Characterization of Thermal-infrared Dust Emission and Refinements to the Nucleus Properties of Centaur 29P/Schwassmann–Wachmann 1

The 16 μm blue PU images (Figure 1) were obtained 1.3 days before the 24 μm MIPS images (Figure 2), which were obtained on UT 2003 November 24 15:05. The 16 μm image's coma did not display any clearly distinguishable large-scale radial or azimuthal features in either the unenhanced or enhanced images. A slight enhancement on the south–southeast through southwest side of the coma is detected in the division by azimuthal average and the 1/ρ-removed enhanced images (Figures 1(b) and (c)). This is further confirmed in Figure 3, which displays radial-surface-brightness profiles for position angles (PAs) at 45° spacings for the 16 μm image. The radial profiles were generated by taking the median pixel value at a given radial position using 10° wide wedges center on the indicated PA. For comparison, each PA plot includes a radial profile for a scaled STINYTIM generated point-spread function (PSF; Krist 2006) representing how a detection of SW1's bare nucleus would behave in the absence of a coma. A C/ρⁿ functional form was fit to the profiles for ρ values between 14'' and 30'' for each PA (i.e., beyond any significant influence from the nucleus point source contribution), where C is a scaling constant representing the peak coma flux near the nucleus and n is the power index of the coma's profile. The fitted profile power-law indices are listed in Table 2. Profiles for PAs spanning from the south-through-west directions, approximately centered on the projected sunward direction, have nearly canonical 1/ρ coma profiles whereas profiles in the northeast have profile powers of approximately n = 2. This asymmetric profile behavior is consistent with preferential emission of grains in the sunward direction (southwest).

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The overall coma morphology as seen in the unenhanced 24 μm (Figure 2(a)) image similarly shows an increased brightness in the southwest direction. This is further confirmed by the division by an azimuthal average and 1/ρ-removed enhanced images. The rotational-shift-differenced enhanced image (Figure 2(d)) contains a curved wing feature that Stansberry et al. (2004) attribute to a rotating jet and from which they derived a ∼60 day rotation period for SW1's nucleus. Taking into consideration the great similarity in the 16 and 24 μm image morphology taken 1.3 days apart, and the relationship between the projected nucleus–Sun vector and the curved wing's structure suggests that this feature is possibly not the result of nucleus rotation but is instead due to solar radiation pressure effects on micron-sized dust grains emitted in the sunward direction being turned back to form the dust tail in the northeast direction (Farnham & Schleicher 2005; Mueller et al. 2013; Li et al. 2014). While the ∼60 day rotation period derived by the earlier work may in fact coincidentally be reflective of SW1 potentially possessing a long rotation period (Miles et al. 2016; Schambeau et al. 2017, 2019), we propose that this curved wing feature is not the result of a slowly rotating nucleus. Interestingly, the wing would be symmetric around the sky-plane-projected nucleus–Sun axis for the case of isotropic emission from a localized nucleus surface area. Instead it is asymmetric, indicating a possible preferential direction for dust lofting from this source region.

Similar asymmetric curve-shaped features have long been seen in broadband visible imaging data of SW1 while undergoing major outbursts. Accounts of these coma morphologies have been reported in the early works of Jeffers (1956) and Roemer (1958). Whipple (1980) presents a detailed analysis of SW1's outburst coma morphology as detected over a 50 yr baseline, resulting in the descriptive term of "ringtailed snorter" for this often seen curve-shaped feature. While it may at first seem appropriate to compare the outburst and quiescent coma morphologies, detailed analyses of SW1's dust coma while in both phases of activity (Hosek et al. 2013; Miles et al. 2016; Schambeau et al. 2017, 2019) have provided descriptions of the underlying processes ongoing in both phases of activity and that the two are different. The morphology of the 24 μm quiescent coma's wing may resemble that of SW1's outburst coma; however, it was produced by different mechanisms (i.e., slow, sustained dust lofting with expansion velocities in the range of 10–50 m s⁻¹, while quiescent (Jewitt 1990) versus impulsive short-lived dust emission at high velocities in the 100–300 m s⁻¹ range during major outbursts (Feldman et al. 1996; Trigo-Rodríguez et al. 2010; Schambeau et al. 2017, 2019)).

The outer edge of the wing feature seen in the 24 μm image in the southwest direction (Figure 2(d)) may indicate an approximate projected length for the turn-back distance of the grains from solar radiation pressure. Using a projected cometocentric distance of ∼90'' (352,000 km) for the turning point of the wing as the approximate turn-back distance and the Mueller et al. (2013) equation for turn-back distance due to solar radiation pressure, we estimate the dust coma's expansion velocity:

$$\begin{eqnarray}&&v={\left[\displaystyle \frac{2{\rho }_{g}\beta g\sin \alpha }{{\left(\cos \gamma \right)}^{2}}\right]}^{1/2},\end{eqnarray} \tag{ 1 }$$

where ρ_g is the projected sky-plane turn-back distance of the dust grains, γ is the angle between the initial direction of the dust grains and the sky plane, β is the ratio of radiation pressure acceleration to acceleration due to solar gravity, α is the solar phase angle of the observations, and $g={{GM}}_{\odot }/{R}_{H}^{2}$ is the solar gravitational acceleration on the dust grains (G is the gravitational constant, M_⊙ is the Sun's mass, and R_H is the heliocentric distance of the dust grains). We estimate a β value based on equations from Finson & Probstein (1968) and Fulle (2004):

$$\begin{eqnarray}&&\beta =\displaystyle \frac{{C}_{\mathrm{pr}}{Q}_{\mathrm{pr}}}{{\rho }_{d}d},\end{eqnarray} \tag{ 2 }$$

where C_pr is a collection of constants equal to 3E_⊙/(8π cGM_⊙), where E_⊙ is the Sun's mean radiation. The parameter Q_pr is the scattering efficiency for radiation pressure for a dust grain of diameter d. Burns et al. (1979) provide a thorough description of Q_pr and explain that a value of Q_pr ≈ 1 is appropriate for the assumed d = 24 μm grains here. We use a value for the dust grain bulk density based on recent spacecraft visited comae in situ measurements: ρ_d = 500 kg m⁻³ (Fulle et al. 2016). With these assumptions we arrive at an estimated value of β = 0.096. The exact value for γ of the dust grains most dominantly contributing to the wing feature is unknown. Most probably it is the result of dust grains emitted over a continuum of angles. For this reason we calculate the outflow velocity for a range of sky-plane-projected dust grain angles: γ = 0° (v = 50 m s⁻¹), γ = 450 (v = 65 m s⁻¹,) and γ = 800 (v = 270 m s⁻¹).

A similar radial-surface-brightness profile analysis for the 24 μm image is shown in Figure 4. The overall appearance of the coma morphology is similar to that seen in the 16 μm image; however, the larger field of view (FOV) and higher S/N coma detection in the 24 μm image allow a more detailed investigation of the underlying processing ongoing within the dust coma. A change in slope of the profiles at a cometocentric distance of ∼130'' for PAs between 0° and 180° is suggestive of possible ongoing fragmentation for larger grains out to a projected cometocentric distance of 520,000 km (i.e., ∼130''). This view is supported by the coma profile's power-law index being shallower than −1 interior to 520,000 km, suggesting an overabundance of dust grains interior to this projected distance when compared to a canonical steady-state dust emission. This behavior is possibly explained by a process of larger grains emitted from the nucleus and their subsequent fragmentation as they expand in the coma, or possibly from the decreasing size via sublimation of larger icy grains losing their volatile content. In Section 3.1.4 we discuss the possibility of icy grains in more detail. These larger (0.1–1.0 mm) grain populations would not contribute significantly to the 24 μm coma cross section close to the nucleus because of its relative lack of surface area but could still easily support the observed number density of 24 micron-sized grains due to a fragmentation cascade (N.B.—as long as there are particles ≫24 μm in radius, they can always fragment/disrupt into many smaller particles and keep the observed particle size distribution (PSD) going) and thus maintain the coma's enhanced 24 μm surface brightness.

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Similar to the 16 μm image, the coma's profiles in 24 μm close to the projected sunward direction (PAs: 225°, 270°, and 315°) all have a single profile index close to −1. A possible explanation for this constant surface brightness could be a preferential sunward emission of dust grains.

For this analysis we calculated the f ρ parameter (Lisse et al. 2002; Kelley et al. 2013), an often-used proxy for dust production rates using infrared emission that is analogous to the Af ρ parameter for reflected dust flux in the visible (A'Hearn et al. 1984). While the assumed canonical dust coma used to derive f ρ is not valid for many comets, the utility of f ρ comes from it establishing a standard procedure for estimating coma dust production rates and allowing a relative comparison between individual comets.

The expression for f ρ used is

$$\begin{eqnarray}&&\epsilon f\rho (\lambda )=\displaystyle \frac{{F}_{\mathrm{th}}(\lambda )}{\pi B(\lambda ,{T}_{c})}\times \displaystyle \frac{{{\rm{\Delta }}}^{2}}{\rho },\end{eqnarray} \tag{ 3 }$$

where is the emissivity of the dust grains at wavelength λ; f is a filling factor expressing the fraction of the photometry aperture containing dust grains; ρ is the linear aperture radius centered on the nucleus, which is being used to measure the flux; F_th(λ) is the flux measured in the photometric aperture for wavelength λ; B(λ, T_c ) is the Planck function calculated at the color temperature T_c of the dust grains; and Δ is the geocentric distance during the observation.

For the 2003 epoch of Spitzer SW1 imaging, we used properties for the dust coma derived from our earlier analysis of IRS observations of SW1. This analysis indicated the coma was dominated by submicron- to micron-sized amorphous silicate and amorphous carbon grains at a color temperature of ∼140 K (Schambeau et al. 2015). The color temperature map shown in Section 3.1.4 also indicates dust grains at similar color temperatures, but also that there is a color temperature structure present in the coma complicating the interpretation of a derived f ρ based on an assumed dust coma with uniform temperature. With these understood limitations, we used Equation (3) to calculate f ρ values for each of the three bands containing extracted coma flux measurements. Additionally, we calculated f ρ values using an expression for dust coma color temperature (T_c = 300 K/$\sqrt{({R}_{H})}$ = 125 K) based on the results of the Survey of Ensemble Physical Properties of Cometary Nuclei (SEPPCoN) for JFC observations by Spitzer (Kelley et al. 2013) and for the case of grains at an ideal blackbody temperature (T_bb = 278 K/$\sqrt{({R}_{H})}$ = 117 K) for comparison. The IRS-derived and SEPPCoN-derived dust color temperatures are slightly hotter than an ideal blackbody at the same heliocentric distance. Most probably this is the result of superheated submicron-sized amorphous carbon grains present in the dust coma (Hanner et al. 1997) and/or potentially from the many emission features present in the thermal-infrared region (Wooden 2002; Markkanen & Agarwal 2019).

For F_th(λ) we subtracted the nucleus's contribution to SW1's overall flux in each aperture based on the scaled PSFs found during the coma removal process presented in Section 3.2. Additionally, flux from background sources (some of them serendipitously detected asteroids) was removed by interpolating the dust coma behavior for regions around each background source.

Figure 5 shows plots of the 16 and 24 μm measured spectral flux density values for an array of aperture radii along with their associated f ρ measurements for the three color temperature assumptions. Table 3 reports the measured flux and f ρ values along with their associated uncertainties for the largest photometry apertures used for each image. The 16 μm's nearly constant f ρ value for aperture radii larger than ∼5'' indicates that the 3D shape of the dust coma primarily contributing to this image maintains a nearly canonical spherical shape (Fink & Rubin 2012). On the other hand, the 24 μm f ρ profile has a slight positive slope indicating deviations from a canonical 1/ρ coma's expected aperture-independent constant value. The 24 μm slope behaviors support the possibility for an overabundance of 24 μm-sized dust grains for larger cometocentric distances. The steep decrease for f ρ profiles for small apertures is an artifact of the coma's image being the convolution of the coma's intrinsic surface-brightness distribution with the telescope's PSF (e.g., the intrinsic surface brightness is spread over a larger projected surface area by the convolution process resulting in a decrease in integrated flux for apertures smaller than the PSF).

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Table 3. SW1 Thermal-infrared Dust Coma Measurements

Band	ρa	Flux	f ρ	$\dot{M}$	f ρ	$\dot{M}$	f ρ	$\dot{M}$
(μm)	('')	(mJy)	(cm)	(kg s−1)	(cm)	(kg s−1)	(cm)	(kg s−1)
			Tc = 117 K		Tc = 125 K		Tc = 140 K
16	20	145 ± 2	9400 ± 150	104 ± 2	5600 ± 90	124 ± 2	2600 ± 43	28.8 ± 0.5
24	20	570 ± 24	8700 ± 360	144 ± 6	6100 ± 260	101 ± 4	3700 ± 150	61 ± 3
24	200	8403 ± 90	13700 ± 150	227 ± 3	9700 ± 105	322 ± 4	5800 ± 63	96 ± 1
70	9	102 ± 50	2600 ± 1300	130 ± 65	2300 ± 1100	113 ± 55	1800 ± 900	90 ± 45

Note.

^a The radius of the sky-plane-projected photometry aperture.

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To verify that the difference in aperture photometry for the coma between the 16 and 24 μm images is not the result of the local infrared background in each image, we compared coadded Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) backgrounds retrieved from the W3 (12 μm) and W4 (22 μm) intensity images downloaded from the NASA/IPAC Infrared Science Archive. W3 and W4 coadded images centered on the SW1's nucleus position during each epoch of imaging were compared, and we found no significant differences that could explain the different photometry behaviors.

The 70 μm image's low-S/N surface-brightness coma detection did not allow a similar radial profile analysis. Instead, we report in Table 3 an updated 9'' radius aperture coma flux measurement. Our earlier reported 70 μm flux density value (Schambeau et al. 2015) did not include an aperture correction for the measurement, so the earlier reported flux measurement is an underestimate. Based on a new reported measurement of 103 ± 50 mJy, we calculated an f ρ value. The large uncertainty in the derived 70 μm coma flux measurement is due to the low S/N present in the mosaicked image and SW1's proximity to one of the jail-bar artifacts often present in MOPEX-generated mosaicked images (see Schambeau et al. 2015, Figure 2(b)).

We use the measured f ρ values to estimate dust production rates during the Spitzer imaging according to

$$\begin{eqnarray}&&\dot{M}=(\epsilon f\rho )\times \displaystyle \frac{8a{\rho }_{d}v}{3\epsilon },\end{eqnarray} \tag{ 4 }$$

where a is the radius of the grains, ρ_d is the density of the grains, and v is the radial velocity of the grains lofted from the nucleus's surface. For our calculations we assumed that the diameter of the grains dominating the emitted flux for each band is equal to the effective wavelength of each band: 15.8, 23.68, and 71.42 μm. For the density of the grains we used the same value of ρ_d = 500 kg m⁻³ (Fulle et al. 2016) that was used for the estimate of the dust expansion velocity. The velocity of the emitted dust grains was chosen to be 50 m s⁻¹ based on the lower approximate values for dust expansion velocity from the 24 μm coma morphology and turn-back distance from solar radiation pressure. While it is likely that larger grains will have slower radial velocities than smaller grains, we adopt the same value for each band, due to the observational uncertainties of the measurements. We use a value for the dust emissivity of = 0.95. Estimated dust production rates are presented in Table 3.

We have collected similar f ρ measurements based on the SEPPCoN (Fernández et al. 2013; Kelley et al. 2013) and WISE/NEOWISE (Bauer et al. 2017) surveys for comets in order to compare SW1's measured values. Results from the WISE/NEOWISE survey (Bauer et al. 2017) enabled them to develop an empirical expression relating an expected thermal dust activity for an individual comet based on its nucleus size:

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{log}\left(\displaystyle \frac{\epsilon f\rho }{1\,\mathrm{cm}}\right) & = & 3.5\left(1-\exp \left(-\displaystyle \frac{{D}_{N}}{5.3\,\mathrm{km}}\right)\right)\\ & & +N(0,0.25),\end{array}\end{eqnarray} \tag{ 5 }$$

where D_N is the nucleus diameter in kilometers and N(0, 0.25) is a Gaussian distribution with a mean of 0 and variance of 0.25. In Figure 6, we plotted measurements from both infrared surveys, the empirical expression developed by Bauer et al. (2017), and SW1's measurements from this work.

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As Figure 6 shows, Equation (5) fits the SEPCCoN f ρ values and SW1 values presented in this work. Interestingly, the expression implies that comets with nuclei diameters larger than ∼20 km have a flattening of activity levels when compared to the steep increase of dust activity versus diameter for comets between 1 km to 10 km diameters. This may be partly due to an observational bias in favor of detecting larger nuclei at larger heliocentric distances in combination with the distant activity being driven by a process other than water ice sublimation. This comparison between SEPPCoN, NEOWISE, and SW1 values is new, and the good fit of Equation (5) to the observations indicates that the equation is a robust estimator of a comet's larger grain coma activity level.

Reports of SW1's dust production rate as derived from visible observations during periods of quiescent activity indicate a typical mass-loss rate for submicron-sized grains on the order of 1–50 kg s⁻¹. We arrived at these typical quiescent dust production rates using reported Af ρ measurements from Trigo-Rodríguez et al. (2010) and Hosek et al. (2013), but here we use a value of grain density ρ_d = 500 kg m⁻³ in order to be consistent with our f ρ-derived dust production rates. We note that these dust production rates are upper limits due to their calculated Af ρ values containing nucleus flux contributions. When compared to the estimated dust production rates as derived from the Spitzer data, which have nucleus flux contributions removed, the estimated dust production rates for grains in the range of 16–70 μm have a higher mass-loss rate (Table 3) than the submicron-sized coma (< μm grains). It would be interesting to see if this trend of higher mass-loss rate for the tens of micron-sized grains is also seen during periods of major dust coma outburst (i.e., is the bulk of SW1's outburst mass loss coming from grains that are on the order of 10s of microns to 100 μm or from submicron-sized grains), enabling investigations of the quiescent versus outburst comae activity mechanisms.

Another approach to determine the dust production rate is to model the thermal emission of an ensemble of particles defined by its size distribution. We used the model described in Bockelée-Morvan et al. (2017), which computes the wavelength-dependent absorption coefficient and temperature of dust particles as a function of grain size using the Mie theory combined with an effective medium theory (EMT) in order to consider mixtures of different materials. EMTs allow us to calculate an effective refractive index for a medium made of a matrix with inclusions of another material. The Maxwell–Garnett mixing rule is used in this model and is also applied to consider the porosity of the grains, set to be 50% at maximum (Bockelée-Morvan et al. 2017). The infrared thermal spectrum is computed by summing the contributions of the individual dust particles. The size distribution of the dust particles is described by a power-law n(a) ∝a^−β , where β is the size index, and the particle radius takes values from ${a}_{\min }$ to ${a}_{\max }$. The dust density is taken equal to 500 kg m⁻³. The effect of ice sublimation on the equilibrium grain temperature was not taken into account, as it has been shown that radiative cooling dominates overcooling by sublimation at far heliocentric distances (Beer et al. 2006).

We consider in this paper three different mixtures (see Bockelée-Morvan et al. 2017 for the references for optical constants): (1) a matrix of amorphous carbon with inclusions of amorphous olivine with an Fe:Mg composition of 50:50; (2) a matrix of crystalline ice with inclusions of amorphous carbon; and (3) a matrix of amorphous carbon with inclusions of crystalline ice. For mixture (1) the carbon/olivine mass ratio is 1, a value consistent with the organic mass fraction measured in comet 67P dust particles (Bardyn et al. 2017). Mixtures (2) and (3) have the same ice fraction in a mass of ∼45% but have different optical properties.

Other parameters set in the model are the dust maximum size ${a}_{\max }$ and the dust velocity as a function of particle size, described as varying ∝ a^−0.5, with a value of 60 m s⁻¹ for 10 μm particles. The maximum liftable size from the surface of SW1's nucleus is estimated to be ${a}_{\max }$ = 250 μm, for a CO-driven activity restricted to a spherical segment with a half-angle of 45° and a total CO production rate of 4 × 10²⁸ s⁻¹, assuming our nucleus radius estimate of 32.3 km (Section 3.2) and a nucleus density of 500 kg m⁻³ (V. Zakharov 2021, personal communication; see Zakharov et al. 2018, 2021). This CO outgassing description is consistent with CO millimeter observations (Gunnarsson et al. 2008; Wierzchos & Womack 2020; Bockelée-Morvan et al. 2021).

The model was applied to simulate the flux density in a 9'' FOV radius at 16, 24, and 70 μm, for comparison with Spitzer data. Simulations were made for a minimum dust particle size ${a}_{\min }$ in the range 0.5–50 μm and size indices in the range 2.5–4.6. These two parameters have indeed a strong influence on the dust thermal spectrum, with, e.g., a larger contribution from small particles for low ${a}_{\min }$ and high β values resulting in a higher dust color temperature. The Spitzer constraints are flux densities in a 9'' FOV radius of 64 ± 2 mJy, 198 ± 14 mJy, 103 ± 50 mJy at 16, 24, and 70 μm, respectively. This corresponds to the color temperatures of T_16/24 = 129 ± 5 K, based on the 16 and 24 μm fluxes, and T_24/70=${177}_{-47}^{+52}$ K based on the 24 and 70 μm fluxes. T_16/24 and T_24/70 are consistent within 1σ with a value of ∼130 K, but the high central value of T_24/70 resulting from the relatively faint 70 μm flux might suggest an excess of small particles poorly radiating at long wavelengths.

Figure 7 shows isocontours of T_16/24 (black plain lines) and T_24/70 (dashed blue lines) as a function of ${a}_{\min }$ and β. Domains consistent with measured T_16/24 and T_24/70 values are filled in orange and blue colors, respectively. We only show results for ice-carbon mixtures (2) and (3), because results for the carbon-silicate mixture (1) are similar to those obtained for mixture (3). For mixtures (1) (not shown) and (3), the orange and blue domains overlap for ${a}_{\min }$ = 2–5 μm, whereas no overlapping is observed for mixture (2) for any set of (${a}_{\min }$, β). Grains made of mixture (2) are hotter than other mixtures for sizes below 30 μm (Figure 8), and this explains the different infrared spectra.

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In Figure 9, we show dust production rates derived from the 24 μm flux density using the (${a}_{\min }$, β) parameters that provide T_16/24 values consistent with the measured value, i.e., those defining the orange region in Figure 7. For mixtures 1) and 3) with matrices of amorphous carbon, the range is 50–200 kg s⁻¹. The low end is obtained for the highest (${a}_{\min }$, β) values (= (5 μm, 4.1–4.4)), which is a steep size distribution where 5–10 μm grains dominate the infrared emission. For size distributions with ${a}_{\min }$ = 4–5 μm, the dust production rates deduced from the 24 and 70 μm fluxes are consistent, and in the range 50–100 kg s⁻¹. However, this is not the case for size distributions with small ${a}_{\min }$ values (and consequently low β values; Figure 7), for which 70 μm derived dust production rates are by a factor of 2–3 lower than those deduced from the 24 μm flux. For the ice/carbon mixture 2 (matrix of crystalline ice), the dust production rate inferred from the 24 μm flux is between 130 and 240 kg s⁻¹ (Figure 9). The values derived from the 70 μm flux are more than two times lower for all sets of (${a}_{\min }$, β) parameters. This is an expected result because for this composition, the model fails in reproducing both the T_16/24 and T_24/70 values.

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The dust production rates derived with model parameters leading to a satisfactory fit to data (50–100 kg s⁻¹) are in overall agreement with those estimated in Section 3.1.2 using a simple approach. The Mie scattering model shows that measuring dust fluxes at several wavelengths in the thermal IR can provide constraints on the PSD and thermal properties. The obtained results are here limited due to the low-S/N of the 70 μm dust coma flux. A flaw in the present analysis is also the known limitations of the Mie scattering theory and of the Maxwell–Garnett mixing rule for modeling dust spectra (Lien 1990; Mishchenko & Travis 2008).

In Figure 10, a color temperature map of the coma based on the 16 and 24 μm images is shown. This was generated by using the spectral flux density values of the coma after removal of flux contributions from the nucleus; the procedure of nucleus versus coma flux contributions is described in Section 3.2 for the 16 μm image and in our earlier work (Schambeau et al. 2015) for the 24 μm data. Masked pixels identified by the teal square near the center represent regions where the PSF's subtraction may have resulted in a significant over- or undersubtraction for individual pixels. The white pixels on the top-left and top-right of the color map are not "hot" but instead are masked as white due to the low-S/N 16 μm detections resulting in negative spectral flux density pixel values after background subtraction. These pixels have been excluded from the color temperature fitting procedure. We note that the actual temperatures of the grains most probably are different from the values derived from fitting a Planck blackbody profile to the individual pixel values from the 16 and 24 μm images due to the silicate emission features present in the 24 μm bandpass and the dust coma PSD (Wooden 2002; Markkanen & Agarwal 2019). The peak temperature of the grains of ∼140 K close to the nucleus is in agreement with a color temperature derived from the IRS spectrum as analyzed in Schambeau et al. 2015.

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Overall, the general trend is a decreasing color temperature with increasing projected distance away from the nucleus. The eastern half of the coma has a higher temperature than the western side by ∼20°. The interpretation of this behavior is uncertain based on the current Spitzer imaging data. We mention here plausible explanations for these color temperature behaviors based on the properties of the dust coma. One possible explanation can be a population of relatively smaller grains on the eastern side of the coma composing the tail that are less efficient at radiating their stored thermal energy. Another possibility is that the western side of the coma has a higher abundance of submicron-sized grains, resulting in an enhanced 24 μm emission above that of an ideal blackbody due to the silicate emission bands around 20 μm. The overall impact of this behavior would be a slightly lower color temperature for the western side of the coma. Future modeling efforts may be able to select between the combination of processes driving the observed color temperature but are beyond the scope of this current work.

Using the color temperature as a proxy for the approximate dust grain temperatures and the results of Beer et al. (2006) indicates that for grain sizes on the order of tens of microns, as we have here for the 16 and 24 μm images, the grains have a dust mass fraction for water ice (X, where X = 1 for pure water ice) in the range of 25%–50%, with smaller grains having a higher ice content. We calculated the expected lifetimes for the water-ice content of assumed spherical icy grains with diameters equal to 16, 24, and 70 μm and dust mass fractions X₁₆ = 0.5, X₂₄ = 0.40, and X₇₀ = 0.25 (Mukai 1986; Lien 1990; Beer et al. 2006). The lifetimes of the water-ice content of the grains are, respectively, 112, 154, and 373 days. For these estimated lifetimes we have ignored the increased temperatures of grains as their sizes decrease due to the ongoing water-ice sublimation, so our derived lifetimes are estimated upper limits.

The presence of grains containing water ice has been inferred by the increased emissivity at longer wavelengths as derived from the modeling of SW1's Spitzer IRS spectrum (Schambeau et al. 2015). Additionally, SW1's H₂O production rates as derived from Herschel/HIFI observations indicate a nonnuclear extended source that is explained by the sublimation of an icy grain coma (Bockelée-Morvan et al. 2021). The H₂O measured production rates based on AKARI and Herschel observations are in the range of ${Q}_{{{\rm{H}}}_{2}{\rm{O}}}$ ∼ 3–7 × 10²⁷ molecules s⁻¹ (Ootsubo et al. 2012; Bockelée-Morvan et al. 2021). These measured production rates are the same order of magnitude as what would be produced by the sublimation of icy grains if we use the dust-to-ice mass fractions as constrained from their color temperature and the dust production rates derived from f ρ. As a first-order estimate of the coma's ${Q}_{{{\rm{H}}}_{2}{\rm{O}}}$ due to the sublimation of icy grains, we calculated the production rate that would be produced from the sublimation of the water ice content of icy grains following the dust production rates presented in Table 3. Assuming that all of the water-ice content for individual grains is fully sublimated, we arrive at an estimated range of ${Q}_{{{\rm{H}}}_{2}{\rm{O}}}\sim$ (1–3) × 10²⁷ molecules s⁻¹, supporting the argument that the measured water production rates may be explained by a nonnuclear source of icy grains in the coma.