# A Systematic Study of Associations between Supernova Remnants and Molecular
Clouds

Xin Zhou11affiliationmark:  , Yang Su11affiliationmark:  , Ji
Yang11affiliationmark:  , Xuepeng Chen11affiliationmark:  , Yan
Sun11affiliationmark:  , Zhibo Jiang11affiliationmark:  , Min
Wang11affiliationmark:  , Hongchi Wang11affiliationmark:  , Shaobo
Zhang11affiliationmark:  , Ye Xu11affiliationmark:  , Qingzeng
Yan11affiliationmark:  , Lixia Yuan11affiliationmark:  , Zhiwei
Chen11affiliationmark:  , Yiping Ao11affiliationmark:  , Yuehui
Ma11affiliationmark:  1Purple Mountain Observatory and Key Laboratory of Radio
Astronomy, Chinese Academy of Sciences, 10 Yuanhua Road, Nanjing 210033,
People’s Republic of China<EMAIL_ADDRESS>
###### Abstract

We universally search for evidence of kinematic and spatial correlation of
supernova remnant (SNR) and molecular cloud (MC) associations for nearly all
SNRs in the coverage of the MWISP CO survey, i.e. 149 SNRs, 170 SNR
candidates, and 18 pure pulsar wind nebulae (PWNe) in
$1^{\circ}<l<230^{\circ}$ and $-5.^{\circ}5<b<5.^{\circ}5$. Based on high-
quality and unbiased 12CO/13CO/C18O (J = 1–0) survey data, we apply automatic
algorithms to identify broad lines and spatial correlations for molecular gas
in each SNR region. The 91% of SNR-MC associations detected previously are
identified in this paper by CO line emission. Overall, there could be as high
as 80% of SNRs associated with MCs. The proportion of SNRs associated with MCs
is high within the Galactic longitude less than $\sim 50^{\circ}$. Kinematic
distances of all SNRs that are associated with MCs are estimated based on
systemic velocities of associated MCs. The radius of SNRs associated with MCs
follows a lognormal distribution, which peaks at $\sim$8.1 pc. The progenitor
initial mass of these SNRs follows a power-law distribution with an index of
$\sim$$-2.3$ that is consistent with the Salpeter index of $-2.35$. We find
that SNR-MC associations are mainly distributed in a thin disk along the
Galactic plane, while a small amount distributed in a thick disk. With the
height of these SNRs from the Galactic plane below $\sim$45 pc, the
distribution of the average radius relative to the height of them is roughly
flat, and the average radius increases with the height when above $\sim$45 pc.

ISM (847) — Supernova remnants (1667) — Molecular clouds (1072) — Galaxy
structure (622)

##  1 Introduction

Supernova remnants (SNRs) release large amounts of momentum, energy, and heavy
elements into the interstellar medium (ISM), which modify the physical and
chemical properties of the ISM and trigger star formation. Such stellar
feedback, affecting the next generation of star formation, primarily
characterizes the nonlinear evolution of the ISM. SNRs are also prime
candidates of Galactic cosmic ray (CR) sources. Some SNRs have bright
$\gamma$-ray emission, which may originate from CR particles impacting on the
surrounding dense medium (e.g., Aharonian et al., 2008a; Giuliani et al.,
2011; Fukui et al., 2021). These sources provide valuable opportunities to
study CR acceleration in SNRs. Many SNRs originate from core-collapse
supernova explosions of massive stars. Because their progenitor massive stars
formed in molecular clouds (MCs) and had relatively short lifetimes, these
SNRs are expected to be associated with their parent MCs. In addition, type Ia
supernovae may also occur near dense molecular gases (e.g., Lee et al., 2004;
Zhou et al., 2016c; Chen et al., 2017b). It is not clear that how many SNRs
are associated with MCs. Supposing half of SNRs originated from core-collapse
supernovae (Reynoso & Mangum, 2001), there may be more than half of SNRs
associated with MCs.

Among different evidences of SNR-MC interaction, i.e. shifted and broadened CO
line emission (e.g., Denoyer, 1979a; Seta et al., 1998b; Kilpatrick et al.,
2016, etc.), OH maser line emission at 1720 MHz (e.g., Goss & Robinson, 1968;
Frail et al., 1994, 1996; Green et al., 1997; Wardle & Yusef-Zadeh, 2002;
Yusef-Zadeh et al., 2003; Hewitt & Yusef-Zadeh, 2009, etc.), shock excited
molecular line emission (e.g., Wootten, 1981, etc.), enhanced IR emission
(e.g., Arendt, 1989; Saken et al., 1992; Reach et al., 2005, 2006; Hewitt et
al., 2009, etc.), etc., molecular line emission is wildly used in searching
associated MC, since it originates from associated molecular gas and provides
its local standard-of-rest (LSR) velocity information. To date, about 80
Galactic SNRs have been confirmed or suggested to be associated with MCs, out
of about 300 Galactic SNRs (Gaensler et al., 2008; Jiang et al., 2010; Tian et
al., 2010; Eger et al., 2011; Jeong et al., 2012; Frail et al., 2013; Chen et
al., 2014; Fukuda et al., 2014; Su et al., 2014b; Zhou et al., 2014; Zhu et
al., 2014; Zhang et al., 2015; Voisin et al., 2016; Zhou et al., 2016a, c; de
Wilt et al., 2017; Lau et al., 2017; Liu et al., 2017; Su et al., 2017b; Liu
et al., 2018; Maxted et al., 2018; Su et al., 2018; Ma et al., 2019; Yu et
al., 2019; Green, 2019; Ranasinghe & Leahy, 2022, and references therein).
Most of these Galactic SNR-MC associations have been confirmed or suggested
through CO or OH maser line emission. In particular, Kilpatrick et al. (2016)
performed an effective systematic search for broad 12CO (J=2–1) line regions
toward 50 SNRs, and confirmed the detection in 19 SNRs including 9 newly
identified ones. Sofue et al. (2021) also provided some supplementary
morphological search results of CO line emission toward 63 Galactic SNRs in
the $10^{\circ}\leq l\leq 50^{\circ}$, $|b|\leq 1^{\circ}$ region. Only a
small percentage of SNRs are confirmed to be associated with MCs with clear
evidence, e.g., uncontaminated broad CO line emission or OH 1720 MHz maser
emission. Many SNRs are located in crowded regions with multiple MCs
overlapping each other in the line-of-sight, hence, molecular lines toward
these SNRs are overlapping each other. It is difficult to distinguish
potential disturbed molecular gases in these SNRs. In addition, physical
conditions for the formation of OH 1720 MHz masers are strict, i.e. in regions
with moderate temperatures and densities ($T\sim 50$–125 K, $n_{\rm H_{2}}\sim
10^{5}~{}\,{\rm cm}^{-3}$) behind slow C-type shocks (Lockett et al., 1999;
Hewitt & Yusef-Zadeh, 2009), and many SNRs do not have such physical
conditions. A large amount of potential SNR-MC associations prohibit general
statistical studies of MC environments around SNRs.

Intending to investigate SNR-MC associations, we present in this work a
general study of CO line emission toward most SNRs in the northern sky, based
on the Milky Way Imaging Scroll Painting (MWISP) unbiased three CO isotope
lines survey using the 13.7-meter millimeter wavelength telescope at Qinghai
station. The survey data has appropriate spatial resolution, high sensitivity,
and large coverage. Both kinematic evidence and spatial correlations are
examined, and further statistical analyses of SNRs associated with MCs are
performed.

##  2 Observations

SNRs in the coverage of the Milky Way Imaging Scroll Painting
(MWISP111http://www.radioast.nsdc.cn/mwisp.php) project, i.e. nearly all SNRs
in $1^{\circ}<l<230^{\circ}$ and $-5.^{\circ}5<b<5.^{\circ}5$, are
investigated. The MWISP project is an unbiased survey of 12CO/13CO/C18O (J =
1–0) emission lines (see Su et al., 2019; Sun et al., 2020, and references
therein, for details), using the Purple Mountain Observatory Delingha (PMODLH)
13.7 m millimeter wavelength telescope (Zuo et al., 2011). The three CO lines
were simultaneously observed by a $3\times 3$ multibeam sideband separating
superconducting receiver (Shan et al., 2012). The region is mapped via on-the-
fly (OTF) observation mode, with a half-power beamwidth (HPBW) of $\sim$51′′.
Spectral resolutions of the three CO lines are $\sim$0.16 km s-1 for 12CO (J =
1–0), and $\sim$0.17 km s-1 for 13CO and C18O (J = 1–0). The typical rms noise
level is about 0.5 K for 12CO (J = 1–0); and about 0.3 K for 13CO and C18O (J
= 1–0), corresponding to their spectral resolutions. All data were processed
using dedicated pipelines by MWISP working group and the GILDAS/CLASS
package222http://www.iram.fr/IRAMFR/GILDAS. A linear fit was performed in the
baseline subtraction. The OTF raw data was meshed with a grid spacing of 30′′,
and was corrected for beam efficiency using Tmb=T${}_{A}^{*}/\eta_{mb}$. The
data of the full extent of each SNR was extracted, covering an area of 2 to 4
times the size of the remnant. Moreover, for pulsar wind nebulae (PWNe), areas
of 16 to 32 times their sizes are covered. SNRs G82.2+5.3 and G93.3+6.9 are
not fully covered, nevertheless, more than half of their extents are covered.

Radio continuum emission data at 200 MHz were obtained from the Galactic and
Extragalactic All-sky Murchison Widefield Array (GLEAM)
survey333https://www.mwatelescope.org/gleam (Wayth et al., 2015; Hurley-Walker
et al., 2017, 2019b). 1.4 GHz radio continuum emission data were obtained from
the NRAO VLA Sky Survey (NVSS; Condon et al., 1998) and The
HI/OH/Recombination line survey (THOR; Beuther et al., 2016; Wang et al.,
2020). 4850 MHz radio continuum data were also obtained from the Green Bank
6-cm/Parkes-MIT-NRAO (GB6) survey (Condon et al., 1991, 1993, 1994). 20 cm
radio continuum data are from the Multi-Array Galactic Plane Imaging Survey
(MAGPIS444http://third.ucllnl.org/gps; Helfand et al., 2006). The information
on SNRs in the Green (2019)
catalog555http://www.mrao.cam.ac.uk/surveys/snrs/snrs.info.html and the
catalog of high-energy SNRs
(SNRcat666http://www.physics.umanitoba.ca/snr/SNRcat; Ferrand & Safi-Harb,
2012) was used. Based on the radio continuum emission, we define circular
regions to designate individual SNRs by visual inspection, mostly along their
outermost bright radio continuum shell.

##  3 Methods

Molecular gases impacted by SNR shock will be disturbed in two respects, i.e.
heating and macro-turbulence. Molecular gas behind a transmitted shock in a
molecular clump will be accelerated and heated, which is usually detected as
broadened line wing in CO line profiles. In addition, molecular gas engulfed
by SNR will become cold as the SNR gets old, but still maintains the injected
momentum. Hence, relative motion between different parts of molecular gas in
SNR, i.e. macro-turbulence, leads to the corresponding CO line profile being
broader than that from surrounding quiescent molecular gas. The macro-
turbulence in molecular gas injected by SNR could be very general, especially
in old SNRs where most of the dense shocked molecular gases become cold.
Overall, these effects would result in broadened CO lines from shocked
molecular gases. Unlike CO lines from molecular outflows in star-forming
regions, these broadened CO lines usually present as extra peaks beside narrow
CO lines from surrounding quiescent molecular gases. Such kinematic evidence
in SNRs is very useful to confirm SNR-MC associations. It is noteworthy that
such broadened CO lines might not be present in some young SNRs that are
associated with MCs, because CO molecules nearby can be dissociated by UV
radiation from progenitor massive stars or strong shock heating of these young
SNRs, and, in general, the kinetic energy of SNR’s shock is not sufficiently
converted into a molecular cloud (e.g., Inoue et al., 2012; Zhou et al.,
2016b; Celli et al., 2019; Sano et al., 2020, and references therein).

An SNR will also reshape nearby MCs, which can destroy less dense molecular
gas and leave a cavity, or can accumulate molecular gas and form a shell
(e.g., Seta et al., 1998a; Inutsuka et al., 2015). Spatial correlation is
commonly used as evidence of SNR-MC association. Many known SNR-MC
associations are proposed based on their spatial correlations (see Table 2 in
Jiang et al., 2010). In some cases, spatially correlated MCs originate from
wind-blown bubbles of the SNR’s progenitor, especially for very young SNRs or
PWNe, for which kinematic evidence barely exists (Chevalier, 1999; Chen et
al., 2013, and references therein). Note that the spatial correlation evidence
is not as robust as the kinematic evidence, since overlapping of multiple MCs
across the Galactic plane through the line of sight would complicate the
spatial distribution of molecular gases.

Our goal is to search universally for evidence of kinematic and spatial
correlation of SNR-MC association. Thereafter, we also need to settle
associated spectral components, by comparing the searching results of broad
line and spatial correlation, comparing them with the radio continuum emission
of SNRs, and eliminating the contamination of overlaid energetic objects.
Finally, we can determine the systemic velocity of MCs associated with SNRs.
In this paper, the velocity of the intensity peak of the associated spectral
component, which represents the local standard of rest (LSR) velocity of the
main part of molecular gas, is considered as the systemic velocity of MCs
associated with SNRs. The detail of searching method is presented in Section
3.1 and 3.2.

###  3.1 Broad Line Identification

Kinematic evidence of SNR-MC associations would present as broadened lines,
and the goal is to search these broadened lines in 12CO (J=1–0) data. At the
beginning, we smooth all 12CO (J=1–0) spectra by bin nearby three channels, to
get a high signal-to-noise ratio in broad line searching. The spectral
resolution after smoothing is 0.48 km s-1, which is about half of the
narrowest 12CO (J=1–0) line. Then, we decompose these spectra into individual
spectral components, of which the minimum intensity of bottoms is $1\sigma$,
the minimum intensity of peak-to-valley differences is $3\sigma$, and the
minimum intensity of peaks is $5\sigma$. Broad line identifications are
performed based on these spectral components. For these spectral components,
we identify broad lines first, then find broader lines in the SNR region than
those in the background if exist. Broad lines are identified by following
criteria.

  * •

The full width at half maximum (FWHM) of the spectral component be larger than
6 km s-1.

  * •

The kurtosis of the component be larger than 1.1 times that of the best-
fitting Gaussian function with the same FWHM in the same velocity range.

  * •

The square rooted variance of channels with intensity greater than the best-
fitting Gaussian function be smaller than or equal to the square rooted
variance of all channels of the whole component.

  * •

All required values be over three times their $\sigma$ errors.

As indicated by the Larson’s line width-size relationship, the typical FWHM of
12CO (J=1–0) lines of normal, parsec scale, quiescent MCs is below $\sim$6 km
s-1 (Heyer & Dame, 2015). The 12CO (J=1–0) line of most shocked molecular
gases is with FWHM greater than 6 km s-1 (e.g., SNR HB3; Zhou et al., 2016c).
The FWHM of the 12CO (J=1–0) line of some small shocked molecular clumps can
be lower than 6 km s-1; however, such clumps only occupy a small part of the
shocked molecular gas in the SNR in most cases. Therefore, we adopted 6 km s-1
as a lower limit of the FWHM of broad lines. Note that, for SNRs adjacent to
MCs of much larger size, a larger FWHM threshold will be applied to identify
broad lines associated with SNRs in the following step, which depends on the
FWHM of background spectral components. The information on the width of
background lines can also help us to eliminate some line overlapping effects.

Figure 1: Test results of broad line identification. The spectrum comprising
two Gaussian components is used for test, with standard deviations of
$\sigma_{1}$ and $\sigma_{2}$ and the distance between their peaks of $\Delta
x_{0}$. The FWHM of the first Gaussian component is set to 3, i.e.
$\sigma_{1}$ is 1.27. Results are similar for other values of $\sigma_{1}$.
Black contours show the distribution of the kurtosis ratio between the
spectrum and a best-fitting Gaussian function. Red contours show the
distribution of the square rooted variance ratio between the part of the
spectrum larger than the best-fitting Gaussian function and the whole
spectrum. Panels in the left column show cases that the broad Gaussian
component is weaker than the narrow component, with peak ratios of 0.2, 0.5,
and 0.8 from top to bottom, respectively. The right column is opposite, with
the ratios of peaks between the broad and narrow components of 5, 2, and 1.2
from top to bottom, respectively. Gray scale regions indicate where two
Gaussian components can be resolved. Blue dashed lines denote regions selected
by full broad line identification criteria.

We use the kurtosis value to characterize the deviation from a Gaussian
profile, of which a larger value indicates a distribution with extra wings.
Together with the variance of channels with intensity greater than the best-
fitting Gaussian function, we can eliminate some line overlapping effects. As
shown in Figure 1, components comprising a strong narrow line plus a weak
broad wing are mostly selected, and those comprising a strong broad line plus
a weak narrow line are eliminated. The CO emission of shocked MC by an SNR
usually presents as a strong narrow line plus a broadened line wing, where the
narrow line originates from the quiescent matrix MC and the broad wing from
shocked molecular gas. Narrow lines of some small molecular clumps in SNRs
could be weaker than broad lines, or no narrow line left at all. However, in
most cases, such small molecular clumps contribute only a small portion of
shocked molecular gas comparing to that from the large matrix MC (e.g., Zhou
et al., 2016c), and velocities of these broad lines are usually significantly
shifted from that of corresponding narrow lines, which are easily to be
distinguished as separate spectral components. Commonly, overlapping CO lines
from different MCs in the line-of-sight do not have such features. For
instance, in some star-forming regions, central dense molecular gases are
mostly disturbed, where broad CO lines are stronger. These criteria are
strict, which may eliminate some individual broad lines, but they provide more
accurate results for SNRs in complicated backgrounds.

In the following step, we further select broader lines within the SNR region
than that in the background. The size of the SNR region is 1.1 times enlarged
than that indicated by its radio continuum emission. These broader lines are
considered as primary kinematic evidence of the SNR-MC association. The final
FWHM threshold for selecting broad lines originating from SNRs satisfies the
condition that their FWHM is larger than or equal to the average FWHM of
background broad lines. In practice, some SNRs still have many broad lines at
different velocities selected. In this case, we add an additional condition to
select broad lines for reference. The additional condition requires that the
final FWHM threshold be larger than all broad lines in at least one of equally
divided sub-regions in the background, which have areas comparable to that of
the SNR region. Note that, for SNRs with simple backgrounds, this additional
condition does not change the broad line identification results. This
additional condition is hereafter referred to as the clean subbackground
region condition. Thereby, we can better identify broad lines originating from
SNRs in backgrounds where CO lines are broad, e.g., nearby the Galactic
center.

As noted above, full broad line identification criteria are strict, which
provide better accuracy but less completeness. Full broad line identification
criteria plus the clean subbackground region condition are even more strict.
As a complement, a second broad line identification procedure is performed,
applying only partial criteria, i.e. FWHM and error criteria, and the final
FWHM threshold being larger than or equal to the average FWHM of background
broad lines. Broad lines identified only by partial criteria are considered as
broad line candidates.

At last, identified broad lines in an SNR are divided into different
components, according to their intensity peaks being in each other’s velocity
range or not. The systemic velocity of broad line groups is determined as the
velocity of the overall intensity peak of corresponding 13CO (J=1–0) emission.
If there is no significant 13CO (J=1–0) emission, the systemic velocity is
applied as the velocity of the overall intensity peak of 12CO (J=1–0)
emission. The case that broad lines being adjacent to the associated narrow
lines is common, since the SNR shock is slow when it transmitted into a dense
cloud. Broad lines are also usually strong near the observed boundary of
shocked MCs, where the column density of shocked molecular gas is high, and
LSR velocities in the line-of-sight direction of these broad lines are low.
The systemic velocity obtained based on broad lines would represent the LSR
velocity of most quiescent molecular gases in most cases. Nevertheless, some
broad lines can be shifted to velocities far away from associated narrow
lines, and are identified as separated broad line components. Therefore,
further examination is needed to settle the systemic velocity of associated
MCs, e.g., spatial correlation examination that is introduced in Section 3.2.

###  3.2 Spatial Correlation Coefficient

To examine spatial correlation between SNRs and MCs, we calculate spatial
correlation coefficients (abbreviated as SCCs below) between a series of
circular rings and channel maps of 12CO (J=1–0) emission. Positions and sizes
of SNRs, which are used to derive circular rings, are mostly determined by
radio continuum emission of SNRs. For preparation, 12CO (J=1–0) data is moment
masked at first (see Dame, 2011, for reference), to eliminate noise that
affects the result of weak emission. 12CO (J=1–0) channel maps are also
linearly interpolated to an $80\times 80$ pixel resolution and normalized to
maximum intensity of 1. The $80\times 80$ pixel resolution would simplify the
calculation, and enables the smallest circular ring to be still resolved. The
minimum inner radius of circular rings, corresponding to a quarter of the
radius of SNRs, is at least 4 pixels, and the maximum inner radius is 20
pixels. The increment of the inner radius of the series of circular rings is 1
pixel. Thicknesses of circular rings are from 2 to 30 pixels at intervals of 2
pixels. The results obtained with these parameters are fully feasible for the
following calculations. After these preparations, we calculate Spearman
correlation coefficients between 12CO tile images and ring template images, as
$\rho=\frac{\Sigma_{i}(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sqrt{\Sigma_{i}(x_{i}-\bar{x})^{2}\Sigma_{i}(y_{i}-\bar{y})^{2}}}$.
This SCC would be large for molecular gases with similar spatial distributions
to circular rings. Since the large number of pixels outside the SNR has a
large impact on the SCC result, we only consider pixels inside ring templates
or within twice the SNR radius. In the following step, we select the largest
coefficient for each channel map, and make a coefficient versus velocity
channel plot. In the plot, velocity channels with coefficients over $3\sigma$
levels usually congregate into different groups that correspond to velocity
components in CO spectra. Groups of coefficients with peaks over $5\sigma$
confidence level, or over $3\sigma$ confidence level and larger than 0.5, are
considered as candidates of correlated components. If there is no coefficient
over $5\sigma$ or larger than 0.5, the maximum coefficient over $3\sigma$ will
be given for reference. In addition, SCCs that consider pixels inside ring
templates or within the SNR radius are also calculated, which can better
examine thin molecular shell structures around an SNR. Note that the SCC would
be underestimated in some cases, e.g., correlations between partial shells or
other irregular shapes, nevertheless, they are still noticeable on the
coefficient versus velocity plot in most cases.

###  3.3 Demonstration

We perform our searching method to several known SNR-MC associations for
demonstration at first, and it helps us to optimize the parameters of the
algorithm. Among these known SNR-MC associations, SNR IC 443, SNR HB 3, and
SNR G16.0$-$0.5 are representative of SNRs with clear, simple, and complicate
CO emission backgrounds, respectively.

####  3.3.1 IC 443

Figure 2: Integrated intensity and index-velocity maps of 12CO (J=1–0)
emission toward SNR IC 443. Both intensity maps in the left column are
integrated over the velocity range of $-$15.9 to $-$1.6 km s-1, which covers
most of the broad lines. The red dashed circle denotes the remnant region,
defined by visual inspection according to the bright radio continuum shell of
the remnant. Regions A, B, C, D, E, F, G, and H are adopted from Denoyer
(1979a), Dickman et al. (1992), where shocked molecular gases were detected by
12CO (J=1–0) emission. Region C′ is an additional shocked molecular clump,
which is adjacent to region C. Locations of broad lines identified by full
(upper) and partial (lower) criteria are denoted by red tiny stars. The
minimum value of 12CO emission intensity shown in the colorbar is at $5\sigma$
confidence level. The beam is represented by a black circle in the lower left
corner. This beam designation is used in all intensity maps in the paper.
Index-velocity maps in the right column contain all significant 12CO (J=1–0)
emission lines in the 1.1 times enlarged remnant region, whose intensity is
normalized and logarithmically scaled for better visibility. The index
indicates the arrangement of the spectrum at each point, sorted by the
distance of the point from the SNR center. Some distances are shown on the
right axis. The center of each region adopted from previous works in intensity
maps is also shown in index-velocity maps. Broad lines identified by full
(upper) and partial (lower) criteria are in red, and remaining lines with FWHM
over 6 km s-1 are in blue.

The association between SNR IC 443 and MCs has been well-established in
previous works. The variety of molecular lines studied for this remnant is the
most complete, providing a good understanding of the physics of the
interaction between the SNR shock and the molecular gas (e.g., van Dishoeck et
al., 1993). There are nine shocked molecular clumps in IC 443, which exhibit
broad 12CO (J=1–0) line emission (Denoyer, 1979a; Huang et al., 1986; Dickman
et al., 1992; Lee et al., 2012a). These clumps are indicated in Figure 2.
Eight of them are labeled as A through H, following the nomenclature in
Dickman et al. (1992), and the remaining one that is adjacent to clump C is
labeled as C′, which was named as SC 05 in the study of Lee et al. (2012a).
Note that we apply a circular region to denote the remnant in our analysis,
which is defined following the northern bright radio continuum shell of the
remnant, and there is also radio continuum emission in the south outside the
region. As shown in Figure 2, we identify broad lines in five clumps by the
full criteria, and in eight clumps by the partial criteria. The broad 12CO
(J=1–0) line emission in clump A is too weak, with $T_{A}^{*}\sim 0.3$ K
(Denoyer, 1979a), which is below our detection limit, hence, we found no broad
line there. The broad line emission in clump H is also weak, and we only
identify broad lines there by partial criteria. In clumps B and C, broad lines
are far blue-shifted, separated from the associated narrow line component,
which are only identified by partial identification criteria. We evaluate the
accuracy of the broad line identification by
$(n_{p,SNR}-n_{p,outside})/(n_{p,SNR}+n_{p,outside})$, where $n_{p,SNR}$ and
$n_{p,outside}$ are numbers of broad line points per unit area inside and
outside the SNR region, respectively. For IC 443, the broad line
identifications using either full or partial criteria have an accuracy of 1.
It benefits from the clean MC background toward the SNR in the outer Galactic
region. We also evaluate the completeness of the broad line identification by
the number ratio between identified broad lines and all lines with FWHM over 6
km s-1. For IC 443, the completeness of broad line identifications using full
and partial criteria is $\sim$0.20 and 1, respectively. Some broad lines
separated from the associated narrow component or stronger than the narrow
component are eliminated by full criteria. Since there is no contamination
from background line emission, the identification by partial criteria is the
most effective.

For SNR IC 443, the SCC has a maximum value of 0.24 at $-2.1$ km s-1, which is
over $3\sigma$ but below $5\sigma$ levels. The velocity of the maximum SCC is
consistent with that of molecular gas associated with the remnant. As seen in
Figure 2, associated molecular gas presents some partial shell structures
surrounding the remnant. These partial shell structures result in large SCCs.
However, central bright CO emission makes the enhancement of the SCC less
significant. These associated partial shells were studied by Su et al.
(2014a), which are possibly swept up by the stellar wind of the remnant’s
progenitor.

Both the kinematic evidence and the spatial correlation result indicate that
SNR IC 443 is associated with the $-$3.0 km s-1 velocity component. Based on a
full distance probability density function777http://bessel.vlbi-
astrometry.org/node/378 (Reid et al., 2016, 2019), the kinematic distance of
the $-$3.0 km s-1 component is estimated as 2.10$\pm 0.03$ kpc, which is
located in the Perseus spiral arm. Note that Yu et al. (2019) also measured
the distance of the associated MC by dust extinction estimation as
1729${}_{-94}^{+116}$ pc.

####  3.3.2 HB 3

Figure 3: Same as Figure 2, but for SNR HB 3. Both integrated intensity maps
in the left column are in the velocity range of $-57.3$ to $-26.8$ km s-1.
Regions a1, a2, b1, b2, c, and d are adopted from Zhou et al. (2016c), which
indicate positions of shocked molecular clumps. All broad lines outside the
SNR region are located in the star-forming region W3.

Figure 4: Maximum spatial correlation coefficients (SCCs) at each velocity
channel and 12CO (J=1–0) intensity maps at the corresponding velocity channel
at the SCC peak for SNR HB 3. Dashed and dotted lines in panels in the left
column denote $5\sigma$ and $3\sigma$ levels, respectively. Black circles in
panels in the right column indicate the annular template applied in the
calculation to obtain the maximum SCC. The red dashed circle is the same as in
Figure 3. Upper panels show SCC results considering pixels inside the ring
template or within twice the SNR radius, which has a significant peak at
$\sim$$-$42.2 km s-1. For comparison, the peak of the SCC at $\sim$$-$41.6 km
s-1 in lower panels, considering pixels inside the ring template or within the
SNR radius, is not above $5\sigma$, however, it distinguishes the molecular
shell structure around the SNR more precisely.

SNR HB 3 was initially suggested to be associated with MCs based on their
spatial correlations (Landecker et al., 1987; Routledge et al., 1991), and
this was further supported by broadened CO lines and H2 2.12 $\mu$m emission
detected in later studies (Zhou et al., 2016c; Rho et al., 2021). Note that
broadened 12CO(J=2–1) line emission toward this remnant was detected by
Kilpatrick et al. (2016), but was suggested to be associated with the H ii
region W3 (OH) rather than HB 3. SNR HB 3 is associated with the nearby H ii
region/MC complex W3 (e.g., Zhou et al., 2016c), hence, there is broad line
emission in the background. Line overlapping effect in the direction of the
outer galaxy toward this SNR is not significant. All shocked molecular clumps
found by detailed examination in Zhou et al. (2016c) are also identified here
by partial criteria, i.e. in regions a1, a2, b1, b2, c, and d (see Figure 3).
Many broad lines outside the SNR region are also identified, and all of them
are located in the star-forming region W3 (see Figure 3), possibly associated
with H ii regions within it. The accuracy and completeness of the broad line
identification using partial criteria are 0.98 and 0.61, respectively. Since
the broad line identification is barely affected by line overlapping effect
for this SNR, the accuracy of using partial criteria is high. There are fewer
broad lines identified in the remnant using full criteria, and the
corresponding accuracy is evaluated as 0.94. The number ratio between broad
lines identified inside and outside the remnant using full criteria is a bit
less than that using partial criteria. The completeness of the broad line
identification using strict full criteria is as low as 0.11.

In the SCC plot in the upper left panel in Figure 4, when considering pixels
inside ring templates or within twice the SNR radius, a component with a peak
above the $5\sigma$ confidence level indicates a correlation between SNR HB 3
and molecular gas at $\sim$$-$42.2 km s-1. The SCC result considering pixels
inside ring templates or within the SNR radius also supports this correlation
(see panels in the bottom row in Figure 4). There is a molecular shell at
$\sim$$-$42.2 km s-1 spatially correlated with the bright radio continuum
shell of the remnant well (also seen in Zhou et al., 2016c). Since the
molecular shell occupies only about a quarter of the ring surrounding the
remnant (see the right panel in Figure 4), the peak of the SCC is only 0.22,
which is underestimated.

The kinematic evidence and the spatial correlation result indicate that SNR HB
3 is associated with the $-$44.0 km s-1 velocity component. Based on the full
distance probability density function, the kinematic distance of the $-$44.0
km s-1 component is estimated as 1.96$\pm 0.04$ kpc, which is located in the
Perseus spiral arm.

####  3.3.3 G16.0-0.5

Figure 5: Same as Figure 2, but for SNR G16.0$-$0.5. Two integrate intensity
maps of 12CO (J=1–0) emission in the upper row are in the velocity ranges of
+35 to +50 km s-1 (left) and +60 to +80 km s-1 (right). Locations of broad
lines at velocities of +43.7 and +67.9 km s-1 are denoted by tiny stars on the
corresponding left and right integrated intensity maps, respectively. Broad
lines identified by partial criteria are in pink, those by full criteria are
in red, and those by full criteria plus the clean subbackground region
condition are in blue. Cyan contours in both integrated intensity maps are at
half the column density maximum of shocked molecular gas obtained by Beaumont
et al. (2011). The GLEAM 200 MHz radio continuum emission map in power-law
scale is superimposed on the upper left corner of the left integrated
intensity map, overlaid with the same red dashed circle as in integrated
intensity maps. In the index-velocity maps in the bottom row, broad lines
identified by full criteria plus the clean subbackground region condition
(left), full criteria (middle), and partial criteria (right) are in red.

Figure 6: Same as Figure 4, but for SNR G16.0$-$0.5. The red dashed circle in
the right panel is the same as in Figure 5. The peak of the SCC at $\sim$+63.3
km s-1 in upper panels is above 0.5, nevertheless, the peak of the SCC in
lower panels at $\sim$+37.6 km s-1 is not so significant.

Beaumont et al. (2011) applied Support Vector Machines (SVMs) machine learning
algorithm to classify broadened 12CO (J=3–2) lines in SNR G16.0$-$0.5, and
found shocked shell-like molecular gas in a wide velocity range from $-5$ to
+90 km s-1. Near-infrared H2 lines at +51 km s-1 were also detected toward
this SNR (Lee et al., 2020). SNR G16.0$-$0.5 locates in the inner galaxy
direction, where line overlapping effect is serious. It needs strict criteria
to identify broad lines in such complicated background. Here, applying full
criteria, we identify three broad line components in the SNR at velocities of
+43.7, +67.9, and +87.5 km s-1. The identification accuracy for the +67.9 km
s-1 component is the highest, which is 0.83, and accuracies of other two
components are around 0.3. The total completeness is only $\sim$0.08. The high
accuracy and low completeness indicate an efficient suppression of line
overlapping effect. The +43.7 and +67.9 km s-1 broad line components are also
identified when using full criteria plus the clean subbackground region
condition. Accordingly, identification accuracies of two components are
improved to 0.59 and 0.92, respectively, and the overall completeness drops to
0.03. Overall, broad line identification using partial criteria seems greatly
affected by line overlapping effect, with broad line candidates identified at
many velocities. Nevertheless, many broad line candidates at +67.9 km s-1 are
identified using partial criteria, and most of them are distributed in the
remnant (see Figure 5). There are also many broad line candidates identified
at +43.7 km s-1 by partial criteria, which are widely distributed inside and
outside the remnant. As shown in Figure 5, the shocked molecular shell
detected by 12CO (J=3–2) emission in the remnant (Beaumont et al., 2011) is
mainly composed of gases of the +67.9 km s-1 velocity component, which also
follows the remnant’s radio continuum shell peak well. Some molecular gas of
the +43.7 km s-1 velocity component contributes to the shocked molecular shell
outside the remnant.

The peak of the SCC for SNR G16.0$-$0.5 is at $\sim$+63.3 km s-1 and above
0.5, which considers pixels inside the ring templates or within twice the
radius of the SNR (see the upper left panel in Figure 6). In addition, the
$\sim$+63.3 km s-1 component in the velocity versus SCC plot is wide. There is
shell-like molecular gas at $\sim$+63.3 km s-1 spatially correlated with the
southeastern radio continuum shell of the remnant. It supports the association
between the remnant and the $67.9$ km s-1 broad line component. Nevertheless,
when considering pixels inside the ring templates or within the radius of the
SNR, the SCC has a nonsignificant peak at $\sim$+37.6 km s-1. Molecular gas at
$\sim$+37.6 km s-1 is distributed around the southeastern and southwestern
boundaries, which belongs to the +43.7 km s-1 broad line component.

There is not much 12CO (J=3–2) emission detected around +67.9 km s-1 as shown
by Beaumont et al. (2011). 12CO (J=3–2) line emission is efficient to trace
hot shocked molecular gas but not cold quiet molecular gas. Based on the
spatial correlation result as well as identified broad CO lines with high
accuracy, the SNR is probably associated with the +67.9 km s-1 component.
However, we cannot totally rule out the possibility of an association between
the SNR and the +43.7 km s-1 component. Note that a further study of the
expanding gas motion suggests that the +43.7 km s-1 component is associated
with another object, which supports the association between SNR G16.0$-$0.5
and the +67.9 km s-1 component (Zhou et al. 2023, in preparation). Based on
the full distance probability density function, the kinematic distance of the
+67.9 km s-1 velocity component is estimated as 3.9$\pm 0.3$ kpc, which is
located in the Norma spiral arm. Kinematic distances of the +43.7 km s-1
component are estimated as 3.2$\pm 0.3$ and 4.0$\pm 0.3$ kpc. The +43.7 km s-1
velocity component might be also located in the Norma spiral arm, as indicated
by the full distance probability density function.

##  4 Results

We universally search for evidence of kinematic and spatial correlation of
SNR-MC association for 149 SNRs, 170 SNR candidates (SNRCs), and 18 pure PWNe
in our coverage. We apply full criteria to identify broad lines associated
with SNRs at first, thereafter, apply the partial criteria to those with no
broad lines found by full criteria. Broad lines identified by the partial
criteria are considered as candidates. In some SNRs, more than one broad line
components at different velocities are found. Multiple broad line components
found in one SNR might all belong to it, which originate from molecular gases
pushed toward and away from us at the near side and far side of the remnant,
respectively. However, such multiple components might also originate from
contamination of the line overlapping effect or overlaid energetic objects. In
particular, in directions perpendicular to the direction of the circular
motion of the solar system barycenter around the Galactic center, i.e. around
l$\sim$$0^{\circ}$ and l$\sim$$180^{\circ}$, MCs in different spiral arms are
with systemic velocities close to each other, where the line overlapping
effect is severe. Some lines are intrinsically indistinguishable in
observations, which affects broad line identification results. For SNRs with
many broad lines at different velocities identified even by full criteria, we
use broad lines identified by full criteria plus the clean subbackground
region condition as a reference. We greatly eliminate the line overlapping
effect in our searching method. Besides, further examination is performed in
settling the systemic velocity of MC associated with SNRs. Spatial
correlations are also examined to support kinematic evidence, or provided as
independent evidence for SNR-MC association candidates. For SNRs and SNRCs
within 10∘ of l$\sim$0∘ or within 5∘ of l$\sim$180∘, where broad line
identifications are affected by serious line overlapping effects, we search
spatial correlation evidence first, and then choose those supported by
identified broad line candidates. For 18 pure PWNe, to identify candidates of
associated MCs, we also search spatial correlation evidence over a large
extent at first, and then further examine related broad lines identified by
full criteria.

Table 1: SNR-MC Associations in Survey.

SNR (Other Name) | GLon | GLat | Coverage | TypeaaType of SNRs, S for shell, C for composite, F for filled center (also known as plerion), and ”?” denotes uncertain ones. | BL $V_{\rm LSR}$bb$V_{\rm LSR}$ of detected broad lines. Those identified only by partial criteria are enclosed by square brackets. | SC $V_{\rm LSR}$ (Coefficient)cc$V_{\rm LSR}$ of spatially correlated molecular gas, with the corresponding spatial correlation coefficient enclosed in brackets. Those with coefficients below 5$\sigma$ confidence level and less than 0.5 are enclosed by square brackets. |  $V_{\rm sys}$ddSystemic velocity of associated MC. ”?” denotes possible ones, see text for details. | DistanceeeKinematic distance corresponding to $V_{\rm sys}$. All kinematic distances are estimated by a full distance probability density function (Reid et al., 2016, 2019), and estimated probabilities are enclosed in brackets. |  $V_{{\rm H{\sc II}}}$ff$V_{\rm LSR}$ of overlapped H ii regions.
---|---|---|---|---|---|---|---|---|---
| ∘ | ∘ | ${}^{\prime}\times^{\prime}$ |  |  km s-1 |  km s-1 |  km s-1 | kpc |  km s-1
G1.4$-$0.1 | 1.460 |  $-$0.154 | 41$\times$41 | S |  +78.9, +127.7 |  [+57.0 (0.40)] |  $-$4.8? |  12.6 (0.23)? |  $-$2.2
G1.9+0.3 | 1.871 | 0.324 | 7$\times$7 | S |  [$-$8.7, $-$2.1, +8.3, +10.0, +49.4] |  - | - |  - |  -
G3.7$-$0.2 | 3.775 |  $-$0.288 | 57$\times$57 | S |  $-$30.6, +9.3, +17.3, +21.3, +83.5 |  +19.2 (0.48), +79.4 (0.55) | +9.3?, +83.5? |  2.9 (0.47)?, 7.7 (0.66)? |  $-$28.9, +4.1
G3.8+0.3 | 3.851 | 0.349 | 81$\times$81 | S |  $-$33.2, $-$0.6, +12.1, +162.9, +173.2, +185.1 |  +8.7 (0.38) | +12.1?, +162.9? |  2.9 (0.60)?, 8.1 (1.00)? |  +7.3
G4.5+6.8 (Kepler) | 4.519 | 6.819 | 14$\times$14 | S |  - |  [+11.7 (0.29)] | - |  - |  -
G4.8+6.2 | 4.776 | 6.231 | 65$\times$65 | S |  - |  [+4.8 (0.46)] | +4.8? |  1.6 (0.26) or 14.8 (0.26) ? |  -
G5.2$-$2.6 | 5.173 |  $-$2.612 | 55$\times$55 | S |  - |  +7.8 (0.30) | +7.8? |  1.5 (0.75)? |  -
G5.4$-$1.2 (Milne 56) | 5.363 |  $-$1.220 | 148$\times$148 | C |  $-$24.9, $-$9.7, +0.3, +11.1, +22.1, +187.5 |  $-$14.8 (0.27), +8.6 (0.27), +29.7 (0.38) |  $-$24.9 |  4.2 (0.56) or 12.1 (0.44) |  -
G5.5+0.3 | 5.545 | 0.368 | 59$\times$59 | S |  +10.3 |  +7.0 (0.55) | +10.3 |  2.9 (0.54) |  -
G6.1+0.5 | 6.104 | 0.479 | 73$\times$73 | S |  +7.0 |  +6.0 (0.33) | +7.0 |  3.0 (0.43) |  -

Note. — The full table is published in machine-readable format with this
paper.

Table 2: SNR candidate-MC Associations in Survey.

SNR candidate | GLon | GLat | Coverage | Type | BL $V_{\rm LSR}$ (Accuracy) | SC $V_{\rm LSR}$ (Coefficient) | $V_{\rm sys}$ | Distance | $V_{{\rm H{\sc II}}}$
---|---|---|---|---|---|---|---|---|---
| ∘ | ∘ | ${}^{\prime}\times^{\prime}$ |  |  km s-1 |  km s-1 |  km s-1 | kpc |  km s-1
G1.95$-$0.10 | 1.929 |  $-$0.091 | 25$\times$25 | F |  $-$42.5, +36.7, +44.7, +88.4, +124.9 |  [+59.5 (0.40)] | +44.7? |  8.1 (0.69)? |  -
G1.98$-$0.46 | 1.975 |  $-$0.460 | 20$\times$20 | S |  +2.2, +12.6, +157.4 |  +5.1 (0.40), +8.6 (0.46) | +12.6? |  2.8 (0.76)? |  -
G2.23+0.06 | 2.228 | 0.058 | 9$\times$9 | S |  [$-$23.2, +11.3, +16.6, +23.7, +156.5] |  $-$15.9 (0.54), $-$6.3 (0.67), $-$2.9 (0.53), $-$1.0 (0.55), +6.0 (0.65), +8.3 (0.51), +19.4 (0.52) | - |  - |  -
G2.28+0.40 | 2.248 | 0.385 | 27$\times$27 | S |  $-$66.8, $-$43.3, +4.8, +13.8, +88.4 |  +3.2 (0.40), +19.0 (0.40) | +4.8? |  2.8 (0.54)? |  +4.9
G2.91$-$0.18 | 2.910 |  $-$0.183 | 48$\times$48 | F |  $-$40.0, $-$13.3, +4.0, +13.3, +18.6, +52.7, +88.8, +102.6, +160.3 |  +14.3 (0.30), +43.3 (0.27) |  $-$40.0 |  4.7 (0.92) |  $-$3.5, $-$2.1, +2.5, +18.1
G3.10$-$0.09 | 3.101 |  $-$0.093 | 16$\times$16 | C |  +23.7 |  $-$18.1 (0.31) | +23.7?, +95.8? |  2.9 (0.29) or 12.6 (0.35) ?, 8.2 (0.90)? |  -
G3.10+0.11 | 3.103 | 0.110 | 9$\times$9 | S |  [+11.3, +22.7, +58.3, +104.9, +123.9, +135.0, +144.5, +153.6] |  +1.7 (0.64), +11.3 (0.55), +17.6 (0.60), +81.9 (0.55), +84.3 (0.61), +87.6 (0.56) | - |  - |  -
G3.1$-$0.6 | 3.100 |  $-$0.600 | 83$\times$83 | C |  $-$41.0, $-$28.4, +6.8, +12.8, +17.4, +19.9, +52.7, +82.2, +102.7 |  [+21.4 (0.37)] |  $-$41.0? |  4.7 (0.71)? |  +0.1, +5.1
G4.20$-$0.30 | 4.164 |  $-$0.333 | 32$\times$32 | C? |  $-$31.4, +7.1, +15.3 |  [+0.8 (0.40)] |  $-$31.4? |  4.7 (0.67)? |  -
G4.49$-$0.39 | 4.482 |  $-$0.391 | 29$\times$29 | F |  +6.0, +14.1, +20.8, +43.2 |  +16.3 (0.37), +44.4 (0.41) | +14.1? |  2.9 (0.61)? |  -

Note. — Same as Table 4 but for SNR candidates. The full table is published in
machine-readable format with this paper.

Table 3: SNR-MC Associations Studied in Previous Works in Our Coverage. SNR (Other Name) |  OH 1720 MHz Maser $V_{\rm LSR}$aa”?” denotes a PWN or pulsar (PSR) candidate. |  CO BL $V_{\rm LSR}$bb$V_{\rm LSR}$ of spatially correlated (SC) molecular gas, with the corresponding spatial correlation coefficient enclosed in brackets. Those with coefficients below 5$\sigma$ confidence level and less than 0.5 are enclosed by square brackets. |  CO SC $V_{\rm LSR}$ccDetection of broad line (BL) emission related to spatially correlated molecular gas. Those identified only by partial criteria are enclosed by squared brackets. |  Other Evidences $V_{\rm LSR}$ddSystemic velocity of candidate MC associated with the PWN, and ”?” denotes possible ones, see text for details. |  ReferenceeeKinematic distance corresponding to $V_{\rm sys}$, with the estimated probability enclosed in brackets. The same calculation method as in Table 4 is used, except the distance of CTB 87 estimated by the extinction-distance relation in previous work (Foster & Routledge, 2002; Kothes et al., 2003), and the distances of G47.38$-$3.88 and Geminga estimated by parallax measurements (Chatterjee et al., 2004; Faherty et al., 2007).
---|---|---|---|---|---
|  km s-1 |  km s-1 |  km s-1 |  km s-1 |
G1.4$-$0.1 |  $-$2.3 to $-$2.5 |  - |  - |  $-$32.6 to +29.9 (CH3OH 36 GHz maser) |  1, 2, 3
G1.9+0.3 |  D |  - |  - |  - |  1
G5.4$-$1.2 (Milne 56) |  $-$21 |  - |  $-$21 |  - |  4, 5
G5.5+0.3 |  - |  - |  +12.5 |  - |  5
G6.4$-$0.1 (W28) |  +2.45 to +15.94 |  +5.8, +7 |  Y |  $-$2.3 (OH 6035 MHz maser), +6.8 to +8.2 (CH3OH 36 and 44 GHz maser), +6.1 to +13.1 (CS line), +6.3 to +7.4 (HCO+) |  1, 10, 11, 12, 13, 14, 3, 6, 7, 8, 9
G8.7$-$0.1 (W30) |  +36 |  - |  - |  - |  4
G9.7$-$0.0 |  +43 |  - |  - |  - |  4
G9.9$-$0.8 |  - |  +31 |  - |  +30 (H2 line) |  15, 16
G11.0$-$0.0 |  - |  - |  +21, +40 |  +30 (SiO and CO lines, CS and HC3N SC) |  17, 18, 19
G11.1+0.1 |  - |  - |  +56 |  - |  18
G11.1$-$0.7 |  - |  - |  +33 |  - |  18
G11.2$-$0.3 |  D |  +32 |  +33 |  +45 (H i absorption), +48 (H2 line) |  1, 15, 16, 18, 20
G11.4$-$0.1 |  D |  - |  +30, +50 |  - |  1, 18
G11.8$-$0.2 |  - |  - |  +49.8 |  - |  18
G12.0$-$0.1 |  D |  - |  +37.4 |  - |  1, 18
G12.2+0.3 |  - |  +50 |  - |  - |  15
G13.3$-$1.3 |  D |  - |  - |  - |  1
G13.5+0.2 |  - |  - |  +24 |  +40 (H2 line) |  16, 18
G15.4+0.1 |  - |  - |  +34, +47.8 |  +60 (H i SC), +60 (H i absorption) |  18, 21, 22
G15.9+0.2 |  - |  - |  +29 |  - |  18
G16.0$-$0.5 |  - |  +40 |  - |  +51 (H2 line) |  16, 23
G16.7+0.1 |  +19.92 to +20.0 |  +25 |  +25.6, +47, +62 |  - |  1, 15, 18, 24, 7
G17.0$-$0.0 |  - |  - |  +31, +93.4 |  - |  18
G17.4$-$2.3 |  D |  - |  - |  - |  1
G17.8$-$2.6 |  D |  - |  - |  - |  1
G18.1$-$0.1 |  - |  - |  +53.1, +49 |  +100, +102, +103.74 (H i absorption), +73 to +85 (H2 line) |  16, 18, 25, 26, 27, 28
G18.6$-$0.2 |  - |  +42 |  +62, +66 |  +62 (H i absorption), +62.84 (H i absorption) |  15, 18, 25, 26, 29
G18.8+0.3 (Kes 67) |  - |  - |  +19, +20, +21.35 |  +20 (CO (2–1)/(1–0) ratio of 1.25), +21.35 (H i absorption), +19 (H i SC) |  18, 26, 30, 31, 32, 33, 34
G18.9$-$1.1 |  - |  - |  +25.6 |  +23 (H i absorption), +70 (H2 line) |  16, 35, 36, 37
G20.0$-$0.2 |  - |  - |  +65, +66, +66.4 |  +66.4 (H i absorption) |  18, 26, 38
G21.5$-$0.9 |  D |  - |  - |  $\sim$+68 (H i absorption) |  1, 26, 39
G21.8$-$0.6 (Kes 69) |  +69.3 to +69.76 (compact), +83.6 to +85.2 (extended) |  - |  +83, +85, +93.35 |  +85 (HCO+ line on radio peak), +86 to +93.35 (H i absorption), +61 (H2 line) |  1, 16, 18, 26, 39, 40, 7
G22.7$-$0.2 |  D |  +77 |  +75, +76.63, +77 |  +76.63 (H i absorption) |  1, 18, 26, 41, 42
G23.3$-$0.3 (W41) |  D (at +71) |  - |  +63, +70, +77, +78.51 |  +63 (H i SC), +78.51 (H i absorption) |  1, 18, 26, 42, 43, 44, 45
G24.7$-$0.6 |  D |  - |  +60, +60.67 |  - |  18, 46, 47
G24.7+0.6 |  - |  - |  +112 |  - |  18
G27.4+0.0 (Kes 73, 4C$-$04.71) |  D |  +100 |  +90, +101 |  +90 (CO (2–1)/(1–0) $\sim$ 1.1), +99.95 (H i absorption), +99 (H2 line) |  1, 15, 16, 18, 26, 48
G27.8+0.6 |  D |  - |  - |  - |  47
G28.6$-$0.1 |  - |  - |  +86 |  - |  18, 46
G29.6+0.1 |  - |  +94 |  +99.2 |  - |  15, 18
G29.7$-$0.3 (Kes 75) |  D |  +53, +54 |  +52, +54, +95, +112 |  +95 to +102 (H i absorption) |  1, 15, 18, 26, 49, 50
G31.5$-$0.6 |  - |  - |  +87.5, +97 |  - |  18
G31.9+0.0 (3C 391) |  +97.04 to +110.2 |  +103.9 to +112 |  +107, +100 |  +100 (H2 line), +104.2 to +108.9 (broad CS line), +111.4 (broad HCO+ line) |  1, 15, 16, 18, 47, 51, 52, 53, 54, 55, 7
G32.1$-$0.9 |  - |  - |  +95 |  +85 (H2 line) |  16, 18
G32.4+0.1 |  - |  +43 |  +10.8, +42.6 |  - |  15, 18
G32.8$-$0.1 (Kes 78) |  +86.1 |  +81 |  +74, +81, +81.81, +103 |  +81 (CO (2–1)/(1–0) ratio enhanced), +81.81 (H i absorption), +90 (H2 line) |  16, 18, 26, 56, 57
G33.2$-$0.6 |  - |  - |  +54, +91 |  +82 (H2 line) |  16, 18
G33.6+0.1 (Kes 79) |  D |  $\sim$+105 |  +70, +80, +103, +105 |  +80 (CO (3–2)/(1–0) $>$ 0.8 and CO shell in P-V map), +105 (HCO+ line), +95 (H i SC), +57.9 (H i absorption) |  1, 15, 18, 26, 58, 59, 60, 61, 62
G34.7$-$0.4 (W44) |  +23.8 to +47.35 |  +40, +45, +46.6, +47.5, +48 |  +40, +48, +52 |  +40 and +45 (high-J CO lines; CO (2–1)/(1–0) $>$ 1), +40 and +47.5 (HCO+ line), +41 to +49 (H2 line), +48 (13CO (1–0)/12CO (1–0) $\sim$ 0.03 and HCO+ (1–0)/12CO (1–0) $\sim$ 0.3), +54.4 (OH 6035 MHz maser), +40.9 to +47.1 and +6.7 to +56.9 (CH3OH 36 and 44 GHz maser), +50.48 (H i absorption) |  1, 10, 11, 16, 18, 26, 6, 63, 64, 65, 66, 67, 68, 69, 7, 70, 71, 72, 8
G35.6$-$0.4 |  - |  - |  +55, +90 |  +63.67 (H i absorption) |  18, 26, 73, 74
G36.6$-$0.7 |  - |  - |  +57, +79 |  - |  18
G39.2$-$0.3 (3C 396) |  D |  +69, +77, +84 |  +51, +67, +69, +69.39, +84 |  +56 (H2 line), +69.39 (H i absorption) |  1, 15, 16, 18, 26, 75, 76, 77
G39.7$-$2.0 (W50) |  - |  +53, +77 |  +32 |  +53 (CO (2–1)/(1–0) $>$ 0.9, CN (3/1–1/2)), +77 (H i SC) |  78, 79, 80
G40.5$-$0.5 |  - |  - |  +55, +58, +67 |  - |  18, 81, 82
G41.1$-$0.3 (3C 397) |  - |  +31, +32 |  +32, +38, +40 |  - |  15, 18, 83, 84
G41.5+0.4 |  - |  - |  +58 |  - |  18
G42.0$-$0.1 |  - |  - |  +66 |  - |  18
G43.3$-$0.2 (W49B) |  - |  +14 |  +10, +32, +40, +45, +62 |  +11 (OH 6035 MHz maser), +63 (HCO+ broad line, high HCO+ (1–0)/CO (1–0) ratio), +12.55 (H i absorption), +40 (H i absorption), +10 (CO high Tex and $\sim$+6 km s-1 expanding motion), +64 (H2 line) |  11, 15, 16, 18, 26, 85, 86, 87, 88
G43.9+1.6 |  - |  +50 |  Y |  - |  89
G45.7$-$0.4 |  - |  - |  +26, +48.5 |  - |  18
G46.8$-$0.3 (HC30) |  - |  +19 |  +19, +52 |  +0 to +40.4 (H i absorption) |  18, 90
G49.2$-$0.7 (W51C) |  +68.9 to +72.13 |  +60 |  +50, +60 |  +67.6 (OH 6035 MHz maser), +60 (HCO+ line), +57.6 to +76.2 (CH3OH 36 GHz maser), $\sim$+70 (H i absorption) |  1, 11, 18, 63, 7, 91, 92, 93
G53.6$-$2.2 (3C 400.2) |  - |  - |  - |  +27 (H i SC) |  94
G54.1+0.3 |  - |  +23 |  +23, +53, +53.66 |  +53.66 (H i absorption) |  26, 95, 96, 97
G54.4$-$0.3 (HC40) |  - |  - |  +36.66, +40 |  +44 (H2 line) |  16, 52, 98
G57.2+0.8 (4C$-$21.53) |  +30 |  - |  +12, +30 |  $-$46 (H i SC) |  100, 99
G59.5+0.1 |  - |  +28 |  Y |  +28 (CO (3–2)/(2–1) $\sim$ 1.58) |  101
G63.7+1.1 |  - |  - |  $\sim$+13, +21 |  $\sim$+13 (H i SC) |  102, 103
G69.0+2.7 (CTB 80) |  - |  +11.5 |  +11.5 |  +13.5 (H i SC) |  104
G73.9+0.9 |  - |  - |  +3 |  - |  105
G74.9+1.2 (CTB 87) |  - |  $-$58 |  $-$58, $-$57.3, $-$57 |  $-$64 (H i SC) |  106, 107, 108, 109
G78.2+2.1 (DR4) |  - |  - |  $-$2 to +13.6 |  - |  110, 111, 112
G84.2$-$0.8 |  - |  - |  $-$39, $-$17 |  - |  105, 106, 113
G85.4+0.7 |  - |  - |  $-$41 |  - |  105
G89.0+4.7 (HB 21) |  - |  $-$5, +3 |  $-$5, $-$3, $\sim$$-$1 ($-$10 to +8) |  +3 (CO (2–1)/(1–0) ratio of 1.6 to 2.3), $\sim$$-$1 (H i SC) |  114, 115, 116, 117
G93.7$-$0.2 (CTB 104A) |  - |  - |  - |  $-$6 (H i SC) |  118
G94.0+1.0 (3C 434.1) |  - |  - |  $-$13 |  $-$13 (CO (2–1)/(1–0) ratio $\sim$ 1.6) |  105, 119
G106.3+2.7 |  - |  - |  $-$6.4 |  $-$6.4 (H i SC) |  120
G109.1$-$1.0 (CTB 109) |  - |  $\sim$$-$55 |  $-$50 to $-$48 |  $-$50 (H i SC) |  121, 122, 123, 124
G111.7$-$2.1 (Cas A) |  - |  $\sim$$-$40 |  Y |  $-$38 (H2CO distance matching), $-$40 (H i SC and multibands consistency) |  125, 126, 127, 128, 129, 15
G116.9+0.2 (CTB 1) |  - |  - |  - |  $-$32 (H i SC) |  130
G120.1+1.4 (Tycho) |  - |  $-$63.5 |  $-$63.5, $-$62, $-$61 |  $-$61 (high CO (2–1)/(1–0) ratio), $-$51.5 (H i SC) |  131, 132, 133, 134, 135
G127.1+0.5 (R5) |  - |  $\sim$+5 |  Y |  - |  136
G130.7+3.1 (3C 58) |  - |  - |  - |  $-$39.1 to $-$34.1, $\sim$$-$38 (H i absorption), $\sim$$-$36 (H i absorption and SC) |  137, 138, 139
G132.7+1.3 (HB 3) |  - |  $-$45, $-$42, $-$40 |  $-$45, $-$43, $-$42, $-$40.5 |  $-$30 (H i SC), $-$42 (high-J CO lines with co-spatial H2 emission) |  140, 141, 142, 143, 15
G141.2+5.0 |  - |  - |  - |  $-$53 (H i SC) |  144
G160.9+2.6 (HB 9) |  - |  - |  - |  $-$6 (H i SC) |  145
G166.0+4.3 (VRO 42.05.01) |  - |  - |  $-$22 |  $-$6 (H i SC and CO velocity gradient), $-$34 (H i SC) |  106, 146, 147
G180.0$-$1.7 (S147) |  - |  - |  - |  $-$2.5 (optical extinction SC) |  148
G182.4+4.3 |  - |  - |  +4 |  - |  105
G189.1+3.0 (IC 443) |  $-$32.0 to $-$3.5 |  $-$40.5 to $-$3.5, $-$5, $-$4.5, $-$4, $-$3, $-$2, +5 |  $-$4.5, $-$4, $-$3.6, +5 |  $-$5 (OH absorption line), $-$4.5 (high-J CO lines, CO line polarization), +9 (Hα line), $-$2 (CO (2–1)/(1–0) ratio $>$ +3, CO (3–2)/(2–1) $\sim$ 1.58), $-$4 (H i line with broad wing), $-$10 (H2 line), $-$5 (HCO+ and HCN self-absorption, CN, SiO, CS, SO, and H2CO lines), $-$44.2 to $-$4.2 (CS, HCN, HNC, DCN, HCO+, H13CO+, H2CO, H213CO, CH3OH, CH3CN, HC3N, CO+, C2H, C3H2, HDO, SiO, SO, SO2, H2S, and H2CS lines), $-$3.5 (H i emission, CO, HCO+, HCN, and H2 lines) |  1, 149, 15, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 6, 68, 7
G205.5+0.5 (Monoceros Loop) |  - |  $\sim$+5, $\sim$+19 |  +5, +10, $\sim$+11, $\sim$+15, +19, +20 |  - |  166, 167, 168, 18
G206.9+2.3 (PKS 0646+06) |  - |  - |  +15 |  - |  166
G213.0$-$0.6 |  - |  $\sim$+9 |  +9, +21 |  - |  166, 18
G5.7$-$0.1 |  +13 |  - |  +12 |  $-$26.4 and $-$24.4 (CH3OH 36 and 44 GHz maser) |  4, 5, 63
G21.8$-$3.0 |  - |  - |  +5.9 |  - |  169
G28.56+0.00 |  - |  - |  - |  +96.6 (RRL of H ii region assumed to be associated by H i absorption) |  37
G29.4+0.1 |  - |  - |  $\sim$+82 |  - |  170
G44.5$-$0.2 |  - |  +60 |  Y |  +60 (H i SC) |  171
G51.21+0.11 (G51.26+0.11) |  - |  - |  - |  +37 to +70 (H i absorption) |  172

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Results of SNRs and SNRCs are listed in Table 4 and 4, respectively. We only
present short versions of Table 4 and 4 here, and full versions are only
available in electronic form. Systemic velocities of MCs associated with SNRs
and SNRCs are settled, and corresponding kinematic distances are estimated by
the full distance probability density function (Reid et al., 2016, 2019). Note
that CO (J=1–0) emission is more advantageous in determining the systemic
velocity of the associated MC, from which sufficient information about quiet
molecular gases can be obtained. The systemic velocity is a directly observed
quantity, and the kinematic distance is model dependent. To avoid bias between
different models, we uniformly apply the full distance probability density
function to estimate kinematic distances here. We also considered available H
i absorption results in previous works for some SNRs to discriminate between
near and far kinematic distances. For comparison, we also list the results of
SNR-MC associations studied in previous works in Table LABEL:tab:snrpre (see
also Table 1 in Ranasinghe & Leahy, 2022, for a summary of known SNR
distances). For known SNRs, about 60% of them were found to be associated with
MCs in previous works, however, new SNR-MC associations have still been
gradually discovered in recent years. For SNRCs and PWNe, the study of MCs
around them is still very limited, of which only about 4 and 11%,
respectively, were found to be associated with MCs in previous works. It is
worth noting that in some SNRs different evidence gives different velocity
results. On the other hand, the interaction details of some SNR-MC
associations were very well studied, with shocked molecular gases investigated
through multiband observations, e.g., W28, W44, IC 443, etc. (see Table
LABEL:tab:snrpre for details).

We present details of searching results of SNRs and SNRCs in Sections
LABEL:sec:snr and LABEL:sec:snrcand, respectively. In Section LABEL:sec:pwn,
we discuss searching results for pure PWNe. Corresponding figures of
individual objects are available online (Zhou et al., 2023).

###  4.1 SNRs

SNR-MC association results are summarized in Table 4. In order to better
confirm the association evidence, further investigations, e.g., on spatial
correlations with partial radio continuum shells or locations of broad lines,
are performed on some objects, especially those with more than one broad line
components identified. We also make efforts to eliminate contaminations of
other energetic sources overlapped, e.g., H ii regions. All considered H ii
regions are introduced from the WISE catalog of Galactic H ii regions
(Anderson et al., 2014), which is one of the most complete catalogs of H ii
regions in the Galaxy. Systemic velocities of H ii regions overlapping SNRs
are listed in Table 4. 12CO or 13CO velocities of H ii regions are applied for
better comparison with our data, and if they do not exist, velocities of other
tracers are used. As noted by Anderson et al. (2014), velocities of most H ii
regions by different tracers are consistent, the mean of absolute velocity
differences between molecular and ionized gas emission is $\sim$4 km s-1.

Among 149 SNRs studied in this paper, 57 of them are found to be associated
with MCs, and 70 of them are considered to be possibly associated with MCs. 40
of the 57 SNR-MC associations and 43 of the 70 possible SNR-MC associations
were studied in previous works (see Table LABEL:tab:snrpre). There are also 7
SNRs with no associated MC found here, but suggested to be associated with
surrounding clouds in previous works, mostly based on spatial correlations
with H i gases. Few SNR-MC association results in this paper are not the same
as those in previous works, including 7 of SNR-MC associations and 4 of
possible SNR-MC associations, i.e. G9.9-0.8, G11.1+0.1, G15.4+0.1, G16.0-0.5,
G18.9-1.1, G24.7+0.6, G41.5+0.4, G21.5-0.9, G29.7-0.3, G84.2-0.8, and
G93.7-0.2. We discuss individual SNRs in Appendix A.

###  4.2 SNR Candidates

We list all results of SNRC-MC associations in Table 4. Most of SNRCs in our
coverage have been recently discovered (Kassim, 1988; Gorham, 1990; Gray,
1994; Trushkin, 2001; Brogan et al., 2006; Helfand et al., 2006; Gerbrandt et
al., 2014; Anderson et al., 2017; Hurley-Walker et al., 2019a; Gao et al.,
2020; Dokara et al., 2021; Ranasinghe et al., 2021), which are not well
studied by multiband observations. A similar approach to study SNR-MC
associations is performed to investigate associations between SNRCs and MCs.
All types of SNRCs are examined in the same way, in particular, no enlargement
of coverage is applied for plerionic SNRCs.

170 SNRCs are examined, and 50 of them are suggested to be associated with
MCs. There are also 91 of SNRCs considered to be possibly associated with MCs.
For all SNRCs, only six of them were studied in previous works, of which five
are considered as possible SNRC-MC associations and one as a fixed SNRC-MC
association here. The result for one of them is not the same as that in
previous works, i.e. G28.56+0.00. We discuss individual SNRCs in Appendix B.

###  4.3 PWNe

We examine MCs around 18 pure PWNe here, to search candidates of associated
MCs. Our results of PWN-MC association candidates are presented in Table
LABEL:tab:pwn. Kinematic distances of PWN-MC association candidates are
estimated. Some of these PWNe have distance estimation results from previous
works, which are comparable to the distance results here. Note that most
distance measurements in previous works are for associated pulsars. Only two
PWNe are with surrounding CO emissions studied in previous works, i.e.
G63.7+1.1 and CTB 87, of which possible associations with MCs are found here.
There are another two PWNe with surrounding H i emission studied in previous
works, i.e. 3C 58 and G141.2+5.0, however, no associated MCs are found here.

We discuss individual PWNe in Appendix C.

##  5 Discussion

###  5.1 Proportion of SNRs associated with MCs

Ratios of SNRs associated with MCs along the Galactic longitude are shown in
Figure LABEL:f:visl, including fixed and all SNR-MC associations in known and
all SNRs, respectively. All SNRs include known and candidate SNRs. The ratio
of previously detected SNR-MC associations in known SNRs is also shown for
reference. All ratios have similar distributions, which are large within the
Galactic longitude of $\sim$50∘. It is consistent with the distribution of the
ratio of previously detected SNR-MC associations. If all previously detected
SNR-MC associations are real, the accuracy of fixed SNR-MC associations
suggested in this paper would be at least 70%, and at least 60% for possible
SNR-MC associations. Among the previously detected SNR-MC associations, 91%
are identified here by 12CO (J=1–0) line emission. 12CO (J=1–0) line emission
of SNR-MC associations can be contaminated by background emission. However, it
is still a good tracer for these associations. Note that there are about 41%
of previously detected SNR-MC associations suggested as fixed SNR-MC
associations here, and about 50% considered as possible ones.

Figure LABEL:f:type shows the number of different types of SNRs and that
associated with MCs. Except for SNRs of certain composite type, all types of
SNRs contain about 30% fixed SNR-MC associations. Considering that only about
half of previously detected SNR-MC associations are identified as fixed SNR-MC
associations, there is probably more than 60% of SNRs associated with MCs. As
indicated by the number of all fixed and possible SNR-MC associations, the
percentage of SNRs associated with MCs could be as high as about 80. Among
different types of SNRs, composite type SNRs have the highest proportion of
being associated with MCs. This is reasonable, since composite SNRs are
originated from core-collapse supernovae, and they are interacting with
surrounding medium. Filled-center type SNRs are also originated from core-
collapse supernovae; however, they have no radio continuum shell indicating
effective interactions with surrounding medium. As indicated by the number of
all fixed and possible SNR-MC associations for composite type SNRs, there
could be close to 90% of core-collapse SNRs interacted with MCs during their
lifetime.

###  5.2 Distribution of SNRs associated with MCs

We estimate radii of SNRs that are associated with MCs, based on their angular
sizes and kinematic distances. Angular sizes are estimated from radio
continuum emission of SNRs or associated molecular shell-like structures for
those with no significant radio continuum emission detected. Kinematic
distances of SNRs are estimated based on systemic velocities of their
associated MCs by applying the full distance probability density
function888http://bessel.vlbi-astrometry.org/node/378 (Reid et al., 2016,
2019). We also estimate progenitor initial masses of some SNRs based on their
linear relationship with the size of the main-sequence interstellar bubble in
a molecular environment, which is reflected by the size of SNRs associated
with MCs (see details in Chen et al., 2013). Since this relationship is only
valid for stars in the mass range of 8 to 25–30 $M_{\sun}$, those with
estimated progenitor masses outside this range are excluded. The number of
SNRs with small-mass progenitors far exceeds the number of SNRs with large-
mass progenitors. SNRs misidentified at large distances have a large impact on
the mass distribution, even though their number is comparable to that of SNRs
misidentified at small distances. Therefore, when estimating progenitor
masses, we use only the smallest distance of all possible distances for each
possible SNR-MC association.

Distributions of the radii and the progenitor initial masses of the SNRs
associated with MCs are shown in Figure LABEL:f:snrprop, which are fitted by
lognormal and power-law distribution functions, respectively. Fitting of the
mass distributions starts at the peak. For both radius and progenitor initial
mass distributions, fitting parameters for fixed SNR-MC associations except
for those within 10∘ of l$\sim$0∘ and 5∘ of l$\sim$180∘ are consistent with
that for all fixed and possible SNR-MC associations. It indicates that
possible SNR-MC associations do not introduce any significant systematic
deviations. The radius distribution of SNRs associated with MCs peaks at
$\sim$8.1 pc. The progenitor initial mass distribution has an index of
$\sim$$-2.3$, which is consistent with the Salpeter index of $-2.35$
(Salpeter, 1955; Bastian et al., 2010, etc.).

The height from the Galactic plane for SNR-MC associations is estimated
according to their kinematic distances. Because of the Sun’s vertical
displacement from the Galactic midplane, there is a small angle between the
Galactic plane and the $b=0^{\circ}$ plane. The position of the Galactic
midplane is derived from fixed SNR-MC associations in known SNRs except for
those within 10∘ of l$\sim$0∘ and 5∘ of l$\sim$180∘ by the least squares
fitting. Thereby, the height of the Sun above the Galactic midplane is
estimated as $\sim$15.7 pc. We use the same Galactic plane position to
calculate the height of all SNR-MC associations. Distributions of the height
from the Galactic plane for SNR-MC associations are shown in Figure
LABEL:f:hgal. The height distribution of all SNR-MC associations has two
components, a major narrow component and a minor broad component. Some
possible SNR-MC associations with uncertain distances may contribute to the
broad component; however, the broad component still exists when we use only
the minimum distance among all possible distances for each possible SNR-MC
association. The number of fixed SNR-MC associations is limited, of which the
height distribution may also have a weak broad component, not significant. It
can be fitted well by one Gaussian function. For the height distribution of
all SNR-MC associations, the thicknesses (i.e. FWHMs) of two components are
estimated as $65\pm 6$ and $182\pm 64$ pc, respectively. The thickness (i.e.
FWHM) is estimated as $90\pm 9$ pc for the height distribution of the fixed
SNR-MC associations, which is consistent with that of the thin CO disk
revealed by Su et al. (2019). However, it may be just an intermediate value
between the thicknesses of two components of the distribution of all SNR-MC
associations. SNR-MC associations may trace MCs of active star-formation. The
thin and thick disks of MCs associated with SNRs found here may be inner
layers of the thin and thick CO disks revealed by Su et al. (2019),
respectively. The ratio of the peak of the thin and thick disks of SNR-MC
associations is about 6, which is larger than that of CO disks, i.e. about 2.
It indicates that the star-formation may be more efficient in the thin disk.

Figure LABEL:f:rh shows correlations between the radius and the height from
the Galactic plane for SNRs associated with MCs. Fixed and all SNR-MC
associations selected from known SNRs except for those within 10∘ of l$\sim$0∘
and 5∘ of l$\sim$180∘ and all SNR-MC associations, respectively, are
considered separately. In the interval where the height is less than $\sim$45
pc, the average radius distribution is roughly flat. When the height is
greater than $\sim$45 pc, the average radius for both fixed and all SNR-MC
associations increases with the height. The turning point of the relation
between the radius and the height, i.e. at $\sim$45 pc, is consistent with the
thickness of the thin CO disk revealed by Su et al. (2019). The radius of an
SNR is related to its age, its ambient particle density, and the energy of its
supernova explosion. The age and supernova explosion energy of SNRs are
probably not correlated with their heights from the Galactic midplane.
Different ages and explosion energies would make the radius scattered very
much in Figure LABEL:f:rh. The relationship between the average radius and the
height may be caused by a height-dependent density distribution of molecular
environments around SNRs. Though, some SNRs associated with MCs are
interacting with cavity or shell-like molecular structures that may be relics
of wind-blown bubbles created by their progenitor stars, yet, the sizes of
these molecular structures are still confined by ambient particle density. As
the ambient particle density becomes larger, the radius of SNRs becomes
smaller. Therefore, such relation between the average radius and the height
probably indicates that the overall density of MCs with active star-formation
does not vary much in the thin CO disk. Beyond the thin CO disk, it decreases
with increasing height from the Galactic plane. Further investigation on MCs
themselves is needed to draw a definite conclusion.

##  6 Summary

The MWISP project is an unbiased 12CO/13CO/C18O (J = 1–0) survey of the
Galactic plane in the northern sky. We universally search for evidence of
kinematic and spatial correlation of SNR-MC associations for nearly all SNRs
in the coverage of the MWISP CO survey, i.e. 149 SNRs, 170 SNRCs, and 18 pure
PWNe in $1^{\circ}<l<230^{\circ}$ and $-5.^{\circ}5<b<5.^{\circ}5$. Based on
the high-quality CO data obtained from the MWISP survey, we apply automatic
algorithms to identify broad lines and spatial correlations for molecular gas
in each SNR region. The searching method is demonstrated to be efficient.
Among 149 SNRs studied in this paper, 57 of them are found to be associated
with MCs, and 70 of them are considered to be possibly associated with MCs. We
find 50 SNRCs to be associated with MCs, and 91 SNRCs to be possibly
associated with MCs. We also find candidates of associated MCs for 14 pure
PWNe. Assuming all SNR-MC associations detected in previous works are real,
the accuracy of fixed SNR-MC associations suggested in this paper would be at
least 70%, and at least 60% for possible SNR-MC associations. The 91%
previously detected SNR-MC associations are identified in this paper by CO
line emission, which indicates that CO line emission is efficient for
detecting SNR-MC associations. The nine previously detected SNR-cloud
associations (about 9%) are not identified here, which are mostly based on
spatial correlations with H i gases. We find that the proportion of SNRs
associated with MCs is high within the Galactic longitude of $\sim$50∘, with
the distribution consistent with that of previously detected SNR-MC
associations. Overall, there could be as high as 80% of SNRs associated with
MCs.

Based on systemic velocities of associated MCs, kinematic distances of SNRs
are estimated. Accordingly, distributions of their radii, progenitor initial
masses, and heights from the Galactic plane are studied. We find that the
radius and progenitor initial mass distributions of SNRs associated with MCs
follow lognormal and power-law distributions, respectively. The radius
distribution peaks at $\sim$8.1 pc, and the progenitor initial mass
distribution has an index of $\sim$$-2.3$ that is consistent with the Salpeter
index of $-2.35$. SNR-MC associations are mainly distributed in a thin disk
and also distributed in a faint thick disk along the Galactic plane. For only
fixed SNR-MC associations except for those within 10∘ of l$\sim$0∘ and 5∘ of
l$\sim$180∘, due to their limited number, the thick disk is hard to
distinguish, and the overall thickness (FWHM) is estimated as 90$\pm 9$ pc.
For both fixed and possible SNR-MC associations, thicknesses (i.e. FWHMs) of
the thin and thick disks are estimated as 65$\pm 6$ and 182$\pm 64$ pc,
respectively. The thin and thick disks found here may be inner layers of the
thin and thick CO disks revealed by Su et al. (2019), respectively. The ratio
of peaks of the thin and thick disks of SNR-MC associations is about 5, which
is larger than that of CO disks, i.e. about 2. It indicates that star-
formation may be more efficient in the thin disk. The Sun’s vertical
displacement from the Galactic midplane is estimated as $\sim$15.7 pc. Radii
of SNRs associated with MCs show some correlations with their heights from the
Galactic plane, with a turning point at the height of $\sim$45 pc. When the
height is below $\sim$45 pc, the average radius distribution is roughly flat,
and the radii of individual SNRs are much scattered. When the height is above
$\sim$45 pc, the average radius increases with the height. It indicates that
the overall density of MCs with active star-formation may not vary much in the
thin CO disk, and it decreases with increasing height from the Galactic plane
beyond the thin CO disk.

We thank the anonymous referee for providing very helpful comments that
improved the paper and its conclusions. This research made use of the data
from the Milky Way Imaging Scroll Painting (MWISP) project, which is a
multiline survey in 12CO/13CO/C18O along the northern Galactic plane with PMO
13.7m telescope. We are grateful to all the members of the MWISP working
group, particularly the staff members at PMO 13.7m telescope, for their long-
term support. MWISP was sponsored by National Key R&D Program of China with
grant 2017YFA0402701 and CAS Key Research Program of Frontier Sciences with
grant QYZDJ-SSW-SLH047. Y.Su and J.Y. are supported by National Natural
Science Foundation of China through grants 12173090 and 12041305,
respectively. Y.Sun acknowledges support by the Youth Innovation Promotion
Association, CAS (Y2022085), and the “Light of West China” Program (No. xbzg-
zdsys-202212).

##### Data Availability

Figures of individual objects are available online in https://www.scidb.cn/en,
at https://doi.org/10.57760/sciencedb.08076 (Zhou et al., 2023).

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##  Appendix A Individual SNRs

G1.4-0.1: This SNR is near the Galactic center, and presents a partial radio
continuum shell in the west. As indicated by the SCC, molecular gas at
$\sim$+3.2 km s-1 is distributed around the remnant. It belongs to the $-$4.8
km s-1 component with broad line candidates identified in the remnant only by
partial criteria. The association between the remnant and the $-$4.8 km s-1
component is also supported by OH 1720 MHz masers detected in the SNR at
$\sim$$-$2.4 km s-1 (see Table LABEL:tab:snrpre). Molecular gas at the
nonsignificant peak of the SCC at $\sim$+57.0 km s-1 is distributed around the
northern boundary of the remnant, which is not well correlated with the
remnant’s radio continuum emission. There is also molecular gas at $\sim$+99.1
km s-1 distributed around the western half of the remnant. It belongs to the
+78.9 km s-1 component with broad line candidates identified in the remnant by
full criteria, of which two alternative kinematic distances are estimated as
8.1$\pm 2.1$ and 11.1$\pm 0.3$ kpc. However, the association between the
remnant and the +78.9 km s-1 component is not supported by OH 1720 MHz and
CH3OH 36 GHz maser emission detected in previous works (see Table
LABEL:tab:snrpre). If the remnant is associated with the $-$4.8 km s-1
component, its kinematic distance can be estimated as 12.6$\pm 0.3$ kpc.
G1.9+0.3: The radius of this SNR is less than the beam size of our
observation, which is too small to examine possible spatial correlations. No
broad line candidate is identified in it by full criteria. G3.7-0.2: This SNR
presents radio continuum shells in the north and south. Molecular gas at the
peak of the SCC at $\sim$+19.2 km s-1 is roughly surrounding the SNR. It
probably belongs to the +9.3 km s-1 component, since broad line candidates at
+17.3 and +21.3 km s-1 can be attributed to the nearby prominent component at
+9.3 km s-1. Kinematic distances corresponding to these velocities are
consistent. In addition, molecular gas at $\sim$+2.5 km s-1 belonging to the
+9.3 km s-1 component is distributed around the northern boundary of the
remnant. Molecular gas at another peak of the SCC at $\sim$+79.4 km s-1 is
distributed around and within the northeastern and southeastern boundaries of
the remnant, which belongs to the +83.5 km s-1 component with broad line
candidates identified in the remnant. There are also molecular gases at
$\sim$$-$27.1 km s-1 distributed around the southern half of the remnant and
also inside, which belongs to the $-$30.6 km s-1 component with broad line
candidates identified in the remnant by full criteria. Some broad line
candidates at $-$30.6 km s-1 are associated with an overlapped H ii region in
the northwest. Based on kinematic evidence and the spatial correlation result,
the SNR is probably associated with the +9.3 km s-1 component, or may be
associated with the +83.5 km s-1 component. Corresponding kinematic distances
are estimated as 2.9$\pm 0.2$ kpc for the +9.3 km s-1 component and 7.7$\pm
2.1$ kpc for the +83.5 km s-1 component. Note that the association between the
SNR and the $-$30.6 km s-1 component cannot by totally ruled out, of which the
kinematic distance is estimated as 4.7$\pm 0.3$ kpc. G3.8+0.3: As indicated by
the SCC, molecular gases at $\sim$+8.7 and $\sim$+165.6 km s-1 are roughly
surrounding the southeast and southwest of this SNR, respectively. These
molecular gases belong to the +12.1 km s-1 and +162.9 km s-1 components,
respectively, which are with broad line candidates identified in the remnant
by full criteria. For the +12.1 km s-1 component, there is also molecular gas
at $\sim$+17.5 km s-1 distributed around the northern boundary of the remnant,
where radio continuum emission is bright. Note that some broad line candidates
at +12.1 km s-1 are probably originated from a small overlapped H ii region in
the east, but not all. Based on these evidences, the SNR is probably
associated with the +12.1 km s-1 component, or may be associated with the
+162.9 km s-1 component. Kinematic distances are estimated as 2.9$\pm 0.2$ kpc
for the +12.1 km s-1 component and 8.1$\pm 2.8$ kpc for the +162.9 km s-1
component. G4.5+6.8 (Kepler): Kepler’s SNR (SN 1604) is believed to have
originated from a Type Ia supernova (Sun & Chen, 2019, and references
therein). There is very little CO emission detected in the SNR region at
velocities of $\sim$+4 and $\sim$+12 km s-1. We find no broad line emission
and no good spatial correlation result for the SNR. G4.8+6.2: This SNR is
located at a high Galactic latitude nearby Kepler’s SNR. Molecular gas at the
peak of the SCC at $\sim$+4.8 km s-1 is roughly surrounding the eastern half
of the remnant. No broad line candidate is identified in the remnant even by
partial criteria. If the remnant is associated with molecular gas at
$\sim$+4.8 km s-1, its near and far kinematic distances can be estimated as
1.6$\pm 0.3$ and 14.8$\pm 0.3$ kpc, respectively. Considering that the
remnant’s height from the Galactic plane would be too high at the far
kinematic distance, i.e. $\sim$1.6 kpc, it is probably located at the near
kinematic distance at 1.6$\pm 0.3$ kpc. G5.2-2.6: A small amount of molecular
gas is detected around this SNR. At the peak of the SCC at $\sim$+7.8 km s-1,
there are three small molecular clumps distributed on the radio continuum
shell of the remnant. There is no broad line candidate identified in the
remnant even by partial criteria. If the remnant is associated with molecular
gas at $\sim$+7.8 km s-1 its kinematic distance can be estimated as 1.5$\pm
0.2$ kpc. G5.4-1.2 (Milne 56): This SNR presents bright shell-like radio
continuum emission in the northwest. Molecular gas at the peak of the SCC at
$\sim$+29.7 km s-1 is roughly surrounding the northeast of the remnant but not
well correlated with its bright radio continuum shell. Among multiple
components with broad line candidates identified in the remnant, only the
$-$24.9 and +187.5 km s-1 components show some spatial correlations with the
remnant’s bright radio continuum shell. Note that broad line candidates at
$-$9.7 km s-1 are probably originated from the nearby prominent component at
$-$24.9 km s-1. The association between the remnant and the $-24.9$ km s-1
component is also supported by the detection of the OH 1720 MHz maser at $-21$
km s-1 (see Table LABEL:tab:snrpre). Therefore, the remnant is suggested to be
associated with the $-24.9$ km s-1 component, of which the near and far
kinematic distances are estimated as $4.2\pm 1.1$ and $12.1\pm 0.9$ kpc,
respectively. G5.5+0.3: As indicated by the SCC, molecular gas at $\sim$+7.0
km s-1 is roughly surrounding the southern half of this SNR, where its radio
continuum emission is bright. There is also molecular gas at $\sim$+7.0 km s-1
distributed around the northern boundary of the remnant. These molecular gases
belong to the +10.3 km s-1 component, which is the only component with broad
line candidates identified in the remnant by full criteria. A small part of
the remnant in the west overlaps with SNRC G5.38+0.35, nevertheless,
identified broad lines are not in this region. These evidences indicate that
the remnant is associated with the +10.3 km s-1 velocity component. This
result is consistent with that in a previous work (see Table
LABEL:tab:snrpre). Accordingly, we estimate the kinematic distance of the
remnant as $2.9\pm 0.2$ kpc. G6.1+0.5: Most of this SNR overlaps with SNRC
G6.06+0.50 and SNRC G6.12+0.39, and it is also adjacent to SNRC G6.31+0.54. It
is difficult to determine the morphology of radio continuum emission from the
SNR. Molecular gas at the peak of the SCC at $\sim$+6.0 km s-1 seems to be
distributed around the northwestern half of the remnant, which belongs to the
+7.0 km s-1 velocity component. The +7.0 km s-1 component is the only
component with broad line candidates identified in the SNR by full criteria.
Most of the broad line points are located in the overlapping region with SNRC
G6.06+0.50, but not all. Based on these evidences, we suggest that the SNR is
associated with the +7.0 km s-1 component, of which the kinematic distance is
estimated as 3.0$\pm 0.2$ kpc. G6.1+1.2: This SNR is circulated by molecular
gas at $\sim$+23.2 km s-1 mostly to the east indicated by the SCC. There is
also molecular gas at $\sim$+13.0 km s-1 distributed around the remnant but
not well correlated. These molecular gases may belong to the +12.2 km s-1
velocity component with broad line candidates identified in the remnant by
partial criteria. No broad line candidate is identified in the remnant by full
criteria. If the remnant is associated with the +12.2 km s-1 component, its
kinematic distance can be estimated as 1.5$\pm 0.2$ kpc. G6.4-0.1 (W28): The
association between this SNR and MCs was studied in multiple bands. Wootten
(1981) detected broad molecular lines in the remnant, and subsequent studies
revealed more details of the interactions between the remnant and surrounding
molecular gases (e.g., those in Table LABEL:tab:snrpre). We find that two
molecular stripes at the minor peak of the SCC at $\sim$$-5.9$ km s-1
spatially correlate well with two inner radio continuum shells, where OH 1720
MHz masers were also detected in previous works (see Table LABEL:tab:snrpre).
Molecular gas at $\sim$$-5.9$ km s-1 belongs to the +6.1 km s-1 velocity
component. Several groups of broad line candidates at the +6.1 km s-1 are
identified in the remnant by full criteria, which are located on the remnant’s
radio continuum shells. Molecular gases at other peaks of the SCC at
$\sim$$-$21.1, $\sim$+22.1, and $\sim$+24.3 km s-1 are mostly distributed in
the remnant, but not well correlated. These evidences indicate that the SNR is
associated with the +6.1 km s-1 MC, of which the near and far kinematic
distances are estimated as 3.0$\pm 0.2$ and 12.6$\pm 0.3$ kpc, respectively.
G6.5-0.4: The northwestern half of this SNR overlaps with SNR W28, and it also
overlaps with SNRC G6.45-0.56 and SNRC G6.54-0.60 in the south. Molecular
gases at minor peaks of the SCC at $\sim$$-$9.7 and $\sim$$-$16.7 km s-1 are
roughly surrounding the northwest and northeast of the remnant, respectively.
They belong to the $-$13.4 km s-1 component with broad line candidates
identified in the remnant by full criteria. Molecular gas at the peak of the
SCC at $\sim$+4.0 km s-1 is distributed around the boundary of the remnant but
not well correlated, which belongs to the +6.5 km s-1 component. Note that
broad line candidates at +6.5 km s-1 identified in the remnant are probably
originated from SNR W28, and that at +20.6 km s-1 may be originated from an
overlapped H ii region. There is no broad line candidate identified in SNRC
G6.45-0.56 and SNRC G6.54-0.60 by full criteria. Based on these evidences, we
suggest that SNR G6.5-0.4 is associated with the $-13.4$ km s-1 component and
locates at a kinematic distance of 4.7$\pm 0.3$ kpc. G7.0-0.1: Molecular gas
at the peak of the SCC at $\sim$+47.3 km s-1 is mostly distributed in this
SNR, not well correlated. Molecular gas at the minor peak of the SCC at
$\sim$+6.5 km s-1 is distributed around the remnant but not well correlated.
Corresponding broad line candidates are identified at +18.3 km s-1 in the
remnant by full criteria, and most of the broad line points are distributed
around the eastern radio continuum shell of the remnant. These evidences
indicate that the remnant is associated with the +18.3 km s-1 component,
accordingly, its kinematic distance can be estimated as 3.6$\pm 0.4$ kpc.
G7.2+0.2: This SNR presents bright radio continuum emission in the southeast.
As indicated by the SCC, molecular gas at $\sim$$-$19.2 km s-1 is roughly
surrounding the east of the remnant and distributed around its southwestern
boundary, which belongs to the $-$12.1 km s-1 component. The $-$12.1 km s-1
component is with many broad line candidates identified by partial criteria,
and all broad line points are located in the remnant. Some broad line points
at $-$12.1 km s-1 are located on the radio continuum shell peak of the
remnant. Molecular gases at $\sim$+0.2 and $\sim$+13.3 km s-1 are roughly
surrounding the southeastern half of the remnant. At the peak of the SCC at
$\sim$+19.5 km s-1, molecular gas is distributed around the remnant but not
well correlated. Broad line candidates corresponding to these molecular gases
are identified at +7.0 and +20.4 km s-1 in the remnant by full criteria,
respectively. However, all these broad line candidates may belong to the
prominent component at +20.4 km s-1. The remnant may be associated with either
the $-$12.1 or +20.4 km s-1 components. Kinematic distances are estimated as
18.7$\pm 0.5$ kpc for the $-$12.1 km s-1 component and 3.6$\pm 0.3$ kpc for
the +20.4 km s-1 component. G8.7-0.1 (W30): This SNR presents bright radio
continuum emission in the southwest. Molecular gas at the nonsignificant peak
of the SCC at $\sim$+13.0 km s-1 is roughly surrounding the west of the
remnant, correlated with its radio continuum emission. It probably belongs to
the +19.3 km s-1 component with broad line candidates identified in the
remnant by full criteria. Molecular gas of the +33.9 km s-1 component is with
enhanced CO emission distributed around the southwestern boundary of the
remnant, which is best correlated with the remnant’s radio continuum emission.
Molecular gas at the peak of the SCC at $\sim$+30.0 km s-1 is distributed near
and within the boundary of the remnant. Molecular gas at the minor peak of the
SCC at $\sim$+41.1 km s-1 belonging to the +33.9 km s-1 component is roughly
surrounding the south of the remnant. An OH 1720 MHz maser was also detected
at +36 km s-1 in previous work (see Table LABEL:tab:snrpre), which also
supports the association between the remnant and the +33.9 km s-1 component.
Molecular gas at the minor peak of the SCC at $\sim$+181.0 km s-1 is roughly
surrounding the north of the remnant but not correlated with its radio
continuum emission. Based on these evidences, we suggest that the remnant is
associated with the +33.9 km s-1 component, and corresponding near and far
kinematic distances are estimated as 2.9$\pm 0.2$ and 12.5$\pm 0.3$ kpc,
respectively. G8.9+0.4: As indicated by the SCC, molecular gas at $\sim$+23.5
km s-1 is roughly surrounding the southeastern half of the remnant, which
belongs to the +21.1 km s-1 component. The +21.1 km s-1 component is with
broad line candidates identified in the remnant by full criteria. The spatial
correlation result as well as the corresponding broad line candidates
indicates the association between the remnant and the +21.1 km s-1 component,
of which the kinematic distance is estimated as 3.7$\pm 0.3$ kpc. This SNR is
close to SNR W30; however, they are probably irrelevant. G9.7-0.0: The SCC of
this SNR has no significant peak. As indicated by the SCC, molecular gas at
$\sim$+40.2 km s-1 is roughly surrounding the remnant, which belongs to the
+43.0 km s-1 component with broad line candidates identified in the remnant by
full criteria. Molecular gas at $\sim$+77.5 km s-1 also shows a spatial
correlation with the remnant, which is distributed around its southern
boundary. It may belong to the +61.8 km s-1 component with only one broad line
candidate identified in the remnant by full criteria. The association between
the remnant and the +43.0 km s-1 component is also supported by OH 1720 MHz
maser emission detected at +43 km s-1 (see Table LABEL:tab:snrpre). Based on
these evidences, we suggest that the remnant is associated with the +43.0 km
s-1 MC, of which the kinematic distance is estimated as 3.8$\pm 0.3$ kpc.
G9.8+0.6: The SCC indicates a spatial correlation between this SNR and
molecular gas at $\sim$+31.3 km s-1, which is roughly surrounding the remnant.
It belongs to the +28.9 km s-1 component with broad line candidates identified
in the remnant by full criteria. Therefore, we suggest that the remnant is
associated with the +28.9 km s-1 MC, with the kinematic distance estimated as
2.8$\pm 0.2$ kpc. G9.9-0.8: Broad 12CO(J=2–1) lines at +31 km s-1 and near-
infrared H2 lines at +30 km s-1 were detected toward this SNR (Kilpatrick et
al., 2016; Lee et al., 2020). Here, we find that molecular gas at a peak of
the SCC at $\sim$+11.3 km s-1 is distributed around the northern boundary of
the remnant, which belongs to the +4.6 km s-1 component with a broad line
candidate identified in this SNR by full criteria. Besides, molecular gas at
$\sim$+16.2 km s-1 may belong to the +4.6 km s-1 component too, which is
roughly surrounding the north of the remnant. No good spatial correlation
result is found for other velocity components. Note that broad line candidates
at +28.9 km s-1 identified in the remnant by full criteria seem to be
originated from an overlapped H ii region. These evidences indicate the
association between the remnant and the +4.6 km s-1 MC, and the corresponding
kinematic distance is estimated as 1.5$\pm 0.1$ kpc. G11.0-0.0: This SNR
presents a partial radio continuum shell in the west. Broad lines at +12.0,
+29.7, and +38.4 km s-1 are identified in this SNR by full criteria. Several
broad line points are at +38.4 km s-1, which may be originated from the nearby
prominent component at +29.7 km s-1. Molecular gas around +38.4 km s-1 is
distributed around the eastern and southern boundaries of the remnant,
however, not well correlated with the remnant’s radio continuum shell.
Molecular gas at the significant peak of the SCC at $\sim$+17.6 km s-1 is
distributed around the remnant. Both the +12.0 and +29.7 km s-1 components may
contribute to molecular gas at $\sim$+17.6 km s-1; however, most of the gas
seems to be from the +29.7 km s-1 component. Therefore, we suggest that the
remnant is associated with the +29.7 km s-1 component, hence, it is probably
associated with the nearby filamentary infrared dark cloud G11.11-0.12 (e.g.,
Chen et al., 2023). The corresponding near and far kinematic distances are
estimated as 2.9$\pm 0.3$ and 12.4$\pm 0.3$ kpc, respectively. The near
kinematic distance is preferred, if it is associated with the G11.11-0.12.
G11.1+0.1: This SNR was previously called G11.18+0.11. Sofue et al. (2021)
found a partial shell structure around it, known as G11.2+0.12, at +56 km s-1.
The SNR presents bright shell-like radio continuum emission in its southern
half. Here, several broad line components are identified in the remnant. Only
the +16.4 km s-1 component has many broad line points, and most of them are
located on the southern radio continuum shell. Molecular gas at $\sim$+24.8 km
s-1 is distributed around the southern and eastern boundaries of the remnant.
It supports the association between the remnant and the +16.4 km s-1
component. Therefore, we suggest that the remnant is associated with the +16.4
km s-1 component, of which the near and far kinematic distances are estimated
as 3.8$\pm 0.3$ and 13.4$\pm 0.3$ kpc, respectively. G11.1-0.7: Broad lines at
three velocities are identified in this SNR; however, only one broad line at
+29.2 km s-1 and two broad lines at +41.0 km s-1 are probably originated from
the nearby prominent component at +37.7 km s-1. As indicated by the SCC,
molecular gas at $\sim$+33.7 km s-1, belonging to the +37.7 km s-1 component,
is spatially correlated with the remnant’s radio continuum emission. These
evidences imply an association between the SNR and the +37.7 km s-1 velocity
component. The corresponding kinematic distance is estimated as 3.0$\pm 0.3$
kpc. G11.2-0.3: Broad 12CO(J=2–1) lines at +32 km s-1 and near-infrared H2
lines at +48 km s-1 were detected toward this SNR (Kilpatrick et al., 2016;
Lee et al., 2020, see Table LABEL:tab:snrpre for more information). Here,
broad lines at +0.5, +33.4, and +40.5 km s-1 are identified in the SNR by full
criteria. Only one broad line at +40.5 km s-1 may be originated from the
nearby prominent component at +33.4 km s-1. The SNR is surrounded by molecular
gas at the significant peak of the SCC at $\sim$+37.3 km s-1, which belongs to
the +33.4 km s-1 component. The +0.5 km s-1 broad line component is not well
spatially correlated with the remnant. Based on these evidences, we suggest
that the remnant is associated with the +33.4 km s-1 MC, with the kinematic
distance estimated as 2.9$\pm 0.3$ kpc. The near kinematic distance obtained
here is consistent with the H i absorption result in previous work (Green et