Atlas of CO-line Shells and Cavities around Galactic Supernova Remnants with FUGIN^*

We present the atlas of molecular cavities, shells, and partial arcs apparently surrounding the SNRs by superposition of ¹²CO channel maps on radio continuum maps at 20 cm.

The search for a CO shell associated with an SNR was done by the following procedure. Since the distance of an SNR is unknown, or uncertain even if it exists, its radial velocity is not known, so the search for the shell structure was done in all the 462 channels of the CO data cube from −100 to 200 km s⁻¹ one channel after the other for each SNR.

First we display the radio continuum image on the screen, and superpose a channel map (T_B map) on the same screen. Then, the CO channel is changed from the first to the 462nd step by step. Numerous CO clouds and filaments will pass by, mostly foreground and background emissions, but at a certain velocity channel, a possible shell/cavity/arc appears apparently associated with the SNR's shell edge.

Once such a candidate was found, its nearby channels are inspected more carefully, the clearest shell feature was chosen as the associated shell, and its channel velocity was adopted as the radial velocity of the shell. This was repeated in the ¹²CO and ¹³CO cubes, each of 462 channels, for all the 63 SNRs. The C¹⁸O data were not used as their brightness was too low for the present purpose.

Table B1 lists the Galactic positions (l, b), radial velocities (v_lsr), kinematic distances (d), and linear diameters (D) of the candidates' cavities and/or shells of the analyzed SNRs. References to molecular-line observations, which report the association of the same or close radial velocities, are cited in the last column. Objects without references are mostly new measurements currently with no information about molecular gas association.

The measured results are presented in the form of T_B maps (sometimes I_CO maps) in the ¹²CO-line emission of the CO shells, arcs, and/or concentric alignment of clumps, as superposed on 20 cm radio continuum maps, in the online figure set associated with Figure 5 in Appendix C. We also present superposed ¹³CO and ¹²CO maps by R (red) and G (green) color-coded images in order to show the degree of condensation of the molecular gas density.

The association of the SNR and the identified molecular shell/cavity has been obtained purely by morphological inspection into the CO-line channel maps. This means that, despite the coincidence of the concave edge of a CO cloud with the SNR's outer edge, the physical (true) association cannot be proved from the present analysis, which applies to all the SNRs studied in this paper. A direct way to prove the association is their distance coincidence on the line of sight with a sufficiently high accuracy, e.g., within an error of a few tens of parsecs. However, the kinematical distance from the molecular line includes an uncertainty of ∼1 kpc, distance estimation by a SNR's brightness to diameter (Σ–D) relation yields an even larger uncertainty, and the method to measure the radio continuum absorption by an H i cloud includes the problem of the association of the H i and CO clouds themselves.

Thus, the atlas presents only the candidate molecular structures. More advanced discussion about the interaction may be obtained by further, sophisticated observations of a signature of the physical compression by a shock wave such as shock-induced molecular lines (Ziurys et al. 1989; Koo & Moon 1997b; Seta et al. 2004; Sashida et al. 2013).

Nevertheless, it may be worthwhile to comment that the radial velocities determined here, hence kinematical distances, of the identified molecular shells for some typical SNRs are in good agreement with those currently reported in the literature such as G11.17-0.35 at v_lsr = 33 km s⁻¹ (Kilpatrick et al. 2016), and W44 at 40–50 km s⁻¹ (Seta et al. 2004), for example. In Table B1 we cite more references, in which the same or close velocity clouds are identified by independent CO-line observations.

An SNR interacting with a molecular cloud will deform the cloud to make a concave boundary with respect to the SNR's center. Thereby, the resulting cloud morphology will depend on the extent and density of the cloud. We categorize the structure of a shell or a cavity of the CO brightness distribution apparently surrounding a SNR as follows.

• (i)  
  Cavity (Ca κ): When the cloud is extended to be comparable to or larger than the SNR's size, a round cavity is created around the SNR due to the dissociation of molecular gas and its accumulation at the shock front. If the cloud size is sufficiently large, the cavity will be fully embedded in the cloud, making a round shape in the sky. We define such a case as a cavity with a completeness of 1% or 100%, and introduce a completeness parameter or the shell measure, κ = 1. If the cloud size is comparable or smaller, the dissociation and/or compression will take place partially, forming an open cavity to the intercloud space. Such a partial cavity may be categorized by its completeness or shell measure with κ < 1, depending on the fraction of the boundary from a perfect loop.
• (ii)  
  Shell (Sh κ): If the cloud's density is lower, the gas will be accumulated or piled up around the shock front, making a shell structure. The shell may be categorized by its completeness from κ = 1 showing a perfect loop, or partial loops with κ < 1.
• (iii)  
  Partial/clumpy shell (Ps = Cs κ): Clouds are often more turbulent and clumpy. In such a case, the interaction front will produce more partial features such as a clumpy shell or an ensemble of partial arcs. We categorize such a case by the fraction of the total partial arcs compared to a round loop by a factor of κ.

Figure 1 illustrates typical morphologies of the CO brightness distribution around an SNR.

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Descriptions of the properties of the obtained maps are given in the figure captions of individual objects in the atlas. We present here an example for G11.17-0.35+32.975 km s⁻¹ in Figure 2. This SNR is a typical bright shell in a radio continuum, and its western half is apparently contacting, on the sky, with a half cavity of a CO-line cloud (Kilpatrick et al. 2016). The image indicates that the edge of the cavity facing the SNR does not show the signature of strong gas compression, which would cause a red-color (¹³CO) excess, if it existed. Also, the molecular mass (luminosity) along the edge of the cavity is far smaller than that expected by piled-up mass from inside the cavity. Such a structure may imply that the shell was created by the dissociation of molecules, but not by a direct piled-up compression.

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The radial velocity, v_r = v_lsr, at a distance d orbiting around the Galactic Center is related to the circular rotation velocity V(R) as a function of the Galactocentric distance R as

$$\begin{eqnarray}&&{v}_{r}=\left(\displaystyle \frac{{R}_{0}}{R}V(R)-{V}_{0}\right)\sin \ l,\end{eqnarray} \tag{ 1 }$$

where R is the Galactocentric distance related to d and Galactic longitude l by

$$\begin{eqnarray}&&d={R}_{0}\cos \ l\pm \sqrt{{R}^{2}-{R}_{0}^{2}{\sin }^{2}l}.\end{eqnarray} \tag{ 2 }$$

We assume here V₀ = 238 km s⁻¹ and R₀ = 8.0 km s⁻¹ (Honma et al. 2015), and adopt the most recent rotation curve derived by the compilation of determined circular velocities in the last two decades as shown in Figure 3 (Sofue 2020). Here, we approximate the rotation curve by an analytic expression,

$$\begin{eqnarray}&&V(R)=\left(\displaystyle \frac{{V}_{1}}{{\left[1+{\left(R/a\right)}^{2}\right]}^{1/2}}+\displaystyle \frac{{V}_{2}}{1+{\left(R/b\right)}^{2}}\right)\left(\displaystyle \frac{R}{c}\right).\end{eqnarray} \tag{ 3 }$$

The parameters, V₁ = 67, V₂ = 1000 km s⁻¹, a = 3.5 kpc, b = 0.44 kpc, and c = 1 kpc, were determined by the iterative fitting of the function to the data by trial and error, until one gets a satisfactory reproduction of the data within the radius range, 1.4 to ∼10 kpc, necessary for the present analysis. The adopted curve is shown by the thick line in Figure 3.

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For a given set of v_r and l, we can determine R by iteration using Equations (1) and (3), and the distance d is obtained by Equation (2). In Table B1 we list the determined distances and diameters of the SNR. The errors are calculated using the uncertainty of radial velocity of the CO line in the measured value as well as the interstellar turbulence, δ v_lsr ∼ 5 km s⁻¹, and the uncertainty in the rotation velocity, δ V_rot ∼ 5 km s⁻¹, propagating through the above equations to d. The uncertainties in R₀ and V₀ are not included.

The molecular mass of associated clouds is one of the most essential quantities. However, the present resolution, 20'' ∼ 0.5 pc at 5 kpc for example, is a few orders of magnitude wider than the expected thickness of shock-compressed filaments at the SNR fronts (Lucas et al. 2020). So, we are not able to estimate meaningful mass of the directly associated molecular gas to the SNRs.

Instead, we try here to estimate the upper limit to the associated cloud for G11.17-0.35 as a typical example. By measuring the excess T_B at the edge of the SNR over that in the ambient emission outside the SNR, the upper limit mass may be calculated by

$$\begin{eqnarray}&&M\sim \mu \ {m}_{{\rm{H}}}2\pi \kappa {R}_{{\rm{s}}}\ \delta {R}_{\mathrm{beam}}{X}_{\mathrm{CO}}\int \delta {Tdv},\end{eqnarray} \tag{ 4 }$$

where μ ∼ 2.6 is the reduced mass per H₂ molecule for solar abundance, m_H is the hydrogen mass, X_CO ∼ 2 × 10²⁰ cm⁻² [K km s⁻¹]⁻¹ (Sofue & Kohno 2020) is the conversion factor, R_S is the SNR radius, δ R_beam = θ_beam r is the beamwidth at the object, κ is the cavity/shell measure, and δ T is the excess brightness temperature of the ¹²CO line at the intensity peak along the shell or the edge of cavity contacting the SNR.

For G11.17-0.35 at 33 km s⁻¹ (Figure 2), we obtain δ T ∼ 5 K and κ ∼ 0.5, and the possibly associated molecular mass is shown to be M < ∼10² and < ∼10³ M_⊙ for the near and far distances, respectively. Similar estimation applies to most of the observed partial CO shells in the analyzed SNR, but we do not present the results for individual objects, because the estimations are simply upper limits to the physically meaningful masses, which are supposed to be a few orders of magnitude smaller, as discussed above.