arXiv subjects

William M. Grundy

Publications and source records attributed to William M. Grundy.

At least 19 recordsLinked to original sources

arXiv2026

The size and mass distribution of cold classical TNOs for $5<H<13$

The cold classical trans-Neptunian objects (CCs) are the only observable \textit{in situ} population of planetesimal remnants believed to have escaped collisional grinding. Recent JWST observations make it possible to fit the differential absolute magnitude distribution $dN/dH$ of the CCs from $5 13$ is unwise, as the different analytic forms diverge. It remains unclear if $dN/dH$ turns over at faint $H.$ The uncertainty in the total mass of the CC belt is dominated by uncertainty in the relation between $M$ and $H$. A calibration using CC binaries suggests a total CC mass of 1.7--2.7$\times10^{-3}\,M_\oplus.$ A trend toward lower density and/or higher albedo for smaller bodies may be present in the data, and would lower the estimated total CC mass. Qualitative comparison of the derived mass distribution to the results of numerical simulations of the streaming instability (SI) suggest the simulations produce $dN/dM$ distributions that are more sharply peaked, and steeper at the bright end, than the CCs. Such differences could be ascribed to inhomogeneous formation conditions in the classical belt that are not yet included in modeling. The variety and uncertainty of $dN/dM$ derived from state-of-the-art SI simulations currently preclude any definitive test of the SI hypothesis.

astro-ph.EP↗

arXiv2026

The Luminosity Function of Ultra-Faint Trans-Neptunian Objects Detected by JWST

We present a definitive discovery of 27 trans-Neptunian objects (TNOs) using the Near-Infrared Camera (NIRCam) aboard the James Webb Space Telescope (JWST). By employing a shift-and-stack technique and a machine learning network geared specifically to identifying false-positive detections in JWST images produced through the shift-and-stack process, we achieved a 40\% detection threshold of $m_{F150W2}=28.8$ mag (corresponding to $m_r\sim29.8$ mag) across a sky area of $0.05 \ \text{deg}^2$. This marks the deepest Solar System survey to date, reaching magnitudes that allow us to explore never-before-seen regions of the TNO size distribution. Our faintest detection has $m_{F150W2}=29.3$ mag and diameter of $\sim10$ km (assuming 15\% albedo). Within our sample, we find that both the Cold and Hot TNO subpopulations exhibit a power-law slope. The distribution of apparent magnitudes of our nominal sample (detections at all epochs) are well fit by a single power law $dN/dm \propto 10^{αm}$ with $α=0.29^{+0.08}_{-0.07}$. The dynamically hot and cold subsamples in our discovery set are consistent with the same power law, suggesting that the planetesimal formation process yields similar slopes despite the differing disk conditions at the presumed $\sim25$ and $\sim45$~au formation regions of the two populations.

astro-ph.EP↗

arXiv2026

Combined JWST and HST Deep Imaging to Characterize the Smallest Known Trans-Neptunian Objects

We present optical-near-infrared (NIR) color measurements for small ($\leq 40$ km) Trans-Neptunian Objects (TNOs) using coordinated and nearly simultaneous observations from the James Webb Space Telescope (JWST) and the Hubble Space Telescope (HST). JWST/NIRCam data provided detections and NIR photometry for faint TNOs, while HST/ACS and WFC3 imaging enabled recovery in the optical, together yielding optical-NIR colors spanning 0.35-3.2 $μ$m. Thirteen JWST-detected TNOs were recovered in the HST observations, and trailed PSF photometry was used to derive mean magnitudes, colors, and rotational lightcurves. The color distribution of our small cold classical TNO discoveries is narrow and consistent with the occupation of a single reflectance (color) sequence previously identified for larger cold classical TNOs. We find no evidence for a change in this sequence at smaller sizes. In contrast, the dynamically excited TNOs we discovered exhibit a broader range of colors consistent with multiple compositional classes seen at larger sizes. Lightcurve amplitudes were generally low for both dynamical groups in our sample. 2015 GK56, a previously known TNO in our field, displays a large-amplitude, structured lightcurve consistent with a contact binary. Our results indicate that the characteristic color distribution of TNOs extends to smaller sizes than previously studied, suggesting a primordial origin rather than size-dependent collisional processing.

astro-ph.EP↗

arXiv2026

Rotation and Mutual Eclipse Events Season in the Kuiper Belt: (524366) 2001 XR$_{254}$

(524366) 2001 XR$_{254}$ is a dynamically Cold Classical Kuiper Belt Object that is a nearly equal-sized wide binary whose upcoming mutual events season makes it a particularly valuable target for physical characterization. In advance of the mutual eclipse events, we conducted a ground-based photometric observing campaign between 2021 and 2026 using the \textit{Lowell Discovery Telescope} to investigate the rotational and physical properties of the system, to refine predictions for its future mutual events, as well as provide a lightcurve we can use as a baseline to identify eclipse events superimposed with the rotation. We derive a double-peaked asymmetric rotational lightcurve with a period of 11.17$\pm$0.04 h and a lightcurve amplitude of 0.42$\pm$0.04 mag. The lightcurve presents a sharp V-shaped minimum consistent with the primary being a close/contact binary, possibly making this a triple system. Using the Keplerian mutual orbit solution, we model the upcoming mutual event season expected between $\sim$2031 and $\sim$2040 and present some individual events for future campaigns. 2001 XR$_{254}$ is one of the few wide binary Kuiper belt systems with a well-determined mutual orbit and a soon observable mutual eclipse event season. Mutual event observations of this possible triple system will provide a rare opportunity to improve component sizes, shapes, densities, and surface properties, offering insights into the formation of the Kuiper Belt.

astro-ph.EP↗

arXiv2026

Tracing the source of carbon oxides on the large moons of Uranus

The Uranian moons Ariel, Umbriel, Titania, and Oberon are enriched in CO2 mixed with CO, but the origin(s) of these carbon oxides, be they primarily native or radiolytic, remains uncertain. Using data collected by NIRSpec on the James Webb Space Telescope (JWST), we measured the spectral signature of CO2 and other carbon oxides to help disentangle these hypotheses. Through comparison to laboratory data, we find that many of the detected spectral features are consistent with CO2 ice, including 12CO2 scattering peaks (4.15 - 4.26 microns), multi-lobe 13CO2 bands (4.35 - 4.43 microns), and CO2 biphonon and triphonon modes (4.80 - 5.25 microns). Our measurements show that CO2 and CO are concentrated on the trailing hemispheres of the inner moons Ariel and Umbriel, potentially supporting a radiolytic production hypothesis, consistent with prior ground-based results. However, many of the identified spectral features are only observed in thick crystalline ice deposits measured in the laboratory, which may be difficult to form via radiolysis of carbon-bearing material mixed in icy regoliths. Similarly, the data exhibit weak 4.02 microns and 4.40 microns bands, hinting at the presence of carbonate minerals and 13CO2 clathrates, respectively, possibly formed in the interiors of these moons. Furthermore, JWST has revealed that CO2 is widespread at Uranus, present in its system of rings, ring moons, and irregular satellites, consistent with its largest moons accreting CO2 and other carbon oxides from the Uranian subnebula. We conclude that exposed carbon oxides are potentially native, with their surface distributions shaped by charged particle irradiation and seasonal sublimation-condensation cycles.

astro-ph.EP↗

arXiv2025

Evidence of Possible Spectral Variability in the Patroclus-Menoetius Binary System

We present new visible-wavelength spectroscopic observations of the Patroclus-Menoetius binary system in the Jupiter Trojan population. Motivated by previously published spectra from different instruments that showed evidence of significant longitudinal variability, we obtained two spectra spanning 440-680 nm at near-opposite rotational phases with the Gemini Multi-Object Spectrograph on the Gemini South telescope during the late 2024 apparition. The same solar analog was used for both observations to remove one source of inconsistency. We measured spectral slopes of 2.51% $\pm$ 0.05%/100 nm and 8.13% $\pm$ 0.05%/100 nm at the two different rotational phases. The first of these measurements was serendipitously obtained during an occultation of Menoetius by Patroclus. Although the statistical significance of the spectral slope discrepancy persists even after considering possible systematic errors stemming from differences in slit position angles and air masses between the asteroid and solar analog exposures, we consider this report of variability to be tentative. We briefly explore several scenarios that could explain the measured spectral slope variability. Additional follow-up observations are necessary to definitively confirm and characterize any inhomogeneities across the surface, which will have major implications for the 2033 flyby of Patroclus-Menoetius by the Lucy spacecraft.

astro-ph.EP↗

arXiv2025

JWST/NIRSpec Observations of Salacia-Actaea and Máni: Exploring Population-level Trends among Water-ice-rich Kuiper Belt Objects

We present observations of the midsized Kuiper Belt objects (KBOs) Salacia$-$Actaea and Máni, obtained with the Near-Infrared Spectrograph on JWST. The satellite Actaea was fully blended with Salacia at the spatial resolution of the integral field unit, and we extracted the combined spectrum. The 0.7$-$5.1 $μ$m reflectance spectra of Salacia$-$Actaea and Máni display prominent water-ice absorption bands at 1.5, 2, 3, and 4$-$5 $μ$m. The $ν_{3}$ fundamental vibrational band of carbon dioxide ice at 4.25 $μ$m is present in both spectra. From a quantitative band-depth analysis of the entire current JWST spectroscopic sample of water-ice-rich KBOs, we find strong evidence for a positive covariance between relative water-ice abundance and size, which may indicate the emergent impacts of internal differentiation and cryovolcanic production of surface water ice on midsized KBOs. A detailed look at the distribution of 2 and 3 $μ$m band depths suggests additional sources of variability, such as different water-ice grain sizes. In addition, we report an apparent transition in the carbon dioxide band depth at object diameters of roughly 300$-$500 km, with larger objects showing systematically weaker absorptions, although selection effects within the sample do not allow us to confidently distinguish between a size-dependent phenomenon and a correlation with dynamical class.

astro-ph.EP↗

arXiv2025

Rotational Dynamics in Pulsational Pair-Instability Supernovae: Implications for Mass-Loss and Transient Events

Pulsational pair-instability supernovae (PPISNe) are transient events occurring in progenitor stars with helium cores of approximately 32-65 solar masses, where rapid electron-positron pair production induces pressure loss, collapse, and pulsations driving episodic mass loss. The number, strength, and duration of these pulses can lead to shell collisions that produce shock-powered transients, potentially explaining some of the most luminous events, such as superluminous supernovae, and other rare transients. Rapid progenitor rotation lowers the PPISN mass threshold and influences the dynamics, energetics, and chemical composition of PPISN-driven pulses. In this study, we computed 1D evolutionary models of massive, rotating PPISN progenitor stars with zero-age main-sequence masses of 85-140 solar masses and solar metallicity and 10% solar metallicity. Our analysis reveals strong correlations between PPISN ejected mass and total energy as well as between ejected mass and peak ejected shell velocity. Additionally, moderate correlations indicate that higher initial PPISN progenitor mass leads to greater mass ejection and energy release, while negative correlations show that rapid rotation appears to reduce mass ejection and kinetic energy of the shells. Subsequent pulses lead to hydrogen-poor, carbon- and oxygen-enriched ejected shells, indicating the effect of rotationally-induced chemical mixing in PPISN-driven episodic mass loss with implications for their transients. We model the light curve and synthetic spectra that arise from the collision of two H-poor shells for one of our models using the radiation transport code SuperLite. We find that shock-heated H-poor PPISN shell collisions from rapidly rotating progenitors can lead to moderately luminous H-poor transients that share some similarities with observed SLSN-I events.

astro-ph.HE↗

arXiv2025

Logos-Zoe: A contact binary triple system in the trans-neptunian belt

The trans-neptunian object (58534) 1997 CQ$_{29}$ (a.k.a. Logos) is a resolved wide binary in the dynamically Cold Classical population. With Hubble Space Telescope resolved observations where the primary Logos is well separated from its secondary Zoe it can be established that Logos has a time-variable brightness. Logos' brightness varied by several tenths of a magnitude over a short timescale of hours while the brightness variability of Zoe was on a longer timescale. New unresolved ground-based observations obtained with the Lowell Discovery Telescope and the Magellan-Baade telescope confirm at least one highly variable component in this system. With our ground-based observations and photometric constraints from space-based observations, we suggest that the primary Logos is likely a close/contact binary whose rotational period is 17.43$\pm$0.06 h for a lightcurve amplitude of 0.70$\pm$0.07 mag while Zoe is potentially a (very) slow rotator with an unknown shape. Using the Candela software, we model the Logos-Zoe system and predict its upcoming mutual events season using rotational, physical, and mutual orbit parameters derived in this work or already published. Zoe's shape and rotational period are still uncertain, so we consider various options to better understand Zoe. The upcoming mutual event season for Logos-Zoe starts in 2026 and will last for four years with up to two events per year. Observations of these mutual events will allow us to significantly improve the physical and rotational properties of both Logos and Zoe.

astro-ph.EP↗

arXiv2024

Observations of Uranus at High Phase Angle as Seen by New Horizons

We present flux measurements of Uranus observed at phase angles of 43.9°, 44.0°, and 52.4° by the Multispectral Visible Imaging Camera (MVIC) on the New Horizons spacecraft during 2023, 2010, and 2019, respectively. New Horizons imaged Uranus at a distance of about 24-70 AU (2023) in four color filters, with bandpasses of 400-550 nm, 540-700 nm, 780-975 nm, and 860-910 nm. High-phase-angle observations are of interest for studying the energy balance of Uranus, constraining the atmospheric scattering behavior, and understanding the planet as an analog for ice giant exoplanets. The new observations from New Horizons provide access to a wider wavelength range and different season compared to previous observations from both Voyager spacecraft. We performed aperture photometry on the New Horizons observations of Uranus to obtain its brightness in each photometric band. The photometry suggests that Uranus may be darker than predicted by a Lambertian phase curve in the Blue and Red filters. Comparison to simultaneous low-phase Hubble WFC3 and ground-based community-led observations indicates a lack of large-scale features at full-phase that would introduce variation in the rotational light curve. The New Horizons reflectance in the Blue (492 nm) and Red (624 nm) filters does not exhibit statistically significant variation and is consistent with the expected error bars. These results place new constraints on the atmospheric model of Uranus and its reflectivity. The observations are analogous to those from future exoplanet direct-imaging missions, which will capture unresolved images of exoplanets at partial phases. These results will serve as a "ground-truth" with which to interpret exo-ice giant data.

astro-ph.EP↗

arXiv2024

JWST near-infrared spectroscopy of the Lucy Jupiter Trojan flyby targets: Evidence for OH absorption, aliphatic organics, and CO$_{2}$

We present observations obtained with the Near Infrared Spectrograph on JWST of the five Jupiter Trojans that will be visited by the Lucy spacecraft -- the Patroclus-Menoetius binary, Eurybates, Orus, Leucus, and Polymele. The measured 1.7-5.3 $μ$m reflectance spectra, which provide increased wavelength coverage, spatial resolution, and signal-to-noise ratio over previous ground-based spectroscopy, reveal several distinct absorption features. We detect a broad OH band centered at 3 $μ$m that is most prominent on the less-red objects Eurybates, Patroclus-Menoetius, and Polymele. An additional absorption feature at 3.3-3.6 $μ$m, indicative of aliphatic organics, is systematically deeper on the red objects Orus and Leucus. The collisional fragment Eurybates is unique in displaying an absorption band at 4.25 $μ$m that we attribute to bound or trapped CO$_2$. Comparisons with other solar system small bodies reveal broad similarities in the 2.7-3.6 $μ$m bands with analogous features on Centaurs, Kuiper belt objects (KBOs), and the active asteroid 238P. In the context of recent solar system evolution models, which posit that the Trojans initially formed in the outer solar system, the significant attenuation of the 2.7-3.6 $μ$m absorption features on Trojans relative to KBOs may be the result of secondary thermal processing of the Trojans' surfaces at the higher temperatures of the Jupiter region. The CO$_2$ band manifested on the surface of Eurybates suggests that CO$_2$ may be a major constituent in the bulk composition of Trojans, but resides in the subsurface or deeper interior and is largely obscured by refractory material that formed from the thermophysical processes that were activated during their inward migration.

astro-ph.EP↗

arXiv2024

Moderate D/H Ratios in Methane Ice on Eris and Makemake as Evidence of Hydrothermal or Metamorphic Processes in Their Interiors: Geochemical Analysis

Dwarf planets Eris and Makemake have surfaces bearing methane ice of unknown origin. D/H ratios were recently determined from James Webb Space Telescope (JWST) observations of Eris and Makemake, giving us new clues to decipher the origin of methane. Here, we develop geochemical models to test if the origin of methane could be primordial, derived from CO$_2$ or CO ("abiotic"), or sourced by organics ("thermogenic"). We find that primordial methane is inconsistent with the observational data, whereas both abiotic and thermogenic methane can have D/H ratios that overlap the observed ranges. This suggests that Eris and Makemake either never acquired a significant amount of methane during their formation, or their original inventories were removed and then replaced by a source of internally produced methane. Because producing abiotic or thermogenic methane likely requires temperatures above ~150°C, we infer that Eris and Makemake have rocky cores that underwent substantial radiogenic heating. Their cores may still be warm/hot enough to make methane. This heating could have driven hydrothermal circulation at the bottom of an ice-covered ocean to generate abiotic methane, and/or metamorphic reactions involving accreted organic matter could have occurred in response to heating in the deeper interior, generating thermogenic methane. Additional analyses of relevant thermal evolution model results and theoretical predictions of the D/H ratio of methane in the solar nebula support our findings of elevated subsurface temperatures and an apparent lack of primordial methane on Eris and Makemake. It remains an open question whether their D/H ratios may have evolved subsequent to methane outgassing. Recommendations are given for future activities to further test proposed scenarios of abiotic and thermogenic methane production on Eris and Makemake, and to explore these worlds up close.

astro-ph.EP↗

arXiv2022

Large-scale cryovolcanic resurfacing on Pluto

The New Horizons spacecraft returned images and compositional data showing that terrains on Pluto span a variety of ages, ranging from relatively ancient, heavily cratered areas to very young surfaces with few-to-no impact craters. One of the regions with very few impact craters is dominated by enormous rises with hummocky flanks. Similar features do not exist anywhere else in the imaged solar system. Here we analyze the geomorphology and composition of the features and conclude this region was resurfaced by cryovolcanic processes, of a type and scale so far unique to Pluto. Creation of this terrain requires multiple eruption sites and a large volume of material (>104 km^3) to form what we propose are multiple, several-km-high domes, some of which merge to form more complex planforms. The existence of these massive features suggests Pluto's interior structure and evolution allows for either enhanced retention of heat or more heat overall than was anticipated before New Horizons, which permitted mobilization of water-ice-rich materials late in Pluto's history.

astro-ph.EP↗

arXiv2021

A CO2 cycle on Ariel? Radiolytic production and migration to low latitude cold traps

CO2 ice is present on the trailing hemisphere of Ariel but is mostly absent from its leading hemisphere. The leading/trailing hemispherical asymmetry in the distribution of CO2 ice is consistent with radiolytic production of CO2, formed by charged particle bombardment of H2O ice and carbonaceous material in Ariel's regolith. This longitudinal distribution of CO2 on Ariel was previously characterized using 13 near-infrared reflectance spectra collected at 'low' sub-observer latitudes between 30S to 30N. Here, we investigated the distribution of CO2 ice on Ariel using 18 new spectra: two collected over low sub-observer latitudes, five collected at 'mid' sub-observer latitudes (31 - 44N), and eleven collected over 'high' sub-observer latitudes (45 - 51N). Analysis of these data indicates that CO2 ice is primarily concentrated on Ariel's trailing hemisphere. However, CO2 ice band strengths are diminished in the spectra collected over mid and high sub-observer latitudes. This sub-observer latitudinal trend may result from radiolytic production of CO2 molecules at high latitudes and subsequent migration of this constituent to low latitude cold traps. We detected a subtle feature near 2.13 microns in two spectra collected over high sub-observer latitudes, which might result from a 'forbidden' transition mode of CO2 ice that is substantially stronger in well mixed substrates composed of CO2 and H2O ice, consistent with regolith-mixed CO2 ice grains formed by radiolysis. Additionally, we detected a 2.35-micron feature in some low sub-observer latitude spectra, which might result from CO formed as part of a CO2 radiolytic production cycle.

astro-ph.EP↗

arXiv2021

Moons Are Planets: Scientific Usefulness Versus Cultural Teleology in the Taxonomy of Planetary Science

We argue that taxonomical concept development is vital for planetary science as in all branches of science, but its importance has been obscured by unique historical developments. The literature shows that the concept of planet developed by scientists during the Copernican Revolution was theory-laden and pragmatic for science. It included both primaries and satellites as planets due to their common intrinsic, geological characteristics. About two centuries later the non-scientific public had just adopted heliocentrism and was motivated to preserve elements of geocentrism including teleology and the assumptions of astrology. This motivated development of a folk concept of planet that contradicted the scientific view. The folk taxonomy was based on what an object orbits, making satellites out to be non-planets and ignoring most asteroids. Astronomers continued to keep primaries and moons classed together as planets and continued teaching that taxonomy until the 1920s. The astronomical community lost interest in planets ca. 1910 to 1955 and during that period complacently accepted the folk concept. Enough time has now elapsed so that modern astronomers forgot this history and rewrote it to claim that the folk taxonomy is the one that was created by the Copernican scientists. Starting ca. 1960 when spacecraft missions were developed to send back detailed new data, there was an explosion of publishing about planets including the satellites, leading to revival of the Copernican planet concept. We present evidence that taxonomical alignment with geological complexity is the most useful scientific taxonomy for planets. It is this complexity of both primary and secondary planets that is a key part of the chain of origins for life in the cosmos.

physics.hist-ph↗

arXiv2021

Evaluation of short-term temporal evolution of Pluto's surface composition from 2014-2017 with APO/TripleSpec

In this work we present the results of a spectral observing campaign of Pluto to search for temporal changes in surface composition on 1- to 3-year timescales. Near-infrared spectra of Pluto were obtained from June 2014 to August 2017 with the TripleSpec cross-dispersed spectrograph at the Apache Point Observatory's 3.5-meter Astrophysical Research Consortium (ARC) telescope. Observations were requested in order to obtain spectra of approximately the same sub-observer hemisphere $\sim$14 months apart, thus removing the effects of viewing geometry and rotation phase. Comparison of the CH$_4$ (methane) band areas and band center shifts between each component of these "matched pairs" revealed a surface in transition. Band areas for the 1.66 and 1.72 $μ$m CH$_4$ absorption features exhibited a $>$5-$σ$ increase between 2014-06-17 and 2015-08-19, corresponding to a sub-observer hemisphere centered at $\sim$280$^{\circ}$E, with the latter date only 1 month after the New Horizons flyby of Pluto. The majority of matched pairs were obtained of the anti-Charon hemisphere, home to the bright, volatile-rich Sputnik Planitia, and did not present statistically significant changes in CH$_4$ band areas. CH$_4$ band center shifts, which provide information on the mixing state of CH$_4$ and N$_2$ in solid solution, were calculated between components of each matched pair, with no significant band shifts detected. The favored explanation for these combined results is the sublimation of more-volatile N$_2$ from the northern latitudes of Pluto in the lead-up to northern hemisphere summer solstice in 2029, leading to an increase in CH$_4$ concentration.

astro-ph.EP↗

arXiv2021

Phase Diagram for the Methane-Ethane System and its Implications for Titan's Lakes

On Titan, methane (CH4) and ethane (C2H6) are the dominant species found in the lakes and seas. In this study, we have combined laboratory work and modeling to refine the methane-ethane binary phase diagram at low temperatures and probe how the molecules interact at these conditions. We used visual inspection for the liquidus and Raman spectroscopy for the solidus. Through these methods we determined a eutectic point of 71.15$\pm$0.5 K at a composition of 0.644$\pm$0.018 methane - 0.356$\pm$0.018 ethane mole fraction from the liquidus data. Using the solidus data, we found a eutectic isotherm temperature of 72.2 K with a standard deviation of 0.4 K. In addition to mapping the binary system, we looked at the solid-solid transitions of pure ethane and found that, when cooling, the transition of solid I-III occurred at 89.45$\pm$0.2 K. The warming sequence showed transitions of solid III-II occurring at 89.85$\pm$0.2 K and solid II-I at 89.65$\pm$0.2 K. Ideal predictions were compared to molecular dynamics simulations to reveal that the methane-ethane system behaves almost ideally, and the largest deviations occur as the mixing ratio approaches the eutectic composition.

astro-ph.EP↗

arXiv2021

A Statistical Review of Light Curves and the Prevalence of Contact Binaries in the Kuiper Belt

We investigate what can be learned about a population of distant KBOs by studying the statistical properties of their light curves. Whereas others have successfully inferred the properties of individual, highly variable KBOs, we show that the fraction of KBOs with low amplitudes also provides fundamental information about a population. Each light curve is primarily the result of two factors: shape and orientation. We consider contact binaries and ellipsoidal shapes, with and without flattening. After developing the mathematical framework, we apply it to the existing body of KBO light curve data. Principal conclusions are as follows. (1) When using absolute magnitude H as a proxy for size, it is more accurate to use the maximum of the light curve rather than the mean. (2) Previous investigators have noted that smaller KBOs have higher-amplitude light curves, and have interpreted this as evidence that they are systematically more irregular in shape than larger KBOs; we show that a population of flattened bodies with uniform proportions could also explain this result. (3) Our analysis indicates that prior assessments of the fraction of contact binaries in the Kuiper Belt may be artificially low. (4) The pole orientations of some KBOs can be inferred from observed changes in their light curves; however, these KBOs constitute a biased sample, whose pole orientations are not representative of the population overall. (5) Although surface topography, albedo patterns, limb darkening, and other surface properties can affect individual light curves, they do not have a strong influence on the statistics overall. (6) Photometry from the OSSOS survey is incompatible with previous results and its statistical properties defy easy interpretation. We also discuss the promise of this approach for the analysis of future, much larger data sets such as the one anticipated from the Rubin Observatory.

astro-ph.EP↗