# An Expanding Shell of Neutral Hydrogen Associated with SN 1006: Hints for
the Single-Degenerate Origin and Faint Hadronic Gamma-Rays

H. Sano Faculty of Engineering, Gifu University, 1-1 Yanagido, Gifu 501-1193,
Japan<EMAIL_ADDRESS>National Astronomical Observatory of Japan, Mitaka,
Tokyo 181-8588, Japan  H. Yamaguchi Institute of Space and Astronautical
Science (ISAS), Japan Aerospace Exploration Agency (JAXA), 3-1-1 Yoshinodai,
Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan  Department of Physics, Graduate
School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo
113-0033, Japan  M. Aruga Department of Physics, Nagoya University, Furo-cho,
Chikusa-ku, Nagoya 464-8601, Japan  Y. Fukui Department of Physics, Nagoya
University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan  K. Tachihara
Department of Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya
464-8601, Japan  M. D. Filipović School of Science, Western Sydney University,
Locked Bag 1797, Penrith South DC, NSW 2751, Australia  G. Rowell School of
Physical Sciences, The University of Adelaide, North Terrace, Adelaide, SA
5005, Australia

###### Abstract

We report new Hi observations of the Type Ia supernova remnant SN 1006 using
the Australia Telescope Compact Array with an angular resolution of $4\farcm
5\times 1\farcm 4$ ($\sim$2 pc at the assumed SNR distance of 2.2 kpc). We
find an expanding gas motion in position–velocity diagrams of Hi with an
expansion velocity of $\sim$4 km s-1 and a mass of $\sim$1000 $M_{\odot}$. The
spatial extent of the expanding shell is roughly the same as that of SN 1006.
We here propose a hypothesis that SN 1006 exploded inside the wind-blown
bubble formed by accretion winds from the progenitor system consisting of a
white dwarf and a companion star, and then the forward shock has already
reached the wind wall. This scenario is consistent with the single-degenerate
model. We also derived the total energy of cosmic-ray protons $W_{\mathrm{p}}$
to be only $\sim$1.2–$2.0\times 10^{47}$ erg by adopting the averaged
interstellar proton density of $\sim$25 cm-3. The small value is compatible
with the relation between the age and $W_{\mathrm{p}}$ of other gamma-ray
supernova remnants with ages below $\sim$6 kyr. The $W_{\mathrm{p}}$ value in
SN 1006 will possibly increase up to several 1049 erg in the next $\sim$5 kyr
via the cosmic-ray diffusion into the Hi wind-shell.

Supernova remnants (1667); Interstellar medium (847); Cosmic ray sources
(328); Gamma-ray sources (633); X-ray sources (1822)

††software: IDL Astronomy User’s Library (Landsman, 1993), MIRIAD (Sault et
al., 1995), CIAO (v 4.12: Fruscione et al., 2006), CALDB (v 4.9.1 Graessle et
al., 2007), KARMA (Gooch, 1996).††facilities: Australia Telescope Compact
Array (ATCA), Parkes, Chandra, High Energy Stereoscopic System (H.E.S.S.),
Fermi.

##  1 Introduction

Identifying the progenitor system of Type Ia supernovae is one of the
important issues of modern astrophysics because of their use as standard
candles for measuring the expansion history of the universe (e.g., Perlmutter
et al., 1999). The single-degenerate (SD) and double-degenerate (DD) models
are widely accepted to describe the progenitor systems of Type Ia SNe: the SD
model in which a white dwarf accreted gaseous materials from a nondegenerate
companion until the white dwarf gets close to the Chandrasekhar mass $\sim$1.4
$M_{\odot}$ (Whelan & Iben, 1973; Nomoto, 1982; Iben & Tutukov, 1984;
Paczynski, 1985), and the DD model represents the merger of two white dwarfs
(Nomoto, 1982; Webbink, 1984). To distinguish two scenarios, a search for a
surviving companion is thought to be essential because it can be seen only in
the SD scenario. Despite many efforts to detect such surviving companions of
Type Ia SNRs, no apparent observational evidence was reported111Although a
strong candidate for a surviving companion was reported in Tycho’s SNR named
“Tycho G” (González Hernández et al., 2009; Bedin et al., 2014; Xue &
Schaefer, 2015; Kerzendorf et al., 2018b; Ruiz-Lapuente et al., 2019), the
progenitor system for Tycho’s SNR is still being debated due to several
significant objections (e.g., Kerzendorf et al., 2013; Woods et al., 2017, see
also a complete review by Ruiz-Lapuente 2019).(see reviews by Maoz et al.,
2014; Maeda & Terada, 2016; Ruiz-Lapuente, 2019).

An expanding shell (also known as “wind-blown bubble”) of interstellar neutral
gas associated with Type Ia supernova remnants (SNRs) has received much
attention as alternative evidence for the SD scenario. Because the expanding
gaseous shell could be formed by accretion winds (also known as “disk wind” or
“optically-thick wind”) from the progenitor system consisting of a white dwarf
and a nondegenerate companion (e.g., Hachisu et al., 1996, 1999a, 1999b, 2008;
Hachisu & Kato, 2003a, b), whereas such wind shell is not expected in the DD
scenario. The first discovery of such expanding gaseous shell was made by CO
observations toward Tycho’s SNR (Zhou et al., 2016). The authors argued that
the expanding shell with the mass of $\sim$220 $M_{\odot}$ and an expansion
velocity of $\sim$5 km s-1 could be explained by the energy injection from
accretion winds, and hence concluded that Tycho’s SNR is consistent with the
SD scenario. The presence of dense-gas wall and the SD scenario were also
supported by the rapid shock deceleration during the last $\sim$15 yr (Tanaka
et al., 2021). Subsequent CO and Hi studies found similar expanding shells of
atomic and/or molecular clouds in the Type Ia SNRs RCW 86 (Sano et al., 2017),
N103B (Sano et al., 2018; Alsaberi et al., 2019), and G344.7$-$0.1 (Fukushima
et al., 2020). To better understand the progenitor system of Type Ia
supernovae, we need further observations of interstellar molecular and atomic
clouds toward other Type Ia SNRs.

SN 1006 (also known as G327.6$+$14.6) is a historical SNR that exploded in AD
1006 (Stephenson & Green, 2002). The small distance of 2.2 kpc from us
(Winkler et al., 2003) is consistent with its young age of $\sim$1000 yr and a
large diameter of 28$\farcm$8 arcmin or $\sim$18 pc. Based on the historical
record, SN 1006 is widely thought to originate from a Type Ia supernova
(Schaefer, 1996). Owing to its location far from the Galactic plane ($\sim$550
pc), SN 1006 is an ideal object to search for a surviving companion with very
little contamination along the line of sight. However, neither non-degenerated
companion nor surviving white dwarf companion has been detected to date (e.g.,
Schweizer & Middleditch, 1980; González Hernández et al., 2012; Kerzendorf et
al., 2012, 2018a). Therefore, SN 1006 is thought to be a remnant that exploded
as the DD progenitor system.

SN 1006 is also noted as an ideal site for cosmic-ray acceleration since the
first detection of synchrotron X-rays from the northeast and southwest shells
(Koyama et al., 1995). Subsequent observations of hard X-rays and GeV/TeV
gamma-rays suggest the presence of high-energy cosmic-ray electrons up to
$\sim$100 TeV (e.g., Bamba et al., 2008; Acero et al., 2010; Xing et al.,
2016; Condon et al., 2017; Li et al., 2018). The latest broadband spectral
modeling by Xing et al. (2019) suggests that gamma-ray emission is
predominantly the leptonic origin that cosmic-ray electron energies a low-
energy photon into the gamma-ray energy via inverse Compton scattering.

The interstellar environments of SN 1006, including both the ionized and
neutral gaseous medium, have been well studied by multiwavelength observations
covering radio to X-rays. Assuming the standard compression ratio for a strong
shock of 4, the optical, infrared, and X-ray observations estimated the pre-
shock density of $\sim$0.02–0.4 cm-3 from the post-shock electron density
(e.g., Kirshner et al., 1987; Bamba et al., 2003; Acero et al., 2007; Raymond
et al., 2007; Yamaguchi et al., 2008; Katsuda et al., 2009; Miceli et al.,
2012; Uchida et al., 2013; Winkler et al., 2013, 2014; Li et al., 2015). For
the neutral hydrogen gas surrounding SN 1006, Dubner et al. (2002) carried out
Hi observations with an angular resolution of $4\farcm 7\times 3\farcm 0$ (or
3 pc $\times$ 2 pc at the distance of 2.2 kpc). The authors concluded that the
Hi clouds at $V_{\mathrm{LSR}}$: $-25$ to $-15$ km s-1 are likely interacting
with the SNR, and the derived ambient density is $\sim$0.3 cm-3. On the other
hand, Miceli et al. (2014) argued that the Hi clouds at $V_{\mathrm{LSR}}$:
$\sim$6 to 11 km s-1 are interacting with the southwest shell of the SNR, by
re-analyzing the same Hi datasets. They also found that the X-ray shell is
slightly deformed in the direction of the southwestern Hi cloud. The
spatially-resolved X-ray spectroscopy along the southwestern shell indicated
that the X-ray-derived absorbing column density is proportional to the Hi
column densities. Moreover, the cutoff energy of the synchrotron emission
decreases in the regions corresponding to the southwestern cloud, suggesting
that shock–cloud interaction occurred. Therefore, SN 1006 is a suitable site
to test the physical relation among the supernova shocks, ambient clouds, and
high-energy radiation.

Here, we report the spatial and kinematic distributions of Hi clouds toward SN
1006 using new Hi observations. Our finding of an expanding Hi shell provides
a unique solution for the cloud association with SN 1006, as well as its
progenitor system and cosmic-ray acceleration. In Section 2 we present the
observations and data reductions. Section 3 comprises of four subsections:
Section 3.1 gives an overview of X-rays and Hi toward SN 1006, Sections 3.2
and 3.3 show the spatial and kinematical distributions of Hi while Section 3.4
represents the mass and density of Hi. In Sections 4 and 5 we discuss and
conclude our findings.

##  2 Observations and Data Reduction

###  2.1 Hi

We performed Hi observations at 1.4 GHz using ATCA, which consists of six 22-m
antennas located at Narrabri, Australia. Observations were conducted during 24
hours on November 28, 2013, and March 12, 2014, with ATCA in the EW352 and
EW367 array configurations (Project ID: C2857). We employed the mosaicking
technique, with seven pointings arranged in a hexagonal grid at the Nyquist
spatial separation of $19^{\prime}$. The absolute flux density was scaled by
observing the quasar PKS 0823$-$500, which was used as the primary amplitude
and bandpass calibrators. We also periodically observed the quasar PKS
1421$-$490 for gain and phase calibration. We utilized the MIRIAD software
package (Sault et al., 1995) for the data reduction. To recover extended
emission, we combined the ATCA data cube with archival single-dish datasets
obtained using the Parkes 64-m radio telescope (McClure-Griffiths et al.,
2009; Kalberla et al., 2010). The resulting beam size of Hi is $4\farcm
5\times 1\farcm 4$ with a position angle of $11\fdg 5$, corresponding to the
spatial resolution of 2.9 pc $\times$ 0.9 pc at an SNR distance of 2.2 kpc.
The typical noise fluctuations are 0.32 K per channel for a velocity
resolution of 1 km s-1.

###  2.2 X-rays

We used archival X-ray data obtained by Chandra with the Advanced CCD Imaging
Spectrometer I-array (Obs IDs: 3838, 4385–4394, 13738–13743, 14423, 14424, and
14435), which have been published by Cassam-Chenaï et al. (2008) and Winkler
et al. (2014). We used CIAO version 4.12 (Fruscione et al., 2006) with CALDB
4.9.1 (Graessle et al., 2007) for data reduction and imaging. After
reprocessing for all data using the chandra_repro task, we created exposure-
corrected, energy-filtered maps using the merge_obs task in the energy bands
of 0.5–7.0 keV (broad band), 0.5–1.2 keV (soft band), 1.2–2.0 keV (medium
band), and 2.0–7.0 keV (hard band). The resulting effective exposure time is
$\sim$800 ks.

Figure 1: (a) RGB X-ray image of SN 1006 obtained with Chandra (Cassam-Chenaï
et al., 2008; Winkler et al., 2014). The red, green, and blue colors
correspond to the energy bands 0.5–1.2 keV, 1.2–2.0 keV, and 2.0–7.0 keV,
respectively. The superposed contours indicate TeV gamma-ray significance
obtained with H.E.S.S. (Acero et al., 2010). The contour levels are 3, 4, 5,
6, and 7 $\sigma$ levels. (b) Velocity integrated intensity map of Hi obtained
with ATCA & Parkes. The integration velocity range is from 4.0 to 12.0 km s-1.
The superposed contours indicate the median-filtered Chandra X-ray intensity
in the energy band of 0.5–7.0 keV. The contour levels are 2.5, 4.2, 9.3, 17.8,
29.7, and $45.0\times 10^{-7}$ photons s-1 pixel-1.

##  3 Results

###  3.1 Overview of X-ray and Hi Distributions

Figure 1(a) shows the false-color image of SN 1006 obtained with Chandra. The
X-ray morphology of SN 1006 is that of a nearly circular shell in the soft-
band (red: 0.5–1.2 keV), while the medium-band (green: 1.2–2.0 keV) and hard-
band (blue: 2.0–7.0 keV) images show strong bilateral symmetry in the
northeast and southwest direction. The soft-band image is dominated by thermal
X-rays except for the northeast and southwest shells. The brightest
northwestern limb is thought to be formed by interactions between the neutral
hydrogen gas and supernova shocks (e.g., Long et al., 2003; Winkler et al.,
2014). The hard-band image in the northeast and southwest shells corresponds
to non-thermal synchrotron X-rays from cosmic-ray electrons (e.g., Koyama et
al., 1995), which is also bright in TeV gamma-rays as shown in contours (Acero
et al., 2010).

Figure 1(b) shows the integrated intensity map of Hi. In the present paper, we
focus on the velocity range from 4.0 to 12.0 km s-1, which includes the shock-
interacting Hi clouds suggested by Miceli et al. (2014). We find Hi clouds not
only in the west shell, but also toward the north shell and the center of the
SNR. Interestingly, no dense Hi clouds are adjacent to the southeast shells,
where the shock velocity shows the maximum value in SN 1006 (Winkler et al.,
2014). We also note that the Hi intensity of SN 1006 is about 3–10 times
weaker than that of the typical Type Ia SNRs interacting with Hi clouds in the
Galactic plane (e.g., Sano et al., 2017; Fukushima et al., 2020).

###  3.2 Velocity Channel Distributions of Hi

Figure 2: Velocity channel distributions of Hi superposed on the Chandra X-ray
contours as shown in Figure 1(b). Each panel shows Hi intensity map integrated
every 2.0 km s-1 in a velocity range from 4.0 to 12.0 km s-1.

Figure 2 shows the velocity channel maps of Hi toward SN 1006. We find diffuse
or clumpy Hi clouds, some of which are along with the X-ray shell boundary.
The Hi clouds at $V_{\mathrm{LSR}}=6.0$–8.0 km s-1 lie on the edges of the
northeast and southwest X-ray limbs. The northwest shell appears to be
associated with Hi clumps at $V_{\mathrm{LSR}}=10.0$–12.0 km s-1. The Hi
intensity at $V_{\mathrm{LSR}}=8.0$–10.0 km s-1 decreases toward the center of
the SNR, whereas Hi clouds fill the remnant in the other velocity maps.

###  3.3 Spatial and Kinematic Distributions of Hi

Figure 3: (a) Same image and contours of Figure 1(b), but the map was rotated
by 45 degrees clockwise. (b–c) Position–velocity (p–v) diagrams of Hi. The Hi
brightness temperature is averaged from $-$0$\fdg$22 to 0$\fdg$17 in Offset-X
for (b) and from $-$0$\fdg$19 to 0$\fdg$21 in Offset-Y for (c). (d)
Radius–velocity (r–v) diagram around the center of the SNR at
($\alpha_{\mathrm{J2000}}$,
$\delta_{\mathrm{J2000}})=(15^{\mathrm{h}}02^{\mathrm{m}}51\fs 1$, $-41\arcdeg
55\arcmin 32\fs 12$). The black dashed circles in the p–v and r–v diagrams
indicate the boundaries of the Hi cavities (see the text).

Figures 3(b) and 3(d) show the position–velocity (p–v) diagrams in the Offset
X and Y coordinates, which were rotated by 45 degrees clockwise from the
equatorial coordinate as shown in Figure 3(a). Because the Hi clouds are
distributed across the SNR from northeast to southwest, the rotated image is
suitable for extracting the p–v diagram along the Hi distribution. We find a
cavity-like distribution in each p–v diagram of Hi, whose velocity range is
from 4.0 to 12.0 km s-1. This trend is not significantly changed by varying
the integration spatial ranges of Offset X and Y. It is noteworthy that the
spatial extent of each Hi cavity in the Offset X or Y direction is roughly
consistent with the apparent diameter of the X-ray shell. We also calculated
an average brightness temperature of Hi on annuli about the center of the SNR
using the tool KSHELL in the KARMA (Gooch, 1996). Figure 3(d) shows the
radius–velocity (r–v) diagram centered at ($\alpha_{\mathrm{J2000}}$,
$\delta_{\mathrm{J2000}})=(15^{\mathrm{h}}02^{\mathrm{m}}51\fs 1$, $-45\arcdeg
55^{\prime}32\farcs 12$)222We used the center position of SN 1006 which was
derived by Acero et al. (2010).. We find a similar cavity-like distribution of
Hi with the velocity range of $V_{\mathrm{LSR}}$: 4.0–12.0 km s-1 and a radius
of $0\fdg 24$ that is compatible with the shell radius of SN 1006.

###  3.4 Mass and density of the Hi clouds

To derive the mass of the Hi clouds $M_{\mathrm{HI}}$ at $V_{\mathrm{LSR}}$:
4.0–12.0 km s-1, we used the following equation:

$\displaystyle M_{\mathrm{HI}}=m_{\mathrm{p}}\Omega
D^{2}\sum_{i}N_{i}(\mathrm{H}{\textsc{i}}),$ (1)

where $m_{\mathrm{p}}$ is the mass of hydrogen, $\Omega$ is the solid angle
for each data pixel, $D$ is the distance to the SNR, and $N$(Hi) is the atomic
hydrogen column density. In general, $N$(Hi) can be derived as $1.823\times
W$(Hi), where $W$(Hi) is the Hi integrated intensity. Note that equation (1)
is valid for the optical depth of Hi$\ll 1$. However, the latest observational
and theoretical studies indicate that almost all Hi clouds are optically thick
(e.g., Fukui et al., 2014, 2015, 2018; Hayashi et al., 2019; Wang et al.,
2020; Seifried et al., 2021). According to Fukui et al. (2015), the optical-
depth-corrected Hi column density $N\mathrm{p}$’(Hi) is typically twice higher
than $N$(Hi) calculated using equation (1). Since the result was derived using
the dust opacity map at 353 GHz (Planck Collaboration et al., 2014) toward the
intermediate- and high galactic latitude clouds, this is applicable to SN 1006
at the intermediate latitude of $\sim$15∘. Here, we use a relation presented
by Fukui et al. (2015, 2017) that derives $N_{\mathrm{p}}$’(Hi) as a function
of $W$(Hi). We then calculated the mass of the Hi clouds within the shell
radius of $0\fdg 24$ (or $\sim$9 pc, Acero et al., 2010) is $\sim$1000
$M_{\odot}$ and the averaged atomic hydrogen column density is $\sim$$4\times
10^{20}$ cm-2.

##  4 Discussion

###  4.1 Atomic Hydrogen Gas Associated with SN 1006

Miceli et al. (2014) proposed that the southwest Hi cloud peaked at $\sim$8 km
s-1 is interacting with the SNR, by comparing spatial distributions of the Hi
cloud, the indentation of the X-ray shell, and the cutoff energy of
synchrotron emission. Here, we suggest that the Hi clouds at
$V_{\mathrm{LSR}}=4.0$–12.0 km s-1 are most likely associated with the SNR
from a kinematic point of view.

We first argue that the cavity-like distributions of Hi in the p–v and r–v
diagrams provide us with a hint for the physical association with the atomic
hydrogen gas at the velocity range of 4.0–12.0 km s-1. Because such cavity-
like distributions in an SNR represent an expanding gas, and they are thought
to be formed by shockwaves and/or strong winds from the progenitor system of
the SNR (e.g., Koo et al., 1990; Koo & Heiles, 1991; Hachisu et al., 1999a,
b). In the case of SN 1006, the expansion velocity is $\sim$4 km s-1 centered
at the systemic velocity of $8\pm 2$ km s-1. It is also noteworthy that the
projected wind-shell gives the maximum extent near the systemic velocity,
where we find a hollowed-out distribution of Hi as shown in Figure 2(c).
Moreover, the maximum spatial extent of the expanding shell is found to be
roughly the same size of the SNR shell as shown in Figure 3. This indicates
that the forward shock has already reached the wind-shell, because the free
expansion phase inside the shell is short enough owing to a much lower density
(e.g., Weaver et al., 1977). In fact, Badenes et al. (2007) have already
predicted such a situation using the one-dimensional numerical simulation.
This can naturally explain the indentation of the X-ray shell toward the
southwest Hi cloud suggested by Miceli et al. (2014).

Next, we emphasize that the Hi-derived systemic velocity at $\sim$8 km s-1
coexists with the conventional source distance of 2.2 kpc. Although the
systemic velocity at the distance of 2.2 kpc represents about –32 km s-1 by
adopting the Galactic rotation curve model (Brand & Blitz, 1993) with
conventional Galactic parameters of $R_{0}=8.5$ kpc and $\Theta_{0}=220$ km
s-1 km s-1 (IAU recommended values, Kerr & Lynden-Bell, 1986), the velocity
difference about 40 km s-1 is not a problem since SN 1006 is placed almost 600
pc away from the Galactic plane. This implies that SN 1006 and its surrounding
gas do not follow the Galactic rotation as also pointed out by Dubner et al.
(2002) and Miceli et al. (2014).

The almost circular shape of SN 1006 without strong deformation is naturally
expected by considering the column density of the shocked clouds (e.g., Lopez
et al., 2009; Bozzetto et al., 2017). In general, the shell morphology
approaches a circular shape with decreasing the density of shock-associated
clouds (e.g., Filipović et al., 2022). The young TeV gamma-ray SNR RX
J0852.0$-$4622 ($\sim$1700 yr) is a good example because the SNR shows almost
circular shell. The total interstellar proton column density of shock-
associated clouds is $\sim 3\times 10^{21}$ cm-2 for RX J0852.0$-$4622 (Fukui
et al., 2017; Maxted et al., 2018). By contrast, young ($\sim$1600 yr) TeV
gamma-ray SNR RX J1713.7$-$3946 shows a strongly deformed X-ray shell owing to
shock-interactions with dense clouds of $\sim 7\times 10^{21}$ cm-2 as
averaged column density (e.g., Fukui et al., 2003, 2012, 2021; Sano et al.,
2010, 2013, 2015). In the case of SN 1006, the column density of the shocked
Hi cloud is $\sim 4\times 10^{20}$ cm-2 (see Section 3.4). Because the cloud
density in SN 1006 is at least one order magnitude smaller than that in the
three similar SNRs, the almost circular shape of SN 1006 is expected even if
the shock-cloud interactions occurred.

Moreover, the previous proper-motion measurements may also be consistent with
the Hi distributions at $V_{\mathrm{LSR}}=4.0$–12.0 km s-1. According to
Winkler et al. (2014), the highest velocity of $\sim$$7400\pm 800$ km s-1 was
found in the southeast shell where no dense Hi clouds are located (see Figure
1b). On the other hand, the slower shock velocities of $\sim$5000 km s-1 are
seen in the northeast and southwest shells with rich Hi clouds (see also
Figure 1b). By considering the forward shock interaction with the inner wall
of the Hi shell, we can possibly find rapid deceleration of the shock wave
toward the northeast and southwest shells of SN 1006 (e.g., Tanaka et al.,
2021).

In conclusion, we claim that the Hi clouds at $V_{\mathrm{LSR}}=4.0$–12.0 km
s-1 are likely associated with SN 1006 in terms of their spatial
distributions, kinetics, and physical properties.

###  4.2 A Hint for a Single Degenerate Origin

As described in Section 3.4, the expanding Hi shell associated with SN 1006
has a mass of $\sim$1000 $M_{\odot}$. If the ambient medium with this large
mass was uniformly distributed over the present volume of the remnant before
being blown out, the initial ambient density is estimated to be $\sim$12 cm-3
(here we assumed the shell radius of $\sim$9 pc (Acero et al., 2010)). On the
other hand, previous X-ray studies indicated the low pre-shock density of
$\sim$0.02–0.4 cm-3, based on the high velocity of the SNR forward shock
(e.g., Katsuda et al., 2009; Winkler et al., 2014) and low ionization state of
the post-shock ISM and Fe ejecta (Acero et al., 2007; Yamaguchi et al., 2014).
This discrepancy implies that the expanding Hi shell was first formed by the
strong pre-explosion winds and subsequently the progenitor of SN 1006 exploded
inside the low-density cavity.

Because such wind activity prior to a Type Ia supernova explosion is thought
to be associated with the SD scenario, we discuss whether the typical SD
progenitor system can form the expanding Hi shell discovered in SN 1006.
Hachisu et al. (1999a, b) presented that the typical wind mass-loss rate is
$\sim$$2\times 10^{-6}$ $M_{\odot}$ yr-1 (up to $\sim$$10^{-4}$ $M_{\odot}$
yr-1, see also Nomoto et al. 2005) and the wind velocity is $\sim$2000 km s-1.
If we adopt the dynamical time scale of expanding Hi shell as the wind
duration period, we derive the momentum of accretion winds to be $\sim$8000
$M_{\odot}$ km s-1 or more. On the other hand, the momentum of expanding Hi
shell is to be $\sim$4000 $M_{\odot}$ km s-1, by adopting the expansion
velocity of $\sim$4 km s-1 and the Hi cloud mass of $\sim$1000 $M_{\odot}$.
Therefore, the SD scenario can adequately explain the momentum of the observed
expanding Hi shell.

Finally, we discuss whether only the SD channel can produce the optically-
thick winds through a phase of accreting material from a companion. According
to Ivanova et al. (2013), the DD channel also undergoes several phases in
their evolution that are not clear, in particular, the “common envelope
phase.” The DD channel also experiences stages of accretion but maybe not
stable enough or extended sufficiently in time compared to the SD channel.
Since there are phases that we do not understand well in the DD channel, this
uncertainty is a limitation of the present study to distinguish the SD and DD
models. Another possibility is that a red supergiant with strong stellar winds
happened to be in the line of sight. This possibility has been eliminated by
the previous dedicated studies of a companion star search (e.g., Schweizer &
Middleditch, 1980; González Hernández et al., 2012; Kerzendorf et al., 2012,
2018a). In any case, we would emphasize that the present Hi results and
current knowledge also favor the SD scenario as the explosion mechanism of SN
1006, nevertheless, no surviving companion has been detected.

Figure 4: Scatter plot between the age of SNRs and the total energy of cosmic-
ray protons $W_{\mathrm{p}}$ (Sano et al., 2021a). The green line indicates
the linear regression of the double-logarithmic plot applying the least-
squares fitting for data points with the ages of SNRs below 6 kyr. The
hadronic gamma-ray luminocity for each SNR was derived from the previous SED
modeling alone except for RX J1713.7$-3946$ (see the text). Table 1:
Comparison of Physical Properties in 13 Gamma-Ray SNRs

Name | Distance | Diameter | Age | $n_{\mathrm{p}}$ | $W_{\mathrm{p}}$ | References
---|---|---|---|---|---|---
| (kpc) | (pc) | (kyr) | (cm-3) | ($10^{49}$ erg) |
(1) | (2) | (3) | (4) | (5) | (6) | (7)
SN 1006 |  02.2a | 18 | 1.0 |  025 |  0iiiii$0.016^{+0.004}_{-0.004}$ | This work
RX J1713.7$-3946$ | 1.0 | 18 | 1.6 | 130 |  00$0.10^{+0.05}_{-0.05}$ | Fukui et al. (2021)
RX J0852.0$-$4622 |  0z0.75b | 24 |  z1.7a | 100 |  00$0.07^{+0.02}_{-0.02}$ | Fukui et al. (2017)
RCW 86 | 2.5 | 30 | 1.8 |  075 |  00$0.11^{+0.01}_{-0.01}$ | Sano et al. (2019a)
HESS J1731$-$347 | 5.7 | 44 | 4.0 |  060 |  00$0.66^{+0.22}_{-0.22}$ | Fukuda et al. (2014)
G39.2$-$0.3 | 6.2 | 14 |  00zw$5.0^{+2.0}_{-2.0}$c | 400 | $3.2^{+1.1}_{-0.8}$ | de Oña Wilhelmi et al. (2020)
W49B | 11.00 | 16 |  00zw$6.0^{+1.0}_{-1.0}$d | 650 | $2.1^{+1.1}_{-0.6}$ | Sano et al. (2021a)
Kes 79 | 5.5 | 16 |  0zw$8.3^{+0.5}_{-0.5}$ | 360 | 0.50zw | Kuriki et al. (2018)
G346.6$-$0.2 | 11.10 | 21 |  0iiiii$14.0^{+2.0}_{-2.0}$ | 280 | $<0.09$ | Sano et al. (2021b)
W44 |  03.0e | 27 | 20.0f | 200 | 1.00zw | Yoshiike et al. (2013)
IC443 |  j1.5g | 20 |  0iiiii$25.0^{+5.0}_{-5.0}$h | 680 | 0.09ccz | Yoshiike et al. (2022)
LMC N132D | 50.00 | 25 |  00zw$2.5^{+0.2}_{-0.2}$j | $<2000$ | $>0.5$ | Sano et al. (2020a)
LMC N63A | 50.00 | 18 |  00zii$3.5^{+1.5}_{-1.5}$j | 190 | $0.9^{+0.5}_{-0.6}$ | Sano et al. (2019b)

Note. — Col. (1): Name of SNRs. Col. (2): Distance to SNRs in units of kpc.
Col. (3): Diameter of SNRs in units of pc. Col. (4): Age of SNRs in units of
kyr. Col. (5): Averaged number density of total interstellar protons
$n_{\mathrm{p}}$ in units of cm-3. Col. (6): Total energy of cosmic-ray
protons $W_{\mathrm{p}}$ in units of 1049 erg. Col. (7): References for CO/H I
derived $n_{\mathrm{p}}$ and $W_{\mathrm{p}}$ for each SNR. Other specific
references are also shown as follows: aWinkler et al. (2003), bKatsuda et al.
(2008), cSu et al. (2011), dZhou & Vink (2018), eCaswell et al. (1975),
fWolszczan et al. (1991), gWelsh & Sallmen (2003), hLee et al. (2008); Olbert
et al. (2001), iLaw et al. (2020), and jHughes et al. (1998).

###  4.3 Total Energy of Cosmic Ray Protons

SNRs are thought to be promising acceleration sites for cosmic-ray protons, up
to at least a few Peta electronvolts through the diffusive shock acceleration
(DSA, e.g., Bell, 1978; Blandford & Ostriker, 1978). By considering the
injection rate of cosmic-rays and the total power of supernova explosions, the
conventional value of the total energy of cosmic-rays $W_{\mathrm{p}}$ is to
be $\sim$$10^{49}$–$10^{50}$ erg per a supernova explosion. Since
$W_{\mathrm{p}}$ is proportional to the gamma-ray luminosity and the inverse
of gas density, we can constrain the value of $W_{\mathrm{p}}$ for each SNR by
observations. However, observational values of $W_{\mathrm{p}}$ still had
large ambiguities because of the lack of unified quantification for shock-
interacting molecular/atomic clouds through the CO/Hi radio line observations.

Most recently, Sano et al. (2021a, b) summarized observational
$W_{\mathrm{p}}$ values for 12 gamma-ray SNRs by adopting the number densities
of shocked clouds using CO/Hi datasets. The authors found a tight relation
between the SNR age and $W_{\mathrm{p}}$ for 12 gamma-ray SNRs: the young SNRs
below $\sim$6 kyr show a positive correlation between them, while the older
SNRs more than $\sim$8 kyr show a steady decrease of $W_{\mathrm{p}}$. The
authors proposed that this trend can be explained as a combination of the age-
limited acceleration (e.g., Ohira et al., 2010) and the energy-dependent
diffusion of cosmic rays (e.g., Aharonian & Atoyan, 1996; Gabici, 2013). If
the trend is real, SN 1006 shows a much lower value of $W_{\mathrm{p}}$
because of the low gamma-ray luminosity and gas density as well as its young
age. In the present section, we derive the $W_{\mathrm{p}}$ value of SN 1006
and compare it with other gamma-ray SNRs.

According to the latest broad-band spectral modeling of SN 1006, almost gamma-
ray emission is leptonic-dominated, which was produced from the inverse
Compton scattering between accelerated cosmic-ray electrons and interstellar
photons. On the other hand, hadronic gamma-rays, produced by interactions
between cosmic-ray protons and interstellar protons, are thought to be
contributed to gamma-rays from SN 1006. The total energy of accelerated
cosmic-ray protons $W_{\mathrm{p}}$ is derived by Xing et al. (2019) as:

$\displaystyle W_{\mathrm{p}}=1.5\mathrm{-}2.5\times
10^{49}(n/0.2\;\mathrm{cm}^{-3})^{-1}\;\;\mathrm{erg}.$ (2)

where $n$ is the number density of interstellar protons. In SN 1006, the
averaged interstellar proton density is estimated to be $\sim$25 cm-3 by
adopting a shell radius of $0\fdg 24$ or $\sim$9.2 pc and a shell thickness of
$0\fdg 05$ degree or $\sim$1.9 pc (Acero et al., 2010). We then obtained
$W_{\mathrm{p}}=1.2$–$2.0\times 10^{47}$ erg, which corresponds to $\sim$0.02%
of the typical released kinetic energy of a supernova explosion of $\sim$1051
erg.

Figure 4 shows the scatter plot between the SNR age and $W_{\mathrm{p}}$ for
13 gamma-ray SNRs that are listed in Table 1. Note that the hadronic gamma-ray
luminosity for deriving the $W_{\mathrm{p}}$ value in each SNR was calculated
by the SED modeling alone except for RX J1713.7$-$3946 (see also Fukui et al.,
2021). We find that SN 1006 lies on the regression line which was fitted using
the data points with the ages of SNRs below 6 kyr, suggesting that the
positive relation between the SNR age and $W_{\mathrm{p}}$ is applicable to
gamma-ray SNRs with ages at least $\sim$1–6 kyr. If so, the $W_{\mathrm{p}}$
value of SN 1006 will increase up to several 1049 erg in the next 5 kyr, even
if the forward shock has already reached the wind-shell (see also Section
4.1). Since it is unlikely that the decelerated forward shock would continue
to accelerate cosmic rays for the next 5 kyr, some other mechanisms to
increasing $W_{\mathrm{p}}$ are needed.

One possible idea is that the cosmic-ray diffusion into the wind wall also
plays an important role in understanding the values of $W_{\mathrm{p}}$ in the
early evolutional stage of the SNRs. In this scenario, cosmic rays are mainly
accelerated inside the low-density wind bubble via the DSA scheme. After the
shock has reached the wind wall, cosmic rays diffuse into the wind-wall. The
penetration depth of cosmic ray protons $l_{\mathrm{pd}}$ can be derived by
(Inoue et al., 2012):

$\displaystyle
l_{\mathrm{pd}}=0.1\;\eta^{0.5}(E/10\;\mathrm{TeV})^{0.5}(B/100\;\mathrm{\mu
G})^{-0.5}$
$\displaystyle(t/1000\;\mathrm{yr})^{0.5}\;\;\mathrm{pc}\;\;\;\;\;$ (3)

where $\eta$ is gyro-factor ($>1$), $E$ is the energy of cosmic rays, $B$ is
the magnetic field, and $t$ is the age of the SNR. By adopting $\eta=4$ for
the inert-cloud region (Tanaka et al., 2020), $E=100$ TeV, and $B=45$ $\mu$G
(Acero et al., 2010), the penetration depth of cosmic-ray protons
$l_{\mathrm{pd}}$ is to be $\sim$0.9 pc for $t=1$ kyr and $\sim$2.3 pc for
$t=6$ kyr. Because the thickness of the wind shell is to be $\sim$1.9 pc,
accelerated cosmic-ray protons will be fully interacting with the Hi clouds
within the wind-shell in the next 5 kyr. In short, accelerated cosmic-rays
below 100 TeV are trapped within the wind-cavity if the SNR age is young
enough.

It should be also noted that the derived $W_{\mathrm{p}}$ values except for RX
J1713.7$-$3946 likely have additional uncertainties (by a factor of two or
three) due to the difficulty in separation of the hadronic and leptonic gamma-
rays by the SED modeling alone (e.g., Inoue et al., 2012). According to Fukui
et al. (2021), each gamma-ray component can be accurately distinguished by a
comparison of gamma-ray, synchrotron X-ray, and total interstellar proton
images. They found that hadronic gamma-ray contribution for RX J1713.7$-$3946
is ($67\pm 8$)% of the total gamma-rays, and hence the accuracy of
$W_{\mathrm{p}}$ (and the hadronic gamma-ray luminosity) in RX J1713.7$-$3946
is significantly better than that in other SNRs derived using the SED modeling
results. Moreover, all derived $W_{\mathrm{p}}$ values should be considered as
an upper limit because we assume the uniform density distribution of the ISM
protons within the shell. Nevertheless, we can find the global trend between
the age and $W_{\mathrm{p}}$ by three orders of magnitude, implying that the
trend itself is reliable.

In any case, the young (age $<6$ kyr) gamma-ray SNRs including SN 1006 show a
good correlation between the SNR age and $W_{\mathrm{p}}$, possibly suggesting
that the diffusion timescale is important in understanding in-situ values of
$W_{\mathrm{p}}$. Further gamma-ray and Hi observations at the high-angular
resolution using the Cherenkov Telescope Array (CTA; Actis et al., 2011;
Cherenkov Telescope Array Consortium et al., 2019) and the Australian Square
Kilometre Array Pathfinder (ASKAP, Johnston et al., 2007; Hotan et al., 2021)
will allow us to reveal the diffusion mechanisms of cosmic rays in detail.

##  5 Conclusions

We summarize our conclusions as follows:

  1. 1.

New Hi observations using the Australia Telescope Compact Array have revealed
the spatial and kinematic distributions of Hi clouds associated with the Type
Ia supernova remnant SN 1006. The Hi clouds at $V_{\mathrm{LSR}}=4.0$–12.0 km
s-1 show a good spatial correspondence with the X-ray shell, particularly in
the southwest, northwest, and northeast. The total mass of Hi clouds is
$\sim$1000 $M_{\odot}$ and the averaged atomic hydrogen column density is
$\sim$$4\times 10^{20}$ cm-2 by assuming the optically thick Hi.

  2. 2.

The Hi cavity-like distributions in the position–velocity and radius–velocity
diagrams indicate the expanding shell, whose expansion velocity is $\sim$4 km
s-1 with the systemic velocity of $8\pm 2$ km s-1. By considering the pre- and
post-shocked gas density and spatial extent of the expanding shell, the
expanding Hi shell was likely formed by strong winds from the progenitor
system, and then the forward shock of SN 1006 has already reached its wind
wall. This scenario coexists with the conventional distance of 2.2 kpc because
SN 1006 and its surroundings do not follow the Galactic rotation owing to
their large distances from the Galactic plane.

  3. 3.

We proposed a possible scenario that the progenitor system of SN 1006 consists
of a white dwarf and a companion star, namely the single-degenerate system
because the kinematics of the Hi expanding shell can be explained by accretion
winds from the progenitors.

  4. 4.

The total energy of accelerated cosmic-ray protons $W_{\mathrm{p}}$ is derived
to be only $\sim$1.2–$2.0\times 10^{47}$ erg by adopting the averaged
interstellar proton density of $\sim$25 cm-3. This small value is compatible
with a positive correlation between the age and $W_{\mathrm{p}}$ of other
gamma-ray supernova remnants with an age less than $\sim$6 kyr. Since the
forward shock of SN 1006 has already reached the wind-shell and was
decelerated, a time-dependent evolution of $W_{\mathrm{p}}$ is possibly
relating the cosmic-ray diffusion into the Hi wind-shell. The cosmic-ray
diffusion can increase the $W_{\mathrm{p}}$ value in SN 1006 up to several
1049 erg in the next $\sim$5 kyr.

## Acknowledgements

The authors acknowledge Tatsuya Fukuda and Satoshi Yoshiike for contributions
on the data reduction and observations of Hi. We are also grateful to the
anonymous referee for useful comments that helped us improve the paper
signiﬁcantly. The Australia Telescope Compact Array (ATCA) and the Parkes
radio telescope are parts of the Australia Telescope National Facility which
is funded by the Australian Government for operation as a National Facility
managed by CSIRO. We acknowledge the Gomeroi people as the traditional owners
of the Observatory site. The scientific results reported in this article are
based on data obtained from the Chandra Data Archive (Obs IDs: 3838,
4385–4394, 13738–13743, 14423, 14424, 14435). This research has made use of
the software provided by the Chandra X-ray Center (CXC) in the application
packages CIAO (v 4.12). This work was supported by JSPS KAKENHI Grant Numbers
JP19H05075 (H. Sano), JP20KK0309 (H. Sano), and JP21H01136 (H. Sano).

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