The Coma Dust of Comet C2013 US10 (Catalina) A Window into Carbon in the Solar System

Comet C/2013 US10 (Catalina) was an dynamically new Oort cloud comet whose apparition presented a favorable geometry for observations near close Earth approach (~0.93au) at heliocentric distances ~2au when insolation and sublimation of volatiles drive maximum activity. Here we present mid-infrared spectrophotometric observations at two temporal epochs from NASA's Stratospheric Observatory for Infrared Astronomy and the NASA Infrared Telescope Facility. The grain composition is dominated by dark dust grains (modeled as amorphous carbon) with a silicate-to-carbon ratio ~0.9, little of crystalline stoichiometry (no distinct 11.2um feature attributed to Mg-rich crystalline olivine), the submicron grain size distribution peaking at ~0.6um. The 10um silicate feature was weak, ~12.8% above the local continuum, and the bolometric grain albedo was low (~14%). Comet Catalina is a carbon-rich object. This material, which is well-represented by the optical constants of amorphous carbon is similar to the material that darkens and reddens the surface of comet 67P/Churyumov-Gerasimenko. We argue this material is endemic the nuclei of comets, synthesizing results from the study of Stardust samples, interplanetary dust particle investigations and micrometeoritic analyses. The atomic carbon-to-silicate ratio of comet Catalina and other comets joins a growing body of evidence suggesting the existence of a C/Si gradient in the primitive solar system.


INTRODUCTION
Traces of primordial materials, and their leastprocessed products, are to be found in the outermost regions of the solar system in the form of ices of volatile materials (H 2 O, CO, CO 2 , and other more rare species), and more refractory dust grains. This is the realm of comets. Nevertheless, it is certain that this outer re-derstand the environment of the early solar system from pebbles to planetesimals to larger bodies (see Poulet et al. 2016, and references therein). These grains likely are minimally processed over the age of the solar system after incorporation into the nuclei of comets. Information on the nature of these grains comes from a variety of sources, including remote sensing through telescopic observations (ground-based, airborne, and spacebased), rendezvous/encounter experiments (i.e., Giotto, Rosetta/Philae, Deep Impact ), collection of interplanetary dust particles (IDPs) in the Earth's stratosphere, and a sample return mission (Stardust ). All these activities have made important contributions to our understanding of these grains. The most detailed information we have comes from the latter two types of studies, where laboratory analysis is possible. Yet, the IDPs from comets 81P/Wild 2 and 26P/Grigg-Skjellerup are vastly different. The former contains material processed at high temperature (Zolensky et al. 2006) while the latter is very "primitive" (Busemann et al. 2009). For these reasons, it is necessary to determine as best we can the properties of dust grains from a large sample of comets using remote techniques (Cochran et al. 2015). These include observations of both the thermal (spectrophotometric) and scattered light (spectrophotometric and polarimetric). The former technique provides our most direct link to the composition (mineral content) of the grains.
With these data, combined with modeling features in the infrared spectral energy distribution (SEDs) arising from mineral species emitting in the comet coma (dust grains) and dynamical models of solar system formation and planetary migration we can address fundamental questions of solar system formation. These question include: What was the method of transport of these materials, and has information on the scale of those transport processes been stored in primitive solar system objects? Do comets, the remnants of that epoch, still contain clues as to what happened?
In this paper we report our post-perihelion (TP = 2015 Nov 15.721 UT) spectrophotometric observations of comet C/2013 US 10 (Catalina), a dynamically new (see Oort 1950, for a definition based on orbital elements) Oort Cloud comet with 1/a org = 5.3 × 10 −6 AU −1 (Williams 2019) and discuss important new interpretations that the coma grain composition of comets from remote sensing observations can bring to understanding disk processing in the primitive solar system.

OBSERVATIONS
Infrared and optical observations of C/2013 US 10 (Catalina) were conducted at two contemporaneous epochs near close Earth approach (∆ ≃ 0.93 au) with the NASA Infrared Telescope Facility (IRTF) and NASA's Stratospheric Observatory for Infrared Astronomy (SOFIA) facility. Table 1 summarizes the all observational data sets discussed herein and physical parameters of the comet.

Ground-based Spectrophotometry
Medium resolution (R ≡ λ/∆λ ≃ 50 − 120) infrared spectroscopy of comet C/2013 US 10 (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 to 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 4. ′′ 0 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. Non-sidereal 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 were 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 US 10 (Catalina) obtained during the course of the 2016 Jan 10.61 UT observational campaign showed no variance in the flux level of the spectral energy distribution (i.e., no outbursts, or jet induced changes in coma brightness were witnessed), or spectral shape. Hence, all spectra where averaged together (with the proper propagation of all statistical point-to-point uncertainties) to produce the final spectrum presented in Fig. 1.
b Vector direction measured CCW (eastward) from celestial north on the plane of the sky.
(5 sec 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 non-sidereal 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 stan-dard IRAF 1 routines. The data was 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 ∼ 2. ′′ 2 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 . UT with the NASA IRTF telescope. This spectrum was derived by averaging all photometrically calibrated individual comet spectra obtained over a 1.33 hr interval. Regions of poor telluric transmission ( < ∼ 30%) where from atmospheric CO2 and H2O vapor have strong absorption bands result in gaps in the data where BASS spectral data points are clipped out. The red curve is the best-fit blackbody, TBB = 265.3±2.6 K fit to the local 10 µm continuum as described in §3.3. The excess over the blackbody curve at short wavelengths is due to scattered, reddened sunlight contributing substantially to the flux.

Airborne SOFIA Observations
Mid-infrared (mid-IR) spectrophotometric observations of comet C/2013 US 10 (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-toback 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 US 10 (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 The red curve is the best-fit blackbody that yields a TBB = 239.5 ± 0.5 K fit using all wavelengths > ∼ 6.0 µm as described in §3.3. configured using a long-slit (4. ′′ 7 × 191 ′′ ) which yields a spectral resolution R = λ/∆λ ∼ 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 2-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 was 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 FOR-CAST Data Products, Rev. B 2 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 (SNR) ratio of the comet spectra, data in each grism spectra segment were binned using a weighted 3-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 spectral energy distribution (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 17. ′′ 54 ± 0. ′′ 74, derived data product keyword PS-FRAD). 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 epoch of the SOFIA observations.
The resultant composite FORCAST spectra of comet C/2013 US 10 (Catalina) is presented in Fig. 2. Figure 3 presents panels for each individual grating segment, spanning the respective spectral grasp, to illustrate spectral details of the observed SEDs.
Optical images in the SDSS i ′ filter also were obtained on each flight series prior to the start of the mid-infrared observing sequence using the Focal Plane Imager (FPI+; Pfüller et al. 2016). The FPI+ field-of-view is 8.7 square arcminutes, with a plate scale of 0. ′′ 51 per pixel, and a FWHM of ≃3. ′′ 75. The comet was tracked using the JPL Horizons non-sidereal 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 .
3. DISCUSSION 3.1. SOFIA Imagery and Photometry Images of comet C/2013 US 10 (Catalina) obtained during the 2016 February 09 UT flight are presented in Fig. 4. Examination of the azimuthally averaged radial profiles of the comet in each filter reveals comet C/2103 US 10 (Catalina) exhibited extended emission beyond the point-spread function (PSF) of point sources observed with FORCAST under optimal telescope jitter performance in each filter. 3 Centroiding on the photocenter of the comet nucleus, photometry in an effective circular aperture of radius 13 pixels, corresponding to 9. ′′ 984, with a background aperture annulus of inner radius 30 pixels (23. ′′ 58) and outer radius of 60 pixels (47. ′′ 16) was performed on the Level 3 pipeline co-3 http://www.sofia.usra.edu/Science/ObserversHandbook/FORCAST.html added (*.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 full width half maximum (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 co-added 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.
The resultant SOFIA photometry is presented in Table 2. For the SOFIA epoch of comet C/2013 US 10 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.

Dust Thermal Models of Infrared Spectra
Infrared spectroscopic observations are fitted with thermal models using standard spectral fitting techniques that minimize χ 2 . 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 as well as semi-refractory organics with limited coma lifetimes (Wooden et al. 2017;Dello Russo et al. 2016). Semi-refractory 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 semi-refractory organics are not (yet) observed in thermal IR spectroscopy but rather indirectly by the observed delayed release of molecules such as CO and/or H 2 CO 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 also are dependent upon organics (Hadamcik et al. 2020). Wooden et al. (2017) and Dello Russo et al. (2016) provide a detailed discussion of semi-refractory organics in cometary comae.
Thermal emission spectroscopy when combined with thermal modeling probes the particle composition from the optical active material in comet coma. A number of approaches have been employed to model the dust thermal emission and study the composition of Figure 3. Comet C/2013 US10 (Catalina) SOFIA FORCAST spectra by individual grating to highlight spectral details and the signal-to-noise quality of the data. The panels are (a) G063, (b) G111, (c) G227, and (d) G329. The original spectra have been binned with a 3-point width (in wavelength-space) median boxcar, with the errors propagated by use of a weighted mean. Gaps in the contiguous spectral coverage arise from regions where the atmospheric transmission was modeled to be < ∼ 70%.
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-radiidependent 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. , 2011(Harker et al. , 2017, or may employ composition "mixtures" calculated using Effective Medium Theory (see Bockelée-Morvan et al. 2017a,b). At a given heliocentric (r h [au]) and geocentric (∆[au]) distance, the particle (dust) composition of the 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 non-negative 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 grainsize 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. 2018Harker et al. , 2011, and references therein). The particle compositions of dust in the coma of comet C/2013 US 10 (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   3.2.1. Optical properties and IDP analogues A particle's composition, structure (crystalline or amorphous), porosity, and effective radius (a) determine its absorption and emission efficiency, Q abs (a grain's absorption efficiency and emission efficiency are equivalent at any given wavelength by Kirchhoff's Law). For an individual particle of effective radius a, F λ (a) ∝ π × a 2 × Q abs (a) × B λ (T dust [a, composition]) where B λ is the Planck blackbody function, evaluated as a function of grain temperature, T (K), particle size, and particle composition .
The optical properties of the materials used in the radiative equilibrium calculations for particle temperatures are derived from either laboratory-generated materials or mineral samples from nature. Materials chosen for our thermal models have available optical constants and are found in or are analogous to materials in cometary samples. Crystalline silicates in Interplanetary dust particles (IDPs, Wooden et al. 2000), Stardust, UltraCarbonaceous Antarctic MicroMeteorites (UCAMMs; Duprat et al. 2010) are of olivine and pyroxene compositions with a range of Mg:Fe contents with typically 1.0 ≤ y ≤ 0.5 and 1.0≤ x ≤ 0.5 (Wooden et al. 2017;Frank et al. 2014;Joswiak et al. 2014;Dobricȃ et al. 2012;Brunetto et al. 2011). Only f Peak grain size (radius) of the Hanner GSD. † Ratio represents the bulk mass properties of the materials in the models.
Mg-rich crystalline olivine resonances have thus far been detected definitively in multiple comets using both the mid-and far-IR resonances. Laboratory studies of crystalline olivine by Koike et al. (2013) show that with decreasing Mg-content (i.e., with y < 0.8), the 11.2 µm peak shifts towards 11.4 µm and the far-IR resonances dramatically change to different central wavelengths with different relative intensities. However, these more fayalitic crystalline olivine resonances have not been detected in comet comae. Amorphous silicates and amorphous carbon in thermal models are considered candidate ISM or dense cloud materials (Wooden et al. 2017). The outer cold disk where comet nuclei accreted is a likely reservoir of inherited interstellar grains (Sterken et al. 2019). However, modeled characteristics of interstellar grains and measured cometary organics differ. Matrajt et al. (2005)   UT at the NASA IRTF telescope. Gaps in the spectra are due to regions of poor telluric transmission within the continuous wavelength range covered by the instrument. The decomposition technique is used to determine the dust composition responsible for the observed coma emission at midinfrared wavelengths. The solid red line is the best-fit model of the emission from the aggregate dust components, wherein the orange line represent the contribution from amorphous carbon, the dark blue solid line is the emission from amorphous pyroxene, the solid cyan turquoise line depicts the amorphous olivine emission, and the green solid line depicts the crystalline olivine ("hot" forsterite). The observed spectral data are the filled black circles with respective uncertainties. The coma dust composition is dominated by amorphous carbon (dark material) and silicate grains with peak grain sizes (radii) of 0.5 µm (Hanner grain size distribution). Some crystalline material is present.
persistently suggest that the origin of the organic fraction of cometary IDPs is a different environment than the diffuse interstellar medium (DISM) because (a) the 3.4 µm band of organics in anhydrous IDPs is significantly narrower than in the DISM (e.g., towards the Galactic Center that is a mixture of diffuse and dense cloud material) and (b) the aliphatic chains in IDPs are longer (less ramified) than in the DISM, based on the −CH 2 /−CH 3 ratio in IDPs. The Heterogeneous dust Evolution Model for Interstellar Solids (THEMIS) model (Jones et al. 2017;Jones 2016) predicts the formation and evolution of interstellar dust, from the harsher UV conditions of the ISM, through the DISM, the translucent clouds at the interface of and into dense clouds. In these regimes dust particles eventually either work their way out to less dense phases of the ISM and thus presumably  UT) circles superposed on the data points (black) are the photometry points taken from the FORCAST imagery in a circular aperture equivalent to the grism extraction area (the average for all grisms was 17. ′′ 54 ± 0. ′′ 74, derived data product keyword PSFRAD) and are used to scale the spectral segments to the photometry. The coma dust composition is dominated by amorphous carbon (dark material) and silicate grains with peak grain sizes (radii) of 0.7 µm (Hanner grain size distribution). Some crystalline material is present.
are cycled into and out of phases, or the dust particles in the dense clouds make their way into protoplanetary disks such as our own. In translucent clouds THEMIS carbon-chemistry facilitates the growth of H-rich and aliphatic-rich matter, denoted a-C(:H), which accretes and then coagulates to tens of nm-size particles through a complex set of chemical reactions. The carbon-chemistry backbones are carbon belt-like molecules with aromatic bonds (n-cyclacenes) and an important process is the epoxylation of the surface materials. The carbonaceous particles, upon return to the harsh UV interstellar radiation field evolve "towards an end-of-the-road H-poor and aromatic-rich a-C material" (Jones & Ysard 2019). Carbonaceous matter in cometary samples appear significantly less dominated by aromatic moieties than implied by THEMIS models. Stardust samples only reveal a small concentration of small PAHs (Clemett et al. 2010). Carbon X-ray Absorption Near Edge Spectroscopy (C-XANES) spectra of Stardust and IDP organics show saturated aliphatic carbon bonds are more recurrent than aromatic C=C bonds as well as amorphous carbon being the only carbon form common between these samples and Bells, Tagish Lake, Orgueil and Murchison meteorites (Wirick et al. 2009;De Gregorio et al. 2017). Laboratory absorption spectra do not quantify amorphous carbon as it has no resonances, although its presence can be discerned through Carbon X-ray Absorption Near Edge Spectroscopy (C-XANES; Keller et al. 2004;Messenger et al. 2008). Amorphous carbon is found in many IDPs Busemann et al. 2009;Wirick et al. 2009;Brunetto et al. 2011) but amorphous carbon is not discussed for all IDPs Ishii et al. 2018) nor for all extraterrestrial particulate samples from primitive small bodies, specifically UCAMMs (Dartois et al. 2018;Mathurin et al. 2019). Despite a diversity of bonding structures in cometary organics (Bardyn et al. 2017) as well as organic matter in asteroids, there is a severe paucity of optical constants (de Bergh et al. 2008). Typically, optical constants of relatively transparent tholens are combined with optical constants of the highly absorbing amorphous carbon to darken the models for surfaces of outer ice-rich bodies (de Bergh et al. 2008). Hence, amorphous carbon, which is devoid of aromatic bond IR resonances, is the best choice for the highly absorbing carbonaceous matter in models of dark surfaces of ice-rich bodies as well as for cometary coma particles.
Amorphous silicates in thermal models are analogous to Glass with Embedded Metal and Sulfides (GEMS) in IDPs (see Floss et al. 2006;Brunetto et al. 2011;Bradley 2013;Ishii et al. 2018;Stroud et al. 2019). The ISM silicate absorption feature has spectral similarities to GEMS (Bradley 2013;Stroud et al. 2019) and radiation damage can explain the non-stiochiometry of GEMS (Jäger et al. 2016). An alternative hightemperature formation scenario for GEMS is proposed for the protoplanetary disk (Keller & Messenger 2011) but is challenged by discovery of GEMS with interior organic matter that could not have survived temperatures above 450 K (Ishii et al. 2018). Amorphous silicates are a ubiquitous component of IR spectra of cometary comae and their radiation equilibrium temperatures require compositions of Mg:Fe≈50:50 .

The Hanner Grain Size Distribution (HGSD)
Our modeling invokes the Hanner grain-size distribution n(a) = (1 − a 0 /a) M (a 0 /a) N , where a is the particle radius, where a 0 = 0.1 µm is the minimum grain radius, and M and N are independent parameters (Hanner 1983;Hanner et al. 1994). The HGSD is a modified power law that rolls over at particle radii smaller than the peak radius a p = (M + N )/N , which is constrained by the thermal model analyses.

Moderately porous particles
The optical properties of porous particles composed of amorphous materials may be calculated by incorporating "vacuum" as one of the material components (Bohren & Huffman 1983). Porous grains are modeled with an increasing vacuous content as expected for hierarchical aggregation, using the porosity prescription or fractional filled volume given by f = 1−(a/0.1 µm) D−3 , where a is the effective particle radius, with the fractal dimension parameter D ranging from D = 3 (solid) to D = 2.5 (fractal porous but still spherical enough to be within the applicability of Mie theory computations; Harker et al. 2018Harker et al. , 2011, and references therein). Particle porosity affects the observed spectra of comets because the porous grains are cooler than solid grains of equivalent radius as their vacuous inclusions make them less absorbent at UV-visible wavelengths . The porosity prescription parameter D is coupled with the grain size distribution slope parameter N , and the two parameters are simultaneously constrained when fitting IR SEDs. Increasing porosity (lowering D) decreases particle temperatures, which can be compensated for by increasing the relative numbers of smaller to larger grains by steepening the slope (increasing N ) of the HGSD as illustrated in Fig. 2 of Wooden (2002).
An extremely porous particle that is an aggregate of submicron compact monomers can have the same temperature as its monomers (P(a) max >80%; Xing & Hanner 1997) or (P(a) max ≥99% with a ≥5 µm; Kolokolova et al. 2007). However, IR spectra of comets are not well-fit by such extremely porous particles that are uniformly as hot as their submicron-radii monomers, regardless of particle size. Thermal models for observed IR spectra of comets need particle size distributions of moderately porous or solid particles. For a comet near 1.5 AU, a HGSD has submicron-to micron-radii particles (a peak ≤ 1 µm) that produce the warmer thermal emission under the 10 µm silicate feature and at shorter near-IR wavelengths, as well as larger cooler particles producing the decline in the thermal emission at longer (far-IR) wavelengths. Compared to a size distribution of compact solid particles (D = 3), a size distribution of moderately porous particles (P(a) ∼66 to 86%, D = 2.727 to D = 2.5, a eff = 5 µm) are cooler and produce enhanced emission at longer wavelengths while still producing a silicate emission feature with the observed contrast compared to the local "pseudo-continuum" (see § 3.4). Hence, the thermal models constrain the porosity of the amorphous materials (amorphous silicates and amorphous carbon), and the slope and the peak radius (a peak ) of the grain size distribution of (see Harker et al. 2018Harker et al. , 2011.

CDE models of solid trirefringent silicate crystals
Silicate crystalline particles are not well modeled as spheres by Mie Theory because of their anisotropic optical constants and irregular shapes (Koike et al. 2010). Crystals are not modeled as porous particles or as mixed-material particles using Effective Medium Theory because modeled resonant features do not match laboratory spectra of the same materials. Discrete solid crystals are better computed using the Continuous Dis-tribution of Ellipsoids (CDE) approach (Fabian et al. 2001) or the discrete dipole approximation (DDA; Lindsay et al. 2013). Crystals of larger sizes than ∼1 µm do not replicate the observed SEDs of comets (Min et al. 2005). CDE with c-axis elongated shapes reasonably reproduces laboratory spectra of crystalline forsterite powders (Fabian et al. 2001) and serves as a starting point for our thermal models. Discrete solid crystals with sizes from 0.1 to 1 µm are included in our admixture of coma dust materials. From our thermal models, we quote the relative mass fractions for the ≤1 µm portion of the HGSD in Table 3.

Comet Crystalline Silicates and Disk Transport
The presence of crystalline silicate materials in cometary spectra and in cometary samples indicates transferal of materials that formed in the inner protoplanetary disk to the outer disk (Westphal et al. 2017;Brownlee et al. 2006;Zolensky et al. 2006) where volatile ices (H 2 O, CO, CO 2 ) were extant along with dust particles to become incorporated into cometary nuclei (Rubin et al. 2020). Crystalline silicates are relatively rare along lines-of-sight through the interstellar medium ( < ∼ 5%, Kemper et al. 2004) and towards embedded young stellar objects or compact HII regions (1 to 2%, with a few sources at >3%, Do-Duy et al. 2020). A significant crystalline silicate component in cometary dust has been clearly demonstrated by laboratory examinations of Stardust (Frank et al. 2014) and IDPs Busemann et al. 2009;Zolensky & Barrett 1992). Crystalline silicate mass fractions (defined as f crys ≡ m cryst /[m amorphous + m cryst ] where m cryst is the mass fraction of crystals) derived from thermal models of cometary IR SEDs typically are ∼20% to 55% Harker et al. 2018Harker et al. , 2011Harker et al. , 2007Wooden et al. 2004, and Appendix I). Detailed laboratory studies of cometary forsterite and enstatite crystals show a small fraction have mineralogical signatures of gas-phase condensation such as low iron manganese enriched (LIME) compositions Frank et al. 2014), 16 O-enrichments commensurate with early disk processes (Defouilloy et al. 2018(Defouilloy et al. , 2016(Defouilloy et al. , 2017, as well as condensation morphologies such as enstatite ribbons in anhydrous IDPs (Bradley et al. 1999).
Moreover, Stardust samples and some cluster IDPs contain olivine crystals with a wider range of Fecontents (10% < ∼ Fe < ∼ 60%) than the low Fe-contents of ≃10% to 20% deduced from the wavelengths of the resonances of olivine crystals in cometary spectra (Wooden et al. 2017;Crovisier et al. 1997Crovisier et al. , 1996. It is a puzzle as to why the spectral signatures of Febearing crystalline silicates are not spectrally detected in comets (Wooden et al. 2017).The Fe-bearing olivine crystals are analogous by their minor element compositions to olivine (Mg ≤ 80%) crystals in type-II chondrules and are called micro-chondrules or chondrule frag-ments Frank et al. 2014).
In Stardust samples, one 15 µm-size type-II chondrule called 'Iris' has an age-date of ≥ 3 million-years (with respect to CAI formation) and is well-modeled as an isolated igneous system (Gainsforth et al. 2015).
Stardust samples pose a number of challenging questions for disk models about the formation of the nucleus of comet 81P/Wild 2. How did particles radially migrate as late as a few million years in disk evolution to the regime of volatile ices of H 2 O, CO and CO 2 ? How did cometary dust minerals that condensed early in disk evolution persist in the disk long enough to be incorporated into this particular cometary nucleus, that is, persist and not be lost via the inward movement of particles? As of yet, satisfactory answers to either of these questions do not exist.
Silicate crystals, specifically referring to forsterite and enstatite that are the abundant Mg-rich silicate crystalline species in comets and/or cometary samples (Wooden et al. 2017), condensed at temperatures near 1800 K or or possibly were annealed materials at temperatures near 1100 to 1200 K in shocks (Harker & Desch 2002) under low oxygen fugacity conditions ). Radial transport may have occurred through a combination of protoplanetary disk processes including advection, diffusion, turbulence and aerodynamic sorting, meridional flows, disk winds, and/or planetary migration (Vokrouhlický et al. 2019;Ciesla 2011;Hughes & Armitage 2010;Wehrstedt & Gail 2008;Gail 2004). Disk models with meridional flows (see Gail 2004) have been successful in predicting ∼20% silicate crystalline mass fractions at disk radii of more than tens of AU in <1 million-years.
Radial transport by advection can work through disk wind angular momentum transport (Bai 2016) but can also be produced by turbulent viscosity in the bulk of the disk. Radial transport by diffusion requires turbulence. It is generally thought that magento-hydrodynamical (MHD) turbulence occurs only in rarified upper layers of the disk atmosphere, if at all (Bai 2016). However even without MHD effects, there are two recently-discussed hydrodynamical mechanisms for producing turbulence: convective over-stability (CO) and vertical shear instability (VSI) that are either individually or collectively operative in various locations in the disk (for example Pfeil & Klahr 2019). Meridional 2D flows are another robust feature of disk models when turbulence mechanisms are considered operative (Lyra & Umurhan 2019;Stoll et al. 2017). Yet, even the qualitative nature of this flow is debated. Meridional flows for 2D and alphadisk models were outwards along the mid-plane and inwards above one scale height (see Gail 2004). Recent 3D models of meridional flow show that the outward flow is above one scale height so particles that are lofted by turbulence to above one scale height above the mid-plane can move outwards (Pfeil & Klahr 2020;Stoll et al. 2017). To date, meridional flows only are inferred from ALMA in 12 CO observations of the >300 au outer disk regions of the ∼5 million-year old more massive Herbig Ae/Be system HD 163296 (Teague et al. 2019;Powell et al. 2019). Large scale gas motions are not yet observed for analogs of our protoplanetary disk but cometary crystalline mass fractions suggest inner disk materials moved over large distances.
Models without meridional flows also show outward movement of small particles, merely following the outward advective motion of the gas, at certain radii and times. Estrada et al. (2016) show disk models (see their Fig. 15) with a range of dust particle masses in which the maximum disk radius reached by particles of a specific particle mass (i.e., size) increases with time, i.e., some particles do move outward and the smaller particles are more successful in moving outwards. Porous particles have larger aerodynamic cross sections compared to solid particles of the same mass so porous particles are favored in outward movement compared to solid particles . Ciesla & Sandford (2012) simulate the migration of particles by randomized turbulent 'kicks', and thereby nicely illustrate the large-distance motions of some particles.
As a complement to transport within the disk, centrifugally driven disk winds may deposit particles with sizes ≥ 1 µm to the outer disk at early times, which "may be relevant to the origin of the 20 µm CAIlike particle discovered in one of the samples returned from comet 81P/Wild 2" (Giacalone et al. 2019). Abrahám et al. (2019) observed the brightest outburst to date from EX Lup using VLTI MIDI interferometry and VLT VISIR IR spectroscopy. Within five years practically all crystalline forsterite that had become enhanced in the inner disk disappeared from the surface of the inner disk. Over that time, the spectral resonances from olivine crystals shifted emphasis from the mid-to far-IR wavelengths indicating that the crystals experienced outward movement.
Disk models are challenged to effectively transport as well as maintain solids in the outer protoplanetary disk against the inward drift of particles, especially as particles grow to 'pebble' size and decouple from the gas. Models that treat particle coagulation as well as particle collisional destruction which maintain a population of fine-grained particles (i.e., smaller particles with lower Stokes numbers [St η ]) then outward movement of small particles with time occurs (see Estrada et al. 2016). Many studies have investigated how material that is injected into the disk spreads outwards and inwards with time (for example, Sengupta 2019). When turbulence is a driving mechanism for radial transport, then aerodynamics affects particle movements, and one can expect signatures of size sorting by St η ∝ρ s a, where a is the particle radius andρ s is the average particle density (Jacquet 2014;Cuzzi et al. 2001). Stardust samples demonstrate that aerodynamic sorting in aggregate formation occurred for particles of olivine compared to FeS, which are denser than olivine (Wozniakiewicz et al. 2013(Wozniakiewicz et al. , 2012. The Rosetta mission's imaging studies showed that comet 67P/Churyumov-Gerasimenko's particles are hierarchical aggregates of hundreds of microns to mm-size with components that are submicron to tens of micron in size (Langevin et al. 2020;Güttler et al. 2019;Hornung et al. 2016) Stardust samples and Rosetta particle studies are commensurate with the idea that aggregate particle components of submicron to tens of micron of size may be favored over larger solid particles in their outward movement to the disk regimes of comet-nuclei formation.

Revised specific density for Amorphous Carbon
Our thermal model adopts an amorphous carbon (Acar) specific density of ρ s (Acar) = 1.5 g cm −3 , from a quoted value of ρ s (Acar) = 1.47 g cm −3 (Williams & Arakawa 1972) measured for the same amorphous carbon material from which our optical constants were derived (Edoh 1983;Hanner et al. 1994). 5 This specific density of ρ s (Acar) used in these analyses of comet C/2013 US 10 (Catalina) herein represents a significant change from our prior thermal models and publications that used an assumed bulk density of carbon of 2.5 g cm −3 (Lisse et al. 1998;, which actually was a specific density slightly higher than that of graphite of 2.2 g cm −3 (Robertson 2002). The relative mass fractions of carbonaceous matter and siliceous matter are important and allow us to take a detailed look at the carbonaceous contribution of comets to the hypothesized gradient of carbon in the solar system ( §3.9) and as discussed by other authors (Hendrix et al. 2016;Gail & Trieloff 2017;Dartois et al. 2018). 6 For completeness, in our thermal models the specific density of amorphous silicates is ρ s (Asil) = 3.3 g cm −3 as discussed by Harker et al. (2002, and references therein).

Coma Dust Composition from Thermal Models
Comet C/2013 US 10 (Catalina) is a dynamically new (DN) Oort cloud with eccentricity of ≃ 1.0003. Compositionally, the dust in the coma of comet C/2013 US 10 (Catalina) is carbon-rich and this comet is among a subset of observed comets that are similarly carbonrich, 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 Fig. 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 US 10 (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 silicateto-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 US 10 (Catalina) is characterized by a moderate particle porosity (D = 2.727). Coma grains extend to submicron size particles, the HGSD (defined in § 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 US 10 (Catalina) share similar characteristics with those found recently for some other long period Oort cloud comets, such as C/2007 N3 (Lulin) which is also DN .
The HGSD slope of comet C/2013 US 10 (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 Examination of the SEDs of comet C/2013 US 10 (Catalina) obtained at two different epoch and the thermal model derived parameters (Table 3) enable us to deconstruct and decipher aspects of the inner coma dust environment (Figs. 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 (Fig. 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 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 US 10 (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 (Wooden 2008;Hanner et al. 1994). 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 US 10 (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-tocarbon ratio is 1.116 +0.072 −0.074 and 0.743 +0.264 −0.220 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 the sharp peak at 11.1 to 11.2 µm (Koike et al. 2010, and references therein) is relatively transparent outside of its resonances. At 1.3 au, crystalline silicate mass fraction (f cryst ) is 0.441 +0.033 −0.035 in the coma of comet C/2013 US 10 (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 §3.2.5).

Silicate feature shape and strength
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 partciles (D = 2.7272) for comet C/2013 US 10 (Catalina). Figure 7 shows the silicate feature shape for comet C/2013 US 10 (Catalina) from the BASS observations. The FORCAST mid-IR spectral data show a similar contrast silicate feature but with lower SNR as the BASS data, so these data are not included in the figure for clarity.
The silicate strength parameter historically enables one to inter-compare 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 fea-ture strength, defined as F 10 /F c , where F 10 is the integrated silicate feature flux over a bandwidth of 10 to 11 µm and F c is that of the local blackbody 'pseudocontinuum' at 10.5 µm (Sitko et al. 2004), is a metric that describes the contrast of silicate emission feature. We find the 10 µm silicate feature to be weak in comet C/2013 US 10 (Catalina), approximately 12.8% ± 0.1% above the local 'pseudo-continuum.' The low silicate feature strength in comet C/2013 US 10 (Catalina) is similar to some other comets (Sitko et al. 2004(Sitko et al. , 2013Woodward et al. 2015Woodward et al. , 2011. 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 to 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 the particles smaller than the wavelength, often is historically referred to as "superheat" S (see Gehrz & Ney 1992). The silicate strength parameter is somewhat correlated to 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 to 0.15) and the dust color (% per 100 nm) (Bockelée-Morvan et al. 2019). Comet C/2013 US 10 (Catalina) has a smaller value for S than comet 67P/Churyumov-Gerasimenko.
C/2013 US 10 (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 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-dusttemperatures shows that the comets with comae particles whose HGSD has a p ≤ 1 µm and that display weak silicate features are carbon-rich.

The "Hot crystal model" and SOFIA in the far-IR
The SOFIA spectrum has enhanced emission that rises near 36 µm but the observations do not extend to longer wavelengths to show a decline in flux density. Laboratory absorption spectra of powders of pure-Mg forsterite show that the absorbance is about equal at 33 µm and 11.1 µm (Koike et al. 2013), while the 19.5 and 23.5 µm features also having significant absorbance. The 33 µm emission from pure-Mg forsterite (Fo100) is not detected in the far-IR. The slope of the HGSD is well constrained by the SOFA data (given the low χ 2 ν ). The SOFIA data provide important constraints on the crystalline resonances in the far-IR and on the slope of the HGSD ( §3.2.2). Our thermal models employ a "hot crystal model" for the temperatures for forsterite and enstatite, where their radiative equilibrium temperatures of crystals are increased by a factor of 1.9±0.1 based on fitting the ISO SWS spectrum of comet C/1995 O1 (Hale-Bopp) . We speculate that hotter crystal temperatures may arise from crystals being in contact with other minerals that are more absorptive or from Fe metal inclusions such as "dusty olivines" (Kracher et al. 1984), or "relict" grains (Ruzicka et al. 2017).

Other mineral species not detected
Within our SNR 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 to 8 µm wavelength region (Roush et al. 1991;Crovisier & Bockelée-Morvan 2008) and neither of these compositions were detected in comet C/2013 US 10 (Catalina).

The search for aliphatic and aromatic carbon
The BASS spectrum spans the 3.0 to 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 -CH 2 , -CH 3 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 nucleus surface of 67P/Churyumov-Gerasimenko is presented by Raponi et al. (2020) and Rinaldi et al. (2017) also argue for the presence for this feature in coma observations. The BASS spectrum spans the 3.0 to 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 -CH 2 , -CH 3 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 nucleus surface of 67P/Churyumov-Gerasimenko is presented by Raponi et al. (2020) and Rinaldi et al. (2017) 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 (−CH 2 , −CH 3 ), 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 US 10 (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 C 2 H 6 and CH 3 OH in the 3.28 to 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 US 10 (Catalina). Thus, no spectral features were seen to indicate the presence of aromatic hydrocarbons (such as HACs, PAHs, a-C(:H) nano-particles) or aliphatic carbons in the coma of C/2013 US 10 (Catalina).
Comet C/2013 US 10 (Catalina) has one of the few reported 5 to 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 hydrogenation or the number of peripheral hydrogen bonds compared to structural C=C bonds ).The UCAMMS are massdominated by organics, richer in N and poorer in O than 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 ≤ 3 σ 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 SNR 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 to 8 µm region.
The lack of resonances from organics in the 5 to 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.

Carbon and Dark Particles
We find amorphous carbon dominates the composition of grain materials in comet C/2013 US 10 (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) ) and C/2001HT50 (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)  Our cometary comae 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 KBOs, respectively (Bergin et al. 2015;Dartois et al. 2018;Burkhardt et al. 2019, and references therein). We choose to compare 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 bond in UCAMMs) because in laboratory baseline-corrected absorption spectra the amorphous carbon component would not be counted because it does not have a resonance.

Endemic Carbonaceous Matter in Comets
A dark refractory carbonaceous material darkens and reddens the surface of the nucleus of 67P/Churyumov-Gerasimenko, the surface material also displays a 3.4 µm (Raponi et al. 2020) and a similar aliphatic feature is suggested to exist in the coma of 67P/Churyumov-Gerasimenko (Rinaldi et al. 2017). We posit that the optical properties of amorphous carbon are representing well the dark refractory carbonaceous dust component observed in cometary comae through IR spectroscopy. Likely this dark refractory carbonaceous material is endemic to the comet's surface. Cosmic rays of a few 10 keV only damage a thin veneer of hundreds of nm of thickness (Strazzulla et al. 2003;Moroz et al. 2004;Quirico et al. 2016). This damage effects the structure (amorphization) and the composition (destruction of C-H and O-H bonds by dehydrogenation) of the materials (Moroz et al. 2004;Lantz et al. 2015;Quirico et al. 2016). Typical particle radii on the nucleus surface of 67P/Churyumov-Gerasimenko is at least tens of microns based on the observed the red color of the surface at visible wavelengths (Jost et al. 2017), so cosmic rays do not damage the full particle volume. For example, IDPs studied by IR spectra indicate aliphatic bonds in particle interiors (Matrajt et al. 2005(Matrajt et al. , 2013Flynn et al. 2015) but a lack of organic bonds in their near-surfaces possibly due to damaging ultraviolet light and particle radiation in space . Lastly, if the redeposition timescales for particles lofted from the nucleus but not escaping its gravity are about the orbital period of comet 67P/Churyumov-Gerasimenko (Marschall et al. 2020) then the ion-irradiation timescales on the surface, which have been shown to amorphize carbon bonds or damage silicates, are too short by orders of magnitude Brunetto et al. 2014;Quirico et al. 2016).
However, the surface properties of the DN comet like C/2103 US 10 (Catalina) may differ from the Jupiterfamily comet like 67P/Churyumov-Gerasimenko. A photon penetration depth of 1 µm for cosmic-rays can induce chemical changes, such as development of an organic crust due to the conversion of low molecular weight hydrocarbons into a web of bound molecular species, from electronic ionization in dose time per 100eV per 16-amu (H 2 O) in the Local Interstellar Medium, which is a harsher environment than within the heliopause at ∼85 au (see discussion in Strazzulla et al. 2003). Comet C/2013 US 10 (Catalina) may have had a radiation damaged dust rime of up to a few cm depth, but DN comets can have their onset of activity at large heliocentric distances (Meech et al. 2009) where likely this material is shed when the comet's activity first turns on. Thus, the amorphous carbon is not from a radiation rime because of the insufficient volume of the nucleus that can be altered by radiation compared to the mass loss pre-perihelion. Coupled with the arguments about in-sufficient time scales for materials recently exposed on cometary surfaces from either erosion or re-deposition to be space weathered, we assert that the amorphous carbon that is in the observed comae of comet C/2013 US 10 (Catalina) is carbonaceous matter is endemic to the comet nucleus. Moreover, the fluence and time scales or temperatures that change carbon bonding structures typically are not reached in cometary comae. The material is refractory and stable. The dark refractory carbonaceous matter that is modeled with the optical constants of amorphous carbon (see § 3.2.1) is endemic to comets. By the ubiquitous detection of a warm particle component in all cometary IR spectra observed to date, the carbonaceous matter is endemic to comets in general.
If dark refractory carbonaceous matter is stable on the surface then this implies the matter will be stable in the coma, unless the temperatures are raised significantly. For example if the size distribution significantly changes to smaller sizes the latter would occur. Laboratory experiments demonstrate that amorphous carbon becomes graphitized at ∼3000 K (De ). Comae dust temperatures remain at < ∼ 400 K dust compositions and particle sizes near 1 µm-radii for comets near 1 au. The exception will be sun-grazers that come close or enter the solar corona. On the other hand, aliphatic carbon may survive temperatures as high as ≃ 823 K if associated with porous minerals (Wirick et al. 2009). In the outburst of 67P/Churyumov-Gerasimenko at 1.3 au, comae dust temperatures reached 550 to 600 K and were modeled by tiny 0.1 µm-radii amorphous carbon particles (Bockelée-Morvan et al. 2019, 2017bRinaldi et al. 2018). Thus, comet comae dust particles do not reach such high temperatures as ≃ 823 K to destroy aliphatic carbon when comets are near 1 au.
The contribution of amorphous carbon is variable between comets.
In some comets, the contribution of amorphous carbon is temporally variable: 103P/Hartley 2 (Harker et al. 2018), C/2001 Q4 (NEAT) (Wooden et al. 2004), and the after the kineticimpactor encounter in inner coma of 9P/Tempel 2 (Sugita et al. 2005;Harker et al. 2007). The variability of amorphous carbon between comets and the temporally variability for a few comets gives clues to the diversity of protoplanetary disk reservoirs out of which comet nuclei formed. The variability in silicate-to-amorphous carbon ratios for an individual comet also may be related to the size sales of variable-compositions of the nucleus (Belton et al. 2007), to jets (Wooden et al. 2004), or variations coupled to changes in solar insolation in different parts of comets orbits (seasonal effects; Combi et al. 2020). These variations asserted for the nucleus are tied to the hypothesis that the refractory dust particle compositions observed in the coma are endemic to the comet.

Amorphous carbon and other forms of carbon
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. 1993b,a).
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), (non-graphitized) aliphatic or aromatic macromolecular material ) 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 micronsized 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 are 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 , 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  and not strictly aromatic (containing aromatic bonds) like meteoritic IOM (Alexander et al. 2007), as well as highly variable in composition and structure.

Cometary comae elemental C/Si ratios
In the following discussion, we investigate the plausible implications of cometary comae 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 inferred elemental ratio C/Si for comet C/2013 US 10 (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 US 10 (Catalina) and a handful of other recently observed and modeled comets are consistent with the average C/Si = 5.5 +1.4 −1.2 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 is propensity of submicron crystalline silicates  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 comae 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: (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 are representing a significant fraction of the carbonaceous matter in the coma §3.9.1.

Counting Carbon Atoms
We are comparing the C/Si atomic ratio derived for cometary samples using different techniques. Mass spectroscopy directly measures the elemental C/Si ratio, which is the method for in situ measurements. However, non-destructive techniques that allow counting the carbon atoms in IDPs or Stardust samples depend on the method. X-ray SEM-EDX techniques (Thomas et al. 1993b) can count all the carbon atoms whereas IR absorption spectroscopy counts the carbon atoms involved in the observed resonances. Laboratory IR absorption spectroscopy measures the C/Si by converting the integrated band strengths into the number of atoms for aliphatic and/or aromatic bands compared to the 10 µm silicate band (Matrajt et al. 2005;Brunetto et al. 2014). Laboratory absorbance spectroscopy fits and subtracts a spline baseline to yield a linear baseline for the purpose of integrating the observed band strengths (see Matrajt et al. 2005). Amorphous carbon is not observed in absorbance in spectroscopy of IDPs because amorphous carbon lacks spectral resonances. To make a comparison between cometary C/Si derived from thermal models of amorphous carbon and C/Si derived from laboratory measurements and in situ measurements, we choose to employ the SEM-EDX measurements that are counting the carbon atoms but not discerning the carbon bonding structures.
Currently we cannot claim knowledge of aliphatic and aromatic content in comet comae dust populations of multiple comets via IR spectroscopy. If we cannot detect signatures of these bonding structures, we cannot definitely determine their contribution to the observed emission. However, we can use IDPs to indicate what the potential increase in C/Si might be if the aliphatic or aromatic bonds were spectroscopically detected.
We can examine what C/Si atomic ratios are derived from organic features in laboratory absorbance spectra of IDPs and compare to the C/Si derived for comets using thermal modeling of the warm particle component that is modeled with amorphous carbon. Many IDPs show the aliphatic 3.4 µm feature. The 3.4 µm feature is composed of the aliphatic CH 2 symmetric vibration (at ∼2850 cm −1 ), the CH 2 asymmetric vibration (at ∼ 2922 cm −1 ) and the weaker CH 3 asymmetric vibration (at ∼ 2958 cm −1 ) as discussed in Matrajt et al. (2005). In six IDPs, the 3.4 µm aliphatic carbon features yield 0.27 ≤ C/Si ≤ 1.4 with a mean C/Si = 0.55 ± 0.43 (see Table 4 of Matrajt et al. 2005). For three out of the six IDPs, acid dissolution of the silicates allowed the detection of the intrinsically weaker aromatic skeletal ring stretch C=C at 6.25 µm (1600 cm −1 ), which raises the atomic ratios for these three IDPs from C aliphatic /Si = {0.78, 0.11, 0.55} to C aliphatic+aromatic /Si = {19.4, 3.1, 5.1} (see Table 5 of Matrajt et al. 2005).
Most IDPs, however, do not possess an aromatic 3.28 µm feature from C-H peripheral bonds on C=C skeletal rings. Keller et al. (2004) suggest the lack of the 3.28 µm aromatic feature is due to "much of the carbonaceous matter is comprised very poorly graphitized carbon, possessing only short range order (<2 nm), or very large PAH molecules." The C=C bonds that are better tracers of the aromatics than the peripheral C-H bonds. As yet, no comet has been observed with organic features that are of comparable absorbance as the silicate features as observed in absorption spectra of three UCAMMs, where organic absorbances are as strong as for the silicate features (Dartois et al. 2018). As other authors suggest, we infer comets have less "outer disk processed organics" than UCAMMs. This conjecture is also supported by noting the ratio of nitrogen-to-carbon (N/C) in 67P/Churyumov-Gerasimenko is less than the N/C in UCAMMs (Bardyn et al. 2017;Dartois et al. 2018). If IR spectra of cometary comae were to detect the 3.4 µm feature at about the same contrast to the silicate feature as is in laboratory absorbance spectra of IDPs (Matrajt et al. 2005;Brunetto et al. 2014;Merouane et al. 2016), then we may infer that C/Si for our comets that we analyze might increase ∼20%.

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 §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 Audi et al. (Method#2, 2017), cognizant of the limitations to this approach (see Possolo et al. 2019;Barlow 2003) to enable standard error propagation techniques. The carbon to silicon atomic ratio is defined as: where α = (0.5 · Mg amu + 0.5 · Fe amu ) × 2 + Si amu + 4 · O amu Si amu β = (0.5 · Mg amu + 0.5 · Fe amu ) + Si amu + 3 · O amu Si amu 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 derived the Ci/Si atomic ratios for comet C/2013 US 10 (Catalina) and other comets observed with SOFIA (+FORCAST) as well as comet C/1995 O1 (Hale-Bopp) . 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 Fig. 8. Recent measurements of solar cosmic abundances creates 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(Dartois et al. , 2018. As measured or computed, cometary comae appear to lack the high C/Si ratios of UCAMMs. Comets by their C/Si appear to be sampling similar abundances of carbon in the optically active composition of comae 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 (Fig. 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 (Bergin et al. 2015;McCauley et al. 2013;Ciaravella et al. 2010). Gail & Trieloff (2017), Dartois et al. (2018Dartois et al. ( , 2013 and other authors suggest that there was a carbon gradient in the early solar system. The comet C/Si values supports this contention of gradient in the carbon with heliocentric distance of formation. 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 US 10 (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 inner disk, which is the long-standing "carbon deficit problem" (Bergin et al. 2015;Lee et al. 2010). Disk modelers are working to predict the carbon depletion gradient with complex chemical networks (Wei et al. 2019). Another model investigates 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 prevent 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 CO 2 . As discussed ( §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 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 (Andrews 2020;Misener et al. 2019). 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 the 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 non-carbonaceous and carbonaceous 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 non-carbonaceous 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 the 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. (2) Woodward et al. (2015).
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 present at redder wavelengths within the i ′ -band (Cochran et al. 2015;Fink et al. 1991;Swings 1956). 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 US 10 (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 7630Å to the i ′ -band long wavelength cut-off (Hyland et al. 2019). The azimuthally-averaged radial profiles of comet C/2013 US 10 (Catalina) derived from the MORIS and FPI+ imagery, presented in Fig. 9, shows little deviation from a 1/ρ profile (Gehrz & Ney 1992) at large cometo-centric distances consistent with a steady-state coma without significant CN contamination. Application of standard comet image enhancement techniques to these optical data (see , reveal no structures in the coma such as jets or spirals at this epoch. The dust production rate of comet C/2013 US 10 (Catalina) during the epoch of the BASS observations (2016 Jan 10.607 UT) was derived using the proxy quantity Af ρ (A' Hearn et al. 1984). When the cometary coma is in steady state, this aperture independent quantity can be parameterized as 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 7 as i ′ ⊙ = −27.002, ρ is the linear radius of the aperture at the comet's position (cm) and r h (AU) and ∆(cm) are the heliocentric and geocentric distances, respectively.
The Halley-Marcus (HM) (Marcus 2007a,b;Schleicher et al. 1998) phase angle correction 8 was used to normalize A(θ)f ρ to 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 Jan 11.633 UT and 2016 February 09.340 UT, respectively. Table 5 reports values of A(0 • )f ρ = (A(θ)f ρ/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 v dust ≈ 20 m s −1 (Rinaldi et al. 2018), and assume a steady outflow of material through a spherical bubble at some distance R(m) near the nucleus surface, the mass loss rate can be estimated aṡ whereṀ dust has units of g s −1 . If the nucleus of comet C/2013 US 10 (Catalina) is comparable in size typically inferred for many comets, 1.5 km, thenṀ dust ≈ 4 × 10 −3 M dust v dust /20(m s −1 ) . At 1.7 au when M dust = 4 × 10 8 g (Table 3) thenṀ dust ≈ 1.6 × 10 6 g s −1 . Fink & Rubin (2012) discuss how the A(θ)f ρ can be tied to the mass production rate, given the HGSD parameters, computing dust mass loss rate (in kg s −1 ) 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 a dq/da ∼ a −3.5 which  Thomas et al. (1993b), and the half-filled circle is average value of the Ci/S atomic ratio of comet 67P/Churyumov-Gerasimenko particles studied by Bardyn et al. (2017). The blue star denotes the values for the UltraCarbonaceous Antarctic MicroMeteorites (UCAMMs) while the limit to the interstellar medium C/Si atomic ratio, brown triangle, is from Dartois et al. (2018). Both C/2011 W3 and C/2003 K7 are sun grazing comets and the determination of the C/Si atomic ratio in these objects is derived from ultra-violet measurements when these comets were in the solar corona (see Bergin et al. 2015 (Table 5) one findsṀ dust ≈ 2.4 × 10 6 g s −1 . This is comparable 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 . Azimuthally averaged relative intensity per pixel as a function of linear radius (ρ) in km as measured in a SDSS i ′ -band filter from the optical photocenter (centroid) of comet C/2013 US10 (Catalina). The solid red line denotes a 1/ρ profile describing a steady-state coma (see Gehrz & Ney 1992). Top: the IRTF MORIS data obtained on 2016 Jan 11.63 UT when the phase angle was 47.80 degrees. Bottom: the SOFIA FPI+ data obtained on 2016 Feb 09.34 UT when the phase angle was 33.06 degrees. Note the change in scale between the two epochs. from the nucleus of comet C/2013 US 10 (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 an DN comet in the local interstellar medium 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 a perspective, cumulative erosion depths for comet 67P/Churyumov-Gerasimenko depended on the nucleus geography and solar insolation and from start of the Rosetta mission until the first equinox were 6 mm to 0.1 m and to the end of the mission were of order 0.3 m to 4 m (Combi et al. 2020).
The quantity ǫf ρ, (see Appendix A of Kelley et al. 2013), a parameter which is the thermal emission corollary of the scattered-light based light Af ρ was also computed using our FORCAST broadband photometry. ǫf ρ is defined as where ǫ is the effective dust emissivity, F ν is the flux density (Jy) of the comet within the aperture of radius ρ, B ν is the Planck function (Jy/sr) evaluated at the temperature T c = T bb = 1.093 × (278 K) r −0.5 h ≃ 232.9 K, where T c is the color temperature. Derived values of ǫ f ρ for comet C/2013 US 10 (Catalina) from SOFIA photometry are presented in Table 2.

Dust Bolometric Albedo
Our near simultaneous optical observations conducted on the same night as our measurement of the infrared SED of comet C/2013 US 10 (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 ] max scattering . An estimate of [λF λ ] max IR 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 US 10 (Catalina) has a low bolometric dust albedo, A(θ), of ≃ 5.1 ± 0.1% at phase angle of 47.80 • and to ≃ 13.8 ± 0.5% at a phase angle of 33.01 • . Fig. 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 US 10 (Catalina). At 1.3 AU, the bolometric albedo of comet C/2013 US 10 (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). Reflectance of individual refractory particles from the coma of comet 67P/Churyumov-Gerasimenko as measured by Rosetta COSIMA/Cosicope are from 3% to 22% at 650 nm (Langevin et al. 2017(Langevin et al. , 2020, which spans the range of bolometric albedos measured for comet comae. 4. CONCLUSION Mid-infrared 6.0 < ∼ λ(µm) < ∼ 40 spectrophotometric observations of comet C/2013 US 10 (Catalina) at two temporal epochs yielded an inventory of the refectory materials in the comet's coma and their physical characteristics through thermal modeling analysis. The coma of C/2013 US 10 (Catalina) has a high abundance of submicron-radii moderately porous (fractal porosity D = 2.727) carbonaceous amorphous grains with a silicate-to-carbon mass ratio < ∼ 0.9. This comet also exhibited a weak 10 µm silicate feature.
Comet C/2013 US 10 (Catalina) is an example of subset of comets with weak silicate features that are definitively shown to have low silicate-to-carbon ratios for the submicron grain component (as deduced from thermal model analysis of the spectral energy distributions), that is, they are carbon-rich. Their thermal emission is dominated by warmer particles that are significantly more absorbing at UV-near-IR wavelengths than silicates. The spectral grasp of SOFIA (+FORCAST) provided a constraint that required the presence of amorphous carbon as a dominate constituent of the coma particle population (submicron dust) as silicate particles cannot provide the lack of contrast above blackbody emission at far-infrared wavelengths. The surface area of the thermal emission is dominated by the smaller grains and for the silicates, the smaller grains produce resonances 19.5, 23.5, 27.5 µm not evident in the spectrum of comet C/2013 US 10 (Catalina), which is a puzzle. A dark refractory carbonaceous material darkens and reddens the surface of the nucleus of 67P/Churyumov-Gerasimenko. Comet C/2013 US 10 (Catalina) is carbonrich. Analysis of comet C/2013 US 10 (Catalina) grain composition and observed infrared spectral features compared to interplanetary dust particles, chondritic materials, and Stardust samples suggest that the dark carbonaceous material is well-represented by the optical properties of amorphous carbon. We argue that this dark material is endemic to comets.
The C/Si atomic ratio of comets in context with that derived from studies of interplanetary dust particles, micrometeroites, and Stardust samples suggest that a carbon gradient was present in the early solar nebula. As we observe more comets, and especially take the opportunities to observe dynamically new comets with SOFIA, the James Webb Space Telescope and other capabilities, a significant subset of comets which are carbon-rich likely will arise providing important constraints on newly proposed interpretations of disk processing in the primitive solar system.

ACKNOWLEDGMENTS
Based in part on observations made with the NASA/DLR Stratospheric Observatory for Infrared Astronomy (SOFIA). SOFIA is jointly operated by the Universities Space Research Association, Inc. (USRA), under NASA contract NNA17BF53C, and the Deutsches SOFIA Institut (DSI) under DLR contract 50 OK 0901 to the University of Stuttgart. Financial support for this work was provided by NASA through award SOF 04-0010 and NASA PAST grant 80NSSC19K0868. The authors wish to thank Dr. Aigen Lee for informative discussion regarding carbonaceous materials and there relevance to interpreting astronomical spectra as well as Dr. Jeff Cuzzi and the NASA Ames research group for their keen insights into disk transport models. The authors also express gratitude for the two anonymous referees' very careful reading of the manuscript and their numerous suggestions and comments that enhanced the final narrative. Software: IRAF (Tody 1986(Tody , 1993, IDL, JPL Horizons (Giorgini et al. 1996), Aperture Photometry Tool (APT) Laher et al. (2012) APPENDIX A. TABLES OF REVISED THERMAL MODELS As described in the text ( §3.2.6) we have adopted a value for 1.5 g cm −3 for the specific density of amorphous carbon, ρ s (ACar), in our thermal models. In early work, we employed a higher specific density of 2.5 g cm −3 . In order to compare the atomic carbon-to-silicate ratios consistently thermal models for all SOFIA observed comets included in this analysis were modeled or remodeled with a common value of ρ s (ACar) = 1.5 g cm −3 . Tables for comets C/2012 K1 (Pan-Starrs) (see Woodward et al. 2015), C/1995 O1 (Hale-Bopp) (see , and C/2013 X1 (Pan-STARRS) and C/2018 W2 (Africano) (Woodward et al. 2020) are given for completeness.