# Are NH3 and CO2 ice present on Miranda?

Riley A. DeColibus Department of Astronomy, New Mexico State University
Box 30001, Dept.4500
Las Cruces, NM 88003, USA  Nancy J. Chanover Department of Astronomy, New
Mexico State University
Box 30001, Dept.4500
Las Cruces, NM 88003, USA  Richard J. Cartwright Visiting Astronomer at the
Infrared Telescope Facility, which is operated by the University of Hawaii
under contract 80HQTR19D0030 with the National Aeronautics and Space
Administration.  The Carl Sagan Center at the SETI Institute
189 Bernardo Ave., Suite 200
Mountain View, CA 94043, USA

(Received June 30, 2023; Revised September 7, 2023; Accepted September 8,
2023)

###### Abstract

Published near-infrared spectra of the four largest classical Uranian
satellites display the presence of discrete deposits of CO2 ice, along with
subtle absorption features around 2.2 µm. The two innermost satellites,
Miranda and Ariel, also possess surfaces heavily modified by past endogenic
activity. Previous observations of the smallest satellite, Miranda, have not
detected the presence of CO2 ice, and a report of an absorption feature at 2.2
$\mu$m has not been confirmed. An absorption feature at 2.2 $\mu$m could
result from exposed or emplaced NH3\- or NH4-bearing species, which have a
limited lifetime on Miranda’s surface, and therefore may imply that Miranda’s
internal activity was relatively recent. In this work, we analyzed near-
infrared spectra of Miranda to determine whether CO2 ice and the 2.2-$\mu$m
feature are present. We measured the band area and depth of the CO2 ice
triplet (1.966, 2.012, and 2.070 µm), a weak 2.13-$\mu$m band attributed to
CO2 ice mixed with H2O ice, and the 2.2-$\mu$m band. We confirmed a prior
detection of a 2.2-$\mu$m band on Miranda, but we found no evidence for CO2
ice, either as discrete deposits or mixed with H2O ice. We compared a high
signal-to-noise spectrum of Miranda to synthetic and laboratory spectra of
various candidate compounds to shed light on what species may be responsible
for the 2.2-$\mu$m band. We conclude that the 2.2-$\mu$m absorption is best
matched by a combination of NH3 ice with NH3-hydrates or NH3-H2O mixtures.
NH4-bearing salts like NH4Cl are also promising candidates that warrant
further investigation.

Planetary surfaces (2113); Surface composition (2115); Surface ices (2117);
Surface processes (2116); Uranian satellites (1750)

††journal: PSJ††facilities: ARC(TripleSpec), Gemini:Gillett(GNIRS),
IRTF(SpeX)††software: AstroPy (Astropy Collaboration et al., 2013), NumPy
(Harris et al., 2020), SciPy (Virtanen et al., 2020), Matplotlib (Hunter,
2007), JPL Horizons Online Ephemeris Service
(https://ssd.jpl.nasa.gov/horizons/), Spextool (Cushing et al., 2004; Vacca et
al., 2003), SIMBAD (Wenger et al., 2000), SpectRes (Carnall, 2017)

##  1 Introduction and Background

Ground-based near-infrared spectroscopic observations of the five classical
Uranian satellites have revealed that their surfaces are dominated by H2O ice,
mixed with a dark, low albedo component (Brown & Cruikshank, 1983; Brown &
Clark, 1984). Ariel, Umbriel, Titania, and Oberon show spectral evidence of
crystalline CO2 ice, primarily concentrated on their trailing hemispheres
(Grundy et al., 2003, 2006; Cartwright et al., 2015). In contrast, Miranda
does not show evidence of CO2 ice (Gourgeot et al., 2014; Cartwright et al.,
2018), possibly because its lower gravity prevents retention of CO2 (Grundy et
al., 2006; Sori et al., 2017).

All five satellites show evidence of a weak absorption feature near 2.2-$\mu$m
(Bauer et al., 2002; Cartwright et al., 2018, 2020b, 2023). This 2.2-$\mu$m
absorption feature appears qualitatively similar to the 2.21-$\mu$m band on
Charon, which has been attributed to NH-bearing species such as NH3-hydrates
and NH4Cl (e.g., Cook et al., 2007, 2018, 2023). Ammonia (NH3) acts as an
antifreeze and is predicted to have been incorporated into these icy bodies
during their formation. Ammonia at the surface of icy bodies is thought to be
dissociated by radiation on relatively short geological timescales (Strazzulla
& Palumbo, 1998; Moore et al., 2007). Detection of NH-bearing species could
then imply recent exposure by impacts, or perhaps emplacement by endogenic
processes like cryovolcanism. Previous work noted a weak 2.2-$\mu$m band in
spectra of Miranda (Bauer et al., 2002), but subsequent studies were unable to
confirm its presence (Gourgeot et al., 2014; Cartwright et al., 2018). New
ground-based near-IR spectra of Miranda were recently published with much
higher signal-to-noise ratios (S/N) compared to prior studies (DeColibus et
al., 2022). This new dataset was used to find subtle variations in H2O ice
band strengths between Miranda’s anti-Uranus and sub-Uranus quadrants
(DeColibus et al., 2022). We analyzed these higher quality spectra to perform
a new, in-depth investigation to determine whether CO2 ice and the 2.2-$\mu$m
absorption feature are present on Miranda.

In the following subsections we describe the state of knowledge for the
surface composition of Miranda and the other classical Uranian moons. We
discuss our Miranda data set in Section 2 and our analysis of integrated band
areas and depths of the CO2 ice triplet and the 2.13-$\mu$m and 2.2-$\mu$m
absorption bands in Section 3. We summarize our results in Section 4, our
spectral modeling in Section 5, and discuss the implications of our findings
in Section 6.

###  1.1 Geology of Miranda

Figure 1: (Left panel): An image mosaic of Miranda’s southern hemisphere from
imaging by Voyager 2 in 1986. We use an orthographic projection centered on
the south pole, using the Miranda mosaic produced by Schenk & Moore (2020).
The ‘coronae’ are regions heavily modified by tectonic activity and possessing
intriguing patches of high-albedo material. Only two of the disk-integrated
spectra in our dataset were observed with sub-observer latitudes on the
southern hemisphere: UT990607, green (Bauer et al., 2002) and UT000907, blue
(Cartwright et al., 2018). Errorbars in longitude represent the range of sub-
observer longitudes covered during the duration of that observation. (Right
panel): All other spectra in our dataset observed Miranda’s northern
hemisphere, which was in darkness at the time of the Voyager flyby and has no
imaging data available. Orange spectra were observed with TripleSpec, blue
spectra were observed with SpeX, and red spectra were observed with GNIRS.
Longitudes appear to increase in opposite directions as seen from the north
and south poles, so we chose to orient the 0°meridian at the top of the figure
in both panels.

Miranda is the smallest of the five classical Uranian satellites. With a
radius of $\sim$ 234 km, it is intermediate in size between the Saturnian
moons Mimas and Enceladus. Prior to the Voyager 2 flyby of Uranus in 1986,
Miranda was expected to possess a surface similar to Mimas (heavily cratered,
with minimal to no evidence of geological activity). However, imaging of
Miranda’s southern hemisphere collected by Voyager 2 revealed an icy body
where three large regions of its surface appeared to be geologically young
(called “coronae”), while other regions appeared to be ancient and heavily
cratered (Figure 1)(Smith et al., 1986; Greenberg et al., 1991; Schenk &
Moore, 2020). The coronae are bounded by large tectonic fault systems, and
both Arden and Inverness Corona possess patches of high albedo material that
might represent deposits of fresher H2O ice. At the time, the incongruity
between such a small icy body possessing complex tectonic and geological
surface features led to the suggestion that Miranda had been disrupted into
large chunks after a giant impact and subsequently reaccreted (Smith et al.,
1986; Janes & Melosh, 1988). Later work suggests that Miranda’s bizarre
coronae instead represent the surface expression of internal upwelling from
low order convection (e.g. Pappalardo et al., 1997; Hammond & Barr, 2014),
likely with tidal interactions from orbital resonances as a heat source.
Crater counts suggest that the coronae are geologically young (0.1 – 1 Gyr,
Zahnle et al. (2003); Kirchoff et al. (2022)), and Miranda’s larger neighbor
Ariel also displays a relatively young surface, implying that Miranda and
Ariel have both experienced complex geological histories.

Furthermore, it has previously been noted that Miranda’s large scale geology
is reminiscent of the similarly sized active ocean world Enceladus, such as
the presence of three regions of heavily tectonized terrain at the south pole
and near the centers of the leading and trailing hemispheres, interspersed
with heavily cratered ancient terrain (Pappalardo & Schubert, 2013;
Beddingfield & Cartwright, 2020). Miranda is not currently in an orbital
resonance that should produce significant internal heating, so the retention
of an Enceladus-like subsurface ocean over geological timescales is unlikely
(Hussmann et al., 2006; Castillo-Rogez et al., 2023). However, the surface
geology indicates that Miranda likely experienced one or more significant
heating events in the past (Beddingfield et al., 2015; Schenk & Moore, 2020;
Beddingfield et al., 2022), and the apparent youthfulness of the coronae
suggests that these events may have been geologically recent.

###  1.2 H2O and CO2 ice

The presence and spectral properties of H2O ice on the Uranian satellites have
been discussed at length in prior work (Brown & Cruikshank, 1983; Brown &
Clark, 1984; Grundy et al., 1999; Bauer et al., 2002; Grundy et al., 2003,
2006; Cartwright et al., 2015, 2018, 2020a; DeColibus et al., 2022). We
therefore give only a brief overview in this section. The surfaces of the
Uranian satellites are characterized primarily by their lower albedos in
comparison to similarly sized Saturnian satellites. These low albedos are
attributed to a dark, spectrally neutral component (often assumed to be
carbonaceous in nature) mantling or intermixed with the icy regolith. This
dark material effectively erases the 1.04-$\mu$m and 1.25-$\mu$m H2O ice bands
and substantially decreases the depth of the 1.5-$\mu$m and 2.0-$\mu$m
absorption band complexes. The four largest Uranian satellites show
leading/trailing asymmetries in the strength of their H2O ice bands, likely
due to a combination of magnetospheric irradiation and impact gardening.
Miranda does not show a leading/trailing asymmetry in the strength of its H2O
ice bands, although it possesses an anti-Uranus/sub-Uranus asymmetry instead
(Cartwright et al., 2018; DeColibus et al., 2022).

Previous work reported the presence of CO2 ice on the four largest Uranian
satellites (Grundy et al., 2003, 2006; Cartwright et al., 2015, 2022). This
CO2 ice is identified via a triplet of narrow absorption features at 1.966,
2.012, and 2.070 µm. Weaker CO2 ice absorption bands are also present at
1.543, 1.578, and 1.609 µm, mostly on Ariel, which has the strongest CO2 ice
signatures. These CO2 ice deposits are thought to be present primarily in pure
deposits and not intermixed with the H2O ice regolith. Furthermore, a
forbidden $2\nu_{3}$ overtone mode of CO2 exhibits an absorption feature near
2.134 $\mu$m (Bernstein et al., 2005), which only appears in molecular
mixtures of CO2 ice in H2O ice and/or methanol (CH3OH) ice, might be present
on Ariel (Cartwright et al., 2022) and Umbriel (Cartwright et al., 2023).

The distribution of CO2 ice on the Uranian moons shows both longitudinal and
planetocentric trends. The CO2 absorption features are stronger on moons
closer to Uranus, and on each individual moon, the CO2 ice bands are stronger
on their trailing hemispheres. This information supports an interpretation in
which CO2 molecules are produced in situ by magnetospheric bombardment of the
trailing hemispheres of the Uranian satellites. Irradiation of the H2O ice and
carbonaceous compounds in the regolith dissociates molecules that then
recombine into CO2, potentially with CO as an intermediary product (Cartwright
et al., 2022). Plasma densities in the magnetosphere are higher closer to
Uranus, implying that a radiolytic production process of CO2 should plausibly
be more effective on moons closer to the planet. This assertion is supported
by the relative strength of the CO2 absorption features across the various
satellites, as the CO2 signature is strongest on Ariel and weakest on Oberon,
which spends part of its orbit outside of the Uranian magnetosphere (Ness et
al., 1986). Thermodynamical modeling work indicates that radiolytically
generated CO2 molecules should preferentially accumulate in cold traps at low
latitudes on the trailing hemispheres of each satellite, assuming radiolytic
production is greater on their trailing sides (Grundy et al., 2006; Sori et
al., 2017). More recent telescope observations show a decrease in the strength
of the CO2 ice bands on Ariel at higher sub-observer latitudes, consistent
with the hypothesis that CO2 cold traps are concentrated at low latitudes
(Cartwright et al., 2022).

Miranda is the innermost of the five classical satellites, and therefore, it
should be the most irradiated by charged particles trapped in the Uranian
magnetosphere. Miranda presumably possesses the same “raw ingredients” in its
regolith (carbonaceous compounds and H2O ice) as the other Uranian satellites
(Brown & Clark, 1984), unless Miranda formed from a different mix of
materials, possibly as a consequence of the Uranus-tilting event (Rufu &
Canup, 2022; Salmon & Canup, 2022). It therefore follows that radiolytic
production of CO2 molecules should also be occurring on Miranda, and it may
also maintain deposits of CO2 ice like the other Uranian moons. However,
previous spectroscopic studies of Miranda have not detected CO2 ice on its
surface (Bauer et al., 2002; Gourgeot et al., 2014; Cartwright et al., 2018).
These prior studies were somewhat limited by low signal-to-noise ratio (S/N)
reflectance spectra in the 2.0-$\mu$m region, due to several observational
limitations. Miranda is much fainter than the other Uranian moons at
K${}_{mag}\sim 15$, compared to K${}_{mag}\sim$12-13 for the larger moons. The
CO2 ice absorption features of interest are narrow, requiring higher spectral
resolving power and therefore lower S/N per spectral pixel. The CO2 ice
absorption bands are superimposed on the wide and deep 2.0-$\mu$m H2O ice
absorption band, and the CO2 ice bands are also in a region of strong telluric
absorption from CO2 in the Earth’s atmosphere. Although the spectral signature
of atmospheric CO2 is distinctly different than that of crystalline CO2 ice
(e.g., Hansen, 1997), telluric contamination introduces additional uncertainty
into the spectral data points. These prior observations established CO2 ice
band depth upper limits of 5% of the continuum on Miranda. Therefore, if CO2
ice is present, it is much less abundant on Miranda than on Ariel (Cartwright
et al., 2018). Additionally, CO2 molecules in a molecular mixture with H2O ice
might be present and detectable prior to escaping Miranda’s low gravity.
Investigating whether Miranda spectra show the 2.13-$\mu$m $2\nu_{3}$ overtone
band could help determine whether regolith-mixed CO2 is present. The primary
questions relating to CO2 that this work aims to answer are therefore twofold:
(1) do concentrated CO2 ice deposits exist on Miranda’s surface at low
abundances, and (2) is there evidence for CO2 in a molecular mixture with H2O
ice in the regolith?

###  1.3 The 2.2-$\mu$m feature

Some icy bodies show evidence for weak absorption features in the region
between 2.18 and 2.26 µm, which we refer to generically as the 2.2-$\mu$m
feature. The 2.2-$\mu$m feature on icy bodies has frequently been attributed
to ammonia (NH3)- or ammonium (NH4)-bearing compounds (which we will
collectively refer to as NH-bearing). NH-bearing species are of significant
geological and astrobiological interest, as NH3 is a potent antifreeze,
capable of reducing the freezing point of liquid H2O by nearly 100 K if
present in sufficiently high abundances (Kargel, 1992). This makes NH3 an
important compound for enabling internal activity and extending the retention
of subsurface oceans on icy bodies. NH4-bearing salts and minerals are much
less effective than NH3 in an antifreeze role (Neveu et al., 2017), but
indicate the past presence of NH3, and NH${}_{4}^{+}$ is readily produced by
irradiation of H2O + NH3 ice mixtures (Moore et al., 2003, 2007).

Despite the expected ubiquity of NH3-bearing compounds in the solar nebula at
intermediate to large heliocentric distances (Lewis, 1971), the 2.2-$\mu$m
feature is not observed in the spectra of many icy bodies, possibly because of
removal by irradiation over short geological timescales. In the case of
Miranda, NH3 may be effectively removed from its surface in timescales as
short as $<$106 years (Moore et al., 2007). Detection of the 2.2-$\mu$m
feature could therefore imply that NH3-bearing compounds have been exposed or
emplaced in the geologically recent past, either via endogenic processes such
as tectonism and cryovolcanism or via mass wasting and impact events. The
possibility of recent endogenic activity on Miranda is particularly
tantalizing given the apparent youth of some regions of its heavily modified
surface, discussed in §1.1, and past reports of a weak 2.2-$\mu$m absorption
feature (Bauer et al., 2002).

####  1.3.1 The 2.2-$\mu$m feature on other icy bodies

One of the icy bodies that shows the most consistent evidence of a 2.2-$\mu$m
feature is Charon (e.g., Brown & Calvin, 2000; Dumas et al., 2001). Prior to
the New Horizons flyby of the Pluto system, ground-based spectroscopic studies
investigated the 2.2-$\mu$m feature on Charon in detail, finding evidence for
longitudinal variation in the strength and wavelength position of the
2.2-$\mu$m band (Cook et al., 2007; Merlin et al., 2010; DeMeo et al., 2015;
Holler et al., 2017). Data acquired during the New Horizons flyby further
confirmed the band’s presence on Charon and an apparent spatial association
with impact craters (Grundy et al., 2016; Cook et al., 2018; Dalle Ore et al.,
2018). Dalle Ore et al. (2019) and Cruikshank et al. (2019) found the
2.2-$\mu$m band to be present near geologically young surface features on
Pluto that also exhibit spectral evidence of H2O ice, strengthening a possible
association with emplacement of NH-bearing compounds via
cryovolcanism/internal activity. In contrast, Cook et al. (2018) reported on
strong 2.2-$\mu$m bands on Pluto’s minor moons Nix and Hydra, which are too
small to support internal geological activity.

In addition to the Uranian satellites and icy bodies in the Pluto system,
detection of weak 2.2-$\mu$m features also have been reported on Enceladus
(Emery et al., 2005; Verbiscer et al., 2006), Tethys (Verbiscer et al., 2008),
Orcus (Carry et al., 2011), Haumea and its satellite Hi’iaka (Barkume et al.,
2006), and Quaoar (Jewitt & Luu, 2004). NH4-bearing species have been reported
on Ceres (King et al., 1992; de Sanctis et al., 2016; Raponi et al., 2019) and
comets (Poch et al., 2020), and the 2.2-$\mu$m feature on Charon and the
smaller moons in the Pluto system has been attributed to NH4Cl (Cook et al.,
2018, 2023). However, a 2.2-$\mu$m absorption band is not exclusive to NH-
bearing species. Other minerals and compounds can also exhibit absorption in
this region, including many phyllosilicates (hydrated silicates) with an Al-OH
bond (Clark et al., 1990). Certain types of phyllosilicates are also prone to
incorporating NH4 into their composition through cation exchange processes
(Bishop et al., 2002; Berg et al., 2016).

####  1.3.2 The 2.2-$\mu$m feature on the Uranian satellites

Bauer et al. (2002) was the first work to identify a 2.2-$\mu$m feature on any
of the Uranian satellites, reporting a relatively strong band on Miranda
(plotted in green in the left panel of Figure 2). The authors reported an
absorption band similar to that of the 2.21-$\mu$m feature on Charon, and
attributed it to ammonia hydrate (NH${}_{3}\cdot n$H2O). At the time, Miranda
was only the third icy body on which a 2.2-$\mu$m band had been reported.
However, subsequent spectral studies of Miranda (Gourgeot et al., 2014;
Cartwright et al., 2018) did not find conclusive evidence of a 2.2-$\mu$m
absorption feature, leaving its existence an open question.

From visual inspection, Cartwright et al. (2018) noted weak absorption
features in the 2.2-$\mu$m region on Ariel, Umbriel, Titania, and Oberon. The
authors followed up with a detailed study of 2.2-$\mu$m features on Ariel in
Cartwright et al. (2020b), finding several different absorption bands
associated with NH3\- and NH4-bearing compounds, which varied in strength and
band center in different spectra. They found no large scale longitudinal
patterns in these variations. They compared these bands with NH3 hydrates
(NH${}_{3}\cdot n$H2O, 2.215 µm), flash frozen NH3-H2O solutions (2.210 µm),
NH3 ice (2.238 µm), and an NH4-bearing species (possibly (NH4)2CO3, 2.181 µm).
Some of these bands have been reported to show double absorptions and
wavelength shifts based on temperature and the ratio of NH3 to H2O (Moore et
al., 2007), further complicating the identification of individual compounds.

Further research has also presented evidence of similar weak absorption
features in the 2.2-$\mu$m region on Umbriel (Cartwright et al., 2023).
However, the surface of Umbriel is ancient and heavily cratered (within the
resolution limits of Voyager 2 imaging), lacking evidence of resurfacing
driven by endogenic activity. The presence of 2.2-$\mu$m bands in spectra of
Umbriel raises important questions about the presumed short lifetime of NH-
bearing species on the surfaces of the Uranian moons (Moore et al., 2007), and
also raises the possibility that other species such as phyllosilicate minerals
or nitrogen-bearing organics contribute to the 2.2-$\mu$m band, at least on
Umbriel.

##  2 Observations

Figure 2: (Left panel): Examples of Miranda spectra displaying weak absorption
features around 2.2 µm. The green spectrum is the (unbinned) spectrum reported
in Bauer et al. (2002). The two blue spectra were obtained with SpeX in the
PRISM and SXD configuration (unbinned and binned by 10 pixels, respectively).
The orange spectra are spectra from individual nights with TripleSpec (binned
by 30 pixels). The text next to each spectrum indicates the date of
observation in format UTYYMMDD (e.g. UT200907 = UT 2020-09-07). This UTYYMMDD
date format is used throughout this work. Vertical lines are placed at the
expected wavelengths for the absorption features studied in this work: brown
lines at 1.966, 2.012, and 2.070 $\mu$m for the CO2 ice triplet, a black line
at 2.134 $\mu$m for a feature associated with molecular mixtures including CO2
ice, a blue line at 2.21 $\mu$m for NH3-hydrates, and a blue line at 2.24
$\mu$m for crystalline NH3 ice. The shaded region indicates the wavelength
range measured for the 2.2-$\mu$m band in this work. (Right panel): The GNIRS
spectra and TripleSpec quadrant and hemisphere grand average spectra
originally reported in DeColibus et al. (2022). Colored points are binned by
15 pixels, and the gray error bars are presented at the native resolution of
the data. Table 1: Miranda Observations

Observing PI | Year(s) | Latitude(s) | Telescope | Instrument | Resolving power | Nspec | Reference
---|---|---|---|---|---|---|---
|  | °N, Sub-Earth |  |  | ($\lambda/\Delta\lambda$) |  |
Bauer | 1999 | -36.5 | UKIRT | CGS4 |  $\sim$200 | 1 | Bauer et al. (2002)
Rivkin | 2000 | -35.4 | IRTF | SpeX SXD |  $\sim$750 | 1 | Cartwright et al. (2018)
Gourgeot | 2012 | 21.4 | IRTF | SpeX SXD |  $\sim$750 | 2 | Gourgeot et al. (2014)
Cartwright | 2014–2017 | 24.7 – 36.7 | IRTF | SpeX SXD |  $\sim$750 | 2 | Cartwright et al. (2018)
Cartwright | 2014–2017 | 24.7 – 36.7 | IRTF | SpeX PRISM |  $\sim$95 | 5 | Cartwright et al. (2018)
DeColibus | 2019–2021 | 42.3 – 50.4 | ARC 3.5m | TripleSpec |  $\sim$3500 | 18 | DeColibus et al. (2022)
DeColibus | 2020 | 47.2 – 49.6 | Gemini N | GNIRS XD |  $\sim$1130 | 2 | DeColibus et al. (2022)
DeColibus | 2021 | 53.3 – 53.8 | Gemini N | GNIRS XD |  $\sim$750 | 2 | DeColibus et al. (2022)

Note. — A table of basic information about the collection of Miranda spectra
analyzed in this work. For more details, we direct the reader to the listed
references.

We analyzed 33 disk-integrated near-IR spectra of Miranda, covering the
wavelengths between $\sim$0.95 – 2.45 µm, summarized in Table 1. Eighteen of
these spectra were obtained with the TripleSpec spectrograph on the ARC
3.5-meter telescope at Apache Point Observatory, four spectra were acquired
with GNIRS on the 8.1-meter Gemini North telescope on Maunakea, and ten
spectra were observed with SpeX on NASA’s 3-meter Infrared Telescope Facility
(IRTF) on Maunakea. For information on the acquisition and data reduction of
the TripleSpec and GNIRS spectra, we refer the reader to DeColibus et al.
(2022), while for the SpeX spectra, we refer the reader to Gourgeot et al.
(2014) and Cartwright et al. (2018). Table 1 lists the average spectral
resolving power ($R=\lambda/\Delta\lambda$) of data acquired with each
instrument configuration. Two spectral data points can be placed across the
narrow CO2 absorption bands at R$\sim$750, so they should be detectable in
spectra acquired at this or higher spectral resolution. All of the spectra
except those acquired with the SpeX PRISM configuration have sufficient
spectral resolution to at least detect the CO2 bands, and the 2.2-$\mu$m
feature is broad enough to be detectable in the PRISM spectra. The dataset
also includes seven TripleSpec ‘grand average’ (GAvg) spectra, which were
constructed as averages of all TripleSpec exposures in which the sub-observer
longitude fell within defined ranges. These are the leading, trailing, sub-
Uranus, and anti-Uranus quadrants; the leading and trailing hemispheres; and
all exposures regardless of longitude. These grand average spectra and the
GNIRS spectra are plotted in Figure 2.

We also modified one spectrum in the above dataset. The GNIRS anti-Uranus
quadrant spectrum from UT211121 displayed a high S/N, but the error bars on
the spectrum were uniformly overestimated compared to what might reasonably be
expected given the apparent S/N of the data and when compared to the other
GNIRS spectra obtained in similar conditions (see Figure 5 of DeColibus et al.
(2022)). In order to calculate more accurate uncertainties for each data point
while retaining wavelength-dependent error information, such as increased
uncertainties in regions of heavy telluric absorption, we adopted a procedure
similar to that of Holler et al. (2022). We calculated the standard deviation
of the flux values and the mean of the original uncertainty values in a region
of the spectrum that could reasonably be described by a flat continuum (1.70 –
1.80 µm). Division of these two quantities results in the factor by which the
errors in the original spectrum were overestimated, approximately $\sim$3.32.
Division by this factor resulted in a more accurate estimate of the
uncertainties for the data points in that spectrum, and the corrected spectrum
was used for all analyses presented here.

Finally, we also digitized the spectrum of Miranda’s leading hemisphere
published in Bauer et al. (2002), in which the presence of a 2.2-$\mu$m
feature was first reported. The K-band portion of this spectrum was acquired
on 1999 June 7 with the CGS4 spectrograph on the 3.8-meter UKIRT telescope on
Maunakea. We utilized timing and observing geometry information provided in
Table 1 of Bauer et al. (2002), combined with the JPL HORIZONS ephemeris
service, to derive a central sub-observer longitude of 75.7°E and a latitude
of 36.5°S. For further information on the Bauer et al. spectrum, we direct the
reader to the original work. This spectrum and one SpeX SXD spectrum acquired
in 2000 at latitude 35.4°S are the only two southern hemisphere spectra in our
data set. All other spectra were acquired at northern sub-observer latitudes
(Figure 1).

##  3 Spectral Analysis

We measured the integrated band areas of three CO2 ice bands in the Miranda
spectra. The CO2 ice bands at 1.966, 2.012, and 2.070 $\mu$m are referred to
in this work as the “CO2 ice triplet” as a whole and as bands 1, 2, and 3
individually. We also measured the integrated band areas and fractional band
depths of a subtle feature at 2.13-$\mu$m and the 2.2-$\mu$m absorption band.

###  3.1 Band measurement methods

Figure 3: A demonstration of the band area and depth measurement process for
the CO2 ice triplet and the 2.13-$\mu$m and 2.2-$\mu$m bands, using the GNIRS
leading hemisphere spectrum of Miranda from UT201008. The data points over
which the band areas are integrated are marked in blue, the points where the
band depth is measured in red, continuum fits are cyan lines, and Gaussian
band fits are orange lines. A copy of the spectrum plotted with an offset has
been binned by five pixels (turquoise points). Vertical lines are the same as
in Figure 2. Table 2: Absorption band wavelengths

Band name | Left continuum | Band width | Right continuum | Center
---|---|---|---|---
| ($\mu m$) | ($\mu m$) | ($\mu m$) | ($\mu m$)
CO2 2$\nu_{1}$+$\nu_{3}$ (Band 1) | 1.957 – 1.962 | 1.962 – 1.969 | 1.969 – 1.974 | 1.966
CO2 $\nu_{1}$+2$\nu_{2}$+$\nu_{3}$ (Band 2) | 2.002 – 2.008 | 2.008 – 2.015 | 2.015 – 2.020 | 2.012
CO2 4$\nu_{2}$+$\nu_{3}$ (Band 3) | 2.062 – 2.068 | 2.068 – 2.073 | 2.073 – 2.079 | 2.070
2.13-$\mu$m band |  $\cdots$ | 2.121 – 2.135 |  $\cdots$ | 2.134
2.2-$\mu$m band |  $\cdots$ | 2.186 – 2.251 |  $\cdots$ | 2.21

Note. — We tabulate the wavelengths we used to define the band continua,
widths, and centers. For the 2.13-$\mu$m and 2.2-$\mu$m band, the continuum
was fit with the 3rd degree polynomial fit described in the text. ‘Center’
refers to the expected central wavelength of the absorption band.

Our band area and depth measurements were conducted with the same analysis
routine described in DeColibus et al. (2022), modified for use on the CO2 ice
bands, 2.13-$\mu$m band, and 2.2-$\mu$m band. This routine is a Python
implementation of the technique described in Cartwright et al. (2015, 2018),
which used a modified version of the SARA band analysis routine originally
developed for asteroid spectra (Lindsay et al., 2015). The band analysis code
generates a sample spectrum, drawing from a Gaussian distribution where the
mean and standard deviation are the flux and errors of the input spectrum,
respectively. The absorption bands of interest (Table 2) are measured by
drawing a line between the continuum on either side of the absorption band,
normalizing by this line, and integrating the area inside the absorption band
with the trapezoidal rule. The CO2 ice absorption bands are further fit by a
Gaussian function to determine the band centers, from which the depths of the
bands are measured using the points within 0.0005 $\mu$m of the center of the
band. This choice of band width for the depth measurement was determined from
inspection of the CO2 ice bands in spectra of Ariel. This process is
demonstrated visually using a GNIRS spectrum of Miranda’s leading hemisphere
in Figure 3. To calculate the uncertainties on each measurement, this entire
sample spectrum generation and measurement process is repeated 20,000 times,
which is a number of samples consistent with other Monte Carlo type approaches
to measurements of band parameters (e.g. Lindsay et al., 2015; Cartwright et
al., 2015). The mean and standard deviation of the measurements of this
ensemble are reported as the final band measurements for each individual
spectrum in Table 3. For each spectrum, we also summed the band area
measurements for the three CO2 bands into a total CO2 band area. Due to
inadequate spectral resolution, we did not measure the CO2 ice triplet for the
Bauer et al. (2002) spectrum nor the SpeX spectra collected in PRISM mode.

The process for the 2.13-$\mu$m and 2.2-$\mu$m bands was slightly different.
Instead of measuring the continuum by drawing a line on either side of the
absorption band, the continuum is defined with a third-order polynomial curve,
fit to the data points between 2.11 – 2.19 $\mu$m and 2.23 – 2.34 µm. The
region between 2.19 – 2.23 $\mu$m is not used in the fit to avoid the
influence of any possible 2.2-$\mu$m absorption features. The spectrum is
divided by this continuum model, and the integrated band areas and fractional
band depths are measured in wavelength ranges corresponding to the absorption
bands of interest. We used a Gaussian fit procedure similar to the one used
for the CO2 ice triplet to measure the central wavelength and depth of the
2.13-$\mu$m band. However, for the 2.2-$\mu$m band, the potential presence of
multiple absorptions across the 2.18 – 2.25 $\mu$m range would be poorly fit
by a Gaussian model. We instead binned the spectrum by five pixels and chose
the lowest data point in the continuum-divided band as the central wavelength.
The fractional band depth for the 2.2-$\mu$m band are measured using the mean
of the unbinned, native resolution data points within $\pm$0.002 $\mu$m of
this central wavelength. This process was also iterated 20,000 times for each
spectrum, and the mean and standard deviation of the measurements for each
individual spectrum are reported in Table 4.

###  3.2 Means, ratios, and sinusoidal models

We calculated the mean band parameters, using the final measurements of each
of the spectra that fall within given sub-observer longitude quadrants and
hemispheres. We also calculated a set of mean measurements that included all
spectra from individual nights (i.e. not including the TripleSpec grand
averages). These mean measurements are tabulated in Table 5 and plotted in
Figure 5. Figure 5 also includes the band measurements from the quadrant and
hemisphere-averaged TripleSpec grand average spectra and the GNIRS spectra for
comparison to the mean measurements.

We took the ratios of the mean band measurements between opposing quadrants
and hemispheres (Table 6) to test whether a band was statistically stronger on
one quadrant/hemisphere versus the other, as might be expected from exogenic
effects. We did not find statistically significant ($\geq 2\sigma$) departures
from a ratio of unity for any of the measurements or quadrant/hemisphere
pairs.

We fit our band measurements to a sinusoidal model to search for longitudinal
variation, with the period fixed at 2$\pi$ to represent one rotation of the
body. This approach has previously been used for Miranda and the other Uranian
satellites (Grundy et al., 2006; Cartwright et al., 2015, 2018; DeColibus et
al., 2022) and we direct the reader to those works for further information. We
also applied an F-test to the sinusoidal models, which allows us to discern
whether the sinusoidal model fit is a statistically significant better fit
compared to the null hypothesis (no variation with sub-observer longitude).
The sinusoidal models and F-tests are tabulated in Table 7.

###  3.3 Hapke-Mie modeling

We constructed spectral models in order to investigate possible absorption
features in the 2.2-$\mu$m region. We chose a hybrid Hapke-Mie model using
intimate (particulate) mixing, as has previously been done for the Uranian
satellites (Cartwright et al., 2015, 2018, 2020a). The Hapke-Mie model
utilizes Mie theory to calculate the single scattering albedo of individual
particles, which are then incorporated into the standard Hapke model
equations. We assume an isotropic single scattering phase function which does
not depend on wavelength. The Hapke-Mie approach accounts for the effects of
grain sizes approaching wavelength, such as diffraction and Rayleigh
scattering (Clark et al., 2012). However, at some particle sizes the exact Mie
solution can introduce periodic resonance artifacts in the resulting spectrum.
We mitigate this effect by calculating the average albedo of a spread of sizes
around the specified grain size, typically with a 10% spread in particle
diameter.

As has been noted by previous studies, Miranda’s spectrum is consistent with a
surface composition incorporating H2O ice and a dark, spectrally neutral
component, such as amorphous carbon (Brown & Clark, 1984; Bauer et al., 2002;
Gourgeot et al., 2014). We scaled our observed spectra to a geometric albedo
of 0.434 at 1.72 $\mu$m (from Figure 7 of Karkoschka (2001)). For our models,
we used the optical constants of crystalline H2O ice at 80 K from Mastrapa et
al. (2008) and optical constants of amorphous carbon (sample BE1) from Rouleau
& Martin (1991).

We found that a small percentage of intimately mixed sub-micron H2O ice grains
assist in reproducing Miranda’s spectrum. The central wavelength of the
2.0-$\mu$m H2O ice band is shifted to slightly longer wavelengths, the
continuum in the 2.2-$\mu$m region is low compared to the 1.8-$\mu$m
continuum, and the blue slope from 2.3 – 2.5 $\mu$m is steeper than in typical
H2O ice models of larger diameter grains. These characteristics are consistent
with the presence of sub-micron H2O ice grains (Clark et al., 2012), and
previous studies have suggested that the regoliths of the Uranian satellites
show a ‘fluffy’ structure and evidence of the presence of tiny grains with
sub-micron diameters, likely composed of H2O ice (Afanasiev et al., 2014;
Cartwright et al., 2020a).

We adjusted individual parameters (grain size and mixing ratio) of the model
components until we found a fit that generally reproduced the continuum shape
of our spectra between 2.0 – 2.4 µm. We specifically attempted to be agnostic
regarding any possible absorption features in the 2.2-$\mu$m region, as the
possible presence of several overlapping weak bands made identifying a ‘clean’
continuum difficult. because of degeneracies between model parameters, our
spectral models provide useful but non-unique solutions. We also experimented
with the addition of small amounts of other compounds (such as NH3 ice) to
study their effects on the resulting spectra. This analysis is described
further in §5.

##  4 Results

Figure 4: Band area and depth measurements for each Miranda spectrum in this
work, with 1$\sigma$ error bars. Band area and depth measurements that are not
statistically significant ($<$2$\sigma$ from zero) are plotted as gray
triangles, while those that are $\geq$2$\sigma$ are plotted as red triangles.
Quadrant-averaged mean band parameters (Table 5) are plotted as purple
squares. The gray shaded regions on either side of each plot represent
overlapping longitudes. Data points are duplicated in these regions to better
visualize possible sinusoidal variations with longitude. The weighted average
and sinusoidal fit to all spectra for each measurement are plotted as golden
horizontal lines and gray dot-dashed lines, respectively. Top left: Total band
areas for the CO2 ice triplet measurements (sum of the 1.966, 2.012, and 2.070
$\mu$m band areas). Center row: Band area measurements (left panel) and band
depths (right panel) for the 2.13-$\mu$m band. Bottom row: Same as the center
row, but for the 2.2-$\mu$m band.

Figure 5: Band area and depth measurements for the high S/N Miranda spectra
(GNIRS spectra and the TripleSpec quadrant/hemisphere grand average spectra),
along with the same mean measurements (purple squares) plotted in the previous
figure. All error bars represent 1$\sigma$ uncertainties. The weighted average
and sinusoidal fits use the mean band measurements. Table 3: CO2 triplet band
measurements

UT Date | Long. | Lat. | Integrated band area | Total CO2 | $>2\sigma$ | Band depths
---|---|---|---|---|---|---
|  |  | 1.966-$\mu$m | 2.012-$\mu$m | 2.070-$\mu$m | band area | total | 1.966-$\mu$m | 2.012-$\mu$m | 2.070-$\mu$m
| (°E) | (°N) | (10${}^{-4}\mu$m) | (10${}^{-4}\mu$m) | (10${}^{-4}\mu$m) | (10${}^{-4}\mu$m) | area? | (%) | (%) | (%)
UT210115 | 11.8 | 47.2 | $-2.32\pm 5.07$ | $-2.60\pm 7.33$ | $0.08\pm 1.97$ | $-4.84\pm 9.13$ | No | $-0.00\pm 0.12$ | $0.01\pm 0.16$ | $0.04\pm 0.08$
UT201229b | 29.7 | 47.2 | $-11.33\pm 13.59$ | $-1.76\pm 17.21$ | $-0.39\pm 3.24$ | $-13.48\pm 22.17$ | No | $-0.07\pm 0.27$ | $0.23\pm 0.32$ | $0.09\pm 0.12$
UT000907 | 36.3 | -35.4 | $0.51\pm 1.07$ | $-0.00\pm 1.91$ | $0.64\pm 0.59$ | $1.15\pm 2.27$ | No | $0.02\pm 0.03$ | $0.07\pm 0.04$ | $0.03\pm 0.04$
UT191022a | 37.7 | 44.3 | $-7.37\pm 14.71$ | $-6.94\pm 25.97$ | $6.28\pm 4.22$ | $-8.03\pm 30.15$ | No | $0.08\pm 0.39$ | $0.00\pm 0.50$ | $0.22\pm 0.16$
UT210101 | 51.8 | 47.2 | $3.31\pm 2.02$ | $-3.14\pm 3.93$ | $-1.41\pm 1.10$ | $-1.23\pm 4.55$ | No | $0.08\pm 0.05$ | $0.01\pm 0.10$ | $-0.01\pm 0.04$
UT201104 | 68.7 | 48.7 | $-0.75\pm 3.21$ | $-7.18\pm 4.97$ | $-1.51\pm 1.38$ | $-9.44\pm 6.07$ | No | $0.08\pm 0.07$ | $-0.06\pm 0.10$ | $-0.05\pm 0.05$
UT990607 | 75.7 | -36.5 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | No |  $\cdots$ |  $\cdots$ |  $\cdots$
UT170930 | 80.2 | 36.7 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | No |  $\cdots$ |  $\cdots$ |  $\cdots$
UT191104 | 80.5 | 43.8 | $1.84\pm 3.57$ | $\mathbf{7.66\pm 3.72}$ | $-0.66\pm 1.38$ | $8.84\pm 5.34$ | No | $0.08\pm 0.11$ | $0.13\pm 0.12$ | $0.00\pm 0.05$
UT150912 | 92.1 | 30.4 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | No |  $\cdots$ |  $\cdots$ |  $\cdots$
UT200907 | 96.1 | 50.4 | $2.12\pm 5.72$ | $2.38\pm 5.36$ | $-3.87\pm 1.85$ | $0.63\pm 8.06$ | No | $0.07\pm 0.12$ | $0.13\pm 0.11$ | $-0.04\pm 0.08$
UT171010 | 107.1 | 36.1 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | No |  $\cdots$ |  $\cdots$ |  $\cdots$
UT201008g | 109.4 | 49.6 | $-0.70\pm 0.98$ | $1.84\pm 1.11$ | $0.17\pm 0.48$ | $1.31\pm 1.56$ | No | $-0.01\pm 0.02$ | $0.03\pm 0.03$ | $0.01\pm 0.03$
UT120926 | 152.6 | 21.4 | $-6.72\pm 8.24$ | $6.31\pm 9.35$ | $-0.14\pm 3.53$ | $-0.55\pm 12.96$ | No | $-0.01\pm 0.19$ | $0.14\pm 0.21$ | $0.06\pm 0.13$
UT201007 | 174.2 | 49.7 | $1.88\pm 2.56$ | $-1.10\pm 3.87$ | $-0.03\pm 1.15$ | $0.75\pm 4.78$ | No | $0.03\pm 0.07$ | $0.05\pm 0.10$ | $0.00\pm 0.05$
UT200913 | 184.9 | 50.3 | $-3.33\pm 5.43$ | $-5.83\pm 7.08$ | $-1.73\pm 1.94$ | $-10.89\pm 9.13$ | No | $-0.02\pm 0.12$ | $-0.04\pm 0.17$ | $0.02\pm 0.07$
UT200930 | 192.8 | 49.9 | $2.79\pm 2.50$ | $3.53\pm 3.78$ | $0.09\pm 1.21$ | $6.41\pm 4.69$ | No | $0.07\pm 0.06$ | $0.11\pm 0.08$ | $0.03\pm 0.05$
UT211121g | 203.7 | 53.3 | $0.45\pm 0.82$ | $1.37\pm 1.00$ | $0.46\pm 0.52$ | $2.28\pm 1.39$ | No | $0.01\pm 0.02$ | $0.04\pm 0.02$ | $0.02\pm 0.02$
UT170925 | 232.5 | 36.7 | $2.16\pm 3.18$ | $-6.70\pm 6.83$ | $-2.47\pm 2.36$ | $-7.01\pm 7.89$ | No | $0.13\pm 0.09$ | $-0.01\pm 0.17$ | $-0.03\pm 0.11$
UT150911 | 236.2 | 30.4 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | No |  $\cdots$ |  $\cdots$ |  $\cdots$
UT120925 | 256.1 | 21.4 | $1.04\pm 6.31$ | $1.87\pm 7.57$ | $0.11\pm 4.34$ | $3.02\pm 10.77$ | No | $0.09\pm 0.15$ | $0.07\pm 0.17$ | $0.06\pm 0.15$
UT201013 | 262.8 | 49.5 | $2.59\pm 2.51$ | $-5.23\pm 4.03$ | $-0.19\pm 1.03$ | $-2.83\pm 4.86$ | No | $0.05\pm 0.05$ | $-0.06\pm 0.09$ | $0.03\pm 0.04$
UT201206 | 274.6 | 47.7 | $1.79\pm 2.80$ | $5.01\pm 3.46$ | $-0.80\pm 1.14$ | $6.00\pm 4.60$ | No | $0.03\pm 0.06$ | $0.10\pm 0.08$ | $-0.02\pm 0.05$
UT141130 | 279.4 | 24.7 | $6.22\pm 3.80$ | $3.88\pm 6.61$ | $1.89\pm 2.40$ | $11.99\pm 8.00$ | No | $0.11\pm 0.15$ | $0.14\pm 0.16$ | $0.06\pm 0.15$
UT150917 | 280.3 | 30.2 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | No |  $\cdots$ |  $\cdots$ |  $\cdots$
UT191013a | 285.7 | 44.6 | $3.95\pm 8.43$ | $8.51\pm 8.52$ | $4.64\pm 3.15$ | $17.10\pm 12.39$ | No | $0.12\pm 0.20$ | $0.19\pm 0.18$ | $0.13\pm 0.13$
UT200912 | 292.4 | 50.3 | $-3.68\pm 5.02$ | $-2.42\pm 6.16$ | $0.89\pm 1.75$ | $-5.21\pm 8.14$ | No | $-0.00\pm 0.10$ | $0.01\pm 0.14$ | $0.01\pm 0.08$
UT191026 | 308.2 | 44.2 | $4.07\pm 3.78$ | $-2.24\pm 6.00$ | $-0.60\pm 1.75$ | $1.23\pm 7.31$ | No | $0.15\pm 0.11$ | $0.03\pm 0.15$ | $0.07\pm 0.06$
UT201230g | 320.4 | 47.2 | $-7.25\pm 2.23$ | $5.07\pm 2.72$ | $0.83\pm 0.83$ | $-1.35\pm 3.62$ | No | $-0.07\pm 0.06$ | $\mathbf{0.14\pm 0.05}$ | $0.02\pm 0.04$
UT201229a | 348.6 | 47.2 | $-2.41\pm 8.91$ | $-20.80\pm 15.85$ | $3.28\pm 3.01$ | $-19.93\pm 18.43$ | No | $0.09\pm 0.24$ | $-0.24\pm 0.29$ | $0.14\pm 0.15$
UT210105 | 351.5 | 47.2 | $1.06\pm 2.48$ | $2.50\pm 3.52$ | $-0.82\pm 1.07$ | $2.74\pm 4.44$ | No | $0.06\pm 0.05$ | $0.07\pm 0.08$ | $-0.01\pm 0.04$
UT211106g | 355.4 | 53.8 | $0.32\pm 0.56$ | $1.13\pm 0.64$ | $0.17\pm 0.34$ | $1.62\pm 0.91$ | No | $0.02\pm 0.01$ | $0.04\pm 0.02$ | $0.01\pm 0.01$
UT201212 | 356.4 | 47.5 | $7.79\pm 4.94$ | $11.04\pm 6.14$ | $-0.93\pm 2.58$ | $\mathbf{17.90\pm 8.29}$ | Yes | $\mathbf{0.21\pm 0.10}$ | $0.20\pm 0.14$ | $-0.00\pm 0.12$
GAvg SQ | 3.8 | 47.0 | $1.48\pm 1.58$ | $0.12\pm 2.43$ | $-0.65\pm 0.72$ | $0.95\pm 2.99$ | No | $0.05\pm 0.03$ | $0.02\pm 0.06$ | $-0.02\pm 0.03$
GAvg LQ | 79.1 | 47.2 | $1.43\pm 1.74$ | $-0.21\pm 2.75$ | $-1.32\pm 0.80$ | $-0.10\pm 3.35$ | No | $0.05\pm 0.04$ | $0.02\pm 0.07$ | $-0.02\pm 0.03$
GAvg LH | 89.9 | 47.6 | $1.42\pm 1.11$ | $-0.48\pm 1.70$ | $-1.07\pm 0.51$ | $-0.13\pm 2.09$ | No | $0.04\pm 0.02$ | $0.01\pm 0.04$ | $-0.03\pm 0.02$
GAvg All | 176.8 | 48.0 | $1.58\pm 0.81$ | $-0.31\pm 1.19$ | $-0.46\pm 0.35$ | $0.82\pm 1.49$ | No | $0.03\pm 0.02$ | $0.00\pm 0.03$ | $-0.01\pm 0.01$
GAvg AQ | 184.1 | 50.0 | $1.60\pm 1.72$ | $0.12\pm 2.52$ | $-0.23\pm 0.77$ | $1.48\pm 3.15$ | No | $0.03\pm 0.04$ | $0.04\pm 0.06$ | $-0.01\pm 0.03$
GAvg TH | 274.6 | 48.3 | $1.78\pm 1.18$ | $-0.08\pm 1.70$ | $0.14\pm 0.50$ | $1.84\pm 2.13$ | No | $0.04\pm 0.02$ | $0.01\pm 0.04$ | $0.00\pm 0.02$
GAvg TQ | 280.7 | 48.1 | $2.06\pm 1.57$ | $-1.15\pm 2.30$ | $0.13\pm 0.65$ | $1.03\pm 2.86$ | No | $0.04\pm 0.03$ | $-0.00\pm 0.06$ | $0.01\pm 0.03$

Note. — The measured CO2 ice integrated band areas for each spectrum. All
errors are 1$\sigma$ errors, and measurements that are positive and $\geq
2\sigma$ from zero are printed in bold. None of the CO2 measurements reached
$\geq 3\sigma$ significance. We did not measure the CO2 ice triplet for
spectra acquired with the CGS4 instrument or the SpeX PRISM configuration. We
use the same UTYYMMDD date code for each spectrum as in the source dataset,
including additional letter suffixes: ‘a’ and ‘b’ refer to two separate
Miranda spectra observed on the same UT date that had a gap of several hours
between acquisition. The ‘g’ suffix indicates spectra obtained with GNIRS. The
last several rows of the table are our ‘TSpec grand average’ spectra, which
are combined spectra that include all TripleSpec exposures in which the
central longitude lies in a specific quadrant (Q) or hemisphere (H). The
quadrants and hemispheres are designated with initials: L, leading; T,
trailing; A, anti-Uranus; S, sub-Uranus.

Table 4: 2.13-$\mu$m and 2.2-$\mu$m band measurements

UT Date | Instrument | Long. | Lat. | 2.13-$\mu$m band | 2.2-$\mu$m band
---|---|---|---|---|---
|  |  |  | Band area | Band depth | Both | Band area | Band depth | Both | Center
|  | (°E) | (°N) | (10${}^{-4}\mu$m) | (%) |  $>2\sigma$? | (10${}^{-4}\mu$m) | (%) |  $>2\sigma$? | ($\mu$m)
UT210115 | TSpec | 11.8 | 47.2 | $1.50\pm 1.51$ | $1.3\pm 4.8$ | No |  $\mathbf{11.57\pm 3.56}$* | $\mathbf{6.3\pm 2.4}$ | Yes | $2.223\pm 0.016$
UT201229b | TSpec | 29.7 | 47.2 | $-1.29\pm 2.38$ | $3.2\pm 7.6$ | No | $7.28\pm 5.62$ | $\mathbf{9.3\pm 3.8}$ | No |  $\cdots$
UT000907 | SpeX SXD | 36.3 | -35.4 | $-0.58\pm 0.69$ | $1.4\pm 1.1$ | No | $0.51\pm 1.45$ | $\mathbf{1.9\pm 0.9}$ | No |  $\cdots$
UT191022a | TSpec | 37.7 | 44.3 | $-4.33\pm 3.99$ | $13.9\pm 10.5$ | No | $4.74\pm 9.17$ | $10.5\pm 5.8$ | No |  $\cdots$
UT210101 | TSpec | 51.8 | 47.2 | $0.29\pm 0.84$ | $3.0\pm 2.3$ | No | $3.58\pm 1.81$ | $\mathbf{3.0\pm 1.2}$ | No |  $\cdots$
UT201104 | TSpec | 68.7 | 48.7 | $0.66\pm 1.00$ | $\mathbf{6.7\pm 2.8}$ | No | $1.95\pm 2.44$ | $3.2\pm 1.7$ | No |  $\cdots$
UT990607 | CGS4 | 75.7 | -36.5 | $-5.41\pm 4.65$ | $-6.4\pm 5.8$ | No |  $\mathbf{30.75\pm 9.01}$* | $9.2\pm 4.8$ | No |  $\cdots$
UT170930 | SpeX PRISM | 80.2 | 36.7 | $0.47\pm 1.40$ | $2.5\pm 2.9$ | No | $5.91\pm 3.84$ | $2.8\pm 2.7$ | No |  $\cdots$
UT191104 | TSpec | 80.5 | 43.8 | $0.61\pm 1.05$ | $3.9\pm 3.5$ | No | $3.46\pm 2.42$ | $3.2\pm 1.6$ | No |  $\cdots$
UT150912 | SpeX PRISM | 92.1 | 30.4 | $0.19\pm 2.74$ | $4.8\pm 6.8$ | No | $4.19\pm 6.16$ | $7.8\pm 4.5$ | No |  $\cdots$
UT200907 | TSpec | 96.1 | 50.4 | $-1.23\pm 1.25$ | $5.0\pm 3.7$ | No | $\mathbf{8.13\pm 2.85}$ |  $\mathbf{5.3\pm 1.7}$* | Yes | $2.214\pm 0.013$
UT171010 | SpeX PRISM | 107.1 | 36.1 | $-1.18\pm 1.38$ | $-1.4\pm 2.5$ | No | $-6.74\pm 3.36$ | $1.1\pm 1.9$ | No |  $\cdots$
UT201008g | GNIRS | 109.4 | 49.6 | $0.19\pm 0.50$ | $1.5\pm 1.6$ | No |  $\mathbf{5.66\pm 1.16}$* |  $\mathbf{2.8\pm 0.5}$* | Yes* | $2.218\pm 0.016$
UT120926 | SpeX SXD | 152.6 | 21.4 | $0.61\pm 3.39$ | $5.2\pm 9.0$ | No | $9.73\pm 10.92$ | $12.2\pm 6.1$ | No |  $\cdots$
UT201007 | TSpec | 174.2 | 49.7 | $\mathbf{2.41\pm 0.90}$ | $5.6\pm 3.9$ | No | $0.49\pm 2.17$ | $2.8\pm 1.6$ | No |  $\cdots$
UT200913 | TSpec | 184.9 | 50.3 | $-0.72\pm 1.39$ | $1.5\pm 4.2$ | No | $-0.33\pm 3.28$ | $4.6\pm 2.6$ | No |  $\cdots$
UT200930 | TSpec | 192.8 | 49.9 | $-0.07\pm 0.91$ | $4.4\pm 3.1$ | No | $2.46\pm 2.14$ | $\mathbf{3.3\pm 1.3}$ | No |  $\cdots$
UT211121g | GNIRS | 203.7 | 53.3 | $-0.09\pm 0.48$ | $0.4\pm 1.5$ | No |  $\mathbf{5.90\pm 1.11}$* |  $\mathbf{2.7\pm 0.5}$* | Yes* | $2.219\pm 0.017$
UT170925 | SpeX SXD | 232.5 | 36.7 | $1.40\pm 1.92$ | $6.2\pm 8.3$ | No | $-15.49\pm 4.68$ | $3.9\pm 2.8$ | No |  $\cdots$
UT150911 | SpeX PRISM | 236.2 | 30.4 | $-5.87\pm 3.53$ | $-2.9\pm 7.4$ | No | $-3.87\pm 9.99$ | $13.3\pm 6.7$ | No |  $\cdots$
UT120925 | SpeX SXD | 256.1 | 21.4 | $-1.34\pm 4.18$ | $3.0\pm 12.3$ | No | $5.57\pm 10.71$ | $\mathbf{11.5\pm 5.2}$ | No |  $\cdots$
UT201013 | TSpec | 262.8 | 49.5 | $0.06\pm 0.78$ | $0.3\pm 2.6$ | No |  $\mathbf{8.27\pm 1.88}$* | $\mathbf{4.3\pm 1.6}$ | Yes | $2.211\pm 0.018$
UT201206 | TSpec | 274.6 | 47.7 | $-0.19\pm 0.87$ | $2.2\pm 2.7$ | No | $0.41\pm 1.96$ | $\mathbf{2.7\pm 1.3}$ | No |  $\cdots$
UT141130 | SpeX SXD | 279.4 | 24.7 | $1.52\pm 1.84$ | $5.0\pm 8.1$ | No | $\mathbf{10.49\pm 4.88}$ | $\mathbf{8.4\pm 2.9}$ | Yes | $2.219\pm 0.016$
UT150917 | SpeX PRISM | 280.3 | 30.2 | $-3.60\pm 1.70$ | $-1.8\pm 3.9$ | No | $-6.52\pm 4.20$ | $3.2\pm 2.7$ | No |  $\cdots$
UT191013a | TSpec | 285.7 | 44.6 | $-1.37\pm 2.37$ | $6.5\pm 6.6$ | No | $-2.41\pm 5.45$ | $\mathbf{6.9\pm 3.4}$ | No |  $\cdots$
UT200912 | TSpec | 292.4 | 50.3 | $-2.13\pm 1.21$ | $0.7\pm 3.8$ | No | $4.78\pm 2.91$ | $4.2\pm 2.1$ | No |  $\cdots$
UT191026 | TSpec | 308.2 | 44.2 | $1.87\pm 1.45$ | $2.9\pm 5.6$ | No |  $\mathbf{11.79\pm 3.25}$* | $\mathbf{6.6\pm 2.4}$ | Yes | $2.210\pm 0.015$
UT201230g | GNIRS | 320.4 | 47.2 | $0.28\pm 0.85$ | $2.9\pm 3.0$ | No | $3.22\pm 1.99$ |  $\mathbf{3.8\pm 1.0}$* | No |  $\cdots$
UT201229a | TSpec | 348.6 | 47.2 | $-0.72\pm 2.44$ | $6.4\pm 8.1$ | No | $3.49\pm 5.75$ | $7.9\pm 4.5$ | No |  $\cdots$
UT210105 | TSpec | 351.5 | 47.2 | $1.33\pm 0.78$ | $3.0\pm 2.0$ | No | $3.39\pm 1.79$ | $\mathbf{2.7\pm 1.1}$ | No |  $\cdots$
UT211106g | GNIRS | 355.4 | 53.8 | $0.32\pm 0.30$ | $0.4\pm 1.0$ | No |  $\mathbf{6.35\pm 0.70}$* |  $\mathbf{2.1\pm 0.3}$* | Yes* | $2.211\pm 0.010$
UT201212 | TSpec | 356.4 | 47.5 | $1.30\pm 1.86$ | $5.3\pm 6.5$ | No | $-4.64\pm 4.26$ | $3.1\pm 2.7$ | No |  $\cdots$
GAvg SQ | TSpec | 3.8 | 47.0 | $\mathbf{1.12\pm 0.53}$ | $2.1\pm 1.4$ | No |  $\mathbf{4.46\pm 1.23}$* | $\mathbf{2.5\pm 0.9}$ | Yes | $2.209\pm 0.011$
GAvg LQ | TSpec | 79.1 | 47.2 | $0.00\pm 0.59$ | $2.1\pm 1.7$ | No |  $\mathbf{4.28\pm 1.33}$* | $\mathbf{2.4\pm 0.9}$ | Yes | $2.215\pm 0.015$
GAvg LH | TSpec | 89.9 | 47.6 | $0.73\pm 0.38$ | $1.8\pm 1.1$ | No |  $\mathbf{3.53\pm 0.86}$* |  $\mathbf{2.3\pm 0.7}$* | Yes* | $2.203\pm 0.014$
GAvg All | TSpec | 176.8 | 48.0 | $0.44\pm 0.27$ | $1.3\pm 0.8$ | No |  $\mathbf{3.89\pm 0.62}$* |  $\mathbf{2.1\pm 0.4}$* | Yes* | $2.204\pm 0.013$
GAvg AQ | TSpec | 184.1 | 50.0 | $0.88\pm 0.58$ | $2.4\pm 1.9$ | No | $1.13\pm 1.40$ | $\mathbf{2.4\pm 1.0}$ | No |  $\cdots$
GAvg TH | TSpec | 274.6 | 48.3 | $0.14\pm 0.38$ | $1.0\pm 1.2$ | No |  $\mathbf{4.08\pm 0.89}$* |  $\mathbf{2.1\pm 0.6}$* | Yes* | $2.215\pm 0.013$
GAvg TQ | TSpec | 280.7 | 48.1 | $-0.14\pm 0.51$ | $0.4\pm 1.6$ | No |  $\mathbf{5.12\pm 1.16}$* | $\mathbf{2.5\pm 1.0}$ | Yes | $2.208\pm 0.013$

Note. — The measured integrated band areas and band depths for the 2.13-$\mu$m
and 2.2-$\mu$m bands in each spectrum. Central wavelengths for the 2.2-$\mu$m
band are only printed if both the area and depth measurements are $\geq
2\sigma$ from zero. Measurements which are $\geq 3\sigma$ from zero have an
asterisk. All errors are 1$\sigma$ errors. Other notation follows that of
Table 3.

Table 5: Mean band measurements

Quadrant | Longitude | Total CO2 area | 2.13-$\mu$m area | 2.13-$\mu$m depth | 2.2-$\mu$m area | 2.2-$\mu$m depth | 2.13-$\mu$m center | 2.2-$\mu$m center
---|---|---|---|---|---|---|---|---
| (range, °E) | (10${}^{-4}\mu$m) | (10${}^{-4}\mu$m) | (%) | (10${}^{-4}\mu$m) | (%) | ($\mu$m) | ($\mu$m)
all | 0 – 360 | $-0.07\pm 2.12$ | $-0.46\pm 0.49$ | $\mathbf{2.9\pm 1.2}$ | $\mathbf{3.76\pm 1.58}$ |  $\mathbf{5.4\pm 0.8}$* | $2.130\pm 0.001$ | $2.218\pm 0.003$
LH | 1 – 180 | $-2.26\pm 3.16$ | $-0.47\pm 0.78$ | $3.3\pm 1.8$ | $\mathbf{6.08\pm 2.50}$ |  $\mathbf{5.4\pm 1.2}$* | $2.130\pm 0.001$ | $2.219\pm 0.004$
TH | 181 – 360 | $1.44\pm 2.84$ | $-0.44\pm 0.64$ | $2.6\pm 1.5$ | $1.82\pm 1.93$ |  $\mathbf{5.3\pm 1.0}$* | $2.130\pm 0.001$ | $2.218\pm 0.004$
LQ | 45 – 135 | $0.02\pm 2.07$ | $-0.60\pm 0.94$ | $2.2\pm 1.9$ | $6.32\pm 3.65$ |  $\mathbf{4.3\pm 1.3}$* | $2.130\pm 0.001$ | $2.218\pm 0.005$
TQ | 225 – 315 | $3.04\pm 3.33$ | $-0.96\pm 1.05$ | $2.2\pm 2.4$ | $1.30\pm 3.26$ |  $\mathbf{6.5\pm 1.6}$* | $2.130\pm 0.001$ | $2.216\pm 0.006$
AQ | 135 – 225 | $-0.40\pm 4.49$ | $0.43\pm 0.95$ | $3.4\pm 2.5$ | $3.65\pm 3.01$ | $\mathbf{5.1\pm 2.3}$ | $2.130\pm 0.001$ | $2.219\pm 0.008$
SQ | 315 – 45 | $-2.69\pm 6.07$ | $-0.24\pm 0.90$ | $4.2\pm 2.4$ | $3.99\pm 2.14$ |  $\mathbf{5.3\pm 1.5}$* | $2.130\pm 0.001$ | $2.221\pm 0.006$

Note. — Mean band area and depth measurements, averaged over quadrants and
hemispheres. All errors are 1$\sigma$ errors. Measurements that are greater
than zero with $\geq 2\sigma$ significance are printed in bold, and $\geq
3\sigma$ with an asterisk. The quadrants (Q) and hemispheres (H) are
designated with initials: L, leading; T, trailing; A, anti-Uranus; S, sub-
Uranus. For example, LH indicates the leading hemisphere average of all
spectra with longitudes between 0 – 180°E.

Table 6: Quadrant/hemisphere ratios

Dataset | Ratio | Total CO2 area | 2.13-$\mu$m area | 2.13-$\mu$m depth | 2.2-$\mu$m area | 2.2-$\mu$m depth
---|---|---|---|---|---|---
All spectra | LQ/TQ | $0.01\pm 0.68$ | $0.62\pm 1.19$ | $0.98\pm 1.35$ | $4.86\pm 12.50$ | $0.66\pm 0.25$
| LH/TH | $-1.57\pm 3.79$ | $1.06\pm 2.33$ | $1.29\pm 1.03$ | $3.33\pm 3.78$ | $1.03\pm 0.31$
| AQ/SQ | $0.15\pm 1.70$ | $-1.77\pm 7.62$ | $0.81\pm 0.75$ | $0.91\pm 0.90$ | $0.97\pm 0.51$

Note. — Ratios of the band parameters between opposing quadrants and
hemispheres. All errors are 1$\sigma$ errors.

Table 7: Sinusoidal models and F-test

Dataset | Measurement | N | Long. Max | F-value | p-value | Reject?
---|---|---|---|---|---|---
All spectra | Total CO2 band area | 27 |  $\cdots$ | 0.198 | 0.82177 | No
| 2.13-$\mu m$ area | 33 |  $\cdots$ | 0.149 | 0.86231 | No
| 2.13-$\mu m$ depth | 33 |  $\cdots$ | 0.444 | 0.64557 | No
| 2.2-$\mu m$ area | 33 |  $\cdots$ | 0.342 | 0.71298 | No
| 2.2-$\mu m$ depth | 33 |  $\cdots$ | 0.902 | 0.41661 | No
| 2.2-$\mu m$ centers | 33 |  $\cdots$ | 0.064 | 0.93848 | No
Mean bands | Total CO2 band area | 4 |  $\cdots$ | 0.425 | 0.73538 | No
| 2.13-$\mu m$ area | 4 |  $\cdots$ | 0.196 | 0.84733 | No
| 2.13-$\mu m$ depth | 4 |  $\cdots$ | 0.056 | 0.94810 | No
| 2.2-$\mu m$ area | 4 | 89.8 | 844.862 | 0.02432 | Yes
| 2.2-$\mu m$ depth | 4 |  $\cdots$ | 105.062 | 0.06882 | No
| 2.2-$\mu m$ centers | 4 |  $\cdots$ | 0.202 | 0.84397 | No

Note. — Sinusoidal model fits versus longitude to the band parameters for two
sets of measurements: the individual band parameters for each spectrum, and
the mean band parameters (averaged over the four longitude quadrants). The
total CO2 band area has fewer measurements because we did not measure CO2 ice
in the CGS4 or SpeX PRISM spectra. The degrees of freedom for the sinusoidal
model fit is N - 3. We only print the longitude of maximum band strength for
the measurements where we rejected the null hypothesis ($p<0.05$).

###  4.1 CO2 ice triplet

The results of our CO2 triplet band measurements are shown in Table 3 and
Figures 4 and 5. Even the highest S/N Miranda spectra do not show adequate
evidence for the presence of the CO2 ice triplet around 2 µm. We measured the
areas and depths of each individual CO2 band, but $\geq$2$\sigma$ significance
in any of the band area or depth measurements were only measured in three
spectra. To assist in the detection of very faint features, we also calculated
the sum of all three CO2 ice band areas. However, only a single spectrum
(UT201212) passes the 2$\sigma$ threshold for the total CO2 band area. Visual
inspection of that spectrum and other spectra in which only a single band was
detected indicates that these ‘detections’ are simply spectral noise, probably
due to imperfect telluric correction, especially in the 1.966-$\mu$m band
affected by atmospheric water vapor. The quadrant- and hemisphere-averaged
means of the total CO2 band area (Table 5) only reinforces our non-detection.
We conclude that discrete deposits of CO2 ice are not present on Miranda in
amounts detectable by our observations.

###  4.2 2.13-$\mu$m feature

We also measured the band area and depth of the 2.13-$\mu$m feature in spectra
of Miranda, as this absorption band could potentially be associated with a
molecular mixture of CO2 and H2O ice (Bernstein et al., 2005). Weak absorption
features near this wavelength have been noted on both Ariel and Umbriel and
suggested to be potential evidence of CO2:H2O ice molecular mixtures as part
of the radiolytic CO2 production cycle (Cartwright et al., 2022, 2023). Our
band parameter measurements for the 2.13-$\mu$m band are shown in Table 4 and
Figures 4 and 5. Two spectra show $\geq 2\sigma$ significance in only the
2.13-$\mu$m area (UT201007 and the TripleSpec sub-Uranus quadrant grand
average) or only the 2.13-$\mu$m depth (UT201104), but none show $\geq
2\sigma$ significance in both. Our mean measurements do show $\geq 2\sigma$
significance in the 2.13-$\mu$m depth when taking the mean of all spectra,
regardless of longitude. However, the lack of consistency in the significance
of the band area and depth measurements leads us to conclude that there is
insufficient evidence for a 2.13-$\mu$m band on Miranda.

###  4.3 2.2-$\mu$m feature

The 2.2-$\mu$m bands in spectra of Miranda are weak, hindering clear
identifications of the compounds that might be responsible. Furthermore,
absorption bands in the 2.2-$\mu$m region can vary in central wavelength, with
absorptions previously reported on other bodies at wavelengths ranging from
2.18 $\mu$m to 2.25 µm. However, we measured non-zero band areas and depths in
many of our spectra: 8 out of the 33 spectra from individual nights have $\geq
2\sigma$ measurements of both 2.2-$\mu$m band areas and 2.2-$\mu$m band
depths, although a 2.2-$\mu$m feature is not always visually apparent. For the
GNIRS spectra, we measured $\geq 3\sigma$ significance in both 2.2-$\mu$m area
and depth for three out of the four spectra. We measured $\geq 3\sigma$
significance for both area and depth in three of the seven TripleSpec grand
average spectra, and $\geq 2\sigma$ significance for six of the seven. The
trailing hemisphere GNIRS spectrum and TripleSpec grand average for the anti-
Uranus quadrant were both only $2\sigma$ significant in depth and not area.
The trailing hemisphere GNIRS spectrum was lower S/N than the other three
GNIRS spectra (Figure 2).

Furthermore, when taking the means of the individual band measurements (not
including the grand averages), we measured $\geq 2\sigma$ 2.2-$\mu$m band
depths for all of the quadrant and hemisphere-averaged means, and the mean of
all spectra and the mean of the leading-hemisphere spectra were measured to
$\geq 2\sigma$ significance for both the 2.2-$\mu$m band area and depth. We
calculated an average band depth (across all spectra) of 5.4$\pm$0.8%. As
discussed in the next section, we do not find convincing evidence for sub-
observer longitudinal trends (i.e. hemispherical asymmetries) in the
2.2-$\mu$m band.

The band center measurements for the 2.2-$\mu$m band in the individual spectra
generally clustered between 2.21 and 2.22 µm. The mean band center for all
spectra was 2.218$\pm$0.003 $\mu$m (Table 5). For individual spectra in which
the band was detected at $>2\sigma$ significance, the minimum band center
wavelength of 2.203$\pm$0.014 $\mu$m was measured for the TripleSpec leading
hemisphere grand average. The maximum wavelength was measured at
2.223$\pm$0.016 µm, for the TripleSpec spectrum from UT210115. This average
central wavelength of 2.218 $\mu$m is at slightly longer wavelengths than
NH3-hydrates and H2O:NH3 ice mixtures, which tend to range between 2.209 and
2.216 µm. Pure cubic NH3 ice exhibits a band at 2.241 $\mu$m (Moore et al.,
2007). However, the range of band centers in our spectra is not definitive, as
we measured band centers based on a single band spanning 2.186 – 2.251 µm. Our
band centers would be skewed towards longer wavelengths by the presence of
crystalline NH3 ice at 2.24 µm, and would also be affected by the presence of
a ‘spike’ in the data at 2.207 µm, in the middle of any band at 2.20 – 2.21
µm, that we attribute to residuals from differences in metal abundances in our
telluric standard stars and the solar spectrum (§A). We discuss possibilities
for candidate materials, including amorphous NH3 ice, other ices, and
NH4-bearing minerals, in sections §5, 6.2, and 6.3.

Finally, what of the Bauer et al. (2002) detection of the 2.2-$\mu$m feature?
For this spectrum (UT990607), we measured a statistically significant
2.2-$\mu$m band area, but the band depth did not reach 2$\sigma$ significance.
Unfortunately, the axial tilt and seasonal illumination conditions of the
Uranian system also makes direct reproduction (reobservation) of the Bauer et
al. study impossible in the next several decades. Their spectrum was observed
at southern latitudes (36.5°S), while all but one of the spectra in our
dataset were observed on the northern hemisphere. It is worth noting that the
Bauer et al. spectrum showing absorption at 2.2-$\mu$m was observed when Arden
Corona was near disk center (Figure 1), supporting the notion that the
2.2-$\mu$m band may be associated with geologically young terrain. Our dataset
also has a single SpeX spectrum of Miranda (UT000907) observed at a similar
southern latitude (35.4°S), but at a different sub-observer longitude that
includes more heavily cratered, older terrain. This SpeX spectrum does not
show strong evidence of a 2.2-$\mu$m band.

###  4.4 Sub-observer longitudinal trends

When considering the quadrant/hemisphere ratios of the band parameters, we did
not find statistically significant ($\geq 2\sigma$) departures from a ratio of
unity for any of the measurements or quadrant/hemisphere pairs (Table 6). Our
non-detection of the CO2 ice bands and 2.13-$\mu$m band precludes discussion
of longitudinal trends for these bands, although the ratio calculations are
included in the tables for completeness.

When fitting a sinusoidal model to the 2.2-$\mu$m band measurements from the
33 individual spectra, none of the sinusoidal models could be considered a
statistically significant better fit than a constant weighted average. We
found that only the model fit to the 2.2-$\mu$m area measurements for the
quadrant-averaged mean band parameters was statistically significant (Table
7). We do not find the sinusoidal fit for the quadrant-averaged mean
2.2-$\mu$m band depth to be significant (although it is close, at $p$ $\sim$
0.07). We are inclined to trust the sinusoidal fit to 33 data points instead
of four data points, even though the four data points are weighted averages of
the 33 individual measurements. Finally, we do not find statistically
significant deviations from unity for any of the calculated quadrant or
hemisphere ratios of band parameters.

When considering the results from the quadrant/hemisphere ratios and F-tests
of the sinusoidal models, we conclude that there is minimal evidence for
large-scale longitudinal trends or hemispherical asymmetries in the presence
or strength of the 2.2-$\mu$m band.

##  5 Spectral modeling

Figure 6: (Left panel): Synthetic spectra generated with a Hapke-Mie modeling
program to investigate potential absorption features in the 2.2-$\mu$m region,
compared to the UT201008 GNIRS spectrum of Miranda’s leading hemisphere
(bottom, binned by 10 pixels). The synthetic spectra are described in Table 8.
The left panel includes comparison spectra in which a small percentage of the
27.5-$\mu$m H2O ice in the base model is replaced with an additional component
of different composition, with a grain size of 10 µm. Vertical lines are
placed at 2.21 and 2.24 µm. (Right panel): as the left panel, but using
synthetic spectra of the corresponding pure (100%) ices at 10 $\mu$m grain
size, scaled by a factor of 0.1. The observed GNIRS spectrum is divided by the
base model.  Table 8: Synthetic spectra for Figure 6

Short name | Component 1 | Component 2 | Component 3 | Component 4 | $\chi_{\nu}^{2}$ | Source
---|---|---|---|---|---|---
Base model | 95.25% H2O 27.5$\mu m$ | 4.5% AC 5$\mu m$ | 0.25% H2O 0.3$\mu m$ |  $\cdots$ | 1.050 | see caption
10% illite | 85.25% H2O 27.5$\mu m$ | 4.5% AC 5$\mu m$ | 0.25% H2O 0.3$\mu m$ | 10% illite 10$\mu m$ | 2.762 | Clark et al. (1990)
5% kaolinite | 90.25% H2O 27.5$\mu m$ | 4.5% AC 5$\mu m$ | 0.25% H2O 0.3$\mu m$ | 5% kaolinite 10$\mu m$ | 1.202 | Clark et al. (1990)
2% propionitrile | 93.25% H2O 27.5$\mu m$ | 4.5% AC 5$\mu m$ | 0.25% H2O 0.3$\mu m$ | 2% C2H5CN 10$\mu m$ | 1.351 | Moore et al. (2010)
2% ethylamine | 93.25% H2O 27.5$\mu m$ | 4.5% AC 5$\mu m$ | 0.25% H2O 0.3$\mu m$ | 2% C2H5NH2 10$\mu m$ | 1.252 | Hudson et al. (2022)
2% methylamine | 93.25% H2O 27.5$\mu m$ | 4.5% AC 5$\mu m$ | 0.25% H2O 0.3$\mu m$ | 2% CH3NH2 10$\mu m$ | 1.236 | Hudson et al. (2022)
2% amo. NH3 | 93.25% H2O 27.5$\mu m$ | 4.5% AC 5$\mu m$ | 0.25% H2O 0.3$\mu m$ | 2% amorph. NH3 10$\mu m$ | 0.938 | Roser et al. (2021b)
1% ethylene | 94.25% H2O 27.5$\mu m$ | 4.5% AC 5$\mu m$ | 0.25% H2O 0.3$\mu m$ | 1% C2H4 10$\mu m$ | 1.212 | Hudson et al. (2014)
1% NH3 | 94.25% H2O 27.5$\mu m$ | 4.5% AC 5$\mu m$ | 0.25% H2O 0.3$\mu m$ | 1% cubic NH3 10$\mu m$ | 0.908 | Hudson et al. (2022)
1% NH${}_{3}\cdot$H2O | 94.25% (1%)NH${}_{3}\cdot$H2O 27.5$\mu m$ | 4.5% AC 5$\mu m$ | 0.25% H2O 0.3$\mu m$ |  $\cdots$ | 1.051 | see caption
3% NH${}_{3}\cdot$H2O | 94.25% (3%)NH${}_{3}\cdot$H2O 27.5$\mu m$ | 4.5% AC 5$\mu m$ | 0.25% H2O 0.3$\mu m$ |  $\cdots$ | 1.602 | see caption
Mixed NH3 | 94.75% (1%)NH${}_{3}\cdot$H2O 27.5$\mu m$ | 4.5% AC 5$\mu m$ | 0.25% H2O 0.3$\mu m$ | 0.5% cubic NH3 10$\mu$m | 0.939 | see caption

Note. — The components of the synthetic Hapke-Mie spectra plotted in Figure 6,
with their mixing ratios and grain sizes for each component. All spectra are
intimate (particulate) mixtures. Components listed as ‘H2O’ use optical
constants of 80 K crystalline ice from Mastrapa et al. (2008), while the
component listed as ‘AC’ is amorphous carbon, using the optical constants of
sample BE1 from Rouleau & Martin (1991). Optical constants for other
components are listed in the table. The NH3-hydrate spectra replace the
primary H2O ice component with the optical constants of 1% and 3% by weight
mixtures (respectively) of NH${}_{3}\cdot$H2O. Reflectance spectra of these
mixtures were originally measured by Brown et al. (1988), with optical
constants derived by T. Roush (personal communication) and published in
Cruikshank et al. (2005).

Figure 7: (Left panel): A close-up of the most promising NH3-bearing synthetic
models from Figure 6, compared to the UT201008 GNIRS spectrum of Miranda’s
leading hemisphere. The synthetic spectra are described in Table 8. Small
periodic variations are visible in the synthetic spectra due to resonances
from the calculated Mie scattering solutions. (Right panel): A demonstration
of the lack of CO2 ice features on Miranda’s trailing hemisphere, compared to
the trailing hemisphere of Ariel (Cartwright et al., 2022). We include several
Hapke model spectra: pure CO2 ice (10 $\mu$m grains), a base model (Table 8),
the base model with 10% areally mixed CO2 ice (27.5 $\mu$m grains), and the
base model with 10% intimately mixed CO2 ice (27.5 $\mu$m grains). We also
include a laboratory spectrum of a H2O:CO2 ice molecular mixture (Bernstein et
al., 2005), which displays a prominent 2.13-$\mu$m 2$\nu_{3}$ overtone band.
Note that this forbidden overtone does not appear in pure CO2 ice or the model
spectra of H2O:CO2 ice intimate mixtures.

Synthetic Hapke-Mie spectra of intimate mixtures including some of the same
materials as in Cartwright et al. (2023) are plotted in Figure 6 and tabulated
in Table 8. We compared these synthetic spectra to a spectrum of Miranda’s
leading hemisphere obtained with GNIRS (spectrum UT201008). This spectrum was
chosen for being both high S/N and showing weak absorption in the 2.2-$\mu$m
region. This absorption is composed of a shallow dip between 2.19 – 2.23 µm,
along with a possible feature at 2.24 $\mu$m (Figure 7). We constructed a base
model composed of two grain sizes of H2O ice (27.5 $\mu$m and 0.3 µm), along
with an amorphous carbon component to act as a dark, spectrally neutral
absorber.

To demonstrate the lack of CO2 ice absorption features, we calculated spectral
models incorporating CO2 ice and plotted them against observed spectra in
Figure 7. Spectral models of pure or intimately-mixed CO2 ice fail to
reproduce the 2.13-$\mu$m 2$\nu_{3}$ overtone band seen in laboratory spectra
of CO2 ice in a molecular mixture with H2O (Bernstein et al., 2005). A
spectrum of Ariel’s trailing hemisphere (Cartwright et al., 2022) shows clear
signatures of CO2 ice, as previously discussed (§1.2). In comparison, the
Miranda trailing hemisphere grand average spectrum shows no evidence of any
absorption features resulting from CO2 ice, either as separate deposits or
trapped in the regolith.

To investigate species that could be contributing to absorption features in
the 2.2-$\mu$m range, we constructed models in which we replaced small
percentages of the H2O ice component in the base model with other materials,
including some of the same materials as in Cartwright et al. (2023) (Figure
6). From visual inspection, the complex absorption bands of propionitrile
(C2H5CN), ethylamine (C2H5NH2) and methylamine (CH3NH2) are somewhat difficult
to interpret, but do not match the Miranda spectrum closely. Ethylamine and
methylamine have band complexes between 1.65 – 1.80 $\mu$m which are also not
apparent in our spectra. The 2.22-$\mu$m band of ethylene (C2H4) is too sharp
compared to the broad absorptions of the Miranda spectra. The 2.2-$\mu$m bands
of the aluminum-bearing phyllosilicates illite and kaolinite are subtle, but
both of these minerals also have bands at 1.4 $\mu$m from bound water
absorption. The wavelengths between 1.38 – 1.43 $\mu$m are hard to observe
from Earth due to strong atmospheric H2O absorption. Spectra with good
telluric correction observed in dry conditions (such as the GNIRS spectra) do
not show convincing evidence for the presence of the 1.4-$\mu$m band, but it
is difficult to rule out either kaolinite or illite given the lower S/N in the
region.

We also calculated $\chi_{\nu}^{2}$ values as a comparison between the
observed spectrum and the constructed models, using the wavelengths between
2.15 – 2.29 $\mu$m (Table 8). The synthetic intimate mixture spectra we
generated are not unique solutions, but are useful as general guidelines for
interpretation of spectral features. Both cubic (crystalline) and amorphous
NH3 mixtures have significantly improved $\chi_{\nu}^{2}$ values compared to
the base model, while a 1% mixture of NH${}_{3}\cdot$ H2O fits the data
equally as well as the base model ($\chi_{\nu}^{2}$ of 1.051 versus 1.050).
Kaolinite, propionitrile, ethylene, ethylamine, methylamine, the 3% mixture of
NH${}_{3}\cdot$ H2O, and illite all have worse $\chi_{\nu}^{2}$ values than
the base model.

While amorphous NH3 ice has one of the most favorable $\chi_{\nu}^{2}$ values,
it is unlikely that amorphous NH3 could persist on Miranda’s surface, as it
transitions to crystalline NH3 when warmed to temperatures between 70 – 90 K
(Moore et al., 2007). Voyager 2 measured a surface brightness temperature for
Miranda of about 86 K (Hanel et al., 1986), and thermodynamical modeling
predicts peak surface temperatures for the Uranian satellites around 90 K
(Sori et al., 2017). Crystalline NH3 ice produces a band at 2.24 µm, which is
at longer wavelengths than the broad 2.2-$\mu$m feature in most of our
spectra, but does correspond to the weak feature at 2.24 $\mu$m seen in this
observed GNIRS spectrum (Figure 7). We also find a promising match between the
spectrum in which the major H2O ice component is replaced with a 1% mixture of
NH3-hydrates, which produces a shallow shoulder feature. However, the 3%
NH3-hydrates mixture produces a distinct 2.2-$\mu$m absorption band that is
too strong compared to the weak absorption in the observed spectrum. We
further investigated the possibility of NH3 species by generating an
additional model with both NH3-hydrates and a small percentage of crystalline
NH3 ice. With the exception of the residual noise spike at 2.207 $\mu$m from
incomplete solar line cancellation (§A), this model visually matches the weak
absorption bands at 2.2 $\mu$m and 2.24 $\mu$m more closely. This ’mixed NH3’
model has effectively the same $\chi_{\nu}^{2}$ value as the amorphous NH3
model.

##  6 Discussion

Our band analysis procedures did not detect any evidence for the presence of
crystalline CO2 ice on Miranda’s surface, unlike its high abundance on the
neighboring moon Ariel. Even in the high S/N spectra from GNIRS and the grand-
average spectra from TripleSpec combining multiple nights of data, the three
prominent CO2 ice bands between 1.9 and 2.1 $\mu$m are not present (Figure 7).
Additionally, we detected essentially no evidence for an absorption feature
near 2.13 $\mu$m that might have hinted at the presence of CO2 in a molecular
mixture. In contrast, a subtle 2.2-$\mu$m band is exhibited by many of the
Miranda spectra we analyzed.

###  6.1 CO2 ice

The prevailing hypothesis for the origin of CO2 ice on the other classical
Uranian moons is a radiolytic production mechanism (§1.2). This hypothesis
states that the observed CO2 is produced in situ via irradiation of surface
carbon compounds and H2O ice, which recombine to form CO2 and other products.
Sublimation, sputtering, and other processes cause the CO2 molecules to ‘hop’
in suborbital trajectories across the surface until they either escape or land
in a cold trap. Because of the large obliquity of the Uranian system, the
parts of the surface that receive the lowest amount of time-averaged sunlight
over the Uranian year are at low latitudes. Crystalline CO2 ice is bright and
highly reflective, decreasing absorbed solar energy and likely reducing
sublimation of CO2 molecules from cold traps once they have been established.
Theoretically, the trailing hemispheres would accumulate more CO2 ice because
the magnetosphere of Uranus rotates faster than the moons orbit, and might
preferentially irradiate their trailing hemispheres and produce CO2 molecules,
thereby explaining the observed distribution of CO2 on Ariel, Umbriel,
Titania, and Oberon (Grundy et al., 2003, 2006; Cartwright et al., 2015,
2022). However, the exact nature of interactions between Uranus’ offset and
tilted magnetosphere and the surfaces of the moons are still poorly understood
(e.g. Kollmann et al., 2020).

In contrast, this lack of CO2 ice on Miranda, where radiolytic production of
CO2 molecules should be possible, could result from its small mass and lower
efficiency of retaining volatiles like CO2. Previous works have extensively
discussed potential mechanisms for production and destruction of CO2 on the
Uranian satellites, such as photolysis or sputtering by charged particles
(Grundy et al., 2006; Cartwright et al., 2015; Sori et al., 2017; Steckloff et
al., 2022). Most importantly, a large fraction of the expected thermal
velocity distribution of sputtered or sublimated CO2 molecules is greater than
the escape velocity of Miranda (193 m s-1). Sori et al. (2017) found that
approximately half of all CO2 molecules sublimated on Miranda would escape
before completing a single suborbital ‘hop’. Steckloff et al. (2022) found a
similar result, adding that the time required for these CO2 molecules to
migrate to the antipode of their initial production site on Miranda ($\sim$14
hours) is more than an order of magnitude longer than their expected residence
time in the exosphere before escape (approximately one hour). Other processes
that could destroy CO2 ice are effectively irrelevant on Miranda, given the
rate at which any produced or otherwise mobilized CO2 molecules would be lost.
Miranda cannot retain significant CO2 ice deposits with such a large loss
fraction. It is therefore not surprising that we do not observe any CO2 ice
deposits on Miranda.

However, given the assumption of ongoing radiolytic production, it is still
possible that CO2 is present in Miranda’s regolith, perhaps as molecules mixed
with H2O ice. This motivated our search for a 2.13-$\mu$m absorption band,
attributed to the forbidden $2\nu_{3}$ first overtone of the strong
4.27-$\mu$m $\nu_{3}$ asymmetric stretch band of CO2. This forbidden feature
is extremely weak in spectra of pure CO2 ice, but becomes apparent when CO2 is
in a molecular mixture with other ices, including H2O and CH3OH (Bernstein et
al., 2005). This overtone can vary significantly in its depth and shape in
laboratory spectra. In many of our high S/N spectra, visual inspection
suggested a weak feature centered at slightly shorter wavelengths ($\sim$2.130
µm), reminiscent of a weak 2.13-$\mu$m band detected on Ariel using SpeX and
TripleSpec data (Cartwright et al., 2022), also centered at $\sim$2.130 $\mu$m
and spanning 2.123 – 2.137 µm. If a molecular mixture including CO2 ice is
responsible for this band on Ariel, then it could also be responsible for a
similar band on Miranda. However, our band analyses did not find convincing
evidence for the 2.13-$\mu$m band on Miranda. If CO2 is being produced on
Miranda, it is not being trapped in the regolith in sufficient quantities to
manifest the 2.13-$\mu$m band at a strength detectable in our spectra.

###  6.2 NH3-bearing species

Figure 8: (Left panel): The UT201008 GNIRS spectrum of Miranda’s leading
hemisphere (gray errorbars native resolution, black errorbars binned by 5
pixels), compared to several laboratory-measured absorbance spectra of NH-
bearing species (digitized from Figures 6 and 14 of Moore et al. (2007)). The
laboratory spectra are arbitrarily scaled and offset. We also include a
reflectance spectrum of NH4Cl at 90 K from Fastelli et al. (2022). (Right
panel): Arbitrarily scaled linear combinations of the lab spectra with our
synthetic base model for qualitative comparison of band shapes and locations.
Vertical lines are placed at 2.21 and 2.24 µm. Table 9: $\chi_{\nu}^{2}$
values of different comparison spectra

Short name | Figure | Spectrum type | $\chi_{\nu}^{2}$
---|---|---|---
Base model |  6,7,8,9 | Hapke-Mie | 1.050
10% illite | 6 | Hapke-Mie | 2.762
5% kaolinite | 6 | Hapke-Mie | 1.202
2% propionitrile | 6 | Hapke-Mie | 1.351
2% ethylamine | 6 | Hapke-Mie | 1.252
2% methylamine | 6 | Hapke-Mie | 1.236
2% amorphous NH3 |  6,7 | Hapke-Mie | 0.938
1% ethylene | 6 | Hapke-Mie | 1.212
1% NH3 |  6,7 | Hapke-Mie | 0.908
1% NH${}_{3}\cdot$H2O |  6,7 | Hapke-Mie | 1.051
3% NH${}_{3}\cdot$H2O | 6 | Hapke-Mie | 1.602
Mixed NH3 |  6,7 | Hapke-Mie | 0.939
Amorphous NH3 | 8 | base + lab absorbance | 0.824
Transition-phase NH3 | 8 | base + lab absorbance | 0.884
Cubic NH3 | 8 | base + lab absorbance | 1.065
NH${}_{3}\cdot$H2O | 8 | base + lab absorbance | 1.014
2NH${}_{3}\cdot$H2O | 8 | base + lab absorbance | 0.928
NH3+H2O ($\sim$5:1) | 8 | base + lab absorbance | 0.959
Moore NH4Cl | 8 | base + lab absorbance | 0.952
Fastelli NH4Cl |  8,9 | base + lab reflectance | 73.222

Note. — Comparison of $\chi_{\nu}^{2}$ values of our constructed comparison
spectra in various figures (measured between the models and unbinned data
between 2.15–2.29 µm). For details on the Hapke-Mie models, see Table 8. The
linear combinations of the Hapke-Mie base model and the laboratory absorbance
spectra are arbitrarily scaled and are not quantitatively comparable to the
other Hapke-Mie synthetic spectra.

In Figure 8, we utilized the laboratory absorption spectra of Moore et al.
(2007) to investigate the potential contributions of NH3 species. Moore et al.
measured the absorption spectra of multiple phases of pure NH3 ice, several
NH3-H2O mixtures, two phases of NH3-hydrates, and NH4Cl (from Moore et al.
(2003)). We also constructed qualitative linear mixtures using these
absorption spectra to qualitatively compare band shapes and locations (right
panel of Figure 8). These are not physically accurate spectral models, but
provide a general idea of how low-level absorption from these features might
appear. Quantitative spectral modeling would require the optical constants of
these species to be measured, and optical constants have only been published
for amorphous NH3 ice, crystalline NH3 ice, and an NH3-hydrate of uncertain
stoichiometry (Figures 6,7).

Pure NH3 ices of any phase produce bands at longer wavelengths than the broad
2.2-$\mu$m band in the Miranda spectrum, but could contribute to shallow
absorptions at 2.24 µm. The NH3-H2O hydrates and NH3-H2O mixture produce a
broad band centered between $\sim$2.21 – 2.22 µm. Both 2NH${}_{3}\cdot$H2O and
the absorbance spectrum of NH4Cl produces a double-band structure with a
2.21-$\mu$m and 2.24-$\mu$m band. From visual inspection, the NH3-hydrates and
NH3-H2O mixtures provide acceptable matches, but NH4Cl (Moore) seems to match
the shape and position of the weak 2.2-$\mu$m bands in the Miranda spectrum
best. When we compare the calculated $\chi_{\nu}^{2}$ values of these linear
combinations to the spectrum (Table 9), all but the cubic NH3 mixture have
improved $\chi_{\nu}^{2}$ values over the base model ($\chi_{\nu}^{2}=$1.050).
As with the synthetic Hapke-Mie spectra, amorphous NH3 ice has the best
$\chi_{\nu}^{2}$, but amorphous and transition-phase NH3 ice do not produce
band shapes that visually match the Miranda spectrum, and their presence on
Miranda is unlikely (§5). The cubic NH3 ice alone produces a visual fit to the
2.24-$\mu$m band, but not the band between 2.18 – 2.23 µm. Conversely, the
2.18 – 2.23-$\mu$m band is well fit by the NH3-hydrates and NH3-H2O mixtures.
The 2NH${}_{3}\cdot$H2O and Moore NH4Cl spectra produce bands at both 2.18 –
2.23 $\mu$m and 2.24 µm, more consistent with the observed Miranda spectrum.
When excluding the amorphous and transition-phase NH3 ices, then
2NH${}_{3}\cdot$H2O, the Moore NH4Cl spectrum, and the NH3-H2O mixture have
the best $\chi_{\nu}^{2}$.

However, all of the Moore et al. lab spectra of NH3-bearing species show the
2.0-$\mu$m band of NH3 ice, which is not visible in our spectra. This
2.0-$\mu$m absorption band is rarely detected on icy bodies. Even in the case
of Charon, where the 2.21-$\mu$m band is obvious, the presence of a
complementary 2.0-$\mu$m band is uncertain (Cook et al., 2018, 2023). The
2.0-$\mu$m band is difficult to detect from ground-based spectra, as it lies
in the spectral noise from a deep telluric CO2 band, and even in spectra from
New Horizons, the 2.0-$\mu$m band is not as strong as would be expected from
laboratory spectra (Cook et al., 2018; Protopapa et al., 2021). The strong H2O
absorption band at 2.0 $\mu$m further means that light penetrates much
shallower into the regolith ($\sim$ 0.1 mm at 2.0 µm) than it does at 2.24
$\mu$m ($\sim$ 1.6 mm), where H2O only contributes weak absorption and the
optical path length is therefore longer (Cartwright et al., 2023). NH3-bearing
species could be present in the subsurface, where they only appear in
absorption in regions of the spectrum where the optical path length is long
enough to reach them, contributing to the difficulty of detecting the NH3
2.0-$\mu$m absorption feature, or an ammonium salt such as NH4Cl that lacks a
2.0-$\mu$m band could be responsible (next section). We also note that these
qualitative linear combinations do not incorporate effects like multiple
scattering that would make a difference in the strength of the 2.0-$\mu$m
band. This is demonstrated by the difference in the strength of the 2.0-$\mu$m
band in the Hapke-Mie synthetic spectra with NH3 ice (Figure 6), in which the
band is much less prominent than in our linear combinations.

The ‘survivability’ of NH3-bearing species is also an open question. As
discussed previously, NH3-bearing species exposed at the surface of icy bodies
are expected to be dissociated by particle irradiation (such as cosmic rays)
on geologically short timescales. Miranda is subject to additional proton and
electron bombardment from charged particles trapped in Uranus’s magnetosphere,
and Moore et al. (2007) estimate timescales for destruction of NH3 ice at
Miranda’s surface as short as $\sim 10^{6}$ years. However, dissociated NH3
does not simply disappear. The radiation products can readily recombine into
similar forms, such as NH${}_{4}^{+}$ ions, which can react with other
compounds to form NH4-bearing salts. Protopapa et al. (2021) provides a
lengthy review of the mechanisms that could destroy NH3 on Charon. While the
radiation environment on Miranda is more hostile to NH3, NH4-bearing species
still possess a 2.2-$\mu$m band, and NH4-bearing salts may be more resistant
to destruction by irradiation.

###  6.3 NH4-bearing species and other refractory compounds

Figure 9: (Left panel): Our base model of Miranda’s spectrum compared to 5%
areal mixtures of NH4-bearing minerals and thermonatrite. The mixture spectra
were normalized to match the base model at 1.754 µm, then offset in increments
of 0.1. The vertical line marks the mean wavelength of our 2.2-$\mu$m band
measurements at 2.218 µm. (Right panel): NH4-bearing mineral reflectance
spectra measured at 90 K from Fastelli et al. (2022) and thermonatrite
measured at 93 K from De Angelis et al. (2019).

Ammonium salts such as NH4Cl have been proposed as a candidate species
partially or wholly responsible for the 2.2-$\mu$m absorption band on Charon
and on other bodies in the Pluto system (Moore et al., 2007; Cook et al.,
2007, 2018, 2023). NH4Cl has also been reported in the bright emplaced
material in Occator Crater on Ceres (Raponi et al., 2019). Other NH4-bearing
species, such as ammonium carbonate ((NH4)2CO3) or ammonium bicarbonate
(NH4HCO3), have also been implicated in the presence of a 2.2-$\mu$m
absorption (de Sanctis et al., 2016; Cartwright et al., 2020b). The
NH${}_{4}^{+}$ ion is a byproduct of irradiation of NH3-H2O mixtures (Moore et
al., 2007), and given other suitable species to react with, it could form
NH4-bearing salts. In Figure 9, we plot reflectance spectra of NH4-bearing
species measured at 90 K from Fastelli et al. (2022), and constructed linear
(areal) mixture models of our synthetic base model spectrum, plus a 5%
abundance of various species. The absorption bands of most of these species,
with the possible exception of NH4Cl, are at too short wavelengths to account
for the 2.2-$\mu$m band we see on Miranda, but could contribute to low-level
absorption between 2.18 – 2.25 µm. As seen in the figure, their broad
absorption features tend to simply depress the 2.2-$\mu$m continuum of H2O ice
relative to the 1.8-$\mu$m continuum. Miranda’s spectrum exhibits the same
characteristic, but the broad nature of these NH4 absorptions observed in
reflectance generally limits the ability to identify them, as a depressed
2.2-$\mu$m continuum could also result from sub-micron H2O ice grains (§3.3)
or any other compound with a strong blue slope between 1.8 and 2.2 µm.

However, linear (areal) mixture modeling comes with additional caveats. Linear
mixture modeling does not incorporate the nonlinear effects of multiple
scattering (important for bright icy surfaces) or other factors in the
reflectance of a particular component, such as grain size. These effects are
treated in intimate mixture models, but an intimate mixture model requires the
optical constants of the material to be measured, and no optical constants for
these NH4-bearing species have been published in the scientific literature.
Furthermore, direct comparison demonstrates that the reflectance spectrum of a
pure compound is distinctly different from the absorption spectrum; compare
and contrast the absorbance spectra and reflectance spectra of NH4Cl in Figure
8. Although the spectra are arbitrarily scaled, the difference in depths and
shapes of the absorption bands are clearly apparent. The Fastelli et al.
sample studied in reflectance is much thicker ($\sim$ mm) than the Moore et
al. sample studied in absorbance (tens of microns), which makes weaker
features easier to detect, but produces saturation and blending of the
stronger absorption features. The relative band strengths are different
between the Moore and Fastelli NH4Cl spectra: the weak absorptions between 2.0
and 2.2 $\mu$m in the Moore spectrum are heavily blended in the Fastelli
spectrum, and the stronger absorptions at 2.21 and 2.24-$\mu$m are effectively
saturated. The Fastelli spectrum also shows a clear band at 2.34-$\mu$m that
is shallow in the Moore spectrum and absent in the Miranda spectra. Finally,
the spectral resolution of the Fastelli spectra are generally inadequate
compared to our Miranda spectra and the Moore spectrum.

While our spectra of Miranda were also observed in reflectance, an intimate
mixture of small percentages of NH4Cl or another NH4-bearing species in H2O
ice could produce a spectral signature more similar to the Moore et al.
absorption spectrum. We also note that unlike the rest of the NH3-bearing
species in Figure 8, NH4Cl lacks a strong 2.0-$\mu$m band, consistent with the
lack of the 2.0-$\mu$m band in our spectra of Miranda. Confident quantitative
estimates are difficult given the weak 2.2-$\mu$m absorption, the limited
nature of the available laboratory data, and the lack of optical constants for
candidate constituents. We suggest that an NH4-bearing species, perhaps NH4Cl,
may be partially or wholly responsible for the 2.2-$\mu$m band, although
NH3-bearing species could contribute to absorption in this range.

The potential sources (and potential destruction) of NH4Cl on Charon is
discussed thoroughly in Cook et al. (2023). Many of these arguments are also
applicable at some level to the Uranian satellites, including Miranda.
Chlorine could be delivered to the surface via impacts, or perhaps an
endogenic process like cryovolcanism emplaced NaCl-bearing or NH4Cl-bearing
brines and/or NH3-rich liquids onto the surface. Some form of this process,
likely impact-induced, appears to have occurred at Ceres in Occator Crater
(Raponi et al., 2019; De Sanctis et al., 2020). Furthermore, carbonaceous
material and H2O are readily available at Miranda’s surface and particle
irradiation is present to dissociate them. In addition to the previously-
discussed CO2, if Miranda’s surface was supplied with NH3\- or NH4-bearing
species, NH4-bearing carbonates could be a common byproduct.

With previous results on Umbriel in mind (Cartwright et al., 2023), we also
generated a synthetic intimate mixture model incorporating the aluminum-
bearing phyllosilicates illite and kaolinite (Figure 6), and an areal mixture
model incorporating the hydrated Na-bearing carbonate thermonatrite (Figure
9). Thermonatrite’s 2.2-$\mu$m band is centered at shorter wavelengths than
our mean band center (2.201 versus 2.218 µm), but could be contributing to
wider low-level absorption between 2.18 – 2.25 $\mu$m (Figure 2). Kaolinite
has a blue slope at wavelengths longer than 1.8 $\mu$m and a double-band
absorption at 2.16 and 2.206 $\mu$m that could produce a similar shoulder
feature, but as discussed in §5, the only other strong indicator of
phyllosilicates in the near-IR ($<$2.5 µm) is generally the 1.4-$\mu$m band,
which is difficult to observe from Earth due to telluric absorption.

##  7 Conclusions

We conclude that there is no crystalline CO2 ice concentrated in discrete
deposits on Miranda’s surface, consistent with the explanation that Miranda’s
weak surface gravity allows CO2 molecules to efficiently escape before being
cold trapped. Similarly, we detected no convincing evidence of a 2.13-$\mu$m
band that could be associated with a molecular mixture of CO2 in H2O or CH3OH
ice.

In contrast, we detected a 2.2-$\mu$m band at $>2\sigma$ significance in
several of our spectra. We do not see evidence for longitudinal trends or
hemispherical asymmetries in the distribution of the 2.2-$\mu$m band. We
compared a high S/N GNIRS spectrum of the leading hemisphere to synthetic
spectra and laboratory spectra of several candidate species, including NH-
bearing species, nitrogen-bearing organics, and phyllosilicates. We found that
the 2.2-$\mu$m feature can be best explained by either a combination of
NH3-bearing species (e.g. NH3-hydrates and NH3 ice) or by an NH4-bearing salt
like NH4Cl, but NH4-carbonates or certain phyllosilicates like kaolinite could
contribute to broad and shallow absorption between 2.18 – 2.25 µm.

However, the study of NH3-bearing and NH4-bearing species is substantially
limited by the available laboratory data. Optical constants of candidate
species are few and far between, and reflectance data are often acquired at
room temperature and with insufficient spectral resolution to properly capture
the blended spectral bands that change position and strength with temperature
and composition. Common minerals often show fine structure in absorption bands
that are not detected in low resolution reflectance spectra (Clark et al.,
1990). Further laboratory work to determine optical constants of NH3-hydrates,
NH3-H2O mixtures, and NH4-bearing salts at high resolution and cryogenic
temperatures in the near- to mid-IR should be a high priority for the icy
satellites community (Dalton, 2010). The results of such laboratory work
(spectra and optical constants) must be made publicly downloadable in a data
repository for current and future scientists (Roser et al., 2021a).

Future investigations of CO2 ice and NH3-bearing species on Miranda could be
carried out with JWST, as the excellent sensitivity of a 6.5-meter IR-
optimized space telescope is hard to match even with larger ground-based
telescopes. JWST has the ability to investigate the 4.27-$\mu$m CO2 ice
$\nu_{3}$ fundamental absorption band, which lies within a wavelength range in
which the Earth’s atmosphere is completely opaque. This fundamental absorption
band is a factor of $\sim$103 stronger than the 2-$\mu$m overtone bands, and
the lack of the 2.13-$\mu$m band suggests that JWST observations of the
4.27-$\mu$m band would be more suitable for further constraining CO2 ice on
Miranda and the other Uranian moons. NH3-bearing species would be detectable
by JWST with the NH3 $\nu_{3}$ fundamental band (2.96-µm) and the hydrated
nitrogen (OH-N) features (3.05-$\mu$m and 3.1 – 3.2 µm) overprinted on the
wide 3.0-$\mu$m H2O ice band. These bands are far stronger than the weak
overtone bands in the near-IR shortward of 2.5 µm, and different NH-bearing
compounds and hydration states are much easier to distinguish from each other
at longer wavelengths (Moore et al., 2007). Similarly, NH4-bearing minerals
can be detected through features between 3.0 – 3.5 $\mu$m (Bishop et al.,
2002; Berg et al., 2016).

Spatially resolved spectroscopy of ices on Miranda and the other Uranian
satellites would be most effectively carried out by a Uranus orbiter equipped
with a NIR imaging spectrometer, analogous to VIMS on Cassini or MISE on the
upcoming Europa Clipper mission. The Uranus Orbiter and Probe was the highest
priority new Flagship mission recommended by the 2023-2032 Decadal Survey.
Such a mission would be able to revolutionize our knowledge of the entire
Uranian system, including the icy satellites, and could investigate spatial
and spectral variations in surface composition in far more detail than could
ever be achieved from Earth.

We wish to extend our gratitude to the observing, engineering, and
administrative staff at Apache Point Observatory, Gemini North, and the IRTF,
without whom this project would not have been possible, and to the anonymous
reviewers whose comments improved this manuscript. This work is funded under
NASA FINESST grant 80NSSC20K1378, and parts of it were previously funded under
the NMSU Astronomy Department’s William Webber Voyager Graduate Fellowship.
This work is partially based on observations obtained with the ARC 3.5-meter
telescope at Apache Point Observatory, which is owned and operated by the
Astrophysical Research Consortium. This work also incorporates observations
previously obtained at the Infrared Telescope Facility (IRTF), which is
operated by the University of Hawaii under contract 80HQTR19D0030 with the
National Aeronautics and Space Administration. Finally, this work is also
based in part on observations obtained under program IDs GN-2020B-FT-205 and
GN-2021B-FT-210 at the international Gemini Observatory, a program of NSF’s
NOIRLab, which is managed by the Association of Universities for Research in
Astronomy (AURA) under a cooperative agreement with the National Science
Foundation on behalf of the Gemini Observatory partnership: the National
Science Foundation (United States), National Research Council (Canada),
Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia,
Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia,
Inovações e Comunicações (Brazil), and Korea Astronomy and Space Science
Institute (Republic of Korea). The Gemini North and IRTF telescopes are
located within the Maunakea Science Reserve and adjacent to the summit of
Maunakea. We are grateful for the privilege of observing the Universe from a
place that is unique in both its astronomical quality and its cultural
significance, and wish to emphasize our respect for the Native Hawaiian
community’s cultural and historical ties to Maunakea. This research has made
use of the SIMBAD database, operated at CDS, Strasbourg, France.

##  Appendix A Spectral contamination

Figure 10: (Left panel): Sources of spectral contamination in K-band. The
atmospheric transmission curves for telluric species are plotted as the
fraction of light transmitted and have correct scaling relative to each other.
The solar spectrum has been divided by a 5777 K blackbody spectrum. The
plotted Miranda spectrum is a grand average of all TripleSpec spectra. The
scaling on the solar, airglow, and Miranda spectrum are arbitrary for
visualization purposes. The wavelengths of the absorption features of interest
in this work are annotated below the Miranda spectrum: the CO2 ice triplet and
the 2.13-$\mu$m band are marked in blue, and features associated with
NH3-bearing species are marked in green. (Right panel): Inset zoom for the box
marked in the left panel. Note the ’spike’ residuals in the Miranda spectrum
that closely match OH and solar lines.

Potential absorption features in the spectrum of Miranda in K-band are also
subject to low-level contamination from various sources (Figure 10).
Absorption from gases in Earth’s atmosphere (telluric absorption) is a
significant concern for ground-based observations in the near-infrared.
Atmospheric H2O vapor is often the most difficult species to correct for, as
it has a multitude of strong, narrow absorption lines, and precipitable water
vapor along the line of sight can vary locally on short spatial and temporal
scales. However, absorption from atmospheric H2O is not a major concern
between 2.00 – 2.40 µm, which encompasses almost all of the absorption
features of interest in this work.

Telluric CO2 has three strong overtone bands which are the major source of
atmospheric absorption between 1.95 – 2.10 µm. Unlike H2O absorption, which
varies strongly due to local weather conditions, CO2 is well-mixed in the
Earth’s atmosphere and variations in absorption strength are largely based on
optical path length through the atmosphere (airmass). However, fine structure
in the deepest parts of the CO2 overtone bands are partially resolved in our
highest-resolution data (R$\sim$3500), and telluric correction procedures
often leave high-frequency residual noise in these regions. This is visible in
many of the Miranda spectra as an increased scatter in the data points between
2.00 – 2.02 µm, and to a lesser extent between 1.95 – 1.97 and 2.05 – 2.07 µm.
These wavelengths ranges overlap the narrow CO2 ice bands, but this should not
prevent the detection of CO2 ice given the high S/N of this dataset.

The 2.2-$\mu$m region experiences weak absorption from narrow atmospheric CH4
bands, with a somewhat stronger feature at 2.200-µm. However, like CO2,
telluric CH4 is generally well-mixed in the Earth’s atmosphere. We find that
the usual telluric standard procedures are effective at correcting absorption
features from atmospheric CH4, as evidenced by the lack of residuals from the
other CH4 absorption lines in K-band, so we do not expect Miranda’s 2.2-$\mu$m
feature to be contaminated to a substantial degree by atmospheric CH4.
Atmospheric CO2 and H2O do not have significant absorption features between
2.10 – 2.35 µm.

OH airglow emission lines are generally well-corrected in our spectra, but
stacking many spectra can leave small positive or negative residual features
and increased error estimates on certain data points, such as at 2.041, 2.150,
and 2.195 µm. The upwards slope of the continuum in the plotted OH spectrum at
longer wavelengths ($>$2.1 µm) is blackbody radiation from the telescope and
atmosphere. This slope is subtracted from the science data during data
reduction procedures and does not factor into the final spectra.

We also note that there are mismatches in the strength of stellar absorption
features between the G-type telluric standard stars and the reflected solar
spectrum. When dividing the observed spectra of the object by the standard
star, these mismatches appear as narrow residual ’spikes’ or ’dips’ in the
final spectrum. This includes the inconvenient presence of a residual spike at
2.207 µm, which appears to be due to a mismatch in the strength of a Si I
metal line (see Figure 7). This identification is supported by other small,
but noticeable positive residuals from other Si I lines in K-band at 2.093,
2.135, and 2.188 $\mu$m (Mohler et al., 1953). Larger mismatches are also
sometimes apparent in the strength of the H I Brackett $\gamma$ line at 2.166
µm, and any apparent absorption features in the range 2.155 – 2.175 $\mu$m
should be treated with suspicion. In general, any narrow residual features in
the high-resolution Miranda spectra appear to be either due to OH airglow
lines or from mismatches in solar/stellar spectra.

Finally, we note that scattered light from the disk of Uranus is a major
source of contamination in spectra of Miranda at wavelengths shorter than
$\sim$1.7 µm. However, Uranus is very faint in K-band due to absorption by CH4
and the H2 pressure-induced dipole (Fink & Larson, 1979; Baines et al., 1998),
which includes the wavelength ranges and absorption features of interest in
this work. The contamination of the Miranda spectra by the spectrum of Uranus
is therefore negligible for the purposes of this study.

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