CONCURRENT FORMATION OF CARBON AND SILICATE DUST IN NOVA V1280 SCO

Figure 6 shows the near- to mid-infrared spectral energy distribution (SED) of V1280 Sco on Day 150. It is dominated by the thermal dust emission with a small absorption structure at around 9.7 μm due to silicate dust. Although the origin of the silicate dust is not clear, it is likely to be predominantly associated with interstellar silicate dust located along the line of sight toward V1280 Sco since neither apparent emission features from newly formed silicate nor infrared light echoes from the circumstellar silicate have been observed between Days 23 and 145 (Chesneau et al. 2008). To our knowledge, the dust components that have ever been identified in CO novae are amorphous carbon, hydrogenated amorphous carbon (HAC), SiC, and silicates (Evans & Gehrz 2012). Taking into account the relatively smooth spectral shape except for a small absorption structure due to interstellar silicate, we expect that amorphous carbon is responsible for the infrared continuum emission observed in V1280 Sco on Day 150.

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Assuming that spherical amorphous carbon dust grains with a uniform radius a and a total mass M_i are located at a distance R from the observer, and that they give off optically thin thermal emission with an equilibrium temperature T_i, the observed flux density is

$$\begin{eqnarray}{f}_{\nu }^{i}(\lambda ) & = & {M}_{i}{\left(\displaystyle \frac{4}{3}\pi {\rho }_{{\rm{a}}.\mathrm{car}.}{a}^{3}\right)}^{-1}\pi {B}_{\nu }(\lambda ,{T}_{i}){Q}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{abs}}(\lambda ){\left(\displaystyle \frac{a}{D}\right)}^{2},\end{eqnarray} \tag{ 2 }$$

where ρ_a.car. is the density of an amorphous carbon dust particle (we use ρ_a.car. = 1.87 g cm⁻³) and ${Q}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{abs}}(\lambda )$ is the absorption efficiency of amorphous carbon of radius a (ACAR sample; Zubko 1996). The optically thin emission from multi-temperature amorphous carbon components with foreground silicate extinction is given by

$$\begin{eqnarray}&&{f}_{\nu }^{\mathrm{model}}(\lambda )=\displaystyle \sum _{i=1}^{N}\;{f}_{\nu }^{i}(\lambda )\mathrm{exp}\left\{-{\tau }_{9.7}\left(\displaystyle \frac{{Q}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{abs}}(\lambda )}{{Q}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{abs}}(9.7\;\mu {\rm{m}})}\right)\right\},\end{eqnarray} \tag{ 3 }$$

where N is the number of amorphous carbon components with different representative temperatures, ${Q}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{abs}}(\lambda )$ is the absorption efficiency of astronomical silicate of radius a (Draine 1985), and τ_9.7 is the optical depth of foreground silicate dust at 9.7 μm. The observed near- to mid-infrared SED on Day 150 is reproduced well by the optically thin emission from amorphous carbon components at two different temperatures (i.e., N = 2), 350 and 900 K, with a foreground silicate extinction with τ_9.7 = 0.24 ± 0.01 (see Figure 6). The best-fit parameters are summarized in Table 5.

A_V = 1.2 mag is inferred from Marshall et al. (2006) toward the direction of V1280 Sco. Assuming the ratio of ${A}_{V}/{\tau }_{9.7}=18.5\pm 1.5$ (Roche & Aitken 1984), the interstellar extinction expected at 9.7 μm toward the direction of V1280 Sco is τ_9.7 = 0.065, which is smaller than the value τ_9.7 = 0.24 obtained from our SED analysis. This discrepancy may be attributed to the uncommon composition of dust grains intervening between V1280 Sco and us, given that the value of A_V/τ_9.7 is sensitive to the abundance ratio of silicate dust to carbon dust. Because no apparent light echoes containing silicate emission have been reported between Days 23 and 145 by Chesneau et al. (2008), it is less likely that the silicate that contributes in producing an absorption structure at 9.7 μm on Day 150 is associated with V1280 Sco. In our SED analysis on Days 1272, 1616, and 1947 in Section 5.3.2, therefore, we assume that the extinction of τ_9.7 = 0.24 is fully associated with interstellar silicate dust located in the line of sight toward V1280 Sco. We note that the results of the SED analysis in Section 5.3.2 are not significantly altered whatever value between τ_9.7 = 0.24 and τ_9.7 = 0.065 we adopt as the foreground silicate extinction in the direction toward V1280 Sco.

The blackbody angular radius θ_bb in arcsecond for the T_i=2 = 350 K component is given by

$$\begin{eqnarray}&&{\theta }_{\mathrm{bb}}=2.06\times {10}^{5}{\left({\displaystyle \int }_{0}^{\infty }{f}_{\nu }^{i=2}(\lambda )d\nu \right)}^{1/2}{(\sigma {T}_{i=2}^{4})}^{-1/2}\end{eqnarray} \tag{ 4 }$$

where ${f}_{\nu }^{i=2}(\lambda )$ is the observed flux density carried by the 350 K component and σ is the Stefan–Boltzmann constant. We get θ_bb = 0054, which is just slightly below the radius of the emitting region of the 350 K component (i.e., 0065) obtained from the deconvolved 24.5 μm image on Day 150. Therefore, the 350 K dust shell must be both optically thick and spatially unresolved. In this case, the dust mass of amorphous carbon becomes 2.7 × 10⁻⁶ M_⊙ by assuming that the Planck mean-emission cross section for a carbon grain of radius a is proportional to ${{aT}}_{i=2}^{2}$ (Gilman 1974; Gehrz et al. 1980) and that the density of amorphous carbon is ρ_a.car. = 1.87 g cm⁻³.

A notable point in the near- to mid-infrared SEDs of V1280 Sco on Days 1272, 1616, and 1947 (see Fig 7) is a conspicuous appearance of the 9.7 and 18 μm amorphous silicate features in emission, which were not present in the SED obtained on Day 150 (see Figure 6).

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To investigate the temporal evolution of properties of constituent dust, a simple SED fitting was carried out at each epoch based on a two-component (astronomical silicate and amorphous carbon) model; a single equilibrium temperature is assumed for each dust component. Assuming optically thin geometry in the infrared, the observed flux density is given by

$$\begin{eqnarray}{f}_{\nu }^{\mathrm{model}}(\lambda ) & = & {M}_{{\rm{a}}.\mathrm{car}.}{\left(\displaystyle \frac{4}{3}\pi {\rho }_{{\rm{a}}.\mathrm{car}.}{a}^{3}\right)}^{-1}\\ & & \times \pi {B}_{\nu }(\lambda ,{T}_{{\rm{a}}.\mathrm{car}.}){Q}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{abs}}(\lambda ){\left(\displaystyle \frac{a}{D}\right)}^{2}\\ & & +{M}_{{\rm{a}}.\mathrm{sil}.}{\left(\displaystyle \frac{4}{3}\pi {\rho }_{{\rm{a}}.\mathrm{sil}.}{a}^{3}\right)}^{-1}\\ & & \times \pi {B}_{\nu }(\lambda ,{T}_{{\rm{a}}.\mathrm{sil}.}){Q}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{abs}}(\lambda ){\left(\displaystyle \frac{a}{D}\right)}^{2},\end{eqnarray} \tag{ 5 }$$

where T_a.car. and T_a.sil. are the equilibrium temperatures, M_a.car. and M_a.sil. are the dust masses, ρ_a.car. (1.87 g cm⁻³), and ρ_a.sil. (3.3 g cm⁻³) are the densities of an amorphous carbon (a.car.) and astronomical silicate (a.sil.) dust particle, respectively. We note that our SED analysis requires the optical depth of ISM silicates at 9.7 μm to be τ_9.7 = 0.24 ± 0.01 to account for the small absorption structure in the spectrum of V1280 Sco on Day 150. Assuming that this extinction is fully of interstellar origin, the best-fit parameters obtained for Days 1272, 1616, and 1947 based on the two-component model are summarized in Table 6. Here we assume that the dust size is smaller than 1 μm and thus ${Q}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{abs}}(\lambda )$ and ${Q}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{abs}}(\lambda )$ are approximately proportional to a in the mid-infrared wavelength range. The obtained dust masses M_a.car. and M_a.sil. are, therefore, almost independent of a.

Table 6.  The Dust Properties in V1280 Sco on Days 1272, 1616, and 1947

Amorphous Carbon Astronomical Silicate

Epoch (days)	1272	1616	1947		1272	1616	1947
Temperature (K)	540 ± 10	500 ± 10	440 ± 10		220 ± 10	230 ± 10	210 ± 10
Mass (10−7 M⊙)	${0.79}_{-0.05}^{+0.05}$	${0.79}_{-0.04}^{+0.05}$	${0.89}_{-0.10}^{+0.12}$		${8.4}_{-1.0}^{+2.8}$	${7.1}_{-1.2}^{+3.2}$	${7.5}_{-2.0}^{+3.8}$

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The temporal evolution of amorphous carbon properties is characterized by a decrement in the temperature without significant mass evolution at those three epochs. This suggests the kinematic behavior of the amorphous carbon dust, which travels farther from the white dwarf without being destroyed. The projected distance corresponding to the semimajor axis of the deconvolved emitting region modeled with an elliptic Gaussian in the Si-1 band, which is supposed to trace the amorphous carbon component in our photometric dataset (Figure 7), is 027 ± 002 on Day 1272, 032 ± 002 on Day 1616, and 040 ± 004 on Day 1947. If the spread of dust is in the shape of a bipolar nebulae and is viewed edge-on (e.g., Chesneau et al. 2012), the size of the emitting region corresponds to the average distance to which the dust has traveled from the white dwarf. Figure 8 shows temperatures of amorphous carbon grains of different radii a = 0.01 μm, 0.1 μm, and 1.0 μm as a function of distance from the white dwarf. We base our calculations on the same WD properties as before, i.e., M_WD = 0.6 M_⊙, T_WD = 1.0 × 10⁵ K, and L_WD = 1.8 × 10⁴L_⊙, and further assume that these values all remain constant on Days 1272, 1616, and 1947. Three data points obtained by fitting the SED are located between the model curves for a = 0.01 and 0.1 μm. Therefore, with our two-component model that assumes a single equilibrium temperature for each, the grain size of amorphous carbon dust formed in the nova ejecta is estimated to be in the range from a = 0.01 to 0.1 μm. We note, however, that a temperature distribution in each dust component is expected but not taken into consideration in this simple model. A more accurate estimate of the grain size of amorphous carbon assuming an appropriate dust geometry is discussed in Section 5.3.2.

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The Qa and Qb images taken on Day 1947 (see Figure 4) are dominated by the astronomical silicate emission, as we have shown above (see Figure 7), and they exhibit an elongated shape along PA ∼ 20°. The similarity between the image shapes taken in Qa and Qb bands and those in Si-1, Si-3, and Si-5 bands may indicate that both the carbon and silicate dust components reside predominantly in a dusty bipolar nebula (Chesneau et al. 2012). The projected distance corresponding to the semimajor axis of the deconvolved emitting region modeled with an elliptic Gaussian is 040 ± 003 in the Qa band and 045 ± 004 in the Qb band on Day 1947.

Figure 9 shows equilibrium temperatures of optically thin astronomical silicate as a function of distance from the white dwarf calculated for different radii a = 0.01, 0.1, and 1.0 μm. Astronomical silicate dust achieves an equilibrium dust temperature of 210 K at a distance of 11 from the white dwarf for a = 0.1 μm and 034 for a = 1.0 μm. Comparing these values with the semimajor axes of the mid-infrared emitting region in the Qa and Qb bands derived above, we conclude that the typical grain size of astronomical silicate around V1280 Sco must be in the range from 0.1 to 1.0 μm. In the next section, the results of the SED analyses taking account of the dust geometry are discussed to examine more detailed physical properties of circumstellar dust around V1280 Sco. Then, the origin of each dust species is discussed by investigating the temporal evolution of the resultant geometric and physical parameters of circumstellar dust around V1280 Sco between the three epochs in Section 5.4.

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The elongated shape of V1280 Sco along PA ∼ 20° seen in both the N- and Q-band images on Day 1947 suggests that the mid-infrared emission is dominated by carbon and silicate dust grains in a bipolar nebula. This leads us to assume a simple geometry, in which both the amorphous carbon and astronomical silicate components are distributed in bipolar cones with a common opening angle ϕ (see Figure 10) and are viewed edge-on.

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This geometry is consistent with the description of the structure of the ejected shells given by Naito et al. (2013). We assume the density distributions of amorphous carbon $[{n}_{{\rm{a}}.\mathrm{car}.}(r)]$ and astronomical silicate [n_a.sil.(r)] to be

$$\begin{eqnarray}{n}_{{\rm{a}}.\mathrm{car}.}(r)=\left\{\begin{array}{ll}0 & (r\lt {r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{in}})\\ {n}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{ini}}\times {\left(\displaystyle \frac{r}{{r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{in}}}\right)}^{2} & ({r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{in}}\lt r\lt {r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{out}})\\ 0 & ({r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{out}}\lt r)\end{array}\right.\end{eqnarray} \tag{ 6 }$$

and

$$\begin{eqnarray}{n}_{{\rm{a}}.\mathrm{sil}.}(r)=\left\{\begin{array}{ll}0 & (r\lt {r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{in}})\\ {n}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{ini}}\times {\left(\displaystyle \frac{r}{{r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{in}}}\right)}^{2} & ({r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{in}}\lt r\lt {r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{out}}),\\ 0 & ({r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{out}}\lt r)\end{array}\right.\end{eqnarray} \tag{ 7 }$$

respectively, as a function of distance r from the white dwarf, where ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{in}}$ and ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{in}}$ are the inner wall radii, ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{out}}$ and ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{out}}$ are the outer wall radii, and ${n}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{ini}}$ and ${n}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{ini}}$ are the initial number densities at the position of the inner wall for amorphous carbon and astronomical silicate, respectively. Analyses are made independently for two different spherical grain radii ${a}_{{\rm{a}}.\mathrm{car}.}={a}_{{\rm{a}}.\mathrm{sil}.}=0.1\;\mu {\rm{m}}$ and ${a}_{{\rm{a}}.\mathrm{car}.}={a}_{{\rm{a}}.\mathrm{sil}.}=0.01\;\mu {\rm{m}}$.

For such a geometric configuration and density distributions, the flux density from the white dwarf, ${f}_{\nu }^{{\rm{WD}}}(\lambda ,\zeta )$, at $r=\zeta$ is given by

$$\begin{eqnarray}{f}_{\nu }^{{\rm{WD}}}(\lambda ,\zeta ) & \simeq & \left(\displaystyle \frac{{L}_{{\rm{WD}}}}{\sigma {T}_{{\rm{WD}}}^{4}}\right)\pi {B}_{\nu }({T}_{{\rm{WD}}})\displaystyle \frac{1}{4\pi {\zeta }^{2}}\\ & & \times \mathrm{exp}\left\{-\pi {a}_{{\rm{a}}.\mathrm{car}.}^{2}{Q}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{abs}}(\lambda ){\displaystyle \int }_{0}^{\zeta }{n}_{{\rm{a}}.\mathrm{car}.}(r){dr}\right\}\\ & & \times \mathrm{exp}\left\{-\pi {a}_{{\rm{a}}.\mathrm{sil}.}^{2}{Q}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{abs}}(\lambda ){\displaystyle \int }_{0}^{\zeta }{n}_{{\rm{a}}.\mathrm{sil}.}(r){dr}\right\}.\end{eqnarray} \tag{ 8 }$$

We do not take into account backward scattering for simplification and assume the same stellar parameters as before for the white dwarf on Days 1272, 1616, and 1947 (i.e., ${T}_{{\rm{WD}}}=1.0\times {10}^{5}$ K and ${L}_{{\rm{WD}}}=1.8\times {10}^{4}{L}_{\odot }$). The temperature of a dust grain, T_χ(ζ), where χ = a.car. or a.sil. in our case, in local radiative equilibrium at r = ζ satisfies

$$\begin{eqnarray}&&{\displaystyle \int }_{0}^{\infty }4\pi {a}_{\chi }^{2}{Q}_{\chi }^{\mathrm{abs}}(\lambda )\pi {B}_{\nu }({T}_{\chi }(\zeta ))d\nu \\ &&\quad ={\displaystyle \int }_{0}^{\infty }\pi {a}_{\chi }^{2}{Q}_{\chi }^{\mathrm{abs}}(\lambda ){f}_{\nu }^{{\rm{WD}}}(\lambda ,\zeta )d\nu .\end{eqnarray} \tag{ 9 }$$

The absorption coefficients of astronomical silicate of radius a at shorter wavelengths (λ < 0.1 μm) are calculated from Dwek & Smith (1996) and those at longer wavelengths (λ > 0.1 μm) are quoted from Draine (1985). The heating due to the energy absorption of thermal infrared emission from other dust particles is not taken into account.

Assuming that V1280 Sco is viewed edge-on, an infrared spectrum produced by amorphous carbon and astronomical silicate in bipolar lobes of V1280 Sco is calculated for a geometric configuration characterized by seven free parameters: ${n}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{ini}}$, ${n}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{ini}}$, ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{in}}$, ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{in}}$, ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{out}}$, ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{out}}$, and ϕ. The optical depth at 9.7 μm, ${\tau }_{9.7}=0.24\pm 0.01$, due to interstellar silicate toward V1280 Sco is fixed. Least-squares fitting is carried out to obtain a set of seven best-fit parameters on Days 1272, 1616, and 1947. Data points used for the model fitting were selected to exclude any possible dust emission features and emission lines, in the N-band low-resolution spectra in addition to the N- and Q-band photometric data.

The best-fit parameters obtained on Days 1272, 1616, and 1947 calculated for the two cases ${a}_{{\rm{a}}.\mathrm{car}.}={a}_{{\rm{a}}.\mathrm{sil}.}=0.01\;\mu {\rm{m}}$ and ${a}_{{\rm{a}}.\mathrm{car}.}={a}_{{\rm{a}}.\mathrm{sil}.}=0.1\;\mu {\rm{m}}$ are summarized in Table 7 and Table 8, respectively. The model spectra calculated with those best-fit parameters are shown in the left panels of Figures 11 and 12. Temperatures of amorphous carbon and astronomical silicate are shown as a function of distance from the white dwarf in the right panels of Figures 11 and 12. In both cases, the temporal evolution of the infrared SED of V1280 Sco at these three epochs can be explained by a simple scenario in which amorphous carbon and astronomical silicate dust grains are moving away from the white dwarf.

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Table 7.  The Best-fit Parameters Obtained for ${a}_{{\rm{a}}.\mathrm{car}.}={a}_{{\rm{a}}.\mathrm{sil}.}=0.01\;\mu {\rm{m}}$

Epoch (days) 1272 1616 1947

Opening angle; ϕ (deg)	24.0 ± 0.5	18.0 ± 0.5	15.0 ± 0.5
Amor. carbon initial number density; ${n}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{ini}}$ (cm−3)	${2.5}_{-0.3}^{+0.3}$ × 10−3	${1.3}_{-0.2}^{+0.2}$ × 10−3	${1.0}_{-0.1}^{+0.2}$ × 10−3
Amor. carbon inner radius; ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{in}}$ (AU)	${1.3}_{-0.1}^{+0.1}$ × 102	${1.5}_{-0.1}^{+0.1}$ × 102	${1.7}_{-0.2}^{+0.1}$ × 102
Amor. carbon outer radius; ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{out}}$ (AU)	${2.4}_{-0.2}^{+0.3}$ × 102	${4.6}_{-0.6}^{+0.8}$ × 102	${6.4}_{-0.9}^{+2.2}$ × 102
Astro. silicate initial number density; ${n}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{ini}}$ (cm−3)	${3.2}_{-0.3}^{+0.4}$ × 10−4	${6.0}_{-0.6}^{+0.7}$ × 10−4	${6.3}_{-0.6}^{+0.8}$ × 10−4
Astro. silicate inner radius; ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{in}}$ (AU)	${3.6}_{-0.3}^{+0.4}$ × 102	${3.5}_{-0.2}^{+0.4}$ × 102	${5.5}_{-0.7}^{+0.6}$ × 102
Astro. silicate outer radius; ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{out}}$ (AU)	${7.0}_{-0.5}^{+0.6}$ × 102	${11.1}_{-2.0}^{+6.5}$ × 102	${8.3}_{-0.8}^{+1.6}$ × 102

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Table 8.  The Best-fit Parameters Obtained for ${a}_{{\rm{a}}.\mathrm{car}.}={a}_{{\rm{a}}.\mathrm{sil}.}=0.1\;\mu {\rm{m}}$

Epoch (days)	1272	1616	1947
Opening angle; ϕ (deg)	26.0 ± 0.5	19.5 ± 0.5	15.0 ± 0.5
Amor. carbon initial number density; ${n}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{ini}}$ (cm−3)	${2.5}_{-0.3}^{+0.3}$ × 10−5	${0.9}_{-0.1}^{+0.1}$ × 10−5	${0.8}_{-0.1}^{+0.1}$ × 10−5
Amor. carbon inner radius; ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{in}}$ (AU)	${5.1}_{-0.6}^{+0.2}$ × 101	${5.4}_{-0.4}^{+0.2}$ × 101	${6.1}_{-0.2}^{+0.6}$ × 101
Amor. carbon outer radius; ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{out}}$ (AU)	${0.9}_{-0.1}^{+0.1}$ × 102	${1.8}_{-0.2}^{+0.4}$ × 102	${3.9}_{-0.8}^{+1.2}$ × 102
Astro. silicate initial number density; ${n}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{ini}}$ (cm−3)	${1.3}_{-0.2}^{+0.2}$ × 10−6	${1.1}_{-0.2}^{+0.2}$ × 10−6	${1.6}_{-0.2}^{+0.2}$ × 10−6
Astro. silicate inner radius; ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{in}}$ (AU)	${2.0}_{-0.2}^{+0.3}$ × 102	${2.4}_{-0.2}^{+0.2}$ × 102	${3.2}_{-0.3}^{+0.2}$ × 102
Astro. silicate outer radius; ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{out}}$ (AU)	${4.8}_{-0.4}^{+0.5}$ × 102	${5.5}_{-0.3}^{+0.5}$ × 102	${5.6}_{-0.2}^{+0.4}$ × 102

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We find that ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{in}}$ on Days 1272, 1616, and 1947 is, respectively, 1.3 × 10², 1.5 × 10², and 1.7 × 10²AU when a_a.car. = 0.01 μm, and 5.1 × 10¹, 5.4 × 10¹, and 6.1 × 10¹AU when a_a.car. = 0.1 μm. The dust expansion velocity of 0.35 ± 0.03 mas day⁻¹ reported by Chesneau et al. (2008) corresponds to 0.19 AU day⁻¹. If the expansion velocity stays constant, the dust will reach distances of 2.4 × 10², 3.1 × 10², and 3.7 × 10² AU on Days 1272, 1616, and 1947, respectively. Moreover, the deconvolved images of V1280 Sco taken in the Si-1 band on Days 1272, 1616, and 1947 exhibit elongated structures along PA ∼ 20° and are modeled with elliptical Gaussian profiles with semimajor axis lengths of 027, 032, and 04, which correspond to 1.5 × 10², 1.8 × 10², and 2.2 × 10² AU, respectively. Judging by the location of amorphous carbon dust in our model, the representative size of amorphous carbon dust produced around V1280 Sco is more likely to be 0.01 μm than 0.1 μm. We note that the uncertainty in the adopted distance toward V1280 Sco can directly affect the distance between the dust and the white dwarf constrained from the observations. However, even if we adopt the shortest distance of D = 0.63 kpc toward V1280 Sco estimated by Hounsell et al. (2010), the semimajor axis lengths of the deconvolved image observed on Days 1272, 1616, and 1947 correspond to 0.9 × 10², 1.0 × 10², and 1.3 × 10² AU, respectively, which are still much larger than the inner wall radii of amorphous carbons obtained for a_a.car. = 0.1 μm, and therefore the representative size of amorphous carbon dust is significantly smaller than 0.1 μm.

The best-fit parameters obtained on Days 1272, 1616, and 1947 calculated for the cases of a_a.car. = 0.01 μm, a_a.sil. = 0.1 μm, 0.2 μm, 0.3 μm, and 0.5 μm are summarized in Tables 9–12, respectively. The model spectra calculated with those best-fit parameters are shown in the left panels of Figures 13–16. Temperatures of amorphous carbon and astronomical silicate are shown as a function of distance from the white dwarf in the right panels of Figures 13–16. The best-fit ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{in}}$'s on Day 1947 are shown in Figure 17 for different a_a.sil. used in the SED analysis. Because ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{in}}$ must be smaller than the semimajor axis of the deconvolved Qb band image of V1280 Sco on Day 1947 (i.e., 045), we conclude that the typical size of silicate dust must be larger than 0.3 μm (see Figure 17). Moreover, the semimajor axis of the deconvolved emitting region measured in the Qb band, which is dominated by astronomical silicate, is systematically larger than that measured in the Si-1 band, which is dominated by amorphous carbon, on Days 1272, 1616, and 1947. This implies that astronomical silicate is located farther from the white dwarf than amorphous carbon. We have found that ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{in}}$ is always larger than ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{in}}$ when ${a}_{{\rm{a}}.\mathrm{sil}.}\lt 0.5\;\mu {\rm{m}}$ (${a}_{{\rm{a}}.\mathrm{car}.}=0.01\;\mu {\rm{m}}$; see Tables 9–12). We therefore conclude that the typical grain size of amorphous carbon is ${a}_{{\rm{a}}.\mathrm{car}.}=0.01\;\mu {\rm{m}}$ and that of astronomical silicate is $0.3\;\mu {\rm{m}}\lt {a}_{{\rm{a}}.\mathrm{sil}.}\lt 0.5\;\mu$m. A relatively large grain size found for silicate dust in our analyses is consistent with the general understanding that the grain size in dust shells of novae is substantially larger than that in the interstellar medium (Gehrz et al. 1998; Witt et al. 2001).

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Table 9.  The Best-fit Parameters Obtained for ${a}_{{\rm{a}}.\mathrm{car}.}=0.01\;\mu {\rm{m}}$ and ${a}_{{\rm{a}}.\mathrm{sil}.}=0.1\;\mu {\rm{m}}$

Epoch (days)	1272	1616	1947
Opening angle; ϕ (deg)	24.0 ± 0.5	18.0 ± 0.5	15.0 ± 0.5
Amor. carbon initial number density; ${n}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{ini}}$ (cm−3)	${2.0}_{-0.2}^{+0.2}$ × 10−3	${1.3}_{-0.2}^{+0.2}$ × 10−3	${1.1}_{-0.1}^{+0.2}$ × 10−3
Amor. carbon inner radius; ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{in}}$ (AU)	${1.3}_{-0.1}^{+0.1}$ × 102	${1.5}_{-0.1}^{+0.1}$ × 102	${1.7}_{-0.2}^{+0.1}$ × 102
Amor. carbon outer radius; ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{out}}$ (AU)	${2.5}_{-0.2}^{+0.3}$ × 102	${4.6}_{-0.5}^{+0.5}$ × 102	${6.6}_{-0.6}^{+0.6}$ × 102
Astro. silicate initial number density; ${n}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{ini}}$ (cm−3)	${1.3}_{-0.1}^{+0.1}$ × 10−6	${1.8}_{-0.2}^{+0.2}$ × 10−6	${1.5}_{-0.2}^{+0.2}$ × 10−6
Astro. silicate inner radius; ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{in}}$ (AU)	${2.0}_{-0.2}^{+0.2}$ × 102	${2.0}_{-0.2}^{+0.2}$ × 102	${2.7}_{-0.2}^{+0.2}$ × 102
Astro. silicate outer radius; ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{out}}$ (AU)	${5.0}_{-0.5}^{+1.0}$ × 102	${6.0}_{-0.5}^{+1.0}$ × 102	${6.7}_{-0.5}^{+1.0}$ × 102

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Table 10.  The Best-fit Parameters Obtained for ${a}_{{\rm{a}}.\mathrm{car}.}=0.01\;\mu {\rm{m}}$ and ${a}_{{\rm{a}}.\mathrm{sil}.}=0.2\;\mu {\rm{m}}$

Epoch (days)	1272	1616	1947
Opening angle; ϕ (deg)	24.0 ± 0.5	18.0 ± 0.5	15.0 ± 0.5
Amor. carbon initial number density; ${n}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{ini}}$ (cm−3)	${2.1}_{-0.2}^{+0.2}$ × 10−3	${1.2}_{-0.2}^{+0.2}$ × 10−3	${1.3}_{-0.2}^{+0.2}$ × 10−3
Amor. carbon inner radius; ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{in}}$ (AU)	${1.3}_{-0.1}^{+0.1}$ × 102	${1.5}_{-0.1}^{+0.1}$ × 102	${1.7}_{-0.2}^{+0.1}$ × 102
Amor. carbon outer radius; ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{out}}$ (AU)	${2.5}_{-0.2}^{+0.3}$ × 102	${4.6}_{-0.5}^{+0.5}$ × 102	${6.6}_{-0.6}^{+0.6}$ × 102
Astro. silicate initial number density; ${n}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{ini}}$ (cm−3)	${1.6}_{-0.1}^{+0.1}$ × 10−7	${1.8}_{-0.2}^{+0.2}$ × 10−7	${1.8}_{-0.2}^{+0.2}$ × 10−7
Astro. silicate inner radius; ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{in}}$ (AU)	${2.0}_{-0.2}^{+0.2}$ × 102	${2.0}_{-0.2}^{+0.2}$ × 102	${2.7}_{-0.2}^{+0.2}$ × 102
Astro. silicate outer radius; ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{out}}$ (AU)	${4.9}_{-0.5}^{+1.0}$ × 102	${6.0}_{-1.0}^{+2.0}$ × 102	${7.0}_{-0.5}^{+1.0}$ × 102

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Table 11.  The Best-fit Parameters Obtained for ${a}_{{\rm{a}}.\mathrm{car}.}=0.01\;\mu {\rm{m}}$ and ${a}_{{\rm{a}}.\mathrm{sil}.}=0.3\;\mu {\rm{m}}$

Epoch (days)	1272	1616	1947
Opening angle; ϕ (deg)	24.0 ± 0.5	18.0 ± 0.5	15.0 ± 0.5
Amor. carbon initial number density; ${n}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{ini}}$ (cm−3)	${2.2}_{-0.2}^{+0.3}$ × 10−3	${1.3}_{-0.2}^{+0.2}$ × 10−3	${1.0}_{-0.2}^{+0.2}$ × 10−3
Amor. carbon inner radius; ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{in}}$ (AU)	${1.3}_{-0.1}^{+0.1}$ × 102	${1.5}_{-0.1}^{+0.1}$ × 102	${1.7}_{-0.2}^{+0.1}$ × 102
Amor. carbon outer radius; ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{out}}$ (AU)	${2.5}_{-0.2}^{+0.3}$ × 102	${4.6}_{-0.5}^{+0.5}$ × 102	${6.6}_{-0.6}^{+0.6}$ × 102
Astro. silicate initial number density; ${n}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{ini}}$ (cm−3)	${7.1}_{-0.7}^{+0.7}$ × 10−8	${7.9}_{-0.8}^{+0.8}$ × 10−8	${6.3}_{-0.7}^{+0.7}$ × 10−8
Astro. silicate inner radius; ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{in}}$ (AU)	${1.5}_{-0.1}^{+0.1}$ × 102	${1.7}_{-0.1}^{+0.1}$ × 102	${2.4}_{-0.2}^{+0.2}$ × 102
Astro. silicate outer radius; ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{out}}$ (AU)	${4.5}_{-0.5}^{+1.0}$ × 102	${5.7}_{-1.0}^{+2.0}$ × 102	${6.4}_{-0.5}^{+1.0}$ × 102

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Table 12.  The Best-fit Parameters Obtained for ${a}_{{\rm{a}}.\mathrm{car}.}=0.01\;\mu {\rm{m}}$ and ${a}_{{\rm{a}}.\mathrm{sil}.}=0.5\;\mu {\rm{m}}$

Epoch (days) 1272 1616 1947

Opening angle; ϕ (deg)	24.0 ± 0.5	18.0 ± 0.5	15.0 ± 0.5
Amor. Carbon initial number density; ${n}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{ini}}$ (cm−3)	${2.1}_{-0.2}^{+0.2}$ × 10−3	${1.2}_{-0.1}^{+0.1}$ × 10−3	${0.9}_{-0.1}^{+0.1}$ × 10−3
Amor. Carbon inner radius; ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{in}}$ (AU)	${1.3}_{-0.1}^{+0.1}$ × 102	${1.5}_{-0.1}^{+0.1}$ × 102	${1.7}_{-0.2}^{+0.1}$ × 102
Amor. Carbon outer radius; ${r}_{{\rm{a}}.\mathrm{car}.}^{\mathrm{out}}$ (AU)	${2.5}_{-0.2}^{+0.3}$ × 102	${4.6}_{-0.5}^{+0.5}$ × 102	${6.6}_{-0.6}^{+0.6}$ × 102
Astro. silicate initial number density; ${n}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{ini}}$ (cm−3)	${7.1}_{-0.7}^{+0.7}$ × 10−8	${7.9}_{-0.8}^{+0.8}$ × 10−8	${6.3}_{-0.6}^{+0.6}$ × 10−8
Astro. silicate inner radius; ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{in}}$ (AU)	${1.3}_{-0.1}^{+0.1}$ × 102	${1.3}_{-0.1}^{+0.1}$ × 102	${1.9}_{-0.2}^{+0.2}$ × 102
Astro. silicate outer radius; ${r}_{{\rm{a}}.\mathrm{sil}.}^{\mathrm{out}}$ (AU)	${4.3}_{-0.5}^{+1.0}$ × 102	${6.3}_{-1.0}^{+2.0}$ × 102	${6.9}_{-0.5}^{+1.0}$ × 102

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The dust masses of amorphous carbon and astronomical silicate calculated for a_a.car. = 0.01 μm and a_a.sil. = 0.3 μm are given in Table 13, where ρ_a.car. (1.87 g cm⁻³) and ρ_a.sil. (3.3 g cm⁻³) are adopted as the densities of an amorphous carbon (a.car.) and astronomical silicate (a.sil.) dust particle, respectively. These values suggest that no significant evolution in dust mass occurred from Day 1272 through 1947. Thus, the masses of amorphous carbon and astronomical silicate around V1280 Sco are ∼8 × 10⁻⁸ M_⊙ and ∼4 × 10⁻⁷ M_⊙, respectively.

Table 13.  The Dust Mass Evolution among Days 1272, 1616 and 1947

Epoch (days)	Amor. Carbon (M⊙)	Astro. Silicate (M⊙)
1272	${6.6}_{-1.4}^{+2.0}$ × 10−8	${3.4}_{-0.4}^{+0.6}$ × 10−7
1616	${8.7}_{-1.5}^{+1.7}$ × 10−8	${4.3}_{-1.2}^{+1.3}$ × 10−7
1947	${8.4}_{-1.7}^{+1.0}$ × 10−8	${4.0}_{-0.8}^{+0.8}$ × 10−7

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