The Coma Dust of Comet C/2013 US₁₀ (Catalina): A Window into Carbon in the Solar System

Medium-resolution (R ≡ λ/Δλ ≃ 50–120) infrared spectroscopy of comet C/2013 US₁₀ (Catalina) was obtained on the NASA IRTF telescope with The Aerospace Corporation's Broadband Array Spectrograph System (BASS; Hackwell et al. 1990) during the early morning (daytime) hours. BASS has no moving parts and observes all wavelengths in its 2–14 μm operable range using two 58 element block impurity band linear arrays simultaneously through the same aperture. All observations were obtained with a fixed 40 diameter circular aperture. Standard infrared observing techniques were employed, using double-beam mode with a chop/nod throw of ≃60''. Sprague et al. (2002) provide a detailed description of the BASS data acquisition and preliminary reduction scheme. Nonsidereal tracking of the comet by the IRTF telescope was performed using Jet Propulsion Laboratory (JPL) Horizons' (Giorgini et al. 1996) generated rates, and fine guiding, to keep the comet photocenter in the BASS aperture, was done either by manually guiding on the visible comet image produced by the BASS sky-filtered visible CCD camera, or off a strip chart using thermal channels of the BASS array.

Photometric calibration of individual comet data sets was performed using observations of α Boo observed at equivalent airmass to minimize telluric corrections. α Boo is a well-characterized infrared standard for ground- and space-based telescopes and has been extensively monitored and modeled by the BASS instrument team and other investigators for decades. The calibration and telluric corrections are uncertain to within ≃3%. Examination of independent, flux-calibrated spectra of comet C/2013 US₁₀ (Catalina) obtained during the course of the 2016 January 10.61 UT observational campaign showed no variance in the flux level of the SED (i.e., no outbursts or jet-induced changes in coma brightness were witnessed) or spectral shape. Hence, all spectra were averaged together (with the proper propagation of all statistical point-to-point uncertainties) to produce the final spectrum presented in Figure 1.

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Optical imagery of the comet was obtained on 2016 January 11.633 UT with the NASA IRTF MORIS camera (Gulbis et al. 2011) in a Sloan Digital Sky Survey (SDSS) i' filter (λ_c  = 0.7630 μm, filter FWHM of 0.1530 μm). Multiple exposures (5 s each) of the comet nucleus and surrounding coma were obtained using AB pairs nodding the telescope by 60'' and dithering the telescope while tracking at the nonsidereal rate corresponding to the predicted motion of the comet in an airmass range of ≈1.18. All images were corrected for overscan and bias with standard IRAF ⁷ routines. The data were photometrically calibrated using GSC 02581–02323 (G2V) SDSS colors reported from SIMBAD transformed to the USNO system as described in Tucker et al. (2006), adopting 3631 Jy for zeroth magnitude. No color corrections for spectral type were applied in the transformation. The average nightly seeing was ∼22 as determined from the standard star. The observed i' flux density of the comet measured in an equivalent BASS aperture was (2.316 ± 0.001) × 10⁻¹⁷ W cm⁻² μm⁻¹.

Mid-infrared (mid-IR) spectrophotometric observations of comet C/2013 US₁₀ (Catalina) were obtained using the Faint Object InfraRed CAmera (FORCAST; Herter et al. 2018) mounted at the Nasmyth focus of the 2.5 m telescope of the SOFIA Observatory (Young et al. 2012). FORCAST is a dual-channel mid-IR imager and grism spectrometer operating from 5 to 40 μm.

The data were acquired on two separate, back-to-back flights, originating from Palmdale, CA, at altitudes of ≃11.89 km in 2016 February, conducted as part of our SOFIA comet programs (P.I. Woodward, AOR_ID 04_0010). Mid-infrared imaging observations of C/2013 US₁₀ (Catalina) in three filters and the The Short Wavelength Camera (SWC) grism (G063) were obtained on the first flight, while on the second flight, imaging in the same three filters was repeated in addition to Long Wavelength Camera (LWC) grism observations with three gratings (G111, G227, and G329). For all spectroscopic observations, the instrument was configured using a long slit (47 × 191''), which yields a spectral resolution R = λ/Δλ ∼ 140–300. The comet was imaged in the SWC using the F197 filter to position the target in the slit. Both imaging and spectroscopic data were obtained using a two-point chop/nod in the nod–match–chop (C2N) mode with 45'' chop and 90'' nod amplitudes at angles of 30°/210° in the equatorial reference frame.

The FORCAST scientific data products were retrieved from the SOFIA archive, after standard pipeline processing and flux calibration were performed (for details, see Clarke et al. 2015; Woodward et al. 2015). An extensive discussion of the FORCAST data pipeline can be found in the Guest Investigator Handbook for FORCAST Data Products, Rev. B ⁸

The computed atmospheric transmission at flight altitudes was used to clip out grism data points in wavelength regions where the transmission was less than 70%. Subsequently, to increase the signal-to-noise ratio (S/N) of the comet spectra, data in each grism spectra segment were binned using a weighted three-point boxcar. As there is no wavelength overlap between individual FORCAST grism segments, combined with an inherent uncertainty in the absolute grism flux calibration, and the fact that observations were conducted on separate nights, photometry derived from the image data was used to scale the grism data to a common SED. Integration of the observed grism data with the corresponding filter transmission profile lying within the respective grism spectral grasp (i.e., FORF111 for G111) was used to construct a synthetic photometric point. This latter photometric point was compared to the observed image aperture photometry derived within an equivalent circular diameter beam corresponding to the grism extraction aperture area (average for all grisms was 1754 ± 074, derived data product keyword PSFRAD).The grism scaling factor was derived from this ratio (≲8%). Neither the shape of the observed SED inferred from the image photometry nor the relative flux level of the SED changed significantly over the two epochs of the SOFIA observations.

The resultant composite FORCAST spectra of comet C/2013 US₁₀ (Catalina) is presented in Figure 2. Figure 3 presents panels for each individual grating segment, spanning the respective spectral grasp, to illustrate the spectral details of the observed SEDs.

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Optical images in the SDSS i' filter also were obtained on each flight series prior to the start of the mid-IR observing sequence using the Focal Plane Imager (FPI+; Pfüller et al. 2016). The FPI+ field of view is 8.7 arcmin², with a plate scale of 051 per pixel and a FWHM of ≃375. The comet was tracked using the JPL Horizons nonsidereal rates. These data frames were bias- and overscanned-corrected using standard routines. The comet's surface brightness was flux calibrated by using aperture photometry of seven stars in the image field of view with known i' magnitudes taken from the USNO UCAC4 catalog to establish the photometric zero point (resultant fractional uncertainty of ≃1%). The observed i' flux density of the comet measured in an equivalent circular aperture corresponding to the average SOFIA FORCAST grism extraction aperture was (8.215 ± 0.009) × 10⁻¹⁷ W cm⁻² μm⁻¹.

Images of comet C/2013 US₁₀ (Catalina) obtained during the 2016 February 9 UT flight are presented in Figure 4. Examination of the azimuthally averaged radial profiles of the comet in each filter reveals comet C/2103 US₁₀ (Catalina) exhibited extended emission beyond the point-spread function (PSF) of point sources observed with FORCAST under optimal telescope jitter performance in each filter. ⁹ Centroiding on the photocenter of the comet nucleus, photometry in an effective circular aperture of radius 13 pixels, corresponding to 9984, with a background aperture annulus of inner radius 30 pixels (2358) and outer radius of 60 pixels (4716), was performed on the Level 3 pipeline coadded (*.COA) image data products using the Aperture Photometry Tool (APT v2.4.7; Laher et al. 2012). The photometric aperture is ≃3× the nominal point-source FWHM and encompassed the majority of the emission of the comet and coma. Sky-annulus median subtraction (ATP Model B as described in Laher et al. 2012) was used in the computation of the source intensity. The stochastic source intensity uncertainty was computed using a depth of coverage value equivalent to the number of coadded image frames. The calibration factors (and associated uncertainties) applied to the resultant aperture sums were included in the Level 3 data distribution and were derived from the weighted average calibration observations of α Boo.

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The resultant SOFIA photometry is presented in Table 2. For the SOFIA epoch of comet C/2013 US₁₀ Catalina, the coma did not appear to have jets or active areas creating discernible coma structures by our visual examination of the photometric images divided by their azimuthally averaged radial profiles.

Table 2. SOFIA Aperture Photometry and fρ of Comet C/2013 US10 (Catalina)

Mean
Observation
Date		Filter	Flux
UT 2016	InstCfg	λc	Density a	λFλ	fρ
(dd-mm hr:min:s)	(Imaging)	(μm)	(Jy)	(×10−16 W cm−2)	(cm)
FORCAST (FOF276)
02-10T07:06:59.6	SWC	7.70	3.238 ± 0.141	1.261 ± 0.055	7096 ± 308
02-10T07:29:47.6	Dual	11.01	13.823 3 ± 0.415	3.767 ± 0.113	7881 ± 236
02-10T07:46:06.4	Dual	19.70	32.467 ± 0.423	4.941 ± 0.064	8522 ± 111
02-10T07:29:47.6	Dual	31.36	29.304 ± 0.303	2.801 ± 0.029	8677 ± 90
FORCAST (FOF275)
02-09T08:09:02.3	SWC	7.70	3.133 ± 0.459	1.220 ± 0.179	6511 ± 954
02-09T08:31:48.8	Dual	11.01	17.961 ± 0.497	4.855 ± 0.135	9721 ± 271
02-09T08:38:42.9 b	Dual	11.01	16.128 ± 0.467	4.390 ± 0.127	8794 ± 255
02-09T08:46:50.0	Dual	19.70	40.100 ± 0.653	6.102 ± 0.099	10159 ± 165
02-09T08:31:48.8	Dual	31.36	34.029 ± 0.809	3.259 ± 0.077	9980 ± 232
02-09T08:38:42.9 b	Dual	31.36	36.494 ± 0.575	3.489 ± 0.055	10470 ± 165

Notes.

^a Measured in a circular aperture with a radius of 17664 centroided on the photocenter of the comet nucleus. ^b Aircraft climbing from 12.497 to 13.106 km during observations.

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Infrared spectroscopic observations are fitted with thermal models using standard spectral fitting techniques that minimize χ². Interpreting thermal models enables investigation into fundamental quantities of comet dust populations including (1) bulk composition, (2) silicate structures of disordered ("amorphous silicates") and/or crystalline forms (forsterite and enstatite), (3) particle structures and size distributions, and (4) coma bolometric albedo. Refractory dust particles are much more robust in maintaining the chemical signatures from the time of formation (see Wooden et al. 2017) than the highly volatile ices and semirefractory organics with limited coma lifetimes (Dello Russo et al. 2016; Wooden et al. 2017). Semirefractory organics are known to exist through their limited lifetimes in comae and are presumed to be organics in the dust that are modified while in the coma. These are the so-called "distributed sources," distributed to the coma by the dust particles. The semirefractory organics are not (yet) observed in thermal IR spectroscopy but rather indirectly by the observed delayed release of molecules such as CO and/or H₂CO as described in Disanti et al. (1999) and Cottin & Fray (2008) or by changes in the color of the scattered light (Tozzi et al. 2004). Polarization properties of particles are also dependent upon organics (Hadamcik et al. 2020). Wooden et al. (2017) and Dello Russo et al. (2016) provide a detailed discussion of semirefractory organics in cometary comae.

Thermal emission spectroscopy when combined with thermal modeling probes the particle composition from the optically active material in comet coma. A number of approaches have been employed to model the dust thermal emission and study the composition of cometary particles. Usually, these involve the simultaneous use of a number of different grain compositions (mineralogy), a size distribution, and a description of the particle porosity. Radiative equilibrium is assumed when deriving particle temperatures, which are strongly composition-dependent as well as particle-radii-dependent for low to moderate particle porosities. Particles of more highly absorbing compositions produce higher temperatures and higher flux density thermal emissions. To produce the combined emission of multiple compositions and integrated over grain-size distributions, thermal models may employ an ensemble (sums) of individual particles of homogeneous dust materials (Harker et al. 2002, 2011, 2017), or may employ composition "mixtures" calculated using effective medium theory (see Bockelée-Morvan et al. 2017a, 2017b).

At a given heliocentric (r_h[au]) and geocentric (Δ[au]) distance, the particle (dust) composition of optically active grains, comprising a linear combination of discrete mineral components, porous amorphous materials, and solid crystals in a comet's coma can be constrained by nonnegative least-squares fitting of the thermal emission model spectra to the observed comet spectrum. The relative mass fractions and their respective correlated errors and the particle properties including the porosity and size distribution, having invoked a Hanner grain-size distribution (HGSD; Hanner 1983) for n(a)da, are given as a prescription for the composition of coma particles (for details, see Harker et al. 2002, 2011, 2018, and references therein). The particle compositions of dust in the coma of comet C/2013 US₁₀ (Catalina) and relevant parameters from the best-fit thermal modeling are summarized in Table 3. The uncertainties on the derived thermal model parameters reflect the 95% confidence limits that result from 1000 Monte Carlo trials (Harker et al. 2018). Figures 5 and 6 show the resultant models.

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Table 3. Derived Grain Composition of Comet C/2013 US10 (Catalina) ^a

	BASS Spectra b		SOFIA Spectra c
		Relative		Relative
		Mass		Mass
		Sub-μm		Sub-μm
Thermal Model SED Details	(Np  × 1020) d	Grains	(Np  × 1020) d	Grains
Dust Components
Amorphous pyroxene (AP)	${0.132}_{-0.014}^{+0.014}$	${0.242}_{-0.023}^{+0.022}$	${0.630}_{-0.494}^{+0.486}$	${0.174}_{-0.134}^{+0.119}$
Amorphous olivine (AO)	${0.029}_{-0.007}^{+0.007}$	${0.053}_{-0.013}^{+0.014}$	${0.515}_{-0.342}^{+0.342}$	${0.142}_{-0.098}^{+0.115}$
Amorphous carbon (AC)	${0.567}_{-0.003}^{+0.003}$	${0.473}_{-0.015}^{+0.017}$	${4.582}_{-0.115}^{+0.116}$	${0.574}_{-0.075}^{+0.083}$
Crystalline olivine (CO)	${0.072}_{-0.009}^{+0.009}$	${0.232}_{-0.024}^{+0.022}$	${0.233}_{-0.233}^{+0.327}$	${0.111}_{-0.111}^{+0.123}$
Crystalline pyroxene (CP)	0.000	0.000	0.000	0.000
Resultants
Total mass of submicron grains (gm) × 108	${0.942}_{-0.031}^{+0.030}$	⋯	${4.853}_{-0.609}^{+0.745}$	⋯
Amorphous silicate dust fraction	${0.295}_{-0.014}^{+0.015}$	⋯	${0.315}_{-0.067}^{+0.066}$	⋯
Crystalline silicate dust fraction	${0.232}_{-0.024}^{+0.022}$	⋯	${0.111}_{-0.111}^{+0.123}$	⋯
Silicate-to-carbon ratio e	${1.116}_{-0.074}^{+0.072}$	⋯	${0.743}_{-0.220}^{+0.264}$	⋯
Crystalline silicate mass to total silicate mass f	${0.441}_{-0.035}^{+0.032}$	⋯	${0.260}_{-0.260}^{+0.217}$	⋯
ap (μm) g	0.7	⋯	0.5	⋯
Fractal porosity (D)	2.727	⋯	2.727	⋯
Other Parameters
Hanner grain-size distribution M:N	22.2:3.7	⋯	13.6:3.4	⋯
Reduced ${\chi }_{\nu }^{2}$	4.98	⋯	0.86	⋯
Degrees of freedom	49	⋯	168	⋯

Notes.

^a Uncertainties represent the 95% confidence level. ^b Comet on 2016 January 10 UT r_h = 1.30 au, Δ = 0.76 au. ^c Comet on 2016 February 9 UT r_h = 1.70 au, Δ = 1.09 au. ^d Number of grains, N_p , at the peak (a_p ) of the Hanner grain-size distribution (HGSD). ^e Ratio represents the bulk mass properties of the materials in the models. ^f f_cryst ≡ m_cryst/[m_amorphous + m_cryst] where m_cryst is the mass fraction of submicron crystals. ^g Peak grain size (radius) of the Hanner GSD.

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3.2.1. Optical Properties and IDP Analogs

3.2.2. The Hanner Grain-size Distribution

3.2.3. Moderately Porous Particles

3.2.4. CDE Models of Solid Trirefringent Silicate Crystals

3.2.5. Comet Crystalline Silicates and Disk Transport

3.2.6. Revised Specific Density for Amorphous Carbon

Comet C/2013 US₁₀ (Catalina) is a dynamically new (DN) Oort cloud with eccentricity of ≃1.0003. Compositionally, the dust in the coma of comet C/2013 US₁₀ (Catalina) is carbon rich, and this comet is among a subset of observed comets that are similarly carbon rich, some of which are also DN. The carbon-rich dust particles of comet 67P/Churyumov–Gerasimenko were measured in situ to have by weight 55% mineral and 45% (carbonaceous) organic (see Figure 10, Bardyn et al. 2017). If we consider their mineral-to-organic ratio to be analogous to our silicate-to-carbon ratio, then 67P/Churyumov–Gerasimenko has a ratio of 1.1 and C/2013 US₁₀ (Catalina) has ratios of 1.55 and 1.03 for 1.3 au (BASS) and 1.7 au (FORCAST), respectively. However, within the thermal model parameter uncertainties, the silicate-to-carbon ratios are the same for both epochs. A decrease by a factor of 1.5 in the silicate-to-carbon ratio for the best-fit values between the two epochs is partly attributed to the definitive detection of crystalline forsterite at 1.3 au that increases the silicate mass fraction relative to the upper limit for forsterite at 1.7 au. Between the two epochs, the amorphous carbon increases by a factor of 1.21 (see Table 3).

The dust particle population in comet C/2013 US₁₀ (Catalina) is characterized by a moderate particle porosity (D = 2.727). Coma grains extend to submicron size particles; the HGSD (defined in Section 3.2.2) peaks at an average a_p  = {0.7, 0.5} μm, with a grain-size distribution slope of N = {3.4, 3.7}, respectively, for the two epochs at 1.3 au and 1.7 au. The derived coma dust properties of C/2013 US₁₀ (Catalina) share similar characteristics to those found recently for some other long-period Oort cloud comets, such as C/2007 N3 (Lulin), which is also DN (Woodward et al. 2011).

The HGSD slope of comet C/2013 US₁₀ (Catalina) is in the range of other comets, including Oort cloud comets, where typically 3.4 ≤ N ≤ 4. However, its HGSD slope is greater (steeper) than found for comet 67P/Churyumov–Gerasimenko, which has multiple measurements of its differential grain-size distribution n(a)da with slopes of N = 3.0 (Bockelée-Morvan et al. 2017a, 2017b), N = 3.1 (Rinaldi et al. 2017), N = 3 (Della Corte et al. 2019), or N ≃ 2.7–3.2 for a < 100 μm and N ≃ 1.8 for 100 ≤ a ≤ 1000 μm (Merouane et al. 2016).

Examination of the SEDs of comet C/2013 US₁₀ (Catalina) obtained at two different epochs and the thermal-model-derived parameters (Table 3) enable us to deconstruct and decipher aspects of the inner coma dust environment (Figures 5 and 6). From the 58% drop in the available ambient solar radiation between the 1.3 au (BASS epoch) and 1.7 au (SOFIA epoch) observations, one would expect on average the particles on the coma to be cooler at the latter epoch. From the long-wavelength shoulder (λ ≳ 12.5 μm) of the 10 μm silicate feature and longward, the SED measured at 1.7 au (Figure 2) shows enhanced emission at longer wavelengths. Thus, the particles contributing to the far-IR emission are cooler at 1.7 au compared to those at 1.3 au as anticipated. However, the thermal emission at 7.8 μm and bluewards is similar for the two epochs. Hence, at 1.7 au, the coma of comet C/2013 US₁₀ (Catalina) must have an increased abundance of smaller warm amorphous carbon particles. Moreover, the number of dust particles in the coma at 1.7 au is increased over that at 1.3 au in order to produce about the same flux density of thermal emission at these two epochs with the cooler particles present at 1.7 au.

There is evidence of a narrow 11.2 μm silicate feature attributable to Mg-rich crystalline olivine (Hanner et al. 1994; Wooden 2008). This is borne out by the detailed thermal modeling of the SED, which constrains the relative mass fraction of crystalline forsterite grains in the coma at 1.3 au. The ratio of the crystalline silicate mass to the total silicate mass was ∼0.44. The crystalline mass fraction determined for comet C/2013 US₁₀ (Catalina) is greater than that determined for other dynamically new comets such as C/2012 K1 (Pan-STARRS) studied with SOFIA (Woodward et al. 2015). The derived values for each observational epoch are summarized in Table 3.

For the portion of the grain-size distribution with radii a ≤ 1 μm (the submicron population), the silicate-to-carbon ratio is ${1.116}_{-0.074}^{+0.072}$ and ${0.743}_{-0.220}^{+0.264}$ at 1.3 au and 1.7 au, respectively (see Table 3). Compared to 1.7 au, the higher silicate-to-carbon ratio at 1.3 au is partly due to a factor of ∼1.25 less amorphous carbon combined with an increase in mass of silicates from the definitive detection of forsterite. This crystalline silicate material produces a sharp peak at 11.1–11.2 μm (Koike et al. 2010 and references therein) and is relatively transparent outside of its resonances. At 1.3 au, crystalline silicate mass fraction (f_cryst) is ${0.441}_{-0.035}^{+0.033}$ in the coma of comet C/2013 US₁₀ (Catalina) so forsterite crystals contribute significantly to the silicate-to-carbon ratio. Crystalline silicates are tracers of radial migration of inner disk condensates or possibly shocked Mg-rich amorphous olivine so the 44% crystalline mass fraction indicates significant radial transport of inner disk materials out to the comet-forming regime (see Section 3.2.5).

The spectral shape of the 10 μm silicate feature can be revealed by dividing the observed flux by a local 10 μm blackbody-fitted "pseudo-continuum." The shape of the 10 μm silicate feature arises from emission from submicron- to at most several-micron-radii silicate particles in the the coma, depending on the porosity. In thermal models, the "pseudo-continuum" has contributions from porous or solid amorphous carbon, which is featureless at all wavelengths. Thermal models require porous particles (D = 2.7272) for comet C/2013 US₁₀ (Catalina). Figure 7 shows the silicate feature shape for comet C/2013 US₁₀ (Catalina) from the BASS observations. The FORCAST mid-IR spectral data show a similar contrast silicate feature but with a lower S/N than the BASS data, so these data are not included in the figure for clarity.

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The silicate strength parameter historically enables one to intercompare the dust properties of different comets by quantifying the silicate feature contrast with respect to the local "pseudo-continuum" (Sitko et al. 2004; Woodward et al. 2015). The 10 μm silicate feature strength, defined as F₁₀/F_c , where F₁₀ is the integrated silicate feature flux over a bandwidth of 10–11 μm and F_c is that of the local blackbody "pseudo-continuum" at 10.5 μm (Sitko et al. 2004), is a metric that describes the contrast of the silicate emission feature. We find the 10 μm silicate feature to be weak in comet C/2013 US₁₀ (Catalina), approximately 12.8% ± 0.1% above the local "pseudo-continuum." The low silicate feature strength in comet C/2013 US₁₀ (Catalina) is similar to some other comets (Sitko et al. 2004, 2013; Woodward et al. 2011, 2015).

A second metric used to compare dust properties of comets is the ratio of the SED color temperature (T_color) to the temperature that solid spheres would have at a given heliocentric distance (r_h (au)) in radiative equilibrium with the solar insolation, T_BB(K) = 1.1 × 278 (r_h)^−0.5 (see Hanner et al. 1997). At the epoch of the the SOFIA observations, the combined grism 6.0–36.5 μm SED can be fit with a single blackbody of temperature 239.5 ± 0.5 K, hence this ratio is ≃1.02. The enhanced color temperature over a graybody, which is expected for particles smaller than the wavelength, often is historically referred to as "superheat" S (see Gehrz & Ney 1992). The silicate strength parameter is somewhat correlated with S (Sitko et al. 2004; Woodward et al. 2015). For comet 67P/Churyumov–Gerasimenko, 1.15 ≤ S ≤ 1.2, and S is plotted along with the bolometric albedo at phase angle 90° (0.05–0.15) and the dust color (percent per 100 nm; Bockelée-Morvan et al. 2019). Comet C/2013 US₁₀ (Catalina) has a smaller value for S than comet 67P/Churyumov–Gerasimenko.

C/2013 US₁₀ (Catalina) and 67P/Churyumov–Gerasimenko, both exhibiting a weak silicate feature and are carbon rich as determined from thermal modeling, provide a direct contradiction to older concepts commonly asserted in the literature. Commonly, many groups argued that some comets totally lacked silicate features because their solid grains were radiating as graybodies and not displaying resonances because the grains were so large that the grains themselves were optically thick (A'Hearn et al. 2005; Lisse et al. 2005). For comets with low dust production rates, estimation and subtraction of the nucleus' contribution to the SED is important. When combined with higher sensitivity observations and subtraction of the nucleus flux density, thermal models that integrate over a size distribution of particles with composition-dependent dust temperatures shows that the comets with coma particles whose HGSD has a_p  ≤ 1 μm and that display weak silicate features are carbon rich.

3.4.1. The "Hot Crystal Model" and SOFIA in the Far-IR

Within our S/N in the SOFIA mid- to far-IR SED, neither hydrated phyllosilicates that have far-IR resonances distinct from anhydrous amorphous olivine and amorphous pyroxene nor the very broad 23 μm troilite (FeS, submicron sized; Keller et al. 2002) spectral signatures were seen (see Schambeau et al. 2015). Phyllosilicates, such as montmorillonite, as well as carbonates have absorptions in the 5–8 μm wavelength region (Roush et al. 1991; Crovisier & Bockelée-Morvan 2008), and neither of these compositions were detected in comet C/2013 US₁₀ (Catalina).

The BASS spectrum spans the 3.0–3.5 μm wavelength region where potentially the 3.28 μm peripheral hydrogen stretch on a ring carbon macromolecule (PAH), and the 3.4 μm −CH₂, −CH₃ aliphatic bonds arrangements that are prevalent in IDPs and Stardust materials (Matrajt et al. 2013) might be detectable. The analyses of a well-defined aliphatic carbon 3.4 μm band on the nucleus surface of 67P/Churyumov–Gerasimenko is presented by Raponi et al. (2020), and Rinaldi et al. (2019) also argue for the presence for this feature in coma observations. A broad 20% deep 3.2 μm features from organic ammonium salts also is discussed for the nucleus Poch et al. (2020). If the aliphatic material in comets is similar to that of IDPs then laboratory absorption spectra by Matrajt et al. (2005) of whole IDPs provide important information on the relative column densities of C atoms participating in different organic bonding groups including aliphatic bonds (−CH₂, −CH₃), aromatic (C=C), carbonyl, and carboxylic acid bonds in ketones, and ammonium salts.

Protopapa et al. (2018) point to the possible presence of an organic emission feature near 3.3 μm in higher spectral resolution observations of comet C/2013 US₁₀ (Catalina) obtained on 2016 January 12 (r_h  = +1.3 au) but do pursue any further detailed analyses. However, there are strong molecular ro-vibrational emission lines of C₂H₆ and CH₃OH in the 3.28–3.5 μm region that significantly complicate deciphering underlying solid state organic features (Bockelée-Morvan et al. 1995; Dello Russo et al. 2006; Yang et al. 2009; Bockelée-Morvan et al. 2017a). Given these challenges, we do not report on detection of any aromatic or aliphatic features in the BASS data at our resolving power and sensitivity for comet C/2013 US₁₀ (Catalina). Thus, no spectral features were seen to indicate the presence of aromatic hydrocarbons (such as hydrogenated amorphous carbons (HACs), PAHs, a-C(:H) nanoparticles) or aliphatic carbons in the coma of C/2013 US₁₀ (Catalina).

Comet C/2013 US₁₀ (Catalina) has one of the few reported 5–8 μm wavelength spectrum from SOFIA (+FORCAST). We searched for spectral signatures of vibration modes of C=C bonds (6.25 μm = 1600 cm⁻¹), based on a constrained search of the observed absorption features in laboratory studies of cometary-like polyaromatic organics in IDPs (Matrajt et al. 2005) and in the UCAMMs (Dartois et al. 2018) as well as asteroid insoluble organic materials (IOM; Alexander et al. 2017). The 6.25 μm C=C resonances are not dependent on the degree of hydrogenation; i.e., the number of peripheral hydrogen bonds compared to structural C=C bonds (Keller et al. 2004). The UCAMMS are mass dominated by organics, richer in N and poorer in O than cometary particles with probable origins in the outer protoplanetary disk (Dobrica et al. 2009). We also searched for C=O bonds (5.85 μm = 1710 cm⁻¹). There are tantalizing ≤3σ fluctuations near 1620 cm⁻¹ and 1510 cm⁻¹ that are in the regions of C=C stretching modes (see Table 2 of Merouane et al. 2014). However, the S/N is insufficient and the width of the fluctuations are narrow, narrower than the widths of the C=C resonances in the UCAMMs that have a preponderance of organics such that their features dominate the 5–8 μm region.

The lack of resonances from organics in the 5–8 μm wavelength region does not discourage us from further searches in cometary comae for these bonding structures with the much higher sensitivity provided by the James Webb Space Telescope (JWST) and its instruments.

We find amorphous carbon dominates the composition of grain materials in comet C/2013 US₁₀ (Catalina). Dominance of carbon as a coma grain species was seen in other ecliptic comets including 103P/Hartley 2 (Harker et al. 2018) as well as the Oort cloud comets C/2007 N3 (Lulin) (Woodward et al. 2011) and C/2001 HT50 (Kelley et al. 2006). The outburst of dusty material from comet 67P/Churyumov–Gerasimenko at 1.3 au was carbon-only grains (with radii of order 0.1 μm), as measured by VIRTIS-H (Bardyn et al. 2017) and VIRTIS-M (Rinaldi et al. 2018) on Rosetta. Comets can exhibit changes in their silicate-to-carbon ratio between observation epochs, and notably, a few comets have had significant changes in their inner comae silicate-to-carbon ratios during a night's observations (C/2001 Q4 (NEAT), Wooden et al. 2004; 103P/Hartley 2, Harker et al. 2018; 9P/Tempel 1, Sugita et al. 2005; Harker et al. 2007).

Our cometary coma dust atomic C/Si ratios are calculated using a number of suppositions and should be taken as indicative values. Cometary atomic C/Si ratios are of interest for comparison with in situ studies of 67P/Churyumov–Gerasimenko and 1P/Halley and of laboratory investigations of IDPs and UCAMMs. The IDPs and UCAMMs are extraterrestrial materials likely to have originated from primitive bodies like comets and Kuiper-belt objects (KBOs), respectively (Bergin et al. 2015; Dartois et al. 2018; Burkhardt et al. 2019, and references therein). We choose to compare the C/Si of the submicron grain component determined from thermal models with bulk elemental composition measurements of IDPs (X-ray measurements). We elect to not compare C/Si ratios derived from resonances (aliphatic 3.4 μm, aromatic 6.2 μm, and other bonds in UCAMMs) because in laboratory baseline-corrected absorption spectra, the amorphous carbon component would not be assessed because it does not have a resonance.

3.7.1. Endemic Carbonaceous Matter in Comets

Amorphous carbon is the one carbon-bonding structure common to IDPs, Stardust, and four carbonaceous chondrites including Bells, Tagish Lake, Orgueil, and Murchison (Wirick et al. 2009; De Gregorio et al. 2017). The amorphous carbon-bonding structure is observed specifically through C-XANES (Matrajt et al. 2008a) and in Stardust particles from comet 81P/Wild 2 (Matrajt et al. 2008b). In addition to C-XANES spectra, regions of some IDPs are described a poorly graphitized or highly disordered carbon (Thomas et al. 1993a, 1993b).

Other organic bonding structures besides amorphous carbon that are found in cometary samples (IDPs and Stardust) are: aliphatic, aromatic, and rarely graphitic. IDP organic matter generally occurs as aliphatic-dominated rims (Flynn 2008; Flynn et al. 2015), rims on mineral grains with aromatic (C=C) and carbonyl group (C=O) bonds (Flynn et al. 2013), (nongraphitized) aliphatic or aromatic macromolecular material (De Gregorio et al. 2017) as submicron-sized pieces associated with mineral crystals (Wirick et al. 2009), or as a matrix (Brunetto et al. 2014). In one IDP, different bonding structures of carbon occurs in micron-sized regions and where amorphous carbon was mixed with GEMS (Brunetto et al. 2014). Two IDPs show N-rich organic rims on GEMS that are in turn inside other GEMS, indicating two formation epochs, and their specific organic matter requires particle temperatures remained cooler than ∼450 K (Ishii et al. 2018). Cometary carbonaceous matter is sometimes referred to as polyaromatic when there are significant moities of aromatic C=C bonds. UCAMMs are noted for abundant aromatic material as well as for their N=C and N−C bonds (Dartois et al. 2018; Mathurin et al. 2019).

Only four cometary samples display graphitic carbon-bonding structures as witnessed through C-XANES. Two of these are from Stardust samples, seen as halos on Fe grain cores which are hypothesized to have formed at high temperatures and at low oxygen fugacity in the protoplanetary disk (De Gregorio et al. 2017), and in two IDPs (L2021C5, L2021Q3), where its close proximity to other bonding structures is discussed respectively by Brunetto et al. (2014) and (L2021Q3; Merouane et al. 2016). Graphite can be formed at high temperatures (≳3273 K) although there are lower temperature processes that form graphite (Wirick et al. 2009). Ion bombardment of amorphous carbon is a competing process between amorphization and graphitization and this process depends on the structure of the starting amorphous carbon (Brunetto et al. 2011). Raman spectroscopy of one IDP shows "localized micrometer-scale distributions of extremely disordered and ordered carbons" (Brunetto et al. 2011).

In summary, cometary carbonaceous matter is macromolecular (De Gregorio et al. 2017) and not strictly aromatic (containing aromatic bonds), which is in contrast to meteoritic IOM (Alexander et al. 2007), as well as highly variable in composition and structure.

In the following discussion, we investigate the plausible implications of the cometary coma thermal model's relative mass fractions (i.e., the mass fraction of amorphous carbon to the mass fractions of the amorphous and crystalline silicates) on the elemental abundance ratio of C/Si. We compare the inferred elemental ratio C/Si for comet C/2013 US₁₀ (Catalina) from thermal models to the C/Si ratio determined for IDPs using scanning electronic microscopy with energy dispersive X-ray analysis (the SEM-EDX method; Thomas et al. 1993b), and by mass spectrometry for comet 1P/Halley and comet 67P/Churyumov–Gerasimenko (COSIMA).

We will show that the relative mass fractions of C/Si derived from our thermal models of comet C/2013 US₁₀ (Catalina) and a handful of other recently observed and modeled comets are consistent with the average C/Si = ${5.5}_{-1.2}^{+1.4}$ derived by COSMIA for thirty 67P/Churyumov–Gerasimenko particles (Bardyn et al. 2017), for 1P/Halley particles measured by Vega-1 and Vega-2 mass spectrometers during spacecraft encounters, and also for the upper range of C/Si for IDPs (see Bergin et al. 2015). The enigmatic comet C/1995 O1 (Hale–Bopp), with its preponderance of submicron crystalline silicates (Harker et al. 2002), also is included in our analysis to demonstrate its lower C/Si ratio that is in the lower range of the IDP C/Si ratios (Bardyn et al. 2017) and also close to the range determined for CI chondrites (Bergin et al. 2015).

Our cometary coma dust C/Si atomic ratios are calculated using a few suppositions and should be taken as indicative values, which are of interest for comparison with in situ studies of 67P/Churyumov–Gerasimenko and 1P/Halley and of laboratory investigations of IDPs and UCAMMs (Matrajt et al. 2005; Brunetto et al. 2014; Bardyn et al. 2017; Dartois et al. 2018). The IDPs and UCAMMs are extraterrestrial materials likely to have originated from primitive bodies like comets and KBOs, respectively (Dobrica et al. 2009 and references therein). Unlike laboratory measurements of IDPs, micrometeoritic samples, or Stardust particles, which generally are the measure of single grains or isolated domains within a matrix, values returned from remote-sensing spectroscopic observations represent a coma-wide measure from a large ensemble of thermally radiating dust particles of various radii.

Our suppositions in deriving C/Si atomic ratios are as follows: (a) amorphous carbon is a good optical analog for dark highly absorbing carbonaceous matter in cometary comae and (b) thermal model relative mass fractions derived for amorphous carbon represent a significant fraction of the carbonaceous matter in the coma (Section 3.9.1).

3.9.1. Counting Carbon Atoms

3.9.2. The C/Si Gradient in the Solar System

We derived the C/Si atomic ratio using the thermal model dust compositions (and relevant atomic amu) described in Section 3.3 and the relative masses of the submicron grains for each composition returned from the best-fit thermal model. The asymmetric uncertainties in the relative masses derived from the thermal models were "symmetrized" following the description discussed by (Method#2, Audi et al. 2017), cognizant of the limitations of this approach (see Barlow 2003; Possolo et al. 2019) to enable standard error propagation techniques. The carbon-to-silicon atomic ratio is defined as

$$\begin{eqnarray}\begin{array}{rcl}\displaystyle \frac{{\rm{C}}}{\mathrm{Si}} & = & \displaystyle \frac{{\rm{C}}}{{\rm{\Sigma }}({\mathrm{Si}}_{\mathrm{species}}^{\mathrm{dust}})}\\ & = & \ \displaystyle \frac{{N}_{p}({\rm{C}})\cdot {{\rm{C}}}_{\mathrm{amu}}}{\tfrac{{N}_{p}(\mathrm{AO})}{\alpha }+\tfrac{{N}_{p}(\mathrm{AP})}{\beta }+\tfrac{{N}_{p}(\mathrm{CO})}{\delta }+\tfrac{{N}_{p}(\mathrm{CP})}{\gamma }},\end{array}\end{eqnarray} \tag{ 1 }$$

where

$$\begin{eqnarray}\begin{array}{rcl}\alpha & = & \displaystyle \frac{(0.5\cdot {\mathrm{Mg}}_{\mathrm{amu}}+0.5\cdot {\mathrm{Fe}}_{\mathrm{amu}})\times 2+{\mathrm{Si}}_{\mathrm{amu}}+4\cdot {{\rm{O}}}_{\mathrm{amu}}}{{\mathrm{Si}}_{\mathrm{amu}}}\\ \beta & = & \displaystyle \frac{(0.5\cdot {\mathrm{Mg}}_{\mathrm{amu}}+0.5\cdot {\mathrm{Fe}}_{\mathrm{amu}})+{\mathrm{Si}}_{\mathrm{amu}}+3\cdot {{\rm{O}}}_{\mathrm{amu}}}{{\mathrm{Si}}_{\mathrm{amu}}}\\ \delta & = & \displaystyle \frac{({\mathrm{Mg}}_{\mathrm{amu}})\times 2+{\mathrm{Si}}_{\mathrm{amu}}+4\cdot {{\rm{O}}}_{\mathrm{amu}}}{{\mathrm{Si}}_{\mathrm{amu}}}\\ \gamma & = & \displaystyle \frac{({\mathrm{Mg}}_{\mathrm{amu}})+{\mathrm{Si}}_{\mathrm{amu}}+3\cdot {{\rm{O}}}_{\mathrm{amu}}}{{\mathrm{Si}}_{\mathrm{amu}}}\end{array}\end{eqnarray} \tag{ 2 }$$

are the α, β, γ, and δ are the number of Si atoms per unit mass, and the values for N_p (the number of grains at the peak [a_p ] of the HGSD) are found in Table 3. Table 4 summarizes the derived the C/Si atomic ratios for comet C/2013 US₁₀ (Catalina) and other comets observed with SOFIA (+FORCAST) as well as comet C/1995 O1 (Hale–Bopp) (Harker et al. 2002). The C/Si atomic ratio for the comets in Table 4, UCAMMs (data from Dartois et al. 2018), and IDPs and other comets (data from Bergin et al. 2015) are presented in Figure 8. Recent measurements of solar cosmic abundances create an upper limit for the ISM C/Si of 10 as discussed in Dartois et al. (2018 and references therein). UCAMMs are above the solar cosmic abundance limit. Thus, those who study UCAMMs suggest that their organics have sequestered carbon from the gas phase and converted it to a solid phase in the cold outer disk or on the surfaces of nitrogen-rich cold body surfaces because of their enhanced N/C ratios (Dartois et al. 2013, 2018). As measured or computed, cometary coma appear to lack the high C/Si ratios of UCAMMs.

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Table 4. Derived Carbon-to-silicon Atomic Ratio of Comets ^a

Comet	Telescope/Instrument	C/Si	(References)
C/2013 US10 (Catalina)	IRTF (+BASS)	4.180 ± 0.308	(1)
C/2013 US10 (Catalina)	SOFIA (+FORCAST)	6.556 ± 3.262	(1)
C/2013 K1 (Pan-STARRS)	SOFIA (+FORCAST)	3.841 ± 1.086	(2)
C/2013 X1 (Pan-STARRS)	SOFIA (+FORCAST)	7.781 ± 6.091	(3)
C/2018 W2 (Africano)	SOFIA (+FORCAST)	6.204 ± 3.858	(3)
C/1995 O1 (Hale–Bopp)	IRTF (+HIFOGS)	0.420 ± 0.001	(4)

Note.

^a Computed from relative mass ratios of thermal model dust composition components, adopting an amorphous carbon density ρ = 1.5 g cm⁻³. The Appendix provides the complete model in Tables 6–9, including the revision to the C/2013 K1 (Pan-STARRS) and C/1995 O1 (Hale–Bopp) models resulting from an amorphous carbon specific density ρ_s (ACar) = 1.5 g cm⁻³.

References. (1) This work. (2) Woodward et al. (2015). (3) C. E. Woodward et al. (2021, in preparation). (4) Harker et al. (2002).

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Comets by their C/Si appear to be sampling similar abundances of carbon in the optically active composition of coma particles as SEM-EDX-derived C/Si ratios are measuring for IDPs. Many, but not all, comets have C/Si commensurate with IDPs, and IDPs are more carbon rich than carbonaceous chondrites (Figure 8). Two Sun-grazing comets from the Kreutz family of comets, C/2003 K7 and C/2011 W3 (Lovejoy), have silicate-rich dust and fall in the carbonaceous chondrites (CC) range (Ciaravella et al. 2010; McCauley et al. 2013; Bergin et al. 2015).

Dartois et al. (2013, 2018), Gail & Trieloff (2017), and other authors suggest that there was a carbon gradient in the early solar system. The comet C/Si values support this contention of gradient in the carbon with heliocentric distance of formation (see Rubin et al. 2019). Commensurate with these results, CONSERT on Rosetta/Philae suggest comets are a large carbon reservoir given the nucleus' permittivity and density constraints on the dust composition in the nucleus (Herique et al. 2016), which agrees within uncertainties with the average specific density of dust particles in the comet C/2013 US₁₀ (Catalina)'s comae. The existence of a carbon gradient in solar systems also is bolstered by the C/Si ratios of IDPs.

Destruction of carbon occurred in the inner disk, which is the long-standing "carbon deficit problem" (Lee et al. 2010; Bergin et al. 2015). Disk modelers are working to predict the carbon-depletion gradient with complex chemical networks (Wei et al. 2019). Another model investigates the removal of carbon through oxidation and photolysis when particles are transported to the exposed upper disk layers but radial transport erases signatures unless other mechanisms quickly destroy carbon, like flash heating from FU Ori outbursts, or mechanisms preventing replenishment of the inner disk, such as sustained particle drift barrier, i.e., a gap opened by the formation of a giant planet. Klarmann et al. (2018) argue that "a sustained drift barrier or strongly reduced radial grain mobility is necessary to prevent replenishment of carbon from the outer disk [to the inner disk]."

Heat and/or high oxygen fugacity conditions in the inner protoplanetary disk can convert carbon from its incorporation in refractory particles to carbon in gas-phase CO or CO₂. As discussed (Section 3.7.1), particle temperatures above ∼823 K can destroy aliphatic carbon. Flash heating of Mg–Fe silicates in the presence of carbon is a possible formation pathway for Type I chondrules (Connolly et al. 1994). If cometary particles can drift interior to the water evaporation front, then cometary materials may deliver carbon to the inner protoplanetary disk. Delivery of carbon to the gas phase of the inner disk by comet grains requires inward delivery mechanisms during the early pebble accretion phase of disk evolution when the motions of aggregating materials are dominated by inward pebble drift (Misener et al. 2019; Andrews 2020). Such delivery requires that amorphous carbon particles already be incorporated into cometary grains in addition to the need that the sublimation temperature of amorphous carbon be higher than water ice so that the delivery of carbon particles is interior enough for carbon to become enhanced in the gas phase. High carbon abundances in the gas phase are required to explain the poorly graphitized carbon (PGC) halos around Fe cores in two terminal Stardust particles (Wirick et al. 2009; De Gregorio et al. 2017).

Earth's bulk C/Si atomic ratio is much smaller and models for its core formation and evolution assume a carbonaceous chondrite supply of carbon was available to form Earth (Bergin et al. 2015). Cometary C/Si atomic ratios are much higher than carbonaceous chondrites. The outer disk was richer in carbon than the inner disk. The carbon gradient may be another indication of planetary gaps sculpting the compositions of small bodies. Burkhardt et al. (2019) hypothesize that the isotope variances of planetary bodies, traced through meteoritic and IDPs, can be explained if there were isotopically distinct nebular reservoirs of noncarbonaceous and carbonaceous chondrites that were not fully mixed in the primordial disk of the solar system. A planetary gap created by Jupiter's formation which inhibited mixing between the inner and outer disk could also explain the dichotomy in between noncarbonaceous and carbonaceous meteorites (Nanne et al. 2019).

Cometary C/Si atomic ratios highlight the "carbon deficit" that occurred in the inner disk and the dichotomy between the inner and outer disk when juxtaposed with the C/Si atomic ratios found for Earth and ordinary chondrites. Furthermore, the dust composition of many comets demonstrates a carbon-rich reservoir existed in the regimes of comet formation that are pertinent to the understanding the evolution of our protoplanetary disk and the formation of the planets.

The optical spectra of comets in the i' band tends to be dominated by dust. However, red CN gas emission bands, CN(2,0) and CN(3,1), can be present at redder wavelengths within the i' band (Swings 1956; Fink et al. 1991; Cochran et al. 2015). The presence of these emission lines may contaminate measurements of the scattered-light dust continuum surface brightness and hence estimates of the dust production rate. Optical spectra of comet C/2013 US₁₀ (Catalina) obtained on 2015 December 18 (Kwon et al. 2017) show weak CN(2,0) and CN(3,1) band emission. However, optical spectra obtained after the epoch of the MORIS and FPI+ imagery in 2016 March 18 show no strong emission features redward of 7630 Å that contribute to the i'-band long-wavelength cutoff (Hyland et al. 2019). The azimuthally averaged radial profiles of comet C/2013 US₁₀ (Catalina) derived from the MORIS and FPI+ imagery, presented in Figure 9, show little deviation from a 1/ρ profile (Gehrz & Ney 1992) at large cometocentric distances consistent with a steady-state coma without significant CN contamination. Application of standard comet image enhancement techniques to these optical data (see Samarasinha & Larson 2014; Samarasinha et al. 2014) reveals no structures in the coma such as jets or spirals at this epoch.

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The dust production rate of comet C/2013 US₁₀ (Catalina) during the epoch of the BASS observations (2016 January 10.633 UT) was derived using the proxy quantity Afρ (A'Hearn et al. 1984). When the cometary coma is in steady state, this aperture-independent quantity can be parameterized as

$$\begin{eqnarray}&&A(\theta )f\rho =\displaystyle \frac{4\,{r}_{h}^{2}\,{{\rm{\Delta }}}^{2}\,{10}^{-0.4({m}_{\mathrm{comet}}-{m}_{\odot })}}{\rho }\,\mathrm{cm}.\end{eqnarray} \tag{ 3 }$$

In this relation, A(θ) is four times the geometric albedo at a phase angle θ, f is the filling factor of the coma, m_comet is the measured cometary magnitude, m_⊙ is the apparent solar magnitude, derived ¹³ as ${i}_{\odot }^{{\prime} }=-27.002$, ρ is the linear radius of the aperture at the comet's position (cm), and r_h (au) and Δ(cm) are the heliocentric and geocentric distances, respectively.

The Halley–Marcus (HM; Schleicher et al. 1998; Marcus 2007a, 2007b) phase angle correction ¹⁴ was used to normalize A(θ)fρ to a 0° phase angle, wherein we adopted an interpolated value of HM = 0.3424 and 0.3946 commensurate with the epoch of our optical observations on 2016 January 11.63 UT and 2016 February 9.34 UT, respectively. Table 5 reports values of A(0°)fρ = (A(θ)fρ/HM) at a selection of aperture sizes (distances from the comet photocenter) in the i' band. The dust production rate is similar to that observed in other moderately active comets, such as C/2012 K1 (Pan-STARRS) discussed by Woodward et al. (2015).

We can roughly estimate the dust mass-loss rate by taking the mass of dust observed in the coma inside of our aperture as the 1/ρ dependence of the surface brightness distribution indicates a steady-state coma. If we adopt for the outflow velocity of 100 μm radii and larger particles which carry most of the mass a value of $\overline{{v}_{\mathrm{dust}}}\approx 20\,{\rm{m}}\,{{\rm{s}}}^{-1}$ (Rinaldi et al. 2018) and assume a steady outflow of material through a spherical bubble at some distance R (meters) near the nucleus surface, the mass-loss rate can be estimated as

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{dust}}\approx \displaystyle \frac{3\,\cdot {M}_{\mathrm{dust}}\times \overline{{v}_{\mathrm{dust}}}}{R},\end{eqnarray} \tag{ 4 }$$

where ${\dot{M}}_{\mathrm{dust}}$ has units of g s⁻¹. If the nucleus of comet C/2013 US₁₀ (Catalina) is comparable in size to that typically inferred for many comets, 1.5 km, then ${\dot{M}}_{\mathrm{dust}}\approx 4\times {10}^{-3}{M}_{\mathrm{dust}}\left[\overline{{v}_{\mathrm{dust}}}/20({\rm{m}}\,{{\rm{s}}}^{-1})\right].$ At 1.7 au, when M_dust = 4 × 10⁸ g (Table 3), then ${\dot{M}}_{\mathrm{dust}}\approx 1.6\times {10}^{6}$ g s⁻¹.

Fink & Rubin (2012) discuss how the A(θ)fρ can be tied to the mass production rate, given the HGSD parameters, computing dust mass-loss rate (in kg s⁻¹) by assuming a particle density of 1 g cm⁻³ for various particle size distribution functions. Taking an average value of N = 3.5, corresponding to dq/da ∼ a^−3.5, which yielded a mass-loss rate of 22.8 k s⁻¹ from the detailed computations of Fink & Rubin (2012; see Table 2) and using Afρ at zero phase for C/2013 US₁₀ (Catalina) of ∼6290 cm (Table 5), one finds ${\dot{M}}_{\mathrm{dust}}\,\approx 2.4\times {10}^{6}$ g s⁻¹. This is comparable to our latter estimate.

If we assume the density of the nucleus, which is a porous dust–ice mixture, is ρ_nuc ∼ 1 g cm⁻³ (Fulle et al. 2019), then a rough estimate of the surface erosion rate from the nucleus of comet C/2013 US₁₀ (Catalina) is ∼1 mm day⁻¹ if the entire surface is active and if the radius of the comet is ∼1.5 km. The depth of space weathering of a DN comet in the local ISM might be at most a centimeter over the age of the solar system, and this material would be shed in a timeframe of ≲2 weeks at the observed dust mass-loss rate, which we have translated to an erosion rate. For perspective, cumulative erosion depths for comet 67P/Churyumov–Gerasimenko depended on the nucleus geography and solar insolation, and from the start of the Rosetta mission until the first equinox were 6 mm–0.1 m and to the end of the mission were of order 0.3–4 m (Combi et al. 2020).

The quantity fρ (see Appendix A of Kelley et al. 2013), a parameter which is the thermal emission corollary of the scattered light, the light-based Afρ was also computed using our FORCAST broadband photometry. fρ is defined as

$$\begin{eqnarray}&&\epsilon f\rho =\displaystyle \frac{{{\rm{\Delta }}}^{2}}{\pi \rho }\displaystyle \frac{{F}_{\nu }}{{B}_{\nu }}\,(\mathrm{cm}),\end{eqnarray} \tag{ 5 }$$

where is the effective dust emissivity, F_ν is the flux density (Jansky) of the comet within the aperture of radius ρ, B_ν is the Planck function (Jy sr⁻¹) evaluated at the temperature ${T}_{{\rm{c}}}={T}_{\mathrm{bb}}=1.093\times (278\,{\rm{K}}){r}_{h}^{-0.5}\simeq 232.9\,{\rm{K}},$ where T_c is the color temperature. Derived values of fρ for comet C/2013 US₁₀ (Catalina) from SOFIA photometry are presented in Table 2.

Our near-simultaneous optical observations conducted on the same night as our measurement of the infrared SED of comet C/2013 US₁₀ (Catalina) enable us to estimate the bolometric dust albedo as described by Woodward et al. (2015). The measured albedo depends on both the composition and structure of the dust grains as well as the phase angle (Sun–comet observer angle) of the observations. As the grain albedo is the ratio of the scattered light to the total incident radiation, the thermal emission at IR wavelengths and the scattered-light component observed at optical wavelengths are linked though this parameter.

The photometry from the i' imagery in an equivalent aperture that corresponds to the apertures used to measure the IR SEDs provides an estimate of [λF_λ ]${}_{\mathrm{scattering}}^{\max }$. An estimate of [λF_λ ]${}_{{IR}}^{\max }$ is obtained from a filter-integrated equivalent photometric point at 10 μm derived by integrating with the observed IR SED over the bandwidth of the FORCAST F111 filter. We find that the coma of comet Oort cloud C/2013 US₁₀ (Catalina) has a low bolometric dust albedo, A(θ), of ≃5.1% ± 0.1% at a phase angle of 4780 to ≃13.8% ± 0.5% at a phase angle of 3301.

Figure 10 shows the derived A(θ) as a function of phase angle, θ, for a variety of comets, where the red stars denoted the values for C/2013 US₁₀ (Catalina). At 1.3 au, the bolometric albedo of comet C/2013 US₁₀ (Catalina) is likely measuring the reflectance properties of the refractory particles because ice grains have very short lifetimes at this heliocentric distance (Beer et al. 2006; Protopapa et al. 2018). The reflectance of individual refractory particles from the coma of comet 67P/Churyumov–Gerasimenko as measured by Rosetta COSIMA/Cosicope is from 3% to 22% at 650 nm (Langevin et al. 2017, 2020), which spans the range of bolometric albedos measured for comet comae.

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