# The interstellar medium in young supernova remnants: key to the production
of cosmic X-rays and $\gamma$-rays

Hidetoshi Sano11affiliationmark:  Yasuo Fukui22affiliationmark:

###### Abstract

We review recent progress in elucidating the relationship between high-energy
radiation and the interstellar medium (ISM) in young supernova remnants (SNRs)
with ages of $\sim$2000 yr, focusing in particular on RX J1713.7$-$3946 and
RCW 86. Both SNRs emit strong nonthermal X-rays and TeV $\gamma$-rays, and
they contain clumpy distributions of interstellar gas that includes both
atomic and molecular hydrogen. We find that shock–cloud interactions provide a
viable explanation for the spatial correlation between the X-rays and ISM. In
these interactions, the supernova shocks hit the typically pc-scale dense
cores, generating a highly turbulent velocity field that amplifies the
magnetic field up to 0.1–1 mG. This amplification leads to enhanced nonthermal
synchrotron emission around the clumps, whereas the cosmic-ray electrons do
not penetrate the clumps. Accordingly, the nonthermal X-rays exhibit a spatial
distribution similar to that of the ISM on the pc scale, while they are
anticorrelated at sub-pc scales. These results predict that hadronic
$\gamma$-rays can be emitted from the dense cores, resulting in a spatial
correspondence between the $\gamma$-rays and the ISM. The current pc-scale
resolution of $\gamma$-ray observations is too low to resolve this
correspondence. Future $\gamma$-ray observations with the Cherenkov Telescope
Array will be able to resolve the sub-pc-scale $\gamma$-ray distribution and
provide clues to the origin of these cosmic $\gamma$-rays.

00footnotetext: National Astronomical Observatory of Japan, Mitaka, Tokyo
181-8588, Japan<EMAIL_ADDRESS>Department of
Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan;
<EMAIL_ADDRESS>

Keywords cosmic rays — $\gamma$-rays: ISM — ISM: clouds — ISM: supernova
remnants

##  1 Introduction

Cosmic-ray acceleration in supernova remnants (SNRs) is the most promising
mechanism for accelerating Galactic cosmic rays, which mainly comprise
relativistic protons with energies less than 1015.5 eV. Considerable efforts
have been devoted to theoretical works to elucidate the details of particle
acceleration (e.g., Bell, 1978; Blandford & Ostriker, 1978). Recent progress
in X-ray and $\gamma$-ray observations has allowed us to explore the origin of
cosmic rays. Young SNRs, which ages around 2000 yr, are of particular interest
because they emit higher-energy X-rays and $\gamma$-rays than SNRs younger
than 1000 yr (e.g., G1.9$+$0.3 at $156\pm 11$ yr, Carlton et al., 2011) or
those older than several tens of thousands of years (e.g., W44 at $\sim$20,000
yr, Wolszczan et al., 1991). In the present article, we focus on the young
SNRs RX J1713.7$-$3946 (hereafter RXJ1713) and RCW 86, which are characterized
by the emission of bright X-rays and TeV $\gamma$-rays.

The origin of $\gamma$-rays from young SNRs is currently under debate, and two
mechanisms have been suggested to explain them. One is a leptonic process in
which cosmic-ray electrons collide with low-energy photons, boosting them into
the $\gamma$-ray regime via the inverse Compton process. The other is a
hadronic process in which cosmic-ray protons collide with interstellar protons
to produce neutral pions that decay into two $\gamma$-rays. It is important to
verify whether the $\gamma$-rays are of hadronic origin for establishing
whether SNRs are a major source of cosmic rays in the Galaxy.

In previous works that considered the hadronic model for the $\gamma$-ray
emissivity of an SNR, the number density of targeted interstellar protons has
been used (e.g., to estimate the cosmic-ray energy from the $\gamma$-ray
luminosity). However, strongly shocked matter (e.g., shock-ionized plasma
traced by optical lines and free–free radio/X-ray continuum and shocked
molecular hydrogen observed as near-infrared lines), which occupies only a
small portion of the interstellar medium (ISM), has mainly been considered as
the target gas. Neutral molecular and atomic hydrogen gas has not been
considered to play a major role in controlling the radiative properties of
SNRs, except for some pioneering works (e.g., Aharonian et al., 1994), while
the interaction of SNRs with the ISM has been a subject of interest in some
other works (e.g., Dubner & Arnal, 1988; Dubner et al., 1998, 1999, 2002a,
2002b, 2004; Tatematsu et al., 1987, 1990a, 1990b; Seta et al., 1998, 2004;
Arikawa et al., 1999). In this article, we focus on the bulk neutral gas that
dominates the mass the ISM. Recent theoretical studies have revealed that the
associated ISM may play a major role in determining the radiative properties
of SNRs, and clarifying clarify the role of inhomogeneities in the ISM in
regulating the high-energy radiations is important (e.g., Inoue et al., 2012;
Celli et al., 2019). Here we review methods used to identify the ISM
associated with a SNR, a theoretical model that incorporates shock–cloud
interactions, and their theoretical implications for the origin of very-high-
energy $\gamma$-rays, with a focus on the SNRs RXJ1713 and RCW 86.

##  2 The Interstellar Medium (ISM)

The neutral ISM consists of the warm neutral medium (WNM) and the cool neutral
medium (CNM) (e.g., Draine, 2011). The WNM has a density of 0.1–10 cm-3 and a
spin temperature of 300–10000 K, while the CNM has a density of 10–103 cm-3
and a spin temperature of 10–300 K (e.g., McKee & Hollenbach, 1980; Heiles &
Troland, 2003). The masses of the two phases are comparable. The CNM comprises
clumps with a volume filling factor of a few percent, while the WNM occupies a
large volume of inter clump space (Draine, 2011; Fukui et al., 2018). The CO
clouds are formed in the CNM clumps, and their volume filling factors are also
very small ($\sim$3–4%, e.g., Inoue & Inutsuka, 2012; Tachihara et al., 2018).
This picture is significantly different from the conventional assumptions made
for (one-dimensional) models, which do not appropriately represent these two-
phase inhomogeneities.

The 21 cm Hi emission and 2.6 mm CO emission are good tracers of the ISM
associated with a SNR. Comparing a high-resolution X-ray image with the CO and
Hi distributions provides a powerful method for identifying the interaction
between an SNR and the ISM. Because electrons cannot penetrate the dense ISM
clumps, we find a small-scale anti correlation between the X-rays and dense
ISM clumps at sub-pc scales. Calculations of the ISM column density can be
performed using a CO-to-H2 conversion factor (for a review, see Bolatto et
al., 2013) and the Hi 21 cm emission, where corrections for the Hi optical
depth are required for the dense CNM.

Fig. 1 : Map of the ROSAT X-ray flux superposed on the NANTEN2 CO($J$ = 1–0)
intensity contours toward RX J1713.7$-$3946\. The CO velocity range is
integrated from $-11$ to $-3$ km s-1, which corresponds to the velocity
component interacting with the supernova remnant (SNR). The lowest contour
level and contour intervals are 4 K km s-1. From Fukui et al. (2003) with
permission

Although the scheme described above works successfully in general, one caveat
is that the intermediate density regime between 100 and 1000 cm-3 may not be
detectable in the CO emission because of the low CO abundance caused by photo
dissociation. In addition, the Hi emission may become optically thick in this
density regime, requiring a correction for saturation. Hi is observed to have
self-absorption dips; thus, some Hi gas is optically thick (e.g., Sato &
Fukui, 1978).

Fig. 2 : (a) Suzaku 5–10 keV X-ray image toward the northwestern shell of RX
J1713.7$-$3946\. The superposed contours represents the 12CO($J$ = 2–1)
integrated intensity obtained with NANTEN2. The black crosses indicate the
positions of IRAS (Infrared Astronomical Satellite) point sources. The area
enclosed by the black box is shown enlarged in Figure 2(b). (b) Enlarged view
of the $Suzaku$ X-ray image toward CO peak C superposed on the 12CO($J$ = 4–3)
core. The black contours indicate the total integrated intensity. The blue and
red contours represent the blue- and red-shifted outflow components,
respectively (from Sano et al. 2010, reproduced by permission of the AAS)

The existence of dark gas, which cannot be probed by either CO or Hi emission,
was suggested by EGRET $\gamma$-ray observations (Grenier et al., 2005) as
well as from submillimeter observations by Planck (e.g., Planck Collaboration
et al., 2011). Two possible explanations exist for the physical entity of the
dark gas: CO-dark H2 gas and optically thick Hi gas. The concept of CO-dark H2
gas is based on numerical simulations of the evolution of the H2/Hi gas
conducted by Wolfire et al. (2010), who showed that the self-shielding of H2
against UV is strong and a phase of H2 without an observable abundance of CO
can exist outside a CO cloud. This gas, which comprises H2 without CO, is a
reasonable model provided that Hi is converted mainly into H2. However, Fukui
et al. (2014, 2015) used the Planck/IRAS dust emission as a proxy for the
hydrogen column density and found that the Hi emission becomes optically thick
under the usual Hi gas condition, in which the Hi column density is assumed to
be proportional to the dust optical depth. The saturated Hi intensity becomes
weaker than in the optically thin case, resulting in a smaller Hi column
density than under the conventional optically thin approximation. The column
density corrected for the optical depth becomes larger than the optically thin
Hi column density by a factor of 1.5–2; this increased column density is large
enough to explain the dark gas (Okamoto et al., 2017; Hayashi et al., 2019a,
b; Mizuno et al., 2020). The optically thick Hi raises the possibility of Hi
being dominant compared with H2, which requires theoretical justification.
Simulations by Inoue & Inutsuka (2012) using a gas-evolution code similar to
that employed by Wolfire et al. (2010) presented another evolutionary model of
Hi flows showing Hi dominant outside the CO clouds. An important difference
exists between the initial conditions in these two simulations. Inoue &
Inutsuka (2012) adopted a lower Hi density, which includes both the CNM and
WNM. This is a realistic Hi distribution compared with dense Hi comprising
only the CNM, which was the initial condition assumed by Wolfire et al.
(2010). The lower density leads to slower Hi–H2 conversion than the high-
density initial condition and produces a rich Hi envelope surrounding the CO
gas instead of CO-dark H2 gas. This lends theoretical support to optically
thick Hi as an alternative. A possible new probe for this density regime is Ci
emission at submillimeter wavelengths, which can serve as another useful tool
(Tachihara et al., 2018).

##  3 RX J1713.7$-$3946

###  3.1 Distance determination: nonthermal X-rays and the interacting ISM

Except for several nearby SNRs with historical records, determining distances
to SNRs in the Milky Way is not straightforward, because most of SNRs lie in
the Galactic plane and are heavily obscured. Although the relation between
radio surface brightness and angular diameters ($\Sigma$–D relation) has been
used to estimate the distances to SNRs, the $\Sigma$–D relation does not
provide an accurate measure of distance because of its large scatter (e.g.,
Pavlovic et al., 2014). Shock-excited masers—e.g., OH (1720 MHz) masers—are
very useful for identifying the shocked interface, and the distance to SNRs
can be obtained from the radial velocities of the masers, although this method
can only be used for middle-aged SNRs that have interacted with the ISM for a
long time (e.g., Chen & Jiang, 2013). The ISM, including CO clouds and Hi gas,
associated with an SNR also provides a kinematic velocity, using which the
distance can be calculated by comparison with a kinematic model of the Galaxy.
The uncertainty is mainly due to the random cloud motions, which are on the
order of 10 km s-1.

Fig. 3 : Correlation between the peak X-ray flux and the clump mass
interacting with the SNR shock. The linear regression obtained by least-
squares fitting is shown by the solid line, for which the correlation
coefficient is $\sim$0.85 on the double-logarithmic scale. The labels indicate
the clump name: A, B, C, D$+$DW, E$+$I, G$+$GE, L, O$+$Ob$+$OSW, R, U, W, and
Z for CO clumps and SE-rim for an Hi clump. From Sano et al. (2013),
reproduced by permission of the AAS Fig. 4 : Schematic illustration of the
distributions of molecular (CO) clumps (open crosses), an atomic (Hi) clump
(open circle), and X-rays (shaded partial or full circles) superposed on the
SNR shell boundary from the $Suzaku$ X-rays (gray contours). The black open
crosses (CO clumps C, E, I, L, and OSW) indicate those fully surrounded by
X-rays. From Sano et al. (2013), reproduced by permission of the AAS Fig. 5 :
Top panels: Velocity channel distributions of Atacama Large
Millimeter/submillimeter Array (ALMA) 12CO($J$ = 1–0) toward the northwestern
shell of RXJ1713. The superposed contours represent Chandra synchrotron X-ray
intensities. The yellow crosses represent the positions of X-ray hotspots
identified by Higurashi et al. (2020). Typical CO cloudlets—named CL1–6—are
also indicated. Bottom panels: CO profiles of CL1–6 (black lines) and Gaussian
curves (red lines) fitted using the least-squares method. From Sano et al.
(2020b), reproduced by permission of the AAS

The nonthermal X-ray SNR RXJ1713 is a case for which two distances that differ
by a factor of 6 had been debated. It was first suggested that this SNR is
located at a distance of 1 kpc, assuming a typical average Hi density for the
X-ray absorption (Koyama et al., 1997), and it was identified as the SNR of
393AD from Chinese historical records (Wang et al., 1997). Slane et al. (1999)
claimed that CO clouds at $-69$ and $-94$ km s-1 are associated with the SNR,
from 8.8 arcmin resolution maps obtained with the CfA 1.2-m telescope, and
they derived a large kinematical distance ($\sim$6 kpc). These authors argued
that the Hi density toward RXJ1713 is lower than the typical Galactic average
owing to an accidental coincidence with a hole in the ISM, while a three-
times-larger distance implies an unusually large radius of $\sim$50 pc for an
age of $\sim$$10^{4}$ yrs. The 6 kpc distance has been questioned by a
subsequent high-resolution CO survey, which found another CO component at
$-10$ km s-1 to be associated with this SNR at the 2.6 arcmin resolution CO
maps obtained with the NANTEN 4-m telescope, as shown in Figure 1 (Fukui et
al., 2003; Moriguchi et al., 2005). The observational signature of this
association is the large-scale correlation (on scales of a few pc) between the
CO map and the ROSAT X-ray survey, which was confirmed in more detail by the
Suzaku data from Sano et al. (2010, 2013) (see Section 3.2). As the low
velocity CO gas is fainter by an order of magnitude than the $-69$ and $-94$
km s-1 clouds, it was ignored by Slane et al. (1999). The smaller distance is
now widely accepted, and it has been established that RXJ1713 is a young SNR
aged 1600 yr, which was historically recorded (Aharonian et al., 2004; Cassam-
Chenaï et al., 2004; Tanaka et al., 2008; Sano et al., 2015a; Tsuji &
Uchiyama, 2016). This shows that high resolution and sensitivity are crucial
in a comparison with the ISM, raising questions about the distance
determinations in previous low-resolution studies.

Fig. 6 : (a) Structure of the interstellar medium generated by the thermal
instability. The colored image shows the number density of atomic hydrogen,
and the black lines represent magnetic field lines. (b, c) Results at $t=1508$
yr after the injection of the parallel shock: (b) number density of atomic
hydrogen and (c) the magnetic field strength. From Inoue et al. (2009),
reproduced by permission of the AAS

###  3.2 Detailed correspondence between X-rays and ISM clumps

Fukui et al. (2012) showed that RXJ1713 is associated with molecular and
atomic gas, each having masses of $\sim$$10^{4}$ $M_{\odot}$. The ISM
distribution is shell-like, which an 8 pc radius, and the molecular cloud
cores are inside the shell. The shell is consistent with a core-collapse SNR,
for which the stellar winds from the high-mass progenitor evacuated the
surrounding ISM prior to the SN explosion.

Fig. 7 : Schematic of the shock–cloud interaction model (see the text). From
Inoue et al. (2012), reproduced by permission of the AAS

A comparison of the Suzaku X-ray data with the CO image revealed details of
the interaction (Sano et al., 2010). Figure 2 shows that the CO peaks A–E, G,
I, and L are anticorrelated with the X-ray peaks111Note that these anti-
correlations are not due to interstellar absorption, because the 5–10 keV
X-ray energy band is thought to be an absorption-free energy range when the
ISM proton column density is less than 1023 cm-2., indicating that the dense
cores hinder cosmic-ray electrons from penetrating them, and the X-rays are
rim-brightened on the surfaces of the CO cores (see also Maxted et al., 2012).
The cores in the shell were formed via gravitational instability over a
timescale of Myr prior to the SN explosion, and three of them (CO peaks A, C,
and D) are forming young stars, as shown by the infrared point sources (Sano
et al., 2010). In fact, peak C shows obvious signs of active star formation,
including bipolar outflows and an IRAS point source (see Figure 2a).

Sano et al. (2013) conducted a comprehensive study of the dense cores probed
by CO as well as by cold Hi, and found that the X-ray intensities are well
correlated with the masses of the ISM cores, as shown in Figure 3. Sano et al.
(2013) showed that more than 80% of the X-ray peaks, brighter than $5\times
10^{-4}$ counts s-1 pixel-1, are associated with the ISM cores, suggesting a
tight close connection between X-ray emission and the masses of the
interacting ISM cores (Figure 4). This suggests that the distribution of the
dense gas had a significant effect on regulating the X-ray distribution in the
recent 1000 yr, assuming a shock velocity of $\sim$4000 km s-1 (c.f., Tsuji &
Uchiyama, 2016), which has stimulated a detailed theoretical study of the
interaction between a shock front and clumpy ISM222According to proper-motion
measurements of the Chandra X-rays, the shock speed is measured to be $3900\pm
300$ km s-1 (Tsuji & Uchiyama, 2016). The shock propagates through low-density
intercloud regions without much deceleration (see also Section 3.3). Because
the shocked molecular clouds are located within $\sim$4 pc from the shock
front, the clouds have regulated the X-ray distribution in the most recent
1000 yr..

Most recently, Sano et al. (2020b) obtained high-resolution CO observations
(with $\sim$0.02 pc resolution) toward the northwestern shell of RXJ1713 using
the Atacama Large Millimeter/submillimeter Array (ALMA). The authors found
dozens of tiny clumps, with typical radii of $\sim$0.03–0.05 pc (referred to
as molecular cloudlets). Figure 5 shows the velocity channel distributions of
ALMA CO intensities superposed on Chandra synchrotron X-ray contours. The
molecular cloudlets are located not only along the synchrotron X-ray
filaments, but also in the vicinity of X-ray hotspots that exhibit flux
variations on timescales of a few months or years (see Uchiyama et al., 2007;
Higurashi et al., 2020). Because the CO profiles of the cloudlets have narrow
widths (see the bottom panels in Figure 5 ), the authors concluded that these
clumpy structures were formed before the supernova explosion.

###  3.3 Simulations of shock-cloud interactions

Magneto-hydrodynamical (MHD) numerical simulations of a supernova shock
propagating in a clumpy ISM show that both the turbulence and the magnetic
field are amplified around the dense cores, offering a theoretical basis for
the ISM–X-ray correspondence (Inoue et al., 2009, 2012).

Figures 6(a) and 6(b) show the density distributions at 0 and 1508 yr after
since the onset of the shock interaction. The low-density gas (with number
density of $\sim$1 cm-3)—i.e., the WNM—is disturbed significantly by the shock
acceleration, while the high-density gas (with number densities exceeding 100
cm-3)—i.e., the CNM—is not much accelerated. In spite of the interaction, the
shock front propagates almost freely at its initial velocity of 3000 km s-1
owing to the low filling factor of the CNM cores. Figure 6(c) shows the
distribution of the magnetic field which indicates a highly entangled field
configuration. The shock front, which was initially planar, is deformed when
it hits a dense core and becomes entangled around the core. This produces a
turbulent velocity field in the WNM, and the magnetic field becomes turbulent
and is amplified to 100 $\mu$G or higher from its initial value of 6 $\mu$G
(Inoue et al., 2009). The amplified magnetic field surrounds the dense cores,
as shown in Figure 6(b), which explains why the synchrotron X-rays are rim-
brightened around the dense cores. The simulations show that the magnetic
field is amplified around the dense core in a layer of sub pc-scale thickness,
where the nonthermal X-rays are enhanced.

Fig. 8 : Spectral energy distributions (SEDs) of RX J1713.7$-$3946 in
$\gamma$-rays. The green-shaded areas show the uncertainty bands obtained from
maximum-likelihood fits, assuming a power-law spectrum extending from 0.5 to
400 GeV. The gray-shaded areas represent systematic uncertainties in the model
fits. The solid and dashed curves represent various models (Berezhko & Völk,
2006; Porter et al., 2006; Ellison et al., 2010; Zirakashvili & Aharonian,
2010). The upper panel shows the hadronic models, whereas the bottom panel
displays the leptonic models. From Abdo et al. (2011), reproduced by
permission of the AAS

Figure 7 shows a schematic of the shock–cloud interaction model of Inoue et
al. (2012). Before the supernova explosion of a high-mass progenitor, ambient
interstellar gas such as diffuse Hi is completely evacuated by a strong
stellar wind. The wind creates a wind bubble with a density of $\sim$0.01 cm-3
(e.g., Weaver et al., 1977). By contrast, dense molecular clouds, with
densities exceeding $\sim$1000 cm-3 can survive in the wind. Consequently, an
inhomogeneous gas distribution with a density difference of five orders of
magnitude is formed by the high-mass progenitor, before the supernova
explosion occurrs. The primary forward shocks from the SN explosion propagate
through the wind bubble with clumpy clouds, where particle acceleration
operates. Shocks transmitted through the gas cloud are stalled, whereas shock
waves in the intercloud medium are not decelerated. These velocity differences
are also observed in measurements of the proper motions of the forward shocks
(e.g., Tsuji & Uchiyama, 2016). The velocity difference generates multiple
eddies around the shocked clouds, which enhance the magnetic field strength up
to $\sim$1 mG. Finally, we observe that the shocked clouds are limb-brightened
by the synchrotron X-rays. The high magnetic field strength causes short-
timescale variability of the synchrotron X-rays, as discovered by Uchiyama et
al. (2007). The shocked gas clouds also act as targets for cosmic-ray protons
and produce hadronic $\gamma$-rays (see Sections 3.4 and 3.5).

###  3.4 The clumpy gas distribution and the $\gamma$-ray spectrum

Many previous theoretical works on gamma-ray production via the hadronic
process have assumed uniform density or radial density gradients, with a
typical ambient density of $\sim$1 cm-3 (e.g., Ellison et al., 2010; Lee et
al., 2013). Even though a low-density environment such as a wind-swept cavity
and non-uniformity have been discussed to explain the observed $\gamma$-ray
spectra, potentially energy dependent propagation effects in the multi phase
ISM have not been considered (cf., Berezhko & Völk, 2010). One reason why the
multi phase ISM has not generally been considered is because MHD effects in
SNRs are mostly negligible for low-density contrasts $\lesssim 10^{2}$
(Berezhko et al., 2013). The real ISM environment surrounding a SNR, however,
contains preexisting inhomogeneities with density contrasts of $\sim$105 in
the ISM, the importance of which was first emphasized by Cox & Smith (1974)
and McKee & Ostriker (1977).

Conventional $\gamma$-ray spectra in the hadronic and leptonic scenarios for a
uniform (or small density-contrast) ISM are shown in Figure 8 (Abdo et al.,
2011). The hadronic spectrum is relatively flat, with a spectral index
$\Gamma$ of $\sim$2.0, while the leptonic spectrum is hard in the GeV band
($\Gamma{\simeq}1.5$). Therefore, on average, over several SNRs—the shape of
the $\gamma$-ray spectra—should allow discrimination between the two scenarios
if we consider a simple one-zone assumption. However, such assumptions do not
hold for individual SNRs, as has been discussed in the community, even for the
typical young SNR Cassiopeia A (e.g., Atoyan et al., 2000; Helder & Vink,
2008). RXJ1713 is also a representative examples: the inclusion of the clumpy
ISM has a significant effect and significantly changes the hadronic spectrum
as discussed below (Zirakashvili & Aharonian, 2010; Inoue et al., 2012; Gabici
& Aharonian, 2014; Celli et al., 2019).

The hadronic $\gamma$-ray scenario requires a high density of target protons,
whereas the large volume of low-density gas is required for efficient particle
acceleration via diffusive shock acceleration (DSA). Because the maximum
energy of the accelerated particles is proportional to the shock speed, it is
assumed to be that a low-density medium (typically less than $\sim$1 cm-3) and
the large volume is needed to efficient acceleration. Under the assumption of
a uniform ISM, an ISM density greater than 1 cm-3 is required to produce the
$\gamma$-rays observed from RXJ1713 (Ellison et al., 2010). For such high
densities, strong thermal X-rays due to shock heating are expected. This is
contradicted the purely nonthermal X-rays observed from RXJ1713. Although some
theoretical studies have avoided this contradiction by considering a wind-
bubble model and/or a thermal nonequilibrium state between the electrons and
protons downstream (e.g., Morlino et al., 2009; Berezhko & Völk, 2010), the
absence of bright thermal X-ray emission has been used to exclude hadronic
$\gamma$-rays and support leptonic $\gamma$-rays (Ellison et al., 2012).

However, the lack of thermal X-ray emission in the presence of high gas
densities can be explained naturally by considering a realistic clumpy ISM
distribution. Most of the volume of the interclump medium is of low density,
which allows the DSA to work, whereas a large fraction of the mass of the ISM
is contained in dense cores, which can work as a dense, massive, target
material, enabling the cosmic-ray protons to produce hadronic $\gamma$-rays
via the p–p reaction. In the dense cores, the shock fronts are decelerated
significantly, with no heating, and thermal X-rays are suppressed, as
indicated by the equation 1 (Inoue et al., 2012):

$\displaystyle k_{\mathrm{B}}T_{\mathrm{c}}=2\times
10^{-4}\;\biggl{(}\frac{v_{\mathrm{sh,d}}}{3000\;\mathrm{km\;s^{-1}}}\biggr{)}^{2}\;\biggl{(}\frac{n_{\mathrm{d}}}{0.01\;\mathrm{cm^{-3}}}\biggr{)}$
$\displaystyle\biggl{(}\frac{n_{\mathrm{c}}}{10^{3}\;\mathrm{cm^{-3}}}\biggr{)}^{-1}\;(\mathrm{keV}),$
(1)

where $k_{\mathrm{B}}T_{\mathrm{c}}$ is the maximum temperature of the
protons, $v_{\mathrm{sh,d}}$ is the shock velocity in the intercloud or
diffuse region, $n_{\mathrm{d}}$ is the number density of the intercloud or
diffuse gas, and $n_{\mathrm{c}}$ is the number density in the dense clouds.
Because the density differences between $n_{\mathrm{d}}$ and $n_{\mathrm{c}}$
are on the order of 5, no strong thermal X-rays are expected from RXJ1713
under the clumpy ISM distribution. The recently discovered thermal X-ray line
emission from RXJ1713 originates from the supernova ejecta (Katsuda et al.,
2015), and hence it is consistent with the shock–cloud interaction model.

Inoue et al. (2012) studied $\gamma$-ray production in the shock–cloud
interaction in RXJ1713 based on MHD numerical simulations, and they showed
that a hard spectrum ($\Gamma_{\mathrm{GeV}}=1.5$ in the GeV band) like that
of leptonic $\gamma$-rays is well reproduced in the hadronic scenario with a
clumpy ISM. Within the SNR shell, the dense cores are exposed to cosmic-ray
protons, and the p–p interactions inside the cores produce $\gamma$-rays. The
p–p reactions thus lead to a spatial correspondence between the $\gamma$-rays
and the ISM mass.

Fig. 9 : Hadronic models for the $\gamma$-ray SEDs of RX J1713.7$-$3946\. The
hadronic models (solid lines) refer to a configuration with a magnetic field
strength inside the gas clump of $B_{\mathrm{c}}$ = 1 $\mu$G (black) or to
$B_{\mathrm{c}}$ = 10 $\mu$ (blue). The field in the skin of the gas clump is
fixed at $B_{\mathrm{s}}$ = 100 $\mu$G in both models. The bottom pane shows
the residuals for the data/model. From Celli et al. (2019) with permission
Fig. 10 : (a) Distribution of the total proton column density
$N_{\mathrm{p}}$(H2+Hi) toward RX J1713.7$-$3946 superposed on the TeV
$\gamma$-ray contours. The lowest contour and the contour intervals are 20 and
10 smoothed counts, respectively. (b) Azimuthal distributions of the proton
column densities of molecular hydrogen $N_{\mathrm{p}}$(H2), atomic hydrogen
$N_{\mathrm{p}}$(Hi) and $N_{\mathrm{p}}$(H2+Hi), and $\gamma$-rays between
the two elliptical rings shown in (a). The same plot for the area inside the
inner ring is also shown on the right-hand side of (b). From Fukui et al.
(2012), reproduced by permission of the AAS

The most essential argument of Inoue et al. (2012) is taking into account the
penetration depths of cosmic-ray protons into dense cores, which are limited
by the amplified turbulent magnetic field around the dense cores (Inoue et al.
2012: see also Zirakashvili & Aharonian 2010). This tends to dilute the
$\gamma$-ray–ISM correspondence. Equation 2 gives an expression for the
penetration depth as a function of the magnetic field from Inoue et al.
(2012),

$\displaystyle
l_{\mathrm{pd}}=0.1\;\eta^{0.5}\;(E/10\;\mathrm{TeV})^{0.5}\;(B/100\;\mathrm{\mu
G})^{-0.5}$
$\displaystyle(t_{\mathrm{age}}/1000\;\mathrm{yr})^{0.5}\;\;(\mathrm{pc}),$
(2)

where $E$ is the particle energy, $t_{\mathrm{age}}$ is the age of the SNR,
and the cosmic-ray energy spectrum is assumed to have the form $N(E)dE\propto
E^{-p}dE$ above the critical energy for $\pi^{0}$ creation and below the
maximum energy of the accelerated nuclei. Here, $\eta$ is the degree of
randomness of the turbulent magnetic field, which is $\sim$1 around the cores
(e.g., Uchiyama et al., 2007). This indicates that the cosmic-ray protons can
penetrate on the order of 0.1 pc into the surface layers of the cores in; this
is smaller than the typical size of 1 pc of the CO cores in RXJ1713.
Consequently, low-energy cosmic-ray protons cannot penetrate deeply into the
dense regions of the cores, and the $\gamma$-ray spectrum is modified
accordingly (Inoue et al., 2012; Gabici & Aharonian, 2014; Celli et al.,
2019). The ISM mass that interacts with the cosmic rays is proportional to the
cosmic-ray energy $E$: $M(E)\propto l_{\mathrm{pd}}(E)\propto E^{1/2}$, if we
assume a cosmic-ray distribution with the spectral index $p=2$ for high-energy
nuclei, as in conventional DSA theory (Inoue et al., 2012). The increase in
$M$ with $E$ produces a hard $\gamma$-ray spectrum ($\Gamma{\approx}1.5$),
similar to the leptonic spectrum produced in a uniform low-density ISM. Figure
9 shows the $\gamma$-ray SED of RXJ1713, which can be well reproduced by the
hadronic scenario when the penetration depths of the cosmic-ray protons are
considered (Celli et al., 2019). In addition, the penetration depth is
expected to cause local anticorrelations between the $\gamma$-rays and the ISM
density on the 0.1-pc scales, which may become directly observable in the
future using high-resolution $\gamma$-ray observations with the Cherenkov
Telescope Array (CTA).

###  3.5 Correspondence between the ISM and $\gamma$-rays

####  3.5.1 ISM–$\gamma$-ray correspondence

In early works (Aharonian et al., 2006; Fukui, 2008), only CO clouds were
compared with the $\gamma$-ray distributions. Fukui et al. (2012) made a
comprehensive comparison between the ISM (including both molecular and atomic
hydrogen) and the TeV $\gamma$-rays observed using H.E.S.S. aiming to test the
spatial correspondence. A new feature of this work was that the Hi emission
was included in the comparison, and the amount of the Hi gas was found to be
comparable with the molecular mass. Figure 10 shows that the azimuthal
distributions of the two quantities have good spatial correspondence at an
effective resolution of 3 pc, which is limited by the H.E.S.S. observations.
These results lend support to the hadronic scenario (see below for further
discussion). The 3-pc resolution is considerably larger than the typical
penetration depth of $\sim$0.1 pc and the effect of the exclusion of low-
energy cosmic rays from the dense region is not significant in the plot. The
good spatial correspondence between the total ISM protons and $\gamma$-rays
shows for the first time that the necessary condition for the hadronic origin
of the $\gamma$-rays, which was not clear in Aharonian et al. (2006), is
satisfied. Subsequent detailed comparative studies among the ISM, gamma-rays,
and synchrotron X-rays supported this result by separating the hadronic and
leptonic gamma-rays quantitively (Fukui et al., 2021).

Fig. 11 : (a) RGB image of RCW 86 observed by $XMM$-$Newton$. Red, green, and
blue represent the X-ray energy bands, 0.5–1.0, 1.0–2.0, and 2.0–4.5 keV,
respectively. The white solid lines outline the region observed. The contours
represent the radio continuum centered at a frequency 843 MHz. (b) RGB image
of RCW 86 and its surroundings. Here, red, blue, and green represent the XMM-
Newton X-rays (0.5–4.5 keV), NANTEN2 12CO($J$ = 2–1), and the ATCA & Parkes Hi
map, respectively. The velocity ranges of CO and Hi are from $-46.0$ to
$-28.0$ km s-1. The contours indicate the Hi integrated intensity. From Sano
et al. (2017a) with permission

####  3.5.2 Cosmic-ray energy

The total cosmic-ray energy $W_{\mathrm{tot}}$ is estimated from equation 3
below (from Aharonian et al., 2006) to be $\sim$$10^{48}$ erg, which
corresponds to 0.1% of the total energy of a typical supernova explosion.

$\displaystyle{W_{\mathrm{tot}}\sim 1-3\times
10^{50}\biggl{(}\frac{d}{1\,\mathrm{kpc}}\biggr{)}^{2}\biggl{(}\frac{n}{1\,\mathrm{cm^{-3}}}\biggr{)}^{-1}}\
\ {\rm(erg),}$ (3)

where $d$ is the 1-kpc distance to the source and $n$ is the average density
of interstellar protons associated with the SNR. This value is unlikely to
represent the total cosmic-ray energy involved in RXJ1713. The number of dense
cores in the shell is around 20, each with a typical radius of 1 pc (Sano et
al., 2013). For the volume of the shell, which has an 8-pc radius, the volume
filling factor of the cores is estimated to be $\sim$10%, implying that about
1/10 of the cosmic-ray protons are interacting with the ISM protons. This
means that the total energy of cosmic rays is 10 times larger than the
estimated value of $W_{\mathrm{tot}}$. The time evolution must be taken into
account further, and we expect the maximum energy of the $\gamma$-rays to
shift to lower values with 10-fold increase in the total energy. The total
cosmic-ray energy in the middle aged SNRs such as W44 and W28 is estimated to
be 1049 erg in the hadronic scenario (e.g., Yoshiike et al., 2013, 2017). In
addition, it is likely that escaping cosmic rays can be more significant than
accelerated cosmic-rays inside the SNR. In W44, Uchiyama et al. (2012) showed
the nearby clouds outside the SNR are $\gamma$-ray bright, and may involve a
significant amount of cosmic rays on the order of (0.3–3)$\times 10^{50}$ erg.
This value corresponds to $\sim$10% of the typical kinematic energy released
by a supernova explosion ($\sim$1051 erg). Therefore, SNRs such as RXJ1713 may
substantially contribute to the Galactic cosmic-ray energy budget because on
average 10% of the total explosion energy is needed to sustain the Galactic
cosmic-ray flux (see Gabici 2013 and references therein).

####  3.5.3 Hadronic vs. leptonic scenarios

The major process responsible for $\gamma$-ray production in RXJ1713 is still
under debate. The similar shell-like distributions in both X-rays and
$\gamma$-rays make two scenarios possible. In the leptonic scenario, cosmic-
ray electrons are responsible for both $\gamma$-ray and X-ray production. In
the hadronic scenario, the shell-like ISM distribution produces shell-like
$\gamma$-rays and the shock–cloud interaction produces a shell-like
distribution owing to the enhanced nonthermal X-rays around the dense cores. A
possible difference between the two is that the shock–cloud interaction causes
spatial offsets on the order of 0.1–0.4 pc between the cores and the
$\gamma$-ray peaks, which are still below the current limit of $\gamma$-ray
resolution.

Fig. 12 : Top left: Thermal X-ray image of RCW 86 in the energy band 0.5–1.0
keV. Other panels: Maps of Hi (right panels, North and Southwest) and 12CO($J$
= 2–1) (bottom-left panel, East) obtained with ATCA $\&$ Parkes and NANTEN2
(color scale) superposed on the X-ray contours. From Sano et al. (2017a) with
permission

Broad-band fitting of the $\gamma$-ray spectrum can be reconciled with the
both scenarios according to a recent analysis by H. E. S. S. Collaboration et
al. (2018). They argued that both the leptonic and hadronic scenarios can
explain the $\gamma$-ray observations obtained by H.E.S.S., based on a
spectral analysis of the $\gamma$-ray observations from 2003 to 2018. In this
work, the H.E.S.S. $\gamma$-rays and Suzaku X-rays were combined and the
broad-band energy spectrum from 1 keV to 10 TeV was presented. The spatial
resolution was conservatively set to 3.2 pc, which was adopted for the Suzaku
analysis (Tanaka et al., 2008), while the new H.E.S.S. data achieved a nominal
resolution of 0.6 pc. In the leptonic scenario, the cosmic-ray electrons are
responsible for the $\gamma$-ray production. The electrons are cooled by
synchrotron energy loss, so the magnetic field has to be small ($\sim$10
$\mu$G) for the leptonic scenario to work. In shock–cloud interactions, the
field may become as strong as 0.1–1 mG locally, although it may not be so
strong over a large volume. H. E. S. S. Collaboration et al. (2018) did not
make a comparison with the ISM, which remains to be done in the future.

##  4 RCW 86

###  4.1 X-rays and the ISM

Fig. 13 : Nonthermal X-ray images ($E$: 2.0–4.5 keV) toward the (a) East and
(b) Southwest. Superposed contours indicate (a) CO and (b) cold Hi. From Sano
et al. (2017a) with permission

The Type Ia SNR RCW 86 is located at ($l$, $b$) = (315.4, $-2.3$) and it
exhibits both thermal and nonthermal X-rays (Figure 11a). The distance has
been determined to be $\sim$2.5 kpc using several methods (e.g., Westerlund,
1969; Rosado et al., 1996; Helder et al., 2013), and its $\sim$1800 yr age is
based on a possible counterpart to the historical supernova event SN 185
recorded in Chinese literature in 185 AD (Stephenson & Green, 2002; Smith,
1997; Dickel et al., 2001; Vink et al., 2006). The ISM in the velocity range
from $-46$ to $-28$ km s-1 is associated with the SNR, as found from the
spatial correlation with the X-rays (Ajello et al., 2016; Sano et al., 2017a).
RCW 86 is close to a CO cloud, that is part of the supershell GS
314.8$-$0.1$-$34 identified in CO emission by Matsunaga et al. (2001). Sano et
al. (2017a) compared the X-rays with CO and Hi for two energy bands, 0.5–1.0
and 2.0–4.5 keV, where the low energy band is dominated by thermal X-rays and
the high energy band by nonthermal X-rays (e.g., Rho et al., 2002; Ajello et
al., 2016, see also Figure 11a).

The ISM surrounding the SNR is dominated by Hi. The overall distribution of
both Hi and CO is shell like, and the X-rays are distributed within the cavity
(Figure 11b). In addition, extended weak Hi emission is found inside the
shell. According to Sano et al. (2017a), the thermal X-ray filaments with a
typical thickness of 1 pc show tight correlations with Hi and CO (Figure 12),
while the nonthermal X-rays are associated with low-density regions of Hi,
with densities around $4\times 10^{21}$ cm-2. The ISM density in RCW 86 is
lower than that in RXJ1713, which is consistent with a Type Ia SNR. Only a CO
cloud with a size of 5 pc $\times$ 3 pc interacts with the shock, as verified
by the high temperature estimated from the high ratio of the two CO
transitions, CO $J$ = 2–1 and 1–0. No heating sources such as IRAS / AKARI
infrared point sources or high-mass stars exsit in these regions, except for
the shock front of RCW 86 (Sano et al., 2017a).

Fig. 14 : (a–b) Synchrotron radiation images from (a) XMM-Newton X-rays ($E$:
2–5 keV) and (b) Molonglo Observatory Synthesis Telescope (MOST) 843 MHz radio
continuum, both toward RCW 86. The superposed solid contours represent the
H.E.S.S. TeV $\gamma$-rays. The dashed contours indicate the intensity
distributions for each map smoothed with the same point-spread function as the
$\gamma$-ray image. (c) Hi map of RCW 86 obtained with ATCA $\&$ Parkes
superposed on the TeV $\gamma$-ray contours. (d) Distribution of
$N_{\mathrm{p}}$(H2 \+ Hi) toward RCW 86 superposed on the TeV $\gamma$-ray
contours. (e) Azimuthal distributions of $\gamma$-rays, $N_{\mathrm{p}}$(H2),
$N_{\mathrm{p}}$(Hi), and $N_{\mathrm{p}}$(H${}_{2}+$Hi), which are averaged
over every 30$\arcdeg$ in azimuthal angle within the region enclosed by the
white circle in Figure 14(d). From Sano et al. (2019a), reproduced by
permission of the AAS

Because the thermal X-rays are produced by shock heating of neutral gas with a
density less than 100 cm-3, the correlation with the Hi gas is a natural
outcome of the shock heating. The critical difference between RCW 86 and
RXJ1713 is probably the total mass of Hi gas inside the SNR shell. For
RXJ1713, dense molecular clouds with densities greater than $10^{4}$ cm-3
remain without being swept up by the SNR shocks. The diffuse and intercloud Hi
gas were completely evacuated by strong stellar winds, and then creating the
very low-density cavity and the swept-up dense wall (e.g., Fukui et al., 2003;
Moriguchi et al., 2005; Sano et al., 2010; Maxted et al., 2013). Therefore, we
did not find any Hi envelopes around the dense molecular clouds in RXJ1713,
and strong thermal X-rays were not detected at the peripheries (see also
Section 3.4). On the other hand, RCW 86 shows an Hi envelope surrounding the
molecular cloud in the east, and a large amount of diffuse Hi gas remains
inside the SNR (see Figure 11b). This difference is explained by the
hypothesis that accretion winds (or disk winds) from the progenitor system of
RCW 86 are weaker than the stellar winds from the high-mass progenitor of
RXJ1713.

Sano et al. (2017a) also studied the association of the ISM with nonthermal
X-rays. Figure 13 shows nonthermal X-ray images superposed on the CO and cold
Hi contours toward the east and southwest regions. The CO and Hi clumps are
limb-brightened in nonthermal X-rays, which are dominated by synchrotron
radiation. This indicates that shock–cloud interactions occur in the surface
layers of dense clumps, where the magnetic filed is strongly amplified. RCW 86
has no clumpy CO inside the shell, and the gas density seems to be smoother
than in RXJ1713. The authors interpreted the lower ISM mass to be related to
the older evolutionary state of the region after star formation because RCW 86
is part of a molecular supershell with an age of $\sim$2 Myr (Matsunaga et
al., 2001). By contrast, in RXJ1713 we see ongoing star formation within the
SNR shell, as evidenced by the protostellar outflow in CO peak “C” and a few
more YSO candidates (Sano et al., 2010).

###  4.2 The origin of the $\gamma$-rays

Figures 14(a) and 14(b) show overlays of the synchrotron X-ray and radio
continuum distributions on the TeV $\gamma$-ray contours, where the lowest
$\gamma$-ray contour level of $\gamma$-ray corresponds to a significance level
of $\sim$$5\sigma$ (see also Figure 1 of H. E. S. S. Collaboration et al.,
2018). In these images, the synchrotron emission appears as a nearly circular
shell, whereas the $\gamma$-ray emission seems to deviate from this shape,
particularly toward the West, where the $\gamma$-ray emission appears to be
shifted toward the SNR interior. If true, this would argue against the
leptonic scenario. However, by employing a quantitative analysis that uses
radial profiles in the different regions of interest, H. E. S. S.
Collaboration et al. (2018) showed that within statistical errors, there is no
significant difference between the TeV $\gamma$-rays and the X-ray synchrotron
emission. Future $\gamma$-ray observations with high sensitivity and high
angular resolution are needed to confirm the spatial match or the difference
between the two images.

Fig. 15 : CO results toward the five Magellanic SNRs N63A (Sano et al.,
2019b), N49 (Yamane et al., 2018), RX J0046.5$-$7308 (Sano et al., 2019c),
N132D (Sano et al., 2020a), N103B (Sano et al., 2018), and the Magellanic
superbubble 30 Doradus C (Yamane et al., 2021). The CO observations of the LMC
SNRs N63A, N49, N132D, N103B, and the LMC superbubble 30 Doradus C were
obtained using ALMA, while the SMC SNR RX J0046.5$-$7308 was observed using
the Atacama Submillimeter Telescope Experiment (ASTE). From Sano et al. (2018,
2019b, 2019c, 2020a) and Yamane et al. (2018, 2021), reproduced by permission
from the AAS

A spatial comparison between the ISM and $\gamma$-rays therefore remains
essential for understanding the origin of the $\gamma$-rays. In Figure 14(c)
the TeV $\gamma$-ray distribution is overlaid on the Hi, and the comparison
shows good spatial correspondence. Figure 14e shows a plot of the azimuthal
distributions of the $\gamma$-rays and of the total proton column density
$N_{\mathrm{p}}$(H${}_{2}+$Hi), derived using both the Hi and the CO. The
$\gamma$-rays show good correspondence with the Hi distribution, while no
enhancement is seen toward the CO cloud (Figures 14d and 14e in the azimuth
angles from $-90^{\circ}$ to $0^{\circ}$). The poor correlation with the CO is
ascribed to the effect of cosmic-ray exclusion due to the small penetration
depths (less than 1 pc; Sano et al., 2019a, see Section 3.4). More precisely,
the radii of the shock-interacting molecular clouds constitute a key
difference between RXJ1713 and RCW 86. For RXJ1713, the cloud radius is
$\sim$1 pc or less; hence, the molecular clouds play a significant role as
targets of cosmic-ray protons. However, the cloud radius of RCW 86 is more
than 5 pc (Sano et al., 2017a). Additionally, the weak disk winds from the
progenitor system of RCW 86 were not able to strip off the Hi envelope from
the surface of molecular cloud. Therefore, cosmic-ray protons accelerated in
RCW 86 can interact only with the low-density Hi gas on the surface of the
molecular cloud.

For the azimuthal angles from $-180^{\circ}$ to $-120^{\circ}$, we find
$\gamma$-ray excesses relative to the total proton column density. We see a
hint of the $\gamma$-ray excess by a factor of 1.2, which may be ascribed to
the contribution from a leptonic $\gamma$-ray component, because bright
synchrotron radiation is detected toward the SE region. The possible
contribution of leptonic $\gamma$-rays to the total $\gamma$-rays may be as
low as 5% if the arguments given above are correct. The total cosmic-ray
energy in RCW 86 is estimated to be $\sim$$1\times 10^{48}$ erg. A similar
argument to the case of RXJ1713 is perhaps applicable here, and the energy is
a typical one for a young SNR with an age of $\sim$2000 yr. Considering the
lower sensitivity of the current H.E.S.S. data for RCW 86, we do not discuss
the $\gamma$-ray origin further until more sensitive $\gamma$-ray data become
available.

##  5 Summary and Future Prospects

We have reviewed the ISM associated with young supernova remnants and its
connection with the observed X-rays and $\gamma$-rays. These high-energy
radiations are closely related to cosmic rays that are probably accelerated
via DSA. The present focus was on the young, bright TeV $\gamma$-ray SNRs
RXJ1713 and RCW 86. Shock–cloud interactions in a clumpy ISM play an important
role in regulating the X-ray properties as well as the $\gamma$-ray
production.

The pursuit of the ISM in SNRs is being extended to nearby galaxies, including
the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC). The ISM
associated with the SNRs has been identified in many of them, providing
promising candidates for further studies on the role of the ISM (Sano et al.,
2015b, 2017b, 2017c, 2018, 2019b, 2019c, 2020a; Yamane et al., 2018, 2021;
Roper et al., 2018; Alsaberi et al., 2019). The smaller contamination along
the line of sight is advantageous for identifying molecular clouds associated
with the SNRs and for using optical and infrared datasets without strong
stellar absorption. Although the Magellanic SNRs lie at 50–60 times larger
distances from us than compared with the distance of RXJ1713 from us (e.g.,
Hilditch et al., 2005; Pietrzyński et al., 2013), ALMA’s unprecedented
sensitivity and spatial resolution have enabled us to resolve spatially the
cloud-scale structures of the ISM associated with the Magellanic SNRs.

Figure 15 shows CO mapping results toward the five Magellanic SNRs and a
superbubble that are bright in X-rays. The molecular clouds lie nicely along,
or embedded within, the SNR shells, indicating that the shock–cloud
interactions have occurred. 30 Doradus C, one of the brightest X- and
$\gamma$-ray superbubbles in the Local group (see Kavanagh 2020 and references
therein), provides one of the best laboratories for studying shock–cloud
interactions because of its large apparent diameter and very bright TeV
$\gamma$-rays (H. E. S. S. Collaboration et al., 2015). Future observations
using ALMA, Chandra, and the CTA will allow us to study in detail not only
shock–cloud interactions but also the hadronic $\gamma$-ray radiation from the
Magellanic SNRs.

We summarize the main points of this review as follows:

  1. 1.

Spatial comparisons between X-rays and the ISM provide a powerful approach for
determining the distances to SNRs, which is otherwise difficult for SNRs in
the Galactic plane because of heavy obscuration. For RXJ1713, the ISM
delineates the outer boundary of the nonthermal X-ray shell at pc scales,
while X-ray bright spots (or filaments) are anti-correlated with the ISM
clouds/cloudlets at small-scales (sub-pc scales), allowing a robust distance
estimate. RCW 86 is an easier case, for which distance has been determined
accurately owing to its relatively high Galactic latitude.

  2. 2.

When we consider the ISM surrounding the SNRs, it is important to recognize
that the neutral ISM is characterized by highly clumped distributions, with
clumps that are much denser than the nominal uniform density of 1 cm-3 assumed
in many previous works. The ISM shell in a SNR surrounds a low-density cavity,
and the shell comprises a layer that includes tiny, dense clumps with a small
volume filling factor. Consequently, an SNR has a large low-density volume,
where DSA works, as well as dense clumps, which interact with the cosmic rays
and shocks. Magnetohydrodynamical numerical simulations of shock–cloud
interactions reveal that the dense clumps cause strong deformations of the
shock fronts. The deformations produce highly turbulent velocity
distributions, which entangle and amplify the magnetic field to mG levels
(Inoue et al., 2012). In most parts of the low-density cavity, however, the
shocks propagate with little deceleration or deformation.

  3. 3.

The clumpy ISM picture requires modification of the previous scenarios that
were based on a homogeneous ISM. The observed $\gamma$-ray spectrum of RXJ1713
is hard, according to the Fermi collaboration, and the spectrum has previous
been interpreted in terms of the leptonic scenario in a uniform ISM picture.
However, we have shown that a the clumpy ISM can explain the hard spectrum in
the GeV band ($\Gamma_{\mathrm{GeV}}$ = 1.5) equally well because the
penetration of cosmic rays into dense clumps is inhibited by diffusive
scattering due to the turbulent magnetic field. We have discussed the
implications of a clumpy ISM for interpreting the observations of several SNRs
and have outlined the future prospects for this field.

Acknowledgements We truly appreciate the anonymous referee for the useful
comments and suggestions, which helped authors to improve the review. We would
like to thank the editors of this Topical Collection Ralf-Jürgen Dettmar,
Manami Sasaki, and Julia Tjus for inviting us to write this review. We are
also grateful to Rei Enokiya for the useful comments, which helped the authors
improve the review paper. This review paper makes use of the following ALMA
data: ADS/JAO.ALMA#2013.1.01042.S, ADS/JAO.ALMA#2015.1.01130.S, ADS/JAO.ALMA
#2015.1.01195.S, ADS/JAO.ALMA#2015.1.01232.S, ADS/JAO.ALMA#2017.1.01363.S, and
ADS/JAO.AL MA#2017.1.01406.S. ALMA is a partnership of ESO (representing its
member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST
and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the
Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and
NAOJ. This review was supported by JSPS KAKENHI Grant Numbers JP15H05694 (YF),
JP19K14758 (HS), JP19H05075 (HS), 21H01136 (HS). The authors would like to
thank Enago (www.enago.jp) for the English language review.

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