02 | – | 2.28${}^{+0.47}_{-0.66}$ | 1.07 | 5128 | 1260
S2 | wabs(mekal+mekal+power law) | 0.08$\pm$0.03 | 0.26${}^{+0.05}_{-0.02}$ | 1.32${}^{+0.60}_{-0.55}$ | 0.73 | 5128 | 1260

In their two-temperature model fit to the emission from the entire galaxy,
Owen & Warwick (2009) found two thermal components characterised by
temperatures of 0.2 keV and 0.65 keV for the halo and disk, respectively. The
temperatures obtained by us in the two thermal component model fits to the
spectra from the spiral arm S1 and the H ii complex B1 correspond well with
these values. As mentioned before, in the low-sensitivity spectrum of the
emission from the spiral arm S2, we may not have detected the disk emission
directly, and both thermal model components describe the halo emission. This
seems justified because typically, much more emission comes from the halo gas
than from the disk (e.g. Tüllmann et al., 2006; Weżgowiec et al., 2020). For
all inter-arm regions, the single-temperature model fits resulted in
temperatures of about 0.2 keV, matching the halo temperature obtained by Owen
& Warwick (2009). Last but not least, from their model fit to the entire
emission from NGC 628, Owen & Warwick (2009) calculated that the flux ratio of
the cool and hot components is higher than 5.4. This can certainly explain
difficulties in the detection of the hot disk component in the lower-
sensitivity spectra from smaller regions of the galaxy.

The highest temperature in the inter-arm regions, although still within
uncertainties, was that derived for the polarised ridge R1, which is a part of
region I1. This suggests that the temperature of the hot gas within I1 and
outside of R1 could be lower. In this case, the highest temperature will be
that for the inter-arm region I3, which corresponds to the bright magnetic arm
(Figs. 1 and 4).

Figure 5: Spectral model fits to the diffuse X-ray emission from the inter-arm
regions of NGC 628. See Tables 5 and 6.

Figure 6: Spectral model fit to the diffuse X-ray emission from the polarised
feature R1 within the inter-arm region I1. See Tables 5 and 6.

Figure 7: Spectral model fits to the diffuse X-ray emission from the spiral arms of NGC 628. See Tables 5 and 6. Table 6:  Total (0.3 - 12 keV) unabsorbed fluxes in 10-14erg cm-2s-1 for the modelled regions in NGC 628. Region | mekal 1 | mekal 2 | power law | total
---|---|---|---|---
B1 | 0.91${}^{+0.30}_{-0.32}$ | – | 1.05${}^{+3.48}_{-0.55}$ | 1.96${}^{+3.78}_{-0.87}$
B1 | 1.10${}^{+0.18}_{-0.26}$ | 0.32${}^{+0.45}_{-0.19}$ | – | 1.42${}^{+0.62}_{-0.46}$
I1 | 3.70${}^{+0.85}_{-0.78}$ | – | 12.80${}^{+11.12}_{-5.67}$ | 16.5${}^{+11.97}_{-6.46}$
I2 | 0.65${}^{+0.46}_{-0.50}$ | – | 3.12${}^{+5.27}_{-1.63}$ | 3.76${}^{+5.72}_{-2.13}$
I3 | 1.50$\pm$0.50 | – | 2.60${}^{+6.21}_{-1.48}$ | 4.10${}^{+6.70}_{-1.97}$
I4 | 1.43${}^{+1.41}_{-0.99}$ | – | 5.36${}^{+3.01}_{-1.39}$ | 6.79${}^{+4.42}_{-2.38}$
R1 | 0.49${}^{+0.25}_{-0.26}$ | – | 2.46${}^{+7.70}_{-1.78}$ | 2.95${}^{+7.96}_{-2.04}$
S1 | 3.53${}^{+0.65}_{-0.63}$ | – | 6.53${}^{+2.68}_{-1.43}$ | 10.07${}^{+3.32}_{-2.06}$
S1 | 4.05${}^{+1.00}_{-1.08}$ | 1.14${}^{+0.60}_{-0.51}$ | 6.02${}^{+33.89}_{-4.06}$ | 11.20${}^{+35.49}_{-5.65}$
S2 | 1.68${}^{+0.64}_{-0.59}$ | – | 3.03${}^{+2.73}_{-0.83}$ | 4.71${}^{+3.37}_{-2.25}$
S2 | 3.06${}^{+7.14}_{-2.20}$ | 2.18${}^{+0.66}_{-0.69}$ | 5.26${}^{+12.80}_{-3.55}$ | 10.5${}^{+20.57}_{-6.45}$

##  4 Discussion

###  4.1 Parameters of the hot gas

We used the model of thermal cooling and ionisation equilibrium of Nulsen et
al. (1984) and the model-fit parameters to calculate the physical properties
of the hot gas. In the ionisation equilibrium model, where
$L_{X}=1.11\cdot\Lambda(T)\,n^{2}_{e}\,V\,\eta$, $\Lambda(T)$ is a cooling
coefficient of about $10^{-22}\,{\rm erg}\,{\rm cm}^{3}\,{\rm s}^{-1}$ for
temperatures of a few million K (Raymond et al., 1976), $n^{2}_{e}$ is number
density, $V$ is the emitting volume, and $\eta$ is an unknown filling factor.
The emitting volume $V$ was calculated as a product of the surface of the
spectral region and the height above the disk plane. We assumed a 10 kpc halo
extending above a 1 kpc thick disk. The former was assumed as a typical extent
of a gaseous halo in normal star-forming spiral galaxies (e.g. Tüllmann et
al., 2006). These volumes and the normalisations of our model fits together
with the derived fluxes allowed us to obtain number densities, gas masses, and
thermal energies of the hot gas. The calculated parameters of the hot gas are
presented in Table 7.

Table 7: Derived parameters of the hot gas from the studied regions in NGC
628.

Reg. | n $\eta^{-0.5}$ | M${}_{gas}\,\eta^{0.5}$ | E${}_{th}\,\eta^{0.5}$ | $\epsilon_{th}\,\eta^{-0.5}$
---|---|---|---|---
| [10-3cm-3] | [106M⊙] | [1054 erg] | [10-12 erg cm-3]
B1 | 1.55${}^{+0.21}_{-0.26}$ | 1.54${}^{+0.21}_{-0.26}$ | 1.01${}^{+0.29}_{-0.25}$ | 0.86${}^{+0.25}_{-0.21}$
I1 | 1.05${}^{+0.08}_{-0.09}$ | 10.5${}^{+0.08}_{-0.09}$ | 6.00$\pm$0.76 | 0.50$\pm 0.06$
I2 | 0.78${}^{+0.16}_{-0.23}$ | 2.69${}^{+0.54}_{-0.80}$ | 1.39${}^{+0.65}_{-0.74}$ | 0.34${}^{+0.16}_{-0.18}$
I3 | 1.14${}^{+0.12}_{-0.17}$ | 3.94${}^{+0.42}_{-0.58}$ | 2.26${}^{+0.49}_{-0.52}$ | 0.55${}^{+0.12}_{-0.13}$
I4 | 0.91${}^{+0.25}_{-0.23}$ | 5.81${}^{+1.62}_{-1.46}$ | 2.66${}^{+1.38}_{-1.17}$ | 0.35${}^{+0.18}_{-0.15}$
R1 | 0.97${}^{+0.18}_{-0.24}$ | 1.42${}^{+0.26}_{-0.35}$ | 0.86${}^{+0.30}_{-0.33}$ | 0.49${}^{+0.17}_{-0.19}$
S1 | 1.40${}^{+0.11}_{-0.12}$ | 6.74${}^{+0.52}_{-0.58}$ | 4.44${}^{+0.55}_{-0.56}$ | 0.77$\pm$+0.10
S2 | 1.23${}^{+0.17}_{-0.20}$ | 3.87${}^{+0.54}_{-0.63}$ | 2.33${}^{+0.58}_{-0.57}$ | 0.40$\pm$0.10
777 The columns are the region name, electron number density, total gas mass,
total thermal energy, thermal energy density, and cooling time. $\eta$ is the
volume-filling factor.

###  4.2 Magnetic fields in NGC 628

The magnetic fields of NGC 628 were thoroughly studied by Mulcahy et al.
(2017), therefore we only focus on the strengths of the total and regular
component and on energy densities of the magnetic fields in our spectral
regions. At the frequency of 3 GHz, the thermal radio emission can still be
significant and should be taken into account in calculations of the strengths
of the magnetic fields. Following the calculations of Mulcahy et al. (2017),
for the star-forming regions, that is, B1, S1, and S2, we used a thermal
fraction of 20%. For the areas of the inter-arm regions and for the polarised
ridges, where no significant star formation is visible, we simultanesouly used
the entire radio emission as non-thermal.

To calculate the strengths and energy densities of the magnetic field, we also
followed Mulcahy et al. (2017) and used the revised formula for the energy
equipartition provided by Beck & Krause (2005). In addition to the non-thermal
intensities, we used a path length through the source of $L=1\,{\rm kpc}$,
which is the thickness of the synchrotron disk, and also took its inclination
of 7$\degr$ into account. Following Mulcahy et al. (2017), we adopted a
synchrotron spectral index of $\alpha_{\rm n}=-1$ and a ratio of cosmic-ray
proton to electron number densities of $K=100$. Following the argumentation of
these authors, we note that because the strength of the total magnetic field
scales with synchrotron intensity $I_{nth}$ as

$B_{tot}=(I_{nth}/(K+1)L)^{1/(3-\alpha_{\rm n}}),$ (1)

realistic uncertainties in $L$ and $K$ of a factor of two lead to a magnetic
field strength variation of about 20%. A change in the non-thermal spectral
index of about 30% does not affect the result by more than 5% either. The
uncertainties of the non-thermal intensity mostly depend on the thermal
fraction, which can change from 0 to 40% (see Fig. 11 in Mulcahy et al., 2017)
within each star-forming region mentioned before. Because for these regions we
assumed a thermal fraction of 20%, we also changed the non-thermal intensities
(for consistency also of the inter-arm regions) by 25% to account for these
local variations of the thermal fraction. Nevertheless, this change in
intensity alters the strength of the magnetic field by less than 10%. Last but
not least, the uncertainties in $K$ and $L$ can be considered systematic
errors because they affect the calculations for all regions in the same
manner. Because our aim is to compare the properties of the magnetic field
(and of the hot gas) between different regions of M 74, these uncertainties
would not be relevant. Therefore, we took the uncertainties in non-thermal
intensity and spectral index into account and assumed an error of 10% for the
strengths and 20% for the energy densities of the magnetic field, because
$\epsilon_{B}\,\propto\,B^{2}$.

Table 8:  Properties of the magnetic fields in NGC 628 derived from the maps
presented in Fig. 1.

Reg. | Ssynch | psynch | Btot | $\epsilon_{B}$ | Bord
---|---|---|---|---|---
| [mJy | [%] | [$\mu$G] | [10-12 | [$\mu$G]
| /beam] |  |  | erg cm-3] |
B1 | 1.17 | 7.5 | 12.8$\pm$1.3 | 6.5$\pm$1.3 | 3.4$\pm$0.3
I1 | 0.46 | 19.9 | 9.9$\pm$1 | 3.9$\pm$0.8 | 4.4$\pm$0.4
I2 | 0.21 | 40.8 | 7.7$\pm$0.8 | 2.4$\pm$0.5 | 5.1$\pm$0.5
I3 | 0.52 | 17.3 | 10.2$\pm$1 | 4.2$\pm$0.8 | 4.2$\pm$0.4
I4 | 0.30 | 22.4 | 8.8$\pm$0.9 | 3.1$\pm$0.6 | 4.2$\pm$0.4
R1 | 0.70 | 19.8 | 10.9$\pm$1.1 | 4.8$\pm$1 | 4.8$\pm$0.5
R2 | 0.58 | 23.9 | 10.3$\pm$1 | 4.3$\pm$0.9 | 5.1$\pm$0.5
R3 | 0.82 | 16.9 | 11.5$\pm$1.2 | 5.2$\pm$1 | 4.6$\pm$0.5
S1 | 0.71 | 6.2 | 11.3$\pm$1.1 | 5.1$\pm$1 | 2.7$\pm$0.3
S2 | 0.41 | 9.4 | 9.8$\pm$1 | 3.8$\pm$0.8 | 2.9$\pm$0.3
888 The columns are the region name, the non-thermal radio flux, the degree of
polarisation, the total magnetic field strength, the energy density of the
magnetic field, and the ordered magnetic field strength.

The calculated strengths of the magnetic fields for all studied regions are in
the range of 8-13 $\mu$G, which agrees with the values obtained by Mulcahy et
al. (2017). The lowest strengths of the magnetic field of 8.2-10 $\mu$G were
obtained for the inter-arm regions hosting the magnetic arms, where little or
no star formation is observed. The highest strengths of the magnetic field
were derived for the largest H ii complexes in region B1, and quite
surprisingly, for the area of the polarised ridge R3. The highest strengths of
the ordered magnetic fields are found in the magnetic arm regions and in the
embedded polarised ridges, reaching 5.1$\pm$0.3 $\mu$G in region R2.
Nevertheless, an equally strong ordered magnetic field can be found in the
inter-arm region I2, which is located in the outer part of the southern
galactic disk.

###  4.3 Hot gas and magnetic fields

The analysis of the X-ray data for NGC 628 provided the global parameters of
the entire hot gas in this galaxy, that is, the disk and the halo.
Correspondingly, the observed radio emission was integrated along the line of
sight and therefore also brought information about the whole galaxy.

Prior to a direct comparison of the densities of energy stored in the hot gas
and the magnetic fields, we needed to take into account that the derived
parameters of the hot gas are related to an unknown filling factor ($\eta$)
that likely varies between the analysed regions, especially the spiral arms
and the inter-arm areas. Because it is difficult to provide reliable values of
the filling factors, we introduced a new quantity, energy per particle
$E_{p}$, which is the ratio of the thermal energy density and the electron
density of the hot gas. In this ratio, the dependence on the filling factor is
removed, which allows measuring the energy stored in the hot gas directly
(Weżgowiec et al., 2016, 2020).

Table 9 and Fig. 9 show the relation between the (hot gas) energy per particle
and the energy density of the magnetic fields. While all regions are labelled
in the plots, the regions of the spiral arms and the inter-arm regions are
marked with black and red, respectively. Because of the large uncertainties of
energies per particle, caused by the low sensitivity of the X-ray spectra and
the resulting large uncertainties of the fitted model normalisations, it is
difficult to determine any possible differences between the regions of the
spiral and the magnetic arms of NGC 628. Nevertheless, it seems that in
contrast to our previous findings for NGC 6946 (Weżgowiec et al., 2016) and M
83 (Weżgowiec et al., 2020), a decrease in the energy density of the magnetic
fields in the magnetic arms is not accompanied by an increase in the energy of
the hot gas. The ordering of the magnetic field (Fig. 10), however, is higher
in the magnetic arms than in the spiral arms, as observed before in NGC 6946
(Weżgowiec et al., 2016) and M 83 (Weżgowiec et al., 2020). It resembles the
former galaxy more because similarly to NGC 6946, the distribution of the
star-forming regions in NGC 628 presents a high contrast between the spiral
arms and the inter-arm regions. As we suggested in Weżgowiec et al. (2016),
this contrast may have an important influence on the formation of the
prominent magnetic arms.

An interesting phenomenon is observed when the relation between energies per
particle and energy densities of the magnetic field is compared to that
obtained for M 83 (Weżgowiec et al., 2020). Surprisingly, while both galaxies
show very similar energies per particle, the derived energy densities of the
magnetic fields in the regions of M 83 are twice higher. The difference
between the energy densities of the magnetic fields can easily be explained
with the star-forming activities of the two galaxies. M 83 is a starburst
galaxy with a very high gas mass density (Lundgren et al., 2004), while the
star-forming activity of NGC 628 currently is at a moderate to low level
(Marcum et al., 2001; Kennicutt et al., 2011). This is further supported by
the overall low level of the X-ray emission in the presented maps of NGC 628
(see Sect. 3.2). If the energies stored in the hot gas were depending only on
star formation, the energies per particle should also be higher in M 83 than
in NGC 628. Because they are comparable, a contribution from a source of
heating that is not directly related to star formation is needed to explain
the increase in the energy of the hot gas in NGC 628. We discuss this in more
detail in Sect. 4.5.

###  4.4 Signs of interaction?

We studied the inter-arm region I2 in the outer southern disk of NGC 628 in
more detail. The isolation of this galaxy and that it has not interacted with
the close group companions for at least 1 Gyr (see Sect. 1) appears to be
doubtful. The magnetic arm in region I2 does not smoothly follow the spiral
pattern of the galaxy, but is significantly bent northwards (right panel of
Fig. 4). This region shows the lowest energy density of the magnetic field
($\epsilon_{B}$) and the highest ordering of the magnetic field (exceeding
60%, Fig. 10) of all regions we studied in our analyses. Furthermore, as
mentioned in Sect. 3.1, the sensitive D-configuration map allowed us to trace
the prominent western magnetic arm already to the north of the galaxy. At the
same time, while the spiral and magnetic arms are usually observed
alternately, the separated magnetic arms I3 and I4 (right panel of Fig. 4)
look just like one magnetic arm that was split in the past. This was also the
conclusion of the analysis performed by Mulcahy et al. (2017). Last but not
least, the southern spiral arm (S1) looks well defined and follows the spiral
structure of the galaxy until the southern position at which the magnetic arm
I2 and I3 meet. S1 broadens slightly in this area and seems truncated (Fig.
4). All these features suggest the possibility of past interaction of NGC 628
with a companion galaxy, during which the currently southern spiral arm was
disturbed and the magnetic arms in this part of the galaxy were pulled-out and
stretched. The resulting shear of the magnetic field caused the observed high
order and low energy density of the magnetic field in region I2. The latter,
together with the lack of an increase in the temperature of the hot gas in
this region, rather excludes the possibility of compression induced by ram-
pressure. This tidal interaction scenario would resemble the very similar case
of the Virgo cluster spiral galaxy NGC 4254 (Weżgowiec et al., 2012). The
shear of the magnetic field is further supported by the fact that region I2 is
located directly at the sharp gradient of the H i emission (Fig. 8).

Figure 8: H i map of NGC 628 from The H i Nearby Galaxy Survey (THINGS; Walter
et al., 2008). Region I2 is marked in white.

###  4.5 Additional heating of the hot gas

While it is widely accepted that the hot X-ray gas in spiral galaxies is
produced in star formation and heated via supernova shocks, other mechanisms
might also allow the ISM to reach X-ray temperatures, one of which is cosmic-
ray streaming (Heintz et al., 2020). This mechanism, however, is expected to
heat gas at densities of about 10-3cm-3 (derived from our spectral fits) to
temperatures of several 105 K or about 0.05 keV. This is significantly lower
than the temperatures of the hot gas observed in NGC 628 (Table 5).

As we mentioned in Sect. 3.3, our analysis of the X-ray data, as well as the
results presented by Owen & Warwick (2009), show that the majority of the
diffuse X-ray emission comes from the hot gas in the halo of NGC 628. Mulcahy
et al. (2017) found signs of an efficient transport of the magnetic fields
into the halo, that is, Parker instabilities and super-bubbles. Their Faraday
rotation and depolarisation study also suggest the presence of vertical
magnetic fields. The most prominent area was found to be our magnetic arm I1.
If these fields form reversing loops like that found in NGC 4631 (Mora-
Partiarroyo et al., 2019), magnetic reconnection is possible. One of its
effects is the heating of the surrounding gas.

In the reconnection heating scenario discussed by us for NGC 6946 (Weżgowiec
et al., 2016) and M 83 (Weżgowiec et al., 2020), magnetic reconnection effects
convert energy of the magnetic fields into energy of the ISM gas. We note here
that this conversion is a complex process that includes ohmic heating or the
creation of high-frequency Alfvén waves, which in turn can cause anisotropic
heating of ions (Lazarian & Vishniac, 1999; Vishniac & Lazarian, 1999).
Furthermore, because the nature of turbulence in the reconnection zone is not
clear, the rate of the energy emission is difficult to estimate. Therefore, in
the following discussion we refer to ’reconnection heating’ as a variety of
effects that convert magnetic into thermal energy. Because they act more
efficiently on the turbulent component (field reversals required), these
effects also lead to a higher order of the magnetic field. The large-scale
vertical magnetic fields in NGC 628 and internal energies of the hot gas,
being similar to that of a massive starburst M 83, allow the possibility that
the additional source of heating mentioned in Sect. 4.3 is reconnection
heating that occurs in the halo of NGC 628. Especially interesting in this
aspect is region R3, where a strong and ordered magnetic field was found by
Mulcahy et al. (2017). The authors argued that this polarisation peak could be
due to compression of the magnetic field by an asymmetrically expanding H i
bubble caused by several supernovae. They also found a low Faraday depth at
this position, which signifies a rather weak magnetic field along the line of
sight, that is, the vertical component. A strong and ordered magnetic field in
the sky plane over the region of around 1 kpc, which is a typical wavelength
of the Parker instability for equipartition conditions (Hanasz & Lesch, 1998),
and a corresponding weak line-of-sight component of the magnetic field can be
well explained by magnetic reconnection that removes the vertical component of
the magnetic field dragged by the expanding supernova bubbles. This would be
done by reconnecting of the anti-parallel field lines around the adjacent
bubbles and leaving the compressed magnetic field at their top. Unfortunately,
the sensitivity of the X-ray data does not allow us to obtain a reliable value
of the hot gas temperature in this area. A detection of an increased
temperature in this region would provide further arguments for reconnection
heating.

The co-existence of hotter gas and the ordered magnetic fields seems to be
crucial for the detection of magnetic reconnection effects. Because the shock-
heated ISM can move to significant distances (up to 10 kpc) in all directions
(Hu, 2019), it can be present both in the inter-arm regions and in the
galactic halo. Nevertheless, it is unlikely that this ISM will have higher
temperatures and internal energies (our energy per particle, independent of
the filling factor) than that found directly in the star-forming regions.
Therefore, we propose here that for a reliable detection of magnetic
reconnection effects, a higher temperature of the hot gas (and the
corresponding energy per particle) and a simultaneous lower energy density of
the magnetic field accompanied with its high order is crucial. Our studies of
the radio and X-ray data for NGC 6946 (Weżgowiec et al., 2016), M 83
(Weżgowiec et al., 2020), and NGC 628 presented in this paper suggest that
only when all these three conditions are fulfilled can magnetic reconnection
heating be distinguished from supernova shock heating.

In this sense, in all inter-arm regions and polarised ridges (I1-4 and R1-R3),
lower energy densities and higher order of the magnetic fields are observed
than in the star-forming regions. However, the temperatures and energies per
particle are rather constant throughout the galaxy when the significant
uncertainties are taken into account. Nevertheless, we note here that this
does not contradict the reconnection heating if most of its effects occur in
the halo of NGC 628, as proposed before. If present above the entire disk, it
could cause similar temperatures of the hot gas throughout the galaxy and
contribute to total energies per particle, which, as mentioned above, are the
same as those for the starbursting galaxy M 83. In this case, a similar
contribution from the reconnection heating is also expected from the halo of M
83. In particular, large-scale ordered magnetic fields in the disk-halo
interface of M 83 were suggested by the polarised radio observations by Heald
et al. (2016). Significant differences, however, are visible when we compare
the densities of the hot gas in the haloes of the two galaxies. They are two
to three times lower in the case of NGC 628. Although all number densities
derived from the spectral model fits depend on an unknown filling factor, for
the halo gas, it is justified to directly compare the obtained values,because
at heights of 2.5 kpc above the disk, the filling factor for the hot gas
reaches unity (de Avillez, 2000). Because magnetic reconnection is more
efficient at lower number densities (Hanasz & Lesch, 1998), this would suggest
a higher contribution from reconnection heating in the halo of NGC 628 and
explain that the energies per particle are comparable to the energy found for
M 83.

To estimate the reduction of the energy density of the magnetic field of NGC
628 due to magnetic reconnection effects, we note here that in regions of star
formation (B1, S1, and S2) the strength of the ordered magnetic field is lower
than that of the total magnetic field by a factor of about three and in the
remaining regions (inter-arm and polarised ridge) by a factor of about two
(Table 8). This means that the energy density of the turbulent magnetic field
is about 75-90% of the total energy density. With total energy densities of
3-6$\cdot$10-12 erg cm-3 (Table 8), this means that energy densities of
2-5$\cdot$10-12 erg cm-3 are stored in the turbulent component of the magnetic
field. Because as much as 90% of this energy can be lost during the expansion
of the magnetic field into the halo (Hanasz & Lesch, 1998), this leaves
2-5$\cdot$10-13 erg cm-3 for the conversion into thermal energy via the
reconnection heating effects. If we assume their efficiency of 50% (Hanasz &
Lesch, 1998), gas at densities of about 10-3 cm-3 (in the inter-arm or
polarised ridge regions, see Table 8) will gain an additional energy of
1-2.5$\sim$10-10 erg per particle. This amounts to 20-50% of the current
energy per particle for the inter-arm regions (Table 9). Consequently, two or
three times higher densities of the hot gas, like that found in M 83
(Weżgowiec et al., 2020), would require two to three times higher energy
densities of the magnetic field to result in a similar increase in the energy
per particle. As we mentioned before, the energy densities of the magnetic
field in M 83 are roughly twice higher than that in M 74. A higher efficiency
of the reconnection heating therefore seems to be possible in the latter
galaxy, especially in its regions of polarised radio ridges.

Table 9: Thermal energy per particle and energy densities of the magnetic field for the studied regions in NGC 628. Region | $E_{p}$ | $\epsilon_{B}$
---|---|---
| [10-10 erg] | [10-12 erg cm-3]
B1 | 5.5${}^{+0.7}_{-0.5}$ | 6.5$\pm$1.3
I1 | 4.8$\pm$0.2 | 3.9$\pm$0.8
I2 | 4.3${}^{+1.0}_{-1.4}$ | 2.4$\pm$0.5
I3 | 4.8$\pm$0.5 | 4.2$\pm$0.8
I4 | 3.9${}^{+0.7}_{-1.0}$ | 3.1$\pm$0.6
R1 | 5.0${}^{+0.7}_{-1.0}$ | 4.8$\pm$1
S1 | 5.5$\pm$0.2 | 5.1$\pm$1
S2 | 3.3$\pm$0.3 | 3.8$\pm$0.8

Figure 9: Relation of the energy per particle (${\rm E}_{\rm P}$) and the
energy density of the magnetic field (${\rm\epsilon}_{\rm B}$) for regions
associated with the spiral (black) and the magnetic (red) arms of NGC 628.

Figure 10: Relation of the energy per particle (${\rm E}_{\rm P}$) and order
(${\rm B}_{\rm ord}/{\rm B}_{\rm tot}$) of the magnetic field for regions
associated with the spiral (black) and the magnetic (red) arms of NGC 628.

##  5 Summary and conclusions

We presented the results of our analyses of properties of the hot gas and
magnetic fields in NGC 628. The studies of the regions of spiral arm, inter-
arm, polarised radio ridges, and the halo above them allowed us to draw the
following conclusions:

  * •

Overall, lower energy densities and higher order of the magnetic fields are
found in the inter-arm regions and in areas of the radio-polarised ridges
compared to the star-forming spiral arms.

  * •

The temperatures of the hot gas and the resulting energies per particle are
similar for all regions within the derived uncertainties.

  * •

The comparison of the above findings with that for the starburst galaxy M 83
(Weżgowiec et al., 2020) suggests that additional heating of the hot gas in
NGC 628 may be present, which does not result directly from star formation. We
propose that magnetic reconnection heating occurs in the halo of NGC 628 to
explain this.

  * •

A more direct evidence of this halo reconnection might be the polarised radio
ridges that show strong ordered magnetic fields and were reported to be
located in or above regions of weak vertical fields. In one of them, a
slightly higher temperature of the hot gas is found, although the increase is
not statistically significant.

  * •

The lack of a compression-induced heating of the hot gas in the southern
outskirts of the disk of NGC 628 and the simultaneous very high order and low
energy density of the magnetic field suggests the shearing of the latter,
which together with a distorted spiral arm (S1) could be a sign of tidal
interaction. This hypothesis seems to be supported by a sharp gradient of the
H i emission in this area.

Although our analyses are not sufficient to provide direct evidence for the
role of magnetic reconnection in heating of the ISM, the proposed scenario
that magnetic reconnection contributes to the heating of the ISM seems
feasible. Because this effect is not very strong, very sensitive X-ray data
are crucial to allow for a statistically significant detection. Studies of
edge-on galaxies that show reversals of the magnetic field are especially
desirable to examine reconnection heating in the galactic halo in more detail.

###### Acknowledgements.

We thank the anonymous referee for comments that helped to improve the clarity
of this paper. M.W., M.S., and M.U. are supported by the National Science
Centre, Poland, with the grant project 2017/27/B/ST9/01050. M. H. acknowledges
the support by the National Science Centre through the OPUS grant No.
2015/19/B/ST9/02959. Research in the field at Ruhr University Bochum is
supported by Deutsche Forschungsgemeinschaft SFB 1491. The National Radio
Astronomy Observatory is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc.

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