11institutetext: Institut de Ciències del Cosmos (ICCUB), Universitat de
Barcelona (IEEC-UB), Martí i Franquès, 1, 08028 Barcelona, Spain
22institutetext: ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain
33institutetext: Department of Physics and Astronomy, Johns Hopkins
University, Baltimore, MD 21218, USA 44institutetext: Space Telescope Science
Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA 55institutetext:
INAF - Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via P.
Gobetti 93/3, 40129 Bologna, Italy 66institutetext: School of Physics and
Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, UK
77institutetext: Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la
Astronomía s/n, 18008, Granada, Spain 88institutetext: Facultad de Ciencias,
Universidad de Zaragoza, Pedro Cerbuna 12, E-50009 Zaragoza, Spain
99institutetext: School of Sciences, European University Cyprus, Diogenes
street, Engomi, 1516 Nicosia, Cyprus

# Origin of the diffuse 4-8 keV emission in M82

K. Iwasawa 1122 C. Norman 3344 R. Gilli 55 P. Gandhi 66 M. A. Peréz-Torres
778899

We present the first spatially resolved, X-ray spectroscopic study of the 4-8
keV diffuse emission found in the central part of the nearby starburst galaxy
M82 on a few arcsecond scales. The new details that we see allow a number of
important conclusions to be drawn on the nature of the hot gas and its origin
as well as feedback on the interstellar medium. We use archival data from the
Chandra X-ray Observatory with an exposure time of 570 ks. The Fe xxv emission
at 6.7 keV, expected from metal-enriched hot gas, is enhanced only in a
limited area close to the starburst disc and is weak or almost absent over the
rest of the diffuse emission, resulting in spatial variations in equivalent
width from $<0.1$ keV to 1.9 keV. This shows the presence of non-thermal
emission due to inverse Compton scattering of the far-infrared photons by
radio emitting cosmic ray electrons. The morphological resemblance between the
diffuse X-ray, radio, and far-infrared emission maps support this concept. Our
decomposition of the diffuse emission spectrum indicates that $\sim$70% of the
4-8 keV luminosity originates from the inverse Compton emission. The metal-
rich hot gas with a temperature of $\simeq 5$ keV makes a minor contribution
to the 4-8 keV continuum, but it accounts for the majority of the observed Fe
xxv line. This hot gas appears to emerge from the circumnuclear starburst ring
and fill the galactic chimneys identified as mid-infrared and radio emission
voids. The energetics argument suggests that much of the supernova energy in
the starburst site has gone into creating of the chimneys and is transported
to the halo. We argue that a hot, rarefied environment produced by strong
supernova feedback results in displacing the brightest X-ray and radio
supernova remnants which are instead found to reside in giant molecular
clouds. We find a faint X-ray source with a radio counterpart, close to the
kinematic centre of the galaxy and we carefully examine the possibility that
this source is a low-luminosity active galactic nucleus in an advection-
dominated accretion flow phase.

###### Key Words.:

X-rays: galaxies - Galaxies: starburst - Galaxies:individual (M82)

##  1 Introduction

A fundamental ingredient of the superwind model of Chevalier & Clegg (1985) is
a hot fluid with a temperature of $\sim 10^{8}$ K, created by an injection of
kinetic energy mainly from supernovae, and to a lesser degree from stellar
winds of massive stars, propagating into a low-density medium in a starburst
region. To maintain the kinetic energy for driving a galactic-scale wind, this
hot fluid has to be minimally radiative with a long cooling time. The
superwind could be observed in hard X-rays above a few keV. The nearby
starburst galaxy M82 shows a large-scale galactic wind at various wavelengths
and is an ideal target to examine the wind-driving mechanism. Earlier X-ray
imaging of M82 at the arcsecond resolution with the Chandra X-ray Observatory
(Chandra) resolved out bright X-ray binaries which dominate the hard X-ray
band and revealed that there is residual diffuse emission surrounding the
starburst disc (Griffiths et al. 2000). The spectrum of the diffuse gas
exhibits a high-ionisation Fe K line from Fe xxv, characteristic of the
thermal emission of a temperature of a few keV, and thus has been identified
with the hot fluid as envisaged in the superwind model. Strickland & Heckman
(2009) argued that the observed Fe xxv luminosity agrees with the expectation
of the Chevalier & Clegg (1985) model. However, if the hard X-ray diffuse
emission spectrum is to be explained by thermal emission, the Fe xxv line
appears too weak, requiring low Fe metallicity of 0.2-0.3 $Z_{\sun}$
(Strickland & Heckman 2007; Liu et al. 2014), in contrast with a highly
enriched interstellar medium enriched by core-collapse supernovae in starburst
galaxies such as M82. Recent findings of several X-ray supernova remnants
(SNRs), which also emit strong Fe xxv but are not resolved in the previous
study (Iwasawa 2021), reduce the Fe xxv luminosity originating from the
diffuse emission further. A possible explanation is that the continuum of the
Fe xxv-emitting gas is much fainter and the majority of the observed continuum
emission comes from an extra source such as non-thermal emission (e.g.
Strickland & Heckman 2009). Although non-thermal emission due to inverse
Compton scattering of far-infrared (FIR) photons by cosmic ray electrons have
long been proposed for the hard X-ray emission in M82 (Hargrave 1974; Schaaf
et al. 1989; Moran & Lehnert 1997), the presence of bright X-ray binaries
hindered a good measurement of the true diffuse emission properties before
Chandra. Even with the Chandra imaging, the inverse Compton emission was
disfavoured by Strickland & Heckman (2007) for being too faint. Given the
$\gamma$-ray detection from M82 (Abdo et al. 2010) and the importance of
cosmic-ray driven winds in starburst galaxies, the starburst-driven non-
thermal process warrants a serious consideration.

In this work, we present an updated spatially resolved spectral analysis of
the X-ray diffuse emission in the 4-8 keV band using the archival Chandra
data. The Fe xxv emission at 6.7 keV is of primary interest, but the cold Fe K
emission at 6.4 keV is also present in the diffuse emission spectrum
(Strickland & Heckman 2007; Liu et al. 2014). We examine the spatial
distributions of these Fe lines and discuss their implications for the origin
of the 4-8 keV emission, which seems to support the presence of both the
inverse Compton emission and also the metal-rich hot gas.

The distance to M82 is assumed to be 3.6 Mpc (Freedman et al. 1994). The
angular scale is thus 17.4 pc arcsec-1 (1 kpc corresponds to approximately 1
arcmin).

##  2 Observations

Table 1: Chandra observations of M82.

Date | ObsID | ACIS | Exp. | $\theta$ | $\phi$
---|---|---|---|---|---
1999-09-20 | 361 | I3 | 33 | 0.3 | 26
1999-09-20 | 1302 | I3 | 15 | 0.3 | 26
2002-06-18 | 2933 | S3 | 18 | 0.6 | 1
2009-06-24 | 10542 | S3 | 118 | 1.4 | 223
2009-07-01 | 10543 | S3 | 118 | 1.1 | 179
2009-07-07 | 10925 | S3 | 45 | 2.6 | 21
2009-07-08 | 10544 | S3 | 74 | 2.6 | 21
2010-06-17 | 11104 | S3 | 10 | 0.4 | 50
2010-07-20 | 11800 | S3 | 17 | 2.7 | 1
2010-07-23 | 10545 | S3 | 95 | 2.7 | 8
2012-08-09 | 13796 | S3 | 20 | 0.3 | 169
2014-02-03 | 16580 | S3 | 47 | 1.2 | 323
2015-01-20 | 16023 | S3 | 10 | 1.2 | 356
111Date: the date when each observation started. ACIS: the ACIS CCD chip on
which the central part of the M82 was placed. Exp.: useful exposure time in
units of $10^{3}$ seconds. $\theta$, $\phi$: Off-axis angle in arcminutes and
roll angle in degrees of the central position of Fig. 1 in each observation.
The first two ACIS-I observations were included only for the imaging analysis.

We used the same 13 Chandra ACIS observations of M82 as in Iwasawa (2021)
where details of the observations can be found. These observations were
selected from all the Chandra ACIS observations of M82 for relatively small
off axis angles (0.3-2.7 arcsec) -for the central starburst region- so that
the point spread function (PSF) has small distortion. The major part of this
work relating to spectral analysis makes use of the 11 observations with the
ACIS-S3, which provide a consistent spectral resolution. The two early AICS-I
observations in 1999 were used only for the imaging analysis. The total
exposure time of the 11 ACIS-S3 observations is 570 ks and the two ACIS-I
observations add an extra 52 ks.

Chandra data reduction and image analysis were carried out by CIAO 4.12
(Fruscione et al. 2006) using the calibration files in CALDB 4.53. Spectral
analysis was performed using HEASoft XSPEC (Blackburn et al. 1999; Arnaud
1996).

##  3 Results

###  3.1 Image of the 4-8 keV diffuse emission

Figure 1: Chandra X-ray images of the central part of M82 integrated over the
13 observations. Top-left: 2-4 keV image; Top-right: 4-8 keV band; The colour
scale of these two images is in logarithmic with the brightest point sources
are saturated. Bottom-left: The 4-6 keV image of the ellipse where the data of
the diffuse emission spectrum were taken. The detected discrete sources were
masked. The region where the brightest ULXs along with a few others are
clustered is masked in a block. This image is in a linear scale as the dynamic
range of the brightness is narrow: 1-19, as a result of the removal of
discrete sources. Bottom-right: The same image as Top right overlaid by the
ellipse and the 38 region segments for spatially resolved spectral study.

The 4-8 keV Chandra image integrated over all the 13 observations is shown in
Fig. 1. The diffuse emission, as well as a number of discrete sources, is
visible. It lies along the starburst disc where the discrete sources are
concentrated. Its extension along the major axis (PA $\simeq 70^{\circ}$) is
$\sim 700$ pc, coinciding with the disc size. The height of the extension
above and below the disc is less than 200 pc and the overall shape is
elliptical. We adopt an ellipse of semi-major and semi-minor axis lengths of
$19\aas@@fstack{\prime\prime}4\times 9\aas@@fstack{\prime\prime}4$ (=338 pc
$\times$ 164 pc) with the major axis inclined to $PA=70^{\circ}$, which
includes most of the 4-8 keV diffuse emission.

The spectral data were taken from this ellipse, masking the individual
discrete sources. We refer to the 21 sources detected within the ellipse in
Iwasawa (2021), Xp0 through Xp20. The western part where the bright
ultraluminous X-ray sources (ULXs) are clustered was masked in a block so that
a sufficiently large area around them is masked to avoid their emission in the
PSF wings as well as the bright core emission. This block contains Xp12
through Xp17. These masks for the discrete sources take up 23% of the entire
ellipse area of 591 arcsec2. The 4-6 keV continuum image from the ellipse with
the masking is also shown in Fig. 1. We note that the 4-6 keV image of the
diffuse emission alone has a relatively flat brightness distribution, in the
absence of peaky discrete sources, and is shown in a linear scale.

Compared with the 4-8 keV emission, the diffuse emission at lower energies
rises sharply towards the disc plane and is more extended, as illustrated by
the 2-4 keV image. This soft X-ray extended emission is considered to be the
entrained, shocked interstellar medium (ISM), forming part of the large-scale
soft X-ray winds. The central part, near the starburst disc in particular, is
obscured and subject to suppression by absorption at the lower energies. Even
in the 2-4 keV image, the light suppression is visible along the disc. This
absorption effect of the order of $N_{\rm H}$ of a few times of $10^{22}$ cm-2
practically diminishes above 4 keV and all the discrete sources embedded in
the starburst disc are visible in the 4-8 keV image. Likewise, the diffuse
emission above 4 keV is largely unaffected by absorption, except for a small
part with excess obscuration.

###  3.2 Total diffuse emission spectrum

####  3.2.1 Thermal emission lines

Although the soft X-ray emission spectrum is beyond the scope of this work, it
is worth illustrating the contrasting characteristics of the emission-line
spectrum above and below 4 keV. The broad-band spectrum (Fig. 2) shows strong
He-like and H-like K-shell emission from Ne, Mg, Si, S, Ar and Ca in the 1-4
keV range. At energies above 4 keV, the most prominent spectral feature is the
Fe K complex in 6-7 keV (Fig. 2), dominated by Fe xxv at $\sim 6.7$ keV. As
previously noted by Strickland & Heckman (2007); Liu et al. (2014), a cold Fe
K line at 6.4 keV is also present. A line-like excess is detected marginally
at 4.5 keV, although the origin is unclear. Since its detection is marginal
and is not essential for this work, we leave further details in Appendix B.
For all the spectral fits presented below unless stated otherwise, a spectrum
was binned so that each bin contains at least one count. A spectral fit was
performed on background-corrected data by comparing with a model folded
through the detector response, using the C-statistic (Cash 1979).

We examined temperature and metallicity inferred from the atomic lines of each
element by fitting the thermal emission spectrum of apec222apec is the code to
calculate a thermal emission spectrum (Foster et al. 2012). Here, gas in a
collisional ionisation equilibrium is assumed. in a narrow energy range, as
follows: 1.1-1.7 keV for Mg; 1.5-2.4 keV for Si; 2.1-3 keV for S; 2.7-3.5 keV
for Ar; and 3.3-4.3 keV for Ca. With the restricted energy ranges, a
temperature and metallicity were inferred by each element independently. A He-
like and H-like line ratio mainly drives the temperature determination for Mg,
Si, S, for which the emission lines dominate the continuum. This is less true
for Ar and Ca, since the slope of strong continuum emission affects the
temperature determination. We did not look into the Ne lines, as the energy
range of this line also contains substantial emission from the Fe L complex
around 1 keV. Cold absorption was fitted. The results are illustrated in Fig.
3. The metallicity remains compatible between the elements at $\simeq
0.6\,Z_{\odot}$. The gas temperatures inferred from individual elements remain
in a limited range of $kT\simeq 0.9$-1.8 keV with a moderately increasing
trend as the selected energy range moves higher. The absorption also shows the
same increasing trend. Both indicate spectral hardening towards higher
energies. This is likely a manifestation of an increasing contribution of a
hard continuum component rather than a true rise of temperature or absorption.
Therefore we consider that the temperature and $N_{\rm H}$ for Ar and Ca
lines, which lie above the strong continuum, are likely similar to those
inferred for S emission.

In contrast, the Fe K line spectrum gives a much higher temperature and a
lower metallicity. Fitting to the 6-7.2 keV spectrum gives $kT=4.6$ (3.8-5.7)
keV and $0.21^{+0.6}_{-0.4}Z_{\odot}$. In the fit, an additional narrow
Gaussian line at 6.4 keV is included. As the energy range is not sensitive to
absorption smaller than $N_{\rm H}$$\sim 10^{23}$ cm-2, the central $N_{\rm
H}$ value obtained for the Ca K band was assumed but it has no effect on the
result. This abrupt change in temperature and metallicity above and below 4
keV, in addition to the morphological difference in image, signals a
transition between the two diffuse emission components of different origins
taking place at around 4 keV. The increasing $kT$ and $N_{\rm H}$ towards the
transition energy suggest spectral hardening which is likely caused by the
harder component and/or more absorption. The soft X-ray wind emission
therefore lies in the foreground of the harder component exhibiting the Fe K
emission.

Figure 2: Diffuse emission spectrum of the central part of M82, obtained from
the Chandra ACIS-S. The flux density is in units of $10^{-14}$ erg s-1 cm-2
keV-1. Upper panel: The 0.7-8 keV spectrum; Lower panel: The Fe K band
spectrum of the same data. The three vertical dotted-lines indicates the
expected centroid energies of 6.4 keV, 6.7 keV and 6.96 keV for cold Fe K, Fe
xxv and Fe xxvi, respectively. The grey line indicates the fitted model of a
power-law and three Gaussian lines.

Figure 3: Temperature ($kT$), metallicity ($Z$) and absorbing column density
($N_{\rm H}$) obtained from fitting the apec to the individual line spectra.
The $N_{\rm H}$ for the Fe K band spectrum was assumed to be $4\times 10^{22}$
cm-2, approximately the middle value obtained for the Ca spectrum, as the
energy range of the data is insensitive to $N_{\rm H}$$<10^{23}$ cm-2.

####  3.2.2 Fe K complex

The Fe K line complex (Fig. 2) is described here by multiple Gaussians. The
dominant Fe xxv is most likely of thermal origin. It is a triplet that is not
resolved at the CCD resolution. Fitting a single Gaussian to a simulated apec
spectrum gives a centroid energy of 6.68 keV with a slight broadening of
$\sigma\sim 30$ eV, when $kT$ is in the range of 4-6 keV (Appendix A), which
is inferred from the apec fit to the Fe K band. The observed data show the
centroid energy of $6.67\pm 0.01$ keV and the width of $\sigma=58\pm 17$ eV,
slightly broader than expected. Two other Gaussian lines for a cold Fe K line
at 6.4 keV and Fe xxvi at 6.96 keV were added, assuming they are narrow and
unresolved. Respective line intensities were fitted and the results are shown
in Table 2. The continuum is modelled by a power-law by fitting the 4.1-8 keV
data (the lower energy bound at 4.1 keV was chosen to eliminate the Ca
emission). The absorbing $N_{\rm H}$ of $4\times 10^{22}$ cm-2 and the
marginally detected 4.5 keV line are also included. The power-law slope,
energy index333We use energy index, $\alpha$, for a spectral slope appropriate
for a spectrum in flux density unit, as defined as $f_{\rm E}\propto
E^{-\alpha}$, where $f_{\rm E}$ is flux density and $E$ is energy. The
conventional photon index, $\Gamma$, is related as $\Gamma=1+\alpha$., was
found to be $\alpha=1.28\pm 0.12$.

Notwithstanding the weak detection of Fe xxvi, the Fe xxvi/Fe xxv ratio of
$0.14\pm 0.09$ indicates a temperature of $kT\approx 4.5\pm 1$ keV (Appendix
A), in agreement with that inferred from the apec fit. However, the Fe xxv
line broadening as observed above may indicate a contribution from a lower
temperature emission, as discussed later, and thus the true temperature of the
gas may be higher than that inferred from the apparent Fe xxv/Fe xxvi ratio
(see further details in Sect. 4).

Table 2: Fe K line complex of the diffuse emission spectrum.

Energy | Intensity | EW | $L_{\rm line}$ | ID
---|---|---|---|---
6.4 | $1.8\pm 0.3$ | $0.13\pm 0.02$ | 2.9 | Cold Fe
6.67 | $4.9\pm 0.5$ | $0.38\pm 0.04$ | 8.1 | Fe xxv
6.96 | $0.68\pm 0.43$ | $0.06\pm 0.04$ | 1.1 | Fe xxvi
444Line energies, width ($\sigma$) and EW are in units of keV. Line
intensities are in units of $10^{-6}$ ph cm-2 s-1. Line luminosities are in
units of $10^{37}$ erg s-1. They are as observed from the spectrum from the
region masking the discrete source apertures.

###  3.3 Spectral variations across the diffuse emission

####  3.3.1 Region segments

Here, we investigate spectral variations across the 4-8 keV diffuse emission
of M82. We set 38 rectangular region-segments covering the diffuse emission
(Fig. 1) and examined the individual spectra taken there. These region
segments were placed by avoiding the discrete sources, except for the two
transient sources (the reason for this exception is described below). We label
them as dX0 through dX37. The segments dX0 through dX20 are on the northern
side of the starburst disc while dX21 through dX33 on the southern side. The
two segments, dX34 and dX35, lie within the starburst disc, placed in the
small gaps between crowded discrete sources.

The two additional segments, dX36 and dX37, contain transient sources, Xp7 and
Xp11 as labelled in Iwasawa (2021), respectively. Since the transient sources
were in quiescence, no excess emission is visible at their positions (Appendix
C) and we used the data for their quiescent state. As the flaring of Xp7
occurred in the two early ACIS-I observations used only for imaging, the
exposure time of the dX36 spectrum remains the same as the spectra of the
other segments, integrated over all the 11 ACIS-S observations. As for Xp11,
the transient flaring occurred in the three observations in 2010. The spectrum
of dX37 was then produced, omitting those observations, and its resulted
exposure time is 450 ks, as opposed to the full 570 ks.

The segment sizes were chosen to minimise the dispersion of source counts
contained between the individual segments where allowed by the positions of
the discrete sources. As a result, the 4-8 keV counts of those segments range
between 150 and 400 counts, with the mean of 274 counts and the standard
deviation of 72 counts. The broad-band spectra of these 38 region segments are
shown in Appendix F (Fig. 22).

####  3.3.2 Mapping the spectral variations

Figure 4: Spatial variations of spectral properties over the hard-band diffuse
emission. Left: Surface brightness (upper panel) in units of $10^{-15}$ erg
s-1 cm-2 arcsec-2 and energy index of power-law continuum (lower panel) in the
4-6 keV band; Middle: Surface brightness of 6.67 keV Fe xxv emission in units
of $10^{-9}$ ph cm-2 s-1 arcsec-2 and line EW in units of keV; and Right:
Surface brightness and line EW of 6.4 keV cold Fe K emission in the same units
as the Fe xxv emission.

Figure 5: Values of the respective region segments in each map in Fig. 4 are
plotted. From the top to the bottom, surface brightness of the 4-6 keV
continuum in units of $10^{-15}$ erg s-1 cm-2 arcsec-2; the 4-6 keV energy
index, $\alpha$; surface brightness of Cold Fe (6.4 keV, in blue) and Hot Fe
(Fe xxv at 6.67 keV, in red) in units of $10^{-9}$ ph s-1 cm-2 arcsec-2; and
EW of Cold Fe (6.4 keV) and Hot Fe (6.67 keV) in units of keV.

Figure 6: Separate CDFs of the surface brightness of the 4-6 keV continuum, Fe
xxv and cold Fe (from left to right) in the northern (N, blue circles) and
southern (S, red triangles) parts with respect to the starburst disc plane.
These plots were made, using 29 segments with the 4-6 keV surface brightness
cut (see text). The 4-6 keV continuum surface brightness is in units of
$10^{-15}$ erg s-1 cm-2 arcsec-2 while the Fe line surface brightness is in
units of $10^{-8}$ ph s-1 cm-2 arcsec-2

Our primary interest is to investigate spatial variations of the Fe K lines.
We modelled the 4-8 keV spectrum of each segment with a power-law continuum
and two Gaussian lines at 6.4 keV and 6.67 keV. No absorption is included. The
Fe lines were assumed to be narrow at those energies and their normalisations
were fitted. The continuum flux of each region was estimated in the 4-6 keV
band from the fit. The power-law energy index, $\alpha$, measured for the
continuum in the same energy range was also recorded for each region.

Based on the above fits, we constructed surface brightness maps of the 4-6 keV
continuum, cold Fe and Fe xxv emission over the 38 region segments, as shown
in Fig. 4. The maps of 4-6 keV continuum slope and equivalent width (EW) of
the two Fe lines are also shown. The same values given in the maps with the
68% error intervals are plotted in the order of the segment number in Fig. 5.
A few spectra with a 4-6 keV slope close to zero indicate that they might be
more absorbed than the rest since they have $N_{\rm H}$ of $\sim 10^{23}$ cm-2
(Appendix D).

The continuum emission shows high surface brightness near the starburst disc
which declines gradually towards larger radii, in agreement with the 4-6 keV
count image shown in Fig. 1. With respect to the disc plane, the brightness
distribution appears to be similar between the northern and southern sides,
when discounting the lowest surface brightness regions on the north-east
corner. On the contrary, the Fe xxv emission is markedly stronger on the
northern side, particularly evident in its eastern part. Such a north-south
asymmetry is not obvious in the cold Fe emission.

The above observation regarding the north-south brightness symmetry and
asymmetry is also illustrated by a comparison of cumulative distribution
functions (CDFs) of surface brightness of those quantities (Fig. 6). The
diffuse continuum emission has the lowest surface brightness at the north-
eastern outskirt (see Fig. 4). On applying the surface brightness cut of
$>0.06\times 10^{-15}$ erg s-1 cm-2 arcsec-2, the area of the faintest
emission is discarded, leaving 17/12 segments (out of 22/14 segments) on the
northern/southern sides. The segments dX34 and dX35 located in the disc plane
were not considered. The median values of the brightness of the northern and
southern segments are found to be comparable: $1.08\times 10^{-9}$ ph cm-2 s-1
arcsec-2 and $1.04\times 10^{-9}$ ph cm-2 s-1 arcsec-2, respectively. Their
CDFs of the 4-6 keV surface brightness are indeed similar, except for the
brightest end.The north-south brightness distributions in the continuum for
the selected segments are balanced. It can then be used as a reference to test
any north-south asymmetry in the Fe line emission when the same selected
segments are used. The CDFs for Fe xxv clearly diverge between the northern
and southern segments towards higher brightness, verifying the brighter
northern side.

A line detection at the confidence level of $>95$% is found to occur when line
intensity exceeds $1\times 10^{-7}$ ph cm-2 s-1. There are 15 segments showing
this relatively strong Fe xxv detection and most of them are located on the
northern side (Fig. 5) and connected to each other (Fig. 4), suggesting a
continuous distribution. Unmatched continuum and line brightness distributions
naturally lead to a non-uniform EW distribution.

The Fe xxv EW map in Fig. 4 shows an excess morphology similar to that of the
surface brightness but extends further to larger radii in both northern and
southern directions. Curiously, these extensions appear to originate from a
particular region in the disc. These excesses show EW ranging from 0.2 keV to
0.6 keV and includes dX37 which shows an exceptionally large EW of $\sim 1.9$
keV. More interesting, however, are the small EWs observed in a number of
segments. Some of them even have no Fe xxv detection with the EW upper limits
of 0.1 keV, despite of having source counts comparable to the other segments.
If the diffuse emission is homogeneous gas, then individual segments are
expected to have a constant Fe xxv EW of 0.38 keV as measured in the whole
diffuse emission spectrum (Table 2). Assuming that the line counts follow a
Poisson distribution, the observed EWs would be found in the 0.2-0.6 keV range
at a probability of 90%, given the observed counts (eight counts in the line,
on average, was assumed). The fact that 17 segments have Fe xxv EW $<0.2$ keV,
as opposed to an expected 2 (equivalent to $\sim 5$% of the total 38
segments), indicates that the observed EW variations are statistically
significant. This spatially biased distribution of Fe xxv means that a
significant portion of the diffuse emission areas are void of Fe xxv or have
much weaker Fe xxv emission than that seen in the average spectrum. This
suggests a presence of a featureless continuum component of non-thermal
emission.

As for cold Fe line at 6.4 keV, its brightness CDFs are, in contrast, similar
between north and south (Fig. 6). We note that there are two brightest
segments, one each in the northern and southern segments, and the shape of the
CDFs suggests that the total cold Fe flux is dominated by a small number of
bright segments: the brightest five segments compose $\approx 40$% of the
total 6.4 keV line flux. The EW of the cold Fe line is similarly balanced
between the north and south. There are 12 segments of $>90$% detection of cold
Fe line. Their EWs are clustered in the 0.16-0.3 keV range with an exception
of 0.56 keV from dX28. If their distribution follows a normal distribution
(the mean of 0.27 keV and standard deviation of 0.1 keV), two more segments
with smaller EWs ($<0.16$ keV) are expected to join this distribution if the
observation sensitivity was not limited. Therefore $\sim 40$% (14/38) of the
segments exhibit cold Fe lines with this moderately large EW of 0.1-0.5 keV.
These segments spread over the whole ellipse region, suggesting a diffuse
nature of the cold Fe line. We discuss its origin later. Because of the large
difference in ionisation stage (and line excitation mechanisms) from Fe xxv,
it is no surprise to find different spatial distributions between their
brightness and EWs.

####  3.3.3 Remarkably strong Fe xxv in dX37

The spectrum of dX37 shows an Fe xxv line with an exceptionally large EW of
1.9 keV (Fig. 5). The Fe K band spectrum shows only the Fe xxv line at
$6.68^{+0.04}_{-0.01}$ keV but no 6.4 keV line (the 90% upper limit of EW 0.35
keV). The 4-7.2 keV spectrum can be described by an apec model with a
temperature of $kT=3.3\pm 0.9$ keV and metallicity of
$1.6^{+1.0}_{-0.6}Z_{\sun}$, which is essentially that of Fe. The temperature
is relatively low, compared to the other regions, resulting in the steep
continuum slope ($\alpha\simeq 2.0$, Fig. 5). Lowering a temperature leads to
a larger Fe line EW at given metallicity (see Appendix A) but this pronounced
line EW is well beyond the effect of varying temperature. The line EW is a
factor of $\sim 5$ larger than that of the mean spectrum, and is comparable or
even larger than those observed in the spectra of X-ray SNRs selected in
Iwasawa (2021).

As described in Sect. 3.3.1, this segment contains the transient source Xp11.
However, as the image taken from the same time intervals used to construct the
spectrum, that is the transient’s quiescence state, shows no point-like source
(Appendix C). No other discrete source, for example, a SNR, is present. No
radio SNR is found in the segment either. The 4-6 keV continuum surface
brightness is comparable to or even slightly lower than the adjacent segments,
dX8 and dX9, located at the similar latitude from the disc. The 6.55-6.9 keV
narrow-band image shows a flat distribution of counts within dX37, supporting
the diffuse nature of the Fe xxv emission.

An unlikely local metallicity enhancement could boost the line EW, but in the
absence of any SN generating objects, such as a star cluster, that coincides
with the region which lies $\sim 90$ pc above the molecular disc plane, it
does not seem to be the case. Incidentally, the Fe metallicity found in this
spectrum is close to $Z_{\rm Fe}\simeq 2\leavevmode\nobreak\ Z_{\sun}$
expected for the metal-rich hot gas with the best estimate of mass loading by
Strickland & Heckman (2009). This leads to a possibility that we might happen
to see nearly pure emission from the hot gas component in this region with a
minimal contribution of non-thermal emission which dominates everywhere else.
This possibility is further explored below (Sect. 4).

####  3.3.4 Relation between continuum slope and Fe xxv strength

Among the measured features, we noted a possible correlation between Fe xxv EW
and continuum slope (Fig 7). Although the data are noisy and the correlation
cannot be firmly established, six EWs of Fe xxv larger than 0.5 keV, for
example, occur only when the 4-6 keV slopes are $\alpha\geq 1.5$ while the
median slope of all the spectra is $\tilde{\alpha}=1.05$.

Given the Fe xxv EW variation (from $<0.1$ keV to 1.9 keV) examined above, an
inclusion of non-thermal emission in addition to the thermal emission
characterised by Fe xxv can provide an explanation. In this hypothesis,
varying composition of the two components across the diffuse emission region
leads to the Fe xxv EW variations. If the non-thermal emission has a harder
spectrum than the thermal emission, a spectral slope of a composite spectrum
varies as a function of Fe xxv EW, as hinted above. We tested this by
inspecting spectra binned into three Fe xxv EW intervals, excluding dX37 with
the exceptionally strong Fe xxv. The three EW intervals were set as follows:
’low’, EWs $\leq 0.15$ keV; ’medium’, $0.15\,{\rm keV}<$ EWs $\leq 0.3$ keV;
and ’high’, $0.3<$ EWs $\leq 1$ keV (Table 3) and averaged spectra from the
three EW bins were obtained. Their spectra, together with the dX37 spectrum as
a comparison, are shown in Fig. 8. The spectra from the three bins have
background-corrected counts of 0.9-7.5 keV: 59645 (4-7.5 keV: 2972), 56247
(3730) and 61650 (3113) for the low, medium and high EW bins. Their mean
fluxes are comparable to one another as well as the quality of their spectra.
The 5.4-7.4 keV band centred on the Fe K line complex of the spectra is also
shown.

The three spectra are nearly identical in the soft X-ray band up to the Ca K
line complex at $\sim 4$ keV, except for small variations at the lowest
energies due to varying absorption across the region which correlates with the
dust lanes visible in the optical image. This confirms homogeneous emission of
the soft X-ray wind covers the entire hard-band diffuse emission region in
foreground.

In contrast, the Fe K band spectra are dramatically different between them.
The continuum slopes of the three spectra measured in the 4-6 keV band are
given in Table 3. The continuum steepens as increasing EW bins (overplotted
also in Fig. 8). This trend continues with the even steeper slope found in the
dX37 spectrum (Table 3). This agrees with the idea that Fe xxv EW is observed
to be small when a contribution of non-thermal emission increases and vice
versa.

Table 3: Fe xxv EW sliced spectra.

Bin | EW(Fe xxv) | $N$ | Counts | $\alpha$
---|---|---|---|---
low | $\leq 0.15$ | 12 | 59645 | $0.84\pm 0.13$
medium | 0.15-0.3 | 13 | 56247 | $1.02\pm 0.12$
high | $>0.3$ | 12 | 61650 | $1.26\pm 0.14$
dX37 | 1.9 | 1 | 3865 | $2.0\pm 0.6$
555EW of Fe xxv are in units of keV. $N$ is the number of integrated segments.
Counts are net source counts in the 0.9-7.5 keV band. The energy index
$\alpha$ is the spectral slope measured in the 4-6 keV band. The same
properties for the spectrum from dX37 are also given for comparison.

Figure 7: Plot of EW (Fe xxv) against continuum slope $\alpha$ of the 38
region segments (in blue filled-squares). The three magenta diamonds indicate
the points for the EW-binned spectra (Table 3), where EW value of each point
is the median of EWs measured in the spectra that went into each bin.

Figure 8: Spectral variations as a function of Fe xxv EW. Left: The broad band
spectrum of dX37, integrated spectra of Fe xxv EW of EW $\geq 0.3$ keV,
0.15-0.3 keV, and $<0.15$ keV (’high’, ’medium’, and ’low’ from the top to
bottom). Each spectra has been multiplied arbitrarily for displaying purpose.
Right: The Fe K band data of the high, medium, and low spectra in the left
panel. The flux density is in units of $10^{-14}$ erg s-1 cm-2 keV-1.

###  3.4 Light distribution in 4-8 keV

To measure the approximate shape of the 4-8 keV diffuse light, we took
projected light profiles along both the major and minor axes of the galactic
disc as shown in Fig. 9. Along the major axis (PA $=70^{\circ}$), one strip
labelled as ’major-Disc’ goes through the molecular disc while the other
strip, ’major-N’, lies $\sim 70$ pc above the disc plane in the middle. The
strips are inevitably disrupted by the discrete sources which were masked out.
Two strips along the minor axis, ’minor-E’ and ’minor-Centre’, are also
placed. The reference (zero) point of all the strips is the position of
SN2008iz (RA = 09h55m51$\aas@@fstack{s}$55, Dec $=+69\degr 40\arcmin
45\aas@@fstack{\prime\prime}8$, Brunthaler et al. (2009)), which is roughly
coincides with the FIR emission peak (see Sect. 3.6). Background-corrected 4-8
keV counts were collected from each rectangular region and the surface
brightness profiles along each strip was constructed.

On inspecting those projected profiles, the brightness peak can be located at
around the reference point. The light distribution along the major axis is
relatively flat and skewed towards the east (Fig. 10a). Along the minor axis,
the light distribution is nearly symmetric at the brighter inner part, as
already seen in the 4-6 keV map (Fig. 4), but shows an enhanced extension
towards north at the fainter brightness level (Fig. 10b). Along each axis, the
profile shapes of the two strips are found to be similar, as shown in the
standardised brightness plots (Fig. 10c), while their absolute fluxes differ.

Figure 9: Image of the 4-8 keV emission overlaid by the two strips along the
major axis: ’Disc’ and ’N’, and the two strips along the minor axis: ’Centre’
and ’E’.

Figure 10: Light distribution in the 4-8 keV band. From top to bottom: a) The
4-8 keV projected light profiles along the major axis taken from the strips
shown in Fig. 9. b) The profiles along the minor axis. c) These two panels
show the same profiles but standardised for a comparison of their shapes. d)
The 4-8 keV diffuse emission image, constructed by two-dimensional
interpolation from the point source masked image. Each pixel has an $\approx
2\times 2$ arcsec2 size and the colour bar indicates the brightness scale in
units of counts per pixel.

Another purpose of creating these projected light profiles is to estimate a
flux of the diffuse emission in the masked area of the clustered ULXs and
other sources, Xp12 though Xp17. By interpolating the four profiles, the 4-8
keV flux in the area was estimated to be $\approx 3.3\times 10^{-13}$ erg s-1
cm-2, by assuming the same counts-to-flux conversion factor obtained for the
diffuse emission spectrum in Sect. 3.2. A two-dimensional interpolation can
also be applied directly to the 4-8 keV image with the point source mask used
for the 4-6 keV image in Fig. 1. For estimating a missing light profile of the
relatively large masked area, we adapted a wide grid-interval and thus the
image was re-binned by four pixels before applying the interpolation
(interpolation.griddata from Scipy) with the ’cubic’ method. The resulted
interpolated image is shown in Fig. 10d. The missing flux of the masked area,
computed from this map, agrees with the above estimate.

###  3.5 Diffuse emission luminosity

In addition to the ULX area, the expected diffuse flux from the other masked
areas of discrete sources was computed by applying the same conversion factor
and it is found to be $0.9\times 10^{-13}$ erg s-1 cm-2. Adding these
estimated fluxes from the masked areas to the $7.2\times 10^{-13}$ erg s-1
cm-2 of the diffuse emission spectrum (Sect. 3.2), the total 4-8 keV flux of
diffuse emission in the ellipse in Fig. 1 is thus $1.1\times 10^{-12}$ erg s-1
cm-2, which corresponds to the 4-8 keV luminosity of $1.7\times 10^{39}$ erg
s-1.

This luminosity, however, contains some contribution of unresolved discrete
sources, that is, X-ray binaries and SNRs. We estimated their contributions
using the cumulative luminosity distribution, $N(>L)$, which can be
approximated by a power-law form ($\propto L^{-\gamma}$). For X-ray binaries
in star-forming galaxies, $\gamma\simeq 0.6$ has been found (Colbert et al.
2004; Grimm et al. 2003; Mineo et al. 2012). As $\gamma<1$ implies that
brighter sources dominate, fainter, unresolved X-ray binaries have a minor
contribution to the observed diffuse emission luminosity anyway. The $N(<L)$
of the X-ray binaries detected by Iwasawa (2021) down to $1\times 10^{-14}$
erg s-1 cm-2 in the 4-8 keV band, below which the detection completeness
declines rapidly, within the diffuse emission region (excluding the far more
luminous ULXs) also show $\gamma\sim 0.6$. Using this slope, we estimated the
4-8 keV luminosity of unresolved X-ray binaries to be $2.0\times 10^{38}$ erg
s-1. The $N(<L)$ slope for X-ray SNRs appears to have a similar value
$\gamma=$0.6-0.7, based on the seven X-ray SNRs (Iwasawa 2021). The 4-8 keV
luminosity from unresolved X-ray SNRs was then found to be $0.4\times 10^{38}$
erg s-1.

A further correction needed is for photons spilled over from the masked
discrete sources. About 10% of each discrete source counts in the PSF wing
fall outside the masked aperture, on average. This is estimated to be $\sim
0.6\times 10^{38}$ erg s-1. Taking all these into account, the net diffuse
emission luminosity in the 4-8 keV band is found to be $1.4\times 10^{39}$ erg
s-1, in which $1.3\times 10^{39}$ erg s-1 comes from the continuum
(approximately 9% of the 4-8 keV luminosity originates in Fe xxv). Unless this
luminosity solely originates in thermal emission described by the apec fit and
in a spheroid as marked by the ellipse in Fig. 1, the mean electron density
would be $n_{e}\sim 0.6$ cm-3, as the volume of the spheroid is $\sim
7.9\times 10^{7}$ pc3.

Strickland & Heckman (2007) estimated the 2-10 keV continuum luminosity of
$4.4\times 10^{39}$ erg s-1, which corresponds to $2.0\times 10^{39}$ erg s-1
in the 4-8 keV band. Our estimate is lower than theirs by about one third. The
difference might be attributed to more rigorous removal of discrete sources,
including the X-ray SNRs, with the much deeper imaging.

###  3.6 X-ray, FIR, and radio images

Figure 11: Diffuse X-ray, FIR, and radio image comparison. Left: The 4-8 keV
Chandra image in grey-scale overlaid by the Herschel-PACS 70 $\mu$m FIR
contours in magenta. Right: The PACS 70 $\mu$m image overlaid by VLA 3-cm
continuum (Adebahr et al. 2013) contours in green. The beam sizes of the PACS
and the VLA images are $\sim 5.5$ arcsec and $7.6\times 7.3$ arcsec,
respectively. Both contours are drawn in seven levels divided in linear scale
with the lowest contour corresponding to 10% of the peak brightness in the
respective images.

The spatial variation of Fe xxv investigated in Sect. 3.3 led us to consider
the hypothesis that the 4-8 keV diffuse emission might be a composite of
thermal and non-thermal emission. The non-thermal emission, in this case,
arises from inverse Compton scattering of FIR photons by (sub-GeV) cosmic ray
electrons (Hargrave 1974). Ample FIR emission is radiated from the dusty
starburst region while the cosmic rays are accelerated by SNRs that are
abundant in the same region. The electron population of the latter is
represented by the synchrotron radio emission. Therefore if this inverse
Compton emission is responsible for the diffuse X-ray emission, its morphology
is expected to match that at the FIR and radio wavelengths.

We used the FIR image (Fig. 11) taken by the Herschel PACS (Bendo et al. 2012,
data were obtained through NED) for a comparison. It provides a
$70\thinspace\mu$m image at the angular resolution of $\sim
5\aas@@fstack{\prime\prime}5$ (PACS Handbook 2019, version 4.01 ESA). A
similar image at $59\,\mu$m (the beam FWHM of $5\aas@@fstack{\prime\prime}5$)
has been also taken by SOFIA (Jones et al. 2019). We used a radio continuum
image (Fig. 11) taken by the VLA at 3 cm (Adebahr et al. 2013) with
D-configuration with a matching beam size ($7\aas@@fstack{\prime\prime}6\times
7\aas@@fstack{\prime\prime}3$) to the FIR image. The radio continuum at 3-cm
represents the high-frequency part of the synchrotron emission with a power-
law spectrum $\nu^{-0.7}$ in the starburst region while the electron
population responsible for the Compton scattering are attributed to those at
lower frequencies (e.g. Strickland & Heckman 2007). The power-law spectrum
shows a turnover below 1 GHz due to free-free absorption (Adebahr et al.
2013), meaning that any image taken at frequencies lower than 1 GHz is
affected by the absorption which suppresses the brightness in the high
obscuration region. For this reason, the high-frequency image is expected to
represent the intrinsic distribution of the cosmic ray electron energy
density.

The FIR and radio images are, unsurprisingly, very similar (Fig. 11 Right).
Their image morphology agrees well with that of the 4-8 keV diffuse emission
(Fig. 11 Left; see also Fig. 10d). The matching morphology between the three
band images is encouraging for the inverse Compton scattering origin for non-
thermal emission. A likely contribution of this non-thermal component to the
4-8 keV continuum luminosity is further discussed in Sect. 4.

###  3.7 Galactic centre source

Figure 12: $K_{\rm s}$ band image of the M82 nuclear peak emission obtained
from 2MASS in grey scale (fainter emission is cut out), overplotted by
positions of the X-ray source, Xp9 (white), radio source 43.21+61.3 (red,
Rodriguez-Rico et al. 2004), H i kinematic centre (green Weliachew et al.
1984), Ne ii kinematic centre (blue, Achtermann & Lacy 1995), H92$\alpha$ ring
centre (cyan, Rodriguez-Rico et al. 2004), WISE peak (yellow, Jarrett et al.
2019), and two previous 2.2 $\mu$m peak measurements (R80,L90: Rieke et al.
1980; Lester et al. 1990). The positional error is $\sim 0.5\arcsec$ for each
measurement, which is represented by the circle, apart from the 2.2 $\mu$m
position of Rieke et al. (1980). The image orientation is north up, east to
the left.

The 2.2 $\mu$m peak (Lester et al. 1990) has often been assumed to be the
galactic centre position of M82, as the near-IR emission is a good tracer of
stellar population and relatively robust against obscuration. However, the
$K$-band emission has a complex structure (see e.g. Alonso-Herrero et al.
2003) and the large X-ray absorbing column of $N_{\rm H}$$\sim 10^{23}$ cm-2
suggests that obscuration could affect the $K$-band peak position. Instead,
there are a few measurements of a kinematic centre determined by H i
(Weliachew et al. 1984), [Ne ii] (Achtermann & Lacy 1995), and radio
H92$\alpha$ line (Rodriguez-Rico et al. 2004) observations. We noted that the
X-ray source, Xp9, detected in Iwasawa (2021)666The source position is
09h55m52.0s, +69d40m47.3s, There was a typo in the Dec. in Iwasawa (2021).
This is the correct position of Xp9. is located at the radio kinematic centre,
and has a relatively faint radio counterpart. The radio source is catalogued
as ’43.21+61.3’ in Rodriguez-Rico et al. (2004) who observed with VLA at 8.3
GHz and 43 GHz and detected with 4 mJy in both frequencies. It is tentatively
classified as a H ii region because of the flat spectrum. These positions,
including the previously measured 2.2 $\mu$m peak positions (Rieke et al.
1980; Lester et al. 1990) and the WISE position (Jarrett et al. 2019, WXSC),
are plotted over the 2MASS $K_{\rm s}$ band image (Fig. 12, retrieved from the
2MASS Image Service of IRSA). The positions of Xp9 and the radio source agree
with the kinematic centre measurements and the WISE position, and is $\la
1\arcsec$ off to the west from the 2MASS peak. This positional coincidence
with the kinematic centre, albeit being tentative, offers a possibility that
Xp9 might be a low-luminosity AGN sitting at the galactic centre of M82. This
possibility is examined in Sect. 4.7.

##  4 Discussion

We discuss the origin of the diffuse 4-8 keV emission which appears to be
composed of multiple components of distinct origins. Three lines of evidence
below suggest the presence of significant non-thermal emission in the 4-8 keV
diffuse emission: 1) Substantial portions of the diffuse emission region
exhibit weak or no Fe xxv in the spectrum (Sect. 3.3.2); 2) The continuum
hardening with decreasing Fe xxv EW (Sect. 3.3.4); and 3) The morphological
resemblance between the X-ray, FIR and radio images (Sect 3.6). Based on this
argument, we present a spectral decomposition of the diffuse X-ray emission
that includes inverse Compton emission, followed by a discussion of the IC
emission, metal-rich hot gas, its feedback on ISM and relation to the X-ray
SNRs, the 6.4 keV Fe line, and the galactic centre source.

###  4.1 Composition of the 4-8 keV diffuse emission

Our hypothesis is that the diffuse emission is inverse Compton emission and
soft X-ray wind emission, added to the hot gas of $kT\sim 5$ keV which
occupies specific regions where the Fe xxv line is detected. Based on this
picture, we tried to assess the components of the 4-8 keV diffuse emission. We
have to consider at least three continuum components: 1) IC: the inverse
Compton emission; 2) Th1: the high-energy tail of the soft X-ray wind
emission; and 3) Th2: the thermal emission giving rise to the Fe xxv line. As
it is not practical to fit all the parameters of such a complex model, we
assumed reasonable spectral parameters for each component as described below.

The inverse Compton emission component (IC) is modelled by a power-law. As the
spectral slope is expected to be approximately the same as the radio
synchrotron spectrum, we assumed the energy index of $\alpha=0.7$. This
component has the hardest spectrum among the three components.

The soft X-ray wind emission (Th1) is modelled by apec with $kT=1.2$ keV. This
component, which dominates in the soft X-ray band, should still have a
significant contribution in continuum emission at energies around 4-5 keV. The
assumed temperature (and also the adopted $N_{\rm H}$ value) was that obtained
for the S K band (Fig. 3). We believe this choice is adequate for the soft
X-ray wind emission spectrum at energies of Ar K and Ca K emission and above 4
keV for the reason described in Sect. 3.2.1. The metallicity is assumed to be
$1\leavevmode\nobreak\ Z_{\sun}$ for the following reasons. It has to be
larger than $0.6\leavevmode\nobreak\ Z_{\odot}$ inferred from the soft X-ray
lines (Fig. 3) to compensate the extra continuum contribution of the IC
component. With this temperature, the spectrum has high-ionisation Fe K
emission including Fe xxv, centred at 6.63 keV (see Appendix A) and it should
not overproduce the Fe xxv feature of the ’low’ spectrum, in which the hot
thermal emission (as described below) contribution is supposed to be
negligible.

The hot thermal emission (Th2) is modelled by apec with a variable temperature
around $kT=5$ keV. The Fe metallicity is a key quantity: since this component
is the primary source of the observed Fe xxv line (and also Fe xxvi). If the
Fe metallicity were known, the continuum strength would automatically be
determined. However, we do not know it a priori. Since the reverse is also
true and the continuum level, which is driven by the IC component strength,
mediates the Fe metallicity, we exploited this route to constrain the Fe
metallicity, as below. Strickland & Heckman (2007) derived the original SN
ejecta to have Fe metallicity of $5\leavevmode\nobreak\ Z_{\sun}$ through a
Starburst99 (Leitherer et al. 1999) simulation. This value can be considered
as the upper bound and coincides also with the upper bound of the apec model
parameter. The lower bound is $1\leavevmode\nobreak\ Z_{\sun}$, since the Th1
component is mass-loaded further to the hot fluid by entraining ISM and
therefore has lower metallicity than that of Th2.

All these components are assumed to be modified by cold absorption of $N_{\rm
H}$$=2\times 10^{22}$ cm-2. The two additional lines at 4.5 keV and 6.4 keV,
which are required to describe the data (Sect. 3.2) but not of our interest
here, were added as narrow Gaussians.

The three Fe xxv EW sliced spectra in Sect. 3.3.4 (Fig. 7 and Table 3) have
continuum slopes that depends on their line EWs. The dX37 spectrum with the
exceptionally large Fe xxv EW follows the same trend. We assessed the
composition of the three continuum components that can reproduce their varying
spectral slopes, which, in turn, constrains the Fe metallicity of Th2. The
’low’ Fe xxv EW spectrum can be considered to have a negligible contribution
of Th2, as its weak Fe xxv line can be accounted for solely by Th1. On the
contrary, the dX37 spectrum should be dominated by Th2. We fitted the three
EW-sliced spectra and dX37 spectrum in the 4-7.2 keV band jointly, leaving the
normalisation of each component and the temperature and (Fe) metallicity of
Th2 as free parameters.

This fit gives a good description of the data with C-stat = 785.3 with 774
bins (754 dof). The temperature was found to be $kT=5.0\pm 0.8$ keV. The best-
fit Fe metallicity was driven to the highest bound of $5\leavevmode\nobreak\
Z_{\sun}$ but the likelihood remains similar above $2.5\leavevmode\nobreak\
Z_{\sun}$ (Fig. 13). This can be compared with the Fe metallicity of $\sim
2\leavevmode\nobreak\ Z_{\sun}$, which would be expected from the best-
estimate of the mass-loading factor of 2.7 by Strickland & Heckman (2009).

We computed 4-8 keV fluxes of the IC, Th1 and Th2 components in the four EW-
sliced spectra, adopting the Th2 Fe metallicity of $3.8\leavevmode\nobreak\
Z_{\sun}$, which is the probability-weighted mean over the expected
metallicity range of 1-5 $Z_{\sun}$. Their proportions of the total 4-8 keV
flux in each spectrum are given in Table 4 (where the contribution of the 4.5
keV and 6.4 keV lines are left out). With the same set of spectral components,
a spectral decomposition for the total diffuse emission spectrum (Fig. 2) is
illustrated in Fig. 14. The relative contributions of the respective
components are also given in Table 4.

We note that the Fe K line at 6.67 keV is actually a sum of the lines from Th1
and Th2. The Fe K feature of Th1 is centred at 6.63 keV, consisting of Fe xxv
and weaker lines originating in lower ionisation stages, given the temperature
of $kT=1.2$ keV. This Th1 contribution probably shifts the line centroid and
broadens the width to the observed 6.67 keV and $\sigma=0.05$ keV (Table 2)
from 6.68 keV and $\sigma=0.03$ keV, expected from a $kT=5$ keV plasma.

The IC flux correlates weakly with the Fe metallicity via the Th2 continuum
flux. In the probable 2.5-5 $Z_{\sun}$ range, the IC component carries 66-70%
($\pm 3$%) of the 4-8 keV diffuse emission luminosity, which corresponds to
(0.9-1) $\times 10^{39}$ erg s-1. This, however, contains the contribution of
unresolved X-ray binaries with a similar spectral shape, which was estimated
to be $0.2\times 10^{39}$ erg s-1 (Sect. 3.5). Correcting for this, the net
4-8 keV luminosity of inverse Compton emission is (0.7-0.8) $\times 10^{39}$
erg s-1.

Figure 13: C-statistic curve for the Fe metallicity of Th2 in the joint fit of
the three EW-sliced spectra and dX37 spectrum with the three continuum
component model.

Figure 14: Same spectrum shown in Fig. 2 with the best estimate of the three
continuum components, IC (blue), Th1 (purple) and Th2 (red) assuming the Fe
metallicity of Th2 to be $3.8\leavevmode\nobreak\ Z_{\sun}$. Two additional
lines at 4.5 keV and 6.4 keV are also plotted in dotted lines. The flux
density is in units of $10^{-14}$ erg s-1 cm-2 keV-1. Table 4: 4-8 keV flux
compositions.

Bin | IC | Th1 | Th2
---|---|---|---
low | $0.82\pm 0.04$ | $0.16\pm 0.02$ | 0.003 ($<0.025$)
medium | $0.74\pm 0.04$ | $0.13\pm 0.02$ | $0.09\pm 0.02$
high | $0.55\pm 0.04$ | $0.17\pm 0.02$ | $0.25\pm 0.03$
dX37 | 0.16 ($<0.33$) | $0.17\pm 0.09$ | $0.67\pm 0.17$
Total | $0.69\pm 0.03$ | $0.14\pm 0.02$ | $0.14\pm 0.02$
777Proportions of the IC, Th1 and Th2 components in the 4-8 keV flux when the
EW-sliced spectra, dX37 and total diffuse emission spectrum are fitted by the
three-component model with the Th2 Fe metallicity of $3.8\leavevmode\nobreak\
Z_{\sun}$.

###  4.2 Inverse Compton emission

The parameters for estimating the energy loss of cosmic ray electrons due to
inverse Compton scattering were obtained by Adebahr et al. (2013), using their
radio data, combined with the FIR data from AKARI. They agree with those used
by Persic et al. (2008) who predicted a 2-10 keV flux of IC X-ray emission,
which assumed that the entire FIR emission (measured with IRAS) comes from
radii $\leq 300$ pc. However, since some fraction extends out, as shown in the
AKARI (Kaneda et al. 2010) and Herschel (Contursi et al. 2013) images, a
correction is needed to obtain the FIR energy density for the X-ray diffuse
emission region. The $L_{\rm FIR}$ of the central $<1\arcmin$ in radius is
$2.4\times 10^{43}$ erg s-1, estimated using the Helou et al. (1988) formula
with $S_{60}=630$ Jy and $S_{100}=529$ Jy, measured with AKARI-FIS (Kaneda et
al. 2010). We found, from the PACS $70\,\mu$m image, that $\approx 60$% of
this luminosity comes from the ellipse of the X-ray diffuse emission.
Weighting with the FIR emission distribution, the mean FIR energy density
within the ellipse was estimated to be $U_{\rm FIR}\sim 0.82\times 10^{-9}$
erg cm-3. Adebahr et al. (2013) derived the magnetic field strength of
$B=98\,\mu$G of the M82 central region, using the revised equipartition
formula of Beck & Krause (2005). It is slightly smaller than $106\,\mu$G of
Persic et al. (2008) but has an uncertainty of $\pm 30$% due to the assumed
proton to electron number density ratio. The slope of the radio spectrum is
assumed to be $\alpha=-0.7$, as in Sect. 3.6. This corresponds to the cosmic
ray electron spectrum in terms of Lorentz factor $\gamma$: $N_{\rm
e}(\gamma)\propto\gamma^{-2.4}$. FIR photons at $70\,\mu$m, for example, are
up-scattered to the 4-8 keV range by $\gamma\sim 500$-700. Following Persic et
al. (2008) with these conditions, the expected 4-8 keV IC luminosity is found
to be $0.6\times 10^{39}$ erg s-1. This agrees with the decomposed IC emission
luminosity found above.

###  4.3 Metal-rich hot gas

Even given its small contribution to the continuum emission, the thermal
emission from the hot gas of $kT\simeq 5$ keV is the source of the majority of
Fe xxv line, as shown above, and can be traced by the enhanced Fe xxv EW (Fig.
4). The map shows that the presence of the hot gas component is limited within
a small distance from the starburst disc and seen to be much stronger on the
northern side, suggesting an asymmetric ejection of hot gas.

A northern asymmetry in outflow structures have also been observed in other
wavelengths. In the mid-infrared (mid-IR) image taken by the Subaru-COMICS
with the [Ne ii] filter at $12.8\thinspace\mu$m, a few wisps are seen only on
the northern side, extending from the starburst disc (Gandhi et al. 2011). The
same features are noted also in radio. Fig. 16 shows the deep JVLA image of
the central part of M82 at 3-GHz, taken on 2015 August 16. The overlaid COMICS
contours shows the coincidence of the northern wisps between mid-IR and radio.
Wills et al. (1999) noted these radio counterparts in the earlier VLA images
and identified four galactic chimneys, based on the emission void to the south
of the radio SNR 41.95+57.5. Here, we refer to a chimney as a collimated
structure of a super bubble breaking out of the galactic disc. The primary
energy source here is a sequence of SNe produced by a starburst and its
formation has been formulated by earlier study (Tomisaka & Ikeuchi 1986; Mac
Low & McCray 1988; Norman & Ikeuchi 1989). The mid-IR and radio emission
voids, embraced by the wisps, correspond to chimneys that are expected to be
filled by hot gas (Tomisaka & Ikeuchi 1988).

Figure 15: Fe xxv EW map overlaid by the Subaru/COMICS mid-IR [Ne ii]
contours. The colour bar shows the Fe xxv EW in keV. The white arrows
indicates the three Fe xxv-enhanced regions I, II, and III, which appear to
fill the chimneys and to be connected to the mid-IR knot ’E1’ (Achtermann &
Lacy 1995). The orange arrow indicates the chimney with an expanding bubble
identified around the SNR 41.95+57.5 by Wills et al. (1999). The two region-
segments dX34 and dX35, discussed in the text, are also indicated.

Fig. 15 shows that the Fe xxv EW enhancement regions, as indicated by arrows
I, II, and III. They appear to fill the mid-IR voids and to be traced back to
the mid-IR knot ’E1’ of Achtermann & Lacy (1995). This can be understood that
the metal-rich hot gas produced in the E1 knot was channelled into the
chimneys and fills their interior.

The mean density of the hot gas is found to be $n=0.09$ cm-3. We note that if
the hot gas does not fill the full diffuse emission volume, the density
increases by $f^{-1/2}$, where $f$ is the filling factor. The pressure of hot
gas with $kT=5$ keV is then log $P\approx 6.7$ [$K$ cm-3]. The hot gas of this
temperature has a thermal velocity ($\sim 3000$ km s-1) much larger than the
galaxy’s escape velocity ($\sim 460$ km s-1, Strickland & Heckman (2009)) and,
consequently, flows out. However, as the dense molecular gas in the starburst
disc has a comparable pressure, log $P\sim 6.5$ [$K$ cm-3], measured by Naylor
et al. (2010), the gas would flow out only in a favourable direction set out
by the chimneys.

###  4.4 Effects of supernova feedback

Figure 16: JVLA map at 3 GHz overlaid by the Subaru-COMICS [NII] contours.
Three (or four) ’wisps’ are seen both in mid-IR and radio on the northern
side. The green diamond indicates the radio source, 43.21+61.3 of Rodriguez-
Rico et al. (2004), which coincides with the X-ray source, Xp9, at the
position of the radio kinematic centre. The five brightest radio SNRs, all of
which have X-ray counterparts, are encircled in white. The radio SNR
41.95+57.5 (=X-ray SNR, Xp15) and presently the brightest radio SNR of
SN2008iz (Brunthaler et al. 2009) are indicated.

The recent star formation in M82 is believed to be triggered by a tidal
interaction with M81 (e,g, Yun et al. 1993), resulting in two short ($\sim 1$
Myr) bursts of star formation 5 Myr and 10 Myr ago (Rieke et al. 1993; Förster
Schreiber et al. 2003). The first intense burst peaking at the nuclear region
was followed by the second burst in a circumnuclear ring. The mid-IR E1 knot
is likely clustered H ii regions and is associated with the eastern part of
the starburst ring, just inside the molecular concentration (Achtermann & Lacy
1995). After the second burst, which had an initial star formation rate (SFR)
of $\sim 43\leavevmode\nobreak\ M_{\sun}$ yr-1, the SFR declined rapidly
(Förster Schreiber et al. 2003). The present SFR, based on the FIR luminosity
(Kennicutt 1998), corrected for the flattened IMF at lower masses (Rieke et
al. 2009), is 4.3 $M_{\sun}$ yr-1 over the mass range of 0.1-100 $M_{\sun}$.

According to the two-burst model, the starburst ring should have accumulated
numerous SNRs but also still keeps producing new SNe. However, some 40 radio
SNRs in M82 all avoid the enhanced star-forming knots. While this has been a
subject of discussion in various articles (e.g. Golla et al. 1996; de Grijs
2001; Alonso-Herrero et al. 2003), it could be understood when taking the
starburst age and local SN feedback into account. We illustrate it using E1 as
an example, since it is part of the starburst ring where the second burst took
place 5 Myr ago for a duration of 1 Myr.

In the simplified starburst episode assumed above, as a massive star with a
mass of $M$ lives for $\sim 30(M/8\,M_{\sun})^{-2.5}$ Myr, stars with masses
of $\ga 17M_{\sun}$ already died, leaving both SNe and SNRs. Taking the
typical SFR surface density $5\times 10^{-4}M_{\sun}$ yr-1 pc-2 for the second
burst (Förster Schreiber et al. 2003), a circular region with a diameter of 3″
gives a SFR of $\sim 1\leavevmode\nobreak\ M_{\sun}$ yr-1 for E1. Then E1 has
accumulated some 2000 SNRs at present time. Here we used the SFR to SN rate
conversion factor of 0.0088 of Horiuchi et al. (2011). The series of SN
explosions produce a hot cavity and its filling factor within the star-forming
knot grows as the number of SNe increases (McKee & Ostriker 1977). In this
rarefied environment, SNe and SNRs do not cool. This means they directly heat
the ambient medium by providing much of the energy in mechanical form and thus
could be difficult to detect due to low brightness.

The above process produces metal-rich hot fluid of a temperature of $10^{8}$ K
(Chevalier & Clegg 1985). In our Chandra observations, the region-segment dX34
coincides with the central part of E1 (Fig. 15). The X-ray spectrum of dX34
shows no Fe xxv line (Fig. 5), suggesting that the putative hot fluid, too,
radiates little with its low emission measure. On the other hand, abundant
amounts of dust are produced by SNe (Gall & Hjorth 2018), providing a source
of strong FIR emission. The region also acts as a cosmic ray reservoir, since
a significant fraction ($\sim 10$%) of SN explosion energy may go efficiently
into cosmic ray acceleration (Pais et al. 2018; Grenier et al. 2015; Caprioli
& Spitkovsky 2014; Bell et al. 2004). Thus the local SN feedback and dust
production together produce IC X-ray emission, which dominates the dX34
spectrum. However, once the metal-enriched hot fluid flows out of E1, it
entrains the surrounding cool ISM. This leads to a drop in temperature, as
demostrated by simulations (e.g. Tomisaka & Ikeuchi 1988), and an increased
density makes the fluid sufficiently radiative, resulting in sub-$10^{8}$ K
gas with strong Fe xxv. This transition can be illustrated by the spectrum of
dX35, which lies immediately outside E1 and at the base of the south-bound Fe
xxv extension III (Fig. 15). The segments dX34 and dX35 are both located in
the disc plane and separated by only $\sim 20$ pc, yet the strong Fe xxv line
in the dX35 spectrum contrasts sharply with that of dX34 with no Fe xxv.

The above hypothesis explains how, despite lacking detectable SNRs, E1
exhibits the X-ray spectrum dominated by IC emission, yet it acts as a hub of
the Fe xxv-enhanced emission. The total energy deposited by 2000 SNe in E1
over the last 5 Myr amounts to $\sim 2\times 10^{54}$ erg. About 10% of this
energy would go to cosmic rays, and $\sim 5$% is radiated away via the Fe xxv-
emitting hot gas, as observed. Therefore the majority of the SN energy should
have gone to the chimney in knetic form and was transported to the halo.

###  4.5 Detectability of radio and X-ray SNRs

The brightest five radio SNRs have X-ray counterparts (Iwasawa 2021, see Fig.
16). An inspection of the deep JVLA image found a faint radio source which
appears to coincide with another X-ray SNR, Xp17. This makes six X-ray–radio
correspondences out of the seven X-ray SNRs detected in Iwasawa (2021), which
is remarkably high, compared to those in other nearby galaxies (Leonidaki et
al. 2010; Long et al. 2010; Pannuti et al. 2007), suggesting that they share a
favourable condition, for example, dense environment, to be highly radiative
in both wavelengths. Such a dense environment no longer exists in the interior
of the past burst sites, as described above. Instead, freshly formed giant
molecular clouds (GMC), whose lifetime could be a few Myr (Dobbs & Pringle
2013), may sustain the present star-forming activity which dispenses young
SNRs. In fact, all the seven X-ray SNRs are found to reside within GMCs with
masses of $4\times 10^{3}\,M_{\sun}$ \- $1.7\times 10^{7}\,M_{\sun}$,
catalogued by Krieger et al. (2021) who mapped them in CO(1-0) with IRAM NOEMA
(the median projected distance of those X-ray SNRs from the respective cloud
centres is 34 pc while the median cloud redius 54 pc), supporting the above
idea. They provide an ideal environment for those young radio and X-ray SNRs
which are less than a few hundreds yr old (e.g. Fenech et al. 2010; Iwasawa
2021), since there have been little pre-existing SN feedback. The estimated
radio SN rates are in the range of 0.03-0.1 yr-1 (Unger et al. 1984; Kronberg
et al. 1985; Muxlow et al. 1994; Huang et al. 1994; Fenech et al. 2008, 2010),
corresponding to SFR of 3.4-11 $M_{\sun}$ yr-1, in agreement with the current
SFR. Different manifestations of SN feedback depending on their molecular gas
environment, as discussed for nearby star-forming galaxies in the PHANGS
survey (Mayker Chen et al. 2022), is also in support of our argument.

###  4.6 6.4 keV cold Fe K line

The origin of the 6.4 keV cold Fe K line is unclear. Liu et al. (2014) argued
irradiation of optically thin $N_{\rm H}$$\sim 10^{22}$ cm-2 cold ISM by the
luminous X-ray binaries can account for the total line luminosity. The two
segments of high surface brightness in 6.4 keV emission (dX14 and 28) near the
bright X-ray binary concentration in the western part may fit this scenario.
However, the mapped distribution of the line emission suggests its diffuse
nature and the extended emission towards the eastern part is difficult to
account for by photoionisation of bright X-ray binaries alone.

Here, we examine an alternative line production mechanism by cosmic ray
bombardment, which has been proposed for explaining 6.4 keV Fe lines seen in
the Galactic centre (Valinia et al. 2000; Dogiel et al. 2009) and the
surroundings of some of the Galactic SNRs (Tatischeff et al. 2012). This
process is compatible with the diffuse nature of the emission across the
starburst region. While the energy density of cosmic ray in M82 is expected to
be high, the line production is inefficient: $\eta=L_{6.4}/L_{\rm CR}\sim
10^{-6}$ at most (Tatischeff et al. 2012). With the SFR $=33M_{\sun}$ yr-1
over the past 15 Myr, the SN rate would be $\nu_{\rm SN}\sim 0.3$ yr-1.
Assuming $\epsilon=10$% of the SN energy ($10^{51}$ erg per SN) goes to cosmic
rays, the efficiency of $\eta=10^{-6}$ gives an expected 6.4 keV line
luminosity of $\sim 1\times 10^{36}(\epsilon/0.1)(\nu_{\rm SN}/0.3\,{\rm
yr}^{-1})(\eta/10^{-6})$ erg s-1, if SNe are the sole accelerator of cosmic
rays. This estimate is more than one order of magnitude below the total 6.4
keV line luminosity (Table 2) and cannot be a major source of the detected
line emission. Similar to the Galactic centre (Sgr B2 clouds, in particular,
Zhang et al. 2015; Rogers et al. 2022; Kuznetsova et al. 2022), while the 6.4
keV line emission of the cosmic ray origin accounts for the low-brightness,
extended emission in M82, the brightest spots need to be explained by
irradiation of transient flaring sources, whether they are M82 X-1 or
transient X-2, which can reach $L_{\rm X}>10^{40}$ erg s-1, (Kaaret et al.
2001; Brightman et al. 2019), or even an active nucleus, as discussed below. A
long term monitoring of the brightest regions can test the photoionisation
scenario through variability in line flux.

###  4.7 Possible AGN at the galactic centre

The previous claim of a low-luminosity AGN in M82 was based on hard X-ray
variability observed with ASCA (Ptak & Griffiths 1999; Matsumoto & Tsuru
1999), which, as we know now, is caused by the ULXs. Here, we examine how
plausible the faint X-ray source, Xp9, at the galactic centre might be an AGN.
Xp9 has been assumed to be an X-ray binary but the presence of the radio
counterpart makes it unique among the X-ray binaries detected in the central
region. The deep JVLA image verifies the radio counterpart, as marked by a
magenta diamond in Fig. 16, whilst none of the other X-ray binaries (including
the ULXs) have a point-like radio counterpart in the JVLA image (Xp6 and Xp16
coincide with compact radio sources but they are radio SNRs, Fenech et al.
(2010)). An X-ray binary could have a radio jet in the hard state. However, as
Galactic black hole binaries typically have radio luminosity $L_{\rm R}\leq
10^{30}$ erg s-1(e.g. Gallo et al. 2012, the micro quasar GRS1915+105
occasionally reaches $1\times 10^{32}$ erg s-1, as an exception) in the hard
state, no radio detection is expected for X-ray binaries in M82, in agreement
with the lack of radio counterpart of the other X-ray binaries. In contrast,
assuming a flat spectrum and 4 mJy at 5GHz, Xp9 has log $L_{\rm R}\simeq 32.5$
[erg s-1], which is comparable to that of Sgr A⋆. In the context of the black
hole fundamental plane (Merloni et al. 2003), radio luminosity, $L_{\rm R}$,
increases with black hole mass, $M_{\rm BH}$, and thus the radio loudness of
Xp9 points to a large $M_{\rm BH}$.

The X-ray spectrum of Xp9 is very hard with the power-law slope of
$\alpha\sim-1$ and the source is visible only above 3 keV. The hard spectrum
is likely due to strong absorption: if an intrinsic slope of $\alpha=0.7$ is
assumed, absorbing column density would be $N_{\rm H}$ $\sim 2\times 10^{23}$
cm-2. The observed 4-8 keV flux is $3.0\times 10^{-14}$ erg s-1 cm-2 and the
absorption-corrected 2-10 keV flux would be $1.2\times 10^{-13}$ erg s-1 cm-2.
The latter corresponds to log $L_{\rm X}\simeq 38.27$ [erg s-1]. The 4-7 keV
light curve remains stable over 16 yr of the Chandra observations (Iwasawa
2021). The X-ray luminosity is compatible to a bright X-ray binary but could
also be of low-luminosity AGN, powered by an intermediate-mass black hole or a
supermassive black hole operating at inefficient accretion flow, such as an
advection-dominated accretion flow (ADAF) (Narayan & Yi 1994).

Gaffney et al. (1993) obtained the nuclear enclosed mass
$M\leavevmode\nobreak\ (r<8.5\thinspace{\rm pc})=3\times 10^{7}M_{\odot}$,
using the CO absorption bandhead kinematics (see also Greco et al. 2012). It
can be considered as an upper limit of the mass of a putative black hole,
$M_{\rm BH}$. However, $M_{\rm BH}\sim 10^{6}\,M_{\sun}$, similar to that of
Sgr A⋆, would be possible only if a significant portion of the stellar disc
was stripped away on the close encounter with M81, leaving M82 as a bulge-
dominated galaxy, as proposed by Sofue (1998), otherwise it is deemed to be
overmassive for the galaxy with the total mass of $10^{10}\,M_{\sun}$ (Greco
et al. 2012). With the observed radio and X-ray luminosities, the black hole
fundamental plane gives $M_{\rm BH}$ of $10^{3}$-$10^{4}\,M_{\sun}$ (Merloni
et al. 2003; Gültekin et al. 2019). While whether black holes in this mass
range exist is presently unclear, it is compatible with the argument of M82 to
be a bulgeless galaxy (Mayya & Carrasco 2009). Some low-luminosity AGNs hosted
by small, bulgeless galaxies, such as NGC 4395, have black hole masses of the
order of $10^{5}\,M_{\sun}$ (Peterson et al. 2005). When $M_{\rm
BH}=10^{5}\,M_{\sun}$ is assumed, the typical bolometric correction of
$\kappa\equiv L_{\rm bol}/L_{\rm X}=16$ for low-luminosity AGN (Ho 2008) gives
the bolometric luminosity of Xp9 to be $3\times 10^{39}(\kappa/16)$ erg s-1.
Then the Eddington ratio would be $\lambda\sim 2\times
10^{-4}(\kappa/16)(M_{\rm BH}/10^{5}\,M_{\sun})^{-1}$, well within the ADAF
range. The flat radio spectrum is similar to Sgr A⋆ and other sources that are
suspected to be operating in ADAF, slightly steeper than $\sim 0.3$ predicted
for ADAF (Mahadevan 1997). There is no notable evidence for past elevated AGN
activity, such as the Fermi bubble in our Galaxy, although the starburst
activity might disguise it.

The radio-to-X-ray spectral energy distribution of Xp9 is shown in Fig. 17.
The mid-IR points are upper limits from Gandhi et al. (2011). The 12-$\mu$m
luminosity predicted by the ADAF models (Mahadevan 1997; Kino et al. 2000) and
the mid-IR–X-ray relation of Gandhi et al. (2009) is around
$10^{38}$-$10^{39}$ erg s-1. This is translated to a flux density of 0.7-7
$\mu$Jy, which may be barely detectable with the upcoming James Webb Space
Telescope-MIRI observation (ID: 1701). As the mid-IR luminosity expected from
an X-ray binary is a few orders of magnitude farther down, any detection with
JWST would point to the low-luminosity AGN hypothesis.

Figure 17: Spectral energy distribution of Xp9. The radio data points are from
Rodriguez-Rico et al. (2004). The mid-IR data points are upper limits obtained
from the Subaru-COMICS images (Gandhi et al. 2011). The luminosity range at 12
$\mu$m, expected from the low-luminosity AGN hypothesis, is indicated by the
dotted-line, which could be within the reach of the upcoming JWST
observations.

##  5 Conclusions

We present the spatially resolved spectral map of the 4-8 keV diffuse emission
in M82 at a few arcsec resolution, after removing point-like sources. Our
findings are summarised as follows.

  1. 1.

The EW of the Fe xxv line from hot gas varies widely across the diffuse
emission region, including areas with EW $<0.1$ keV, suggesting the presence
of non-thermal emission. The morphology of the diffuse X-ray emission
resembles those of the FIR and radio emission, in favour of inverse Compton
scattering off the FIR photons by cosmic ray electrons as the origin of the
non-thermal emission.

  2. 2.

We found that the 4-8 keV diffuse emission is composed of three spectral
components with distinct origins: 1) inverse Compton emission which carries
$\sim 70$% of the continuum luminosity in the band; 2) the hard tail of the
soft X-ray wind emission of $kT\sim 1$ keV; and 3) metal-rich, hot gas
emission of $kT\sim 5$ keV, which accounts for the majority of the observed Fe
xxv line but is a minor component of the continuum.

  3. 3.

The hot gas, traced by enhanced Fe xxv EW, is found in a limited area near the
galactic disc and appears to flow out from the eastern part of the starburst
ring and fills the chimneys marked by mid-IR and radio voids. The chimneys
dominate in transporting the flow of SN energy from the disc to halo in M82.

  4. 4.

The brightest, young X-ray and radio SNRs are found to reside in GMCs that are
presumably newly formed and thus free from strong SN feedback. This could
explain their positional displacement from the past active star-forming sites
where any SN would be little radiative due to the hot, low-dendity interior.

  5. 5.

The faint X-ray source, Xp9, located at the galactic centre, is unusual for an
X-ray binary to have a luminous radio counterpart with a flat spectrum,
offering a possibility to be a low-luminosity AGN with $L_{\rm X}\sim 10^{38}$
erg s-1 in an ADAF phase.

A similar technique employed in this work can be applied with advanced future
X-ray mission with high angular resolution, such as AXIS or LYNX, to reveal
effects of feedback on the ISM in a range of nearby galaxies, including those
with central AGN.

###### Acknowledgements.

We thank the referee for helpful comments. This research made use of data
obtained from Chandra X-ray Observatory, of which the archive is maintained by
Chandra X-ray Center (CXC) and NASA/IPAC Extragalactic Databases (NED) and
Infrared Science Archive (IRSA), which are funded by the NASA and operated by
the California Institute of Technology. Software packages of CIAO 4.12,
HEASoft 6.27.1, Astropy, PyMC, Matplotlib, Numpy, Pandas, Scipy and IPython
were used for data analysis. KI acknowledges support by grant
PID2019-105510GB-C33 funded by MCIN/AEI/10.13039/501100011033 and “Unit of
excellence María de Maeztu 2020-2023” awarded to ICCUB (CEX2019-000918-M). MPT
acknowledges financial support from the Spanish Ministerio de Ciencia e
Innovación (MCIN), the Agencia Estatal de Investigación (AEI) through the
”Center of Excellence Severo Ochoa” award to the Instituto de Astrofísica de
Andalucía (SEV-2017-0709) and through grant PID2020-117404GB-C21 funded by
MCIN/AEI/10.13039/501100011033.

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##  Appendix A Fe K lines in thermal emission spectrum

Properties of Fe K line emission seen in a thermal emission spectrum, when
described by a Gaussian as done in this work, are illustrated in Fig 18. We
simulated spectra using apec assuming the collisional ionisation equilibrium
condition and obtained these properties. When the gas temperature $kT$ exceeds
2 keV, Fe xxv emission becomes prominent. The line centroid energy moves
depending on $kT$. When $kT$ is in the range of 4-6 keV, the centroid energy
in found at 6.68 keV. Fe xxv is a triplet which is unresolved at the CCD
resolution. A single Gaussian fit would give $\sigma\simeq 30$ eV for the line
blend. The H-like Fe xxvi emission arises when $kT$ exceeds $\sim$3 keV, and
the line intensity ratio between Fe xxvi and Fe xxv changes as a function of
$kT$. The observed line ratio of $0.14\pm 0.09$ indicates $kT\approx 4.5\pm 1$
keV, if it is a single component gas. Fe xxv EW varies as a function of
temperature at a given metallicity. This is illustrated in the figure in the
case of the Solar metallicity. Finally, metallicity dependence of Fe xxv EW
for gas temperatures of $kT=3$ keV and 5 keV is shown. We note that the
dependence is not linear but flattened as increasing metallicity.

Figure 18: Fe K line properties of thermal emission spectrum. Top-left: Line
centroid energy as a function of gas temperature; Top-right: Line intensity
ratio of Fe xxvi and Fe xxv as a function of gas temperature. The dashed-line
indicates the observed line ratio with 68% error region in grey shade; Bottom-
left: Fe xxv EW as a function of temperature when the Solar metallity is
assumed; and Bottom-right: Fe xxv EW as a function of metallicity for gas
temperature of $kT=3$ keV (blue) and $kT=5$ keV (red).

##  Appendix B An unidentified 4.5 keV emission feature

Figure 19: Diffuse emission spectrum of the central part of M82 in the 3.3-5
keV band. It illustrates the excess emission at 4.5 keV. The red histogram
indicates the best fitting apec model, which describes the Ca feature at 3.9
keV. No strong atomic line feature that corresponds to the 4.5 keV emission is
expected. The flux density is in units of $10^{-14}$ erg s-1 cm-2 keV-1.

There is a possible line-like excess at 4.5 keV in the total diffuse emission
spectrum. The Ca K band spectrum at $\sim 4$ keV indicates the temperature
$kT\sim 1.8$ keV (Fig. 19). No emission-line feature is expected at 4.5 keV in
a thermal emission spectrum of a similar temperature. We examined the 4.1-5
keV data for its detection with a power-law model with or without a narrow
Gaussian line. The lower energy bound was chosen to avoid the Ca K emission.
To optimise a line detection, we rebinned the data with 60-eV intervals, which
samples the major part of a line feature by three bins at 4.5 keV, where the
spectral resolution is FWHM $\simeq 140$ eV. The Gaussian centroid is found at
$4.51\pm 0.03$ keV. The line intensity is $(7.8\pm 2.3)\times 10^{-7}$ ph cm-2
s-1, corresponding to a EW of $26\pm 8$ eV. The continuum slope is
$\alpha=1.8\pm 0.3$ when $N_{\rm H}$$=4\times 10^{22}$ cm-2 is assumed. We
compared between the fits with and without the Gaussian line, using the Akaike
Information Criterion (AIC) and Bayesian Information Criterion (BIC). The
relative likelihood of the inclusion of the 4.5 keV line is 20 from BIC and 40
from AIC. The difference comes from the degree of penalisation on extra
parameters. The detection of the line feature is reasonably strong. A possible
identification is a neutral Ti K at 4.51 keV. The cold Fe K line at 6.4 keV is
detected and might share the same origin. However, the 4.5 keV line is far too
strong to match the cosmic abundance of Ti, which is $\sim 2$ orders of
magnitude smaller than Fe. Although the cosmic rays have much more elevated Ti
abundance relative to Fe due to spallation, it is not relevant unless the line
production is due to the charge exchange.

##  Appendix C Image of dX36 and dX37 region from no transient flaring
intervals

Figure 20: Comparison of the 4-8 keV images of the transient sources Xp7 and
Xp11, taken from a) the total 13 exposures; and b) the eight exposures where
both sources were in quiescence. The two transient sources are marked on the
left panel.

The region segments dX36 and dX37 contain the transient sources Xp7 and Xp11,
respectively. Xp7 exhibited flares during the first two observations in 1999,
while Xp11 during the three observations in 2010 (see the Chandra observation
log in Table 1.). Fig. 20 shows the 4-8 keV image of the region around the two
transient sources, obtained from the full 13 exposures (in the left panel) and
that of the same region from eight exposures in which neither of them were in
the flaring states (in the right panel). No point-like excess is seen at the
positions of the two sources in the image when they were in quiescence. This
justifies the use of their quiescence data to study the diffuse emission
properties in the segments dX36 and dX37.

##  Appendix D X-ray extinction map

The distribution of X-ray absorbing column density over the diffuse emission
region is presented in Fig. 21. The absorbing column density in each region-
segment was obtained in two steps. The segment dX31 shows the least absorbed
soft-band spectrum and fitting an absorbed apec model to the 0.9-1.7 keV
spectrum gives a temperature of $kT=0.87^{+0.02}_{-0.01}$ keV, metallicity of
$1.0^{+0.4}_{-0.2}Z_{\odot}$ and $N_{\rm H}$ $=1.11(1.07-1.14)\times 10^{22}$
cm-2. Firstly, we fitted $N_{\rm H}$ of the spectra of all the other segments
in the same band, assuming the same temperature and metallicity. These $N_{\rm
H}$ are all in the range of (1-2) $\times 10^{22}$ cm-2. They represent
absorption for the soft X-ray wind and might not reflect the absorption
towards the inner part where the hard X-ray emission comes from. All the
spectra were fitted again but in the 4-7 keV band, assuming $kT=6$ keV. When
this hard-band $N_{\rm H}$ exceeds that for the soft band, the hard-band
$N_{\rm H}$ was adopted. This applies to dX1, 14, 15, 18, 19, 26, 27, and 28,
for which the 4-7 keV continua show a hard slope. It is found that a few
regions show $N_{\rm H}$ up to $10^{23}$ cm-2.

For comparison, the optical image of the region taken in $R$ band by the Bok
2.3-m telescope at Kitt Peak National Observatory, overlaid by the X-ray
region segments, is also shown in Fig. 21. The image was retrieved from NED.
The region segments showing high $N_{\rm H}$ values generally coincide with
the dust lanes seen in the optical image.

Figure 21: Extinction across the 4-8 keV diffuse emission region. a) X-ray
absorbing column density, $N_{\rm H}$, map in units of $10^{22}$ cm-2. b) The
$R$-band image of the central part of M82, taken by the Bok 2.3-m telescope at
Kitt Peak National Observatory, overlaid by the 38 region segments where the
X-ray absorbing columns were measured.

##  Appendix E Galactic centre positions

The positions of Xp9, radio source 43.21+61.3, the three kinematic centre
measurements, the nuclear position measured by WISE ($W1$) in the WISE
eXtended Source Catalogue (WXSC), and the two 2.2 $\mu$m peak measurements,
plotted in Fig 12, are reproduced in the Table below.

Table 5: Galactic centre positions

| R.A.(J2000) | Dec. (J2000) | ref
---|---|---|---
Xp9 | 52.0 | 47.3 | 1
43.21+61.3 | 51.95 | 47.2 | 2
H i kinematic centre | 51.9 | 47.2 | 3
Ne ii kinematic centre | 52.14 | 46.4 | 4
H92$\alpha$ ring centre | 52.0 | 46.9 | 5
WISE | 51.95 | 47.2 | 6
$2.2\mu$m peak (R80) | 52.6 | 47.2 | 7
$2.2\mu$m peak (L90) | 52.3 | 46.2 | 8
888Positions in J2000. The RA and Dec are given as the offset from RA =
$09^{\rm h}55^{\rm m}00^{\rm s}$, Dec = $+69\degr 40\arcmin 00\arcsec$. 1:
X-ray source in Iwasawa (2021); 2: Radio source in Rodriguez-Rico et al.
(2004); 3: Radio kinematic centre of Weliachew et al. (1984); 4: Ne ii
kinematic centre with an ellipse ring fit of Achtermann & Lacy (1995); 5:
H92$\alpha$ ring centre from Rodriguez-Rico et al. (2004); 6: WISE nuclear
position of Jarrett et al. (2019); 7: 2.2 $\mu$m peak from Rieke et al.
(1980); and 8: Lester et al. (1990). The positional errors are all $\sim
0.5\arcsec$ except for 1.5″ for the declination of the $2.2\mu$m peak of Rieke
et al. (1980).

##  Appendix F X-ray spectra of the diffuse emission from the 38 segments

Figure 22: 0.7-7 keV Chandra spectra of the 38 region segments, dX0 through
dX37, over the diffuse emission. The flux density, $F_{\rm E}$, is in units of
$10^{-14}$ erg s-1 cm-2 keV-1. The two highest energy bins corresponds to the
two Fe-line bands of cold Fe K at 6.4 keV and Fe xxv at 6.7 keV.