On the Origin of the Asymmetry of the Ejecta Structure and Explosion of G350.1–0.3

To visually grasp the slight change in the image from 2009 to 2018, we adopted one of the dynamic image analyses called "optical flow." It calculates the flow's 2D vector fields, which obey the conservation law of the total intensity in the image. A similar approach has been applied to Cassiopeia A (Sato et al. 2018). More specifically, a derived version of the optical flow called the Gunnar Farnebäck method (Farnebäck 2003) is used to focus more on the small movement of patchy areas. The parameters and the setups are the same as used in Sato et al. (2018). When a flux in a pixel is less than 1 × 10⁻⁷ counts cm⁻² s⁻¹, it is regarded as background, and the corresponding pixel is discarded in this calculation. The result of the optical flow is shown in Figure 2(a). The obtained vector fields are indicated by the length and the direction of the arrows. In this way, we succeeded in visualizing the change in the two images in the bright eastern region and revealing at least two distinctive flows on a large scale: from west to east in the upper half and from west to southeast in the bottom half. Note that only vectors with an amplitude greater than ∼1'' (1152 km s⁻¹ at the distance of 4.5 kpc) are shown in Figure 2(a), where the counts are significantly higher than the typical level of the background.

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We then proceed in visualizing a change on a much smaller spatial scale. The X-ray image of 2009 is subtracted from that of 2018 and shown in Figure 2(b), which works to emphasize the difference between the two images. The positive part (white in the figure) means that the X-ray intensity in 2018 is brighter than in 2009, and vice versa. In other words, the pairs of the black and white region indicate the movement of the image. Filamentary structures are extending from north to south in several places, indicating that the ejecta moved in an east–west direction, which is consistent with the results obtained by optical flow. Furthermore, it vividly illustrates a more pronounced but detailed internal structure of the movement in the remnant.

To further confirm the flow, 1D radial profiles are created from the box regions shown in Figure 2(b). The direction of the flow is defined as the positive values from east to south. The unit is the number of pixels (1 pixel = 0492). The projection of the flux is performed by integrating along the direction perpendicular to the flow direction. As a result, the projected profiles of the fluxes are obtained from each image of 2009 and 2018. The projection profile from box4 is shown in Figure 3 as an example. Each profile is fitted with a Gaussian function using the least-squares method. The centers of the Gaussian functions obtained refer to the distance of the move over the two observations, resulting in the velocity of the ejecta. By assuming that the distance to G350.1–0.3 is 4.5 kpc (Lovchinsky et al. 2011), the proper-motion velocities in all six box regions are calculated and summarized in Table 2. The ejecta velocities are found to range from 3500 to 5000 km s⁻¹.

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Table 2. Velocity Measurements in the Regions Shown in Figures 1 and 2(b) from Chandra and Suzaku Data

Region a	Angular Velocity		Line-of-sight Velocity	Total	χ2/dof	χ2/dof
	(arcsec yr−1)	(km s−1) b	(km s−1)	(km s−1)	z = 0 (fixed)	z = free
East-1	0.218 ± 0.014	4640 ± 290	${1280}_{-20}^{+20}$	${4820}_{-280}^{+280}$	527/251	369/250
East-2	0.149 ± 0.014	3180 ± 290	${1100}_{-190}^{+170}$	${3360}_{-280}^{+280}$	760/299	433/298
North	0.138 ± 0.027	2940 ± 580	${660}_{-110}^{+160}$	${3010}_{-570}^{+570}$	244/252	231/251
South	0.097 ± 0.027	2080 ± 580	${2570}_{-40}^{+140}$	${3300}_{-370}^{+380}$	615/219	255/218
CCO	0.030 ± 0.014	640 ± 290	⋯	⋯	⋯	⋯
box1	0.174 ± 0.028	3720 ± 600	${1160}_{-230}^{+1400}$	${3900}_{-580}^{+710}$	168/131	134/130
box2	0.192 ± 0.008	4100 ± 170	${1310}_{-30}^{+700}$	${4310}_{-160}^{+270}$	147/132	121/131
box3	0.172 ± 0.015	3670 ± 330	${1070}_{-150}^{+220}$	${3820}_{-320}^{+320}$	130/114	115/113
box4	0.167 ± 0.009	3650 ± 200	${670}_{-490}^{+250}$	${3620}_{-220}^{+200}$	167/144	156/143
box5	0.181 ± 0.014	3860 ± 290	${470}_{-100}^{+330}$	${3890}_{-290}^{+290}$	136/116	126/115
box6	0.227 ± 0.018	4850 ± 390	${1540}_{-1210}^{+300}$	${5090}_{-520}^{+380}$	148/123	127/122
Suzaku East	⋯	⋯	${1460}_{-10}^{+40}$	⋯	1096/776	599/775

Notes. All errors listed in the table represent statistical errors. The systematic errors are discussed in Section 2.

^a East-1, East-2, North, South, and CCO are indicated in Figure 1; box1, box2, box3, box4, box5, and box6 are indicated in Figure 2(b). ^b The distance to the G350.1–0.3 is assumed to be 4.5 kpc. The systematic error obtained from the point-source correction described in Section 2 is 884 km s⁻¹ by assuming 4.5 kpc as well.

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To estimate the direction of the flow with statistical significance, we calculate the 2D proper motions for the box regions in Figure 1 by using the maximum likelihood method. The method is based on the previous work (Sato & Hughes 2017; Sato et al. 2018; Millard et al. 2020). The image of 2018 is used as a template, while that of 2009 is floated to find a 2D vector to maximize the likelihood. Here the likelihood function is defined as

$$\begin{eqnarray}&&L=\displaystyle \prod _{i,j}\displaystyle \frac{{\lambda }_{i,j}^{{k}_{i,j}}{e}^{-{\lambda }_{i,j}}}{{k}_{i,j}!},\end{eqnarray} \tag{ 2 }$$

where (i, j), k_i,j , and λ_i,j are the integers to specify the location of the pixel, the photon counts in a pixel (i, j) of 2018, and the photon counts in a pixel (i, j) of 2009, respectively. ⁶ By searching the local extrema of the likelihood function by changing the pairs of i and j, we obtain the significance map in the space of i and j. It gives the range and the peak of the significance. As a result, the ejecta's best-fit transverse velocities are estimated to be ∼2000–4600 km s⁻¹ as shown in Table 2, which is consistent with the result of the 1D projection. Furthermore, the best-fit 2D vectors are evaluated with their statistical significance.

We apply the same method to the CCO and obtain its proper motion of ∼640 km s⁻¹. Since the CCO is a point source, the systematic uncertainty on the point-spread function (PSF) is not negligible. As the roll angle is different between the 2009 and 2018 observations (see Table 1), the nonaxisymmetric pattern of the PSF needs to be taken into account. Therefore, we created the simulation images by using a simulator called MARX. ⁷ The center of the point source in the observed image is assessed by using the maximum likelihood method with the simulation image. By subtracting the corrected coordinate of 2018 from that of 2009, the CCO's proper motion between two epochs is evaluated to be ∼640 ± 290 km s⁻¹.

We measure the line-of-sight velocities of the ejecta using the X-ray spectra's Doppler effect. We extracted the spectra from four regions (East-1, East-2, North, and South in Figure 1) and six regions (box1–box6 in Figure 2(b)) using the CIAO specextract command. The energy band of 0.5–6.0 keV was used in the analysis.

The spectra were fitted with two components in XSPEC (version 12.10.1): a nonequilibrium ionization plasma model (NEI), "vvpshock," and a photoelectric absorption model with the "angr" abundance (Anders & Grevesse 1989). In the fitting procedure, kT_e , n_e t, and normalization are treated as free parameters. Abundances of Mg, Al, Si, S, Ar, and Ca are allowed to vary freely, while the other abundances of elements are frozen to the solar values. The typical value of the equivalent hydrogen column density of the neutral absorber along the line of sight, N_H, is (3–4) × 10²² cm⁻². The spectra of the two epochs are combined in combine_spectra because the shape of each datum is similar (see Appendix). Figure 4 shows the spectra of G350.1–0.3, the best-fit model, and its residuals for East-1 and East-2 in the energy range of 1.65–2.3 keV. Figure 4(a) shows the fitting result of East-1 when the redshift (z) parameter of the NEI model is frozen at zero, resulting in χ²/dof of 527/251. The residuals are still present near the emission lines, suggesting the shift of the energy scale. Therefore, we continue fitting with a floating redshift, and Figure 4(b) shows the fitting results. The residuals significantly decrease (χ²/dof = 369/250). By fitting all the spectra with the redshift freed, the best-fit values of the redshift are obtained and summarized in Table 2. Si Lyα emission lines (∼2 keV) are visible in the spectra in Figure 4. They are the emission lines for which the centroid energy does not depend on the ionization state and are well fitted when z parameters are set to free in this study. By measuring the center and intensity of the Si Kα + Lyα lines, we can determine the ion fraction, or ionization state. Now that they are well fitted as well, the ionization state can be determined independently of the Doppler effect. The X-ray plasma in the east, the north, and the south are redshifted at 1000–1300 km s⁻¹, at ∼660 km s⁻¹, and above 2500 km s⁻¹, respectively.

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Since it is commonly challenging to calibrate the energy scale of CCD in orbit, it is prudent to confirm the result by using more than one mission. We thus analyzed the Suzaku data because it has a larger effective area and a higher signal-to-background ratio per arcmin². The spectra are obtained from a circle with a radius of $1\buildrel{\,\prime}\over{.} 5$ covering the bright eastern structure. As shown in Figures 4(c) and (d), the residuals become smaller when the redshift parameter is floated. The line-of-sight velocity is estimated to be ∼1500 km s⁻¹. The result is consistent with those obtained with Chandra.

The CCO spectrum is fitted phenomenologically with the absorbed blackbody radiation model in XSPEC. The energy band of 0.5–6.0 keV is used in the analysis. The spectra of the 2009, 2013, and 2018 observations are individually fitted and then joint-fitted (but only untied for normalization for each epoch). The results of the best-fit parameters are shown in Table 3. The fit is acceptable even without adding extra complex components, and there are no significant changes in parameters between different epochs of observations. The blackbody temperature kT_e was also consistent with Lovchinsky et al. (2011). We then fitted the data with a physically motivated model. According to Potekhin et al. (2020), the CCO spectrum was fitted with the absorbed nsx model (Ho & Heinke 2009) reproducing the spectrum of the atmosphere from the NS. In the analysis of Potekhin et al. (2020), the 2009 and 2013 observations targeting XMMU J172054.5–372652 (ID: 14806) are also used in the spectral analysis. For better statistics, we add observations from 2018, which are not included in the analysis of Potekhin et al. (2020). The spectrum of XMMU J172054.5–372652 superimposed on the absorbed nsx model is shown in Figure 5. Note that there are no significant changes in surface temperature or flux between 2009 and 2018. It can be seen from Table 3 that the amount of flux in 2013 with different ACIS modes is larger than that in other epochs. We estimated the amount of pileup in 2009 and 2018 using the tool PIMMS, ⁸ and we found that it was 13% and 8%, respectively. Thus, the pileup may be the reason why the flux in the 2013 observation appears to be the largest in the observations of three epochs.

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Table 3. Best-fit Spectral Parameters of XMMU J172054.5–372652

Model	Parameter	2009	2018	2013	Joint Fit
Absorbed blackbody model
tbabs	NH (1022 cm−2)	${3.02}_{-0.18}^{+0.19}$	${3.12}_{-0.14}^{+0.15}$	${2.70}_{-0.16}^{+0.17}$	${3.00}_{-0.09}^{+0.10}$
bbody	kTe (keV)	${0.52}_{-0.02}^{+0.02}$	${0.51}_{-0.01}^{+0.01}$	${0.50}_{-0.02}^{+0.02}$	${0.51}_{-0.01}^{+0.01}$
	flux a (10−13 erg cm−2 s−1)	${4.59}_{-0.11}^{+0.15}$	${4.64}_{-0.09}^{+0.08}$	${5.96}_{-0.14}^{+0.15}$	⋯
	χ2/dof	120/110	173/178	225/202	574/494
Absorbed nsx model
tbabs	NH (1022 cm−2)	${3.71}_{-0.23}^{+0.23}$	${3.89}_{-0.18}^{+0.17}$	${3.41}_{-0.20}^{+0.20}$	${3.72}_{-0.11}^{+0.12}$
nsx	$\mathrm{log}{T}_{\mathrm{eff}}$ (K)	${6.37}_{-0.03}^{+0.03}$	${6.34}_{-0.02}^{+0.03}$	${6.33}_{-0.03}^{+0.03}$	${6.34}_{-0.02}^{+0.02}$
	flux a (10−13 erg cm−2 s−1)	${4.61}_{-0.57}^{+0.09}$	${4.64}_{-0.28}^{+0.09}$	${5.99}_{-0.52}^{+0.10}$	⋯
	χ2/dof	112/110	153/178	220/202	539/494

Note.

^a Flux is calculated in the range of 1.0–6.0 keV.

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In this asymmetric object, the location of the center of the explosion is an extremely important aspect, especially in considering the relationship between the motion of CCO and the ejecta. Regarding the center of the explosion, previous studies (e.g., Gaensler et al. 2008; Lovchinsky et al. 2011) simply defined it as being in the middle of the bright region in X-rays or at the lowest point of the radio contour. But especially for CC SNRs, these explosion centers are poorly defined owing to their asymmetric tendencies. Extrapolating the proper motion measured by image analysis can determine the kinematic center (Fesen et al. 2006; Sato & Hughes 2017).

We estimated the time since the explosion by assuming that the ejecta had a common origin and drawing lines back to the presumed center adopting the velocities we measured and allowing the time since explosion to be a free parameter. Specifically, we calculated the time at which the variance of each origin point with respect to the presumed center was minimized. We investigated (i) the case that used two regions in the east and (ii) the case that used all five regions for which the maximum likelihood was used. In case (i), the center is at the position shown in the left panel of Figure 6, 460 yr ago. The location of the explosion appears to be precisely determined, but the motion of the CCO cannot be explained. In this case, XMMU J172054.5−372652 would not be associated with the SNR. In case (ii), the center is located at the position shown in the right panel of Figure 6, 655 yr ago. The error circle is larger, but it explains the movement of the CCO. However, the degree of deceleration should vary from region to region, so there is that indeterminacy in the estimate of the explosion center (e.g., Sato et al. 2018). Our measurements assert that the center of the explosion lies closer to the CCO than previously thought.

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Combining the proper motions and line-of-sight velocities measured for the same region, we can construct a total velocity vector for each since the two speeds are orthogonal. The four regions except for the CCO in Figure 1 and the six small boxes in Figure 2(b) were used for this study. For the large regions shown in Figure 1, velocity magnitudes of ∼5000 km s⁻¹ were obtained for East-1 and ∼3000 km s⁻¹ for East-2, North, and South. For all six regions along the eastern ejecta shown in Figure 2(b), velocities of more than 4000 km s⁻¹ or close to 4000 km s⁻¹ were obtained. In particular, the ejecta motion was found to reach velocities of ∼5000 km s⁻¹ for box6, which is located at the lower end of the remnant.

We used the software to model the evolution of an SNR (Leahy & Williams 2017) to infer SNR properties from the 3D velocities obtained in this study. We assumed a red supergiant as a progenitor and used a range of possible parameters of stellar wind mass loss and wind speed from Smith (2014). The power-law indices of the interstellar medium and ejecta density profiles were fixed at 2 and 10 (Matzner & McKee 1999). The velocity of contact discontinuity was assumed to be 0.75 times the velocity of the blast-wave shock, and the radius of contact discontinuity was assumed to be 0.75 times the radius of the blast-wave shock (Laming & Hwang 2003). The measured velocity (∼4800 km s⁻¹ for East-1) is assumed to be the contact discontinuity velocity, and the distance of 3.64 pc (by assuming 4.5 kpc) from the explosion center to the edge of the bright ejecta is considered to be the contact discontinuity radius. The age of the SNR was assumed to be 655 yr. We searched for SNR properties consistent with these conditions. Given the above assumptions, a model with ejecta energy of E_ej = (0.8–2) × 10⁵¹ erg, ejecta mass of M_ej = 4–15 M_⊙ (Yasumi et al. 2014), and stellar wind mass loss of 10⁻⁶ M_⊙ yr⁻¹ provides a reasonable interpretation for our measurements and the size observed by Chandra in X-ray only in the area of East-1. However, when it comes to the South and North regions, it is impossible to explain the velocity with these properties. This implies that the spherically symmetric model cannot explain this object.

The geometric centers of the X-ray SNR and XMMU J172054.5−372652 are about 15 apart, so the relationship between the two parties should be noted. The typical values of the N_H for the ejecta and the N_H for the CCO are in agreement, with values ranging from 3 × 10²² cm⁻² to 4 × 10²² cm⁻², consistent with the ejecta and the CCO having a common distance.

We explore the age of XMMU J172054.5−372652 from the theoretical cooling curves of the NS (Potekhin et al. 2020) and the surface temperature of the NS obtained by observations. The fit gives the effective temperature $\mathrm{log}{T}_{\mathrm{eff}}={6.34}_{-0.01}^{+0.02}$ K. This result is reasonable given the cooling curve (Potekhin et al. 2020), with the age being around 655 yr, and a young NS. In other words, XMMU J172054.5−372652 is most likely an NS associated with G350.1–0.3.

G350.1–0.3 shows a highly asymmetric ejecta distribution; however, its kinematics has been unclear. Based on our ejecta velocity measurements in 3D space, we found that most of the shocked ejecta at the eastern region in G350.1–0.3 are expanding with high velocities of >3500 km s⁻¹, which is comparable to that in the youngest Galactic CC SNR Cassiopeia A (DeLaney et al. 2010), to the opposite direction from the NS position. As shown in Figure 6, the estimated explosion centers in the two cases are both located to the east of the current NS position, so if the NS is receiving a kick, it should be receiving a kick to the west (opposite to the ejecta). The asymmetric ejecta/NS distribution and their kinematics in this remnant allow us to examine how asymmetric effects work for exploding massive stars.

The ejecta expansion in the opposite direction to the NS kick supports a "hydrodynamic kick" mechanism. In theory, neutrino-driven convective mass flows (Burrows et al. 1995) and standing accretion shock instability (SASI) sloshing motions (Blondin et al. 2003) could lead to large-scale asymmetries of the ejecta. The aspherical expanding ejecta gain radial momentum, and its center of mass begins to shift away from the coordinate origin. Here the NS must receive the negative of the total momentum of the anisotropically expanding ejecta mass owing to linear momentum conservation, which causes an NS kick in the opposite direction of the SN mass ejection. Recent hydrodynamic simulations of the neutrino-driven mechanism show such NS kicks up to more than 1000 km s⁻¹ (e.g., Scheck et al. 2006; Wongwathanarat et al. 2010, 2013). The NS kick could also originate from an anisotropic emission of neutrinos ("neutrino-driven kick"; Fryer & Kusenko 2006); however, the strongest mass ejection in the direction of the NS motion is predicted in this scenario, which is not suitable for G350.1–0.3.

The nucleosynthesis in G350.1–0.3 would be useful for understanding the asymmetric effects during the explosion. In the neutrino-driven mechanism, "high-entropy bubbles" in the process of forming large-scale asymmetries play an important role in the explosive nucleosynthesis (e.g., Wongwathanarat et al. 2017). In the high-entropy nuclear burning region, the abundant α-particles (⁴He) are captured by heavy elements. Thus, the production of α-elements (e.g., ⁴⁴Ti) is enhanced in the high-entropy process. Thus, the strong asymmetry in the remnant implies a large production of ⁴⁴Ti as in Cassiopeia A (e.g., Grefenstette et al. 2014), and the age of the remnant would encourage us to investigate the ⁴⁴Ti emission. ⁹ On the other hand, the ⁴⁴Ti production depends not only on the entropy but also on the electron fraction Y_e (the average electron number per baryon) in the high-entropy region (e.g., Magkotsios et al. 2010; Wanajo et al. 2013). In particular, the amount of ⁴⁴Ti in proton-rich high-entropy ejecta predicted in several theoretical simulations (e.g., Wanajo et al. 2018) is much smaller than that in the neutron-rich ejecta (Wongwathanarat et al. 2017). Therefore, the neutron-rich environment is needed to create the abundant ⁴⁴Ti in the remnant. The Suzaku observation of G350.1–0.3 shows extremely high abundances of Ni compared to Fe (Z_Ni/Z_Fe ≈ 8; Yasumi et al. 2014), which implies a suitable environment for the ⁴⁴Ti production. As discussed here, the mass ratio among the iron-group elements and titanium could be a tracer of the nuclear burning conditions around the birthplace of the NS. Further investigations for the element compositions in the remnant will be helpful to understand the SN engine for driving CC SNe.

The asymmetric ejecta distribution and NS kick in G350.1–0.3 have not received much attention until now (e.g., the remnant is out of samples in Holland-Ashford et al. 2017; Katsuda et al. 2018). We here succeeded in revealing the detailed kinematics of both ejecta and CCO in the remnant, which supports that the asymmetry in the kinematics of the remnant could originate from the neutrino-driven explosion and the strong hydrodynamic kick associated with the mechanism. Based on our results, it is more certain that the remnant can be one of the best samples in the future studies for discussing the origin of asymmetry in CC SNe such as Cassiopeia A.