# Non-detection of water-ice grains in the coma of comet 46P/Wirtanen and
implications for hyperactivity

Silvia Protopapa Visiting Astronomer at the Infrared Telescope Facility, which
is operated by the University of Hawaii under contract 80HQTR19D003 with the
National Aeronautics and Space Administration.  Southwest Research Institute,
1050 Walnut Street, Suite 300, Boulder, CO 80302, USA  Michael S. P. Kelley
Visiting Astronomer at the Infrared Telescope Facility, which is operated by
the University of Hawaii under contract 80HQTR19D003 with the National
Aeronautics and Space Administration.  Department of Astronomy, University of
Maryland, College Park, MD 20742, USA  Charles E. Woodward  Visiting
Astronomer at the Infrared Telescope Facility, which is operated by the
University of Hawaii under contract 80HQTR19D003 with the National Aeronautics
and Space Administration.  Minnesota Institute for Astrophysics, University of
Minnesota, Minneapolis, MN 55455, USA  Bin Yang Visiting Astronomer at the
Infrared Telescope Facility, which is operated by the University of Hawaii
under contract 80HQTR19D003 with the National Aeronautics and Space
Administration.  European Southern Observatory, Alonso de Còrdova 3107,
Vitacura, Casilla 19001, Santiago, Chile

(Received September 30, 2020; Revised October 25, 2020; Accepted June 30,
2021)

###### Abstract

Hyperactive comets have high water production rates, with inferred sublimation
areas of order the surface area of the nucleus. Comets 46P/Wirtanen and
103P/Hartley 2 are two examples of this cometary class. Based on observations
of comet Hartley 2 by the Deep Impact spacecraft, hyperactivity appears to be
caused by the ejection of water-ice grains and/or water-ice rich chunks of
nucleus into the coma. These materials increase the sublimating surface area,
and yield high water production rates. The historic close approach of comet
Wirtanen to Earth in 2018 afforded an opportunity to test Hartley 2 style
hyperactivity in a second Jupiter-family comet. We present high spatial
resolution, near-infrared spectroscopy of the inner coma of Wirtanen. No
evidence for the 1.5- or 2.0-µm water-ice absorption bands is found in six
0.8–2.5 µm spectra taken around perihelion and closest approach to Earth. In
addition, the strong 3.0-µm water-ice absorption band is absent in a 2.0–5.3
µm spectrum taken near perihelion. Using spectroscopic and sublimation
lifetime models we set constraints on the physical properties of the ice
grains in the coma, assuming they are responsible for the comet’s
hyperactivity. We rule out pure water-ice grains of any size, given their long
lifetime. Instead, the hyperactivity of the nucleus and lack of water-ice
absorption features in our spectra can be explained either by icy grains on
the order of 1 $\mu$m in size with a small amount of low albedo dust (greater
than 0.5% by volume), or large chunks containing significant amounts of water
ice.

Short period comets (1452); Coma dust (2159); Near Infrared astronomy (1093)

††journal: The Planetary Science Journal††facilities: NASA IRTF
(SpeX)††software: astropy (Astropy Collaboration et al., 2018), JPL Horizons
(Giorgini et al., 1996), IDL, Spextool (Cushing et al., 2004)

##  1 Introduction

The Deep Impact eXtended Investigation (DIXI) flyby of comet 103P/Hartley 2
(hereafter, H2) provided new insight into the role of water ice and its
relation to the activity level of comets (A’Hearn et al., 2011). H2 is a
hyperactive comet, i.e., a comet with an extremely high water production rate
for the given nucleus size. Cometary activity is commonly expressed in terms
of active fraction: the surface area of water ice needed to sustain the
activity, generally referred to as “minimum active area” (Keller, 1990; Combi
et al., 2011), divided by the surface area of the nucleus. For most comets,
the active fraction is typically between a few percent to 30% (A’Hearn et al.
1995, after correcting for the factor of 2 error noted by Knight et al. 2021;
see also Lis et al. 2019). Hyperactive comets are unusual in that their gas
production rates require an active fraction of $\sim$100% (A’Hearn et al.,
1995). In the specific case of H2, Combi et al. (2011) estimated an active
fraction of $\sim$100% during the 2010 apparition. However, rather than a 100%
active surface, Deep Impact’s close up view of H2 on November 2010 revealed
heterogeneous surface activity, dominated by a single small active area
(A’Hearn et al., 2011). This area produced bright jets in the inner few
kilometers of the coma, enriched in CO2 gas and pure water-ice grains on the
order of 1 $\mu$m in diameter (Protopapa et al., 2014). These observations of
H2 have formed the basis for our current understanding of comet hyperactivity:
the ejection of water-ice grains into the coma increases the available surface
area for water sublimation, which in turn contributes to the high observed
water production rate. However, this remains an hypothesis given that the
contribution of the small icy grains to the comet’s water production rate was
poorly constrained. In addition to the 1-$\mu$m water-ice grains, a second
population of particles was detected: distinct, isolated grains that in
visible images surround the nucleus of H2, estimated by their brightness to be
cm-sized or larger (Kelley et al., 2013, 2015). The true composition of these
particles is unknown. However, if these would be ice-rich chunks and would
behave as mini-comet nuclei with photometric properties similar to the nucleus
of H2, they could account for the comet’s hyperactivity (Kelley et al., 2015).
Therefore, to summarize, sublimating water-ice in the coma, whether in the
form of small grains and/or in large chunks of nucleus, could explain the high
activity fraction of comet H2.

To test the scenario laid out by Deep Impact’s observations at comet H2, and
to verify whether the H2 case is an isolated phenomenon or other small
hyperactive comets display a water-ice grain halo, we took advantage of the
historic close approach between Earth and comet 46P/Wirtanen (2018 December
16, 0.078 au from the Earth and 1.1 au from the Sun, hereafter Wirtanen).
Similar to H2, comet Wirtanen: (1) has a sub-km radius (0.56$\pm$0.04 km;
Boehnhardt et al., 2002; Lamy et al., 2004); (2) belongs to the Jupiter-family
comet dynamical class; and (3) is hyperactive (Lamy et al., 1998; Groussin &
Lamy, 2003; Lis et al., 2019). Because Wirtanen strikingly resembles comet H2
in dynamical class, size, and activity level, it represents the best target to
test the hypothesis of hyperactivity framed by the DIXI observations and
therefore to look for evidence of water ice in its coma.

Low resolution reflectance spectroscopy (0.8–5.3 µm) is ideally suited for
detecting water-ice grain halos in cometary comae through the identification
of the broad water-ice absorption bands at 1.5, 2.0, 3.0 and 4.5 $\micron$
(e.g., Fink & Sill, 1982; Warren, 1984; Mastrapa et al., 2008, 2009). The
relative strength and shape of these features give us information on the
abundance, grain size and purity (i.e., fraction of refractory materials) of
the water ice. Direct detection of ice grains in cometary comae via near-
infrared spectroscopy has been reported not only by means of in situ
observations (Sunshine et al., 2007; A’Hearn et al., 2011; Protopapa et al.,
2014) but also through ground-based facilities (Davies et al., 1997; Kawakita
et al., 2004; Yang et al., 2009; Yang & Sarid, 2010; Yang et al., 2014;
Protopapa et al., 2018).

Once in the coma, the observability of water-ice grains is controlled by the
ice grain sublimation lifetime, which strongly depends on the presence of
refractory material (i.e., “impurities”) within the grain, grain size, and
heliocentric distance ($R_{\mathrm{h}}$). Theoretical considerations by Hanner
(1981) established that dirty ice grains have very short lifetimes at 1 au
from the Sun, on the order of a few hundred seconds, depending on their size.
Pure ice grains generally have longer lifetimes, varying from hours to
hundreds of years for grains of radius of 1 µm and 50 µm, respectively. This
analysis led to the general understanding that, unless water-ice grains are
pure, their detection is difficult at small heliocentric distances. An example
is given by comet C/2013 US10 Catalina (hereafter US10): ground-based near
infrared spectroscopic measurements revealed clear evidence of water-ice
grains in the coma when the comet was at large heliocentric distances
($R_{\mathrm{h}}\geq 3.9$ au), while a featureless spectrum was recorded at
$R_{\mathrm{h}}\lesssim 2.5$ au (Protopapa et al., 2018). The changing ice
fraction in the coma has been interpreted by Protopapa et al. (2018) in terms
of the limited lifetime of the water-ice grains with respect to the field-of-
view when closer to the Sun. Under the assumption that the ice was
continuously ejected from the nucleus, the non-detection of water-ice
absorption bands close to perihelion enabled them to further constrain the
physical properties of the grains and rule out the case of pure icy grains.
Micrometer-sized grains of water ice mixed with a small fraction of low-albedo
dust, 0.5% by volume, were found to be consistent with all US10 spectroscopic
measurements. Additionally, based on the presence of a CO2 coma, the authors
put forth the idea of US10 being a possible hyperactive comet, although the
nucleus size is still unknown.

The close approach of comet Wirtanen to Earth enabled exceptional spatial
scale observations (1″$\geq$60 km), which are critical for detecting water ice
at 1 au from the Sun, given the limited water-ice lifetime at such
heliocentric distances. Specifically, 1-$\mu$m pure water-ice grains similar
to those observed by Deep Impact at comet H2 should be detectable from the
ground in the coma of Wirtanen during the comet’s closest approach to Earth
(see Section 3.6). Nevertheless, as noted by A’Hearn et al. (1981), even a non
detection of solid state water in spectroscopic measurements does not rule out
the presence of ice. Instead, when combined with ice sublimation models, it
enables us to set constraints on the physical properties of the water ice.

Here, we present NASA Infrared Telescope Facility (IRTF) SpeX observations of
the hyperactive comet Wirtanen during its closest approach to Earth (Section
2) acquired with the objective of addressing the question: can the present
model for hyperactivity based on comet H2 be generalized to other hyperactive
comets? A series of near-infrared spectroscopic observations of comet Wirtanen
were collected to monitor and assess the composition of ejected grains as
insolation varies on the nucleus, due to changes in heliocentric distance, and
as the comet undergoes vigorous coma activity. The spectral results and the
sensitivity to detect water ice are discussed in Section 3.1, while the
contribution of the nucleus to the observed flux density is presented in
Section 3.2. The spectral modeling used to interpret the data and the
constraints derived on the dust properties are outlined in Sections 3.3 and
3.4, respectively. Sections 3.5 and 3.6 provide constraints on the relative
abundance and physical properties (i.e., purity and grain size) of the water-
ice grains in the coma based on spectroscopic and sublimation lifetime models,
respectively. Specifically, we test for the presence of water-ice grains with
physical properties identical to those detected in the coma of H2 and US10, a
confirmed and hypothetical hyperactive comet, respectively. The lack of
variation in the color of the dust across our observational data set is
discussed in Section 3.7. A summary and discussion follows in Section 4.

Figure 1: IRTF SpeX prism mode observations of Wirtanen acquired at
$|R_{\mathrm{h}}|$ between 1.05–1.11 au, binned to a spectral resolution of
$\sim$300 at 2.0 µm. Right panel: Spectra are normalized between 0.98 and 1.02
µm to unity. Overplotted is the best fit model (solid line) of the C/2013 US10
observations acquired at $|R_{\mathrm{h}}|\geq$3.9 au consistent with the
presence of water-ice grains of uniform size, with a diameter of 1.2 µm, and a
coma ice-to-dust ratio of 0.18 (Protopapa et al., 2018). Left panel: Spectra
are normalized to unity between 0.98 and 1.02 µm and shifted along the y-axis
by values shown in parentheses. The gray shaded rectangles are regions of
strong telluric absorption. The spectra show no water-ice absorption features.
The data used to create this figure are available.  Table 1: Observational
Parameters for 46P/Wirtanen.

UT date | Mode | Slitaafootnotemark:  | AMtargetbbfootnotemark:  | SA (spectral type)ccfootnotemark:  | AMSAddfootnotemark:  |  $R_{\mathrm{h}}$eefootnotemark:  |  $\Delta$fffootnotemark:  | T-magggfootnotemark:  | Shhfootnotemark:  | STOiifootnotemark:
---|---|---|---|---|---|---|---|---|---|---
(YYYY-MM-DD HR:MN) |  | (arcsec) |  |  |  | au | au |  | %/(100 nm) | deg
2018-11-27 06:55 | Prism | 0.8$\times$15 | 1.51$\pm$0.03 | HD 17883 (G2V C) | 1.64$\pm$0.01 | -1.076 | 0.14 | 12.3 | — | 46.5
2018-12-13 06:55 | Prism | 0.8$\times$60 | 1.10$\pm$0.03 | HD 25680 (G5V C) | 1.04$\pm$0.01 | +1.055 | 0.08 | 11.1 | 1.9 | 26.4
2018-12-13 08:36 | LXD$\\_$l | 0.8$\times$15 | 1.01$\pm$0.01 | HD 21379 (A0V C) | 1.03$\pm$0.01 | +1.055 | 0.08 | 11.1 |  | 26.3
2018-12-15 07:08 | Prism | 0.8$\times$60 | 1.07$\pm$0.03 | HD 30246 (G5 D) | 1.11$\pm$0.01 | +1.056 | 0.08 | 11.1 | 2.3 | 22.2
2018-12-17 06:20 | Prism | 0.8$\times$60 | 1.21$\pm$0.01 | HD 30246 (G5 D) | 1.16$\pm$0.01 | +1.057 | 0.08 | 11.1 | 2.1 | 19.2
2018-12-28 07:03 | Prism | 0.8$\times$60 | 1.55$\pm$0.02 | HD 30246 (G5 D) | 1.51$\pm$0.01 | +1.076 | 0.10 | 11.8 | 1.9 | 27.7
2019-01-07 12:51 | Prism | 0.8 $\times$60 | 1.36$\pm$0.01 | HD 292561 (F8 E) | 1.31$\pm$0.01 | +1.110 | 0.16 | 12.7 | 2.5 | 33.2

aafootnotemark:

Slit width $\times$ slit length. bbfootnotemark: Average airmass of the comet
observations. ccfootnotemark: Star used for calibration purposes, its spectral
type and precision from SIMBAD. ddfootnotemark: Average airmass of the solar
type star observations. eefootnotemark: The Sun-to-target distance ($<$0 au
indicates pre-perihelion epochs). fffootnotemark: The target-to-observer
distance. ggfootnotemark: Comet’s approximate apparent visual total magnitude
as reported by Horizons. hhfootnotemark: Comet spectral slope (at 1 µm). The
uncertainty is 0.3 %/100 nm (see text for details). iifootnotemark: The Sun-
Target-Observer angle as reported by Horizons, which differs from the true
phase angle at the few arcsecond level.

##  2 Observations

Observations of Wirtanen were obtained using the IRTF/SpeX (Rayner et al.,
1998, 2003) high-throughput low-resolution prism mode covering the wavelength
range 0.7–2.52 µm (Fig. 1, Table 1), under program IDs 2018B006, 2018B088,
2018B132. All observations were acquired with the 0$\farcs$8$\times$15″ or
0$\farcs$8$\times$60″ slit configurations, resulting in a spectral resolving
power ($R=\lambda/\Delta\lambda$) of $\sim$112 at 2.0 µm. We reduced the data
using IDL codes, based on Spextool (Cushing et al., 2004). The latter does not
reduce observations taken with the 60″ long slit, which was used extensively
in our observing campaign to optimize the background subtraction in the
standard infrared method of moving the object between two positions A and B on
the slit. Given the high activity of the comet and extended coma, the 60″ long
slit prevented the overlapping of the cometary coma in the A and B pair
images. Spectra were extracted, then wavelength calibrated and combined using
a robust mean with a 2.5$\sigma$-clipping threshold. The uncertainty is given
by the standard deviation on the good pixels. Calibrated spectra were binned
by 3 pixels to yield a spectral resolution ($\lambda/\Delta\lambda$, where
$\Delta\lambda$ represents the spectral sampling) of $\sim$300 at 2.0 µm (Fig.
1). The spectral extraction aperture was set to the limit beyond which the
object’s signal does not improve and only the noise increases. This means that
the choice of aperture size is a compromise between statistical noise and
photometric accuracy. The spectral extraction radius varied between 1″ on 2018
November 27 and 7″ close to perihelion.

Figure 2: Spectral variations among the solar type reference stars observed
during the Wirtanen campaign. The ratio between each solar type star (SA) and
a reference one, arbitrarily chosen, HD 30246 (G5 D) observed on 2018 December
17, is displayed, normalized to unity between 0.98 and 1.02 $\mu$m. Overlaid
on each ratio spectrum is the linear model (solid black line). The spectral
slope resulting from the linear fit, expressed in %/100 nm, is reported in
each panel.

To remove telluric absorptions, instrumental effects, and the solar spectrum,
all Wirtanen observations were interspersed between observations of solar type
stars. The comet-to-solar-type-star ratio produced a spectrum proportional to
the comet reflectance. We notice that the correction of telluric features in
our comet spectra (Fig. 1) is sometimes imperfect not only near 1.4 and 1.9
µm, where telluric H2O vapor absorption occurs, but also near 2.0 µm, where
lies strong and narrow telluric CO2 absorptions (marked in the figure), which
make sky transparency variable in time. It was not possible to always observe
the same star, and stars with spectral type G2, G5, and F8 were adopted for
calibration purposes (Table 1). To investigate the spectral variations
introduced by the different calibration stars, we have compared the ratios of
each solar type star to a common reference, HD 30246 (G5; White et al., 2007)
observed on 2018 December 17 (Fig. 2). The ratio is performed after airmass-
correcting each solar type spectrum using telluric absorption models from the
Planetary Spectrum Generator (Villanueva et al., 2018). The spectral gradient
of each solar type star with respect to HD 30246 is reported in Fig. 2 and
estimated through a linear fit of the ratio spectrum, normalized to unity at 1
$\mu$m, in the wavelength ranges between 0.95–1.05, 1.165–1.32, 1.45–1.75, and
2.1–2.2 $\mu$m to avoid spectral regions contaminated by strong telluric
absorptions. Most calibration stars present a similar spectral behavior to
that of HD 30246, apart from a slight spectral slope on the order of
$\sim$0.2%/100 nm (at 1 $\mu$m). The standard deviation among these spectral
gradients equals 0.3%/100 nm and is adopted as the uncertainty on the comet
spectral slopes reported in Table 1. The latter are also estimated through a
linear fit of the comet spectrum, normalized to unity at 1 $\mu$m, in the
wavelength ranges between 0.95–1.05, 1.165–1.32, 1.45–1.75, and 2.1–2.2 $\mu$m
to avoid spectral regions contaminated by strong telluric absorptions. The
calibration star HD 17883 observed on 2018 November 27 is the only one that
does not display a linear featureless spectrum after normalization to HD
30246, but instead presents broad spectral features at 1.6 $\mu$m and 2.1
$\mu$m, as an example. However, because the corresponding comet spectrum does
not display those features (Fig. 1) and a different slit configuration was
adopted when observing HD 17883 and HD 30246 on 2018 November 27 and 2018
December 17, respectively (Table 1), we attribute these features to
instrumental effects. We conclude that all calibration stars in our analysis
are good solar type stars and the deviation of their spectral behavior from
that of the Sun is accounted for in the comet spectral gradient uncertainty.

The 2018 November 27 data are the only prism-mode spectra in our observing
campaign acquired with the 15″ slit length, and are the only data for which
the subtraction between frames taken in the A and B slit positions resulted in
a positive and negative image of the coma overlapping each other. This overlap
prevents an accurate sky background subtraction in the data reduction, which
might affect the spectral slope. Therefore, while the resulting spectrum is
reliable to search for the presence of water-ice features, we do not report
its spectral gradient in Table 1.

The comparison between each comet spectrum (Fig. 1) and that of the
corresponding solar type reference star (Fig. 2) enables us to infer whether
absorption or emission features observed in the comet reflectance spectrum are
to be attributed to the comet or to the calibration star instead. The comet
spectrum recorded on 2019 January 07 (red filled rightfacing triangles in Fig.
1) presents two clear emission features which originate from CN. The strongest
of these bands is the 0-0 transition at 1.097 $\mu$m, followed by the 1-0
transition at 0.917 $\mu$m (Johnson et al., 1983). Because these features do
not appear in the solar type spectrum (Fig. 2, bottom panel), we attribute
them to the comet.

On 2018 December 13, immediately post perihelion (perihelion date as reported
by the MPC occurred on 2018 December 12 at 22:33:34 UT, JD 2458465.43998,
1.055 au from the Sun), observations were also carried out with the long
wavelength cross-dispersed (LXD_long) mode covering the wavelength range
1.98–5.3 µm ($R\sim 840$ at 4.5 $\mu$m for the 0$\farcs$8$\times$15″ slit).
The comet was centered in the slit and the sky background measured by nodding
off source. The LXD_long data (Fig. 3) were extracted with a 2″ radius
aperture, calibrated with a nearby A0V star, following Vacca et al. (2003),
and normalized by the solar spectrum assembled by Willmer (2018). The latter
is a composite spectrum of the Sun, combining empirical spectra assembled by
Haberreiter et al. (2017) up to 2 $\mu$m and a model by Fontenla et al. (2011)
between 2.0 $\mu$m and 100 $\mu$m. The calibrated spectrum was binned by 8
pixels to yield a spectral resolution equal to the resolving power of
$\sim$840 at 4.5 $\mu$m.

Figure 3: Comet Wirtanen reflectance spectra acquired a few hours after
perihelion over the wavelength range 0.8–5.3 $\mu$m. The LXD_long spectrum
(blue open circles) has been normalized between 2.1 and 2.3 $\mu$m to match
the prism observations (yellow filled triangles). The spectrum is featureless
but for molecular/organic emission at $\sim$3.3 µm, and residual telluric
features. The imaginary part of the refractive index k of crystalline water
ice by Warren & Brandt (2008, a peak in k corresponds to an absorption band),
is shown for comparison (green dashed line). No water-ice absorption features
are observed in the spectrum of comet Wirtanen throughout the full wavelength
range. The Deep Impact/HRI-IR spectrum of 103P/Hartley 2 (Protopapa et al.,
2014) and the IRTF/SpeX spectrum of C/2013 US10 (Protopapa et al., 2018),
which clearly exhibit the characteristic water-ice spectral features, are
shown also for comparison. The spectra of 103P/Hartley 2 and C/2013 US10 have
been normalized between 2.15 and 2.25 $\mu$m to match the prism observations
of 46P/Wirtanen and shifted along the y-axis for clarity.

##  3 Analysis and Results

###  3.1 Qualitative analysis of the spectral results

Water ice has absorption bands in the near-infrared at 1.5, 2.0, 3.0, and 4.5
µm. The strongest of these absorption features is the 3.0-µm band. Based on a
visual inspection of the prism (0.8–2.4 µm) spectra in Fig. 1, we find no
evidence for the 1.5- or 2.0-µm bands. To emphasize this point, we show, for
comparison purposes only, the model spectrum of the icy coma of comet US10
from Protopapa et al. (2018). The US10 model consists of a heterogeneous coma
of dust grains and water-ice grains, where the ice grains are an intimate
mixture of amorphous carbon and water ice (0.5% carbon by volume) and have a
best-fit ice grain diameter of 1.2 µm. However, the difference in the 1.5- and
2.0-µm band shapes between 0.5% dirty ice and pure ice is subtle (see Fig. 3
of Protopapa et al. 2018). The LXD_long spectrum of comet Wirtanen (Fig. 3)
also lacks the 2.0-, 3.0-, and 4.5-µm water-ice absorption bands. However,
thermal emission from the nucleus is substantial in the LXD_long spectrum (see
Section 3.2); it dilutes the spectral signature of water ice at 3.0 µm, and
likely overwhelms any feature at 4.5 µm (see the imaginary part of the
refractive index of water ice in Figure 3, green dashed line).

The non-detection of water-ice spectral features in the IRTF/SpeX measurements
of Wirtanen can not be attributed to the sensitivity of the instrument. These
features are readily available with IRTF/SpeX and they were already detected
in the coma of several comets observed with the same instrument and
spectroscopic modes adopted for the Wirtanen spectroscopic measurements
presented here (Yang et al., 2009; Yang, 2013; Yang et al., 2014; Protopapa et
al., 2018).

The detection of cometary water-ice features depends on 1) spectral resolution
and 2) signal-to-noise ratio (SNR) of the observations. Low spectral
resolutions, $R$ = 100–200, with SNR of $\sim$30 per bin are sufficient to
detect water-ice absorption bands of a few percent by depth in the near-
infrared wavelength range. As an example, the Deep Impact spectrum of comet H2
has a spectral resolution of 240 at 2.0 $\mu$m with SNR around 40 in the
1.8–2.5 $\mu$m range, and a 2.0-$\mu$m water-ice band depth of $\sim$10%
(Figure 3, orange squares, Protopapa et al., 2014). IRTF/SpeX observations of
US10 acquired in prism mode on 2014 Aug 13 have R$\sim$300 at 2.0 $\mu$m and a
SNR of $\sim$30 in the range 1.8–2.5 $\mu$m (Figure 3, magenta filled dots,
Protopapa et al., 2018). Therefore, the IRTF/SpeX and Deep Impact/HRI-IR
observations of US10 and H2, respectively, are comparable in terms of
sensitivity. Observations of US10 display a water-ice band depth at 2.0 $\mu$m
of $\sim$10%, similar to that observed in the spectrum of comet H2. The
spectroscopic data of comet Wirtanen presented here all have the sensitivity
to detect US10-like water-ice absorption features. They have the same
resolving power as the US10 measurements and an SNR of 320 in the range
1.8–2.5 $\mu$m, which is a factor of ten larger than the US10 spectral data.

With spectral sensitivity ruled out, the non-detection of water-ice absorption
bands has to be attributed either to the lack of any solid ice in the coma, or
to the presence of water-ice grains with physical properties (grain size and
purity) that limit their lifetime with respect to the field- of-view at the
time of the observations. The first case is explored in Section 3.4, while the
second is addressed in Sections 3.5 and 3.6.

To investigate the properties of both refractories and ice in the coma of
Wirtanen, we combined the LXD_long and prism data collected on the same date,
only a few hours apart, yielding a nearly complete spectrum from 0.8 to 5.3 µm
(Figs. 3 and 4). The LXD_long spectrum, normalized to match the prism
measurements between 2.1 and 2.3 µm, is in near agreement with the short
wavelength data between 2.0 and 2.4 µm.

###  3.2 Estimate of the nucleus contribution

The close approach to the Earth made for a rare set of circumstances, and the
possibility that the nucleus makes a significant contribution to the observed
flux density. We modeled the reflected light and thermal emission from the
nucleus with the $H,G$ model and the Near-Earth Asteroid Thermal Model
(NEATM), respectively (Bowell et al., 1989; Harris, 1998). The $H,G$ model
parameters and assumed values are effective radius, 555 m, geometric albedo,
4% at 0.55 µm (used to compute the absolute magnitude $H$), and phase function
parameter $G$ (0.15 assumed; see Bowell et al., 1989). In addition, we redden
the nucleus with the same spectral gradient as measured from the near-infrared
coma. The NEATM parameters include all of the $H,G$ parameters, mean infrared
emissivity, 0.95, and infrared beaming parameter, 1.03. The emissivity and
beaming parameter values are based on the results for cometary nuclei by
Fernández et al. (2013). With these parameters, we compute a model spectrum of
the nucleus and compare it to the SpeX LXD data. We find that the nucleus
could account for 15, 35, 61, and 68% of the spectral flux at 2, 3, 4, and 5
µm, respectively. The thermal emission from the comet appears to be dominated
by the nucleus. In contrast, the scattered component is dominated by the coma.

In principle, one could subtract the model nucleus spectrum from the LXD
spectrum and analyze the residuals as a spectrum of the coma. However, we made
several assumptions in order to arrive at our nucleus estimate, and there is
enough uncertainty in the parameters that deriving a useful thermal emission
spectrum of the nucleus is not possible. The most uncertain parameter is the
size of the nucleus, derived under the most unlikely assumption of a spherical
nucleus. Lamy et al. (1998) and Boehnhardt et al. (2002) found peak-to-peak
amplitudes of 0.2 and 0.4 mag, respectively. Given that the shape and
rotational state of the nucleus is unknown at the time of our observations, we
immediately have an uncertainty of $\pm$20% on our nucleus estimate at all
wavelengths. Furthermore, the shape of the LXD spectrum relative to the
nominal nucleus spectrum is unexpected. Cometary dust comae should have cooler
spectral temperatures than cometary nuclei, due to the fact that small grains
can re-radiate absorbed sunlight isotropically, but nuclei tend to re-radiate
that energy from the sun-lit hemisphere only. In contrast to the expectations,
our nucleus model suggests an increasing nucleus fraction in the LXD spectrum
from 3 to 5 µm, which indicates the nucleus has a cooler spectrum. The
spectral temperature of the NEATM is controlled by the beaming parameter. We
based our assumed value on the results of the photometric survey by Fernández
et al. (2013), who find a population averaged beaming parameter of
1.03$\pm$0.11 based on 16- and 22-µm photometry. By decreasing the beaming
parameter, we could produce a warmer spectral temperature which would lead to
a higher nucleus contribution. A 2-$\sigma$ variation of the Fernández et al.
(2013) beaming parameter results in a spectrum that accounts up to 110% of the
LXD spectrum at $>3.5$ µm. However, the contribution at 2 µm, which is
dominated by reflected light, is still 15%.

Given the likely high contribution of the nucleus, we cannot separately
analyze the thermal emission of the dust. We instead elect to characterize the
thermal emission with an empirical model, e.g., the Planck function, which
allows us to avoid a physical interpretation of the thermal emission, but
still is a good description of the data (as we show below). For the scattered
light, we account for the nucleus by assuming it contributes 15% of the flux,
i.e., the remaining 85% is the coma.

###  3.3 Modeling

The reflectance spectrum of the coma in the wavelength range covered by the
prism and LXD_long data combined is modeled as the sum of the scattered and
thermal components of the coma. In this section we describe the general
philosophy of the modeling approach.

The thermal component of the reflectance spectrum is approximated by

$R_{thermal}=\frac{\pi\>R_{h}^{2}\>B(T_{c},\lambda)f}{F_{\sun}},$ (1)

where $B(T_{c},\lambda)$ is the Planck function, which depends on the color
temperature $T_{c}$, $F_{\sun}$ is the solar flux at 1 au, $R_{h}$ is the
comet heliocentric distance in au, and $f$ is the filling factor of the
grains. The latter is obtained by normalizing the thermal component of the
modeling to the data at 3.9–4.1 µm after subtracting the scattered component.

The scattered component of the spectrum is modeled as an areal mixture of two
components, one of polydisperse porous dust particles, or equivalently dust
aggregates, and one of polydisperse water-ice aggregates, to which we refer to
as type-A and type-B aggregates, respectively.

We consider the type-A and type-B components separated from one another, such
that

$R_{scattered}=\sum_{j}F_{j}r_{j}(\lambda)=F_{A}r_{A}+(1-F_{A})r_{B}$ (2)

where $F_{j}$ is the fraction of the area occupied by the $j$th component with
$\sum_{j}F_{j}=1$, and the subscripts A and B denote the type-A aggregates and
type-B grains, respectively.

The reflectance of the $j$th-type of aggregates is approximated by diffusive
reflectance and is given by

$r_{j}(\lambda)=\frac{1-\sqrt{(1-\textrm{w}_{j}(\lambda))}}{1+\sqrt{(1-\textrm{w}_{j}(\lambda))}},$
(3)

where $\textrm{w}_{j}$ is the single scattering albedo of the $j$th type of
aggregates. This is

$\textrm{w}_{j}(\lambda)=\frac{\int_{a_{1}}^{a_{2}}\,a^{2}\>Q_{S}(a,m(\lambda))\>n(a)da}{\int_{a_{1}}^{a_{2}}\,a^{2}\>Q_{E}(a,m(\lambda))\>n(a)da}$
(4)

where $a_{1}$ and $a_{2}$ are the smallest and largest particle radii in the
size distribution. $Q_{S}(a,m)$ and $Q_{E}(a,m)$ are the scattering and
extinction efficiencies of the aggregates as a function of radius $a$ and
complex refractive index $m$, respectively. These are computed by means of Mie
scattering theory, so that we can model grains with any size parameter
($\textrm{X}=2\pi a$/$\lambda$), even those outside the geometric optics
regime ($\textrm{X}<1$). The real and imaginary parts of the refractive index
as a function of $\lambda$ are estimated from effective medium theory
(Bruggeman mixing formula, Bohren & Huffman, 1983). We adopt a fractal model
for the internal structure (i.e., porosity) of the grains. Thus, the
fractional volume filled by material in a porous grain is given by

$\delta=(a/a_{0})^{D-3}$ (5)

where $a_{0}$ is the radius of the basic structural unit of the grain, which
we set equal to 0.1 $\mu$m (e.g., Harker et al., 2002), and $D$ is the fractal
porosity, which ranges between 2.5 and 3 (Lisse et al., 1998). Solid spheres
are represented by $D=3$, while for porous spheres $D<$3 (Harker et al.,
2002). The differential particle size distribution $n(a)da$ is the number of
particles per unit volume with radius between $a$ and $a+da$, following the
formula

$n(a)\propto{}a^{-\alpha}.$ (6)

Figure 4: (A) Comet Wirtanen reflectance spectra over the wavelength range
0.8–5.3 $\mu$m, identical to those shown in Figure 3. The ice-free (model 1)
and ice-rich (model 2) models, with an upper limit of 2.2% for the water-ice
abundance, are shown in red and gray solid lines, respectively. Both models do
not fit the emission feature as expected. (B and C) Residuals of each fit,
with the resulting $\chi^{2}_{\nu}$ indicated in each case.  Figure 5: 2D
$\chi_{\nu}^{2}$ distributions resulting from the parameter exploration of the
fit to the prism+LXD_long spectrum in the case of an ice-free model (model 1,
Figure 4). $T_{c}$, $a_{1}$, and $\alpha$ are the color temperature, the
minimum radius in the particle size distribution, and the differential dust
size distribution power-law index, respectively. In each panel, for each point
in the grid, we search for the value of the third parameter the minimizes
$\chi_{\nu}^{2}$, and the minimum $\chi_{\nu}^{2}$ is displayed. The solid
curves shown in white and gray with $\Delta\chi_{\nu}^{2}$ = 1.00 and 2.71
represent the 68% and 90% confidence levels, respectively. Horizontal and
vertical lines indicate the best-fit parameter values. The best fit to the
data is found for $T_{c}$ = $375_{10}^{10}$ K, $a_{1}$ = $0.55_{0.15}^{0.15}$
$\mu$m, and $\alpha$ = $3.3_{0.6}^{0.5}$. The uncertainties on the best fit
parameter values correspond to 1-$\sigma$ errors.

###  3.4 Ice free model: Properties of the dust coma

Given the absence of any ice feature, we first model the spectrum by a power-
law size distribution of porous dust aggregates only (type-A aggregates). This
implies that $F_{A}$ is set equal to 1 in Eq. 2.

There is a broad literature investigating the dust mineralogy of cometary
comae and is based on several techniques, including but not limited to,
laboratory studies of IDPs (Wooden et al., 2000), micrometeorites (Bradley et
al., 1999), and STARDUST grains (Brownlee et al., 2006); analysis of ground
and space-based mid-IR observations (Harker et al., 2002; Woodward et al.,
2021); and in situ analysis of coma grains with spacecraft instrumentation
(e.g., Fomenkova et al., 1992; Fulle et al., 2016a). Given the featureless
behaviour of the Wirtanen spectrum, the chemistry of the refractory component
cannot be unambiguously identified. However, it is possible to derive
information on the size distribution of the dust, once its chemical nature is
assumed. We follow the same approach adopted by Bockelée-Morvan et al. (2017a,
b) and consider amorphous carbon and amorphous olivine as coma refractories,
with a silicate to carbon ratio of 0.3, based on the results by Fulle et al.
(2016a) at 67P/Churyumov-Gerasimenko (hereafter 67P). We adopt the optical
constants by Edoh (1983) and Dorschner et al. (1995) for amorphous carbon and
amorphous olivine (Mg = Fe = 0.5), respectively.

The free parameters in the model are the exponent, $\alpha$, and the minimum
radius, $a_{1}$, of the particle size distribution as well as the color
temperature $T_{c}$. Because large particles do not contribute significantly
to infrared radiation (e.g., Harker et al., 2002), the grain size distribution
is truncated at 100 $\mu$m in diameter. This step reduces computation time.
The fractal porosity $D$ is set to 2.5 (Bockelée-Morvan et al., 2017a, b). We
acknowledge that this parameter was initially set free, and found it to be
unconstrained by our data. We use a Levenberg–Marquardt $\chi^{2}$
minimization algorithm to find the best fit solutions (Markwardt, 2009). The
model quality is quantified by means of the reduced $\chi_{\nu}^{2}$, defined
as

$\chi_{\nu}^{2}=\frac{1}{\nu}\sum_{i=0}^{N}\Bigg{(}\frac{\mathrm{R}_{i}-\mathrm{R}_{i,model}(\alpha,a_{1},T_{c})}{\mathrm{ERR}_{i}}\Bigg{)}^{2},$
(7)

where $\mathrm{R}_{i}$, $\mathrm{ERR}_{i}$, and $\mathrm{R}_{i,model}$
represent the measured relative reflectance, the error on the relative
reflectance, and the modeled relative reflectance, respectively, in
correspondence of the individual wavelength, identified by the subscript $i$.
The sum is over all $N$ wavelength points selected for the best fit
minimization. The degree of freedom, $\nu$, equals the number of spectral
elements $N$ minus the number of fitted parameters.

Table 2: Properties of the refractory (type-A) and ice aggregates (type-B) in
the coma of 46P/Wirtanen as derived from spectroscopic modeling. Model 1
corresponds to an ice free model and accounts for aggregates of amorphous
carbon and amorphous olivine into vacuum (type-A aggregates). Model 2 is an
areal mixture of type-A aggregates and US10-like water-ice grains (1.2-$\mu$m
diameter monodisperse water-ice grains with a small, 0.5%, dirt fraction by
volume). Model 3 is an areal mixture of type-A aggregates and H2-like water-
ice grains (1.0-$\mu$m diameter monodisperse pure water-ice grains).

| Type-A aggregates (refractory) | Type-B aggregates (icy) | $T_{c}$ | $\chi_{\nu}^{2}$
---|---|---|---|---
Model |  $F[\%]$aafootnotemark:  |  $|\alpha|$bbfootnotemark:  |  $D$ccfootnotemark:  |  $a_{1}[\micron]$ddfootnotemark:  |  $a_{2}[\micron]$eefootnotemark:  | $F[\%]$ | $|\alpha|$ | $D$ | $a[\micron]$ |  |
Model 1 | 100**This parameter has been set as constant. | $3.3_{0.6}^{0.5}$ |  $2.5$**This parameter has been set as constant. | $0.55_{0.15}^{0.15}$ |  $100$**This parameter has been set as constant. | 0**This parameter has been set as constant. | … | … | … | $375_{10}^{10}$ | 2.9
Model 2 | $>97.8$ |  $3.3$**This parameter has been set as constant. |  $2.5$**This parameter has been set as constant. |  $0.55$**This parameter has been set as constant. |  $100$**This parameter has been set as constant. | $<2.2$ |  $0$**This parameter has been set as constant. |  $3$**This parameter has been set as constant. |  $0.6$**This parameter has been set as constant. |  $375$**This parameter has been set as constant. | 9.1
Model 3 | $>98.6$ |  $3.3$**This parameter has been set as constant. |  $2.5$**This parameter has been set as constant. |  $0.55$**This parameter has been set as constant. |  $100$**This parameter has been set as constant. | $<1.4$ |  $0$**This parameter has been set as constant. |  $3$**This parameter has been set as constant. |  $0.5$**This parameter has been set as constant. |  $375$**This parameter has been set as constant. | 9.3

aafootnotemark:

Fraction of the area occupied by the aggregates bbfootnotemark: Differential
size distribution power-law index ccfootnotemark: Fractal porosity
ddfootnotemark: Minimum particle radius in the size distribution
eefootnotemark: Maximum particle radius in the size distribution

To ensure that the solution obtained from the best-fit minimization algorithm
is that of a global minimum rather than a local minimum and to investigate the
possible inter-correlation between the free parameters, we explore a wide
parameter space ($\alpha$,$a_{1}$), ($\alpha$,$T_{c}$) and ($a_{1}$,$T_{c}$)
with $\alpha$ ranging between 2 and 5 with a step of 0.1, $T_{c}$ between 300
K and 500 K with a step of 5 K, and $a_{1}$ between 0.1 and 5 $\mu$m with a
step of 0.025 $\mu$m. We determine the reduced $\chi_{\nu}^{2}$ distributions
and the degree of confidence in the best-fit values. The joint error
distribution of ($\alpha$,$a_{1}$), ($\alpha$,$T_{c}$) and ($a_{1}$,$T_{c}$)
is shown in Fig. 5. For each point in the grid, which defines the values of
the two parameters under consideration, we solve for the third parameter. The
2D contours of constant $\chi_{\nu}^{2}$ corresponding to 68% and 90%
confidence level are displayed in white and gray, respectively. Best-fit
parameter values and the correspondent 1-$\sigma$ errors are listed in Table
2. There is evidence for a slight correlation between the exponent of the
particle size distribution, $\alpha$, and minimum size of the particle
distribution, $a_{1}$, but both parameters are well constrained. To exclude
the locations where emission bands occur and regions of strong telluric
absorption, the best-fit optimization is performed in the wavelength ranges
between 1.16–1.34 µm, 1.45–1.79 µm, 1.92–2.53 µm, 2.94–3.20 µm, 3.55–4.18 µm,
and 4.52–5.34 µm. The best-fit result (Figure 4, red solid line, model 1 in
Table 2) has a differential dust size distribution power-law index of 3.3,
minimum size $a_{1}$ equal to 0.55 $\mu$m and a color temperature of 375 K.
The derived color temperature is in excess with respect to the equilibrium
temperature $T_{eq}=278R_{\mathrm{h}}^{-0.5}=271~{}K$. This could be
attributed to the presence of $\mu$m- and sub-$\mu$m sized grains comprising
absorbing material. However, we report in Section 3.2 that the thermal
emission has a substantial contribution from the nucleus, which is challenging
to remove. Therefore, we do not interpret this result any further.

###  3.5 An upper limit for water ice

Our data do not display spectral evidence of water ice in the coma.
Nevertheless, this does not necessarily rule out the presence of water ice in
the coma of Wirtanen. We investigate this possibility and assess an upper
limit for water-ice abundance by modeling the composite spectrum
prism+LXD_long acquired on 2018 December 13 (Figure 4) with two components
(see Sec. 3.3), one of polydisperse porous dust aggregates (type-A aggregates)
and one of polydisperse water-ice particles (type-B aggregates). We hold fixed
the physical properties of the dust aggregates using the best-fit values from
the ice-free model (model 1, Section 3.4). This limits the number of free
parameters. Additionally, given the lack of water-ice absorption features and
therefore the impossibility to solve for both the physical properties of the
ice grains and their abundance, we assume that water-ice particles with the
same properties as those found in comet C/2013 US10 (model 2) and 103P/Hartley
2 (model 3) were ejected by comet Wirtanen. Therefore, either 1.2 µm in
diameter ice grains containing 0.5% amorphous carbon by volume (model 2,
Protopapa et al., 2018) or 1.0 µm in diameter pure ice grains (model 3,
Protopapa et al., 2014) are assumed to be present in the coma of Wirtanen. We
consider the type-A and type-B components separated from one another (see Eq.
2). The free parameter in the model is the fraction of type-B grains in %. We
varied the fraction of type-B grains ($F_{B}$, or equivalently $1-F_{A}$)
between 0 and 1 with a step interval of 0.1%. For each value of $F_{B}$ we
computed $\chi_{\nu}^{2}$ as discussed in Section 3.4. In Figure 6 we present
a plot of $\chi_{\nu}^{2}$ versus $F_{B}$. The two curves corresponding to
model 2 (blue dots) and model 3 (orange squares) have a minimum for
$F_{B}=0.1\%$, which is almost identical to model 1 (red line in Figure 4).
However, in the case of US10-like water-ice grains (model 2), the data are
consistent with an upper limit of water-ice abundance on the order of 1.4% and
2.2% at the 90% and 99% confidence levels, respectively (for 1 free parameter,
$\Delta\chi^{2}=2.71$ and $6.63$ corresponds to a confidence level of 90% and
99%, respectively, Avni, 1976). In the case of pure water-ice grains (H2-like
water-ice grains, orange squares in Figure 6) an upper limit of 0.9% and 1.4%
at the 90% and 99% confidence levels, respectively, is estimated. Model 2,
with an upper limit of 2.2% for the water-ice abundance is shown in Figure 4
(gray line). Model 3 with a 1.4% water-ice fraction is almost identical to
model 2 and therefore it is not shown in Figure 4. The upper limit of water-
ice abundance is systematically lower in model 3 with respect to model 2. This
is because pure water ice displays stronger water-ice absorption bands with
respect to ice grains with refractory inclusions. We point out that the band
depth of water-ice absorption features increases with increasing path length
or equivalently particle diameter. Therefore, assuming water-ice particles
larger than those observed in the coma of US10 and H2 would lead to even lower
upper limits of the water-ice areal fraction. The upper limit for the
fractional area of US10-like and H2-like water-ice grains of 2.2% and 1.4%
translates into an ice-to-dust areal ratio of 3% and 2%, respectively. These
values are estimated accounting for the 15% nucleus contribution to the
scattered component of the spectrum (Section 3.2). We conclude that the coma
of Wirtanen is dominated by dust. If water-ice grains were ejected by comet
Wirtanen, their abundance would be negligible.

Figure 6: Upper limits for the abundance in the coma of Wirtanen of 1.2-$\mu$m
diameter water-ice grains with 0.5% amorphous carbon by volume (spectral model
2, blue dots) and 1.0-$\mu$m diameter pure water-ice grains (spectral model 3,
orange squares). The upper limit for the water-ice fraction $F$ is given at
the 68%, 90%, and 99% confidence levels for both models. Models 2 and 3 differ
exclusively for the physical properties (purity and particle size) of the ice
grains (type-B grains), as the properties of the refractory aggregates (type-A
particles) are the same in both simulations (see text for details).

###  3.6 Water-ice grain sublimation lifetime

In order for water-ice grains to be a candidate for hyperactivity, they must
be ejected in high enough abundance and sublimate quickly enough to account
for the observed total water production rates. We did not detect any water-ice
features in our spectra, therefore we additionally require the grains to fully
sublimate before they travel $\sim$1″ from the nucleus, this distance based on
our spectral aperture sizes.

Pure ice grains have the longest sublimation lifetimes, and dust impurities
tend to reduce that lifetime. Protopapa et al. (2018) modeled grain lifetimes
following Hanner (1981), Lien (1990), and Beer et al. (2006), and we adopt
this model for the analysis of comet Wirtanen. It computes grain temperatures
based on the absorption of sunlight, grain thermal emission, and cooling from
sublimation. Radiative transfer calculations are based on Mie theory (code of
Bohren & Huffman, 1983, modified by B. Draine)111Available at
https://www.astro.princeton.edu/~draine/scattering.html. Mass loss by
sublimation decreases the grain radius, as does sputtering from the solar
wind. Grain radii are integrated down to 10 nm, at which point they are
considered destroyed. We present calculations for mixtures of water ice
(optical constants by Warren & Brandt, 2008) and amorphous carbon (Edoh,
1983), using effective medium theory (Bruggeman mixing rule; Bohren & Huffman,
1983). Calculations for water-ice grain lifetimes at 1.055 au with 0, 0.2,
0.5, and 1% amorphous carbon by volume as a function of grain diameter are
presented in Fig. 7, with an initial grain diameter of 20 µm.

Based on our calculated water-ice grain lifetimes, micrometer-sized pure
water-ice grains have a lifetime of 1 to 3 hr at 1.055 au, and dirty ice
grains have lifetimes that are shorter by an order of magnitude or more.
Beyond 3 µm in size, the difference is even more dramatic. Pure-ice grain
lifetimes increase to $10^{4}$ hr for 10-µm diameter grains, whereas dirty-ice
grain lifetimes are still less than 1 hr, even for the low carbon fraction of
0.2%.

Figure 7: Water-ice grain lifetimes at 1.055 au for pure water ice, and
mixtures of water ice with 0.2, 0.5, and 1.0% amorphous carbon dust by volume.
The right axes indicates the distance in arcseconds at $\Delta=0.08$ au
traveled before sublimating for two coma expansion speeds: 50 and 100 m s-1,
based on grain speeds estimated by Fulle (2000). Model lines which fall in the
shaded regions are more likely to produce a dust dominated spectrum, as we
observed at 46P.

To further distinguish between the type of ice (pure versus dirty) that could
be present in the inner coma of comet Wirtanen, we need to consider the time
it takes for a coma grain to travel to the edge of the spectral aperture in
projection. Faster coma expansion speeds require rapid sublimation rates in
order to account for the lack of water-ice absorption features in our spectra.
Fulle (2000) estimated several dust parameters, including expansion speed, for
comet Wirtanen with a dynamical model of dust and an image of the comet near
its 1997 perihelion. They estimated expansion speeds for 1 µm diameter dust to
be 65 to 95 m s-1, and we assume the dust and ice grain expansion speeds are
the same. The aperture crossing times for these speeds are 0.17 to 0.25 hr for
$\Delta=0.08$ au. In Fig. 7, we provide alternative y-axes showing the
distance traveled by a grain moving at 50 and 100 m s-1 in the image plane.

Water-ice grains with sublimation lifetimes longer than the aperture crossing
timescales (i.e., $\gtrsim$1 hr) would have been detected in our spectra if
their abundance was higher than a few percent (Section 3.5). Assuming that
higher abundances are needed to account for the hyperactivity, we rule out
pure water ice grains, which have lifetimes $\gtrsim 1$ hr for diameters
$\gtrsim 0.1$ µm, and therefore would survive the time of flight to the edges
of our spectral apertures. In contrast, dirty-ice grains are likely to have
sublimated before reaching the edge of our LXD spectral aperture. Given that
Fulle (2000) estimated expansion speeds from 65 to 95 m s-1 for 1 µm grains,
we consider dirty ice with carbon fractions $\gtrsim 0.5$% as candidates for
explaining the hyperactivity of comet Wirtanen.

###  3.7 Coma reddening

The color of the dust coma of comet Wirtanen ($S$, expressed in %/100 nm) as
inferred from the IRTF SpeX measurements (Section 2) in the near-infrared
wavelength range lacks variation across our observational data set (Table 1).
To investigate its significance, we considered putative correlations between
$S$ and aperture extraction, heliocentric distance, time, and phase angle
(Figure 8).

First we looked at whether the spectral color might be influenced by the
spectral aperture in projection $d$ (in km, $d\sim\delta\Delta/206265$, where
$\delta$ is the spectral aperture diameter in arcsec and $\Delta$ is the
geocentric distance expressed in km). No color gradient is observed with
aperture extraction (Figure 8, panel A). The linear fit to the data, shown in
panel A as a solid line, has a $\chi^{2}_{\nu}$ = 1.0 and a slope of
$10^{-5}$% per 100 nm per km.

Color variations in cometary comae can be diagnostic of the coma dust
properties, but also the ice-to-dust ratio (e.g., Filacchione et al., 2020).
Water ice is stable at large heliocentric distances, but sublimation rates
vary inversely with heliocentric distance. Our data (Figure 8, panel B) do not
display any color variation with heliocentric distance. This is not unexpected
given that the range of heliocentric distances covered by our observations is
not wide enough to be sensitive to changes in ice-to-dust ratio.

Occasional variations in the spectral gradient could also be due to rapid
changes in the coma composition and particularly in the ice-to-dust ratio as
the result of impulsive events, such as outbursts, which eject fresh new
material into the coma. The coma color is constant as a function of time from
perihelion (Figure 8, panel C). An outburst was identified by Kelley et al.
(2021) during the time period covered by our data with an apparent strength on
the order of $-0.5$ mag (see green data points in panel C of Figure 8). If
water-ice would be ejected during the outburst, we would expect a sudden
blueing of the coma followed by a reddening due to sublimation. However, the
outburst ejecta moved rapidly, with speeds $>$23 m s-1, leaving little to no
material near the nucleus at the time our spectrum was taken (Kelley et al.,
2021). In addition, anticipating the post-ejection evolution in the ice
properties is not straightforward. But no significant trend is observed in the
color gradient after the time of the outburst.

Finally, no correlation between the coma color and phase angle (Sun-Target-
Observer angle, STO in Table 1) over the range between 20∘ and 50∘ is observed
(Figure 8, panel D). An increase of reddening with phase angle for cometary
dust has been reported for the first time by Bockelée-Morvan et al. (2019) for
comet 67P. Specifically, Bockelée-Morvan et al. (2019) reported a phase
reddening in the near-IR of the dust coma in the near-nucleus of 67P of
0.031%/100 nm deg-1 in the phase angle range 50∘-120∘. This phenomena has been
attributed by Bockelée-Morvan et al. (2019) to the roughness of the dust
particles (Beck et al., 2012; Schröder et al., 2014). As observed by Hartmann
& Cruikshank (1984), changes in the water-ice-to-dust ratio could produce an
apparent phase reddening due to the relationship between phase angle and
heliocentric (or observer-target) distance. A comet observed at large
heliocentric distances and therefore low phase angles would display a coma
color that is bluer with respect to the same comet observed closer-in at
larger phase due to the sublimation lifetime of the ice grains. Therefore, to
test for the presence of a true phase reddening and rule out the hypothesis of
compositional (ice-to-dust ratio) changes, the correlation between spectral
gradient and heliocentric distance needs to be tested as well. Bockelée-Morvan
et al. (2019) reported no significant heliocentric variations in the dust
color of 67P, which reinforces the result of a true phase reddening. No phase
reddening is observed in our data.

Figure 8: Dust coma spectral gradient of comet 46P/Wirtanen expressed in %/100
nm as a function of projected aperture diameter in km (panel A), heliocentric
distance $R_{h}$ (panel B), observing time since perihelion (panel C) and Sun-
target-observer (STO) angle (panel D). The comparison between the spectral
gradient behavior as a function of time and comet Wirtanen light curve (green
dots) during an outburst close to perihelion discussed in detail by Kelley et
al. (2021) is also shown in panel C.

##  4 Summary and discussion

We report a detailed characterization of the inner coma of comet 46P/Wirtanen
through infrared spectroscopic measurements acquired with IRTF SpeX during the
close approach of the comet to the Earth in December 2018. Our findings are:

  1. 1.

No water-ice absorption features are detected in our data, which span a range
of heliocentric distance from 1.1 au inbound, to 1.05 au near perihelion, and
back to 1.1 au outbound.

  2. 2.

The modeling analysis of the observations acquired immediately post perihelion
and covering the wavelength range 0.8–5.3 µm indicates the coma is composed of
porous refractory aggregates (fractal porosity assumed equal to 2.5) spanning
1.1–100 µm in diameter with a differential dust size distribution power-law
index of –3.3$\pm$0.5 and a color temperature of 375$\pm$10 K.

  3. 3.

An upper limit of 1.4% in water-ice abundance is estimated, assuming water-ice
grains with physical properties identical to those observed in the coma of the
hyperactive comet H2 (1.0-$\mu$m in diameter pure water-ice grains Protopapa
et al., 2014). A water-ice fraction up to 2.2% is consistent with Wirtanen
data in the case of water-ice grains of 1.2 µm in diameter with 0.5% amorphous
carbon by volume, like those observed in the coma of US10, a possible but
unconfirmed hyperactive comet (Protopapa et al., 2018). Lower carbon fractions
and/or larger water-ice particle diameters would lower this upper limit.

  4. 4.

No significant variations in spectral slope are observed among our spectral
data.

Comet Wirtanen was identified as a hyperactive comet by Lamy et al. (1998),
Groussin & Lamy (2003) and Lis et al. (2019) with an active fraction between
60% and 120% at perihelion during the 1997 and 2002 apparitions. However,
water production rate can vary from apparition to apparition, as was the case
for comet H2 (Combi et al., 2011). Therefore, to put into context our
observations and test whether hyperactivity is associated with the presence of
a water-ice grain halo, it is critical to first estimate the active fraction
of comet Wirtanen during the 2018 apparition. For this purpose, we used the
sublimation model by Cowan & A’Hearn (1979) for a rotational pole pointed at
the Sun222Code available at https://github.com/Small-Bodies-Node/ice-
sublimation. This is the same model as employed by Lis et al. (2019). Adopting
the mean nucleus radius of 555$\pm$40 m estimated by Boehnhardt et al. (2002),
we translated the water production rate of $Q_{\mathrm{{H_{2}O}}}=7.2\times
10^{27}$ molecules s-1 reported by Knight et al. (2021) on 2018 December 16
($\mathrm{Z}=3.19\times 10^{21}~{}\mathrm{molecules~{}s^{-1}~{}m^{-2}}$ at
$\mathrm{R_{h}}$=1.056 au), close in time to our spectroscopic measurements,
into an active fraction of 58%. The water production rate reported by Knight
et al. (2021) and derived from measurements of the OH 309 nm (0-0) band is in
agreement with the H${}_{2}^{16}$O production rate of
(7.7$\pm$1.5)$\times$1027 molecules s-1 quoted by Lis et al. (2019) and based
on observations of the $1_{1,0}-1_{0,1}$ transition of H${}_{2}^{18}$O between
2018 December 14 and 20 UT. The water production rate was 10% higher on 2018
December 3 (8$\times$1027 molecules s-1; Knight et al., 2021), which
translates into an active fraction of 65%. This active fraction is similar to
that of comet H2 during the Deep Impact observations ($\sim$72%, Lis et al.,
2019) and it is at least 2 times higher than the typical active fraction for
most comets (e.g., A’Hearn et al., 1995).

In this paper, we test the hypothesis put forth by A’Hearn et al. (2011),
Protopapa et al. (2014), and Kelley et al. (2013) that sublimating water ice
in the coma in the form of small grains and/or large chunks is responsible for
a comet hyperactivity. We point out that Knight et al. (2021) and Bonev et al.
(2021) both provide indirect evidence for the presence of an extended source
of water vapor in the coma of Wirtanen. However, no information on the
properties of the ice that produces the water vapor, such as particle size and
ice-to-dust ratio, has been retrieved based on their work.

Radiative transfer modeling of the spectroscopic data combined with
calculations of water-ice grain sublimation lifetimes rule out H2-like small
water-ice grains (Protopapa et al., 2014) in the coma of Wirtanen. The long
lifetime of 1-$\mu$m in diameter pure water-ice particles is inconsistent with
an upper limit of only 1.4% for the abundance of these grains in the coma and
the assumption that high water-ice mass-loss is needed to account for the
hyperactivity. We consider instead dirty small ice grains (1.2-$\mu$m in
diameter) with carbon fractions $\gtrsim$0.5% as possible candidates to
account for the comet water production rates. The small amount of low albedo
dust limits the observability of the water-ice grains at heliocentric
distances of 1.0–1.1 au, accounting for our observations. Moreover, it quickly
converts the ice into water vapor, which is needed to account for the
hyperactivity. This model is based, in part, on the ice grains observed in the
coma of US10, which has been suggested to be an hyperactive comet by Protopapa
et al. (2018) based on the detection of water-ice grains in the coma
presumably ejected by sublimation of the hyper-volatile CO2, a process
observed at H2 (A’Hearn et al., 2011; Protopapa et al., 2014). Interestingly,
CO2 has been detected in comet Wirtanen as well (Bauer et al., 2021). Notice
that the detection of CO2 does not necessarily imply a water-ice grain halo.
As an example, while CO2 has been mapped in the coma of comet 67P (Fink et
al., 2016), a regular comet in terms of level of activity (non hyperactive),
no water-ice grains have been detected in the quiescent coma of the comet
(Bockelée-Morvan et al., 2017a, b). Small water-ice grains on the order of a
$\mu$m (5 $\mu$m in diameter) have been reported by Davies et al. (1997) in
the quiescent coma of comet Hale-Bopp, which is on the high end of a typical
comet (Lis et al., 2019, report an active fraction on the order of 34% at 0.91
au). We stress that the water-ice physical properties (purity, grain size,
abundance) depend on the radiative transfer model applied to the spectroscopic
measurements. Therefore, a consistent comparison between H2, US10, Wirtanen
and Hale-Bopp requires the same modeling strategy to be applied to all the
data. We reserve this investigation for future work.

Kelley et al. (2013) examined a population of point sources surrounding the
nucleus of comet H2 in Deep Impact images. Kelley et al. (2015) revised their
estimates and found sizes up to 8 m in diameter for the point sources and
suggested they could be responsible for the comet’s extended water vapor
production and hyperactivity. Radar observations are sensitive to particles of
the same size range. In fact, the radar cross section of $\gtrsim 2$ cm
particles is the same order of magnitude as the one reported by Kelley et al.
(2015) for the point sources, assuming nucleus-like properties (e.g., low
albedo). This suggests that the two populations, those in the Deep Impact
images and those in the radar, could be related. Radar observations of comet
Wirtanen in 2018 also indicate the presence of centimeter-sized grains in the
coma. The total cross section of grains with radii $\gtrsim 2$ cm is roughly
the same than that observed at comet H2, 0.89 km2, (Harmon et al., 2011, and
E. Howell, private communication).

If the centimeter-sized radar observed particles would be responsible for the
hyperactivity of comet Wirtanen, then the lack of water-ice spectral
signatures in our observations suggests that the centimeter-sized grains are
either a small areal fraction of the coma or are not icy on the surface.
Putting the Wirtanen and H2 data together, the one possible scenario that can
explain all observations and account for the hyperactivity of both comets
requires large centimeter-to-decimeter sized particles that behave like mini-
cometary nuclei, i.e., the water-releasing materials would reside just under
the surface at a depth deeper than that sampled by near-IR remote sensing
(i.e., on the order of $\mu$m). However, this does not account for any
contribution from the fine-grained water ice observed near the nucleus of H2
(A’Hearn et al., 2011; Protopapa et al., 2014). We point out that large chunks
were observed in the coma of 67P by Rotundi et al. (2015), Fulle et al. (2015,
2016b) and Agarwal et al. (2016), nevertheless this comet is not hyperactive.

In summary, we provide observational limits on the physical properties of the
icy grains responsible for hyperactivity in comet Wirtanen: either icy grains
on the order of 1 µm in size with a small amount of dust, or large chunks
containing significant amounts of water ice.

The authors thank D. Wooden for helping to identify the cometary CN emission.
Support for this work was provided through the NASA Solar System Observations
program grant number 80NSSC20K0673. S.P. thanks the NASA grant 80NSSC19K0402
and the Space Telescope Science Institute grant (HST-GO-15372) for partial
funding that supported her work. C.E.W. acknowledges partial support from NASA
Solar System Observations grant 80NSSC19K0868. We thank the anonymous referee
and D. Bockelée-Morvan for valuable comments that improved the manuscript.

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