# High-resolution Near-infrared Spectroscopic Study of Galactic Supernova
Remnants. I. Kinematic Distances

Yong-Hyun Lee<EMAIL_ADDRESS>Korea Astronomy and Space Science
Institute, Daejeon 305-348, Korea  Department of Physics and Astronomy, Seoul
National University, Seoul 151-747, Korea  Bon-Chul Koo Department of Physics
and Astronomy, Seoul National University, Seoul 151-747, Korea  Jae-Joon Lee
Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea

###### Abstract

We have carried out high-resolution near-infrared spectroscopic observations
toward 16 Galactic supernova remnants (SNRs) showing strong H2 emission
features. A dozen bright H2 emission lines are clearly detected for individual
SNRs, and we have measured their central velocities, line widths, and fluxes.
For all SNRs except one (G9.9$-$0.8), the H2 line ratios are well consistent
with that of thermal excitation at $T\sim 2000$ K, indicating that the H2
emission lines are most likely from shock-excited gas and therefore that they
are physically associated with the remnants. The kinematic distances to the 15
SNRs are derived from the central velocities of the H2 lines using a Galactic
rotation model. We derive for the first time the kinematic distances to four
SNRs: G13.5$+$0.2, G16.0$-$0.5, G32.1$-$0.9, and G33.2$-$0.6. Among the
remaining 11 SNRs, the central velocities of the H2 emission lines for six
SNRs are well consistent ($\pm 5~{}{\rm km~{}s}^{-1}$) with those obtained in
previous radio observations, while for the other five SNRs (G18.1$-$0.1,
G18.9$-$1.1, Kes 69, 3C 396, W49B) they are significantly different. We
discuss the velocity discrepancies in these five SNRs. In G9.9$-$0.8, the H2
emission shows nonthermal line ratios and narrow line width ($\sim 4~{}{\rm
km~{}s}^{-1}$), and we discuss its origin.

Supernova Remnants (1667); Distance measure (395); Molecular clouds (1072);
High resolution spectroscopy (2096); Interstellar line emission (844)

##  1 Introduction

Distance is an essential and important parameter for the study of Galactic
supernova remnants (SNRs), but its determination is difficult as in most areas
of astronomy. Among the $\sim 300$ known Galactic SNRs, therefore, only a
limited number of SNRs have reliable distance estimates (Green, 2019).

A most popular distance determination method for SNRs is to derive the
kinematic distance from velocity information using a Galactic rotation model.
The classical method is to observe H I 21 cm absorption, which was introduced
in the mid-1950s and was first applied to the SNR Cassiopeia A (Williams &
Davies 1954; Hagen et al. 1955; see also Muller 1959). In this H I absorption
technique, the absorption of 21 cm continuum from an SNR by intervening cold H
I clouds is observed, and the maximum velocity where the absorption occurs
provides a lower and/or upper limit to the distance to the SNR. For SNRs
bright in radio, it is straightforward to apply this technique because the
absorption profiles can be obtained directly from either single-dish or
interferometric observations, although the noncircular motions of H I gas due
to streaming along the spiral arms can hamper the derivation of accurate
limits (e.g., Clark et al., 1962; Green & Gull, 1989; Koo et al., 1993; Kothes
et al., 2003; Kothes, 2013). For SNRs faint in radio, however, it is not
straightforward because, in order to obtain the absorption spectrum by an SNR,
the background spectrum needs to be derived from the observation of the
surrounding area and subtracted from the SNR spectrum, where the random
fluctuation of H I profiles along different lines of sight could produce
artificial absorption features (e.g., Green & Gull, 1982). Recently, an
improved method using high-resolution H I data, together with CO observation
data, has been devised and systematically applied to two dozen SNRs (Leahy &
Tian, 2010; Ranasinghe & Leahy, 2018a, b, and references therein).

For SNRs interacting with ambient molecular clouds (MCs), their kinematic
distances can also be derived from the velocities of the MCs. According to the
compilation by Jiang et al. (2010) and Kilpatrick et al. (2016), there are
$\sim 50$ SNRs suggested to be interacting with MCs. The evidence for the
interaction ranges from a simple morphological association to the presence or
detection of shock signatures such as the broad molecular lines, the high 12CO
$J=$2–1/1–0 line ratios, 1720 MHz OH masers, and near-infrared (NIR)
rovibrational H2 emission lines. The kinematic distances to SNRs have been
derived mainly from the velocities of CO emission lines (Jiang et al., 2010;
Kothes et al., 2003; Kilpatrick et al., 2016, and references therein) or OH
masers (Frail et al., 1996; Green et al., 1997; Yusef-Zadeh et al., 2003;
Hewitt et al., 2008, and references therein). The studies using H2 emission
lines are relatively sparse. The H2 2.122 µm line had been first detected in
the SNR IC 443 in 1979 (Treffers, 1979), and later in several well-studied
SNRs (see Lee et al. 2019 and references therein). There have, however, been
neither systematic studies of SNRs in the H2 2.122 µm line nor spectroscopic
studies to measure the distance of SNRs using the H2 2.122 µm line until very
recently (see below). This contrasts with CO $J=$1–0 115 GHz or OH 1720 MHz
maser lines, the importance of which as a distance indicator had been realized
early and for which systematic surveys toward SNRs were carried out (e.g.,
Huang & Thaddeus, 1986; Frail et al., 1996; Green et al., 1997). The major
reason for the sparseness of such studies in the H2 2.122 µm line might be
because high-performance NIR detector arrays became available relatively
recently (e.g., Rieke, 2007).

Recently, we have carried out a systematic H2-emission line study of SNRs in
the inner Galaxy using the UKIRT Wide-field Infrared survey for H2 (UWISH2;
Froebrich et al., 2011), which is an unbiased survey of the inner Galactic
plane ($7\arcdeg<l<65\arcdeg$ and $|b|<1.3\arcdeg$) in the H2 2.122 µm
emission line (Lee et al., 2019). Among the 79 Galactic SNRs in the survey
area, we detected a total of 19 SNRs with H2 emission features. Comparing the
H2 and radio continuum morphologies, we suggested that the H2 emission
features are associated with the SNRs. Some H2 emission features are found
outside the [Fe II]/X-ray/radio boundaries (known as the “[Fe II]-H2 reversal”
phenomena), but their spatial distribution, together with the H2 emission-line
ratios from a follow-up NIR spectroscopy, indicates that these H2 features are
also probably associated with the SNRs (see also Section 3.1).

In this paper, we present results from high-resolution NIR spectroscopy of the
H2 emission features around the Galactic SNRs detected by Lee et al. (2019).
The purpose of the study is to derive their kinematic distances by measuring
accurate central velocities of H2 lines. This paper is organized as follows.
In Section 2, we describe our NIR spectroscopic observations and the data
reduction procedure. In Section 3, we examine the physical association of H2
emission with the SNRs by investigating the excitation mechanism of the H2
emission from their line ratios and line widths. We also derive their
kinematic distances from the central velocities and compare them with those of
previous radio observations. In Section 4, we discuss one SNR showing
nonthermal excitation of H2 emission lines and also five SNRs whose H2 central
velocities are significantly different from previous results. The summary of
this paper is given in Section 5.

##  2 Observations and Data Reduction

###  2.1 Near-infrared Spectroscopy

We carried out NIR spectroscopy of H2 emission-line features detected around
the Galactic SNRs using the Immersion GRating INfrared Spectrograph (IGRINS)
mounted on the Harlan J. Smith 2.7 m telescope located at McDonald
Observatory. IGRINS is a high-resolution (resolving power $R\sim 45{,}000$)
NIR spectrograph that provides simultaneous wavelength coverage of H and K
band (1.5–1.8 µm and 1.9–2.5 µm, respectively; Yuk et al., 2010; Park et al.,
2014). The slit width and length are $1\arcsec$ and $15\arcsec$, respectively.

The observations had been carried out in 2014 May, 2015 June, and 2016 July.
Among the 19 H2-emitting SNRs confirmed by Lee et al. (2019), 16 were observed
(Figure 1). We carefully selected slit positions to obtain spectra of strong
H2 emission features at the border of the remnants. For several SNRs, the
spectra at multiple slit positions had been obtained. The slit positions of
all the targets are shown in Figure 1. The sizes of the emission features are
either comparable to or larger than the slit length, so we took “OFF”-position
spectra just before or after the target observations to subtract the sky-
background emission/continuum. The single exposure time per frame was limited
to 300 s in order to prevent saturation of the bright-sky airglow emission
lines. To increase the sensitivity for weak H2 emission-line features,
however, we took multiple observations for several H2 emission features. We
also took several spectra of nearby A0V standard stars for photometric
calibration.

For the data reduction, we utilized the dedicated pipeline for IGRINS written
in Python111PLP version 2.2.0. The pipeline package is downloadable at
https://github.com/igrins/plp. The pipeline performs flat-fielding correction
and sky subtraction at the beginning of the data reduction. Then, it performs
distortion correction to produce two-dimensional spectra. Wavelength
calibration was done by comparing the observed OH airglow emission lines with
their vacuum wavelengths, and the overall $1\sigma$ uncertainty is about half-
pixel width, which corresponds to $\sim 1~{}{\rm km~{}s}^{-1}$. For
photometric calibration together with telluric absorption correction, we
derived the wavelength-dependent conversion factor from digital to physical
units by comparing the observed A0V standard stars with the Kurucz model
spectra222Kurucz, R. L. 2003, http://kurucz.harvard.edu/, and we multiplied it
by each target spectrum.

In all the spectra, we clearly detected bright H2 2.122 µm emission lines.
Most of them show other H2 emission lines in $H$ and $K$ bands too. We
performed a single Gaussian fit for all the detected H2 lines (Figure 2),
except for the lines detected in four slits (G18.9$-$1.1-C, Kes 69-NE, and 3C
391-NE and SW), to derive their central velocities, line widths, and fluxes.
For the four exceptions, the observed lines are broad and not well fitted by a
single Gaussian shape (Figure 2). In such cases, we first performed fitting
the H2 2.122 µm line with two Gaussian components, and then we applied its
profile to the remaining H2 lines to measure their fluxes. Therefore, the
relative flux ratio of the two velocity components is the same for every H2
line. All the observed central velocities have been corrected to the
velocities with respect to the local standard of rest (LSR; $v_{\rm LSR}$),
and the observed line widths have been corrected for the instrumental
broadening (7 ${\rm km~{}s}^{-1}$). The extinction correction for the observed
line fluxes has been done by using the hydrogen column density ($N_{\rm H}$)
derived from previous studies (see Table 4 of Lee et al. (2019)), adopting a
general interstellar extinction model with $R_{V}=3.1$ (Draine, 2003). For
four SNRs, G9.9$-$0.8, G13.5$+$0.2, G16.0$-$0.5, and G33.2$-$0.6, however,
$N_{\rm H}$ are not available, so we estimated the visual extinction $A_{V}$
from the kinematic distance derived in this work by using the average ratio of
visual extinction to path length in the solar neighborhood $\left\langle
A_{V}/L\right\rangle\approx 1.8$ mag kpc-1 (Whittet, 1992) and converted it to
the NIR extinction using the extinction model of Draine (2003). The derived
physical properties are listed in Table 1.

###  2.2 ${}^{12}CO$ $J=1$–$0$ Archival Data

In order to search MCs associated with the SNRs, we utilize the high-
resolution 12CO $J=1$–$0$ data from the FOREST (FOur-beam REceiver System on
the 45 m Telescope) Unbiased Galactic Plane Survey with Nobeyama 45 m
telescope (FUGIN; Umemoto et al., 2017), which is one of the legacy projects
utilizing the new multibeam receiver FOREST. The receiver has a wide bandwidth
to obtain $J=1$–$0$ emission-line data of 12CO, 13CO, and C18O simultaneously.
The survey was carried out from April 2014 to March 2017 to cover the first
($10\arcdeg<l<50\arcdeg$, $|b|<1\arcdeg$) and the third
($198\arcdeg<l<236\arcdeg$; $|b|<1\arcdeg$) quadrants of the Galactic plane.
The telescope has a beam size of $\sim 15\arcsec$ at 115 GHz, and the mapping
was done with a sampling interval of $8\farcs 5$. The archival data provide an
effective angular resolution of $20\arcsec$ and velocity resolution of 1.3
${\rm km~{}s}^{-1}$. The typical sensitivity of the 12CO data is 0.24 K. The
calibrated data cubes in FITS format were retrieved from the Japanese Virtual
Observatory portal 333http://jvo.nao.ac.jp/portal/ operated by the Astronomy
Data Center of the National Astronomical Observatory of Japan.

##  3 Results

###  3.1 Association with SNRs

The H2 emission features in the 16 SNRs in Table 1 are “morphologically”
associated with the SNRs (Lee et al., 2019). We, however, cannot rule out the
chance projection of the H2 emission features on the SNRs. In order to confirm
their physical association, we investigate the excitation mechanism of the H2
emission using H2 line ratios. Previous NIR spectroscopic studies of several
SNRs have shown that the H2 lines excited by SNR shocks have thermal line
ratios corresponding to $T\sim 2000$–$3000$ K (IC 443, Burton et al. 1988,
1989; Moorhouse et al. 1991; RCW 103, Oliva et al. 1990; Burton & Spyromilio
1993; Cygnus Loop, Graham et al. 1991; G11.2$-$0.3, Koo et al. 2007; Lee et
al. 2019; Kes 69, Lee et al. 2019). In this paper, we use the flux ratios of
2–1 S(1)/1–0 S(1), 1–0 S(2)/1–0 S(0), and 1–0 S(1)/1–0 S(0) (Table 1) to
confirm the physical association between the observed H2 lines and the SNRs.

The flux ratio of 1–0 S(1) 2.122 µm and 2–1 S(1) 2.248 µm lines has been
widely used to distinguish thermal and nonthermal excitation. (e.g., Burton,
1992; Mouri, 1994; Pak et al., 2004; Mazzalay et al., 2013; Le et al., 2017).
Since these two lines originate from the same rotational state but from
different vibrational states, their flux ratio is independent of the ortho-to-
para ratio (OPR) that could affect the observed line ratio. For the
collisionally excited emission lines from warm ($T=2000$–3000 K) H2 gas, the
flux ratio is in the range of 0.1–0.2 (e.g., Mouri, 1994). Nonthermal
excitation by UV fluorescence, on the other hand, involves the UV pumping of
H2 molecules to the excited electronic states and the cascade to the lower
states, and the H2 line ratios depend on the branching ratios in the downward
cascade. This increases the populations of the high-energy levels ($v\geq 2$),
which yields a flux ratio 2–1 S(1)/1–0 S(1) higher than that from the
collisionally excited H2 gas. For the pure UV fluorescence emission from the
diffuse H2 gas ($\lesssim 10^{4}$ cm-3) irradiated by UV photons, the 2–1
S(1)/1–0 S(1) ratio is in the range of 0.5–0.6 (Black & van Dishoeck, 1987;
Sternberg & Dalgarno, 1989; Burton, 1992). The ratios among the $v=1$–0
rovibrational lines in UV fluorescence emission are also different from those
in thermal emission, so that the flux ratios 1–0 S(2)/1–0 S(0) and 1–0
S(1)/1–0 S(0) are also useful to discriminate between thermal and nonthermal
excitation. At higher densities, a substantial column of UV-heated, warm gas
develops and the thermal emission dominates the $v=1$–0 lines, but the
temperature of this UV-heated thermal gas is $T\leq 1000$ K (Sternberg &
Dalgarno, 1989), substantially lower than that of the shocked gas, so that the
UV-heated thermal gas is clearly separated from the shock-excited gas in the
H2 line ratio diagrams (e.g., Mouri, 1994).

Figure 3 shows the distribution of H2 line ratios of 34 positions in 16 SNRs
where the abscissa is 2–1 S(1)/1–0 S(1) and the ordinate is 1–0 S(2)/1–0 S(0)
or 1–0 S(0)/1–0 S(1). The solid line represents the locus of thermal emission
from a source in local thermodynamic equilibrium (LTE). In the figure, we also
mark the locations of nonthermal UV fluorescence emission (Black & van
Dishoeck, 1987) and UV-heated thermal emission (Sternberg & Dalgarno, 1989).
Figure 3 shows that most data points are located around the $T\sim 2000$ K in
LTE, consistent with collisionally excited thermal emission from shocked gas.
Their line ratios are significantly different from either the UV fluorescence
emission or the UV-heated thermal emission. There are several positions with
upper limits in 2–1 S(1)/1–0 S(1) (i.e., G11.2$-$0.3-N, G13.5$+$0.2-S,
G16.0$-$0.5-E1 and E2, G18.1$-$0.1-SE, G32.1$-$0.9-NW and C, G33.2$-$0.6-W,
and 3C 396-W2), but their upper limits are much smaller than that of the pure
nonthermal UV fluorescence (0.50–0.60; Black & van Dishoeck, 1987), and their
1–0 S(2)/1–0 S(0) and/or 1–0 S(0)/1–0 S(1) are significantly different from
that of the UV-heated thermal emission. Therefore, the 1–0 S(1) H2 emission
lines from those positions are also probably collisionally excited thermal
emission (see below). The only exception is G9.9$-$0.8-NW. Its 2–1 S(1)/1–0
S(1) ratio is $0.31\pm 0.04$, which is clearly larger than that of the thermal
emission at 2000 K. But the ratio is also considerably smaller than the
typical line ratio of the pure UV fluorescence emission. Its 1–0 S(0)/1–0 S(1)
ratio ($0.49\pm 0.04$) is also much larger than that of the thermal emission
and is almost comparable to those of the pure nonthermal UV fluorescence
(0.45–0.60; Black & van Dishoeck, 1987). These line ratios suggest that the H2
emission in G9.9$-$0.8-NW is likely a mixture of thermal and nonthermal
emission. It is worthwhile to note that its line width is also very small
($4.4\pm 0.1$ ${\rm km~{}s}^{-1}$) compared to the other SNRs, whose line
widths are larger than $9~{}{\rm km~{}s}^{-1}$. It is comparable to the line
width (2–6 ${\rm km~{}s}^{-1}$; Kaplan et al., 2017; Le et al., 2017; Oh et
al., 2018) of nearby photodissociation regions (PDRs). We will discuss the
nature of this source in Section 4.1.

One thing to note in Figure 3 is that there is a large scatter in the line
ratios around the solid line representing the thermal H2 gas in LTE
conditions. This might be mostly due to the uncertainty in the 1–0 S(0) and
1–0 S(2) line fluxes, although it could also be partly due to the uncertainty
in extinction correction. The weighted means for the line ratios are 2–1
S(1)/1–0 S(1) = $0.101\pm 0.003$, 1–0 S(2)/1–0 S(0) = $1.98\pm 0.03$, and 1–0
S(0)/1–0 S(1) = $0.188\pm 0.003$, which agree well with the thermal emission
at 2000 K. It is, however, worthwhile to note that several H2 emission
features are beyond the SNR boundary in radio: G11.2$-$0.3-N, S, SE, and NE;
Kes 73-W; W44-N; 3C 396-W1 and W2; and W49B-E1 and E2 (Figure 1; see also Lee
et al. 2019). Most of them have some morphological connection with the SNRs,
i.e., they are either connected to an SNR filament (W44) or parallel to the
SNR boundary (Kes 73, 3C 396, and W49B). This, together with their thermal
line ratios, strongly supports their physical association with the SNRs. Their
central velocities are also comparable to those of the other positions in
individual SNRs (Table 1). Perhaps the only exception is G11.2$-$0.3. In this
SNR, the H2 emission features extend far beyond the SNR boundary and there is
no obvious morphological connection between the H2 emission features and the
SNR. We can find no H II region spatially coincident with the H2 emission in
the WISE Catalog of Galactic H II regions (V2.2; Anderson et al., 2014). On
the other hand, the line ratios of all four positions are consistent with the
shock excitation, and their central velocities are comparable to the suggested
systemic velocity of the SNR ($+45$ ${\rm km~{}s}^{-1}$; Green et al., 1988),
so that the association with the SNR is likely (see also Koo et al. 2007).
Such H2 filaments have been known from the early days of NIR observations, and
it was pointed out that heating/exciting sources other than the SNR shock are
required for the H2 emission (Oliva et al., 1990; Graham et al., 1991; Burton
& Spyromilio, 1993). One possibility is the X-ray emission from SNRs; if
molecular gas is irradiated by X-ray, the temperature can reach $\leq 3000$ K
and the H2 line ratios can be close to those of shocked gas (Lepp & McCray,
1983; Draine & Woods, 1990). We will explore this possibility and the origin
of such H2 emission in our forthcoming paper. In this work, we will not
distinguish those positions from the rest, which is acceptable because their
velocities are comparable to those of the other positions in an SNR.

###  3.2 Kinematic Distances

Our analysis in Section 3.1 suggests that the observed H2 emission features
are all physically associated with the SNRs except one (G9.9$-$0.8). The
central velocities of the H2 2.122 µm emission lines in Table 1, therefore,
should be close to the systemic velocities of the SNRs. For the H2 emission
features in the central areas of the SNRs, however, there could be a large
contribution from the shock motion to the central velocity. Indeed, in
G32.1$-$0.9 and W44, the central velocities from the central area slits are
either much ($\sim 20~{}{\rm km~{}s}^{-1}$) larger (G32.1$-$0.9) or smaller
(W44) than those from the other slits. We therefore exclude the data from the
central area slits (i.e., slit name with “C” in Table 1) in deriving the
systemic velocities. We also exclude the data from the slits showing two
velocity components (see Figure 2), although one of the two components could
represent the systemic velocity of the SNR. We then proceed to obtain the
systemic velocities of the SNRs as follows: (1) For the SNRs with a single
slit observation, we simply take the central velocities. (2) For the SNRs with
multiple slit observations and with the spread in velocity less than 5 ${\rm
km~{}s}^{-1}$, which is comparable to the cloud-to-cloud velocity dispersion
of MCs in the inner Galaxy (e.g., see Figure 4 of Clemens, 1985), we take the
average of the central velocities weighted by 1/$\sigma_{v}^{2}$, where
$\sigma_{v}$ is the $1\sigma$ uncertainty of the central velocity from the
Gaussian fitting (Section 2.1). (3) For the SNRs with multiple slit
observations and with velocity spread larger than 5 ${\rm km~{}s}^{-1}$, we
present the range given by the minimum and maximum central velocities.

Table High-resolution Near-infrared Spectroscopic Study of Galactic Supernova
Remnants. I. Kinematic Distances shows the systemic velocities ($v_{\rm LSR}$)
of the 16 SNRs derived from our H2 emission lines. Note that we have included
SNR G9.9$-$0.8 in parentheses, although the association of the H2 emission
with the SNR is not certain. The table also shows the systemic velocities
determined from H I absorption, CO emission, or OH maser observations in
previous studies. For four SNRs (G13.5$+$0.2, G16.0$-$0.5, G32.1$-$0.9, and
G33.2$-$0.6), no velocity information can be found in the literature. The left
panel of Figure 4 compares the systemic velocities of 12 SNRs from our work
with those from previous studies in radio ($v_{\rm LSR,radio}$). For seven
SNRs, they agree with each other within $\pm 5~{}{\rm km~{}s}^{-1}$,
supporting the association of all emission features with the SNRs. On the
other hand, for five SNRs (G18.1$-$0.1, G18.9$-$1.1, Kes 69, 3C 396, and W49B)
the discrepancy between the two velocities is large (12–52 ${\rm
km~{}s}^{-1}$). There could be several possible explanations. First, the H2
emission-line velocities could have some contribution from shock motion,
although it might be small because the H2 filaments are located near the edge
of the SNRs. Alternatively, the velocities obtained in previous studies,
mostly from H I and/or CO observations, can be in substantial error. In
Section 4, we will discuss the origin of the discrepancies in these five SNRs.

The $v_{\rm LSR}$ derived either from our H2 emission lines or from radio
observations can be converted to kinematic distance, adopting an appropriate
Galactic rotation curve model. We use the recent model of Reid et al. (2014),
which is based on $\sim 100$ high-mass star forming regions with accurate
distances determined by trigonometric parallax. The model adopts the
‘universal’ rotation curve of Persic et al. (1996) with new Galactic
parameters ($R_{0}=8.34$ kpc and $V_{0}=241~{}{\rm km~{}s}^{-1}$). The
kinematic distances obtained by using the model of Reid et al. (2014) are
listed in Table High-resolution Near-infrared Spectroscopic Study of Galactic
Supernova Remnants. I. Kinematic Distances. For the SNRs without previous
systemic velocity measurements, we present the distances estimated from other
nonkinematic methods such as the $\Sigma$-$D$ relation, where $\Sigma$ and $D$
are the radio surface brightness and the diameter of the SNRs or the Sedov
analysis for comparison (see Table High-resolution Near-infrared Spectroscopic
Study of Galactic Supernova Remnants. I. Kinematic Distances). The Sedov
analysis assumes that the SNR is in the Sedov phase and has a canonical SN
explosion energy of $10^{51}$ erg. These distance estimates can be used but
have a large uncertainty. For G18.9$-$1.1, we also give the distance (1.8 kpc)
derived from the comparison of the X-ray absorbing columns and the extinction
variation to the SNR direction (Shan et al., 2018). It is worth noticing that
there are two kinematic distances, near-side and far-side distances,
corresponding to a $v_{\rm LSR}$. For the majority of SNRs, this distance
ambiguity has been resolved by H I absorption studies (see Section 1). For the
SNRs without such information, we have adopted the kinematic distances close
to those from the $\Sigma-D$ relation or the Sedov analysis. They are marked
by question marks in Column (3) of Table High-resolution Near-infrared
Spectroscopic Study of Galactic Supernova Remnants. I. Kinematic Distances.
The right panel of Figure 4 compares the distances derived from our NIR H2
observations with those from previous studies. Not surprisingly, the five SNRs
with a large discrepancy in $v_{\rm LSR}$ (G18.1$-$0.1, G18.9$-$1.1, Kes 69,
3C 396, and W49B) also show large distance discrepancy ($\Delta d>1$ kpc). For
the four SNRs (G13.5$+$0.2, G16.0$-$0.5, G32.1$-$0.9, G33.2$-$0.6), previous
distance estimates have large uncertainties, and our result provides reliable
kinematic distances for the first time, although the near-far distance
ambiguity needs to be resolved for them.

##  4 Discussion

In this section, we discuss the origin of the dense molecular gas emitting H2
emission lines detected in the northwestern border of G9.9-0.8. We also
discuss the five SNRs (G18.1$-$0.1, G18.9$-$1.1, Kes 69, 3C 396, and W49B)
showing a large discrepancy in $v_{\rm LSR}$ between our NIR H2 emission-line
observations and the previous radio observations.

###  4.1 G9.9$-$0.8

SNR G9.9$-$0.8 was first identified by Brogan et al. (2006) in their VLA 90 cm
observation and shows a broken shell-like morphology with a radius of 6′.
Stupar & Parker (2011) detected strong H$\alpha$ emission features in the
northwestern border of the remnant and suggested that the emission is
associated with the remnant based on the positional coincidence of the bright
radio continuum and the H$\alpha$ emission. Kilpatrick et al. (2016) detected
broadened CO emission at $v_{\rm LSR}=+27$–$+33~{}{\rm km~{}s}^{-1}$ near the
southwestern border of the remnant and obtained the kinematic distance of
$\sim 4$ kpc assuming that the broadening is due to the interaction with the
SNR.

In Lee et al. (2019), we found narrow H2 filaments in the northwestern border
of the remnant where the radio continuum is bright and optical H$\alpha$
emission is detected (Brogan et al., 2006; Stupar & Parker, 2011). In our NIR
spectroscopy of the filaments, we found very narrow H2 emission lines (FWHM
$\sim 4~{}{\rm km~{}s}^{-1}$; Table 1) with nonthermal line ratios (Figure 3),
indicating that they are likely arising from unshocked interstellar medium
(ISM) irradiated by nearby UV sources (Section 3.1). We also check the level
population diagram of the H2 emission as shown in Figure 5. In the figure, we
clearly see that the populations are not explained by thermal excitation
models at temperatures of 2000–4000 K. Instead, they show “zigzag” patterns
between ortho- and para-levels. We estimate the OPR of the H2 gas using two H2
emission lines, 1–0 S(1) and 1–0 S(0). Since the extinction-corrected 1–0
S(1)/1–0 S(0) is $2.1\pm 0.2$, assuming the rotational temperature of $\sim
1700$ K from 1–0 S(2)/1–0 S(0) of $1.6\pm 0.2$, the OPR of the H2 gas is $\sim
1.4$, which is much smaller than 3.0 expected in thermal H2 gas in LTE
condition. The zigzag patterns in the level population diagram, together with
low OPR, seem to be consistent with typical characteristics of nonthermal UV
fluorescence excitation (e.g., Hasegawa et al., 1987; Sternberg & Neufeld,
1999). But, as we pointed out in Section 3.1, the observed 2–1 S(1)/1–0 S(1)
ratio ($\sim 0.3$) is considerably smaller than that (0.6–0.7) in pure UV
fluorescence excitation, suggesting that there could be some contribution from
collisional excitation. The model calculations of Draine & Bertoldi (1996)
show that warm PDRs in low-density media can yield H2 line ratios similar to
what we observe in G9.9$-$0.8. The solid line in Figure 5 shows the line
ratios obtained in one such model (the “bh3d” model of Draine & Bertoldi
1996).

In Figure 6, we compare the spatial distribution of the H2 emission features
with that of the optical H$\alpha$ emission features detected in Stupar &
Parker (2011). As seen in the figure, the H2 filaments are detected just
outside the H$\alpha$ emission features, and their morphologies and
distributions are almost anticorrelated. The spatial distributions of the
atomic and molecular emission lines suggest a PDR where UV photons from
massive stars heat H2 molecules in MCs in contact with the H II region
(Hollenbach & Tielens, 1997, 1999). Indeed, there is an H II region
(G9.982$-$0.752) around the H2 filaments (Figure 6). This H II region was
identified by Lockman (1989), who performed a radio recombination line survey
of continuum sources in the northern Galactic plane. Its location is well
consistent with those of the H2 and H$\alpha$ emission features, and its
$v_{\rm LSR}$ (=$+34.4\pm 1.5~{}{\rm km~{}s}^{-1}$) is also similar to that of
the H2 emission line.

All the information described above indicates that the optical H$\alpha$ and
NIR H2 emission is arising from the PDR of the H II region, rather than the
SNR G9.9$-$0.8. It is, however, worth noticing that the velocity center of the
broadened CO emission (+31 ${\rm km~{}s}^{-1}$; Kilpatrick et al., 2016)
detected around the southwestern border of the remnant is very close to this
velocity. If the broadened CO emission is due to the interaction of the SNR
and nearby MCs as suggested by Kilpatrick et al. (2016), it is likely that the
H II region and the SNR are located at nearly the same distance ($\sim 3.8$
kpc; see Table High-resolution Near-infrared Spectroscopic Study of Galactic
Supernova Remnants. I. Kinematic Distances) and that they are possibly
associated. Additional observations with multi-wave-band instruments may
reveal their physical connection.

###  4.2 G18.1$-$0.1

G18.1$-$0.1 is an SNR that belongs to the H II region/SNR complex at $l=18\fdg
2$ and $b=-0\fdg 3$. The complex is composed of at least four H II regions and
one SNR. G18.1$-$0.1 is located at the western edge of the complex, and it was
first confirmed as an SNR by Brogan et al. (2006). In radio continuum, it has
a broken ring-like morphology with the bright northern and eastern arcs.
Although the remnant belongs to the H II region/SNR complex, their physical
association is not clear (e.g., Paron et al., 2013; Leahy et al., 2014). Using
13CO line data, Paron et al. (2013) suggested that a big molecular shell at
$v_{\rm LSR}=+51$–$+55~{}{\rm km~{}s}^{-1}$ is physically associated with the
H II region/SNR complex, placing the complex at the kinematic distance of
$\sim 4$ kpc. For the SNR, however, Leahy et al. (2014) proposed a distance of
$\sim 6$ kpc based on its H I spectrum showing absorption up to $+100~{}{\rm
km~{}s}^{-1}$, and argued that the remnant is located at 2–3 kpc behind of the
H II regions without any physical association with them.

In Lee et al. (2019), we detected strong, narrow H2 filaments at the northern
and eastern borders of the remnant, where the radio continuum brightness is
enhanced (Brogan et al., 2006). We also found additional diffuse H2 emission
outside of the remnant’s western boundary, but those emission features are
likely associated with the nearby H II regions. We took NIR spectra of the
northern and eastern borders of the remnant (Figure 1). The morphological
relation with the SNR and the line ratios (Section 3.1) indicate that the H2
emission features are associated with the remnant. The $v_{\rm LSR}$ of the
northern filament is $+73~{}{\rm km~{}s}^{-1}$, whereas that of the eastern
filament is $+85~{}{\rm km~{}s}^{-1}$ (Table 1). These velocities are
considerably different from those of previous CO/H I results ($+53~{}{\rm
km~{}s}^{-1}$ or $+100~{}{\rm km~{}s}^{-1}$; Paron et al., 2013; Leahy et al.,
2014; Ranasinghe & Leahy, 2018b).

In order to find MCs associated with the SNR, we have investigated high-
resolution 12CO $J=1$–0 data obtained as a part of the FUGIN CO survey
(Umemoto et al. 2017; see also Section 2.2). Figure 7 displays the 12CO
$J=1$–0 line channel maps between $+48$ and $+85~{}{\rm km~{}s}^{-1}$. In the
channel maps, the most prominent feature is the large MCs between $v_{\rm
LSR}=+48$ and $+56~{}{\rm km~{}s}^{-1}$. In the middle of the velocity range,
a ring-like structure emerges, which is clearly seen in the $+51~{}{\rm
km~{}s}^{-1}$ channel map. The ring structure appears to be encircling the
remnant, with the eastern border of the remnant in contact with it. Paron et
al. (2013) suggested that the H II region/SNR complex is located at this
velocity and that they are physically associated with the MCs. But there is a
large gap between the ring structure and the northwestern shell of the SNR,
where the NIR H2 emission lines are detected. The large molecular ring
disappears at velocities higher than $+53~{}{\rm km~{}s}^{-1}$, but instead,
an additional MC filament emerges in the northeastern outer region of the
remnant. The filament also seems to be in contact with the eastern and
northeastern boundary of the remnant, but again its overall morphology does
not match well the remnant. From $+61$ to $+72~{}{\rm km~{}s}^{-1}$, on the
other hand, we see a large molecular “wall” that appears to be in contact with
the eastern boundary of the remnant. The morphology is suggestive of the
interaction, but the velocity of the H2 emission in this region (+85 ${\rm
km~{}s}^{-1}$) is considerably different from the CO emission.

At the velocities of the H2 emission (+72 and +85 ${\rm km~{}s}^{-1}$), no
dense MCs are visible. Instead, there are diffuse CO emission features around
the remnant, some of which are spatially coincident with the remnant (Figure
7). In Figure 8, we show a close-up view of the diffuse CO emission and
compare its distribution with the radio continuum and H2 emission
distributions. The diffuse CO emission is bright along the southern boundary
of the SNR, where the radio continuum emission is faint. There are CO ‘clumps’
around the northwestern boundary of the SNR, but there is no clear spatial
correlation between these CO clumps and the northwestern H2 filament. At the
eastern boundary of the remnant, we see a faint CO filament that appears to be
spatially coincident with the radio/H2 filament, but the CO emission is
complex in this area and their association is not clear.

To summarize, we could not identify CO clouds clearly associated with the H2
filaments (and the SNR). The large molecular shell at $v_{\rm
LSR}=+51$–$+55~{}{\rm km~{}s}^{-1}$ has been proposed to be associated with
the SNR (Paron et al., 2013), but its velocity is very different from that of
the H2 filaments, and there is no spatial correlation between the two.
Instead, we have detected diffuse CO emission features spatially coincident
with the SNR at the velocities of the H2 filaments ($+72$–$+85~{}{\rm
km~{}s}^{-1}$). Their association is possible, although there is no clear
spatial correlation between the CO and H2 emission features. The kinematic
distance corresponding to the H2 emission-line velocities (+73–+85 ${\rm
km~{}s}^{-1}$) is 5.0–5.5 kpc (Table High-resolution Near-infrared
Spectroscopic Study of Galactic Supernova Remnants. I. Kinematic Distances)
assuming the near-side distance.

###  4.3 G18.9$-$1.1

G18.9$-$1.1 belongs to the composite-type SNR with a size larger than a half
degree. Early radio observations showed weak, diffuse radio continuum filling
inside the remnant, together with two strong pillar-like features at the
center and near the western border (e.g., Fürst et al., 1985, 1989, 1997).
X-ray observations found a point-like hard X-ray source with an associated
diffuse nebula at the tip of the central radio pillar, and it was suggested
that these objects are a pulsar and its wind nebula (Harrus et al., 2004;
Tüllmann et al., 2010). Fürst et al. (1989) reported the detection of H I
depression at $+18~{}{\rm km~{}s}^{-1}$ toward the remnant and suggested that
the depression is caused by a cavity associated with the remnant (see below).
The $v_{\rm LSR}$ of $+18~{}{\rm km~{}s}^{-1}$ corresponds to the kinematic
distance of either $\sim 2$ kpc within the Sagittarius Arm or $\sim 15$ kpc on
the far side of the tangential point. The latter, however, was ruled out
because in that case the SNR should have very unusual properties (e.g, huge
explosion energy of ($1$–$2$)$\times 10^{52}$ erg; Fürst et al., 1989; Harrus
et al., 2004). A recent NIR study using the red clump stars toward the remnant
suggested the distance of $1.8\pm 0.2$ kpc (Shan et al., 2018), which is
consistent with the above kinematic distance.

In Lee et al. (2019), we detected weak, patchy H2 emission inside the remnant.
Most of the H2 emission, which has a complex morphology, arises from the
central and northeastern regions, $3\arcmin$–$10\arcmin$ apart from the
central radio pillar. Additional weak, patchy H2 emission features were also
detected in the western border of the remnant. We obtained two NIR spectra:
one at the H2 filament close to the central radio pillar, and the other at the
H2 clump near the northeastern border (Figure 1). The central velocity of the
latter is +70 ${\rm km~{}s}^{-1}$, while the spectrum of the former is
composed of two velocity components centered at +74 and +53 ${\rm
km~{}s}^{-1}$, respectively (Table 1; see also Figure 2). If we adopt the
central velocity of the northeastern H2 clump as the systemic velocity of the
SNR, the kinematic distance to the SNR would be 4.7 kpc (Table High-resolution
Near-infrared Spectroscopic Study of Galactic Supernova Remnants. I. Kinematic
Distances). But this $v_{\rm LSR}$ is more than $50~{}{\rm km~{}s}^{-1}$
larger than that ($+18~{}{\rm km~{}s}^{-1}$) suggested by Fürst et al. (1989),
and the distance is $\sim 3$ kpc larger than those ($\sim 2$ kpc) obtained in
the previous radio and NIR studies (Fürst et al., 1989; Shan et al., 2018).

The large velocity difference in $v_{\rm LSR}$ between our H2 emission and the
previous H I absorption could be due to the peculiar velocity of the H2 gas
accelerated by the SN shock along the line of sight. However, the systemic
velocity ($v_{\rm LSR}=+70$ ${\rm km~{}s}^{-1}$) is taken from the
northeastern H2 clump near the SNR boundary, so the peculiar line-of-sight
velocity by the SN shock might not be large. Furthermore, the velocity
difference of $50~{}{\rm km~{}s}^{-1}$ seems to be rather large for a
nondissociative shock (e.g., Draine & McKee, 1993). Therefore, it is possible
that the $v_{\rm LSR}$ of the H2 emission lines traces the systematic velocity
of the remnant. Another possibility is that these central and northeastern H2
emission features are not physically associated with the SNR, even though they
are located inside the remnant (Figure 1). We searched the WISE Catalog of
Galactic H II Regions (V2.2; Anderson et al., 2014) and the HASH Planetary
Nebulae Database444 The University of Hong Kong/Australian Astronomical
Observatory/Strasbourg Observatory H$\alpha$ Planetary Nebula Database (V4.6;
Parker et al., 2016) to find sources responsible for the H2 emission, but we
could not find any candidate.

In order to explore the large discrepancies in $v_{\rm LSR}$ and distance
between our H2 and previous results, we examined the H I absorption toward the
SNR using the VLA Galactic Plane Survey (VGPS) H I data (Stil et al., 2006).
The VGPS survey has an angular resolution of $1\arcmin$, which is much higher
than that ($6\arcmin$) of the previous study (Fürst et al., 1989). We first
extracted H I spectra toward the two central radio pillars and compared them
with the spectra of the surrounding regions, but we could not identify clear
absorption features because of the random fluctuations in the
foreground/background H I emission. We then looked at individual channel maps
and confirmed the depression at $v_{\rm LSR}\sim+18$ ${\rm km~{}s}^{-1}$
(Figure 9). The depression has a very good morphological correlation with
radio continuum, e.g., there is a filamentary depression along the radio
pillars, suggesting that the depression is probably due to absorption rather
than a cavity as proposed by Fürst et al. (1989). We could not find absorption
features at higher velocities, but the nondetection of absorption does not
rule out the possibility that the SNR is at a greater distance because there
is a large background fluctuation due to the nonuniform structure of the H I
gas along the line of sight. The H I absorption at $+18~{}{\rm km~{}s}^{-1}$
indicates that the SNR is at a distance greater than $\sim 2$ kpc. The
distance $1.8\pm 0.2$ kpc of Shan et al. (2018) has been obtained by comparing
the X-ray absorbing hydrogen column density ($(8.3\pm 0.5)\times 10^{21}$
cm-2; Harrus et al., 2004) to the extinction-distance relation derived by
using red clump stars. Harrus et al. (2004), however, obtained an extinction
$A_{V}=5.1$ mag, which is 1 mag greater than the value of 4.1 mag from Shan et
al. (2018). And the extinction-distance relation of Shan et al. (2018) shows
that $A_{V}$ is almost constant at $\sim 5.2$ mag beyond 2 kpc. (They derived
the relation up to 2.8 kpc.) Therefore, we consider that the distance 2 kpc
obtained in previous studies is a minimum distance, and the distance to
G18.9$-$1.1 is still uncertain. Future spectroscopic studies of the H2
emission features detected in the western radio shell (Lee et al., 2019) might
be helpful to clarify the issue.

###  4.4 G21.8$-$0.6 (Kes 69)

Kes 69 is a shell-type SNR, showing a bright incomplete radio shell along the
southeastern border of the remnant. H I absorption is seen up to $+85~{}{\rm
km~{}s}^{-1}$ with no absorption lines around the tangential velocity
($\sim+110~{}{\rm km~{}s}^{-1}$), indicating that the remnant is located on
the near side of the tangential point (Tian & Leahy, 2008; Zhou et al., 2009).
The kinematic distance of the SNR corresponding to $+85~{}{\rm km~{}s}^{-1}$
is 5.2 kpc (see Ranasinghe & Leahy, 2018a). Zhou et al. (2009) showed that a
molecular arc at $+77$–$+86~{}{\rm km~{}s}^{-1}$ is morphologically correlated
with the southeastern radio shell. Hewitt et al. (2008) detected extended
faint OH 1720 MHz maser emission at $v_{\rm LSR}=+85~{}{\rm km~{}s}^{-1}$
toward the brightest portion of the southeastern radio shell. A compact OH
(1720 MHz) maser spot was also detected in the northeastern region of the
remnant, but at $v_{\rm LSR}=+69.3~{}{\rm km~{}s}^{-1}$ (Green et al., 1997).

In Lee et al. (2019), we reported the detection of an extended bright H2
emission feature composed of multiple narrow filaments in the southeastern
border of the remnant along the bright radio shell. We also detected
additional complex H2 emission features in the northeastern region of the
remnant, where the OH maser has been detected (Green et al., 1997). We took
NIR spectra at three positions: two in the southeastern shell and one in the
northeastern region (Table 1). The $v_{\rm LSR}$ of the H2 emission in the
southeastern shell is $+60~{}{\rm km~{}s}^{-1}$, and it is consistent with the
previous NIR spectroscopy with medium resolution for the southeastern shell
($+57\pm 3~{}{\rm km~{}s}^{-1}$; Lee et al., 2019). Interestingly, this
velocity is almost $30~{}{\rm km~{}s}^{-1}$ smaller than the $v_{\rm LSR}$ of
the molecular arc detected in CO and OH maser emission ($+85~{}{\rm
km~{}s}^{-1}$; Hewitt et al., 2008; Zhou et al., 2009). The large velocity
difference is difficult to understand because the H2 filaments are located at
the border of the remnant, so that the expansion velocity of H2 gas along the
line of sight might be small.

We have investigated the presence of MCs associated with the remnant at the
velocity of the H2 emission using the FUGIN 12CO $J=1$–$0$ data. Figure 10
shows CO channel maps at velocities from +57 to +93 ${\rm km~{}s}^{-1}$, where
we see that the most prominent MCs are at $+78$–$+88~{}{\rm km~{}s}^{-1}$. As
shown by Zhou et al. (2009), the MCs in this velocity range have some
morphological correlation with the SNR. In particular, the filamentary MC in
the southeastern area at $\sim+80$ ${\rm km~{}s}^{-1}$ correlates well with
the remnant’s bright southeastern radio continuum shell. There is also
extended OH maser emission with a broad line width at +85 ${\rm
km~{}s}^{-1}$along the radio shell (Hewitt et al., 2008). At lower velocities,
the CO emission is relatively faint with some large, extended CO clouds inside
and around the SNR. At the velocity of the H2 emission ($\sim+61~{}{\rm
km~{}s}^{-1}$), we can see a faint, clumpy MC that appears to be in contact
with the southern SNR boundary (Figure 11). It has a thin, extended
filamentary structure parallel to the H2 filament in the southeastern shell,
but the overall morphological correlation between the MC and the radio shell
is relatively weak.

If the MCs at $+78$–$+88~{}{\rm km~{}s}^{-1}$ in Figure 10 are associated with
the SNR, as has been suggested in previous molecular line studies, the
kinematic distance to Kes 69 is 5.2 kpc, adopting +85 ${\rm km~{}s}^{-1}$ as
its systemic velocity (Hewitt et al., 2008; Zhou et al., 2009). The H2
emission with a central velocity of +61 ${\rm km~{}s}^{-1}$, then indicates
that the MC is on the front side of the SNR and that a $\sim 24$ ${\rm
km~{}s}^{-1}$ shock is propagating into the MC. On the other hand, if the
central velocity of the H2 emission (+61 ${\rm km~{}s}^{-1}$) represents the
systemic velocity of the SNR, the faint CO cloud in Figure 11 is possibly
interacting with the SNR, and the association of the extended OH maser
emission detected by Hewitt et al. (2008) becomes unclear. The kinematic
distance corresponding to the systemic velocity of $+61~{}{\rm km~{}s}^{-1}$
is 4.1 kpc. Future spectral mapping of the H2 emission might be helpful to
resolve the issue.

###  4.5 G39.2$-$0.3 (3C 396)

3C 396 is a composite-type SNR exhibiting both a central X-ray pulsar wind
nebula (PWN) and an incomplete radio shell composed of multiple filaments
(Harrus & Slane, 1999). Previous H I and OH absorption studies suggested that
the remnant is located on the far side of the tangential point at $v_{\rm
LSR}\lesssim+60~{}{\rm km~{}s}^{-1}$ (Caswell et al. 1975; see also Green
1989). The remnant is believed to be interacting with MCs in the west, where
the bright radio shell and NIR H2 filaments are detected. According to CO
observations, there are two large MCs that could be possibly associated with
the remnant: one at $+69~{}{\rm km~{}s}^{-1}$ and the other at $+84~{}{\rm
km~{}s}^{-1}$. Lee et al. (2009) found MCs at $v_{\rm LSR}=+68$–$+70~{}{\rm
km~{}s}^{-1}$ surrounding the remnant and pointed out that the western H2
filament is in contact with the inner boundary of the MCs. Kilpatrick et al.
(2016) also suggested the association of these MCs with the SNR. On the other
hand, Su et al. (2011) found a thick molecular wall at $+84~{}{\rm
km~{}s}^{-1}$ in the western border of the remnant with high 12CO
$J$=2–1/$J$=1–0 line ratios and suggested that the SNR is interacting with
these MCs.

Previous NIR H2 narrowband imaging observations had detected two long H2
filaments aligned along the north-south direction, leaving an interval of
$\sim 1\farcm 5$ in the western region of the remnant (Lee et al., 2009,
2019). The brighter filament is located near the western edge of the remnant,
slightly outside the radio boundary of the SNR. Lee et al. (2009) attributed
the H2 filaments to the interaction between the SNR and nearby MCs at
$+69~{}{\rm km~{}s}^{-1}$. Our NIR spectroscopy toward the two locations in
the filament shows that $v_{\rm LSR}$ of the filament is $+56~{}{\rm
km~{}s}^{-1}$ (Table 1). This is consistent with the result of an early H I
absorption study (Caswell et al., 1975), but it is considerably (by
$10$–$20~{}{\rm km~{}s}^{-1}$) smaller than those inferred from previous CO
observations ($+69$, $+84~{}{\rm km~{}s}^{-1}$; Lee et al., 2009; Su et al.,
2011; Kilpatrick et al., 2016).

In Figure 12, we revisit the 12CO $J=1$–$0$ channel maps from $+52$ to
$+91~{}{\rm km~{}s}^{-1}$ to find the molecular features associated with the
remnant. The most prominent feature are the large MCs at velocities from $+52$
to $+70~{}{\rm km~{}s}^{-1}$ in the northern and western regions of the
remnant. At $+52~{}{\rm km~{}s}^{-1}$, these large MCs appear in the western
region, $2\arcmin$–$4\arcmin$ apart from the remnant boundary. They move to
the central area of the field at higher velocities, so that at $\sim+57~{}{\rm
km~{}s}^{-1}$ they are almost in contact with the remnant boundary. Around
$+54$–$+57~{}{\rm km~{}s}^{-1}$, we also see extended MCs in the eastern
region of the remnant, which seems to be in contact with the eastern boundary
of the remnant. From $+62$ to $+70~{}{\rm km~{}s}^{-1}$, large MCs appear in
the northern region. A couple of MC filaments extend from the northern MCs
toward the south, and one of them at $+70~{}{\rm km~{}s}^{-1}$ is almost in
contact with the SNR along the southwestern boundary of the remnant. Lee et
al. (2009) suggested that this MC filament is physically associated with the
remnant. At velocities $>+72~{}{\rm km~{}s}^{-1}$, we see relatively diffuse,
extended MCs around the remnant, which disappear at velocities higher than the
tangential velocity ($\sim+85~{}{\rm km~{}s}^{-1}$). In particular, at +85
${\rm km~{}s}^{-1}$, we see several clouds superposed on the bright western
radio shell. Su et al. (2011) found high 12CO $J$=2–1/$J$=1–0 line ratios at
the velocity channel and suggested that these CO clouds are interacting with
the remnant.

Figure 13 shows the zoomed-in 12CO channel map of 3C 396 at $+56~{}{\rm
km~{}s}^{-1}$, which is the central velocity of the H2 emission lines. An
interesting thing is that the remnant is located inside a cavity surrounded by
MCs. The western half of the cavity is prominent, and its inner boundary
appears to be parallel to the SNR boundary. Except the northwestern region,
there is a $\sim 2\arcmin$ gap between the remnant boundary and the cavity
wall. But there is a filamentary cloud spatially coincident with the H2
filament inside the cavity. The eastern half of the cavity is surrounded by
relatively faint MCs. The SNR radio emission is faint in this area, but the
SNR appears to be in contact with the cavity wall along the southeastern
boundary of the SNR.

As we have shown in Figure 12, there are at least three possible MCs at
velocities +56, +69, and +84 ${\rm km~{}s}^{-1}$, respectively, that could be
associated with the SNR (see also Lee et al., 2009; Su et al., 2011;
Kilpatrick et al., 2016). They all have some morphological relation with the
SNR. At the velocity of the H2 emission, i.e., at +56 ${\rm km~{}s}^{-1}$, we
see a CO cavity surrounding the SNR and a faint filamentary MC spatially
coincident with the bright western shell. Therefore, the MCs at +56 ${\rm
km~{}s}^{-1}$ are very likely to be associated with the SNR. The cavity
surrounding the SNR could be a wind bubble produced by the progenitor. The SNR
is on the far side (Caswell et al., 1975), so that the kinematic distance
corresponding to +56 ${\rm km~{}s}^{-1}$ is 9.5 kpc.

###  4.6 G43.3$-$0.2 (W49B)

W49B is a member of the W49 complex that includes multiple H II regions (W49A)
and one SNR (W49B). Previous H I 21 cm observations toward the W49 complex
showed that the absorption is seen up to the tangential velocity
($\sim+70~{}{\rm km~{}s}^{-1}$) at positive velocities, but not at negative
velocities (Lockhart & Goss, 1978; Brogan & Troland, 2001; Zhu et al., 2014;
Ranasinghe & Leahy, 2018b). This indicates that the sources in the W49 complex
are located beyond the tangential point but inside the solar circle. There
have been many efforts to reveal the relative distances to W49A and W49B and
the physical association between them. In H I and H2CO absorption spectra, it
was found that there is an absorption at $\sim+10~{}{\rm km~{}s}^{-1}$ toward
W49A that is not seen toward W49B (Kazes, 1970; Wilson, 1970; Radhakrishnan et
al., 1972). This suggests that W49A is most likely located at the far distance
(11.5 kpc), corresponding to $+10~{}{\rm km~{}s}^{-1}$ and that W49B is in
front of W49A without any physical association between them (Kazes, 1970;
Wilson, 1970; Radhakrishnan et al., 1972). This distance to W49A was later
confirmed by the comparison of proper motions of the H2CO masers and their
Doppler velocities ($11.4\pm 1.2$ kpc; Gwinn et al., 1992). The early H I and
H2CO absorption studies suggested that W49B is located at $\sim 8$ kpc
(Moffett & Reynolds, 1994) corresponding to the maximum velocity of the
absorption lines ($+63~{}{\rm km~{}s}^{-1}$; Kazes, 1970; Wilson, 1970;
Radhakrishnan et al., 1972). Brogan & Troland (2001), however, suggested that
the different absorption velocities between W49A and W49B could be due to the
differences of H I kinematics, distribution, and temperature in the direction
of W49 complex and that one cannot rule out the physical association between
them. Another distance estimate for W49B is from CO observations. Toward W49B,
there are three large MCs at different $v_{\rm LSR}$: $+10$, $+40$, and
$+60~{}{\rm km~{}s}^{-1}$ (Zhu et al., 2014; Kilpatrick et al., 2016). Zhu et
al. (2014) argued that the MCs at $+40~{}{\rm km~{}s}^{-1}$ are
morphologically associated with the remnant and suggested a distance of $\sim
10$ kpc. Kilpatrick et al. (2016), on the other hand, reported the detection
of broadened 12CO emission centered at $v_{\rm LSR}=+14~{}{\rm km~{}s}^{-1}$
in the southwestern boundary of the remnant and suggested 11.3 kpc, although
the physical association between the remnant and the MCs is not clear.

In Lee et al. (2019), we found bright H2 emission features in the eastern and
western areas of the remnant. In the eastern area, we see several narrow,
extended filaments along the NE-SW direction outside the X-ray/[Fe II]/radio
boundary. In the western area, on the other hand, the H2 emission features are
rather clumpy and mostly detected inside the remnant. There are also some
additional H2 filaments aligned along the NE-SW direction in the central area
of the remnant, but they are much fainter than those in the eastern and
western areas. The morphology and the H2 line ratios (Section 3.1) indicate
that the bright H2 emission features in the east and west areas (and probably
the faint filaments in the central area too) are thermally excited and
physically associated with the remnant. We obtained NIR spectra at four
positions: two for the eastern filaments, and one for each of the northern and
the western H2 emission features (Figure 1). We found that their $v_{\rm LSR}$
are $\sim+64~{}{\rm km~{}s}^{-1}$ without any significant variations (only
$\pm 2~{}{\rm km~{}s}^{-1}$), and this led us to conclude that the systematic
velocity of the remnant is $+64~{}{\rm km~{}s}^{-1}$. Our result is consistent
with the suggestions by the early H I and H2CO absorption studies (Kazes,
1970; Wilson, 1970; Radhakrishnan et al., 1972), but is very different from
those of previous CO observations, i.e., $+10$ or $+40~{}{\rm km~{}s}^{-1}$
(Zhu et al., 2014; Kilpatrick et al., 2016). The kinematic distance
corresponding to $+64~{}{\rm km~{}s}^{-1}$ is 7.5 kpc (Table High-resolution
Near-infrared Spectroscopic Study of Galactic Supernova Remnants. I. Kinematic
Distances).

We revisit 12CO channel maps to confirm the MC(s) associated with the SNR.
Figure 14 shows the 12CO $J=1$–$0$ channel maps toward W49B in three different
velocity ranges where the large MCs are located (Zhu et al., 2014; Kilpatrick
et al., 2016): (1) $+7$–$+17~{}{\rm km~{}s}^{-1}$, (2) $+38$–$+48~{}{\rm
km~{}s}^{-1}$, and (3) $+59$–$+69~{}{\rm km~{}s}^{-1}$. In the velocity range
from $+7$ to $+17~{}{\rm km~{}s}^{-1}$, there are two large prominent MCs,
i.e., an extended filamentary MC in the northern area of the field and a large
MC outside the western boundary of the SNR. There is diffuse CO emission
spread over the SNR that appears to be extended from these two MCs. There is
no clear overall morphological correlation between the diffuse emission and
the H2 emission. But at $+14~{}{\rm km~{}s}^{-1}$, there is a $\sim
4\arcmin$-long filamentary CO cloud along the southwestern boundary of the SNR
that appears to surround the H2-bright area. Kilpatrick et al. (2016) found
broadened CO emission lines toward this cloud suggesting the association of
the MC with the SNR. The presence of the H2 emission further supports the SNR-
MC interaction, but the large ($\sim 50~{}{\rm km~{}s}^{-1}$) velocity
difference between the H2 and the CO emission is difficult to reconcile. In
the velocity range from $+38~{}{\rm km~{}s}^{-1}$ to $+48~{}{\rm
km~{}s}^{-1}$, there are diffuse CO clouds around the remnant. As pointed out
by Zhu et al. (2014), the MCs appear to surround the SNR (see also Figure 1 of
Chen et al. 2014). In particular, at $+43~{}{\rm km~{}s}^{-1}$, there are MCs
just outside the eastern and southwestern H2-bright regions. If these MCs are
interacting with the SNR, the velocity of the H2 emission ($+64~{}{\rm
km~{}s}^{-1}$) implies that the MCs are on the backside of the SNR. In the
velocity range $+59$–$+69$ ${\rm km~{}s}^{-1}$, the CO emission is complex
with several velocity components. Note that this is the velocity range where H
I and H2CO absorption is prominent, especially toward the southwestern area of
the SNR (Bieging et al. 1982; Brogan & Troland 2001; see also Lacey et al.
2001). Toward the southwestern H2-bright region, there are at least two
velocity components at $+61$ and $+66~{}{\rm km~{}s}^{-1}$, respectively. The
$+61~{}{\rm km~{}s}^{-1}$ component is part of the large MC aligned along the
northeast-southwest direction crossing the remnant’s center. At this velocity,
we also see a relatively faint CO filament outside the eastern SNR boundary
that appears to be aligned with the eastern H2-bright region (see next
paragraph). The $+66~{}{\rm km~{}s}^{-1}$ component seems to be part of the
large MC cloud in the western area of the field, which partly overlaps with
the southwestern H2-bright region. There is also some faint CO emission at
this velocity just outside the eastern H2-bright region, but only in its
southern area.

Figure 15 is a zoomed-in 12CO channel map integrated from $+61$ to $+66~{}{\rm
km~{}s}^{-1}$, where we found the H2 emission lines. Note that the color scale
is changed from that in Figure 14. The figure shows that the $+61~{}{\rm
km~{}s}^{-1}$ MC crossing the SNR has a “tuning-fork” morphology with the
U-shaped prongs in the interior. The left prong runs along the northeast-
southwest direction, spatially coincident with one of the radio filaments in
the interior, while the western prong is located just inside the western radio
shell, where the radio continuum is bright and the H2 emission lines are
detected. In the eastern area, along the extended H2-bright region, there are
faint MCs that appear, blocking the H2 region. These MCs are aligned with the
tuning-fork MC but with a gap between them. There is also diffuse emission
spread over the field, including the areas around the southwestern H2-bright
region.

As we have shown in Figure 14, the CO emission toward W49B is complicated, and
it is difficult to identify MCs associated with the SNR based on their
morphology. Instead, the roughly constant central velocities of the H2
emission over the SNR suggest that the systemic velocity of the SNR is
probably $\sim+64~{}{\rm km~{}s}^{-1}$. We therefore consider that the MCs at
$+59$–$+69~{}{\rm km~{}s}^{-1}$ are associated with the SNR. In particular,
the MCs at $+61$–$+66~{}{\rm km~{}s}^{-1}$ seem to have a good morphological
correlation with the SNR (Figure 15). The interaction of the SNR with these
MCs aligned along the northeast-southwest direction could have resulted in the
barrel-like morphology of the SNR. The kinematic distance 7.5 kpc
corresponding to +64 ${\rm km~{}s}^{-1}$ is $\sim 4$ kpc closer than W49A
($11.4\pm 1.2$ kpc; Gwinn et al., 1992).

##  5 Summary

Distance is a basic parameter of the Galactic SNRs and is essential for
deriving their physical parameters, such as radius, luminosity, age, and
explosion energy. Diverse methods have been devised, each of which has its own
strengths and weaknesses. A popular method is to identify an object associated
with the SNR and derive the kinematic distance from its LSR velocity. This
technique has been most widely used in radio by using the CO emission from MCs
or OH maser emission. In this paper, we have shown that the NIR H2 emission,
which is a strong signature of the interaction between SNRs and MCs, can also
be used for the distance determination. We performed high-resolution NIR
spectroscopy for 16 SNRs detected in our systematic H2 emission-line study of
SNRs in the inner Galaxy (Lee et al., 2019). In all SNRs, bright H2 1–0 S(1)
2.122 µm emission lines, together with additional H2 emission lines from
different excitation levels, were clearly detected. We examined the excitation
mechanism of the H2 emission lines in order to confirm their physical
association with the SNRs, and we derived the kinematic distances of SNRs from
the central velocities of the H2 lines. For four SNRs, the kinematic distances
have been determined in this work for the first time.

The comparison showed that the central velocities of H2 emission lines are
considerably ($>5~{}{\rm km~{}s}^{-1}$) different from those obtained from
radio observations for fives SNRs: G18.1$-$0.1, G18.9$-$1.1, Kes 69, 3C 396,
and W49B. Since the detection of collisionally excited H2 emission in an SNR
is strong evidence that the SNR is interacting with an MC, we consider that
the H2 central velocities and the inferred kinematic distances should be
preferred to those based on morphological association if there is a large
discrepancy. However, as pointed out in Section 3.2, the kinematic distance
from the H2 line, with the matter of their physical association put aside,
also has its inherent uncertainties. Firstly, the measured velocity is that of
the shocked gas, not the ambient gas. Secondly, the H2 emission samples a
highly localized region within an MC, so that the velocity may represent the
outskirts of cloud velocity distribution rather than the central velocity of
the cloud. More detailed studies are needed to fully accept the H2 line-based
distances for these five SNRs.

Our main results are summarized in the following:

1\. In all SNRs, except G9.9$-$0.8, the H2 lines show thermal line ratios with
$T\sim 2000$ K, indicating that they are emitted from warm, collisionally
excited H2 gas. The thermal line ratios support that most, if not all, H2
emission features are associated with the SNRs.

2\. We have derived the kinematic distances of 16 SNRs (including G9.9$-$0.8)
by using the velocities of the H2 emission lines (see below for the discussion
about G9.9$-$0.8). For four SNRs (G13.5$+$0.2, G16.0$-$0.5, G32.1$-$0.9, and
G33.2$-$0.6), the kinematic distances have been determined in this work for
the first time. For 6 out of the remaining 11 SNRs, $v_{\rm LSR}$ derived from
our H2 emission lines are well consistent ($<\pm 5~{}{\rm km~{}s}^{-1}$) with
those from previous radio observations, which provides a support to the
derived kinematic distances. For five SNRs, however, there is a large
discrepancy between the two velocities, which casts doubt on the derived
kinematic distances.

3\. For five SNRs showing large discrepancy in $v_{\rm LSR}$ between our H2
and the previous radio observations (G18.1$-$0.1, G18.9$-$1.1, Kes 69, 3C 396,
W49B), we have explored the origin of the discrepancy using CO and H I data.
The results on individual SNRs are summarized below.

(1) G18.1$-$0.1: The velocities of the two extended H2 filaments along the
northern and eastern radio boundaries have been measured as $+73$ and
$+85~{}{\rm km~{}s}^{-1}$, respectively. These velocities are very different
from those suggested from previous CO ($+51$–$+55~{}{\rm km~{}s}^{-1}$; Paron
et al., 2013) and H I ($+100~{}{\rm km~{}s}^{-1}$; Leahy et al., 2014;
Ranasinghe & Leahy, 2018b) observations. At the velocities of the H2 emission,
there are some diffuse CO emission features spatially coincident with the
remnant. Their association is possible. The near-side kinematic distance
corresponding to the H2 emission line velocities is 5.0–5.5 kpc.

(2) G18.9$-$1.1: The velocities of two short H2 filaments have been measured:
one near the northeastern boundary ($+70~{}{\rm km~{}s}^{-1}$), and the other
in the central area ($+74$ and $+53~{}{\rm km~{}s}^{-1}$; see Figure 2). The
near-side kinematic distance corresponding to $+70~{}{\rm km~{}s}^{-1}$ is 4.7
kpc. These are much greater than those suggested in previous H I ($+18~{}{\rm
km~{}s}^{-1}$; Fürst et al., 1989) and red clump star (1.8 kpc Shan et al.,
2018) studies. The discrepancy may indicate that either the H2 filaments have
a large peculiar velocity or they are not associated with the SNR. The ISM
structure along this line of sight, however, appears complicated, and the
previous velocity/distance estimates could be lower limits.

(3) Kes 69: The velocity of the H2 filament in the southeastern bright radio
shell has been measured as $+60~{}{\rm km~{}s}^{-1}$. This is much smaller
than the value of $+85~{}{\rm km~{}s}^{-1}$ of the molecular arc suggested to
be interacting with the SNR from CO and OH maser emission ($+85~{}{\rm
km~{}s}^{-1}$; Hewitt et al., 2008; Tian & Leahy, 2008; Zhou et al., 2009). At
the velocity of the H2 emission, however, we see a faint, clumpy MC that could
be responsible for the H2 emission. If this $+61~{}{\rm km~{}s}^{-1}$ MC is
interacting with the SNR, the near-side kinematic distance becomes 4.1 kpc.

(4) 3C 396: The velocity of the bright H2 filament coincident with the western
radio shell has been measured as $+57~{}{\rm km~{}s}^{-1}$. This velocity is
considerably smaller than those suggested from previous CO observations, i.e.,
$+69~{}{\rm km~{}s}^{-1}$ (Lee et al., 2009; Kilpatrick et al., 2016) and
$+84{\rm km~{}s}^{-1}$ (Su et al., 2011). We have found that, at $+56~{}{\rm
km~{}s}^{-1}$, there are MCs spatially well correlated with the SNR: a CO
cavity surrounding the SNR and a faint filamentary MC spatially coincident
with the bright western shell. If the MCs at $+56~{}{\rm km~{}s}^{-1}$ are
associated with the SNR, the kinematic distance to 3C 396, which is on the far
side (Caswell et al., 1975), becomes 9.5 kpc.

(5) W49B: The velocities of the bright H2 filaments in the the eastern and
western SNR shells have been measured as $\sim+64~{}{\rm km~{}s}^{-1}$. This
velocity is very different from those suggested from CO observations, i.e.,
$+40~{}{\rm km~{}s}^{-1}$ (Zhu et al., 2014) and $+14~{}{\rm km~{}s}^{-1}$
(Kilpatrick et al., 2016). The roughly constant velocity of the H2 emission
over the SNR suggests that the systemic velocity of the SNR is probably
$\sim+64~{}{\rm km~{}s}^{-1}$. At $+61$–$+66~{}{\rm km~{}s}^{-1}$, we have
found MCs that appear to have a good morphological correlation with the
barrel-like morphology of the SNR. Adopting $+64~{}{\rm km~{}s}^{-1}$ as the
systemic velocity of the SNR, the kinematic distance to W49B, which is on the
far side (Lockhart & Goss, 1978; Brogan & Troland, 2001; Zhu et al., 2014;
Ranasinghe & Leahy, 2018b), becomes 7.5 kpc.

4\. For G9.9$-$0.8, the nonthermal lines ratios and the narrow line widths
indicate that the H2 lines are probably excited by UV radiation. The H2
emission is most likely arising from a PDR surrounding the H II region
(G9.982$-$0.752), rather than the SNR. However, the central velocity of the H2
line ($+30~{}{\rm km~{}s}^{-1}$) is almost identical to the systematic
velocity of the remnant estimated from previous CO observations ($+31~{}{\rm
km~{}s}^{-1}$; Kilpatrick et al., 2016), suggesting the possible physical
association between the H II region and the SNR.

Y.-H.L. acknowledges support from the National Research Foundation of Korea
(NRF) grant funded by the Ministry of Science and ICT (MSIT) of Korea
(NRF-2018M1A3A3A02065645). The work of B.-C.K. was supported by the Basic
Science Research Program through the National Research Foundation of Korea
(NRF) funded by the Ministry of Science, ICT and future Planning
(2020R1A2B5B01001994). This work used the Immersion Grating Infrared
Spectrograph (IGRINS) that was developed under a collaboration between the
University of Texas at Austin and the Korea Astronomy and Space Science
Institute (KASI) with the financial support of the US National Science
Foundation under grant AST-1229522, the University of Texas at Austin, and the
Korean GMT Project of KASI. This paper includes data taken at the McDonald
Observatory of the University of Texas at Austin. This publication also makes
use of data from FUGIN, the FOREST Unbiased Galactic plane Imaging survey with
the Nobeyama 45 m telescope, a legacy project in the Nobeyama 45 m radio
telescope. The 45 m radio telescope is operated by the Nobeyama Radio
Observatory, a branch of the National Astronomical Observatory of Japan.

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Table 1: Properties of H2 Lines

SNR | Slit | Slit Position | $v_{\rm LSR}$ | FWHM | $\dfrac{2-1~{}S(1)}{1-0~{}S(1)}$ | $\dfrac{1-0~{}S(2)}{1-0~{}S(0)}$ | $\dfrac{1-0~{}S(0)}{1-0~{}S(1)}$
---|---|---|---|---|---|---|---
[ $\alpha$(J2000) $\delta$(J2000) ] | (${\rm km~{}s}^{-1}$) | (${\rm km~{}s}^{-1}$)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
G9.9$-$0.8 | NW | 18:10:26.33 $-$20:39:41.9 |  $+$30.4 (0.1) | 4.4 (0.1) | 0.31 (0.04) | 1.62 (0.19) | 0.49 (0.04)
G11.2$-$0.3 | N | 18:11:26.64 $-$19:21:52.2 |  $+$47.3 (0.2) | 12.6 (0.4) |  $<$0.16 |  $<$15.2 | 0.18 (0.04)
| S | 18:11:28.85 $-$19:27:51.5 |  $+$46.5 (0.1) | 13.2 (0.3) | 0.11 (0.03) |  $<$5.54 | 0.15 (0.02)
| SE | 18:11:32.35 $-$19:27:12.0 |  $+$49.2 (0.1) | 12.0 (0.1) | 0.12 (0.01) | 2.30 (0.07) | 0.17 (0.01)
| NE | 18:11:34.82 $-$19:23:43.0 |  $+$48.9 (0.1) | 11.4 (0.1) | 0.07 (0.02) | 2.84 (0.47) | 0.16 (0.01)
G13.5$+$0.2 | S | 18:14:20.85 $-$17:13:57.4 |  $+$40.1 (0.9) | 32.8 (2.1) |  $<$0.28 | 1.67 (1.02) | 0.13 (0.05)
G16.0$-$0.5 | E1 | 18:22:13.88 $-$15:18:15.9 |  $+$50.0 (0.3) | 17.5 (0.8) |  $<$0.18 | 2.30 (0.94) | 0.20 (0.06)
| E2 | 18:22:16.47 $-$15:16:27.5 |  $+$52.7 (0.4) | 17.1 (0.8) |  $<$0.11 | 1.61 (0.54) | 0.19 (0.05)
G18.1$-$0.1 | NW | 18:24:29.08 $-$13:10:20.7 |  $+$73.1 (0.4) | 26.6 (0.8) | 0.09 (0.05) | 1.60 (0.40) | 0.19 (0.04)
| SE | 18:24:49.55 $-$13:12:25.9 |  $+$85.3 (0.2) | 13.5 (0.4) |  $<$0.09 | 1.99 (0.53) | 0.20 (0.04)
G18.9$-$1.1 | C (p)aa The H2 line profiles are fitted by two Gaussian components: primary (p) and secondary (s). See Figure 2 and the explanation in Section 2.1.  | 18:29:31.05 $-$12:51:23.7 |  $+$74.0 (1.1) | 26.0 (2.2) | 0.13 (0.05) | 2.26 (0.78) | 0.18 (0.06)
| C (s)aa The H2 line profiles are fitted by two Gaussian components: primary (p) and secondary (s). See Figure 2 and the explanation in Section 2.1.  | - |  $+$53.3 (1.1) | 12.0 (2.1) | - | - | -
| NE | 18:30:04.44 $-$12:51:43.0 |  $+$69.7 (0.5) | 40.7 (1.3) | 0.15 (0.06) | 2.71 (0.80) | 0.16 (0.04)
Kes 69 | SE1 | 18:33:01.92 $-$10:13:43.6 |  $+$59.0 (0.4) | 40.7 (1.0) | 0.16 (0.03) | 1.70 (0.39) | 0.19 (0.03)
| SE2 | 18:33:14.96 $-$10:12:12.8 |  $+$61.7 (0.3) | 28.5 (0.7) | 0.15 (0.03) | 1.62 (0.30) | 0.23 (0.04)
| NE (p)aa The H2 line profiles are fitted by two Gaussian components: primary (p) and secondary (s). See Figure 2 and the explanation in Section 2.1.  | 18:33:10.12 $-$10:00:52.0 |  $+$77.0 (0.8) | 28.8 (1.6) | 0.12 (0.05) | 2.51 (0.91) | 0.18 (0.06)
| NE (s)aa The H2 line profiles are fitted by two Gaussian components: primary (p) and secondary (s). See Figure 2 and the explanation in Section 2.1.  | - |  $+$33.4 (6.6) | 43.9 (15.2) | - | - | -
Kes 73 | W | 18:41:12.15 $-$04:56:42.6 |  $+$99.4 (0.1) | 10.9 (0.2) | 0.09 (0.02) | 2.24 (0.34) | 0.18 (0.02)
3C 391 | NW | 18:49:16.00 $-$00:55:04.4 |  $+$99.7 (0.8) | 53.3 (2.1) | 0.11 (0.04) | 2.66 (1.00) | 0.13 (0.04)
| NE (p)aa The H2 line profiles are fitted by two Gaussian components: primary (p) and secondary (s). See Figure 2 and the explanation in Section 2.1.  | 18:49:27.86 $-$00:55:01.4 |  $+$96.4 (0.4) | 29.2 (1.8) | 0.09 (0.02) | 2.13 (0.29) | 0.19 (0.04)
| NE (s)aa The H2 line profiles are fitted by two Gaussian components: primary (p) and secondary (s). See Figure 2 and the explanation in Section 2.1.  | - |  $+$76.2 (4.7) | 50.6 (4.0) | - | - | -
| SW (p)aa The H2 line profiles are fitted by two Gaussian components: primary (p) and secondary (s). See Figure 2 and the explanation in Section 2.1.  | 18:49:23.26 $-$00:57:41.0 |  $+$107.0 (0.1) | 25.4 (0.4) | 0.09 (0.01) | 1.96 (0.11) | 0.20 (0.01)
| SW (s)aa The H2 line profiles are fitted by two Gaussian components: primary (p) and secondary (s). See Figure 2 and the explanation in Section 2.1.  | - |  $+$84.0 (1.0) | 58.0 (1.1) | - | - | -
G32.1$-$0.9 | NW | 18:52:40.73 $-$00:56:57.4 |  $+$84.5 (0.2) | 18.5 (0.5) |  $<$0.10 | 1.74 (0.45) | 0.22 (0.05)
| C | 18:53:42.22 $-$01:02:01.8 |  $+$100.4 (0.1) | 10.7 (0.2) |  $<$0.07 | 1.95 (0.32) | 0.21 (0.03)
Kes 78 | E | 18:51:46.34 $-$00:11:27.7 |  $+$89.5 (0.2) | 22.4 (0.4) | 0.11 (0.03) | 2.10 (0.34) | 0.19 (0.03)
G33.2$-$0.6 | W | 18:53:25.70 $+$00:01:09.4 |  $+$81.7 (0.5) | 26.4 (1.2) |  $<$0.17 | 2.26 (0.79) | 0.20 (0.06)
W44 | W | 18:55:17.10 $+$01:21:50.0 |  $+$46.2 (0.1) | 38.4 (0.1) | 0.10 (0.01) | 1.84 (0.04) | 0.21 (0.01)
| N | 18:55:39.80 $+$01:37:56.4 |  $+$41.2 (0.1) | 17.3 (0.3) | 0.14 (0.02) | 2.04 (0.25) | 0.24 (0.02)
| C | 18:56:14.70 $+$01:20:52.7 |  $+$26.7 (0.2) | 20.0 (0.4) | 0.06 (0.04) | 1.61 (0.32) | 0.24 (0.03)
| S | 18:56:35.46 $+$01:06:44.1 |  $+$48.9 (0.1) | 24.7 (0.3) | 0.16 (0.02) | 1.82 (0.25) | 0.20 (0.02)
3C 396 | W1 | 19:03:55.86 $+$05:25:36.9 |  $+$55.9 (0.1) | 10.6 (0.2) | 0.08 (0.02) |  $<$5.83 | 0.23 (0.02)
| W2 | 19:03:56.94 $+$05:24:38.3 |  $+$57.5 (0.3) | 11.9 (0.5) |  $<$0.10 |  $<$13.9 | 0.13 (0.04)
W49B | E1 | 19:11:16.14 $+$09:05:04.9 |  $+$65.5 (0.1) | 8.7 (0.1) | 0.07 (0.01) | 2.44 (0.24) | 0.18 (0.01)
| E2 | 19:11:16.91 $+$09:06:17.5 |  $+$64.3 (0.1) | 9.2 (0.1) | 0.10 (0.01) | 2.19 (0.17) | 0.18 (0.01)
| W | 19:11:00.15 $+$09:05:07.9 |  $+$61.7 (0.1) | 25.7 (0.2) | 0.11 (0.01) | 2.41 (0.16) | 0.20 (0.01)
| N | 19:11:06.46 $+$09:06:47.9 |  $+$64.1 (0.1) | 9.3 (0.3) | 0.08 (0.03) | 1.95 (0.49) | 0.18 (0.04)
HC 40 | NW | 19:32:14.18 $+$19:07:31.4 |  $+$44.2 (0.4) | 23.6 (0.9) | 0.12 (0.05) |  $<$3.08 | 0.19 (0.05)

Note. — Column (1): SNR name. Column (2): slit name. Column (3): central
coordinate of the slit. Column (4): central velocity of the H2 1–0 S(1) 2.122
µm line in the LSR frame. The uncertainties in parentheses are formal
1$\sigma$ statistical errors. The uncertainty in absolute wavelength
calibration is about $1~{}{\rm km~{}s}^{-1}$. Column (5): FWHM of the H2 1–0
S(1) lines corrected for the instrument broadening (7 ${\rm km~{}s}^{-1}$).
Columns (6)–(8): extinction-corrected flux ratios (see text). The numbers in
parentheses are $1\sigma$ errors, whereas the numbers with “$<$” are $3\sigma$
upper limits.

Table 2: Kinematic Distances of 16 Galactic SNRs

SNR | Literature | H2
---|---|---
$v_{\rm LSR}$ | KDA | $d$ | Method | Reference | $v_{\rm LSR}$ | $d$
(km s-1) | (kpc) | (km s-1) | (kpc)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
G9.9$-$0.8 | $+31$ | N? | 3.8 | CO, $\Sigma$-$D$ | 1 |  $+30~{}(\pm 1)$aa The H2 emission is most likely arising from a PDR, and its association with the SNR is not clear (see Section 4.1).  |  $3.8~{}(\pm 0.1)$aa The H2 emission is most likely arising from a PDR, and its association with the SNR is not clear (see Section 4.1).
G11.2$-$0.3 | $+45$ | N | 4.6 | H I | 2 | $+48~{}(\pm 2)$ | $4.7~{}(\pm 0.1)$
G13.5$+$0.2 | … | F? | $13\pm 7$ |  $\Sigma$-$D$ | 3 | $+40~{}(\pm 1)$ | $12.4~{}(\pm 0.1)$
G16.0$-$0.5 | … | N? | $8\pm 4$ |  $\Sigma$-$D$ | 3 | $+51~{}(\pm 2)$ | $4.1~{}(\pm 0.1)$
G18.1$-$0.1 |  $+53$, $+100$ | N | 4.0, 6.2 | H I, CO | 4, 5, 6 |  $+73$–$+85$ | 5.0–5.5
G18.9$-$1.1 | $+18$ | N | 1.7–1.8bb 1.7 kpc is from H I absorption, and 1.8 kpc is from the RCS method.  | H I, RCS | 7, 8 | $+70~{}(\pm 1)$ | $4.7~{}(\pm 0.1)$
Kes 69 | $+85$ | N | 5.2 | H I, CO, OH | 9, 10, 11 | $+61~{}(\pm 2)$ | $4.1~{}(\pm 0.1)$
Kes 73 | $+100$ | N | 5.9 | H I, CO | 1, 6 | $+99~{}(\pm 1)$ | $5.8~{}(\pm 0.1)$
3C 391 |  $+100$–$+110$ | TP | 7.1 | H I, CO, OH | 1, 12, 13 | $+100~{}(\pm 1)$ | $7.1~{}(\pm 0.1)$
G32.1$-$0.9 | … | N? | 4.6 | Sedov | 14 | $+85~{}(\pm 1)$ | $5.0~{}(\pm 0.1)$
Kes 78 |  $+82$–$+86$ | N | 4.9–5.1 | H I, CO, OH | 6, 15, 16 | $+90~{}(\pm 1)$ | $5.4~{}(\pm 0.1)$
G33.2$-$0.6 | … | N? | $6\pm 3$ |  $\Sigma$-$D$ | 3 | $+82~{}(\pm 1)$ | $4.9~{}(\pm 0.1)$
W44 |  $+42$–$+50$ | N | 2.6–3.1 | H I, OH | 6, 17, 18 |  $+41$–$+49$ | 2.6–3.0
3C 396 |  $+69$, $+84$ | F | 8.6, 6.8 | H I, CO | 6, 19, 20 | $+56~{}(\pm 2)$ | $9.5~{}(\pm 0.1)$
W49B |  $+13$, $+40$ | F | 11.3, 9.6 | H I, CO | 1, 6, 21 | $+64~{}(\pm 2)$ | $7.5~{}(\pm 0.2)$
HC 40 |  $+36$–$+44$ | F | 5.4–6.8 | H I, CO | 13, 22 | $+44~{}(\pm 1)$ | $5.4~{}(\pm 0.1)$

Note. — Column (1): SNR name. Column (2): systemic velocity of SNR from the
literature. Column (3): kinematic distance ambiguity, indicating whether the
SNR is at the near (N), far (F), or tangent point (TP) distance. Those with
“?” indicate that the distance ambiguity had not been resolved in previous H I
absorption studies and that we have adopted either near or far distance based
on other studies (see text). Column (4): kinematic distance derived from the
systemic velocity in Column (2). For those without the velocity information,
we list the distances from other methods listed in Column (5). Column (5):
distance estimation method: H I absorption (H I), CO emission (CO),
$\Sigma$-$D$ relation ($\Sigma$-$D$), Sedov analysis (Sedov), and red clump
star (RCS) method (see text). Column (6): references for the systemic velocity
or the distance. Column (7): systemic velocity of the SNR derived from the
central velocities of the H2 lines. The numbers in the parentheses are
$1\sigma$ uncertainties, which are obtained by adding the absolute wavelength
calibration uncertainty ($1~{}{\rm km~{}s}^{-1}$) and the standard deviation
of the central velocities in quadrature. For the SNRs with multiple slit
observations and with velocity spread larger than 5 ${\rm km~{}s}^{-1}$, the
minimum and maximum central velocities are given (see Section 3.2). Column
(8): kinematic distance derived from the systemic velocity in Column (7).

References. — (1) Kilpatrick et al. 2016; (2) Green et al. 1988; (3) Pavlovic
et al. 2014; (4) Paron et al. 2013; (5) Leahy et al. 2014; (6) Ranasinghe &
Leahy 2018b; (7) Fürst et al. 1989; (8) Shan et al. 2018; (9) Hewitt et al.
2008; (10) Tian & Leahy 2008; (11) Zhou et al. 2009; (12) Frail et al. 1996;
(13) Ranasinghe & Leahy 2017; (14) Folgheraiter et al. 1997; (15) Koralesky et
al. 1998; (16) Zhou & Chen 2011; (17) Caswell et al. 1975; (18) Claussen et
al. 1997; (19) Lee et al. 2009; (20) Su et al. 2011; (21) Zhu et al. 2014;
(22) Junkes et al. 1992.

Figure 1:  Radio and H2 $2.122~{}\micron$ narrowband images of the 16 SNRs
studied in this paper. North is up, and east is to the left. The radio images
are from either the VLA 20/90 cm Galactic Plane Survey (GPS 20/90cm; Helfand
et al., 2006) or the VLA 21 cm Galactic Plane Survey (VGPS; Stil et al.,
2006), while the H2 images are from Lee et al. (2019). The gray scales are
linear, and the blue contours represent the SNR boundary in radio continuum.
In the radio images, the red box marks the boundary of the H2 image of the
source and the magenta symbols represent the locations of X-ray/radio sources
associated with the SNR: crosses = OH masers; open diamonds = pulsars or
point-like X-ray sources. The slit positions for the NIR spectroscopy are
marked on the H2 images (red bars). The slit names represent the directions
from the SNR’s center to the slits (i.e., N, S, E, and W indicate north,
south, east, and west, respectively, whereas C indicates the central area
inside the SNR boundary).

Figure 1:  (Continued)

Figure 2:  H2 1–0 S(1) 2.122 µm spectra of the 34 targets in Table 1. The gray
dots with vertical bars represent the observed spectra with $1\sigma$
uncertainties, while the black solid lines are the model profiles resulting
from Gaussian fittings. For four targets, G18.9$-$1.1-C, Kes 69-NE, 3C 391-NE,
and 3C 391-SW, the spectra are fitted by two Gaussian components (see Section
2.1), and each component is shown by a red solid line.

Figure 3:  Flux ratios of H2 emission lines: 2–1 S(1) (2.248 µm) / 1–0 S(1)
(2.122 µm) vs. 1–0 S(2) (2.034 µm) / 1–0 S(0) (2.224 µm) (left), and 2–1 S(1)
(2.248 µm) / 1–0 S(1) (2.122 µm) vs. 1–0 S(0) (2.224 µm) / 1–0 S(1) (2.122 µm)
(right). The filled squares represent the extinction-corrected flux ratios of
34 targets (Table 1), while the open squares with arrows indicate the
$3\sigma$ upper limits of the ratios. The black solid line represents the flux
ratios of thermal gas in LTE at $T=1000$–4000 K. The vertical and horizontal
stripes indicate the areas of the diagram corresponding to nonthermal UV
fluorescence (Black & van Dishoeck, 1987) and UV-heated thermal excitation
models (Sternberg & Dalgarno, 1989), respectively. Note that the $y$-axis of
the left panel has a discontinuity at $\sim 5$.

Figure 4:  Left: comparisons of the systemic velocities of the 16 SNRs
obtained from H2 2.122 µm lines ($v_{\rm LSR,H_{2}}$) with the previous
results ($v_{\rm LSR,radio}$). The gray solid line represents the perfect
agreement, whereas the dashed lines indicate $\pm 10~{}{\rm km~{}s}^{-1}$
differences between them. For the sources with very different suggested
systemic velocities in previous studies (G18.1$-$0.1, 3C 396, W49B), we mark
their minimum and maximum $v_{\rm LSR,radio}$ connected by horizontal dashed
lines. G9.9$-$0.8 is marked with an open symbol because the association
between the H2 emission and the SNR is suspicious (see Section 4.1). Right:
same as the left panel, but for the distances. The dashed lines indicate $\pm
1$ kpc differences from the perfect agreement.

Figure 5:  Excitation diagram of H2 lines detected in G9.9$-$0.8. The y-axis
is the column density ($N_{v,J}$) divided by the level degeneracy ($g_{J}$),
and is normalized by that of the H2 1–0 S(1) line. The symbols with a
downward-pointing arrow denote $3\sigma$ upper limits. The dashed lines
represent the Boltzmann distribution with $T=2000$, 3000, and 4000 K. The
solid lines represent the level populations expected from a warm, diffuse PDR
with a significant contribution from collisional excitation (i.e., the “bh3d”
model of Draine & Bertoldi 1996 with $n_{\rm H}=10^{2}$ cm-3, $\chi=10$, and
$T_{0}=1000$ K, where $\chi$ is a parameter characterizing the UV intensity
and $T_{0}$ is the temperature at the PDR boundary).

Figure 6:  Multiwavelength images of G9.9$-$0.8: (a) radio continuum taken
from the VLA 90 cm Galactic Plane Survey (GPS 90 cm; Helfand et al., 2006),
(b) continuum-subtracted H2 2.122 µm from the UWISH2 survey (Froebrich et al.,
2011; Lee et al., 2019), and (c) continuum-subtracted H$\alpha$ images taken
from the SuperCOSMOS H$\alpha$ Survey (SHS; Parker et al., 2005; Stupar &
Parker, 2011). The gray scales of the three images are linear. The red box in
panel (a) marks the field of view of panels (b) and (c). The blue contours in
panels (a)–(c) and the red contours in panels (b)–(c) represent the 90 cm
continuum and H$\alpha$ emission features, respectively. The location of the H
II region G9.982$-$0.752 identified by Lockman (1989) is marked by a purple
circle, where the size of the circle corresponds to the half-power beam width
of his radio observation ($\sim 3\arcmin$). The green horizontal bar
represents the slit position of our NIR spectroscopy. The bar is made longer
than the true slit length ($15\arcsec$) for display purposes.

Figure 7:  12CO $J=1$–0 channel maps of G18.1$-$0.1 in the velocity range of
$+48$–$+85~{}{\rm km~{}s}^{-1}$. Each channel map has been obtained by
integrating over 2.6 ${\rm km~{}s}^{-1}$. The color scale is linear with the
low and high thresholds of 0 and 90 K ${\rm km~{}s}^{-1}$, respectively. The
blue contour represents the boundary of the remnant in 20 cm continuum (see
Figure 1).

Figure 8:  Top: 20 cm continuum and H2 2.122 µm narrowband images of
G18.1$-$0.1. The blue and red contours show the appearance of the SNR in 20 cm
continuum and H2 emission, respectively. The contour levels in the radio
continuum image are 1.8 and 2.6 mJy/beam. The green bars represent the slit
positions of our NIR spectroscopy. Bottom: zoomed-in 12CO $J=1$–0 intensity
maps of G18.1$-$0.1 integrated from $+72$ to $+85~{}{\rm km~{}s}^{-1}$. The
color scale is linear with the low and high thresholds of 0 and 120 K ${\rm
km~{}s}^{-1}$, respectively.

Figure 9:  Left: 21 cm continuum image of G18.9$-$1.1. The color scale is
linear with the low and high thresholds of 12 and 30 K, respectively. Right: H
I 21 cm line channel map at $v_{\rm LSR}=+18.3~{}{\rm km~{}s}^{-1}$. The color
scale is linear with the low and high thresholds of 50 and 110 K,
respectively. The blue contours show the appearance of the SNR in 21 cm
continuum, and the contour levels are 15, 20, and 25 K.

Figure 10:  12CO $J=1$–0 channel maps of Kes 69 in the velocity range of
$+57$–$+93~{}{\rm km~{}s}^{-1}$. Each channel map has been obtained by
integrating over 2.6 ${\rm km~{}s}^{-1}$. The color scale is linear with the
low and high thresholds of 0 and 60 K ${\rm km~{}s}^{-1}$, respectively. The
blue contour represents the boundary of the remnant in 20 cm continuum (see
Figure 1).

Figure 11:  Top: 20 cm continuum and H2 2.122 µm narrowband images of Kes 69.
The blue and red contours show the appearance of the SNR in 20 cm continuum
and H2 emission of the SNR, respectively. The contour levels in the radio
continuum image are 2 and 6 mJy/beam. The green bars represent the slit
positions of our NIR spectroscopy. Bottom: zoomed-in 12CO $J=1$–0 channel map
of Kes 69 at $+62~{}{\rm km~{}s}^{-1}$. The color scales are linear, and the
low and high thresholds are 10 and 50 K ${\rm km~{}s}^{-1}$, respectively.

Figure 12:  12CO $J=1$–0 channel maps of 3C 396 in a velocity range of
$+52$–$+91~{}{\rm km~{}s}^{-1}$. Each channel map has been obtained by
integrating over 2.6 ${\rm km~{}s}^{-1}$. The color scales are linear, and the
low and high thresholds are 0 and 60 K ${\rm km~{}s}^{-1}$, respectively. The
blue contour shows the appearance of the SNR in 20 cm continuum (see Figure
1).

Figure 13:  Top: 20 cm continuum and H2 2.122 µm narrowband images of 3C 396.
The blue and red contours show the appearance of the SNR in 20 cm continuum
and H2 emission of the SNR, respectively. The contour levels in the radio
continuum image are 0.3 and 3.0 mJy/beam. The green bars represent the slit
positions of our NIR spectroscopy. Bottom: zoomed-in 12CO $J=1$–0 channel map
of 3C 396 at $+56.6~{}{\rm km~{}s}^{-1}$. The color scales are linear, and the
low and high thresholds are 10 and 50 K ${\rm km~{}s}^{-1}$, respectively.

Figure 14:  12CO $J=1$–0 channel maps of W49B in three different velocity
ranges: $+7$–$+17~{}{\rm km~{}s}^{-1}$ (top), $+38$–$+48~{}{\rm km~{}s}^{-1}$
(middle), and $+59$–$+69~{}{\rm km~{}s}^{-1}$ (bottom). Each channel map has
been obtained by integrating over 2.6 ${\rm km~{}s}^{-1}$. The color scales
are linear, and the low and high thresholds are 0 and 80 K ${\rm
km~{}s}^{-1}$, respectively. The blue contour shows the appearance of the SNR
in 20 cm continuum (see Figure 1).

Figure 15:  Top: 20 cm continuum and H2 2.122 µm narrowband images of W49B.
The blue and red contours show the appearance of the SNR in 20 cm continuum
and H2 emission of the SNR, respectively. The contour levels in the radio
continuum image are 3 and 30 mJy/beam. The green bars represent the slit
positions of our NIR spectroscopy. Bottom: zoomed-in 12CO $J=1$–0 intensity
map of W49B integrated from $+61$ to $+66~{}{\rm km~{}s}^{-1}$. The color
scales are linear, and the low and high thresholds are 40 and 200 K ${\rm
km~{}s}^{-1}$, respectively.