X-Ray Studies of the Inverted Ejecta Layers in the Southeast Area of Cassiopeia A

We measure the proper motions of the Fe-rich and Si/O-rich ejecta in the southeastern region using some techniques to evaluate their kinematics in detail. Here we used X-ray images in the 0.5–1.7 keV band, which includes the Fe-L and O emissions, taken in 2000 and 2019.

To visualize expansions of local structures in Cas A, we used a technique called "optical flow" (Farnebäck 2003), which has been first applied to the remnant in Sato et al. (2018). We used the calcOpticalFlowFarneback function in OpenCV with the following arguments: pyr_scale = 0.5, which specifies the image scale to build pyramids for each image; levels = 3; the number of pyramid layers; winsize = 15; averaging window size; and poly_n = 5, which is the size of the pixel neighborhood used for the polynomial approximation. Assuming the distance of 3.4 kpc (Reed et al. 1995), the velocity vectors were calculated as shown in Figure 2. The moving structures at outer regions of the remnant have higher velocities, where the tip of the southeast region shows the velocities of >6000 km s⁻¹.

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We also measured the proper motions of 11 blob regions shown in Figure 3 using the maximum-likelihood method (e.g., Sato & Hughes 2017; Sato et al. 2018; Tsuchioka et al. 2021) to obtain the directions and magnitudes of the motions of each structure. Blobs 5–12 in Figure 3 show the regions where the Doppler velocity measurements using High Energy Transmission Grating Spectrometer were performed in Rutherford et al. (2013). The regions from blob 1 to blob 4 were defined as the outermost regions where Fe is abundant. As a result, the best-fit velocities in the plane of the sky (see third and fourth rows in Table 2) were estimated to be ∼4000–7000 km s⁻¹ for the Fe-rich structures (blobs 1–6), ∼2000–3000 km s⁻¹ for the Fe/Si-rich structures (Blob 7–9), and ∼1500–2500 km s⁻¹ for the Si/O-rich structures (blobs 10–12). The estimated velocities agree with those with the optical flow measurements. We found that the velocities of the Fe-rich structures in the plane of the sky are higher than those of the Si/O-rich structures. Even if we considered the line-of-sight (LoS) velocities obtained in Rutherford et al. (2013), the velocities of the Fe-rich structures are higher than those of the Si/O-rich structures (see the fifth and sixth rows in Table 2). On the other hand, the expansion index m (r ∝ t^m , where r and t are the radius and age of the remnant, respectively) in the Si/O-rich structures estimated from the proper motion measurements is lower than that in the Fe-rich structures, which means that the Si/O-rich structures were subjected to stronger deceleration. In Section 4.1, we discuss the deceleration in more detail.

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Table 2. Velocity Measurements in the Regions Shown in Figure 3 from Chandra Data

Region a	(R.A., Decl.)		Angular	LoS	Total	Expansion	Free Expansion
		Velocity	Velocity c		index, md	Velocity d
		(arcsec yr−1)	(km s−1) b	(km s−1)	(km s−1)		(km s−1)
Blob 1	${23}^{{\rm{h}}}{23}^{{\rm{m}}}48\buildrel{\rm{s}}\over{.} 89,58^\circ {49}^{{\prime} }05\buildrel{\prime\prime}\over{.} 59$	0.415 ± 0.026	6700 ± 410	⋯	⋯	0.859 ± 0.053	7790
Blob 2	${23}^{{\rm{h}}}{23}^{{\rm{m}}}46\buildrel{\rm{s}}\over{.} 38,58^\circ {48}^{{\prime} }29\buildrel{\prime\prime}\over{.} 94$	0.282 ± 0.026	4540 ± 410	⋯	⋯	0.666 ± 0.060	6820
Blob 3	${23}^{{\rm{h}}}{23}^{{\rm{m}}}46\buildrel{\rm{s}}\over{.} 85,58^\circ {47}^{{\prime} }36\buildrel{\prime\prime}\over{.} 06$	0.342 ± 0.026	5520 ± 410	⋯	⋯	0.722 ± 0.054	7640
Blob 4	${23}^{{\rm{h}}}{23}^{{\rm{m}}}43\buildrel{\rm{s}}\over{.} 16,58^\circ {47}^{{\prime} }32\buildrel{\prime\prime}\over{.} 19$	0.311 ± 0.026	5020 ± 410	⋯	⋯	0.769 ± 0.063	6520
Blob 5	${23}^{{\rm{h}}}{23}^{{\rm{m}}}44\buildrel{\rm{s}}\over{.} 77,58^\circ {49}^{{\prime} }13\buildrel{\prime\prime}\over{.} 00$	0.308 ± 0.026	4970 ± 410	−1710	5260	0.781 ± 0.065	6370
Blob 6	${23}^{{\rm{h}}}{23}^{{\rm{m}}}42\buildrel{\rm{s}}\over{.} 71,58^\circ {48}^{{\prime} }59\buildrel{\prime\prime}\over{.} 48$	0.266 ± 0.026	4290 ± 410	−1360	4500	0.781 ± 0.075	5500
Blob 7	${23}^{{\rm{h}}}{23}^{{\rm{m}}}39\buildrel{\rm{s}}\over{.} 41,58^\circ {48}^{{\prime} }11\buildrel{\prime\prime}\over{.} 28$	0.128 ± 0.026	2060 ± 410	−540	2130	0.460 ± 0.092	4480
Blob 8	${23}^{{\rm{h}}}{23}^{{\rm{m}}}35\buildrel{\rm{s}}\over{.} 74,58^\circ {47}^{{\prime} }33\buildrel{\prime\prime}\over{.} 40$	0.163 ± 0.026	2630 ± 410	−880	2780	0.607 ± 0.095	4340
Blob 9	${23}^{{\rm{h}}}{23}^{{\rm{m}}}35\buildrel{\rm{s}}\over{.} 74,58^\circ {47}^{{\prime} }33\buildrel{\prime\prime}\over{.} 40$	0.163 ± 0.026	2630 ± 410	−810	2750	0.607 ± 0.095	4340
Blob 10	${23}^{{\rm{h}}}{23}^{{\rm{m}}}33\buildrel{\rm{s}}\over{.} 21,58^\circ {47}^{{\prime} }48\buildrel{\prime\prime}\over{.} 17$	0.108 ± 0.026	1750 ± 410	−2340	2920	0.542 ± 0.128	3220
Blob 11	${23}^{{\rm{h}}}{23}^{{\rm{m}}}32\buildrel{\rm{s}}\over{.} 45,58^\circ {47}^{{\prime} }47\buildrel{\prime\prime}\over{.} 18$	0.105 ± 0.026	1700 ± 410	−2300	2860	0.548 ± 0.133	3100
Blob 12	${23}^{{\rm{h}}}{23}^{{\rm{m}}}31\buildrel{\rm{s}}\over{.} 62,58^\circ {47}^{{\prime} }45\buildrel{\prime\prime}\over{.} 71$	0.130 ± 0.026	2100 ± 410	−1360	2500	0.698 ± 0.137	3010

Notes. All errors listed in the table represent statistical errors.

^a See Figure 3 for the regions. Each feature corresponds to the three regions in Figure 1: blobs 1–6 correspond to region A (Fe-rich), blobs 7–9 to region B (Fe/Si-rich), and blobs 10–12 to region C (Si/O-rich). ^b The distance to Cas A is assumed to be 3.4 kpc (Reed et al. 1995). ^c The LoS velocities were measured with Chandra High Energy Transmission Grating in Rutherford et al. (2013). ^d Only the values of angular velocity were used.

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In Figure 4, we showed X-ray spectra extracted from regions A (Fe-rich region), B (Fe/Si-rich region), and C (Si/O-rich region). The comparison of the spectra shows that abundant elements are different from region to region, where elements that are prominent in the image appear as strong features in the spectra. We here focus on the fact that the Si/Fe-rich structure (region B) is located just inside the Fe-rich structure (region A). In general, Si/Fe-rich ejecta (i.e., the production in the incomplete Si burning layer) should be produced at the outside of Fe-rich ejecta (i.e., the production in the complete Si burning layer) in the SN explosion. Therefore, the positional relationship between region A and region B may indicate an inversion that has not been reported yet.

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To demonstrate the inversion between the complete and incomplete Si burning layers, we measured the abundances of Cr and Fe in region A and B by fitting the spectra in 3.7–7.1 keV. Since the magnitude of the Cr/Fe ratio changes between the complete Si burning regime and incomplete Si burning regime (e.g., Yamaguchi et al. 2017; Sato et al. 2020a, 2021), we chose Cr and Fe to quantify their mass ratio and identify the Si burning regime. The spectra were fitted with tbabs, a model for interstellar absorption, and vvpshock, a nonequilibrium ionized plasma model. We also used a gsmooth model for expressing the thermal broadening and the Doppler effects. As a result, we found that the Cr/Fe mass ratio in region B is significantly higher than that in region A (Figure 5 and Table 3), which implies that they were synthesized in different burning regimes (see Section 4.2 for a detailed discussion). The best-fit parameters and the significance of the Cr detection are summarized in Table 3.

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Table 3. The Best-fit Parameters of Spectral Fittings for Regions A and B

Region	Model	Fe	Cr	Mass Ratio (%)	χ2/dof	χ2/dof	Significance a
				(Cr/Fe)	Cr = 0	Cr = free	(Cr)
A	tbabs∗gsmooth∗vvpshock	${7.18}_{-0.27}^{+0.29}$	${3.96}_{-0.66}^{+0.66}$	${0.51}_{-0.10}^{+0.11}$	313.08/220	234.99/219	7.91 σ
B	tbabs∗gsmooth∗(vvpshock + Gauss×2)	${2.86}_{-0.05}^{+0.02}$	${3.82}_{-0.58}^{+0.51}$	${1.24}_{-0.20}^{+0.19}$	496.79/214	385.42/213	7.35 σ
B	tbabs∗gsmooth∗(vvpshock + Gauss×3)	${2.12}_{-0.16}^{+0.12}$	${3.20}_{-0.43}^{+0.44}$	${1.40}_{-0.25}^{+0.32}$	445.78/211	297.50/210	8.27 σ

Note.

^a 1σ corresponds to a confidence interval of 68.3%.

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In the spectral analysis, the hydrogen column density was fixed at 1.2 × 10²² cm⁻², which is a typical value for the southeast region (Hwang & Laming 2003; Sato et al. 2021; Ikeda et al. 2022), while kT_e , n_e t, and normalization and abundances of Ca, Ti, Cr, Mn, and Fe are treated as free parameters and the other abundances of elements are frozen to the solar values in Anders & Grevesse (1989). In region B, we found that the spectrum has significant contributions from pileup events due to the strong Si/S Heα emissions (see the broken lines in the bottom panels in Figure 5). Therefore, we here added two Gaussian components (Gauss in XSPEC) at ∼4.3 keV (Si Heα + S Heα) and ∼4.9 keV (S Heα × 2 or Si Heα + Ar Heα) to express the line features from the pileup effect. The pileup effect would rarely affect our measurements of Cr and Fe abundances because line structures due to the pileup are expected to be too weak around these emission lines. Also, we added a Gaussian component at ∼6.5 keV to obtain a better fit for the Fe Kα emission in region B. One possible reason for the failure to reproduce the Fe Kα emission is that it is mixed with radiation from plasmas that are less ionized or moving away from the LoS direction compared with the majority of plasmas. The addition of this Gaussian model changes the estimated Cr/Fe ratio slightly (Table 3) but does not affect our interpretation in Section 4.2.

In Section 3.1, we found that the current velocities of the Fe-rich structures are higher than those of the Si/O-rich structures based on our proper motion measurements and the Doppler velocity measurements in Rutherford et al. (2013). In contrast, the estimations of the expansion index implied that the Si/O-rich structures seem to have undergone stronger deceleration than the Fe-rich structures. In the piston mechanism proposed in DeLaney et al. (2010), the Si/O-rich materials have higher velocities and larger radii at the beginning. Orlando et al. (2021) have demonstrated that the dense Fe-rich ejecta push out the less dense ejecta above (including Si), breaking through some of it (see also Orlando et al. 2016). Here, the low-density Si/O-rich ejecta should experience strong deceleration, which may support our observations well. We here discuss the history of the expansion of each structure, taking the deceleration into account.

We calculated the expansion index (see Table 2), which keeps the information of the ejecta deceleration, using the following equation:

$$\begin{eqnarray}&&m=\mu \times \displaystyle \frac{r}{t},\end{eqnarray} \tag{ 1 }$$

where m, μ, r, and t indicate the expansion index, the observed proper motion, the distance from the explosion center, and the age of the remnant, respectively. Dividing the current velocity by the expansion index, we can obtain a free expansion velocity for traveling the current distance (shown in the eighth row of the Table 2), which would reflect the initial ejecta velocity roughly. As a result, we found that the free expansion velocities of the Fe-rich ejecta are still higher than those of the Si/O-rich ejecta.

In order to more accurately discuss the amount of deceleration, we solved for the time evolution of the SNR assuming the momentum conservation law. Assuming two patterns of density profiles of the interstellar medium (ISM), we consider a simple model for each in which the mass of the expanding ejecta is increased by sweeping through the ISM. First, a simple model assuming uniform ISM with density ρ₀ is as follows:

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{v}{{v}_{0}}=\displaystyle \frac{1}{1+\tfrac{4\pi {\rho }_{0}{r}_{1}^{3}}{3{M}_{\mathrm{ej}}}{\left(\tfrac{r}{{r}_{1}}\right)}^{3}}\equiv \displaystyle \frac{1}{1+A{\left(\tfrac{r}{{r}_{1}}\right)}^{3}},\end{array}\end{eqnarray} \tag{ 2 }$$

where M_ej, v₀, and $A=\tfrac{4\pi {\rho }_{0}{r}_{1}^{3}}{3{M}_{\mathrm{ej}}}$ are the ejecta mass, the initial ejecta velocity, and the mass ratio between the swept-up ISM and the ejecta as defined in Equation (2) when the ejecta expands to r₁, respectively. Here, r₁ is introduced to let the parameters be nondimensional, and it is arbitrarily set (r₁ = 1 pc is assumed throughout this paper). For example, if we set the typical parameters for Cas A as M_ej = 2–4 M_⊙ (Laming & Hwang 2003; Young et al. 2006) and ρ₀ = 10⁻²⁴ g cm⁻³, we get A = 3.09–1.55 × 10⁻².

When solving the momentum conservation law, the initial parameters required for the calculation are only the initial velocity v₀ and the mass ratio A. We solved this equation to reproduce the observational properties obtained from the image analysis in the Fe-rich (blob 1) and Si/O-rich (blob 10) ejecta.

The left panels of Figure 6 show the time evolution of the radius, velocity, and expansion index obtained from our calculations. Here we set v₀ = 8200 km s⁻¹ and A = 1.16 × 10⁻² for the Fe-rich ejecta (red curve) and v₀ = 4440 km s⁻¹ and A = 1.17 for the Si/O-rich ejecta (blue curve), which reproduces the observational properties well. As a result, we found that the velocity of the Si/O-rich ejecta cannot be higher than that of the Fe-rich ejecta in the entire history of the expansion, even taking into account the statistical errors. Therefore, the inversion of the ejecta kinematics seems to have been produced at a very early stage of the remnant evolution or during the explosion, although there could be a large uncertainty in the initial velocity estimations using our simple calculations.

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We would note that the mass ratio A = 1.17 for the Si/O-rich ejecta is almost two orders of magnitude larger than that for the Fe-rich ejecta, which implies that the Si/O-rich ejecta has encountered a denser ISM/circumstellar media (CSM) environment and/or had a lower ejecta density. Here the ejecta piston mechanism may explain this larger deceleration for the Si/O-rich ejecta (e.g., DeLaney et al. 2010; Orlando et al. 2021). In the simulations of Orlando et al. (2021), the density of Si ejecta at the outermost region in the early remnant stage is much lower than that of Fe ejecta (see top panels of Figure 9 in that paper). The low-density Si ejecta undergo a stronger slowdown and are eventually overtaken by the high-density Fe ejecta, which could be the main reason for the high mass ratio A for the Si/O-rich ejecta in this region.

Assuming another density profile, a model of time variation of SNR is investigated. The expansion parameters observed in Cas A are known to be well explained with a pre-SN wind of a red supergiant, where the surrounding density profile is expressed with a function of ρ ∝ r⁻² (e.g., Chevalier & Oishi 2003). To calculate the SNR evolution in the progenitor's wind, we define the wind density profile of $\rho ={A}^{{\prime} }{r}^{-2}$. For a steady wind, ${A}^{{\prime} }$ can be written as ${A}^{{\prime} }=\dot{M}/4\pi {v}_{w}$ using the mass loss rate $\dot{M}$ and wind speed v_w (Chevalier & Oishi 2003). In this case, Equation (2) can be rewritten as follows:

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{v}{{v}_{0}}=\displaystyle \frac{1}{1+\tfrac{4\pi {A}^{{\prime} }{r}_{1}}{3{M}_{\mathrm{ej}}}\left(\tfrac{r}{{r}_{1}}\right)}\equiv \displaystyle \frac{1}{1+B\left(\tfrac{r}{{r}_{1}}\right)},\end{array}\end{eqnarray} \tag{ 3 }$$

where $B=\tfrac{4\pi {A}^{{\prime} }{r}_{1}}{3{M}_{\mathrm{ej}}}$ and the other parameters are the same as in Equation (2). The time evolution of the case with v₀ = 9280 km s⁻¹ and B = 0.148 (red line) and with v₀ = 21,510 km s⁻¹ and B = 10.2 (blue line) is shown in the right panels of Figure 6, which reproduces well the observed results for Fe-rich and Si/O-rich ejecta, respectively. Here, assuming M_ej = 4 M_⊙, the parameter ${A}^{{\prime} }$ of the equations that well represent the observed values for the Fe-rich and O-rich ejecta are 9.12 × 10¹³ g cm⁻¹ and 6.29 × 10¹⁵ g cm⁻¹, respectively. The obtained values for the Fe-rich ejecta are consistent with 1.00 × 10¹⁴ g cm⁻¹, the value obtained in Chevalier & Oishi (2003). This result suggests that the kinetic and spatial inversion should have occurred ∼10–30 yr after the explosion even when assuming the expansion in the power-law density profile, which would be consistent with the piston mechanism proposed by DeLaney et al. (2010) and Orlando et al. (2021). Therefore, even when assuming either of the two density profiles, our results support the inversion at the early stage of the remnant evolution.

In Section 3.2, we found that the Cr/Fe mass ratio in the Fe/Si-rich region (region B) is larger than that in the Fe-rich region (region A), which implies that the complete Si burning layer is located just above the incomplete Si burning layer. In this section, we quantitatively discuss the observed mass ratios compared with a theoretical model to understand the nucleosynthetic origin of each region.

The observed Cr/Fe mass ratio can be used for determining the peak temperature during the Si burning regime (Yamaguchi et al. 2017; Sato et al. 2020a, 2021; Ikeda et al. 2022). Figure 7 shows the relation between the peak temperature during the nuclear burning and the Cr/Fe mass ratio in a 1D SN model used in Sato et al. (2020b, 2021). Around T_peak = 5.5 GK, there is a transition between the incomplete and complete Si burning regimes, where the Cr/Fe mass ratio shows a difference of almost one order of magnitude. As for the Fe-rich region, the observed mass ratio (red area in the figure) falls within the complete Si burning regime as already reported in Sato et al. (2021). On the other hand, the Cr/Fe mass ratio in the Fe/Si-rich ejecta (blue area in the figure) is significantly out of the range of the complete Si burning regime, suggesting the incomplete Si burning origin (T_peak < 5.5 GK) for this structure.

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The Cr/Fe mass ratio in the Fe/Si-rich ejecta is inconsistent with the production at the complete Si burning regime, although it is lower than the typical value at the incomplete Si burning around T_peak ≈ 5 GK. One possibility is that most of the incomplete Si burning products are still not heated (e.g., Laming & Temim 2020). Another is the strong α-rich freeze-out. Maeda & Nomoto (2003) have shown that strong α-rich freeze-out realized by asymmetric explosions suppresses the production of elements produced by the incomplete Si burning regime, such as Cr and Mn.

To consider the amount of contamination from the ejecta produced by the complete Si burning would allow us to discuss the low Cr/Fe ratio in region B quantitatively. In the SN model we used, the typical Cr/Fe mass ratios by the complete and incomplete Si burning are about 0.004 and 0.04, respectively. Using these values, we have roughly estimated that the contribution from the complete Si burning ejecta in this region is ∼80% to reproduce the observed ratio in region B. Interestingly, the contribution of the incomplete Si burning is small even in the inner Fe/Si-rich region, indicating that most Fe (≳80%) in the entire east region is of complete Si burning (i.e., α-rich freeze-out) origin.

The inversion of these Si burning layers would be useful to discuss the formation process of the inverted layers in the southeastern region of Cas A. Currently, the ejecta pistons during the SNR evolution would be the reasonable mechanism to explain the formation process. On the other hand, the inversion of the adjacent Si burning layers should occur before the inversion between Fe and Si ejecta, which may indicate the ejecta overturning during the explosion. In addition, such strong asymmetry could suppress the incomplete Si burning products (Maeda & Nomoto 2003), and this picture supports our results well. Further theoretical studies that can be compared with our observations will be helpful to understand the origin of the layered structure and the strong asymmetry during the SN explosion.