INTERSTELLAR AND EJECTA DUST IN THE CAS A SUPERNOVA REMNANT

One of the primary goals of this analysis was to find the continuum spectra of dust that is found in regions of various physical parameters and compositions throughout the SNR. The regions to be investigated are identified via six distinct spatial templates. These templates are shown in Figure 1 and Table 2, and are described in more detail in the Appendix. To identify the spectra associated with each of the six emission templates, we superimposed all the templates and for each one we identified the zones where its relative emission was the dominant component. Because of the strong and widespread [Ar ii] emission, in some cases the zones necessarily included [Ar ii] emission as well. The zones selected for each of the templates are outlined in Figure 2.

For all pixels, i, of each zone of the six selected emission templates, T_j(i), the data D(i, λ) can be represented by

$$\begin{equation} D(i,\lambda) = \sum _{j=1}^6{S_j(\lambda)T_j(i)}\ + \ C(\lambda). \end{equation} \tag{ 1 }$$

The parameters C(λ), a constant term (which should be small) to account for errors in the background levels, and S_j(λ), the spectra associated with each of the templates, can thus be derived via a least-squares fit or linear regression between the data and the templates.

For the Ar ii zone, the sum is strongly dominated by this template, and $S_{{\rm Ar}\,{\scriptsize{II}}}(\lambda)$ is determined as the slope of a linear least squares fit between D(i, λ) and $T_{{\rm Ar}\,{\scriptsize{II}}}(i)$. Some Ar ii emission is unavoidable in all other zones; therefore, for the other zones the spectra S_j(λ) were derived using a linear regression between D(i, λ) and two templates: T_j(i) and $T_{{\rm Ar}\,{\scriptsize{II}}}(i)$. The characteristic spectra derived are shown in Figure 3.

When these derived spectra are multiplied by the spatial templates over the entire SNR (not just within the selected zones) and the result is subtracted from the data cube, we found that there was one region of residual emission that was particularly strong and consistently positive at all wavelengths. This region is in the south central portion of the SNR. One additional zone was created to cover this region (the "South Spot" in Figure 2), and the measured spectrum within this zone is included in Figure 3.

The characteristic spectra are key data that allow for the detailed examination of the nature of the dust in different regions of the SNR. The modeling and analysis of the characteristic spectra are presented in Section 4.

In principle, the spatial templates, T_j(i), and their characteristic spectra, S_j(λ), provide a complete description of the continuum data cube. However, because the characteristic spectra were derived only from limited zones of the SNR, it is informative to revisit the data modeling given by Equation (1), but instead using the seven S_j(λ) characteristic spectra as known quantities and solve for the spatial distributions, I_j(i), of each spectum over the entire SNR:

$$\begin{equation} D(i,\lambda) = \sum _{j=1}^7{S_j(\lambda)I_j(i)}\ + \ C(i). \end{equation} \tag{ 2 }$$

In this fitting, a constant term, C(i), is still present to account for background errors, but now this constant is a function of position rather than wavelength. If the characteristic spectra are uniquely and perfectly correlated with the spatial templates, then we should find that the spatial distributions are identical to the templates, I_j(i) = T_j(i). Differences between the initial templates and these derived spatial distributions would identify (1) regions where the template emission is present but not accompanied by the characteristic spectrum, and (2) regions where emission matching a characteristic spectrum is present but without corresponding emission of the initial template.

The derived spatial distributions of the different characteristic spectra are shown in Figure 4. Comparison with Figure 1 shows that the derived spatial distribution of the dust associated with Ar ii emission is very similar to the input template, $I_{{\rm Ar}\,{\scriptsize{II}}}(i) \approx T_{{\rm Ar}\,{\scriptsize{II}}}(i)$. Differences are more evident for dust associated with Ne ii and X-ray Fe emission. However, in both cases, the brightest portions of the derived spatial distributions do follow the original templates, even in areas that were outside of the zones where the characteristic spectra were derived. The spatial distribution of the radio dust (i.e., dust associated with the radio template) is very different from original template, as it tends to be concentrated in areas at the periphery of the SNR that are expected to lie between the forward shock and the reverse shock. Material here should be dominated by swept up interstellar or circumstellar material. Interestingly, the spatial distribution identifies a large area on the east side of the SNR which matches the characteristic spectrum, but had not been within the zone used to define that spectrum. The agreement between the Si ii dust's spatial distribution and the initial template is very rough. This spatial distribution is dominated by the morphology of the emission at wavelengths λ ⩾ 70 μm. The spatial distribution of dust matching the Ar iii characteristic spectrum is confined to a few of the brightest peaks in the continuum and [Ar iii] images.

Guided by these results, we find that a traditional three-color image can be constructed to emphasize the different components via the tint of the continuum emission, as shown in Figure 5. This image combines the emission at 11.8, 20.8, and 70 μm from the smoothed continuum data cube. These wavelengths are chosen by selecting those where the characteristic spectra (Figure 3) have the greatest differences from one another.

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Figure 6 shows the seven Cas A characteristic spectra with their actual intensities (i.e., without normalization). The total emission of each is calculated by integrating the characteristic spectra, S_j(λ) (Figure 3), over the regions of the corresponding spatial distributions, I_j(i) (Figure 4). This comparison shows that in the ejecta, the Ar ii dust component is dominant at wavelengths from 8 to 35 μm. The dust associated with the radio emission is assumed to be swept up ISM dust rather than ejecta because its spatial distribution turns out to be largely confined to the periphery of the SNR. The brightness of the ISM dust is generally <one third of the brightness of the ejecta dust. The sum of the all the spectra is also shown as a "fit" to the total Cas A spectrum as measured directly from Spitzer and Herschel data. The general agreement at 10–35 μm indicates that there are no major missing components. At shorter wavelengths, as the SNR emission drops toward the level of the background and the noise, the comparison is not as good.

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The characteristic dust spectrum associated with Ar ii exhibits the sharpest peaks at 9 and 21 μm and has a third, weaker peak at ∼12 μm. The astronomical silicate of the typical ISM does not have silicate peaks sharp enough to produce the observed features. Magnesium silicates (particularly Mg_0.7SiO_2.7, characterized by Mg/Si = 0.7) have peaks that are in roughly the right locations, but their shapes are not a good match to the data. However, when two-composition fits are performed, the addition of a second component lacking strong spectral features (e.g., graphite, amorphous C, or Al₂O₃), can soften and smooth the appearance of the silicate peaks to provide a much better fit to the spectrum.

The best two-component fit (see Figure 14) employs Mg_0.7SiO_2.7 to fit the 9 and 21 μm silicate peaks, and graphite as the featureless component that weakens the relative strength of the peaks. The fit to these peaks is very good, although the weaker 12 μm peak is not fit at all. Despite the overall good fit, the temperature components needed for the Mg silicate are somewhat suspicious. Components at 71–63 K are needed to fit the 21 μm feature, but are too cold to contribute to the 9 μm feature. Conversely, a 500 K component produces the 9 μm peak while contributing little to the 21 μm peak. Small, stochastically heated grains might be expected to be heated to this range of temperatures, but it is problematic that there is no indication of grains at intermediate temperatures (70 K <T < 400 K). This suggests that the absorption efficiencies used here are not a true physical representation of the Ar ii dust. The actual dust must either have a relatively stronger 9 μm peak so that it can produce the observed spectrum from cooler dust, or it must have a somewhat lower absorption efficiency at roughly 10–20 μm so that the presence of grains at intermediate temperatures would be required.

As suggested by the best two-component fits, the best three-component fit combines the Mg_0.7SiO_2.7 with graphite (to weaken the silicate peaks) and adds a nonstoichiometric spinel to provide the 12 μm peak (see Figure 14). However, there is still a tendency in this fit to use distinctly different temperatures and/or compositions to fit each different spectral feature. The spinel material that produces the 12 μm peak is required to be at extremely high temperatures so that it only contributes to this peak. Alternate sources of the 12 μm feature are SiO₂ and SiC. For both of these materials, the spectral features are too sharp and slightly too blue to provide a good match when the mass absorption coefficients, κ(λ), are calculated from Mie theory for spherical grains. However, calculations assuming a continuous distribution of ellipsoids (CDE) for particle shapes (Bohren & Huffman 1983), result in spectral features that are broader and redder. The dust temperatures required to produce the features are also much more reasonable. Figure 14 also shows the fits when CDE calculations are used for a third composition of SiO₂ or α-SiC. SiO₂ provides some contribution to all three of the observed peaks. SiC only provides the 12 μm peak.

The Ar iii dust spectrum is very similar to that of the Ar ii dust. It was derived separately to determine whether there might be an identifiable shift in dust temperature or composition in these closely related regions. Not surprisingly, the combinations that produced good fits to the Ar ii spectrum also produce good fits to the Ar iii spectrum (see Figure 15). The increased strength of the 9 μm peak relative to the 21 μm peak would usually suggest warmer dust temperatures in association with the Ar iii. However, because the dust features arise largely from separate components of the models, the temperature of the components are largely unchanged, but the relative mass in the hotter components is higher for the Ar iii than for the Ar ii spectrum.

For the Ar iii spectrum, we consistently find that the amorphous C (ac) provides a slightly better fit than the graphite that was somewhat preferred for Ar ii spectrum. The Ar iii spectrum is also slightly better fit when hibonite (CaAl₁₂O₁₉) rather than a spinel composition is used as a third component; however, if CDE calculations are applied, SiO₂ and SiC can again provide equally good fits as the third component.

The dust associated with Ne ii exhibits an unusually smooth spectrum. This spectrum excludes significant amounts of warm silicates, but can be fit by compositions with relatively featureless spectra, e.g., graphite and amorphous carbon. The best fits are found by combining featureless dust with Al₂O₃. The latter component has a very broad emission peak between 10 and 20 μm that improves the fit. Figure 16 shows the fit for an amorphous carbon (be) and Al₂O₃ mixture. The fit suggests that some fraction of the Al₂O₃ component is fairly warm (T ≈ 150 K), while the brightest carbon dust has a temperature of ∼75 K. A significant cool (∼40 K) dust component helps to fit the Herschel data at 70–160 μm. The model attributes this to Al₂O₃, but this identification is degenerate because neither of these compositions have any characteristic spectral features at these wavelengths. The composition of very cool components cannot be very conclusively identified because the shape of the spectra are not very affected by composition.

Figure 16 also shows the best-fit model that does not contain Al₂O₃. In this case, a nonstoichiometric spinel provides a relatively small perturbation to an otherwise smooth amorphous C spectrum. Amorphous C picks up the intermediate temperature (∼135 K) components that account for the bulk of the 10–20 μm emission.

Finally, Figure 16 also shows the best three-component model for the Ne ii dust. The addition of TiO₂ nominally improves the fit over the best two-component model, but the changes to the spectrum are too minor to suggest that any third component is warranted.

The spectrum of dust associated with the X-ray Fe emission does exhibit apparent silicate peaks at ∼10 and 20 μm. The 10 μm peak is relatively weak, suggesting a lack of hot silicate grains. As with the Ar ii dust, mixing silicate and more featureless emission (e.g., amorphous C) improves the quality of the fit. The preferred silicates here tend to have higher Mg/Si ratios than those that fit the Ar ii and Ar iii dust. Figure 17 shows the best two-composition fit. The temperatures for both components are warm, T ≈ 100–112 K, with additional hot and cold components to account for the short and long wavelength emission. The figure also shows the best two-component fit that can be obtained without the use of silicate compositions. This marginal fit uses Mg_0.6Fe_0.4O to adjust the shape of the model spectrum near 20 μm, but contains no replacement for a 10 μm silicate feature. The best three-component fit (see Figure 17) merely adds PAH⁺ emission to reproduce a bump at 8 μm and sharpen the spectral feature at ∼10 μm. The overall change in χ² is small.

The South Spot spectrum looks rather different than the X-ray Fe spectrum, yet it tends to be best fit by similar dust compositions. Here the temperatures of the components that produce the <20 μm emission are higher than those for the X-ray Fe dust. Figure 18 shows the best two-component fit that uses similar compositions as the X-ray Fe spectrum (see, e.g., Figure 17). It also shows a marginal fit obtained without the use of silicates, and thus without any component that provides a 10 μm feature in the spectrum. The best three-component fit (see Figure 18) uses nonstoichiometric spinel to make minor adjustments to the shape of a good two-component model.

As for the X-ray Fe and South Spot spectra, the spectrum associated with the radio emission tends to be best fit with a mix of silicate and featureless dust (Figure 19). A marginal two-composition fit, in which Mg_0.1Fe_0.9S serves as the "featureless" component across the 10–20 μm part of the spectrum is also shown in Figure 19. The best three-component fit (see Figure 19) is not significantly different from the best two-component fit, using two featureless components instead of one. The last example in Figure 19 shows the best results when dust compositions are restricted to the astronomical silicate, graphite, PAH, and PAH⁺, which are commonly used to fit general interstellar material (e.g., Draine & Lee 1984; Zubko et al. 2004; Draine & Li 2007). The shape of the astronomical silicate's 10 μm emission peak is not as sharp as the observed spectrum. Cool PAH⁺ emission provides sufficient adjustment to the shape of the silicate spectrum such that the model does not require graphite or neutral PAH components.

The Si ii dust spectrum essentially contains only the Herschel PACS measurements at 70, 100, and 160 μm, with only upper limits on the emission at shorter wavelengths. Because of this lack of detailed spectral information, the spectrum was only fit with single composition dust models. The measured Si ii spectrum apparently has a relatively sharp peak compared to a blackbody spectrum. The best fit is provided by hibonite (CaAl₁₂O₁₉), which has a broad emission feature at ∼80 μm making it an especially good fit to the data. Figure 20 shows the best-fit spectrum (CaAl₁₂O₁₉), and a fit using a more typical Mg silicate (Mg₂SiO₄). Compositions that have a steeper spectral index at long wavelengths provide better fits, but the relatively good fit for TiO₂ (3) (rutile; second lowest χ² in Figure 13) is an artifact of an unphysically steep extrapolation (λ^−3.5) of the measured optical constants which are not published for λ ⩾ 70 μm. For the Si ii spectrum, any models that are within a factor of four of the minimum χ² are deemed acceptable. This includes most dust compositions and only excludes compositions that have strong features near ∼40 μm that would have exceeded the upper limits provided by the Spitzer IRS data.

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The identifications of possible dust compositions in the different environments in Cas A are summarized in Table 4. A single dust composition can never provide a good fit to the observed spectra, except for the Si ii spectrum which has only upper limits at <70 μm. In general, two compositions are sufficient to get acceptable fits to the spectra. The Ar ii and Ar iii spectra are the only ones that show significant (though small) benefit for the addition of a third composition. Among the seven characteristic dust spectra examined, the results can be grouped into three different families of dust.

The first family is found in association with the Ar ii- and Ar iii-emitting ejecta, which are distributed widely across the SNR. This family consists of the Mg silicate with the lowest Mg/Si ratio in combination with one or more other compositions that have featureless spectra. The Mg_0.7SiO_2.7 is a good fit to the 9 and 21 μm peaks in the observed spectrum, but only if a featureless dust composition is also present to reduce the apparent strength of these features. However, the Ar dust spectra also contain a weaker 12 μm feature which is not accounted for by any Mg silicate. Nonstoichiometric spinel with low Mg/Al ratios can provide a feature at approximately the correct wavelength, but only when the dust grains are extremely hot, such that longer wavelength spinel features are relatively faint. A better explanation for the 12 μm feature may be provided by SiO₂. The spectrum of SiO₂ exhibits all three peaks seen in Ar ii and Ar iii spectra, although they are significantly sharper and slightly bluer than the observed ones, and even in combination with other materials the fits are not very good. However, this is when Mie theory is used to calculate the absorption cross sections assuming small spherical grains. Using a CDE approximation instead broadens and shifts the SiO₂ features to be a better match as a third component. Jäger et al. (2003) point out that the 12 μm SiO₂ feature disappears in Mg silicates when Mg/Si >0.5. Therefore, it seems likely that the dust associated with the Ar emission is a mixture of silica and Mg silicate (with Mg/Si ≲ 0.5) in combination with a separate featureless dust component. SiC can also provide the 12 μm feature, but again only if CDE calculations are applied to this component. If SiC is present, this would be the only direct evidence of carbon-bearing dust. Table 5 lists the possible origins for the 12 μm feature of the Ar dust.

The strong 21 μm peak in this family has been the hallmark of Cas A IR spectra since it was first observed using the Kuiper Airborne Observatory and the Infrared Space Observatory (ISO). On the basis of those data, the peak was suggested to arise from Mg protosilicate (Arendt et al. 1999). Subsequent analysis by Douvion et al. (2001) modeled an ISO spectrum as MgSiO₃, SiO₂ and Al₂O₃ with the weak 12 μm feature largely produced by the Al₂O₃ as proposed for the feature in "spectrum 2" of Douvion et al. (1999). Ennis et al. (2006), using Spitzer IRS data, noted the distinction of several different dust spectra in different parts of Cas A and referred to this as the "strong 21 μm" spectrum. Calling it "21 μm peak dust," Rho et al. (2008) modeled it as Mg protosilicate and MgSiO₃ with secondary components of SiO₂, FeO, FeS, Si, and Al₂O₃ and/or Fe. Later work indicated that the 21 μm feature may be fit primarily by SiO₂ grains if CDE calculations rather than spherical grain approximations are used (Rho et al. 2009).

The second dust family is associated with the Ne ii emission, which is especially prominent in two opposing "Ne crescents" (Ennis et al. 2006; Smith et al. 2009) in the north and south parts of the SNR. These morphological features are evident in the derived spatial distribution of the Ne ii dust shown in Figure 4. This dust has a very smooth spectrum that does not suggest any silicate material. The best fits to the spectrum are found with Al₂O₃ in combination with other featureless dust. Featureless dust alone can provide moderately good fits, but a broad asymmetric feature in the 10–20 μm portion of the Al₂O₃ absorption cross section seems to match the observed spectrum especially well. Alternately, nonstoichiometric spinel can provide the needed emission at 10–20 μm, although the spinel absorption efficiency has more detailed substructure that is not evident in the observed spectrum.

This second family corresponds to the "weak 21 μm" components noted by (Ennis et al. 2006) and Rho et al. (2008), which they also associate with relatively strong Ne emission. However, the fact that they see even a weak 21 μm peak in their spectrum suggests that it is a mixture of what we identify as very distinct Ar and Ne dust families. As in our fitting, (Rho et al. 2008) fit this spectrum with hot and cool featureless dust (C glass) and with an intermediate temperature Al₂O₃ components. They included other components to add the weak 21 μm peak that appears in their spectrum. Douvion et al. (1999) had also noted an anti-correlation between the 9 μm silicate emission and Ne ii and Ne iii emission.

The third dust family is associated with the X-ray Fe emission and the South Spot. This family also seems to match the dust associated with the radio emission, which is expected to be dust that has been swept up from the ISM or CSM by the forward shock. The primary component in this family is one of the Mg silicates with high Mg/Si ratios or MgFe silicate: Mg₂SiO₄, Mg_2.4SiO_4.4, MgFeSiO₄. Other Mg silicates with Mg/Si ⩾1 can provide acceptable fits, but the silicates with lower ratios that were needed for the Ar dust are not suitable here because of the changing placement and shape of the 9 and 21 μm features.

This dust family is matched by the "broad" component identified by Ennis et al. (2006) and the "featureless" component modeled by Rho et al. (2008). In both cases, this component is not associated with Ar or Ne emission lines, just as we also find. Rho et al. (2008) modeled this component as MgSiO₃, FeS, and Si combined with Al₂O₃, Mg₂SiO₄ and/or Fe. Using 5–17 μm ISO data, Douvion et al. (1999) extracted a spectrum ("Spectrum 3") from a region that should match our radio spectrum. Despite the limited wavelength coverage, they also found that the spectrum could be fit with astronomical silicate (Draine & Lee 1984) at T ∼ 105 K, as we confirm (in Figure 19).

The Si ii dust has no significant emission across the 5–40 μm wavelength range of the IRS. The three Herschel PACS measurements at 70, 100, and 160 are insufficient to constrain the composition of the associated dust. The Si ii dust may belong to one of the above families or it may be an entirely different composition.

The modeled dust temperatures and compositions allow for the determination of the dust mass in each of the components. The dust mass, M_d, is calculated as

$$\begin{equation} M_d = {D^2 S_\nu (\lambda)\over {\kappa _\nu (\lambda) B_\nu (\lambda,T_d)}}, \end{equation} \tag{ 4 }$$

where D = 3.4 kpc is the distance to Cas A (Reed et al. 1995), S_ν(λ) is the total flux density of the component in question, κ_ν(λ) is the mass absorption coefficient appropriate for the derived composition of the dust, and B_ν(λ, T_d) is the Planck function evaluated at the derived temperature. For each of the models fit to the characteristic spectra, the total mass was calculated by summing Equation (4) over all temperature components of each of the compositions used in the fit. Generally, the total dust mass is dominated by a warm component (60–130 K) that also produces the bulk of the luminosity. However, the X-ray Fe spectrum is an exception where an additional cold component dominates the mass because the Herschel PACS data at 70–160 μm are elevated relative to the shorter wavelength emission. The composition of this cold component is uncertain because absorption efficiencies are smooth and the spectral resolution is poor at the long wavelengths. This situation is worse for the Si ii dust which is only detected at ⩾70 μm. Its temperature is relatively well constrained, but its composition, and therefore its mass, is not. If the dust is composed of Mg silicates, then the total mass of the Si ii dust is ≲ 0.1 M_☉, but this value can be much lower if other compositions are appropriate. Much higher masses are ruled out by the expected nucleosynthetic yields of various elements, and would imply very high condensation efficiencies given that the mass of the unshocked gas is only ∼0.4 M_☉ (DeLaney et al. 2014).

The derived dust masses averaged over all models that fit within a factor of two of the minimum χ² and are dominated by Mg silicates (or Al₂O₃ for the Ne ii spectrum) are listed in Table 4. Figure 21 plots the total dust mass for all two-component models of the Ar ii dust spectrum as a function of χ² with color coding to indicate compositions and temperatures. The "good" models are within a factor of two of the minimum χ² (to the left of the dashed line). The figure shows that although there are correlations between composition and temperatures, the derived mass is more strongly dependent on the composition than the temperature.

The total mass of warm and hot dust for all components that contribute to the <35 μm spectrum is found to be 0.04  ±  0.01 M_☉ (see Table 3). This is consistent with other measurements from IRAS (Braun 1987; Arendt 1989; Saken et al. 1992) and other analysis of the Spitzer IRS data (Rho et al. 2008) because the mid-IR (12–100 μm) flux density S_ν(λ) remains basically the unchanged since the IRAS measurements. This is the primary observable factor in determining the mass. When corrected for the same distance, previously published mass estimates contain modest differences (factors of ∼two) due to different assumptions of the mass absorption coefficients, κ_ν(λ), and dust temperature, T_d. ISO, Akari, BLAST, and Herschel have revealed an additional cool dust component in Cas A which contains ∼0.08 M_☉ of dust (e.g., Tuffs et al. 1999, 2005; Sibthorpe et al. 2010; Barlow et al. 2010). This cool component is what we associated with the Si ii. Our mass estimate of this component is consistent, but is very uncertain due to the unknown composition of the dust, and the difficulty in distinguishing the SNR dust from the heavy confusion of the line of sight ISM at these wavelengths.