CO J = 1–0 AND J = 2–1 LINE OBSERVATIONS OF THE MOLECULAR-CLOUD-BLOCKED SUPERNOVA REMNANT 3C434.1

Several molecular clouds are detected in the velocity range covered by our observations. Figure 2 shows the average spectrum of the area: several velocity components are apparent; bright components between −20 and +20 km s⁻¹ and faint components between −70 and −35 km s⁻¹.

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Figure 3 shows the channel maps of the prominent velocity components. The components at large negative velocities (−70 ∼ −35 km s⁻¹) are located outside the remnant; the −44 km s⁻¹ cloud is located a few arc minutes beyond the southeast boundary. The −55 and −61 km s⁻¹ molecular clouds are located close to the SNR boundary, but their intensities are very weak and line widths are narrow. Thus, we consider it unlikely that these features have any relation with the remnant. The positive velocity (v_LSR ⩾ 0 km s⁻¹) components are associated with the complex local clouds of Cep OB2 and Cyg OB7 at 0.8 kpc (Humphreys 1978). These clouds are located in the southern part of the field, and we do not find any correlated features with the radio continuum emission.

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It is the −13 km s⁻¹ cloud that shows a clear spatial correlation with the radio continuum emission. The cloud is widely distributed over the western part of the remnant where the radio continuum intensity is low. Figure 4 compares the distributions of the CO and radio continuum intensities in detail from v_LSR = −9.8 to −15.8 km s⁻¹. The cloud is elongated vertically along the western boundary of the remnant. At −11.8 to −12.8 km s⁻¹, the southern part of the cloud is bright and there is a thin filamentary structure that matches well with the western boundary of the torus structure in the radio continuum. The bright CO region matches well with the southern curved edge of the radio continuum. At −12.8 to −13.8 km s⁻¹, the northern and southern parts of the cloud are about equally bright and there is emission along the bar structure in the radio continuum.

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The above morphological correlation between the CO and radio continuum strongly suggests that the CO cloud is interacting with the SNR and that the complex radio morphology of the SNR is caused by this interaction. We estimate the mass of the western molecular cloud by integrating the CO emission over v_LSR = −8 to −18 km s⁻¹ in an area of 23' × 39' and assuming a Galactic CO-to-H₂ conversion factor of 2.3 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹ (Strong et al. 1988). The resulting mass is (1.00 ± 0.02) × 10⁴ $d_{3} ^{2}$ M_☉ where d₃ is the distance to the SNR normalized to 3 kpc (see Section 4.1) and the error is 1σ rms error.

A high ¹²CO J = 2–1/1–0 ratio identifies shocked warm and dense CO gas. Figure 5 shows the spatial variation of the ¹²CO J = 2–1/1–0 ratio obtained from the SRAO ¹²CO J = 1–0 and KOSMA ¹²CO J = 2–1 maps integrated over v_LSR =−16 to −8 km s⁻¹ and binned to 2' × 2'. We exclude pixels with an integrated intensity less than 2.5 K km s⁻¹ in order to exclude positions with low signal-to-noise ratios from the map. In Figure 5, high (⩾1.0) ratios are found toward the southern molecular cloud. The spectra of this area are shown in Figure 6. Note that the 0 km s⁻¹ component shows J = 2–1 emission weaker than the J = 1–0 emission with ¹²CO J = 2–1/J = 1–0 ratio of 0.3–1.0 which is typical for giant molecular clouds (Sakamoto et al. 1994). The position (− 4, −10) also shows an example of ordinary CO line profiles of unshocked molecular clouds between −16 and −8 km s⁻¹. Here, the ratio is 0.5 at a velocity of −11 km s⁻¹. On the other hand, the −13 km s⁻¹ component has a higher J = 2–1/J = 1–0 ratio. The ¹²CO J = 2–1/J = 1–0 integrated intensity ratio varies from 0.5 to 1.6 in region A in Figure 5 and the highest value (1.6) is at (21^h24^m8^s, 51°50'30'') or at (− 6, −2) in Figure 6. Typically, the high-ratio regions are located at the boundary of the southern molecular clouds with a peak velocity of −13 km s⁻¹. However, at position (− 4, −4), only the −11 km s⁻¹ velocity component shows the high-ratio CO line emissions. The ratio is 0.95 at this position using CO integrated intensity results.

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A ratio higher than ∼1 indicates the presence of warm and dense CO gas, presumably heated and compressed by the SNR shock (e.g., Koo et al. 2001). We use the large velocity gradient model (Scoville & Solomon 1974; Goldreich & Kwan 1974) to estimate the physical parameters of the shocked gas. Using T_mb,_{J = 1–0} = 0.5 K and ¹²R_2–1/1–0 = 1.6 at the (− 6, −2) position, we obtain n(H₂) ∼2.0 × 10³ cm⁻³ and X(¹²CO)/(dv/dr) ∼7.9 × 10⁻⁸ pc (km s⁻¹)⁻¹ for T_k = 100 K where X(¹²CO)/(dv/dr) is the fractional abundance of ¹²CO relative to H₂ [X(¹²CO)] per unit velocity gradient interval. This gives a CO column density of 2.4 × 10¹⁵ cm⁻² assuming a velocity width of Δv = 5 km s⁻¹. This is valid when the emitting region fills the telescope beam (FWHM = 130''). If the beam filling factor is lower, e.g., ∼0.1, the source intrinsic brightnesses and the column density derived scale up by the inverse factor, i.e., by ∼10, whereas the density, derived from the line ratio, stays roughly the same.

The morphological relation and the high ¹²R_2–1/1–0 ratio strongly suggest that the SNR 3C434.1 is interacting with the molecular cloud that shows CO emission at −13 km s⁻¹. The kinematic distance corresponding to −13 km s⁻¹ is 3.0 kpc assuming the Galactic rotation curve of Brand & Blitz (1993) with R₀ = 8.5 kpc and v₀ = 220 km s⁻¹. Our kinematic distance is less than the 4.5 ± 0.9 kpc distance proposed by Foster (2005).

Foster et al. (2004) noted fragmented H i filaments along the SNR boundary at −80 km s⁻¹ and interpreted them as parts of a preexisting stellar wind bubble produced by the massive progenitor of the SNR. According to our result, however, the velocity difference is too large for this component to be associated with the SNR. We instead examine the correlation of the H i emission at around v_LSR = −13 km s⁻¹ with the SNR. Figure 7 shows the CGPS H i channel maps from −9.7 to −15.5 km s⁻¹. We first note that there is a large-scale gradient in H i intensity over the field: the northwestern area is brighter than the southeastern area. Second, there is a large filamentary H i-absorption structure in the northwestern area of the field, but it is not related to the SNR. Absorption from the −13 km s⁻¹ cloud interacting with the SNR is not apparent. Third, there is a long, linear H i structure just outside of and along the southern SNR boundary at velocities from −11 to −15 km s⁻¹ (labeled "Filament S"). The radio brightness drops sharply across the H i filament. Therefore, the linearly shaped southwestern radio boundary seems to be related to this H i structure.

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The geometrical center of the shell is (21^h24^m45^s, 51°52'27'') and its radius (R_s) is 13' or 11.3 pc at 3.0 kpc. The spherical morphology suggests that we can apply a standard model to this part of the remnant, as has been confirmed by hydrodynamic simulations (e.g., Tenorio-Tagle et al. 1985). From the ROSAT X-ray spectra, Foster (2005) derived an electron temperature of T_e = 4.5 × 10⁶ K for the host X-ray emitting gas, which corresponds to a shock speed v_s = (16k_BT_e/3μ)^1/2 = 570 km s⁻¹ (where μ = 1.4m_H/2.3 = 0.61m_H is the mean mass per particle, m_H is the mass of H nuclei, and k_B is Boltzmann's constant). This speed is large and we may assume that the SNR is in its adiabatic phase. Then, from the Sedov solution, the radius and the velocity give an age of 0.4R_s/v_s = 7900 yr. The estimated volume emission measure is $\int n_e^2 dV=4.5\times 10^{57}$ cm⁻⁶ pc³ (scaled to 3.0 kpc). Foster (2005) assumed that this X-ray emission comes from a thin shell in contact with the stellar wind bubble. We instead assume that the X-ray emitting gas is roughly filling the eastern half because the X-ray emission is centrally brightened, which gives an rms electron density of 0.23 cm⁻³. Then the supernova (SN) explosion energy is, from the Sedov solution, E_SN = 2.1 × 10⁵¹ n₀(R/10 pc)³(v_s/10³ km s⁻¹)² = 0.19 × 10⁵¹ erg, where n₀(= n_e/1.2) = 0.19 cm⁻³ is the number density of hydrogen nuclei of the medium taking into account an He abundance of 10% by number. This is smaller than the canonical value of 10⁵¹ erg but not unreasonable. The derived parameters of the SNR are summarized in Table 1. The dynamical evolution of the SNR including the western part interacting with the molecular cloud will be discussed in Section 4.3.

SNRs interacting with molecular clouds often show flattening or a turnover of the radio synchrotron spectrum at low frequencies around the areas of the interaction, i.e., the spectral index becomes larger than the typical value (α ∼ −0.5; S_ν∝ν^α) of shell-type SNRs or even becomes positive. Some examples are IC 443 (Green 1986), the Cygnus Loop (Leahy & Roger 1998), HB 21 (Koo et al. 2001; Leahy 2006), 3C391 (Brogan et al. 2005), and W44 (Castelletti et al. 2007). Several mechanisms have been proposed for the flat radio spectrum: free–free absorption by thermal plasma in the dense postshock region, ionization losses from mixed dense molecular material, second-order Fermi acceleration by the turbulent medium in the postshock region (Leahy & Roger 1998; Ostrowski 1999), the higher compression ratio owing to the energy loss to cosmic-ray particles (Bykov et al. 2000), and the relatively flat spectrum of ambient cosmic rays entering the shock (Chevalier 1999). For 3C434.1, Foster et al. (2004) derived a spectral index of −0.38 ± 0.03 from 150 MHz to 2.7 GHz and noted that the western extension has a slightly flatter spectrum (⩽0.3) than the eastern radio shell. Later, Kothes et al. (2006) derived a somewhat steeper index of −0.48 ± 0.02 by fitting the total fluxes from 30 MHz to 5 GHz.

We produce a spectral index map using the CGPS 1420 and 408 MHz radio continuum data. We first convolve the 1420 MHz image (FWHM = 49'') to the beam size (168'') of the 408 MHz image, and we subtract a constant background in each image: 7.3 and 77 K for 1420 and 408 MHz, respectively. The resulting spectral index map is shown in Figure 8, which confirms the flat spectrum in the western area. The eastern bright area has an index of −0.45 to −0.3 whereas the southwestern area has −0.1 to 0.0. The area around (21^h23^m20^s, 51°49'10'') has a particular flat spectrum (∼0.0). The average spectral index of the entire SNR is −0.33.

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We also derive the spectral index using the "T-T plot method," wherein we make a pixel-to-pixel comparison of the brightness temperatures at two different frequencies and derive the slope. The advantage of this method is that the slope is not affected by potentially different zero levels of each set of frequency data and smooth background emission (Turtle et al. 1962). We divide the target area into four regions and derive the index in each region from 1420 and 408 MHz data. Figure 9 shows the boundary of the four regions in the convolved 1420 MHz radio continuum image, and Figure 10 shows their pixel-to-pixel comparison of the brightness at two frequencies, respectively. The indices derived from least-squares fitting are given in the individual graphs. In three regions, the index varies little (−0.47 to −0.41), but in the southwestern area (region 4), the index is −0.28  ±  0.01 which is considerably flatter than the other regions. This flat spectral index could be due to the interaction with the molecular cloud, confirming the reasoning given above. The average spectral index of all areas is −0.42 ± 0.01.

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The dynamical evolution of an SNR originating near the boundary of a dense molecular cloud has been numerically studied by several authors (e.g., Tenorio-Tagle et al. 1985; Wang et al. 1992; Ferreira & de Jager 2008). The details of the evolution depend on the physical and geometrical parameters of the simulation, e.g., the SN explosion energy, the densities of the molecular cloud and diffuse gas, the location of SN explosion site, etc. If the SN explodes in the diffuse medium close to the boundary of the molecular cloud, the SN blast wave expands adiabatically until it encounters the cloud. When the blast wave hits the dense cloud, two waves are produced: a shock wave propagating into the cloud and a reflected wave propagating back to the interior of the SNR. The propagating shock wave decelerates rapidly because of the high density and also because the reflective wave lowers the driving pressure near the cloud. Because the molecular cloud's density is considerably larger than that of the diffuse medium, it is not overly disrupted, and the SNR appears as a semicircular shell. The semicircular morphology of the SNR CTB 109, which is another SNR blocked by a molecular cloud (Tatematsu et al. 1987, 1990; Sasaki et al. 2006), has been acceptably explained by this scenario (Wang et al. 1992).

The SNR 3C434.1 also has a semicircular shape, but it does not quite fit into the above scenario: it has a narrow, convergent tail that originates from the western end of the shell and extends much further (>25' from the center) to the west. Also, there is a torus that appears to surround the western end of the tail. The inner boundary of the torus is quite circular with a clear limb brightening. This probably indicates that the cloud that is interacting with 3C434.1 is thin and that the blast wave has broken through it. This hypothesis is consistent with the presence of an elongated CO cloud along the western boundary of the SNR.

We have developed a hydrodynamic model to confirm the above hypothesis. We assume that the SN explodes at 1 pc from the boundary of a sheet-like cloud that has a thickness of 5 pc. The H-nuclei number density of the cloud is assumed to be 20 cm⁻³, which is a typical density for the interclump medium of giant molecular clouds (e.g., Chevalier 1999 and references therein). For the density of the diffuse medium and SN explosion energy, we adopt 1 cm⁻³ and 10⁵¹ erg, respectively. These canonical values are both about five times larger than those of 3C434.1, but since the radius (and velocity) scales with (E_SN/n)^0.2 in the Sedov phase, the resulting morphological evolution in time should be approximately correct. The density distribution of a core-collapse SN is characterized by a central region of approximately constant density and an outer region with a steep gradient (e.g., Matzner & McKee 1999). We assume that the SN ejecta, which are freely expanding, are composed of a central region of constant density and an outer region with a steep power law (ρ(r)∝r⁻⁹) with a total mass of 8 M_☉. When the steep power-law portion of the ejecta is interacting with the ambient medium, a similarity solution exists (Chevalier 1982). Our numerical simulation starts at t = 350 yr, and the distributions of the physical parameters at this time are taken from this similarity solution. We first considered a model in which the cloud was shaped like an infinitely extended disk. This model, however, did not produce the torus-like structure in the west in time. We therefore assume that the cloud has a cylindrical hole at the center, so that the shock can penetrate through the central hole. The radius of the hole is assumed to be 3 pc. For the calculation, we adopt the three-dimensional hydrodynamic code developed by Harten, Lax, and van Leer (HLL) with a modified cooling effect (Harten et al. 1983). This HLL code is efficient for describing the shock propagation. The simulation box consists of 512 × 256 × 256 grid points with a spatial resolution of 1/16 pc. We calculate one quadrant column along the symmetric axis (x-axis), and we copy the results to the other quadrants by assuming symmetry.

The results of the numerical simulations are shown in Figure 11 where we show the time evolution of the density and velocity distributions in the upper and lower panels, respectively. Figure 11(a) shows the initial distributions at t = 350 yr. The ambient shock is at 1.89 pc, while the reverse shock propagating into the SN ejecta is at 1.60 pc from the explosion center. Between these two shocks, the shocked ambient medium and the shocked ejecta are separated by a contact discontinuity which is at 1.66 pc (see Chevalier 1982). At t = 1950 yr (Figure 11(b)), the SNR blast wave propagating to the right has been significantly distorted by the interaction with the cylindrical wall of the cloud. The cloud boundary has been compressed to high density while the shock propagating into the dense cloud is considerably decelerated. Note that the reverse shock in the interacting region is now propagating backward into the central area in the rest frame, whereas the reverse shocks in the other regions are still propagating forward in the rest frame. At t = 4950 yr (Figure 11(c)), the radius of the left half of the SNR becomes 9.4 pc, which is close to that of the Sedov solution, as expected. Meanwhile, the blast wave propagating to the right has propagated through the cylindrical hole and popped out of the cloud producing a mushroom-like structure. In the interior, the reverse shocks from the side walls collide and produce a fast flow to the east. At t = 7950 yr (Figure 11(d)), which is close to the age of 3C434.1, again the radius of the left half of the SNR agrees with that (11.3 pc) of the Sedov solution. The blast wave on the right by now appears almost spherical. Note that the velocity of the blast wave on the right is larger than on the left, so that the distance to the rightmost front from the explosion center is more than 13 pc. The density and velocity distributions in the interior of the SNR become complex owing to the collision of waves and hydrodynamic instabilities. Meanwhile, the shock propagating into the dense cloud became partially radiative, so that the density of the shocked cloud is very high (∼10³ cm⁻³).

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The resulting morphology of the numerical simulation is close to the radio morphology of 3C434.1, but there are some differences. In Figure 12, we draw a schematic diagram of 3C434.1 including its radio-continuum features, i.e., torus, bar, and tail. The spherical eastern half of the SNR with a radius of 11 pc is quite consistent with the hydrodynamic model. The torus structure partly matches the mushroom structure in the model. The shocked, highly compressed boundary of the molecular cloud corresponds to the northwestern SNR boundary with enhanced radio brightness in the radio map. The bar structure represents the dense swept-up cloud material embedded within the SNR. The long, radio-continuum tail that extends much further than the overall radius of the SNR, however, is not easy to explain. It seems to indicate that there might have been a preexisting tunnel of much lower density in the interstellar medium (ISM). An interesting possibility would be a "star trail" as in the Crab Nebula (Blandford et al. 1983; Cox et al. 1991). In the Crab Nebula, there is a thin (∼0.5 pc) jet-like structure in the radio continuum to the north, and it was attributed to the trail of the progenitor star; the progenitor star was moving before the explosion and its red supergiant wind leaves a trail through which the SN blast wave can propagate beyond. In 3C434.1, the radius of the tail is wide, i.e., 5' or ∼4.4 pc just behind the torus. However, if the trail is filled with hot, shocked gas, the trail will expand sideways at about the velocity of the sound speed of the hot gas, which is 250 km s⁻¹ for 4.5 × 10⁶ K X-ray emitting gas, the maximum increment of the radius of the tunnel by the SNR would be <2 pc. Therefore, the tunnel might have had a large radius initially.

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