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

Charles A. Schambeau Florida Space Institute, University of Central Florida
12354 Research Parkway, Partnership 1
Orlando, FL 32826, USA  Department of Physics, University of Central Florida
Orlando, FL 32816, USA  Yanga R. Fernández Department of Physics, University
of Central Florida
Orlando, FL 32816, USA  Florida Space Institute, University of Central Florida
12354 Research Parkway, Partnership 1
Orlando, FL 32826, USA  Nalin H. Samarasinha Planetary Science Institute
Tucson, AZ 85719, USA  M. Womack National Science Foundation, Alexandria, VA
22314 USA  Department of Physics, University of Central Florida
Orlando, FL 32816, USA  Dominique Bockelée-Morvan LESIA, Observatoire de
Paris, PSL Research University, CNRS, Sorbonne Université, Université de
Paris,
5 place Jules Janssen, 92195 Meudon, France  Carey M. Lisse Johns Hopkins
University, Applied Physics Laboratory
Laurel, MD 20723, USA  Laura M. Woodney Department of Physics, California
State University, San Bernardino
San Bernardino, CA 92407, USA

(Received October 01, 2020; Revised April 18, 2021; April 30, 2021; Accepted
May 4, 2021)

###### Abstract

We present analyses of Spitzer observations of 29P/Schwassmann-Wachmann 1
using 16 $\mu$m IRS “blue” peak-up (PU) and 24 $\mu$m and 70 $\mu$m MIPS
images obtained on UT 2003 November 23 and 24 that characterize the Centaur’s
large-grain (10-100 $\mu$m) dust coma during a time of non-outbursting
“quiescent” activity. Estimates of $\epsilon f\rho$ for each band (16 $\mu$m
(2600 $\pm$ 43 cm), 24 $\mu$m (5800 $\pm$ 63 cm), and 70 $\mu$m (1800 $\pm$
900 cm)) follow the trend between nucleus size vs. $\epsilon f\rho$ that was
observed for the WISE/NEOWISE comet ensemble. A coma model was used to derive
a dust production rate in the range of 50-100 kg/s. For the first time, a
color temperature map of SW1’s coma was constructed using the 16 $\mu$m and 24
$\mu$m imaging data. With peaks at $\sim$ 140K, this map implies that coma
water ice grains should be slowly sublimating and producing water gas in the
coma. We analyzed the persistent 24 $\mu$m “wing” (a curved southwestern coma)
feature at 352,000 km (90′′) from the nucleus attributed by Stansberry et al.
(2004) to nucleus rotation and instead propose that it is largely created by
solar radiation pressure and gravity acting on micron sized grains. We
performed coma removal to the 16 $\mu$m PU image in order to refine the
nucleus’ emitted thermal flux. A new application of the Near Earth Asteroid
Thermal Model (NEATM; Harris (1998)) at five wavelengths (5.730 $\mu$m, 7.873
$\mu$m, 15.80 $\mu$m, 23.68 $\mu$m, and 71.42 $\mu$m) was then used to refine
SW1’s effective radius measurement to $R=32.3\pm 3.1$ km and infrared beaming
parameter to $\eta=1.1\pm 0.2$, respectively.

general, centaurs — individual, 29P/Schwassmann-Wachmann 1 — Spitzer Space
Telescope — infrared observations

††journal: the Planetary Science Journal

##  1 Introduction

29P/Schwassmann-Wachmann 1 (SW1) is a continuously active Centaur at the inner
cusp of the Centaur-to-Jupiter-Family transition region and presents a rare
opportunity to investigate activity drivers and ongoing material processing
that occurs in a region too cold for vigorous water-ice sublimation. Recent
dynamical simulations have shown that its current nearly-circular trans-Jovian
orbit (eccentricity, semi-major axis and perihelion respectively: $e$ = 0.04,
$a$ = 6.03 au and $q$ = 5.77 au)111Minor Planet Circular (MPC) 111773. is
typical for Centaurs in a short-lived transitional “gateway” from the outer
solar system to the Jupiter-family comets (JFCs) population (Sarid et al.,
2019). Interestingly, despite SW1’s modest variation in energy input from the
Sun, it frequently undergoes major outbursts superimposed on its normally-
present background, or “quiescent” coma (Whipple, 1980; Larson, 1980; Jewitt,
1990; Trigo-Rodríguez et al., 2010; Kossacki & Szutowicz, 2013; Hosek et al.,
2013; Miles et al., 2016; Schambeau et al., 2017, 2019). Additionally, the CO-
production rate during periods of quiescent activity is more similar to long-
period comets at similar heliocentric distances than JFCs (Bauer et al., 2015;
Wierzchos et al., 2017; Womack et al., 2017; Bockelée-Morvan & et al., 2021),
and its dust outbursts may be uncorrelated with large fluctuations of its CO
outgassing rate (Wierzchos & Womack, 2020). Thus questions naturally arise as
to what activity drivers explain its enigmatic activity, and do all JFCs
experience a period of similar behaviors while they are in the gateway region?
Are SW1’s activity behaviors reflective of outer solar system materials being
thermally activated in the gateway, after a long period of cryogenic storage?
Or, are they an intrinsic property to it alone?

In 2015, we reported a new analysis of 2003 November Spitzer Infrared Array
Camera (IRAC) 5.8 $\mu$m & 8.0 $\mu$m and Multiband Imaging Photometer (MIPS)
24 $\mu$m & 70 $\mu$m imaging, originally published by Stansberry et al.
(2004). Using a new Spitzer data pipeline and intensive image processing
techniques, the 2015 paper presented a new nucleus radius, beaming parameter,
and infrared geometric albedo of SW1 (Schambeau et al., 2015). Subsequently,
we determined that the Spitzer “blue” (i.e. at 16 $\mu$m) images obtained in
the 2003 dataset have sufficient coma detected for its analysis, modeling, and
removal, and thus, they can provide new physical insights and constraints to
SW1 models.

Here, for the first time, we present the Spitzer 16 $\mu$m images, and analyze
them in the context of the 5.8 $\mu$m, 8.0 $\mu$m, 24 $\mu$m, and 70 $\mu$m
data. We describe relevant observational details of the UT 2003 Nov. epoch in
Section 2. In Section 3.1, we present characterization of thermal infrared
emission using the 16 $\mu$m, 24 $\mu$m, and 70 $\mu$m imaging data through
coma morphology analysis, estimates of the $\epsilon f\rho$ parameter, coma
modeling of the dust grain size distribution and dust-production rates for
micron sized and larger grains, and derivation of a coma color temperature
map. In Section 3.2 we present analysis of these images to provide a fifth
nucleus photometry measurement at 16 $\mu$m. Using the five spectral flux
density measurements of the nucleus, we implemented a NEATM (Harris, 1998) to
derive a new measurement of the nucleus’ effective size and infrared beaming
parameter ($\eta$; a proxy for nucleus surface thermal inertia and/or surface
roughness). In Section 4 we summarize our results and implications for SW1’s
nucleus, quiescent large grain coma, and activity state.

##  2 Observations

This work analyzes the Spitzer imaging data obtained with the 16 $\mu$m IRS
blue PU and 24 $\mu$m and 70 $\mu$m MIPS instruments. Here we address the
observational details of the 16 $\mu$m data, and direct readers to our earlier
work, Schambeau et al. (2015), for information about the 24 $\mu$m and 70
$\mu$m images.

During the Spitzer in-orbit checkout and science verification phase (Werner et
al., 2004) SW1 was observed with the InfraRed Spectrograph (IRS; AORKEY:
6068992; Houck et al. (2004)). Shortly before the IRS observations, blue-
channel PU images were acquired in order to center SW1’s position on the
detector’s “sweet spot” (the detector pixel location of the target’s centroid
peak enabling optimal alignment and centering for the IRS slit). The blue PU
channel of IRS’s Si:As array detector has dimensions of 44 $\times$ 31 pixels,
an effective monochromatic wavelength equivalent to 15.8 $\mu$m, and an
effective pixel scale of 1′′.85/pixel in detector X direction and 1′′.82/pixel
in detector Y direction. A total of six independent blue PU images were
acquired: three images with SW1’s peak located on the center of the detector
and three on the detector’s sweet spot, approximately 3 pixels away from the
center of the array. Level 1 basic calibrated images were downloaded from the
Spitzer Heritage Archive (SHA). An example image of SW1 located on the sweet
spot is shown in Figure 1 along with enhanced images to highlight the coma’s
morphology (Larson & Sekanina, 1984; Samarasinha & Larson, 2014). Table 1
provides a summary of the observational circumstances. The coma is slightly
enhanced in the south-southeast direction and has a similar morphology to that
seen in the MIPS 24 $\mu$m images, suggesting that the same particles are
being measured in both bandpasses. Overall, aside from the slight increase in
dust emission on the south-southeast side of the coma, as indicated by the
division of an azimuthal average enhanced image (Figure 1(b)), the coma is
lacking any defining coma morphology. A faint linear feature can be seen from
approximately the 1 o’clock to 7 o’clock positions.

Table 1: Observations and Geometry Summary for UT 2003 November 23

Parameter |  |  |  | Value
---|---|---|---|---
Observations [Start:Stop] |  |  |  | [(07:15:32.960):(07:17:13.409)]
Exposure Time Per Image |  |  |  | 9.44 s
Heliocentric Distance to SW1 ($R_{H}$) |  |  |  | 5.73 au
Spitzer-SW1 Distance ($\Delta$) |  |  |  | 5.54 au
Solar Phase Angle of SW1 ($\alpha$) |  |  |  | 10.0∘
True Anomaly of SW1 |  |  |  | 342.8∘
Position Angle of Skyplane Projected Sun Direction${}^{\textrm{a}}$ |  |  |  | 248.2∘
Position Angle of Skyplane Projected Heliocentric Velocity Vector${}^{\textrm{a}}$ |  |  |  | 59.9∘

Note. — ${}^{\textrm{a}}$ The position angle is measured counter clockwise
from north through east.

Figure 1: One of the Spitzer 16 $\mu$m blue PU images (with color scale black
to blue to white indicating increasing surface brightness): (a) original
image, (b) division by azimuthal average, (c) 1/$\rho$ profile removal, and
(d) rotational shift differencing of 18∘ (Larson & Sekanina, 1984; Samarasinha
& Larson, 2014). Equatorial north and east are indicated. The skyplane
projected directions for the Sun and SW1’s heliocentric velocity vector are
indicated by the yellow and red arrows, respectively. A black arrow on panel
(c) indicates the slight coma enhancement in the south-southeast direction
that is the south-southeast end of the 1 to 7 o’clock linear feature.

For reference, the filter bandpasses of the 16, 24, and 70 $\mu$m images are
respectively: 13.3$-$18.7 $\mu$m, 20.8$-$26.1 $\mu$m, and 60.9$-$80.6 $\mu$m.

##  3 Image Analysis and Discussion

###  3.1 Thermal Infrared Coma Analysis

Thermal infrared imaging of cometary dust comae allows for preferential
probing of grain sizes on the order of microns and larger, such as those
recorded with the IRS PU and MIPS, because smaller grains with 2$\pi
a/\lambda<$ 1, where $a$ is the grain radius, are inefficient emitters in the
infrared (see Hanner et al., 1994; Lisse et al., 1998, 2004). Our Spitzer 16
$\mu$m, 24 $\mu$m, and 70 $\mu$m images were analysed to characterize the
continuum emission created by $\mu$m-sized and larger grains in SW1’s
quiescent dust coma. We note that micron and sub-micron sized grains also
contain silicate emission bands between $\sim 8-13$ $\mu$m and at $\sim$ 20
$\mu$m, which probably contribute a few percent to the flux in the 24 $\mu$m
images (see Schambeau et al., 2015, Figures 13 and 14). However, a detailed
analysis of these emission features and their relatively minor impacts on the
24 $\mu$m imaging is beyond the scope of our current work.

In this section we take advantage of these thermal infrared images in
combination with Spitzer’s stable and well characterized point spread function
(PSF) in order to accurately isolate SW1’s dust coma flux contributions in
each image. We assumed that the dominant grain sizes contributing to the
detected flux in each band were approximately the size of their effective
monochromatic bandpass wavelengths: 15.80 $\mu$m, 23.68 $\mu$m, and 71.42
$\mu$m (as used by e.g., Bauer et al. (2015, 2017a)).

To aid in the analysis of comae morphology, it is useful to reference an
idealized “canonical” coma, containing an isotropic and steady state emission
of dust grains from the nucleus, with negligible dust grain fragmentation and
solar radiation pressure. This canonical coma has a surface brightness profile
following a $1/\rho$ behavior (where $\rho$ is the skyplane projected
conetocentric distance from the nucleus’s position), and is assumed in the
derivation of the often used $Af\rho$ and $\epsilon f\rho$ parameters (A’Hearn
et al., 1984; Lisse et al., 2002; Kelley et al., 2013) that are described in
more detail in Section 3.1.2. In practice the assumptions used to derive
$\epsilon f\rho$ break down for real comae, but its calculation provides a
first order estimate of comae dust production behaviors. SW1 experienced
quiescent activity for at least two months surrounding the UT 2003 Nov. epoch
of Spitzer observations, based on Minor Planet Center (MPC) reported magnitude
measurements222Minor Planet Circulars: 49762, 49871, 49872, 49873, 50347,
50348., so the canonical coma assumption is reasonable for these observations.

####  3.1.1 16 $\mu$m and 24 $\mu$m Coma Morphology

Figure 2: Shown is a cropped version of the 24 $\mu$m image (a), along with
enhanced images: (b) division by an azimuthal average, (c) 1/$\rho$ profile
removal, and (d) rotational shift differencing of 18∘. Equatorial north and
east are indicated. The sky-plane projected directions for the Sun and SW1’s
heliocentric velocity vector are indicated by the yellow and red arrows. The
16 $\mu$m image (Figure 1(a)) is shown to highlight the differences in the
field of views between the 16 $\mu$m and 24 $\mu$m images. The large scale
coma morphology shows an increased brightness in the south-west direction,
possibly indicating preferential sunward emission. Also present are a more
compact curved feature initially directed towards the south-southwest, curving
towards the south-east and a linear feature from 1 o’clock to 7 o’clock
similar to that in the 16 $\mu$m image.

The 16$\mu$m blue PU images (Fig. 1) were obtained 1.3 days before the 24
$\mu$m MIPS images (Fig. 2), which were obtained on UT 2003-11-24 15:05. The
16 $\mu$m image’s coma did not display any clearly distinguishable large scale
radial or azimuthal features in either the un-enhanced or enhanced images. A
slight enhancement on the south-southeast through south-west side of the coma
is detected in the division by azimuthal average and the 1/$\rho$-removed
enhanced images (Figure 1(b) and (c)). This is further confirmed in Figure 3,
which displays radial surface-brightness profiles for position angles (PA) at
45∘ spacings for the 16$\mu$m 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 $C/\rho^{n}$ functional form was fit to the profiles for
$\rho$ 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/$\rho$ 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
(south-west).

Figure 3: Radial profiles of the 16 $\mu$m image for different position angles
in SW1. The 16 $\mu$m image is shown in the center of the plots for reference
with the location of the nucleus indicated by a black circle; orientation of
the image is equatorial north up and east to the left. Best-fit profiles are
indicated by the yellow dashed lines for each PA and provided in Table 2. For
reference, included in each plot are two black lines representing a 1/$\rho$
and 1/$\rho^{2}$ coma behavior. The “roller coaster” shaped profile for the
PSF is the result of the Airy diffraction pattern of the space-based
telescope.  Table 2: 16 $\mu$m and 24 $\mu$m Coma Profile Power Law Indices

Position Angle | 16 $\mu$m (14′′ \- 30′′) | 24 $\mu$m (14′′ \- 30′′) | 24 $\mu$m (30′′ \- 130′′) | 24 $\mu$m (200′′ \- 470′′)
---|---|---|---|---
| (56,000 - 120,000 km) | (56,000 - 120,000 km) | (120,000 - 520,000 km) | (800,000 - 1,900,000 km)
0∘ | -1.7 | -1.1 | -0.8 | -1.4
45∘ | -2.1 | -0.9 | -0.7 | -1.5
90∘ | -1.6 | -0.7 | -0.7 | -1.5
135∘ | -1.1 | -0.6 | -0.6 | -1.7
180∘ | -1.0 | -0.7 | -0.6 | -1.1
225∘ | -1.0 | -0.6 | -0.8 | -0.8${}^{\textrm{a}}$
270∘ | -1.0 | -0.9 | -0.9 | -0.9${}^{\textrm{a}}$
315∘ | -1.8 | -0.9 | -1.0 | -1.0${}^{\textrm{a}}$

Note. — ${}^{\textrm{a}}$ The coma surface brightness profile power index
between 30′′ \- 470′′ was best fitted to a single value indicated in the
column to the left.

The overall coma morphology as seen in the unenhanced 24 $\mu$m (Fig. 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/$\rho$-removed enhanced images. The rotational-shift-differenced enhanced
image (Fig. 2(d)) contains a curved wing feature that Stansberry et al. (2004)
attribute to a rotating jet and from which they derived an $\sim$ 60 day
rotation period for SW1’s nucleus. Taking into consideration the great
similarity in the 16 $\mu$m and 24 $\mu$m 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 north-east direction (Li et al., 2014; Farnham &
Schleicher, 2005; Mueller et al., 2013). While the $\sim$ 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 skyplane 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 curved-shapes 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 year baseline, resulting in the
descriptive term of “ringtailed snorter” for this often seen curved shape
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 $\mu$m 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
while quiescent (Jewitt, 1990) vs. impulsive short lived dust emission at high
velocities in the 100-300 m/s range during major outbursts (Trigo-Rodríguez et
al., 2010; Schambeau et al., 2017, 2019; Feldman, 1995).)

The outer edge of the wing feature seen in the 24 $\mu$m image in the south-
west direction (Fig. 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 $\sim$ 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:

$v=\Bigg{[}\frac{2\rho_{g}\beta
g\sin{\alpha}}{(\cos{\gamma})^{2}}\Bigg{]}^{1/2},$ (1)

where, $\rho_{g}$ is the projected sky-plane turn back distance of the dust
grains, $\gamma$ is the angle between the initial direction of the dust grains
and the sky-plane, $\beta$ is the ratio of radiation pressure acceleration to
acceleration due to solar gravity, $\alpha$ 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,
$M_{\odot}$ is the Sun’s mass and $R_{H}$ is the heliocentric distance of the
dust grains). We estimate a $\beta$ value based on equations from Finson &
Probstein (1968) and Fulle (2004):

$\beta=\frac{C_{pr}Q_{pr}}{\rho_{d}d}$ (2)

where $C_{pr}$ is a collection of constants equal to $3E_{\odot}/(8\pi
cGM_{\odot})$, where $E_{\odot}$ 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 $Q_{pr}\approx 1$ is appropriate for the
assumed $d=24$ $\mu$m grains here. We use a value for the dust grain bulk
density based on recent spacecraft visited comae in situ measurements:
$\rho_{d}=500$ kg/m3 (Fulle et al., 2016). With these assumptions we arrive at
an estimated value of $\beta=0.096$. The exact value for $\gamma$ 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: $\gamma=0^{\circ}$ ($v=50$ m/s),
$\gamma=45.0^{\circ}$ ($v=65$ m/s) and $\gamma=80.0^{\circ}$ ($v=270$ m/s).

A similar radial surface brightness profile analysis for the 24 $\mu$m image
is shown in Figure 4. The overall appearance of the coma morphology is similar
to that seen in the 16 $\mu$m image, however the larger field of view (FOV)
and higher S/N coma detection in the 24 $\mu$m image allows 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 $\sim$ 130′′
for PAs between 0 - 180∘ is suggestive of possible ongoing fragmentation for
larger grains out to a projected cometocentric distance of 520,000 km (i.e.,
$\sim$ 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
$\mu$m 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 $\mu$m 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 $\mu$m surface brightness.

Figure 4: Radial profiles of the 24 $\mu$m image for different position
angles. The coma morphology for radial profiles between 0∘ \- 180∘ contains a
knee-shaped feature at $\rho\sim$ 130′′ (520,000 km) that is suggestive of a
projected skyplane length for ongoing coma grain fragmentation and/or the
projected turnback distance of dust grains from solar radiation pressure.
Fitted power law indices corresponding to the yellow, red and orange curves
are presented in Table 2. The location of the nucleus is indicated by the
black circle in the center image. For reference, included in each plot are two
black lines representing a 1/$\rho$ and 1/$\rho^{2}$ coma behavior. The roller
coaster shaped profile for the PSF is the result of the Airy diffraction
pattern of the space-based telescope.

Similar to the 16 $\mu$m image, the coma’s profiles in 24 $\mu$m 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.

####  3.1.2 $\epsilon f\rho$ Measurements and Dust Production Estimates

For this analysis we calculated the $\epsilon f\rho$ 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 $Af\rho$ parameter for
reflected dust flux in the visible (A’Hearn et al., 1984). While the assumed
canonical dust coma used to derive $\epsilon f\rho$ is not valid for many
comets, the utility of $\epsilon f\rho$ comes from it establishing a standard
procedure for estimating comae dust production rates and allowing a relative
comparison between individual comets.

The expression for $\epsilon f\rho$ used is

$\epsilon f\rho(\lambda)=\frac{F_{th}(\lambda)}{\pi
B(\lambda,T_{c})}\times\frac{\Delta^{2}}{\rho},$ (3)

where $\epsilon$ is the emissivity of the dust grains at wavelength $\lambda$,
$f$ is a filling factor expressing the fraction of the photometry aperture
containing dust grains, $\rho$ is the linear aperture radius centered on the
nucleus which is being used to measure the flux, $F_{th}(\lambda)$ is the flux
measured in the photometric aperture for wavelength $\lambda$,
$B(\lambda,T_{c})$ is the Planck function calculated at the color temperature
$T_{c}$ of the dust grains, and $\Delta$ 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 sub-$\mu$m to $\mu$m-sized
amorphous silicate and amorphous carbon grains at a color temperature of
$\sim$ 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 color temperature structure present in the coma
complicating the interpretation of a derived $\epsilon f\rho$ based on an
assumed dust coma with uniform temperature. With these understood limitations,
we used Equation 3 to calculate $\epsilon f\rho$ values for each of the three
bands containing extracted coma flux measurements. Additionally, we calculated
$\epsilon f\rho$ 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 JFCs
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 super-heated sub-$\mu$m 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 $F_{th}(\lambda)$ we subtracted the nucleus’ 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 $\mu$m measured spectral flux density
values for an array of aperture radii along with their associated $\epsilon
f\rho$ measurements for the three color temperature assumptions. Table 3
reports the measured flux and $\epsilon f\rho$ values along with their
associated uncertainties for the largest photometry apertures used for each
image. The 16 $\mu$m’s nearly constant $\epsilon f\rho$ value for aperture
radii larger than $\sim$ 5′′ indicates that the 3-D 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 $\mu$m $\epsilon f\rho$
profile has a slight positive slope indicating deviations from a canonical
1/$\rho$ coma’s expected aperture-independent constant value. The 24 $\mu$m
slope behaviors support the possibility for an overabundance of 24 $\mu$m
sized dust grains for larger cometocentric distances. The steep decrease for
$\epsilon f\rho$ 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).

Figure 5: Top panel: SW1’s coma spectral flux density measurements and
associated $\epsilon f\rho$ measurements for the 16 $\mu$m image. Bottom
panel: Similar to top, but for the 24 $\mu$m image. The 16 $\mu$m image
appears to behave as a canonical dust coma with a semi-independent
relationship between $\epsilon f\rho$ and aperture size, while the 24 $\mu$m
has an increased value with increasing aperture size once past 5′′.

To verify that the difference in aperture photometry for the coma between the
16 $\mu$m and 24 $\mu$m 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
$\mu$m) and W4 (22 $\mu$m) intensity images downloaded from the NASA/IPAC
Infrared Science Archive. W3 and W4 coadded images centered on 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 $\mu$m 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
$9^{\prime\prime}$ radius aperture coma flux measurement. Our earlier reported
70 $\mu$m flux density value (Schambeau et al., 2015) did not included an
aperture correction for the measurement, so the earlier reported flux
measurement is an underestimate. Based on a new reported measurement of 103
$\pm$ 50 mJy, we calculated an $\epsilon f\rho$ value. The large uncertainty
in the derived 70 $\mu$m 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 $\epsilon f\rho$ values to estimate dust production rates
during the Spitzer imaging according to:

$\dot{M}=(\epsilon f\rho)\times\frac{8a\rho_{d}v}{3\epsilon},$ (4)

where $a$ is the radius of the grains, $\rho_{d}$ is the density of the
grains, and $v$ is the radial velocity of the grains lofted from the nucleus’
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 $\mu$m. For the density of the grains we
used the same value of $\rho_{d}$ = 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 based on the lower approximate
values for dust expansion velocity from the 24 $\mu$m coma morphology and
turnback 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 $\epsilon=$ 0.95.
Estimated dust production rates are presented in Table 3.

Table 3: SW1 Thermal Infrared Dust Coma Measurements

Band | $\rho^{\textrm{a}}$ | Flux | $\epsilon f\rho$ | $\dot{M}$ | $\epsilon f\rho$ | $\dot{M}$ | $\epsilon f\rho$ | $\dot{M}$
---|---|---|---|---|---|---|---|---
($\mu$m) | (′′) | (mJy) | (cm) | (kg/s) | (cm) | (kg/s) | (cm) | (kg/s)
|  |  |  $T_{c}$ = 117 K |  $T_{c}$ = 125 K |  $T_{c}$ = 140 K
16 | 20 | 145 $\pm$ 2 | 9400 $\pm$ 150 | 104 $\pm$ 2 | 5600 $\pm$ 90 | 124 $\pm$ 2 | 2600 $\pm$ 43 | 28.8 $\pm$ 0.5
24 | 20 | 570 $\pm$ 24 | 8700 $\pm$ 360 | 144 $\pm$ 6 | 6100 $\pm$ 260 | 101 $\pm$ 4 | 3700 $\pm$ 150 | 61 $\pm$ 3
24 | 200 | 8403 $\pm$ 90 | 13700 $\pm$ 150 | 227 $\pm$ 3 | 9700 $\pm$ 105 | 322 $\pm$ 4 | 5800 $\pm$ 63 | 96 $\pm$ 1
70 | 9 | 102 $\pm$ 50 | 2600 $\pm$ 1300 | 130 $\pm$ 65 | 2300 $\pm$ 1100 | 113 $\pm$ 55 | 1800 $\pm$ 900 | 90 $\pm$ 45

Note. — ${}^{\textrm{a}}$ The radius of the sky-plane projected photometry
aperture.

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

$\log\Bigg{(}\frac{\epsilon f\rho}{\textrm{1
cm}}\Bigg{)}=3.5\Bigg{(}1-\textrm{exp}\Bigg{(}-\frac{D_{N}}{\textrm{5.3
km}}\Bigg{)}\Bigg{)}+N(0,0.25),$ (5)

where $D_{N}$ is the nucleus diameter in km and $N(0,0.25)$ is a Gaussian
distribution with 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. (2017a), and SW1’s measurements from this work.

As Figure 6 shows, Equation 5 fits the SEPCCoN $\epsilon f\rho$ values and SW1
values presented in this work. Interestingly, the expression implies that
comets with nuclei diameters larger $\sim$ 20 km have a flattening of activity
levels when compared to the steep increase of dust activity vs. 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 to 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.

Figure 6: Comparison of measured $\epsilon f\rho$ values vs. nucleus diameter
for comets and Centaurs from two infrared surveys and data presented here for
SW1. The solid black curve indicates the empirically derived relation between
$\epsilon f\rho$ vs. nucleus diameter presented in Bauer et al. (2017a) using
the WISE/NEOWISE detected comets; Equation 5 in this paper. Points for SW1 are
based on the values from Table 3 for the dust temperature of $T=140$ K.
Uncertainties for the 16 $\mu$m and 24 $\mu$m points are smaller than data
markers. The colors of individual markers of the WISE/NEOWISE and SEPPCoN
values indicate the comet’s heliocentric distance at the time of the $\epsilon
f\rho$ measurement. A color bar to the right of the figure indicates the
heliocentric distance color scale.

Reports of SW1’s dust production rate as derived from visible observations
during periods of quiescent activity indicate a typical mass loss rate for
sub-micron sized grains on the order of 1 - 50 kg/s. We arrived at these
typical quiescent dust production rates using reported $Af\rho$ measurements
from Trigo-Rodríguez et al. (2010) and Hosek et al. (2013), but here we use a
value of grain density $\rho_{d}$ = 500 kg/m3 in order to be consistent with
our $\epsilon f\rho$ derived dust production rates. We note that these dust
production rates are upper limits due to their calculated $Af\rho$ 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 $\mu$m to 70 $\mu$m have a higher mass loss rate (Table 3) than
the sub-micron sized coma ($<$ 1 $\mu$m 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 microns or from sub-micron sized grains), enabling
investigations of the quiescent vs. outburst comae activity mechanisms.

####  3.1.3 Coma Modeling

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 in order to consider mixtures of different materials. Effective
medium theories (EMT) 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 $n$($a$) $\propto$ $a^{-\beta}$, where $\beta$ is
the size index and the particle radius takes values from $a_{\rm min}$ to
$a_{\rm max}$. The dust density is taken equal to 500 kg/m3. The effect of ice
sublimation on the equilibrium grain temperature was not taken into account,
as it has been shown that radiative cooling dominates over cooling 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 a Fe:Mg composition of 50:50;
2) a matrix of crystalline ice with inclusions of amorphous carbon; 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 mass of $\sim$ 45%, but have different
optical properties.

Other parameters set in the model are the dust maximum size $a_{\rm max}$ and
the dust velocity as a function of particle size, described as varying
$\propto$ $a^{-0.5}$, with a value of 60 m/s for 10-$\mu$m particles. The
maximum liftable size from the surface of SW1’s nucleus is estimated to be
$a_{\rm max}$ = 250 $\mu$m, for a CO-driven activity restricted to a spherical
segment with half-angle of 45∘ and a total CO production rate of 4 $\times$
1028 s-1, assuming our nucleus radius estimate of 32.3 km (Section 3.2) and a
nucleus density of 500 kg/m3 (V. Zakharov, 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 $\mu$m, for comparison with Spitzer data. Simulations were made for
a minimum dust particle size $a_{\rm min}$ in the range 0.5–50$\mu$m 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 $a_{\rm min}$ and high $\beta$ values resulting in a
higher dust color temperature. The Spitzer constraints are flux densities in a
9” FOV radius of 64 $\pm$ 2 mJy, 198 $\pm$ 14 mJy, 103 $\pm$ 50 mJy at 16, 24
and 70 $\mu$m, respectively. This corresponds to color temperatures of
$T_{16/24}$ = 129 $\pm$ 5 K, based on the 16 & 24 $\mu$m fluxes, and
$T_{24/70}$ = 177${}^{+52}_{-47}$ K based on the 24 & 70 $\mu$m fluxes.
$T_{16/24}$ and $T_{24/70}$ are consistent within 1-$\sigma$ with a value of
$\sim$ 130 K, but the high central value of $T_{24/70}$ resulting from the
relatively faint 70$\mu$m flux might suggest an excess of small particles
poorly radiating at long wavelengths.

Figure 7 shows iso-contours of $T_{16/24}$ (black plain lines) and $T_{24/70}$
(dashed blue lines) as a function of $a_{\rm min}$ and $\beta$. Domains
consistent with measured $T_{16/24}$, $T_{24/70}$ values are filled in orange
and blue colors, respectively. We only show results for ice-carbon mixtures 2)
and 3), since results for 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 $a_{\rm min}$ = 2–5 $\mu$m, whereas no overlapping is
observed for mixture 2) for any set of ($a_{\rm min}$,$\beta$). Grains made of
mixture 2) are hotter than other mixtures for sizes below 30$\mu$m (Fig. 8),
and this explains the different infrared spectra.

Figure 7: Modelled dust color temperatures $T_{16/24}$, $T_{24/70}$ as a
function of minimum particle size and size index, for ice/carbon mixtures 2
(panel A) and 3 (panel B). Black plain lines show contours at constant
$T_{16/24}$, in steps of 10 K. Blue dashed lines show contours at constant
$T_{24/70}$, in steps of 10 K, for $T_{24/70}$ $\geq$ 130 K. Color
temperatures consistent with Spitzer measured $T_{16/24}$ and $T_{24/70}$
values are colored in orange and blue, respectively. The assumed maximum
particle size is $a_{\rm max}$ = 250 $\mu$m.

In Figure 9, we show dust production rates derived from the 24 $\mu$m flux
density using the ($a_{\rm min}$,$\beta$) parameters that provide $T_{16/24}$
values consistent with the measured value, i.e., those defining the orange
region in Fig. 7. For mixtures 1) and 3) with matrices of amorphous carbon,
the range is 50–200 kg/s. The low end is obtained for the highest ($a_{\rm
min}$,$\beta$) values (= (5$\mu$m, 4.1–4.4)), that is a steep size
distribution where 5–10 $\mu$m grains dominate the infrared emission. For size
distributions with $a_{\rm min}$= 4–5 $\mu$m, the dust production rates
deduced from the 24 and 70-$\mu$m fluxes are consistent, and in the range
50–100 kg/s. However, this is not the case for size distributions with small
$a_{\rm min}$ values (and consequently low $\beta$ values, Fig. 7), for which
70-$\mu$m derived dust production rates are by a factor 2–3 lower than those
deduced from the 24-$\mu$m flux. For the ice/carbon mixture 2 (matrix of
crystalline ice), the dust production rate inferred from the 24 $\mu$m flux is
between 130–240 kg/s (Fig. 9). The values derived from the 70 $\mu$m flux are
more than 2 times lower for all sets of ($a_{\rm min}$,$\beta$) parameters.
This is an expected result since for this composition, the model fails in
reproducing both the $T_{16/24}$ and $T_{24/70}$ values.

Figure 8: Temperature of the dust particles as a funtion of particle radius.
Results for mixtures 1 (matrix of carbon with ice inclusions), 2 (matrix of
ice with carbon inclusions), and 3 (matrix of carbon with olivine inclusions)
are shown in blue, turquoise and red, respectively.

The dust production rates derived with model parameters leading to a
satisfactory fit to data (50–100 kg/s) 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 particle size distribution and thermal properties.
The obtained results are here limited due to the low SNR of the 70 $\mu$m 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 modelling
dust spectra (Lien, 1990; Mishchenko & Travis, 2008).

Figure 9: Dust production rates derived from the 24-$\mu$m flux density
measured in a 9” FOV radius, using ($a_{\rm min}$,$\beta$) parameters
providing color temperature $T_{16/24}$ values consistent with the measured
value of 129 $\pm$ 5 K. The range of production rate values for a given
minimum size reflects the range of $\beta$ values fulfilling the requirement,
and the uncertainty in the 24-$\mu$m flux. Results for mixtures 1, 2, and 3
are shown in blue, turquoise and red, respectively.

####  3.1.4 Coma Color Temperature Map

In Figure 10, a color temperature map of the coma based on the 16 $\mu$m and
24 $\mu$m 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 vs. coma flux contributions is described in
Section 3.2 for the 16 $\mu$m image, and in our earlier work (Schambeau et
al., 2015) for the 24 $\mu$m 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 under subtraction 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 $\mu$m 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
than the values derived from fitting a Planck blackbody profile to the
individual pixel values from the 16 $\mu$m and 24 $\mu$m images due to the
silicate emission features present in the 24 $\mu$m bandpass and the dust coma
PSD (Wooden, 2002; Markkanen & Agarwal, 2019). The peak temperature of the
grains of $\sim$ 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).

Figure 10: Coma color temperature map based on the 16 $\mu$m and 24 $\mu$m
images.

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 $\sim$ 20 degrees. 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 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 sub-micron sized grains, resulting in an
enhanced 24 $\mu$m emission above that of an ideal blackbody due to the
silicate emission bands around 20 $\mu$m. 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 $\mu$m and
24 $\mu$m 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
$\mu$m, 24 $\mu$m, and 70 $\mu$m and dust mass fractions $X_{16}$ = 0.5,
$X_{24}$ = 0.40, $X_{70}$ = 0.25 (Mukai, 1986; Beer et al., 2006; Lien, 1990).
The lifetimes of the water ice content of the grains is respectively: 112
days, 154 days, 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 non-nuclear
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
$Q_{\textrm{H}_{2}\textrm{O}}$ $\sim$ 3 - 7$\times$1027 molecules/s (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 $\epsilon
f\rho$. As a first order estimate of the coma’s $Q_{\textrm{H}_{2}\textrm{O}}$
due to the sublimation of icy grains, we calculated the production rate that
would be produced from 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 estimate range of $Q_{\textrm{H}_{2}\textrm{O}}\sim$ (1 - 3)$\times
10^{27}$ molecules/s, supporting the argument that the measured water
production rates may be explained by a non-nuclear source of icy grains in the
coma.

###  3.2 Nucleus Spectral Flux Density Measurements and a new NEATM

To obtain nucleus photometry measurements from the blue PU images, the flux
from SW1’s coma was modeled and removed. We used a well-established coma
modeling technique (Lamy & Toth, 1995; Lisse et al., 1999; Fernandez, 1999)
for this procedure, where the azimuthal coma behavior is measured in regions
outside of significant contribution from the nucleus’ PSF in order to generate
a synthetic coma model. The model coma’s flux contribution is then subtracted
from the observations resulting in an approximately bare-nucleus residual
image. The residual image is then used to scale an STINYTIM generated PSF
(Krist, 2006) to represent the nucleus’s total flux. The reader is referred to
our previous work (Schambeau et al., 2015) for a detailed description of this
procedure.

The coma modeling and removal procedure was applied to each of the PU images
resulting in six independent nucleus photometry measurements from six images
at an effective 15.8 $\mu$m wavelength. The individual color corrected
measurements are: 84.1, 85.0, 85.0, 87.5, 89.6, and 88.4 mJy, with a typical
uncertainty of $\pm$ 7 mJy. The final measurement used for thermal modeling
analysis was taken as the average of the individual measurements: 86 $\pm$ 2
mJy, with the stated 1-$\sigma$ uncertainty being the standard deviation of
the six measurements.

Figure 11 shows the new 15.8 $\mu$m measurement plotted along with the other
four Spitzer nucleus photometry values that we reported earlier (Schambeau et
al., 2015). We also plot the best-fitting 4-band thermal model (NEATM, Harris
(1998)) that we used in the earlier work to extract the nucleus’ effective
radius $R$ = $30.2^{+3.7}_{-2.9}$ km and beaming parameter $\eta$ =
0.99${}^{0.26}_{-0.19}$. A re-fit using the now five spectral flux density
measurements produces a nucleus size estimate and infrared beaming parameter
that are slightly larger, but within the 1-sigma uncertainties of the earlier
results: $R=32.3\pm 3.1$ km and $\eta=1.1\pm 0.2$. We propose these new values
be used in future investigation of SW1 in lieu of our earlier analysis
(Schambeau et al., 2015), because of the reduced uncertainty due to modeling
with five, rather than four points. For our new NEATM analysis similar
assumptions as those used for our previous work and for (e.g.) SEPPCoN
(Fernández et al., 2013) were used: bolometric bond albedo $A=0.012$ (assuming
a visible-wavelength geometrical albedo $p=0.04$ and phase integral relation
$q=0.290+0.684G$, (Harris & Lagerros, 2002), emissivity $\epsilon=0.95$, and
slope parameter $G=0.05$.

Figure 11: Five spectral flux density measurements of SW1, incorporating the
new blue PU data at 16$\mu$m, all acquired during 2003 November with Spitzer.
Also shown is a new 5-band NEATM, which produces a nucleus radius estimate and
infrared beaming parameter of $R=32.3\pm 3.1$ km and $\eta=1.1\pm 0.2$, along
with the previous 4-band NEATM from Schambeau et al. (2015). Uncertainties are
1-$\sigma$. The consistently higher than fit value for the 8 $\mu$m
measurement may be the result of enhanced emission due to silicate emission
bands in this region.

##  4 Summary and Conclusions

A more detailed analysis of November 2003 Spitzer observations of SW1
(Schambeau et al., 2015) is presented, which incorporates 16$\mu$m data for
the first time, and significantly improves characterization of the Centaur’s
tens of microns dust coma during a period of quiescent activity.

The 16 $\mu$m blue PU images were remarkably symmetric with evidence for an
$\sim$ 70 percent coma enhancement in the south-southeast direction, which may
be reflective of tail formation. The 16 $\mu$m coma’s morphology indicated
preferential sunward emission of dust grains. No signs of grain fragmentation
were indicated by the data within the image FOV (273,000 $\times$ 386,000 km).

Re-analysis of the 24 $\mu$m images reveal a large scale coma morphology of
increased brightness in the southwest direction, consistent with preferential
sunward emission. These data also show a more compact wing feature initially
directed toward the south-southwest to a projected cometocentric distance of
352,000 km (90′′) and curving toward the southeast. This feature has
previously been interpreted to be due to the nucleus’ rotation, but we propose
instead that this is the result of solar radiation pressure effects and
gravity on micron sized dust grains that were emitted in the sunward direction
and were turned back to form a dust tail. Further analysis of this feature is
encouraged. Interestingly, analysis of the 24 $\mu$m surface brightness radial
profiles shows a noticeable change of slope at $\sim$ 520,000 km cometocentric
distance at positions angles $\sim$ 0 through 180 degrees. This change in
slope is consistent with the projected distance to the outer edge of the
curved feature. We used measurements of this turning-back point of the curved
feature to estimate a dust grain outflow velocity in the range of 50$-$270 m/s
depending on the ejection direction of grains.

Using the improved 140 K color temperature measured from the IRS spectrum
(Schambeau et al., 2015) and in this work (Section 3.1.4) we calculated the
$\epsilon f\rho$ parameters: 16 $\mu$m (2600 $\pm$ 43 cm), 24 $\mu$m (5800
$\pm$ 63 cm), and 70 $\mu$m (1800 $\pm$ 900 cm). SW1’s values were found to
follow the $\epsilon f\rho$ vs. nucleus size relation observed from the
WISE/NEOWISE observed comets (Bauer et al., 2017a). Additionally, for the
first time, we compare the WISE/NEOWISE and SEPPCoN (Kelley et al., 2013)
derived $\epsilon f\rho$ measurements and see agreement between the two
surveys, strengthening the argument for the empirically derived relationship’s
application as a predictor of cometary comae.

A coma model (Bockelée-Morvan et al., 2017) was used to constrain the coma’s
dust grain size distribution and mass loss rate. The model was constrained by
9′′ radius aperture photometry measurements of 16 $\mu$m, 24 $\mu$m, and 70
$\mu$m coma flux density. Models with a dust grain composition of a matrix of
amorphous carbon with inclusions of (1) amorphous olivine or (2) crystalline
water ice were in agreement with the Spitzer data. The two models had similar
ranges for the best-fit grain size distributions: power-law index $\beta$
ranging from 4.1 to 4.4, minimum grain size $a_{\rm min}$ ranging from 4
$\mu$m to 5 $\mu$m, and maximum grain radius $a_{\rm max}$ = 250 $\mu$m. The
dust production rates derived with model parameters leading to a satisfactory
fit to data (50–100 kg/s) are in overall agreement with those estimated using
the measured $\epsilon f\rho$ values.

Using the 16 $\mu$m and 24 $\mu$m images we constructed a coma color-
temperature map, which also peaks at $\sim$ 140 K, decreasing with increasing
cometocentric distance, and an east-to-west asymmetry with the eastern coma
being $\sim$ 20 degrees higher. This behavior is the result of a particle size
distribution of grains of varying compositions. Future analyses of these data
are encouraged to better constrain SW1’s large grain coma environment.

We used the 140 K color temperature as a plausible physical temperatures for
individual grains. This assumption is supported by our earlier analysis of the
IRS spectrum (Schambeau et al., 2015). Using the dust production rates
measured here we estimated a H2O production rate from the sublimation of icy
coma grains: $Q_{\textrm{H}_{2}\textrm{O}}\sim$ (1 - 3)$\times 10^{27}$
molecules/s. This range agrees with other measurements of SW1’s water
production rate (Ootsubo et al., 2012; Bockelée-Morvan & et al., 2021)

Coma modeling and its removal from the IRS blue PU imaging data at 16 $\mu$m
were used, along with measurements at other infrared wavelengths, to produce a
nucleus radius of $R$ = 32.3 $\pm$ 3.1 km for SW1, which is within 1-$\sigma$
of and has smaller uncertainties than prior measurements using Spitzer data
(Stansberry et al., 2004, 2008; Schambeau et al., 2015). This analysis also
yields a slightly higher NEATM derived beaming parameter ($\eta=1.1\pm 0.2$).
The size of SW1 places it on the smaller end of the currently-known Centaur
size distribution (Bauer et al., 2013; Duffard et al., 2014; Lellouch et al.,
2013), but on the larger end for small bodies with known cometary activity
(Stansberry et al., 2008; Fernández et al., 2013). With the refined nucleus
size estimate presented here, we encourage future modeling efforts to better
understand the bound inner coma environment of SW1.

The Centaur SW1’s large size among active objects, in combination with its
orbital history that indicates it has not spent a significant amount of time
interior to Jupiter (Sarid et al., 2019), positions it as a high-priority
target for future observational and in situ investigations to better
understand moderately sized and relatively pristine planetesimals to better
understand the period of thermal evolution experienced while in the gateway
transition from Centaur to JFC. We encourage the community to undertake new
observations of SW1 and also for any currently existing and planned new
observations to be listed on the SW1 observing campaign website:
wirtanen.astro.umd.edu/29P/29P_obs.shtml. Additionally, we provide here links
to the following resources emphasizing the importance of continued
observations of SW1 and best practices for new observations: (1) the call for
observations from Womack et al. (2020) and (2) a guide for new observations
provided by the British Astronomical Association (Miles, 2019).

We would like to thank Dr. Richard Miles for his helpful discussions during
the preparation of this manuscript. Additionally, we would like to thank our
two anonymous reviewers, who’s thorough review of the manuscript provided
improvements to the presentation of the analyses. We also thank the NASA Earth
and Space Science Fellowship (NNX16AP41H) and the Center for Lunar and
Asteroid Surface Science (CLASS, NNA14AB05A) for support of this work. This
work is based on observations made with the Spitzer Space Telescope, which is
operated by the Jet Propulsion Laboratory, California Institute of Technology
under a contract with NASA. This research made use of Tiny Tim/Spitzer,
developed by John Krist for the Spitzer Science Center. The Center is managed
by the California Institute of Technology under a contract with NASA. This
publication makes use of data products from the Wide-field Infrared Survey
Explorer, which is a joint project of the University of California, Los
Angeles, and the Jet Propulsion Laboratory/California Institute of Technology,
funded by the National Aeronautics and Space Administration.

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