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

# Magnetic fields and hot gas in M 101 ††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.  Studies of nearby spiral galaxies in radio and X-ray wavelengths
reveal the structure and energy balance of the magnetic fields and the hot
interstellar medium (ISM). In some spiral galaxies, large-scale ordered
magnetic fields have been found between the spiral stellar arms (the so-called
magnetic arms). One of the considered explanations of their origin is magnetic
reconnection, which according to theoretical studies can efficiently heat the
low-density ISM.

Aims.  We present, for the first time, high-resolution C-band (5 GHz) radio
maps of the nearby face-on spiral galaxy M 101 to study the magnetic fields
and verify the existence of the magnetic arms. The analysis of the archival
XMM-Newton X-ray data is performed to search for signatures of gas heating by
magnetic reconnection effects in the disk and the halo of this galaxy.

Methods.  We combine the Very Large Array (VLA) and Effelsberg radio maps of M
101 to restore the large-scale emission lost in the interferometric
observations. From the obtained maps, we derive magnetic field strengths and
energy densities, and compare them with the properties of the hot gas found
with the spectral analysis of the X-ray data.

Results.  Most of the X-ray emission likely comes from the hot gas in the halo
of M 101. Its temperature is highest above the massive stellar arm and an
inter-arm region with enhanced polarised radio emission, as well as in the
inter-arm area where neither H$\alpha$ nor H i emission is visible. In regions
outside of the spiral arms lower strengths, energy densities and higher orders
of the magnetic fields were observed.

Conclusions.  Although M 101 does not possess well-defined magnetic arms, a
rudimentary magnetic arm was identified in one of the inter-arm regions. We
found weak signatures of additional heating of the ISM there, as well as in
the galactic halo, which could be explained by the action of magnetic
reconnection.

###### Key Words.:

galaxies: individual: M 101 – galaxies: ISM – galaxies: spiral – galaxies:
magnetic fields

††offprints: M. Weżgowiec

##  1 Introduction

In the analysis of the properties of the interstellar medium (ISM) in spiral
galaxies, the role of the magnetic fields cannot be neglected because they
take part in many dynamical processes (e.g. Beck, 2004). Being also a product
of star formation, magnetic fields are found to be most prominent in galactic
spiral arms, where radio emission, both thermal and non-thermal, is brightest.
Nevertheless, in some spiral galaxies, large-scale ordered magnetic fields
have been found between the spiral arms (e.g. Beck et al., 2019). However, the
real nature of these magnetic arms is still a matter of debate.

A possible explanation of magnetic field ordering is magnetic reconnection
involving annihilation of anti-parallel magnetic field components. Magnetic
reconnection is a fundamental process in astrophysical plasma (see Lazarian et
al., 2020, for a recent review). The classical Sweet-Parker model relies on
the ohmic dissipation of electric currents concentrated in thin current
sheets, which form on the interface of two regions with anti-parallel magnetic
fields. The classical model results in slow action of these effects, because
the small thickness of the naturally formed current sheet becomes a bottleneck
for the out-flowing plasma carrying the reconnected magnetic field lines. A
new paradigm (Lazarian & Vishniac, 1999) of magnetic reconnection invokes a
turbulent magnetic field, permitting the occurrence of magnetic field
dissipation in microscopic current sheets that form due to magnetic field line
wandering. Recent investigations have shown that magnetic reconnection is fast
in the presence of turbulence since it does not depend on resistivity (Kowal
et al., 2009, 2012) and the effective reconnection speed reaches 10% of the
Alfvén speed. We adopt the turbulent reconnection model as the natural
regularisation process of turbulent magnetic fields in the ISM. In galaxies
the turbulent magnetic fields are transported by the gas flow from spiral arms
to the inter-arm regions. It is plausible that magnetic reconnection could
occur there, leading to regularisation of the magnetic fields and
simultaneously to the conversion of magnetic energy into thermal energy
(Hanasz & Lesch, 1998).

The energy of an annihilated magnetic field is partially converted to thermal
energy in the surrounding plasma. Such heating has been considered in a number
of theoretical studies (e.g. Raymond, 1992; Tanuma et al., 1999; Reynolds et
al., 1999; Tanuma et al., 2003). The most effective heating is expected for
higher strengths of the magnetic field and for the lower densities of the
interstellar gas. For a magnetic field strength of around 3 $\mu$G and gas
number densities of the order of 10${}^{-3}\,{\rm cm}^{-3}$, the gas can be
heated to 1 million K (Tanuma et al., 2003). Therefore, it should be possible
to find signatures of the reconnection heating in the X-ray data of spiral
galaxies. The magnetic reconnection is more efficient in the star-forming
regions due to stronger field tangling, but might be difficult to detect
because high turbulence prevents long-lasting ordering of the magnetic field.
Also, the heating is expected to be less significant in regions of higher gas
density, where the cooling is faster. In the inter-arm regions and in galactic
halos, however, lower gas densities provide favourable conditions for
detecting reconnection heating.

We admit that the transformation of magnetic to thermal energy is a complex
process. Following Lazarian & Vishniac (1999) and Vishniac & Lazarian (1999),
only a fraction of magnetic flux is annihilated by ohmic heating of electrons
within the reconnection zone. Another part of magnetic energy is converted to
high-frequency Alfvén waves. These waves may play a role in, for example, the
anisotropic heating of ions in stellar coronae. Finally, according to these
authors, the rate of energy emission is hard to estimate since the nature of
the turbulence in the reconnection zone is uncertain. Having in mind these
uncertainties, we do not favour any specific energy conversion mechanism, but
rather consider their variety as a plausible source of heating of the ISM. In
the following we shall use the term ‘reconnection heating’ as a set of
processes that convert the magnetic energy to thermal energy.

Nevertheless, detection of an increased temperature or thermal energy of hot
gas in areas free from significant star formation is not sufficient to
associate it directly with magnetic reconnection. As recent theoretical
studies show, the ISM expelled from star-forming regions and heated via
supernova shocks can move in all directions, and to significant distances from
its place of origin (up to 10 kpc; Hu, 2019). Another possibility of ISM
heating, which is not directly related to star formation and is likely to
occur away from star-forming regions, is cosmic-ray streaming, as recently
presented by Heintz et al. (2020).

Therefore, it seems very important to simultaneously study the properties of
the magnetic field that could help to point to a more probable heating
mechanism. If the temperature increase is supposed to be a result of the
magnetic reconnection effects, lower energy densities and higher degrees of
order of the magnetic fields should be observed simultaneously, being the
signature of the conversion of the energy of the turbulent magnetic field.

We already analysed radio and X-ray data for two spiral galaxies in which
magnetic arms were observed. In NGC 6946 we found a slight increase in
temperature of the hot gas in the inter-arm regions when compared to the
spiral arms (Weżgowiec et al., 2016). This was accompanied by lower energies
and higher degrees of order of the magnetic fields, which suggested detection
of magnetic reconnection heating. A similar analysis of the deep XMM-Newton
X-ray space telescope (Jansen et al., 2001) data for a massive starburst
galaxy, M 83, suggested that effects of reconnection heating could have been
detected also in the galactic halo (Weżgowiec et al., 2020).

The spiral galaxy M 101 is a nearby galaxy seen nearly face-on (see Table 1).
Its disk is strongly lopsided; the eastern arm likely bears signs of past
encounters with one or more companion galaxies, and together with M 101 they
form a galaxy group (Mihos et al., 2013). The galaxy has been observed at many
wavelengths but, likely due to the large angular size, no high-resolution data
at high radio frequencies have been published. The available low-resolution
radio data suggest that most of the ordered magnetic fields are found along
the spiral arms, while some of the large-scale polarised radio emission was
also present outside of the star-forming regions (Berkhuijsen et al., 2016).

In this paper we present for the first time the radio data from M 101 at 5 GHz
with sub-arc-minute angular resolution. We also analyse archival XMM-Newton
X-ray data that can help to perform studies of possible gas heating by
magnetic reconnection effects, both in the disk and in the halo of M 101.

Table 1: Basic properties of NGC 5457 (M 101)

Morphological type | SABc
---|---
Inclinationaa$a$Kamphuis (1993). | 30°
Diameter D25 | 24′
R.A.2000 | 14h03m13s
Dec2000 | +54°20′57″
Distancebb$b$Kelson et al. (1996). | 7.4 Mpc
Column density $N_{\rm H}$cc$c$Weighted average value from HI4PI Collaboration et al. (2016). | 8.58$\times$1020 cm-2
111 All data except inclination, distance, and column density are taken from
the HYPERLEDA database – http://leda.univ-lyon1.fr – see Makarov et al.
(2014).

Using the sensitive radio data in C-band (4.5-6.5 GHz) and the X-ray emission
from M 101 in this paper, we analyse the properties of the hot gas and the
magnetic fields in this galaxy. Especially interesting is the search for
regions of enhanced polarised radio emission between the spiral arms of the
galaxy; the so-called ‘magnetic arms’ observed in NGC 6946 (Beck et al., 2019)
and M 83 (Frick et al., 2016). Such features were not found in M 101 by
Berkhuijsen et al. (2016) in the sensitive single-dish data, probably due to
the low resolution of the observations. The data presented by us should be
sufficient to verify this. The comparable spatial resolutions of the radio and
the X-ray observations presented in this paper will allow us to study in more
detail the spiral arms and other regions of M 101. The X-ray data will
additionally give clues about the emission from the halo gas and its possible
interactions with the magnetic fields.

M 101 was observed with the Effelsberg telescope at 6.2 and 11.1 cm by
Berkhuijsen et al. (2016), who analysed both the total and the polarised radio
intensity. Although the low angular resolution of the single-dish observations
did not allow them to study the galaxy in detail, thorough analyses performed
by the authors revealed the global structure of the magnetic field and
provided important information about the rotation measures and the
depolarisation between the two frequencies. This can be used to obtain
information about the magnetic fields along the line of sight, that is, the
halo component.

To study the X-ray emission from the hot gas in M 101, high resolution (both
spatial and spectral), and high sensitivity to diffuse structures, are needed.
In this paper we focus only on the X-ray data obtained by the XMM-Newton X-ray
space telescope (Jansen et al., 2001). M 101 has been observed with this
telescope four times. Three observations between 2002 and 2005 were used in a
number of papers, the most important of which (in terms of the analyses
presented in this paper), is the work of Warwick et al. (2007), who also
analysed the diffuse X-ray emission. The authors focused on the total X-ray
emission and analysed the global spectrum extracted from the central 10′ of
the galaxy. This was likely caused by the relatively low sensitivity of these
moderate-length observations, further diminished by the use of the medium
filter in two of the observations, which reduces the sensitivity for the
softest part of energy range accessible to XMM-Newton. The most recent data
(December 2018) are the sensitive thin-filter observations, aiming to study
the ultra-luminous X-ray source (ULX) population in the disk of M 101. At the
moment of the writing of this paper, they remain unpublished.

We also note that M 101 was observed multiple times with the CHANDRA X-ray
Observatory for a total of 1 Ms. An analysis of these data was presented by
Kuntz & Snowden (2010), who, similarly to Warwick et al. (2007), studied the
total X-ray emission from the galaxy. This included a single spectrum
extracted from almost entire galactic disk, the spectrum of the central bulge,
as well as two giant star-forming regions. Because the results of these
studies correspond well to our analyses, throughout this paper we refer to
this work (KS10 hereafter).

##  2 Observations and data reduction

In this paper we present new and archival Karl G. Jansky Very Large
Array222https://science.nrao.edu/facilities/vla (VLA) C-band radio
observations of M 101, as well as archival X-ray observations performed with
the XMM-Newton telescope. For the overlays, the optical image in B-band from
the Digital Sky Survey, as well as the H$\alpha$ image by Hoopes et al.
(2001), have been used. In the following section, details of the data
reduction are presented.

###  2.1 Radio data

The new C-band D-configuration radio data were observed by the authors within
the project 19B-027 in November 2019. Because of the angular size of the
galaxy, whose radio extent at 5 GHz is of the order of 15$\arcmin$
(Berkhuijsen et al., 2016), and the size of the primary beam of the VLA
333https://science.nrao.edu/facilities/vla/docs/manuals/
oss2019B/performance/resolution around 9$\arcmin$ at this frequency, the
galaxy had to be observed with several offset pointings. We chose a hexagonal
layout consisting of seven fields with the inner pointing at the centre of the
galaxy. The observations were performed in three scheduling blocks (1.5 hours
each) consisting of calibrator scans and each of the seven fields covering the
galaxy. Unfortunately, due to bad weather conditions (heavy snow), one of the
observations was not suitable for further processing. As a result, the two
remaining observations provided 21 minutes per pointing. To further increase
the sensitivity and the coverage of the galaxy we also used archival C-band
D-configuration data for M 101 obtained within the project 15B-292 that used a
different layout of the pointings. The observations in this project were
scheduled so that each of the fields was observed separately for 60 minutes
per pointing. The positioning of all observation pointings used in this paper
is presented in Fig. 1.

Figure 1:  Pointings used for the observations of M 101 presented in this
paper. Red and black circles refer to the projects 19B-027 and 15B-292,
respectively, and their diameters show the primary beam of the VLA at 5 GHz.

The data were reduced with the Common Astronomy Software Applications (CASA)
package444http://casa.nrao.edu (McMullin et al., 2007). All data affected by
shadowed antennas or the radio frequency interference (RFI) were flagged
manually. In both projects, the radio sources 3C 286 and J1349+5341 were used
for the flux density scale and phase calibration, respectively. Because the
latter source is unpolarised, it was also used to solve for polarisation
leakage. The calibration of the polarisation angle was performed with the use
of 3C 286.

Because the observations of the 19B-027 blocks were not consecutive, we
calibrated all three data sets separately. The separate calibration of the
15B-292 data sets was straightforward. Eventually, we obtained ten calibrated
data sets for each of the Stokes parameters. To deconvolve the point spread
function (PSF) of the interferometer from the dirty map, we used CASA task
tclean, which performs the Clark CLEAN algorithm (Clark, 1980). For each
Stokes parameter, the cleaning runs were performed for all data sets
simultaneously using the mosaic mode of tclean. We find that the best quality
images are produced with the use of the robust weighting of the data (robust
parameter set to one) and the multi-scale CLEAN with scales ranging from
1$\arcsec$ (the cell size) to 600$\arcsec$. The final images were restored
with an elliptical beam of 16$\arcsec\times$13$\arcsec$, which we then
convolved to a circular beam of 30$\arcsec$ to further improve the signal-to-
noise ratio of the faint extended emission.

Despite the high sensitivity of the radio data, due to the large angular
extent of M 101, only little large-scale emission was restored. Therefore, we
combined our final Stokes I, Q, and U maps with the respective Effelsberg maps
at 4.85 GHz, published by Berkhuijsen et al. (2016). The combination of data
was done using the task imerg of the aips package555http://www.aips.nrao.edu.
Because the aim of this task was to restore the large-scale diffuse emission
that cannot be detected via interferometric observations, we compared the
total radio flux densities of the combined and the Effelsberg map within the
elliptical area encompassing the entire radio emission from M 101 visible in
the latter map. Table 2 presents the comparison of the total flux densities
derived from the Effelsberg, the VLA, and the combined maps. The total flux
densities measured in the Effelsberg and the combined maps agree within 1%,
which confirms the successful merging of the data. At the same time, a
significantly lower (by almost 60%) flux density in the VLA maps clearly shows
the need to add the single-dish data to interferometric observations of
spatially extended objects. Nevertheless, no loss of flux was found in the
polarised intensity VLA map, which shows the same flux density as the
Effelsberg map. In the combined map, however, a 10% higher total flux density
was measured. Although this still agrees within uncertainties with the total
flux densities measured separately in both maps, it is possible that the
merging of the maps could at least partially restore some of the emission
depolarised by the large beam of the Effelsberg telescope or not detected by
the small beam of the VLA.

Table 2: C-band total radio flux densities (in mJy) of M 101.

Map | Effaa$a$from Berkhuijsen et al. (2016) | VLA | VLA+Eff
---|---|---|---
Total intensity | 310$\pm$20 | 127$\pm$6 | 308$\pm$15
Polarised intensity | 28$\pm$3 | 28$\pm$1 | 31$\pm$2
666 .

###  2.2 X-ray data

Table 3: Characteristics of the XMM-Newton X-ray observations of M 101

Obs ID | EPIC-pn filter | EPIC-pn observing mode | total time [ks] | clean time [ks]
---|---|---|---|---
0104260101 | medium | full frame | 40.5 | 24.3
0164560701 | medium | full frame | 30.3 | 20.6
0212480201 | thin | full frame | 30.5 | 14.8
0824450501 | thin | full frame | 97.3 | 64.9
777 Only observations marked in italics were used for the spectral analysis
(see text for details).

####  2.2.1 Data processing and image creation

As mentioned in Sect. 1, M 101 has been observed with the XMM-Newton telescope
four times. For the purpose of this paper, we use all observations to produce
images of the diffuse X-ray emission. For the spectral analysis, however, only
the most recent, sensitive thin-filter data are used. The argumentation for
this choice will be presented later in this section. Table 3 presents the
details of all of the observations. All of the data were processed with the
standard procedures of the SAS 19.0.0 package (Gabriel et al., 2004).
Calibrated event lists were produced for all three EPIC cameras, using the
meta-tasks $emchain$ and $epchain$ for two EPIC-MOS cameras (Turner et al.,
2001) and the EPIC-pn camera (Strüder et al., 2001), respectively. To
effectively analyse the diffuse emission from the hot gas, all of the data
collected during periods of intense background radiation needed to be removed.
These periods are identified with the use of the light curves of the high-
energy emission. The light curves allow us to determine the good time interval
(GTI) tables that later allow us to filter the event lists for bad data. For
the creation of the GTI tables, the thresholds 0.35 cts/s and 0.4 cts/s were
used for the light curves (in the 10-12 keV energy band) of the EPIC-MOS and
the EPIC-pn cameras, respectively. Such limits are recommended for the
analysis of the soft diffuse emission.

Apart from the high-energy background, a significant influence on the faint
diffuse emission (especially its spectral analysis) can come from the soft
proton flare contamination. The filtered event lists were checked for the
existence of such contamination with the use of a
script888https://www.cosmos.esa.int/web/xmm-newton/epic-scripts#flare that
applies the calculations developed by De Luca & Molendi (2004). As a result,
medium-filter observations 0104260101 and 0164560701 were found to be slightly
contaminated with soft proton flares, while the thin-filter observation
0212480201 was contaminated to a very high level. The most sensitive data set,
observation 0824450501 was not contaminated with soft proton flares.

With each of the filtered event lists, we created images and exposure maps
(without a vignetting correction) using the images
script999https://www.cosmos.esa.int/web/xmm-newton/images, modified by the
authors to allow for adaptive smoothing. We used only events with FLAG=0 and
PATTERN$\leq$4 (EPIC-pn) or FLAG=0 and PATTERN$\leq$12 (EPIC-MOS), which
guaranteed the best quality data for the analysis of the diffuse X-ray
emission. To detect the entire diffuse X-ray emission, as well as to enable
the creation of a hardness ratio map, images in two energy bands, 0.2-1 and
1-2 keV, were produced. Because data from four observations were used, we
combined the separate images into final EPIC images using the SAS task
emosaic. The combined images were adaptively smoothed with a maximum smoothing
scale of 30$\arcsec$, and a signal-to-noise ratio of 30. This allowed us to
reveal the faint diffuse emission and provided a match in resolution with the
radio maps.

####  2.2.2 Spectral analysis and background subtraction

Although still suitable for image creation, observation 0212480201, being very
contaminated by soft protons, needed to be excluded from spectral analysis. To
assure the highest sensitivity in the soft energy band, as well as to allow
for a direct comparison with our similar studies of other face-on spiral
galaxies, NGC 6946 (Weżgowiec et al., 2016) and M 83 (Weżgowiec et al., 2020),
we used only the EPIC-pn camera for the spectral analysis. In the direction to
M 101, a relatively high galactic foreground column density $N_{\rm H}$ was
measured (see Table 1). This resulted in a significant absorption that
influenced the detection of the softest X-ray emission. This, together with
the characteristics of the internal background of the pn
camera101010https://xmm-tools.cosmos.esa.int/external/xmm_user_support
/documentation/uhb/epicintbkgd.html, led us to only use the data above 0.4 keV
for spectral analysis.

Prior to the spectra extraction, we used the event files and the corresponding
calibration data of all of the observations to run the edetect_stack meta task
that performs all stages of the source detection routine, taking advantage of
the combined sensitivity of the data. The meta task was run with the use of
standard parameters. The obtained list of detected sources was then used to
exclude the detected point-like sources from the spectral analysis. The radii
of these areas were adjusted to include the brightest emission of the point
sources. Because of the extended wings of the PSF of the EPIC-pn camera, some
residual emission from point sources could still be present in the spectra.
This, however, was later taken into account by adding to the spectral model a
power-law component, which also was used to model the emission from
potentially unresolved sources.

Because of the large angular extent of M 101 (regions used for spectral
analysis spread over the central 20$\arcmin$ of the field of view), a proper
background subtraction becomes challenging. Clearly the use of local
background is almost impossible, because it would need to be extracted from
areas that are significantly off-axis and the potential scaling would
introduce unwanted biases. The often used blank-sky event lists (see Carter &
Read, 2007), most likely due to a relatively high column density, led to an
overestimated background level and the subtracted spectra could not be fit
with theoretical models. Having checked that, we decided to account only for
the instrumental background. We argue that when the external background in the
softest energy band is weakened by the higher column density, the contribution
from the detector might become the most important component of the X-ray
background, especially when extended areas of low surface-brightness emission
are analysed, just like the regions used in our studies. Furthermore, the
relatively low sensitivity of the analysed data will likely mean that the
derived uncertainties of the fitted model parameters will be larger than the
influence of the external X-ray background.

The instrumental background was modelled with the use of the filter wheel
closed (FWC) data111111https://www.cosmos.esa.int/web/xmm-newton/filter-
closed. From the repository we chose only those FWC observations that best
matched the time of each observation. This was done to best represent the
detector background, which is known to change over time. The FWC event lists
were then filtered in the same way as the source event lists. Response
matrices and effective area files were created for each spectrum with the use
of a detector map (image in detector coordinates) that is needed for spectral
analysis of extended emission. The final spectra, background spectra, response
matrices, and effective area files were correspondingly merged for all
observations with the use of the SAS task epicspeccombine. The advantage of
this approach, when compared to simultaneous fitting, is that all
corresponding files are combined first and the background subtraction is
performed in the last step, which is especially useful in the case of low
sensitivity of separate spectra.

Nevertheless, the final background-subtracted spectra, especially that of the
lowest sensitivity, still showed a noticeable contribution from the detector
Al-K$\alpha$ line at 1.5 keV, as well as an increased level of the softest
emission, which was a sign that the background was not entirely removed. To
look for a solution, we compared the results with spectra obtained from the
most sensitive observation only (thin-filter ObsID 0824450501). We found that
in both cases, the same model fit parameters were obtained, and they were only
slightly better constrained in the models fitted to the combined spectra. Most
importantly, however, the inspection of the thin-filter spectra showed no
significant contribution from the detector background mentioned before.
Therefore, for the spectral analysis presented in this paper, we eventually
decided to use only the most sensitive thin-filter observation (ObsID
0824450501).

To further improve the signal-to-noise ratio, spectra were binned. A number of
25 counts per energy bin seems to be a good value for a wide range of
sensitivities, and was used by us before (Weżgowiec et al., 2016, 2020). The
spectra were fitted using xspec12 (Arnaud, 1996).

##  3 Results

###  3.1 Radio emission

Figure 2:  Map of total radio intensity at 4.85 GHz ($\lambda$ 6 cm) of M 101
overlaid on the DSS blue map. The contours are 3, 5, 8, 16, 32, 64, 128, and
256 $\times$ 35 $\mu$Jy/beam. The vectors show the orientation of the magnetic
fields and their length of 1$\arcmin$ is proportional to the polarised
intensity of 0.17 mJy/beam. The beam size of 30$\arcsec$ is shown in the
bottom right corner of the map.

The total radio emission closely follows the star-forming disk of M 101 with
distinct enhancements visible in the spiral arms (Fig. 2), especially the
bright H$\alpha$ complexes in the south and at the end of the eastern spiral
arm. Northeast from the centre (around position R.A. 14h03m15s, Dec +54$\degr$
22$\arcmin$), a bright polarised radio source is visible, although its degree
of polarisation remains rather low (Fig. 3). The polarised emission also
closely follows the star-forming arms with only slight extensions in the south
and south-west, as well as the inter-arm region between the centre and the
eastern arm (around position R.A. 14h03m45s, Dec +54$\degr$ 23$\arcmin$). The
pitch angle of the magnetic field is relatively low along the spiral arms, but
shows a noticeable increase in the southern extensions of the polarised
emission and in the eastern inter-arm region. The polarisation map also shows
a significant asymmetry, with most of the (highly polarised) emission coming
from the eastern spiral arm (Fig. 3).

Figure 3:  Map of polarised radio intensity at 4.85 GHz ($\lambda$ 6 cm) of M
101 overlaid on the H$\alpha$ map. The contours are 3, 5, 8, 16, 32, 64, 128,
and 256 $\times$ 15 $\mu$Jy/beam. The vectors show the orientation of the
magnetic fields and their length of 1$\arcmin$ is proportional to the degree
of polarisation of 50%. The beam size of 30$\arcsec$ is shown in the bottom
left corner of the map.

Between the centre and the western spiral arm (around position R.A. 14h02m40s,
Dec +54$\degr$ 18$\arcmin$), an interesting area that does not show any
H$\alpha$ or polarised radio emission can be found (Fig. 3). A similar feature
was also visible in the low-resolution single-dish maps of Berkhuijsen et al.
(2016) and the H i map, in which a significant depression was observed in this
area (Braun, 1995).

###  3.2 Distribution of the X-ray emission

Figure 4:  Maps of X-ray emission from M 101. Left: Soft-band (0.2 - 1 keV)
overlaid on an H$\alpha$ image. The contours are 3, 6, 12, 24, 48, and 96
$\times$ r.m.s. The map is adaptively smoothed with the largest scale of
30$\arcsec$. Right: Medium-band (1 - 2 keV) overlaid on a DSS blue image. The
contours are 3, 6, 12, 24, 48, and 96 $\times$ r.m.s. The map is adaptively
smoothed with the largest scale of 30$\arcsec$, which is shown in the bottom
corners of the maps.

The soft X-ray map (left panel of Fig. 4) shows diffuse emission from the
entire disk of M 101. Contrary to the radio maps, the emission extends
significantly beyond the eastern spiral arm. Although a number of point
sources is visible in this area, this diffuse emission cannot be attributed to
the beam-smearing effect; the largest scale used in the adaptive smoothing is
30$\arcsec$ (see the beam size symbol in the bottom left corner of the map),
much smaller than the scale of the emission. The emission of the central star-
forming disk (visible in the H$\alpha$ image) is at the level of 24$\sigma$.
The right panel of Fig. 4 shows that the emission in the higher energy range
can be visible to a similar extent than in the lower energy range, or even
larger (left panel of Fig. 4), and the emission reaches 12$\sigma$ at the
brightest central part of the galaxy. This harder emission also seems to be
more extended in the area of the eastern inter-arm region, where the polarised
radio emission can be seen (Fig. 3).

To identify areas with significantly different amounts of cooler and hotter
X-ray gas, a hardness ratio (HR) map becomes very useful. Such a map,
presented in Fig. 5, is derived from the two maps from Fig. 4, as the ratio of
their difference and sum. The map is presented with the vectors of the
magnetic fields proportional to the degree of polarisation. The overall
softest emission (shown in blue) comes from the most central part of the disk,
where the majority of the H$\alpha$ emission can be seen. Although no clear
correlation between the hardness of the X-ray emission and the polarised radio
emission can be seen, the areas of the highest degree of polarisation tend to
be located just outside of the softest emission. Still, most of the diffuse
X-ray emission shows the hardness ratios not higher than 0.1, which identifies
the emission as coming mainly from the soft component.

Figure 5: Map of the hardness ratio between medium and soft bands of the X-ray
emission from M 101 (cf. Fig. 4) overlaid with the B-field vectors
proportional to the degree of polarisation. The map is truncated at the
3$\sigma$ level of the medium-band X-ray map.

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

To investigate the properties of the hot gas in regions of significant
polarisation of radio emission, we used the polarisation intensity map
together with the H$\alpha$ map (Fig. 3) to select separate regions for the
spectral analysis. This approach is similar to what was presented by us for
other spiral galaxies: NGC 6946 (Weżgowiec et al., 2016) and M 83 (Weżgowiec
et al., 2020). However, in M 101 some of these regions correspond to
significant H$\alpha$ emission. This is discussed in Sect. 4.3.

Contrary to the two galaxies mentioned above, M 101 possesses only rudimentary
‘magnetic arms’, that is, regions of enhanced polarised radio emission in
areas between the spiral stellar arms. Instead, we selected areas of
significant polarised emission that are found just outside of the spiral arms.
For a comparison, we also selected areas of the two most prominent spiral arms
and the central 4$\arcmin$ of the galaxy that correspond to the inner part of
the disk, having a diameter of about 8.6 kpc at the assumed distance (see
Table 1). The most interesting region is region V, where only little H i is
visible and no H$\alpha$ or radio emission is present. However, significant
X-ray emission in this region is visible. All regions are described in Table 4
and shown in Fig. 6.

Figure 6:  Regions used in the analysis of diffuse X-ray emission from M 101 (see text for a detailed description) overlaid on the H$\alpha$ map (top left), the polarised radio intensity map from Fig. 3 (top right), the soft X-ray emission map from Fig. 4 (bottom left), and the hardness ratio map from Fig. 5 (bottom right).  Table 4: Regions of M 101 used for the spectral analysis. Region name | Region description
---|---
C | central 4$\arcmin$ (8.6 kpc) of M 101
P1 | southern polarised arm
P2 | south-eastern polarised feature
I | north-eastern polarised inter-arm region
S1 | western spiral arm
S2X | eastern spiral arm
V | ‘void’ - area between the centre and S1

We performed the spectral analysis for all of the regions. Because of the
sensitivity of the data available for M 101, for regions not associated with
the spiral arms, it was not possible to fit a model with two thermal plasma
components that would account for the emission from the disk and the halo.
Instead, the fitted model to the spectra consisted of only one thermal plasma
component to account for the entire diffuse emission from the hot gas.
Therefore, we could obtain information about the combined emission from both
the disk and the halo. The separation of both fractions, (i.e. the use of two
thermal components), was possible for the models fitted to spectra from the
spiral arms, as well as from the central region, which assured the sufficient
number of net counts. All models have an additional power-law component that
accounts for unresolved sources and the possible residual emission of sources
excluded during the source detection procedure (see Sect. 2.2.2). The thermal
plasma was modelled with the use of the mekal model (Mewe et al., 1985;
Kaastra, 1992). All models include the absorption component wabs to account
for the influence of the neutral hydrogen in the halo of our Galaxy.

The models fitted to spectra from all of the regions are presented in Table 5,
together with the derived parameters. The plots of all of the models are
presented in Figs. 7 and 8, and the derived unabsorbed fluxes of all spectral
components are shown in Table 6. The spectrum from the spiral arm S2 could be
fitted with two models, consisting of the same components but with different
values of the parameters derived. In the first fit, temperatures similar to
that found in the other two-temperature model fits were derived. The second
fit (marked throughout this paper as S2X) resulted in higher temperatures (see
Table 5) and a much steeper slope of the photon index of the power-law
component. Nevertheless, the latter fits the data slightly better, as can be
seen in the model curve and residuals for both models (bottom row of Fig. 7).
We note here that such ambiguity was not found for the very similar spectrum
of the S1 spiral arm region. It is possible that it was caused by the
difference in sensitivities of both spectra (see Table 5), and the slight
flattening around 0.9 keV (likely attributed to the hotter thermal component)
is not sufficiently pronounced in the spectrum of region S1 (Fig. 7). On the
other hand, the much higher photon index in the S2X model fit might suggest
that some of the (residual) emission from (unresolved) point sources in the
spectrum from the S2 region, was accounted in the S2X model fit for the hotter
thermal component. We already discussed this phenomenon in Weżgowiec et al.
(2016). We argue that with the present data, it is difficult to find one of
the models more plausible, especially when the uncertainties of the fitted
model parameters are taken into account.

Another important technical issue of our spectral fitting is related to
reaching the lower limit for the mekal temperature allowed by xspec12 when
deriving uncertainties for the model fits to spectra from regions C, P2, S1,
and S2 (low temperatures version). In the case of the spectrum from region C,
the fitted value of the temperature was also set to this lower limit. As a
result, the lower uncertainties of the temperatures of the halo component for
these regions are underestimated. We note here, however, that obtaining these
lower limit values is unlikely to be related to the sensitivity or quality of
the spectra, because the temperature values and their uncertainties are not
correlated with the values of net counts or net counts per square arc-minute,
as shown in Table 5. For example, the lower limit for the temperature was
reached in the model fitted to the most sensitive spectrum in our analysis
(region C). Because such low temperatures of the hot gas fit well the scenario
of very low star-forming activity in the central disk of M 101 (see Sect.
4.1), it is justified to claim that the derived low temperatures reflect real
physical conditions of the hot gas, and especially given that the spectra of
the CHANDRA data analysed by KS10 were also fitted with temperatures of
$\sim$0.1 and $\sim$0.3 keV.

The parameters of the fitted models suggest, however, an interesting
possibility that the two-temperature models C, S1, and S2, refer only to the
emission from the halo. In such a case, the faint disk emission would be
detected indirectly in the low-sensitivity spectra as additional flux of one
of the model components. The obtained temperatures of around 0.1 keV and 0.3
keV correspond well to typical temperatures derived from spectra of halos of
edge-on galaxies (e.g. Strickland et al., 2004a; Tüllmann et al., 2006).

As we mentioned before, for the most sensitive spectrum (spiral arm S2) it was
possible to fit a different model (S2X), which yielded
0.18${}^{+0.01}_{-0.02}$ and 0.60${}^{+0.19}_{-0.36}$ keV for both thermal
components, and a power-law component with a steeper photon index than in the
low-temperature model. In that model, the lower and the higher temperature
referred to the halo and the disk, respectively. We note that such an
interpretation does not contradict the findings of KS10. Although they
obtained temperatures of $\sim$0.1 and $\sim$0.3 keV for the global spectrum,
the spectra of the emission from the two giant star-forming regions, NGC 5461
and NGC 5462, were best fitted with two thermal components with lower
temperatures of $\sim$0.21 and $\sim$0.26 keV, and higher temperatures of
$\sim$0.60 and $\sim$0.72 keV, respectively. Both these regions are found
within our region S2 (and marked with labelled circles in Fig. 6).

Therefore, we argue that the faint emission from the galactic disk of M 101
might remain undetected in the analysed spectra, except for in the most
sensitive one (spiral arm S2). For this one, it was also possible to fit a
model that accounts for the hot disk component (owing to the bright emission
from NGC 5461 and NGC 5462 star-forming regions), whose signs are visible as a
‘knee’-like feature around 0.9 keV (see the bottom right panel in Fig. 7).
Such a feature seems to be present also in the spectrum of the other spiral
arm (S1, upper right panel in Fig. 7), as well as the central region (C, upper
left panel in Fig. 7), but a fitting of the model with thermal components at
temperatures around 0.2 and 0.6 keV was not possible, likely due to lower
sensitivity and the resulting larger spread of energy bins.

Table 5: Model-fit parameters for the regions studied in M 101.

Region | Model | kT1 | kT2 | Photon | $\chi_{\rm red}^{2}$ | Net | Net cts
---|---|---|---|---|---|---|---
| type | [keV] | [keV] | Index |  | counts | /sqarcmin
C | wabs(mekal+mekal+power law) | 0.08aafootnotemark: $a$${}^{+0.01}_{-0.00}$ | 0.28$\pm$0.02 | 1.49${}^{+0.21}_{-0.17}$ | 1.17 | 5152 | 447
P1 | wabs(mekal+power law) | 0.11${}^{+0.04}_{-0.02}$ | – | 1.59${}^{+0.46}_{-0.47}$ | 0.87 | 1332 | 120
P2 | wabs(mekal+power law) | 0.09${}^{+0.02}_{-0.01}$bbfootnotemark: $b$ | – | 1.95${}^{+0.37}_{-0.35}$ | 1.14 | 1342 | 174
I | wabs(mekal+power law) | 0.17${}^{+0.02}_{-0.03}$ | – | 1.65${}^{+1.04}_{-1.67}$ | 1.04 | 1322 | 176
S1 | wabs(mekal+mekal+power law) | 0.09${}^{+0.02}_{-0.01}$bbfootnotemark: $b$ | 0.26$\pm$0.03 | 1.44${}^{+0.21}_{-0.20}$ | 0.99 | 6811 | 227
S2 | wabs(mekal+mekal+power law) | 0.09${}^{+0.03}_{-0.01}$bbfootnotemark: $b$ | 0.26$\pm$0.03 | 1.68${}^{+0.28}_{-0.26}$ | 1.29 | 7545 | 303
S2X | wabs(mekal+mekal+power law) | 0.18${}^{+0.01}_{-0.02}$ | 0.60${}^{+0.19}_{-0.36}$ | 2.42${}^{+0.22}_{-0.27}$ | 1.22 | 7545 | 303
V | wabs(mekal+power law) | 0.18${}^{+0.02}_{-0.05}$ | – | 1.98${}^{+0.41}_{-0.48}$ | 1.08 | 1573 | 137

121212 aafootnotemark: $a$ Value set at the lower limit of xspec12 (0.08 keV).
bbfootnotemark: $b$ Lower uncertainty set at the lower limit of xspec12 (0.08
keV)

Figure 7: Spectral model fits to the diffuse X-ray emission from star-forming
regions in M 101 (see Table 4 for description). Tables 5 and 6 present the
parameters of the model fits and the derived fluxes, respectively.

Figure 8: Spectral model fits to the diffuse X-ray emission from regions
without star formation in M 101 (see Table 4 for description). Tables 5 and 6
present the parameters of the model fits and the derived fluxes, respectively.
Table 6: Total (0.3 - 12 keV) unabsorbed fluxes in 10-13erg cm-2s-1 for the
modelled regions in M 101.

Reg. | mekal 1 | mekal 2 | power law | total
---|---|---|---|---
C | 3.4${}^{+1.9}_{-1.5}$ (42) | 1.1$\pm$0.2 (14) | 3.6${}^{+1.5}_{-1.1}$ (44) | 8.1${}^{+3.5}_{-2.7}$
P1 | 0.6${}^{+2.7}_{-0.5}$ (19) | – | 2.6${}^{+2.9}_{-1.1}$ (81) | 3.2${}^{+5.5}_{-1.5}$
P2 | 0.6${}^{+1.2}_{-0.4}$ (33) | – | 1.2${}^{+0.6}_{-0.3}$ (67) | 1.8${}^{+1.8}_{-0.7}$
I | 0.3${}^{+0.3}_{-0.2}$ (27) | – | 0.8${}^{+14.2}_{-0.5}$ (73) | 1.1${}^{+14.4}_{-0.7}$
S1 | 3.1${}^{+5.7}_{-2.2}$ (25) | 1.8$\pm$0.5 (15) | 7.4${}^{+3.6}_{-2.3}$ (60) | 12.3${}^{+9.8}_{-5.0}$
S2 | 3.1${}^{+9.0}_{-2.4}$ (34) | 1.5$\pm$0.4 (16) | 4.6${}^{+2.6}_{-1.5}$ (50) | 9.2${}^{+12.1}_{-4.3}$
S2X | 2.1${}^{+0.4}_{-0.5}$ (34) | 0.3${}^{+0.1}_{-0.2}$ (5) | 3.8${}^{+0.8}_{-0.5}$ (61) | 6.2${}^{+1.3}_{-1.2}$
V | 0.5$\pm$0.3 (19) | – | 2.2${}^{+1.8}_{-0.7}$ (81) | 2.7${}^{+2.1}_{-1.0}$
131313 Values in parentheses are fractions of the total flux (in percent) for
a given component.

##  4 Discussion

###  4.1 Parameters of the hot gas

To calculate the physical parameters of the hot gas from the obtained model
fits, assumptions about the emitting volumes need to be made. M 101 is known
to present moderate star-forming activity (2.33 M☉/yr; Kennicutt et al.,
2011), which is lower than that in M 83 (3.20 M☉/yr; Barnes et al., 2014) and
significantly lower than in NGC 6946 (7.12 M☉/yr; Kennicutt et al., 2011).
Because the extent of the X-ray halo of a galaxy depends on the star-forming
activity in the underlying disk (e.g. Strickland et al., 2004b), the moderate
SFR of M 101 suggests that an extent of the hot gaseous halo of 10 kpc, as
seen in many edge-on galaxies (e.g. Tüllmann et al., 2006), is a justified
assumption.

The volume assumptions and the model fit parameters allowed us to calculate
number densities, gas masses, and thermal energies and their densities. This
was done using the model of thermal cooling and ionisation equilibrium of
Nulsen et al. (1984):

$L_{X}=1.11\cdot\Lambda(T)\,n^{2}_{e}\,V\,\eta,$

where $L_{X}$ is X-ray luminosity, $n_{e}$ is electron number density, $V$ is
volume, $\eta$ is an unknown filling factor, and $\Lambda(T)$ is a cooling
coefficient of the order of $10^{-22}\,{\rm erg}\,{\rm cm}^{3}\,{\rm s}^{-1}$
for temperatures of a few million K (Raymond et al., 1976).

The obtained parameters of the hot gas are presented for both of the thermal
components separately (Tables 7 and 8). In Sect. 3.3, we argue that the two
thermal component models describe the emission mainly from the hot gas in the
halo. It was possible to tract the contribution from the disk gas only in the
case of the most sensitive spectrum from the spiral arm S2. In the alternative
model fitted to this spectrum (S2X), the flux calculated for this disk
component amounts to just 5% of the total model flux. This of course does not
mean that this weak emission from the hot gas in the disk is not observed in
other spectra related to the star forming arms, but rather that it cannot be
separated from the significantly more pronounced halo emission. For the single
thermal component model fits, the straightforward assumption is that the
entire emission is described with only one temperature, which consists of
contributions from both the disk and halo emission at an unknown ratio.
Consequently, to be able to compare the properties of the hot gas in all of
the regions, we need to calculate the global values from the two thermal
components model fits (i.e. for regions C, S1, S2, and S2X). The temperatures
and number densities of both of the thermal components were averaged and the
gas masses and thermal energies were simply added. As a result we obtained the
new set of global values, which are presented in Table 9, together with the
values calculated for regions for which single-thermal component models were
fitted.

Table 7: Derived parameters of the hot gas in the first thermal component of M
101.

Region | n${}^{1st}\eta^{-0.5}$ | M${}^{1st}_{gas}\eta^{0.5}$ | E${}^{1st}_{th}\eta^{0.5}$ | $\epsilon^{1st}_{th}\eta^{-0.5}$
---|---|---|---|---
| [10-3cm-3] | [106M⊙] | [1054 erg] | [10-12 erg cm-3]
C | 6.9${}^{+0.4}_{-1.7}$ | 92${}^{+5}_{-23}$ | 21${}^{+4}_{-5}$ | 1.33${}^{+0.25}_{-0.33}$
P1 | 1.7${}^{+1.5}_{-0.7}$ | 25${}^{+21}_{-10}$ | 8${}^{+12}_{-4}$ | 0.46${}^{+0.70}_{-0.23}$
P2 | 2.9${}^{+1.0}_{-1.1}$ | 28$\pm$10 | 7${}^{+5}_{-3}$ | 0.62${}^{+0.40}_{-0.27}$
I | 1.1${}^{+0.3}_{-0.2}$ | 10${}^{+3}_{-2}$ | 5$\pm$2 | 0.45${}^{+0.19}_{-0.15}$
S1 | 3.7${}^{+0.8}_{-1.5}$ | 129${}^{+26}_{-53}$ | 33$\pm$16 | 0.81$\pm$0.38
S2 | 3.8${}^{+1.4}_{-1.7}$ | 108${}^{+39}_{-48}$ | 28${}^{+23}_{-14}$ | 0.82${}^{+0.66}_{-0.41}$
S2X | 1.6$\pm$0.1 | 45$\pm$3 | 23${}^{+3}_{-4}$ | 0.67${}^{+0.09}_{-0.12}$
V | 1.1$\pm$0.1 | 15$\pm$3 | 8${}^{+2}_{-3}$ | 0.45${}^{+0.14}_{-0.20}$
141414 Columns are the region name, electron number density, total gas mass,
total thermal energy, and thermal energy density. $\eta$ is the unknown volume
filling factor.

Table 8: Derived parameters of the hot gas in the second thermal component of
M 101.

Region | n${}^{2nd}\eta^{-0.5}$ | M${}^{2nd}_{gas}\eta^{0.5}$ | E${}^{2nd}_{th}\eta^{0.5}$ | $\epsilon^{2nd}_{th}\eta^{-0.5}$
---|---|---|---|---
| [10-3cm-3] | [106M⊙] | [1054 erg] | [10-12 erg cm-3]
C | 4.5${}^{+0.4}_{-0.3}$ | 6.0${}^{+0.5}_{-0.4}$ | 4.8${}^{+0.8}_{-0.7}$ | 3.0${}^{+0.5}_{-0.4}$
S1 | 3.7${}^{+0.3}_{-0.5}$ | 12.8${}^{+1.3}_{-1.6}$ | 9.5${}^{+2.2}_{-2.1}$ | 2.3$\pm$0.5
S2 | 3.7${}^{+0.4}_{-0.5}$ | 10.6${}^{+1.2}_{-1.4}$ | 7.9${}^{+1.9}_{-1.8}$ | 2.3${}^{+0.6}_{-0.5}$
S2X | 1.4${}^{+0.4}_{-0.5}$ | 4.0${}^{+1.1}_{-1.5}$ | 6.9${}^{+4.6}_{-5.2}$ | 2.0${}^{+1.4}_{-1.5}$
151515 Columns are the region name, electron number density, total gas mass,
total thermal energy, and thermal energy density. $\eta$ is the unknown volume
filling factor.

Table 9:  Global parameters of the hot gas in the spectral regions of M 101.

Reg. | kT | n${}^{avg}\eta^{-0.5}$ | M${}^{tot}_{gas}\eta^{0.5}$ | E${}^{tot}_{th}\eta^{0.5}$ | $\epsilon^{tot}_{th}\eta^{-0.5}$
---|---|---|---|---|---
| [keV] | [10-3cm-3] | [106M⊙] | [1054 erg] | [10-12
|  |  |  |  | erg cm-3]
C | 0.09${}^{+0.01}_{-0.00}$ | 6.70${}^{+0.38}_{-1.61}$ | 98${}^{+6}_{-24}$ | 26${}^{+5}_{-6}$ | 1.48${}^{+0.27}_{-0.34}$
P1 | 0.11${}^{+0.04}_{-0.02}$ | 1.73${}^{+1.46}_{-0.68}$ | 25${}^{+21}_{-10}$ | 8${}^{+12}_{-4}$ | 0.46${}^{+0.70}_{-0.23}$
P2 | 0.09${}^{+0.02}_{-0.01}$ | 2.86${}^{+1.00}_{-1.06}$ | 28$\pm$10 | 7${}^{+5}_{-3}$ | 0.62${}^{+0.40}_{-0.27}$
I | 0.17${}^{+0.02}_{-0.03}$ | 1.10${}^{+0.30}_{-0.20}$ | 10${}^{+3}_{-2}$ | 5$\pm$2 | 0.45${}^{+0.19}_{-0.15}$
S1 | 0.11${}^{+0.02}_{-0.00}$ | 3.72${}^{+0.73}_{-1.42}$ | 141${}^{+28}_{-54}$ | 43$\pm$18 | 0.94$\pm$0.40
S2 | 0.10${}^{+0.03}_{-0.00}$ | 3.76${}^{+1.27}_{-1.56}$ | 119${}^{+40}_{-49}$ | 36${}^{+25}_{-16}$ | 0.95${}^{+0.65}_{-0.42}$
S2X | 0.21${}^{+0.04}_{-0.05}$ | 1.54${}^{+0.13}_{-0.15}$ | 49${}^{+4}_{-5}$ | 30${}^{+8}_{-9}$ | 0.79${}^{+0.20}_{-0.24}$
V | 0.18${}^{+0.02}_{-0.05}$ | 1.05${}^{+0.18}_{-0.24}$ | 15$\pm$3 | 8${}^{+2}_{-3}$ | 0.45${}^{+0.14}_{-0.20}$
161616 Columns are the region name, normalisation-weighted average
temperature, electron number density, total gas mass, total thermal energy,
and thermal energy density. $\eta$ is the volume filling factor.

It is not surprising that the highest average temperature of the hot gas is
derived from the S2X model fit, which accounts for the emission from the
spiral arm S2 (especially the two giant star-forming regions) and the halo
above it. However, this value agrees (within errors) with temperatures derived
for the inter-arm polarised region I, where no significant star formation is
visible, as well as temperatures derived for the ‘void’ region V, in which no
emission other than that visible in the X-ray map is present. Because, as we
argued before, most of the observed X-ray emission comes from the halo of M
101, we expect that in these two regions the temperature of the gas halo is
comparable to that derived from the S2X model. While the latter can easily be
due to the underlying massive star-forming arm, in the case of regions I and
V, a different explanation is needed.

Of course, there is a possibility that the hot gas found in these areas
originated in the nearby regions of star formation, for example at the end of
the spiral arm S1 or in NGC 5462 (Fig. 6). Another possibility would be to
associate these higher temperatures with lower gas densities (Table 9), but
the large uncertainties make it difficult, especially given that the gas
density derived from the S2X model is comparable to that in the P1 region,
another area without significant star formation, and hosting the hot gas at a
temperature as low as 0.11${}^{+0.04}_{-0.02}$ keV.

Interestingly, the analysis of the FUV data performed by KS10 suggests that
the flow of the hot gas due to rotation of the galaxy should be mainly along
the spiral arms, and therefore a detection of this gas is unlikely at larger
distances from the arms. The difference between the distribution of the hot
gas in the maps derived from CHANDRA and XMM-Newton data can be a result of a
much higher sensitivity to diffuse emission, but also lower resolution of the
latter. We note here that because of the angular size of M 101, the resolution
difference can be neglected, contrary to the sensitivity to faint large-scale
structures. Therefore, the detection of the diffuse X-ray emission from the
inter-arm regions in our maps could be further evidence that the hot gas was
not transported from the spiral arms, but rather heated or reheated on site.

Nevertheless, the comparison of gas densities and temperatures does not take
into account the unknown filling factor ($\eta$), which can and likely does
vary across the galaxy. To remove its influence on our results and following
our earlier studies (Weżgowiec et al., 2016, 2020), for each region we
calculated the energy per particle $E_{p}$, which is the ratio of the thermal
energy density and the electron density of the hot gas. Because both
parameters show the same dependence on the filling factor, the calculated
energies per particle can be more easily related to gas temperatures, and also
compared with the energy densities of the magnetic fields. This is discussed
in Sect. 4.3.

Last, but not least, we note that the derived densities of the hot gas in M
101 (Table 9) somewhat exclude the possibility that cosmic-ray streaming,
mentioned in Sect. 1, could be the main heating mechanism. Assuming a filling
factor of one, gas at densities of a few 10-3cm-3 would be heated to around
106 K, which is comparable to the lowest temperature that we derived from the
fit (0.08 keV). Lower values of the filling factor, down to 0.23 for the gas
in the disk (de Avillez, 2000), will result in higher gas densities and
consequently even lower temperatures.

###  4.2 Magnetic fields in M 101

For all of the regions for which the spectral analysis of the X-ray emission
was performed, we measured fluxes in the total and polarised radio intensity
maps (Figs. 2 and 3). Then, using the energy equipartition revised formula
developed by Beck & Krause (2005), we calculated strengths of the total
magnetic field, as well as its ordered component and its total energy density.
Because the information about the magnetic fields can be obtained only from
the non-thermal component of the radio emission, for our calculations we
needed to estimate the contribution of this component in the observed total
radio emission. To do that, we used the findings of Berkhuijsen et al. (2016),
who estimated an average thermal fraction to be $f_{th}$ = 0.45. Because this
was based on low-resolution observations and the nature of our analysis is to
compare regions of star formation with those residing between the star-forming
spiral arms, we decided to use a thermal fraction of $f_{th}$ = 0.5 for
regions with significant star formation (C, S1, and S2) and considered the
radio emission from “inter-arm regions” P1, P2, I, and V to be purely non-
thermal. Such assumptions are likely conservative and the derived non-thermal
intensities could be considered as upper limits. Therefore, to minimise this
effect, in our error calculations we used the derived non-thermal intensities
decreased by 25%. We also used the non-thermal spectral index of the radio
emission from M 101 of $\alpha_{nth}$ = 0.92, as derived by Graeve et al.
(1990) and used by Berkhuijsen et al. (2016), as well as assumed a proton-to-
electron ratio of 100. For the path-length we used a disk thickness of 1 kpc.
We note here that the uncertainties in the proton-to-electron ratio and the
path-length result in systematic errors, affecting measurements for all of the
regions in the same manner. Therefore, in our error calculations we included
only the lower non-thermal intensities mentioned before. The calculated
properties of the magnetic fields in the studied regions of M 101 are
presented in Table 10.

Table 10:  Properties of the magnetic fields in M 101.

Region | Ssynch | psynch | Btot | $\epsilon_{B}$ | Bord
---|---|---|---|---|---
| [mJy/beam] | [%] | [$\mu$G] | [10-12 erg cm-3] | [$\mu$G]
C | 0.45 | 14.9 | 10.7$\pm$0.8 | 4.6$\pm$0.7 | 4.1$\pm$0.4
P1 | 0.13 | 37.5 | 7.5$\pm$0.7 | 2.2$\pm$0.3 | 4.9$\pm$0.4
P2 | 0.26 | 20.8 | 9.2$\pm$0.7 | 3.4$\pm$0.5 | 4.3$\pm$0.4
I | 0.18 | 32.3 | 8.2$\pm$0.8 | 2.7$\pm$0.5 | 4.9$\pm$0.3
S1 | 0.28 | 17.0 | 9.4$\pm$0.7 | 3.5$\pm$0.5 | 3.9$\pm$0.4
S2 | 0.41 | 17.9 | 10.4$\pm$0.9 | 4.3$\pm$0.7 | 4.4$\pm$0.4
V | 0.19 | 5.5 | 8.8$\pm$0.7 | 3.1$\pm$0.5 | 2.0$\pm$0.1
171717 Columns are the region name, non-thermal radio flux, degree of
polarisation, total magnetic field strength, magnetic field energy, and
ordered magnetic field strength.

The derived strengths of the magnetic field are between 9 and 11 $\mu$G for
most of the regions, which corresponds well with the findings by Berkhuijsen
et al. (2016). Lower values were obtained for three regions: P1, I, and V,
which do not correspond to regions of star formation. Consequently, these
three areas show the lowest energy densities of the magnetic field. Two of
them, regions P1 and I, show at the same time the highest strengths of the
ordered component of the magnetic field, reaching as high as 4.9 $\mu$G. This
suggests a significant ordering of the magnetic field in M 101. The third one
of these regions (V) shows a comparable strength of the total magnetic field,
but the strength of the ordered component is significantly lower than for any
other regions within the galactic disk. A straightforward explanation is the
fact that region V looks like a large hole in the map of the polarised radio
emission from M 101 (Fig. 3). This hole is accompanied by a lack of any
significant star formation, with a prominent depression visible in the H i
map. If we assume that the radio emission has been depolarised by Faraday
rotation (e.g. by vertical magnetic fields) in this area, this would need to
be a strong effect, as the degree of polarisation is lower by a factor of
three or more than in other regions. Such significant depolarisation would
require rotation measures of —RM— ¿ 300 rad/${\rm m}^{2}$, while the observed
ones are much smaller, as shown by Berkhuijsen et al. (2016). Therefore, the
lack of any substantial polarised emission from the ordered magnetic field
seems to be real.

The two spiral arms and the central region of the galaxy show the highest
strengths, and thus the highest energy densities of the magnetic field.
Although this seems obvious, given the star-forming activity in these regions,
significant emission can be seen in the polarisation map. This is reflected in
the strengths of the ordered component of the magnetic field, which are
comparable to those of the remaining regions. The eastern spiral arm S2 shows
a slightly stronger magnetic field and with a higher energy density than the
western spiral arm S1. Because this arm looks distorted, likely due to intra-
group interactions, this increase could be explained by the gravitation-
induced enhancement of the star formation and consequently the amplification
of the magnetic field. The tidal interactions could also simply stretch the
magnetic fields, leading to their amplification and the enhancement of the
ordered component, which is also observed in this arm.

###  4.3 Hot gas and magnetic fields in M 101

As mentioned in Sect. 4.1, the X-ray observations of M 101 provide information
about the physical properties of the hot gas both in the galactic disk and the
halo. Although the observed non-thermal radio emission also comes from the
entire galaxy (being integrated along the line of sight), we do not have any
direct information about the halo magnetic fields, (i.e. their structure and
strengths), because in this paper the radio data at only one frequency are
presented. Therefore, being unable to disentangle the radio emission from the
disk from that from the halo, we needed to calculate the global properties of
the hot gas, as presented in Sect. 4.1, including the energies per particle,
which provide direct information about the energy stored in the hot gas.
Consequently, we could compare these energies per particle with the energy
densities of the magnetic fields for all of the regions of M 101 that are
analysed in this paper.

In Table 11, the energies per particle together with energy densities of the
magnetic field are presented and their relation is shown in Fig. 9. The
highest energies per particle are calculated for the polarised inter-arm
region I (magenta), S2X (the higher temperature model for spectrum of the
spiral arm S2), and the inter-arm region V (blue). The corresponding energy
densities of the magnetic field are lower for I and V, when compared to other
regions, but among the highest in the case of S2X. Fig. 10 presents the
relation of the energies per particle and the degree of order of the magnetic
field, defined here as the ratio of the strengths of the ordered and the total
magnetic fields. The values that are clearly above the average are for one of
the two polarised regions (P1, red dot) and for I. The lowest degree of order
of the magnetic field is found, as discussed before, in region V.

As we can see, all three conditions required to suggest the magnetic
reconnection is a mechanism of the ISM heating (Sect. 1) are met only in
region I, which is in fact the only magnetic arm in M 101. While the strong
and moderately ordered magnetic fields in the spiral arm S2, together with the
highest temperature of the hot gas (derived from S2X model), are likely due to
the tidal interactions discussed in Sect. 4.2, the properties of the hot gas
and magnetic field in region V need a quite different explanation.
Interestingly, the properties of the hot gas, that is, temperatures, number
densities, and thermal energy densities are in fact identical in regions I and
V. Furthermore, the total strengths of the magnetic fields, as well as their
energy densities are also very similar, with the values for region V being
slightly higher, though still within the derived uncertainties. This makes the
degree of order of the magnetic field the only property that is quite
different between both regions. Because of the significant extent of region V
(roughly 5 $\times$10 kpc) and the absence of star formation, only little
turbulence is expected in this area, which in turn would prevent the formation
of ordered magnetic fields. This, however, would not explain the higher
temperature of the hot gas in this area, when compared to the other regions,
especially the neighbouring regions, of M 101. As the hot gas in region V is
expected to originate in the nearby star-forming regions, such as the one
visible at the end of the S1 spiral arm (Fig. 6), its temperature should be
comparable to that of the gas in regions P1 or P2. In fact, we note here that
the sensitivity of the spectrum from region V is low and it is likely that the
real temperature of the hot gas in this region is indeed comparable to the
temperatures in P1 and P2, as the uncertainties suggest. Therefore, more
sensitive X-ray data from region V are needed to verify the temperature of the
hot gas.

If the present temperature was confirmed, the existence of the hotter gas in
region V could be, to some extent, also due to the effects of magnetic
reconnection. These would operate on the vertical component of the magnetic
field in this area. Although the Faraday rotation measures obtained by
Berkhuijsen et al. (2016) are not sufficient to support the depolarisation
scenario, they are higher in this region than in the other parts of the
galaxy, which would suggest the existence of (weaker) vertical magnetic
fields. In such a case, the increase in the degree of order of this vertical
component would not be visible in our map of the polarised emission because
this emission is sensitive only to the field components in the sky plane.

Table 11: Thermal energy per particle and energy densities of the magnetic field in the spectral regions of M 101. Region | $E_{p}$ | $\epsilon_{B}$
---|---|---
| [10-10 erg] | [10-12 erg cm-3]
C | 2.2$\pm$0.3 | 4.6$\pm$0.7
P1 | 2.7$\pm$1 | 2.2$\pm$0.3
P2 | 2.2$\pm$0.5 | 3.4$\pm$0.5
I | 4.1$\pm$0.5 | 2.7$\pm$0.5
S1 | 2.5$\pm$0.5 | 3.5$\pm$0.5
S2 | 2.5$\pm$0.7 | 4.3$\pm$0.7
S2X | 5.2$\pm$0.8 | 4.3$\pm$0.7
V | 4.3$\pm$0.5 | 3.1$\pm$0.5

Figure 9: Relation between energy per particle (${\rm E}_{\rm P}$) and energy
density of the magnetic field (${\rm\epsilon}_{\rm B}$ in the regions of M
101.

Figure 10: Relation between energy per particle (${\rm E}_{\rm P}$) and degree
of order (${\rm B}_{\rm ord}/{\rm B}_{\rm tot}$) of the magnetic field in the
regions of M 101.

###  4.4 Reconnection heating

As already suggested in Sect. 1, in order to propose magnetic reconnection as
the source of gas heating, three conditions need to be fulfilled
simultaneously. Apart from the increase in the temperature of the hot gas, a
lower energy density of the magnetic field should be observed, as some of the
kinetic and magnetic energy of turbulence is being dissipated and converted to
thermal energy in the surrounding medium. Additionally, a decrease in the
turbulent energy of the magnetic field would result in a lower ratio of total
and ordered magnetic fields, and thus their higher level of magnetic field
ordering. All these properties of the hot gas and the magnetic fields seem to
be present in region I (the only magnetic arm), as already mentioned in the
previous section. Still, it is important to ask if the increase in temperature
of the hot gas due to reconnection heating can be detected, and if the
required energy of the magnetic field is consistent with the values derived
from our observations. We discuss these problems and present our estimates in
the following sections.

####  4.4.1 Gas heating

The chances of detecting reconnection heating in galaxies depend on where and
when the energy of dissipated magnetic fields is released. The essential
difficulty stems from the fact that most of the supernova explosion energy
(canonical value of 1051 erg) is converted to thermal energy during the shock
passing through the ISM. Shock waves in the ISM heat up the post-shock gas to
106 \- 107 K. Expansion of the over-pressured bubbles, especially those
related to multiple supernova explosions in star-forming regions, drives
turbulence. According to Mac Low & Klessen (2004), about $\sim$10% of
supernova energy is converted to turbulent energy, which drives the turbulence
in the ISM. Another 10-50% of supernova energy is spent on acceleration of
cosmic rays (e.g. Grenier et al., 2015). The remaining part (40-80%) of the
explosion energy is deposited in the hot-ISM phase. Hot gas together with
cosmic rays drive galactic outflows. The hot bubbles expand and cool down
adiabatically, while the hot gas cools down via radiative processes. Turbulent
cascade transports the kinetic and magnetic energies of chaotic flows to
smaller and smaller scales. Assuming that magnetic energy constitutes about
half of the turbulent energy density, we note that $\sim$5% of the supernova
explosion energy is absorbed in the amplification of random magnetic fields.
In a turbulence decay timescale, which is of the order of eddy turnover time,
the chaotic fluctuations reach dissipation scales, where turbulent
reconnection (Lazarian et al., 2020) operates and dissipates magnetic fields,
converting their energy into thermal energy.

The above estimations lead to the conclusion that reconnection heating can
contribute $\sim$10% of energy of the hot-ISM phase. As a result, it seems
that reconnection heating is sub-dominant and difficult to detect if both
heating processes act simultaneously. However, it is possible that
reconnection heating is delayed and/or displaced from star-forming regions,
where the hot gas phase is most efficiently produced.

To identify the plausible time lags and space shifts of magnetic field
dissipation in turbulence, we note that supernovae produce hot gas during the
Sedov phase, when a part of the supernova energy is converted to kinetic
energy of the expansion. This leads to motions of gas on scales of the order
of supernova or super-bubble (SB) scales, which range from $\sim$ 50 pc to 300
pc. Parker instability, due to buoyancy of magnetic fields and cosmic rays, is
considered as another driver of interstellar turbulence on even larger scales
of 0.5 - 1 kpc. These scales can be identified as energy injection scales
(outer scale) for ISM turbulence, corresponding to velocities at the outer
scale to 10 km s-1 and 50 km s-1, respectively (see Shukurov et al., 2019).
Knowing the scales ($L$) and velocities ($v$), we can estimate the time lag
between the energy injection on the outer scale of turbulence and the
dissipation of kinetic and magnetic energies at the dissipation scales. With
the above values, the full cascade and the associated reconnection takes place
in about 5 to 10 Myr in both the disk and the halo. In that time, the disk
interstellar gas, orbiting with a velocity of 200 km s-1 ($\simeq$200 pc
Myr-1), covers the azimuthal distance of $\Delta L_{\varphi}\sim$1-2 kpc.
Inside the co-rotation radius, the difference between the ISM gas speed and
the pattern speed can lead to a significant displacement of the turbulent ISM
with respect to the spiral arms. The plausible scenario is that the turbulence
driven in the spiral arms gradually decays with the distance from the arms.
The effects of magnetic reconnection result in the ordering of the magnetic
field structure, and these should both be noticeable in the wakes of the past
star forming regions, or in general at distances of the order of $\sim$1–2
kpc. If this scenario is valid, the azimuthal distance $\Delta L_{\varphi}$
denotes the displacement of the magnetic arms with respect to the spiral arms.

On the other hand, supernova shock-heated gas expands rapidly and drives both
turbulence and mostly vertical outflows. The rapid expansion of the over-
pressured gas leads to adiabatic cooling, which acts together with the
radiative cooling processes. Between the initial temperature of shock-heated
gas of $\sim$107 K and temperatures around 106 K, the adiabatic cooling
dominates over radiative processes. Due to the bump in the cooling curve
(Dalgarno & McCray, 1972), where the cooling rates increase from
$\sim$2$\times$10-23erg cm3 s-1 at 106 K to $\sim$10-21 erg cm3 s-1 at around
5$\times$105 K, the radiative cooling processes become significantly more
efficient below 106 K. Then, the cooling times may fall below 10 Myr for the
gas at number densities of a few 10-3 cm-3 (see eq. 38 and Fig. 4. in Hanasz &
Lesch, 1998). This means that supernova-driven outflows have a good chance to
cool down in a period shorter than or comparable to the period of turbulence
dissipation and magnetic reconnection. Therefore, when conditions are
favourable, the shock-heated gas may already be significantly cooled down,
while the reconnection heating still operates. The outflow velocities of the
post-shock gas are of the order of the escape velocity from the disk of
$\sim$300 km/s or more, which follows the thermal expansion acting together
with the outflow acceleration by cosmic ray pressure gradient. While thermal
expansion might fail due to the rapid cooling of the hot gas fraction, cosmic
rays lose their energy much less efficiently and can therefore serve as a wind
driver even without the active support from the hot gas fraction (Hanasz et
al., 2013).

We estimate that in 5-10 Myr, the outflow of the hot gas propagating at
velocities of 300 km/s covers a vertical distance of $\Delta L_{z}\sim$1.5-3
kpc and at the same time an azimuthal distance of $\Delta
L_{\varphi}$$\sim$1-2 kpc, because the out-flowing gas continues its orbital
movement. This implies that the effects of magnetic reconnection in the hot
gas can potentially be detectable at vertical distances $\pm\Delta L_{z}$
above and below the disk, with the azimuthal displacement of $\Delta
L_{\varphi}$. This means that radiative losses of the reconnection-heated gas
might be located above and below the inter-arm regions.

####  4.4.2 Dissipation of the magnetic field

The total energy densities of the magnetic fields in the studied regions of M
101 are roughly 2-5$\cdot$10-12 erg cm-3 (Table 10). Because the strengths of
the ordered magnetic fields are two to three times lower than those of the
total magnetic fields, we can assume that about 80% of the total energy is
stored in the turbulent component, which gives 1.6-4$\cdot$10-12 erg cm-3 for
our regions. To estimate the lower limit of energies available for magnetic
reconnection and for simplicity of the calculations, we assume 2$\cdot$10-12
erg cm-3 as the total energy density of the turbulent magnetic field. We
assume that about 90% of this energy is lost during the expansion of the
magnetic field into the halo (Hanasz & Lesch, 1998). This leaves 2$\cdot$10-13
erg cm-3 that would be converted to thermal energy via the magnetic
reconnection effects. Assuming an efficiency of 0.5 for the conversion of the
magnetic energy to thermal energy, the energy of the hot gas with a density of
around 10-3 cm-3 (regions I and V, Table 9) would increase by $\sim$10-10 erg
per particle, that is by 25-30% (Table 11). If we consider region I, a
decrease in the energy density of the magnetic field by 2$\cdot$10-13 erg cm-3
would require an initial strength of the magnetic field of around 8.5 $\mu$G
for this region. Although the derived values are still within the
uncertainties, we note that these are lower limits, as we assumed above.

Furthermore, these calculations could also support the idea of magnetic
reconnection in region V, in which the vertical expansion of the magnetic
fields should be easier. The potential increase in the degree of order of the
magnetic field would not be observed (see Sect. 4.3), but, similarly to region
I, around 2$\cdot$10-13 erg cm-3 of the magnetic field energy would be
converted to additional $\sim$10-10 erg per particle of the hot gas. Then, for
both regions (I and V), reconnection heating would be responsible for the
shift visible in Figs. 9 and 10. The corresponding change in the temperature
of the hot gas (by 25-30%) would also be consistent with values derived for
the other regions (Table 9).

##  5 Summary and Conclusions

In this paper we present an analysis of the radio and X-ray data for the
spiral galaxy M 101. Studies of the properties of the hot gas and the magnetic
fields in different parts of the disk and the halo of the galaxy are
performed. Our findings can be summarised as follows:

  1. 1.

For the first time, a high-resolution map of M 101 at a high radio frequency
was obtained. Because of the very large angular size of this galaxy, a single-
dish map was needed to restore the large-scale emission lost in the
interferometric observations.

  2. 2.

Although the majority of the polarised emission is associated with the
galactic spiral arms, as suggested by the low-resolution observations by
Berkhuijsen et al. (2016), region I, that is the inter-arm region between the
massive eastern spiral arm and the galactic centre, hosts a rudimentary
magnetic arm.

  3. 3.

The X-ray data show diffuse emission from the hot gas that extends beyond the
eastern part of the galactic disk and suggests interactions within the group
environment. This seems to be confirmed by strong and moderately ordered
magnetic fields in the massive spiral arm, which hosts two prominent star-
forming regions that could also be a product of enhanced star formation
induced by these interactions.

  4. 4.

The spectral analysis of the X-ray data suggests that most of the emission
comes from the hot gas in the halo of M 101.

  5. 5.

Three galactic regions, I, V, and S2X, show an increase in the temperature of
the hot gas (and thus higher energies per particle), when compared to other
regions. However, only in region I are both lower energy density and a higher
order of the magnetic field found, which is characteristic of magnetic arms.
We propose that these features can be explained with magnetic reconnection
effects, which convert energy of the magnetic field to thermal energy of the
hot gas.

  6. 6.

In region V, an area devoid of H$\alpha$ and H i emission between the eastern
spiral arm and the galactic centre, our low-sensitivity spectrum suggests the
existence of gas hotter than in the surrounding regions. This could be a
result of heating by magnetic reconnection. In this region, due to a lack of
any significant polarised radio emission that would suggest ordered magnetic
fields, magnetic reconnection would need to occur in the vertical component of
the magnetic fields. As we argue in this paper, due to lower gas densities and
the time required to start the magnetic reconnection, galactic halos should
host the most efficient reconnection heating, and which is thus easier to
detect.

Our results, together with our previous study of NGC 6946 (Weżgowiec et al.,
2016) and M 83 (Weżgowiec et al., 2020), suggest that the gas heating by
magnetic reconnection might be possible to detect. More analyses, also of
edge-on galaxies, are planned in order to give these detections a more
statistical significance.

###### Acknowledgements.

We thank the anonymous referee for comments that helped to improve 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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