PROPERTIES OF NEWLY FORMED DUST BY SN 2006JC BASED ON NEAR- TO MID-INFRARED OBSERVATION WITH AKARI

In order to separate the emission carried by the SN 2006jc from that by the host galaxy, the signal count profiles of the host-galaxy component have to be modeled and reproduced. For this purpose, we first derive the most appropriate point-spread function (PSF) in the image and then assume the galaxy component as a convolution of the source with PSF. These procedures are carried out both in the vertical and horizontal directions independently to check the reliability and consistency of the results.

We define the reference pixel row so that it goes across only the host galaxy UGC4904, and obtain the signal count profile P(X) in units of ADU pixel⁻¹ along the reference pixel row (see Figure 2(b)). The position of the reference pixel row is selected so that P(X) has as sharp a profile as possible, and therefore we use P(X) as the PSF. We obtain the signal count profile P_i(X) (i = 1, 2, ..., n) in units of ADU pixel⁻¹ along the ith pixel row (see Figure 2(c)), where n is defined by the number of the pixel rows that cover the SN 2006jc (see Figure 2(a)). Then we assume the signal count profile of the UGC4904 component, P^UGC4904_i(X), in P_i(X) as a convolution of the PSF written as

$$\begin{eqnarray} &&P_i^{\rm UGC4904}(X)=\sum ^{\infty }_{k=-\infty }\eta _i(k) P(X-k), \end{eqnarray} \tag{ 1 }$$

where the distribution function η_i(k) is assumed to have the Gaussian form given by

$$\begin{eqnarray} &&\eta _i(k)=h_i \exp \left\lbrace -\left(\frac{k-\delta _i}{s_i}\right) \right\rbrace. \end{eqnarray} \tag{ 2 }$$

The best-fit parameters of h_i, δ_i, and s_i (i = 1, 2, ..., n) are obtained, so that the sum of |P_i(X) − P^UGC4904_i(X)|² for 50 ⩽ X ⩽ 69 and 79 ⩽ X ⩽ 90 becomes minimum, where the data of P_i(X) in 70 ⩽ X ⩽ 78 have contribution from the signal of SN 2006jc and have been excluded. The signal count profile of the SN 2006jc component P^SN2006jc_i(X) is then calculated as

$$\begin{eqnarray} &&P^{\rm SN2006jc}_i(X) = P_i(X) - P_i^{\rm UGC4904}(X). \end{eqnarray} \tag{ 3 }$$

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In order to evaluate how well the signal count profile of the UGC4904 component is reproduced by a convolution of the PSF modeled by the signal count profile P(X) obtained along the reference pixel row, we define the test pixel row so that it goes across only the galaxy UGC4904 (see Figure 2(d)), apply the same methods described above to the the signal count profile along the test pixel row P_test(X), and obtain the best-fit signal count profile P^UGC4904_test(X) modeled by Equation (1). The standard deviation of the residual profile, P_test(X) − P^UGC4904_test(X), from the zero value is only 6.8 ADU pixel⁻¹ for NIR/N3 compared to the peak signal of ∼ 150 ADU pixel⁻¹ (Figure 2(d)), which confirms that the signal count profile of the UGC4904 component is well reproduced by our method. The value of 6.8 ADU pixel⁻¹ is used to estimate the uncertainty in the N3 band flux of SN 2006jc due to the subtraction procedure of the UGC4904 component.

Finally, the total N3 band flux estimated from the analysis on the signal count profiles along the X direction, f^X_ν(N3), is derived as

$$\begin{eqnarray} &&f_{\nu }^{X}(N3) = \alpha _{N3} \sum ^{n}_{i=1} \int P^{\rm SN2006jc}_i(X) dX, \end{eqnarray} \tag{ 4 }$$

where α_N3 is the unit conversion factor from ADU to Jansky for N3 band (Tanabé et al. 2008). The uncertainty in the N3 band flux of SN 2006jc is calculated as {(σ^BG_N3)² + (σ^UGC4904_N3)²}^0.5, where σ^BG_N3 is the 1σ noise-equivalent flux for NIR N3 band data, taken with the AOT04 mode in units of mJy calculated from the typical fluctuation of the sky counts, and σ^UGC4904_N3 is the uncertainty which stems from the subtraction procedures of the host-galaxy component given by 6.8 × α_N3π(n/2)². Here n is the number of the pixel rows to cover the whole region of SN 2006jc.

The same decomposition techniques are applied in the vertical direction to derive the total N3 band flux, f^Y_ν(N3), estimated from the analysis on the signal count profiles along the Y direction. The obtained N3 band fluxes, f^X_ν(N3) and f^Y_ν(N3), are listed in Table 1. These two values are in good agreement within uncertainties. We adopted the weighted average of the two values taking account of the error as the final N3 band flux of SN 2006jc.

We obtain the flux densities of SN 2006jc with the MIR-S/S7, S9W, and S11 bands using the same decomposition technique as that adopted for the NIR/N3 band, and the results are summarized in Table 1. The flux densities estimated from the signal count profiles along the X and Y directions are in good agreement within uncertainties for any of the MIR-S/S7, S9W, and S11 bands. Finally, we also tried PSF photometry of SN 2006jc using stars in the field and found that the results are the same within the uncertainty. We note that the uncertainty in the subtraction of the host-galaxy light dominates in the photometry uncertainty for both cases, and that the apertures for the photometry used in our methods are adequately large.

The NIR spectrum of SN 2006jc is obtained by the slitless spectroscopy with NIR/NP, in which the spectrum is dispersed in the X direction, and a spectrum of a certain source is contaminated by the spectra of other sources aligning in the dispersion direction. Therefore, the spectrum of SN 2006jc suffers severe blending with the light from UGC4904. We have developed a spectral decomposition technique for the spectral image of NIR/NP. We use the imaging data taken with NIR/N3 to investigate the structure of UGC4904 and to reproduce the spectral components of UGC4904 in the spectral image of NIR/NP, and obtain a pure spectrum of SN 2006jc.

For the first step, the position in the Y direction of the NIR/N3 data is adjusted to that of the NIR/NP data with an accuracy of one-tenth of the pixel.

We define the reference pixel row in the imaging data taken with NIR/N3 covering from Y = 28 to Y = 29, so that it goes across only UGC4904 and does not include SN 2006jc (see Figure 3(a)). The signal count profile along the reference pixel row, I_Y[28:29](X), is obtained by averaging the data from Y = 28 to Y = 29 (see Figure 3(b)). Then we define the target pixel row covering from Y = 20 to Y = 25, so that it goes across the major part of SN 2006jc (see Figure 3(a)), and the signal count profile along the target pixel row, I_Y[20:25](X), is obtained by averaging the data from Y = 20 to Y = 25 (see Figure 3(c)).

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We model the signal count profile of the UGC4904 component, I^UGC4904_Y[20:25](X), contained in I_Y[20:25](X) with

$$\begin{eqnarray} &&I_{{\rm {Y[20:25]}}}^{\rm UGC4904}(X)=\sum ^{\infty }_{k=-\infty }\eta _{{\rm {Y[20:25]}}}(k) I_{{\rm {Y[28:29]}}}(X-k), \end{eqnarray} \tag{ 5 }$$

where the free distribution function, η_Y[20:25](k), is determined so that the sum of $\vert I_{{\rm {Y[20:25]}}}(X) - I_{{\rm {Y[20:25]}}}^{\rm UGC4904}(X) \vert ^2$ for 50 ⩽ X ⩽ 69 and 79 ⩽ X ⩽ 100 becomes minimum, where the data of P_i(X) in 70 ⩽ X ⩽ 78 have contribution from the signal of SN 2006jc and have been excluded (see Figure 3(c)). The obtained result of η_Y[20:25](k) is shown in Figure 4(a).

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Then we define the reference pixel row and the target pixel row in the spectral image of NIR/NP, so that each has the same Y range as that defined in the image of NIR/N3. The signal count profiles along the reference pixel row, S_Y[28:29](X) (see Figure 3(f)), and along the target pixel row, S_Y[20:25](X) (see Figure 3(g)), in the spectral image of NIR/NP are obtained.

Using the signal count profile along the reference pixel row, S_Y[28:29](X), and the obtained distribution function η_Y[20:25](k), the signal count profile of the UGC4904 component, S^UGC4904_Y[20:25](X), contained in S_Y[20:25](X) can be modeled with

$$\begin{eqnarray} &&S_{{\rm {Y[20:25]}}}^{\rm UGC4904}(X)=\sum ^{\infty }_{k=-\infty }\eta _{{\rm {Y[20:25]}}}(k) S_{{\rm {Y[28:29]}}}(X-k), \end{eqnarray} \tag{ 6 }$$

which is shown with the gray line in Figure 3(g). The signal count profile of SN 2006jc, S^SN2006jc_Y[20:25](X), contained in S_Y[20:25](X) is given by

$$\begin{eqnarray} &&S_{{\rm {Y[20:25]}}}^{\rm SN2006jc}(X)=S_{{\rm {Y[20:25]}}}(X)-S_{{\rm {Y[20:25]}}}^{\rm UGC4904}(X), \end{eqnarray} \tag{ 7 }$$

and is shown with the thin black line in Figure 3(g).

In order to evaluate the accuracy in the estimate of the signal count profile of the UGC4904 component in the spectral image of NIR/NP by this spectral decomposition technique, we define the test pixel row both in the image of NIR/N3 and NP covering from Y = 35 to Y = 40, so that it goes across the host galaxy UGC4904 (see Figures 3(a) and 3(e)) and applied the same technique (see Figures 3(d) and 3(h)).

We model the signal count profile of the UGC4904 component, I^UGC4904_Y[35:40](X), contained in I_Y[35:40](X) with

$$\begin{eqnarray} &&I_{{\rm {Y[35:40]}}}^{\rm UGC4904}(X)=\sum ^{\infty }_{k=-\infty }\eta _{{\rm {Y[35:40]}}}(k) I_{{\rm {Y[28:29]}}}(X-k), \end{eqnarray} \tag{ 8 }$$

where the free distribution function η_Y[35:40](k) is derived in the same way as η_Y[20:25](k) (see Figure 3(d)). The obtained result of η_Y[35:40](k) is shown in Figure 4(b).

The signal count profile of the UGC4904 component, S^UGC4904_Y[35:40](X), is given by

$$\begin{eqnarray} &&S_{{\rm {Y[35:40]}}}^{\rm UGC4904}(X)=\sum ^{\infty }_{k=-\infty }\eta _{{\rm {Y[35:40]}}}(k) S_{{\rm {Y[28:29]}}}(X-k). \end{eqnarray} \tag{ 9 }$$

The obtained results of S^UGC4904_Y[35:40](X) and the residual profile given by S_Y[35:40](X) − S^UGC4904_Y[35:40](X) are shown with the gray line and the thin line in Figure 3(h), respectively. The standard deviation of the residual profile from zero is 8.1 (ADU pixel⁻¹), which confirms that the signal count profile of the UGC4904 component is properly estimated by our spectral decomposition technique. The value of 8.1 (ADU pixel⁻¹) is used to estimate the systematic error in the spectral decomposition procedure.

We have made the wavelength calibration and the division by the system spectral response of NIR/NP, r_NP(λ) in units of ADU mJy⁻¹, for the obtained signal count profile S^SN2006jc_Y[20:25](X) following the procedure in the IRC Spectroscopic toolkit (Ohyama et al. 2007). The absolute flux calibration for the NP spectrum of SN 2006jc has been made by using the ratio of the total flux count of SN 2006jc in I_Y[20:25](X) to that obtained by the photometric decomposition technique in Section 2.1. The 1σ error of the NP spectrum of SN 2006jc is obtained as {σ^UGC4904_NP(λ)² + σ^BG_NP(λ)²}^0.5, where σ^UGC4904_NP(λ) is the uncertainty in the subtraction of the UGC4904 component in units of mJy, which is given by 8.1/r_NP(λ), and σ^BG_NP(λ) is the 1σ noise-equivalent flux for NIR/NP spectrum taken with the AOT04 mode in units of mJy quoted from Ohyama et al. (2007).

The results of the photometry of SN 2006jc with AKARI/IRC N3, S7, S9W, and S11 bands are listed in Table 2. NIR photometry of SN 2006jc with H and K bands was performed simultaneously on and 2007 April 28 and 29 (Minezaki et al. 2007), using the multicolor imaging photometer (MIP) mounted on the MAGNUM 2 m telescope at Haleakala Observatories in Hawaii (Kobayashi et al. 1998a, 1998b), and the results are summarized also in Table 2.

The obtained NIR spectrum of SN 2006jc on day 200, together with the photometric results are plotted in Figure 5. The NIR spectrum of SN 2006jc is characterized by a continuum emission peaking around at ∼ 4 μm, which can be attributed to the thermal emission from dust grains. Possible atomic hydrogen recombination lines of Pf-ζ at 2.87 μm, Pf- at 3.04 μm, Pf-δ at 3.30 μm, Pf-γ at 3.74 μm, Br-α at 4.07 μm, and Br-β at 2.63 μm are recognized, though they are significant only within 2σ–3σ (see Figure 5). We also note a small dent around at 4.6 μm, possibly attributed to the CO absorption band.

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Assuming that spherical dust grains of a certain kind X with a uniform particle radius a_X and a total mass of M_X are located at a distance of R from the observer, and that they emit optically thin thermal radiation of the temperature of T_X(K), the observed flux density profile is given by

$$\begin{equation} f^{X}_{\nu }(\lambda)= M_X \left(\frac{4}{3}\pi \rho _{X}a_{X}^{3}\right)^{-1} \pi B_{\nu }(\lambda,T_{X}) Q^{\rm abs}_{X}(\lambda) \bigg(\frac{a_{X}}{R} \bigg)^{2}, \end{equation} \tag{ 10 }$$

where Q^abs_X(λ) is the absorption efficiency and ρ_X is the density of a dust particle of composition X. The NIR spectral energy distribution (SED) of SN 2006jc on day 200 of H- and K-band photometric data and the 2–5 μm spectroscopic data is fitted with f^X_ν(λ) for each case of the amorphous carbon (X = a.car.), and the astronomical silicate (X = a.sil.) as a composition of dust. We assume the distance of R = 25.8 Mpc (Pastorello et al. 2007) for SN 2006jc.

In the following analysis a_X is set as 0.01 μm, taking account of the fact that the average radius of the newly formed dust in the expanding ejecta is less than 0.01 μm due to the low density and the rapid cooling timescale of the ejecta gas (Nozawa et al. 2008).

As for the amorphous carbon case, the absorption efficiency, Q^abs_a.car.(λ), for a spherical amorphous carbon grain with a radius of a_a.car. = 0.01 μm is calculated from the optical constants of Edo (1983). Assuming ρ_a.car. = 2.26 g cm⁻³, the fit is carried out with the equilibrium temperature T_a.car. and the total mass M_a.car. being free parameters. The result of the fit is shown in Figure 6(a), and the best-fit parameters of T_a.car. = 800 ± 10 K and M_a.car. = 6.9 ± 0.5 × 10⁻⁵ M_☉ are obtained.

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The flux density at each AKARI/IRC imaging band is calculated for the model spectrum taking account of the color correction, which is given by

$$\begin{eqnarray} &&f^{\rm a.car.}_{\nu }({\rm band})=\frac{\int ^{\infty }_{0} R_{\rm band}(\nu) f^{\rm a.car.}_{\nu }(\nu) d\nu }{\int ^{\infty }_{0} \big(\frac{\nu _{\rm band}}{\nu } \big) R_{\rm band}(\nu)d\nu }, \end{eqnarray} \tag{ 11 }$$

where R_band(ν) is the relative system spectral response of each AKARI/IRC band, and ν_band = c/λ_band corresponds to the reference frequency of each AKARI/IRC band defined with λ_N3 = 3.2 μm, λ_S7 = 7.0 μm, λ_S9W = 9.0 μm, and λ_S11 = 11.0 μm (Onaka et al. 2007). The model values that were converted into the AKARI/IRC calibration system of f^a.car._ν(N3), f^a.car._ν(S7), f^a.car._ν(S9W), and f^a.car._ν(S11) are plotted by crosses in Figure 6(a). The observed data at S7, S9W, and S11 bands have excess emission over f^a.car._ν(S7), f^a.car._ν(S9W), and f^a.car._ν(S11), respectively. The interpretation for the excess component is discussed in Section 4.

As for the silicate case, the absorption efficiency, Q^abs_a.sil.(λ), for a spherical astronomical silicate grain with a radius of a_a.car. = 0.01 μm is taken from the values in Draine (1985), and ρ_a.sil. = 3.3 g cm⁻³ is assumed. The fit was carried out in the same way as for the amorphous carbon grains. The result of the fit is shown in Figure 6(b), and the best-fit parameters of T_a.sil. = 920 ± 10 K and M_a.sil. = 4.2 ± 0.3 × 10⁻⁴ M_☉ are obtained. The flux density at N3, S7, S9W, and S11 bands is calculated for the best-fit model spectrum, taking account of the color correction and is shown in Figure 6(b). The model values of f^a.sil._ν(S7), f^a.sil._ν(S9W), and f^a.sil._ν(S11) largely exceed the observed flux density at S7, S9W, and S11 bands. The disagreement in the MIR flux shows that astronomical silicate is not a likely carrier of the continuum in the 2–5 μm region on day 200.

We conclude that amorphous carbon is a likely carrier of the NIR continuum on day 200. The spectrum is well accounted for by the amorphous carbon dust with the temperature of 800 ±  10 K and with the total mass of M_a.car. = 6.9 ± 0.5 × 10⁻⁵ M_☉. This result is consistent with the suggestion made by Smith et al. (2008) that the rebrightened NIR emission on 79 days is likely to be carried by carbonaceous dust with an equilibrium temperature of 1600 K, but not by silicate dust. The equilibrium temperature of 800 K on day 200 derived in our analysis is consistent with the scenario that this component is newly formed dust in the free-expanding ejecta of the SN (Nozawa et al. 2008), in which the illuminating radiation is assumed to be the thermal emission from the gas ejecta heated by γ-rays and positrons produced via the decay of radioactive elements such as ⁵⁶Ni and ⁵⁶Co (Tominaga et al. 2008).

One possible candidate for the excess emission in S7, S9W, and S11 bands is the dust band emission of the silicate and/or amorphous silica dust. In Figure 7, the absorption-efficiency profiles Q^abs_X(λ) of amorphous carbon (X = a.car.) from Edo (1983), astronomical silicate (X = a.sil.) from Draine (1985), and amorphous SiO₂ (X = silica) from Philipp (1985) are shown together with the system spectral response curve of the AKARI/IRC NIR/N3, MIR-S/S7, S9W, and S11 bands. While Q^abs_a.car.(λ) shows a smooth featureless profile without any band structures, Q^abs_a.sil.(λ) and Q^abs_silica(λ) show the band structure peaking at ∼ 9.5–10.0 μm and ∼ 8.5–9.0 μm, respectively. Therefore, these band structures intrinsic to the silicate-related dust could contribute to the excess emission in S7, S9W, and S11 bands.

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Firstly, a two-component (N = 2) model of the amorphous carbon (X₁ = a.car.) and the astronomical silicate (X₂ = a.sil.) is employed. The near- to mid-infrared data of SN 2006jc on day 200 are fitted with Equation (12), where T_a.car. = 800 K and M_a.car. = 6.9 × 10⁻⁵ M_☉ are fixed, and T_a.sil. and M_a.sil. are taken as the free parameters. The grain radii of both components are set as 0.01 μm. The best-fit model spectrum is shown in Figure 8(a), and we obtain T_a.sil. = 710 ± 10 K and M_a.sil. = 1.12 ± 0.02 × 10⁻⁴ M_☉.

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However, the flux densities in S7, S9W, and S11 bands predicted for this two-component (amorphous carbon + astronomical silicate) model taking account of the color correction cannot well reproduce the observed MIR SED characterized by the enhanced S9W flux density (see Figure 8(a)). For one thing, the band structure of astronomical silicate peaking at ∼ 9.5–10.0 μm is almost fully included not only in S9W, but also sometimes more efficiently depending on the dust temperature in S11. For the other, the predicted model spectrum is too low in 6 < λ < 8.5 μm, where the S11 band does not have its sensitivity, but the S9W band does. Therefore, we need to have another dust component that has a band structure in λ < 8.5 μm in its absorption-efficiency profile. Amorphous SiO₂ (silica) is one of the candidates for such component (see Figure 7(c)). Moreover, silica should be able to be produced in SN ejecta (Nozawa et al. 2003, 2007). Its presence in the Cas An SN remnant has been reported by a MIR spectroscopic observation with the Short Wavelength Spectrometer (SWS) on board the Infrared Space Observatory (ISO; Douvion et al. (2001) and also by a recent Spitzer observation (Rho et al. 2008).

We assume a two-component (N = 2) model consisting of hot amorphous carbon (X₁ = a.car.) and amorphous silica (X₂ = silica), where T_a.car. = 800 K and M_a.car. = 6.9 × 10⁻⁵ M_☉ are fixed, and T_silica and M_silica are taken as the free parameters. The grain radii of both components are set to be 0.01 μm, and we assume the density of amorphous SiO₂ ρ_silica = 2.62 g cm⁻³. The best-fit model spectrum is shown in Figure 8(b), and we obtain T_silica = 790 ± 10 K and M_silica = 6.5 ± 0.1 × 10⁻⁵ M_☉. This time, the predicted flux densities are in good agreement with the MIR SED characterized by the enhanced S9W flux density.

Another possible candidate for the excess component is the thermal emission from the featureless dust with temperature lower than 800 K. Our NIR to MIR data of SN 2006jc on day 200 are fitted with Equation (12), assuming a two-component (N = 2) model of hot amorphous carbon (X₁ = h.a.car.) and warm amorphous carbon (X₂ = w.a.car.). The temperature and the integrated mass of the former component are fixed to the values obtained in Section 3.2 and those of the latter component, T_w.a.car. and M_w.a.car., are taken as the free parameters. The same properties of the absorption-efficiency profile, the grain radius and the density are assumed both for the warm and hot components. The fitting is made, so that the flux densities of the model spectrum at S7, S9W, and S11 bands that were converted into the AKARI/IRC calibration system should best reproduce the observed flux density at S7, S9W, and S11 bands. The best-fit model spectrum is shown in Figure 9, and we obtain T_w.a.car. = 320 ± 10 K and M_w.a.car. = 2.7^+0.7_−0.5 × 10⁻³ M_☉ 10⁻³ M_☉.

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We note that the observed NIR to MIR SED has double-peaked characteristics, with one peak being located in the NIR and the other peak in the MIR, and that the model fit with two-temperature amorphous carbon dust results in a considerable temperature gap between the two. This temperature gap can be explained if we assume the situation such that only the hot component with the temperature of 800 K is the newly formed dust in the ejecta of SN 2006jc, and that the 320 K warm component corresponds to thermal emission from the preexisting circumstellar dust farther away from the newly formed dust with a dust-depleted region in between. The dust-depleted region may have been created by the dust evaporation due to the shock breakout in the initial phase of the SN explosion.

Observational evidence for the presence of silicate and/or silica grains formed in SN ejecta has been reported for the Cas A SN remnant (Douvion et al. 2001; Rho et al. 2008, and references therein) and SN 2003gd (Sugerman et al. (2006), and the presence of silicate dust in the CSM is confirmed for SN 1987A (Bouchet et al. 2006). Ercolano et al. (2007) have shown that no more than 15% by mass of dust in the SN 1987A has been in the form of silicates, whilst Sugerman et al. (2006) have reported that the dust that condensed around SN 2003gd has been predominantly silicate.

The progenitor of Type Ib SN 2006jc is considered to be a Wolf–Rayet star, suffering the mass loss during its late evolution and forming a dense He-rich CSM (Foley et al. 2007). The He layer of core-collapse SNe is suggested to contain more carbon than oxygen (Nomoto & Hashimoto 1988) and, especially, the Wolf–Rayet star with strong mass loss leads to thick C-rich CSM and envelope (Limongi & Chieffi 2006; Tominaga et al. 2008). Therefore, the formation of silicate and/or silica grains in the C-rich CSM of SN 2006jc is less likely (e.g., Nozawa et al. 2003).

Even if the silicate and/or silica dust is newly formed in the ejecta of SN 2006jc, their temperature reaches only up to 100 K taking account of the optical absorption and the collision with ejecta gas with 1000 K on day ∼ 200 after the discovery (Nozawa et al. 2008). AKARI/IRC S7/S11 band colors calculated for astronomical silicate and silica with 100 K are f^a.sil_ν(S7)/f^a.sil._ν(S11) = 5.2 × 10⁻³ and f^silica_ν(S7)/f^silica_ν(S11) = 4.1 × 10⁻², respectively, which are by far smaller than the S7/S11 band color of ∼0.5 ± 0.2 obtained for the observed MIR excess component. Therefore, both the astronomical silicate and amorphous silica with 100 K cannot reproduce the flux density at S7, S9W, and S11 bands of the excess component and should not be the major carriers of the excess. Consequently, the MIR excess component over the model spectrum of the amorphous carbon of 800 K is likely to be IR light echo by amorphous carbon with 320 ± 10 K in the CSM discussed in Section 4.2, and we conclude that amorphous carbon of 800 ± 10 K of 6.9 ± 0.4 × 10⁻⁵ M_☉ is newly formed in the ejecta of SN 2006jc on day 200.

The present analysis assumes a single grain size of 0.01 μm. As far as the size is small compared to the wavelength in question, the derived dust mass does not depend on the grain size. The grain temperature is a slow function of the grain size, and thus the introduction of the size distribution will not affect the mass estimate. In particular, the nucleation model suggests the formation of very small grains in the very rapid cooling gas of SN 2006jc (Nozawa et al. 2008). In the present analysis, we did not apply a thorough radiative transfer and employed a single-temperature approximation because the uncertainties in the observational results are too large to warrant detailed modeling. As far as the dust-forming layer is thin and does not have a significant temperature gradient, a single temperature provides a reasonable approximation for the emission from the shell. The major aim of the present analysis is to discuss the nature and origin of the infrared emission detected by the present observations, and is not intended to derive an accurate estimate of the dust mass.

On the other hand, Mattila et al. (2008) have also presented the Spitzer IRAC photometric data obtained at the similar epoch to ours and explained their data in terms of the dust formation in the cool dense shell (CDS) produced by the interaction of the ejecta onward shock with a dense shell of the circumstellar material ejected by the progenitor. They obtained 3 × 10⁻⁴ M_☉ of amorphous carbon as the mass of newly formed dust.

In any cases, the newly formed dust mass around the SN 2006jc is more than 3 orders of magnitude smaller than the amount needed for core-collapse SNe to contribute efficiently to the early-universe dust budget (Morgan & Edmunds 2003). Recent observational studies report the evidence of dust formation in the ejecta of several core-collapse SNe, but the produced dust mass in the SN ejecta is generally found to be much smaller than theoretically predicted values of 0.1–1 M_☉ (Nozawa et al. 2003), i.e., no more than 7.5 × 10⁻⁴ M_☉ for SN 1987A (Ercolano et al. 2007), ∼10⁻⁴ M_☉ for SN 1999em (Elmhamdi et al. 2003), and 4 × 10⁻⁵ M_☉ for SN 2003gd (Meikle et al. 2007). The obtained amorphous carbon dust mass for SN 2006jc on day 200 in our study is consistent with those relatively small values obtained for other several dust-forming core-collapse SNe, although our data is almost insensitive to the newly formed silicate of ∼ 100 K.

In addition to the dust formed in the ejecta, on the other hand, our MIR photometric data suggest the presence of another amorphous carbon dust of 320 ± 10 K of 2.7^+0.7_−0.5 × 10⁻³ M_☉ as the circumstellar component. This component is expected to be formed in the mass-loss wind associated with the Wolf–Rayet stellar activity (e.g., Williams et al. 1992; Waters et al. 1997; Molster et al. 1999; Voors et al. 2000). It follows that the dust condensation not only in the SN ejecta itself, but also in the mass-loss wind associated with the prior events to the SN explosion could make a significant contribution to the dust formation by a massive star in its whole evolutional history.