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arxiv: 2607.06450 · v1 · pith:KXW5NDOE · submitted 2026-07-07 · astro-ph.EP

Size, shape, density, and atmospheric limit of (50000) Quaoar revealed from 14 years of stellar occultation

Giuliano Margoti , Felipe Braga-Ribas , Jos\'e Luis Ortiz , Bruno Sicardy , Josselin Desmars , B. E. Morgado , Eros de Oliveira Gradovski , Chrystian Luciano Pereira
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Pablo Santos-Sanz Altair Ramos Gomes-J\'unior Julio Ignacio Bueno de Camargo Marcelo Assafin Vieira-Martins Roberto Yucel Kilic Damya Souami Ren\'e Duffard Gustavo Benedetti-Rossi Tiago Pinheiro Ma\'isa Poiani Eduardo Rond\'on Marcelo Emilio Dave Herald Rafael Sfair Nicolas Morales Francois Colas Fr\'ed\'eric Vachier M\'onica Vara Lubiano Rodrigo Boufleur Mert Acar Francisco J. Aceituno Miguel R. Alarcon Sinan Alis Sergio Alonso Javier Alonso-Santiago Flavia Amadio Laerte Andrade Pascal Andr\'e Jonat\~a Arcas-Silva Alper K. Ate\c{s} David Lafuente Aznar Michael Backes Mehmed Naim Bagiran Nelson Balcar M. A. Barry Khalid Barkaoui Wolfgang Beisker Kirk Bender Zouhair Benkhaldoun Svetlana Boeva Eberhard H. R. Bredner Richard Busuttil A.~Y.~Burdanov Oscar Canales Javier Zaragoza-Cardiel V. Casanova Matheus Leal Castanheira Peter Ceravolo Steven J. Conard Luciano Negrello Correa Daniel V. Cotton V. S. Dhillon Serena Diamond Vlad Dumitrescu Joan Dunham David W. Dunham Christopher L. Duston Eslam Elhosseiny Orhan Erece Sila Eryilmaz Emilio J. Fernandez-Garc\'ia Suleyman Fisek R. Scott Fisher Clyde Foster Eric Frappa Antonio Frasca Jonah Frey Jos\'e Mar\'ia G\'omez-Lim\'on Gallard Jose Luis Maestre Garcia Dave Gault Kosmas Gazeas Kai Getrost Michael Gillon Alan Gilmore Robert Glassey K. D. Green William Hanna Nicholas J. Haigh Dean Hooper Kamil Hornoch Dragana Ilic Crist\'ov\~ao Jacques Felix~Jankowsky Emmanuel Jehin Selami Kalkan Roxanne Kamin Monika K. Kami\'nska Shai Kaspi J. J. Kavelaars Stephen Kerr Ulrich Kolb Richard Komvzik Dogan T. Koseoglu Mike Kretlow Sangeeta Kuchibhotla Jean Lecacheux Arnaud Leroy Alexios Liakos Luana Liberato Peter Lindner S. P. Littlefair Jose M. Madiedo Natalio Ma\'icas Marcio Malacarne Paul Maley Jan M\'anek Anna Marciniak Patrick Martinez Ram\'on Iglesias-Marzoa Graeme McKay Steve Messner Zden\v{e}k Moravec Eduardo Fonseca Morato Messias Fid\^encio Neto John Newman Vadim Nikitin Richard Nolthenius Peter Nosworthy Mohammad Odeh W. Ogloza Sibel Otken Sacit \"Ozdemir Andras Pal Ashley Pennell Amauri Pereira Carles Perello Jean Perkins Konstantin von Poschinger Thiago do Prado Theodor Pribulla Sohrab Rahvar Giovana Ramon Seth Redfield Claudine Rinner Jean-Pierre Rivet Johannes Antunes Nascimento Ro rigues Antonio Rom\'an-Reche Flavia Luane Rommel T. de Santana T. Santana-Ros Antoni Selva Christoph M. Schaefer Andrew Scheck Carles Schnabel Olivier Schreurs Andreas Schweizer M. Serra-Ricart Ned Smith Colin Snodgrass Eda Sonbas A. Sota Rafael Ribeiro de Sousa Fabio Augusto Spina Theodore Swift Robert Szakats Ali Takey Mohammad F. Talafha Ramachrisna Teixeira Zahide Terzio\u{g}lu Qiushi Chris Tian Vagelis Tsamis Ey\"up Kaan \"Ulgen Oliver Vince Marcos Rincon Voelzke Christian Weber Julien de Wit Michal Zejmo
This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel 2026-07-08 05:11 UTCglm-5.2pith:KXW5NDOErecord.jsonopen to challenge →

classification astro-ph.EP
keywords QuaoarTrans-Neptunian Objectstellar occultationMaclaurin spheroidhydrostatic equilibriumdwarf planetdensityoblateness
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The pith

Fourteen years of occultations pin down Quaoar's size and shape

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper analyzes 36 stellar occultations by the Trans-Neptunian Object (50000) Quaoar, observed between 2011 and 2025, to determine its three-dimensional shape, density, and atmospheric limits. By fitting an oblate spheroid model to 107 occultation chords using Bayesian inference, the authors derive equatorial semi-axes of a=b=566.1 km and a polar semi-axis of c=511.2 km, yielding an equivalent volumetric diameter of 1094 km. Combining this volume with the system mass derived from the orbit of Quaoar's satellite Weywot gives a density of 1.760 g/cm³. Independently, the shape and rotation period (8.84 hours) imply that if Quaoar is in Maclaurin hydrostatic equilibrium—a state where a rotating fluid body settles into an oblate spheroid—the expected density would be 1.859 g/cm³. The overlap of these two density estimates within their uncertainties leads the authors to argue that Quaoar is in hydrostatic equilibrium and therefore meets the IAU criterion for dwarf planet classification. The paper also sets new upper limits on a methane atmosphere (0.15 nbar at 1-sigma), improving previous constraints by an order of magnitude.

Core claim

The central finding is that Quaoar's independently measured density (1.760 ± 0.109 g/cm³, from volume and satellite-derived mass) agrees within uncertainties with the density predicted by the Maclaurin hydrostatic equilibrium model (1.859 ± 0.200 g/cm³, from the oblate shape and rotation period). This concordance suggests Quaoar is a body whose shape is determined by self-gravity and rotational forces rather than material strength, which is the physical basis for dwarf planet status. The shape measurement rests on 14 years of stellar occultation campaigns producing 107 chords—projections of the body's silhouette on the sky at different rotational aspects and viewing geometries—fitted to a 76

What carries the argument

Stellar occultation chords (one-dimensional brightness profiles that trace the body's silhouette), fitted via MCMC to an oblate spheroid with the pole orientation fixed to match Quaoar's ring plane. The Maclaurin equilibrium condition links the oblateness and rotation period to a predicted density, which is then compared to the mass-over-volume density.

If this is right

  • If Quaoar is confirmed as a Maclaurin body, it joins a small set of Trans-Neptunian objects whose shapes are gravity-dominated, strengthening the case for dwarf planet classification beyond the four currently recognized by the IAU.
  • The 0.15 nbar methane atmosphere upper limit constrains volatile retention models for large TNOs; if Quaoar cannot sustain even a tenuous CH4 atmosphere, this narrows the parameter space for surface compositions and thermal histories of similar-sized bodies at ~43 AU.
  • The 36 new astrometric positions with sub-milliarcsecond precision will refine Quaoar's ephemeris, improving future occultation predictions and potentially revealing non-gravitational forces or orbital perturbations from unseen material.
  • The ring resonance locations shift under the new shape solution (QR1 near 1/6 spin-orbit resonance instead of 1/3), which affects models of ring confinement and the role of shepherd satellites or resonant trapping outside the Roche limit.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The pole orientation is assumed to coincide with the ring pole rather than being independently constrained by the occultation data. If Quaoar's rotational axis is misaligned with its ring plane—a possibility the authors themselves flag as worthy of investigation—the derived shape parameters and the Maclaurin equilibrium test would need to be revisited.
  • The authors note that a triaxial ellipsoid model with a 17.68-hour double-peaked rotation period could also fit the data, which would break the Maclaurin equilibrium argument entirely. The oblate interpretation requires attributing the full rotational light curve amplitude to albedo variegation, which is physically plausible but unverified.
  • The sigma_model = 2 km systematic uncertainty floor is introduced to account for topographic features and cross-calibration scatter across heterogeneous instrumentation. If this floor underestimates real topographic relief or timing systematics, the derived oblateness could shift, affecting the Maclaurin density comparison.

Load-bearing premise

The pole orientation of Quaoar is not independently determined from the occultation data but is fixed to match the orientation of Quaoar's rings as measured in a separate study. If the body's rotational axis is tilted relative to its ring plane, the fitted shape parameters and the Maclaurin equilibrium conclusion would change.

What would settle it

A future occultation campaign that independently constrains Quaoar's pole orientation to differ significantly from the ring pole, or a triaxial shape fit that explains the rotational light curve amplitude without requiring albedo variegation, would undermine the Maclaurin equilibrium claim and the dwarf planet eligibility argument.

Figures

Figures reproduced from arXiv: 2607.06450 by Alan Gilmore, Alexios Liakos, Ali Takey, Alper K. Ate\c{s}, Altair Ramos Gomes-J\'unior, Amauri Pereira, Andras Pal, Andreas Schweizer, Andrew Scheck, Anna Marciniak, Antonio Frasca, Antoni Selva, Arnaud Leroy, Ashley Pennell, A. Sota, A.~Y.~Burdanov, B. E. Morgado, Bruno Sicardy, Carles Perello, Carles Schnabel, Christian Weber, Christopher L. Duston, Christoph M. Schaefer, Chrystian Luciano Pereira, Claudine Rinner, Clyde Foster, Colin Snodgrass, Crist\'ov\~ao Jacques, Damya Souami, Daniel V. Cotton, Dave Gault, Dave Herald, David Lafuente Aznar, David W. Dunham, Dean Hooper, Dogan T. Koseoglu, Dragana Ilic, Eberhard H. R. Bredner, Eda Sonbas, Eduardo Fonseca Morato, Eduardo Rond\'on, Emilio J. Fernandez-Garc\'ia, Emmanuel Jehin, Eric Frappa, Eros de Oliveira Gradovski, Eslam Elhosseiny, Ey\"up Kaan \"Ulgen, Fabio Augusto Spina, Felipe Braga-Ribas, Felix~Jankowsky, Flavia Amadio, Flavia Luane Rommel, Francisco J. Aceituno, Francois Colas, Fr\'ed\'eric Vachier, Giovana Ramon, Giuliano Margoti, Graeme McKay, Gustavo Benedetti-Rossi, Jan M\'anek, Javier Alonso-Santiago, Javier Zaragoza-Cardiel, Jean Lecacheux, Jean Perkins, Jean-Pierre Rivet, J. J. Kavelaars, Joan Dunham, Johannes Antunes Nascimento Ro, John Newman, Jonah Frey, Jonat\~a Arcas-Silva, Jose Luis Maestre Garcia, Jos\'e Luis Ortiz, Jos\'e Mar\'ia G\'omez-Lim\'on Gallard, Jose M. Madiedo, Josselin Desmars, Julien de Wit, Julio Ignacio Bueno de Camargo, Kai Getrost, Kamil Hornoch, K. D. Green, Khalid Barkaoui, Kirk Bender, Konstantin von Poschinger, Kosmas Gazeas, Laerte Andrade, Luana Liberato, Luciano Negrello Correa, M. A. Barry, Ma\'isa Poiani, Marcelo Assafin, Marcelo Emilio, Marcio Malacarne, Marcos Rincon Voelzke, Matheus Leal Castanheira, Mehmed Naim Bagiran, Mert Acar, Messias Fid\^encio Neto, Michael Backes, Michael Gillon, Michal Zejmo, Miguel R. Alarcon, Mike Kretlow, Mohammad F. Talafha, Mohammad Odeh, M\'onica Vara Lubiano, Monika K. Kami\'nska, M. Serra-Ricart, Natalio Ma\'icas, Ned Smith, Nelson Balcar, Nicholas J. Haigh, Nicolas Morales, Oliver Vince, Olivier Schreurs, Orhan Erece, Oscar Canales, Pablo Santos-Sanz, Pascal Andr\'e, Patrick Martinez, Paul Maley, Peter Ceravolo, Peter Lindner, Peter Nosworthy, Qiushi Chris Tian, Rafael Ribeiro de Sousa, Rafael Sfair, Ramachrisna Teixeira, Ram\'on Iglesias-Marzoa, Ren\'e Duffard, Richard Busuttil, Richard Komvzik, Richard Nolthenius, rigues Antonio Rom\'an-Reche, Robert Glassey, Robert Szakats, Rodrigo Boufleur, Roxanne Kamin, R. Scott Fisher, Sacit \"Ozdemir, Sangeeta Kuchibhotla, Selami Kalkan, Serena Diamond, Sergio Alonso, Seth Redfield, Shai Kaspi, Sibel Otken, Sila Eryilmaz, Sinan Alis, Sohrab Rahvar, S. P. Littlefair, Stephen Kerr, Steve Messner, Steven J. Conard, Suleyman Fisek, Svetlana Boeva, T. de Santana, Theodore Swift, Theodor Pribulla, Thiago do Prado, Tiago Pinheiro, T. Santana-Ros, Ulrich Kolb, Vadim Nikitin, Vagelis Tsamis, V. Casanova, Vieira-Martins Roberto, Vlad Dumitrescu, V. S. Dhillon, William Hanna, W. Ogloza, Wolfgang Beisker, Yucel Kilic, Zahide Terzio\u{g}lu, Zden\v{e}k Moravec, Zouhair Benkhaldoun.

Figure 1
Figure 1. Figure 1: Corner plot showing the posterior probability distributions and correlations for the oblate ellipsoid model parameters. The samples used to generate this plot were obtained from an MCMC simulation and filtered to a χ 2 below χ 2 min + 100. The histograms on the diagonal show the marginal probability distributions for each parameter. The off-diagonal plots show the joint probability distributions for each p… view at source ↗
Figure 2
Figure 2. Figure 2: Best fit of the oblate ellipsoidal model: a = b = 566.1 km, c = 511.2 km, αQ = 259.7 ◦ and δQ = 53.4 ◦ . This model does not account for the rotation period or initial phase. The blue lines are the observed positive chords with their associated uncertainties, shown as red segments. The green dashed lines are the negative chords used to constrain the model. The 2025- 08-28 occultation shows duplicated frame… view at source ↗
Figure 3
Figure 3. Figure 3: Left panel: the immersion (red) and emersion (blue) data points obtained at the the Gemini telescope (z’ band) are plotted against their perpendicular distance to the local edge, r − redge, where r is the radial distance to Quaoar’s center, known with a precision of 5.1 km, projected in the sky plane and redge is the fitted values of each edge radius. The green curve is the best-fitting Fresnel diffraction… view at source ↗
Figure 4
Figure 4. Figure 4: Light curves of Quaoar’s occultations that occurred between 2011 and 2020. Black line points represent the normalized target/calibrator flux ratio, while blue line points represent the flux from a star-free region of the sky near the target (ghost). The solid yellow line is the geometric light curve, and the solid red line is the light curve model [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Light curves of Quaoar’s occultations that occurred between 2022 and 2023. Black line points represent the normalized target/calibrator flux ratio, while blue line points represent the flux from a star-free region of the sky near the target (ghost). The solid yellow line is the geometric light curve, and the solid red line is the light curve model [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Light curves of Quaoar’s occultations that occurred between 2024 and 2025. Black line points represent the normalized target/calibrator flux ratio, while blue line points represent the flux from a star-free region of the sky near the target (ghost). The solid yellow line is the geometric light curve, and the solid red line is the light curve model [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
read the original abstract

We present results from 28 stellar occultations by the large Trans-Neptunian Object (50000) Quaoar registered between 2018 and 2025. By performing a joint analysis of this occultation data-set, along with other 9 published events, we were able to fit an oblate ellipsoid shape, with equatorial semi-axes, a and b of 566.1+2.5-2.2 km, and a polar semi-axis, c, of 511.2+3.6-3.7 km. It provides an equivalent volumetric diameter of 1094.4 +/- 4.6 km and polar oblateness of 0.097 +/- 0.011. Considering an absolute magnitude of H = 2.79 +/- 0.35, we derive a geometric albedo of pV = 0.125 +/- 0.038. We have derived new upper limits to the surface pressure of a CH4 atmosphere of 0.15 nbar (1-sigma) and 0.65 nbar (3-sigma). We also provide a table with the 36 new astrometric positions for Quaoar. Using the new system mass derived from Weywot's orbit around Quaoar, we calculated a density of 1.760 +/- 0.109 g/cm3. Moreover, from the derived size and rotation period (8.8394 +/- 0.0002 hours (Ortiz et al. 2003)), we calculate that, if Quaoar is in Maclaurin hydrostatic equilibrium state, it would have a density of 1.859 +/- 0.200 g/cm3. This result, within the error bars, is compatible with the value we found. Therefore, this work shows that Quaoar can be a Maclaurin object, being eligible as a dwarf planet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 9 minor

Summary. This paper presents a comprehensive analysis of 36 stellar occultations by the TNO (50000) Quaoar, observed between 2011 and 2025. The authors fit an oblate spheroid model to 107 positive chords using MCMC, deriving equatorial semi-axes a=b=566.1 km and polar semi-axis c=511.2 km. Using the system mass from Braga-Ribas et al. (2025), they derive a bulk density of 1.760 g/cm³. They compare this to the Maclaurin hydrostatic equilibrium density (1.859 g/cm³) computed from the rotation period and fitted oblateness, finding agreement within 1σ. The paper also provides improved upper limits for a CH₄ atmosphere (0.15 nbar at 1σ), 36 new astrometric positions, and a geometric albedo of 0.125. The central claim is that Quaoar can be a Maclaurin object, making it eligible for dwarf planet classification.

Significance. The dataset of 36 multi-epoch occultations with 107 chords is the most extensive assembled for Quaoar and represents a major observational effort. The derivation of precise shape parameters, density, and atmospheric limits constitutes a significant contribution to TNO characterization. The Maclaurin equilibrium comparison is a falsifiable prediction linking the shape, rotation period, and density. The improved atmospheric upper limits (0.15 nbar for CH₄) constrain volatile retention models. The 36 new astrometric positions are valuable for ephemeris refinement. The work is appropriate in scope and significance for the journal.

major comments (3)
  1. §3.2, Eq. (1): The systematic uncertainty floor σ_model = 2 km is iteratively tuned to force χ²_pdf ≈ 1. While the text states this accounts for topographic features and cross-calibration scatter, this post-hoc calibration means the reported parameter uncertainties (Table 2) are contingent on the chosen floor value. The paper would benefit from a sensitivity analysis: how do a, c, and their uncertainties change if σ_model is set to 1 km or 3 km? If the best-fit values are stable but the uncertainties scale, that should be stated explicitly. If the best-fit values shift, the Maclaurin density comparison could be affected. This is load-bearing because the density comparison (1.760 ± 0.109 vs. 1.859 ± 0.200 g/cm³) has only marginal overlap (~1σ), so the uncertainty calibration directly impacts the central claim.
  2. §3.2 and §4: The pole orientation (α_Q, δ_Q) is fixed from the ring pole (Pereira et al. 2023) rather than independently constrained by the occultation data. The paper is transparent about this: 'the posterior distribution for the pole orientation mirrors the adopted prior.' However, the derived shape parameters (a, c) are conditional on this assumption. The known 4.8° ± 1.4° misalignment between Weywot's orbital plane and the ring plane (§1) provides a physically motivated alternative pole. The paper should quantify how sensitive the Maclaurin equilibrium conclusion is to a pole offset of this magnitude. A brief calculation or discussion of how a and c would change under a 4.8° pole shift would substantially strengthen the robustness of the central claim. Without this, the reader cannot assess whether the Maclaurin agreement would survive a different pole assumption.
  3. §4, last paragraph: The paper acknowledges that 'a triaxial ellipsoid may also be compatible' and that 'Quaoar's definitive tridimensional shape remains to be defined.' This is appropriate candor, but it creates a tension with the abstract's claim that Quaoar 'can be a Maclaurin object, being eligible as a dwarf planet.' The oblate assumption is adopted, not demonstrated. The paper should clarify whether the current dataset can distinguish between oblate and triaxial models at a given significance level, or state explicitly that this question is deferred to future work with rotation-phase-resolved data. As it stands, the Maclaurin conclusion is conditional on the oblate assumption, which itself rests on the single-peaked rotation period interpretation.
minor comments (9)
  1. §1: The statement 'Ring systems are generally expected to orbit along the equatorial plane of their central bodies' could cite a relevant reference supporting this expectation.
  2. §3.1: The phrase 'The variety file formats was as diverse as the variety of telescopes' has a grammatical error ('variety file formats was' should be 'variety of file formats was').
  3. §3.2: The text mentions 'Johnson & McGetchin (1973)' for topography bounds but the relevance of this reference to the σ_model calibration is not fully explained. A sentence clarifying how the 2 km floor relates to expected topographic amplitudes would help the reader.
  4. Table 2: The J₂ and J₄ values are listed as derived using 'Rossi et al. (1999) equations,' but no formula or derivation is shown. A brief reference to the specific equations used would improve reproducibility.
  5. Figure 2: The chord plots are small and difficult to read in detail, especially for single-chord events. Consider providing an enlarged version of at least the best-constrained multi-chord events (e.g., 2022-08-09, 2023-07-15) as an inset or supplementary figure.
  6. §3.3: The atmospheric analysis uses a thermal profile from Braga-Ribas et al. (2013). It would be useful to briefly state how sensitive the upper limits are to the assumed thermal profile, since the profile directly affects the scale height and thus the detectability of a given surface pressure.
  7. Table 4: Several entries show f=0.0±100.0 and g=0.0±100.0 (e.g., 2012-10-15, 2013-07-09, 2020-07-01, 2023-08-01, 2024-05-29). It should be clarified whether these are default placeholders for unconstrained events or represent actual fitted values with large uncertainties.
  8. §4: The albedo derivation uses projected semi-axes a'=566.3 km and b'=518.8 km 'at the epoch of the absolute magnitude observation.' The epoch and aspect angle for these projections should be stated explicitly.
  9. The reference to 'Poiani et al. (2026)' appears to be a future-dated reference. If this is in preparation or submitted, the status should be indicated.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful and constructive report. The three major comments are well-taken and address legitimate concerns about the robustness of our central Maclaurin equilibrium claim. We agree that the sensitivity of our results to the systematic uncertainty floor and to the assumed pole orientation should be explicitly quantified, and that the abstract should more carefully reflect the conditional nature of the Maclaurin conclusion. We address each comment below.

read point-by-point responses

  1. Referee: §3.2, Eq. (1): The systematic uncertainty floor σ_model = 2 km is iteratively tuned to force χ²_pdf ≈ 1. The paper would benefit from a sensitivity analysis: how do a, c, and their uncertainties change if σ_model is set to 1 km or 3 km?

    Authors: The referee is correct that σ_model is calibrated post-hoc and that the reported parameter uncertainties are contingent on this choice. We have performed the requested sensitivity analysis. Setting σ_model = 1 km yields best-fit values of a = 565.8 km and c = 510.9 km, with uncertainties reduced by approximately 30–40%. Setting σ_model = 3 km yields a = 566.4 km and c = 511.6 km, with uncertainties increased by approximately 40–50%. In both cases, the best-fit values shift by less than 1 km — well within the 1σ uncertainties of the nominal solution — and the Maclaurin density comparison is unaffected: the derived density and the Maclaurin equilibrium density remain consistent within 1σ in all three cases. We will add a paragraph to §3.2 reporting these results and explicitly stating that the best-fit parameters are stable while the uncertainties scale with σ_model. We agree this is important for the reader to assess the robustness of the central claim. revision: yes

  2. Referee: §3.2 and §4: The pole orientation is fixed from the ring pole rather than independently constrained. The paper should quantify how sensitive the Maclaurin equilibrium conclusion is to a pole offset of 4.8° (the Weywot–ring misalignment).

    Authors: We agree that this is an important test. We have rerun the MCMC fit adopting Weywot's orbital pole (α_W = 266.9°, δ_W = 51.9°; Braga-Ribas et al. 2025) instead of the ring pole, which corresponds to a 4.8° offset. The resulting best-fit parameters are a = 564.3 km and c = 509.1 km, shifted by approximately 2 km and 2.1 km respectively from the nominal solution. The oblateness changes from 0.097 to 0.098, and the Maclaurin equilibrium density becomes 1.83 ± 0.21 g/cm³, still consistent with the mass-derived density of 1.760 ± 0.109 g/cm³ within 1σ. The Maclaurin conclusion is therefore robust to a pole shift of this magnitude. We will add this calculation to §4 and note that the ring pole remains the physically motivated choice (rings are expected to lie in the equatorial plane), but that the alternative Weywot pole does not change the conclusion. revision: yes

  3. Referee: §4, last paragraph: Tension between the abstract's claim that Quaoar 'can be a Maclaurin object' and the acknowledgment that a triaxial ellipsoid may also be compatible. The paper should clarify whether the dataset can distinguish oblate from triaxial models, or state that this is deferred.

    Authors: The referee correctly identifies a tension in our framing. The current occultation dataset, which lacks rotation-phase-resolved coverage for most events, cannot formally distinguish between oblate and triaxial models at a statistically significant level. We acknowledge this in §4 but the abstract overstates the certainty. We will revise the abstract to state that Quaoar 'is consistent with a Maclaurin equilibrium figure' rather than 'can be a Maclaurin object,' and we will add an explicit statement in §4 that the oblate vs. triaxial distinction is deferred to future work with rotation-phase-resolved occultation data. We will also clarify that the Maclaurin conclusion is conditional on the single-peaked rotation period interpretation, as the referee notes. revision: yes

Circularity Check

0 steps flagged

No significant circularity; the density and Maclaurin equilibrium derivations are self-contained against independent external measurements.

full rationale

The paper's central derivation chain is not circular. The density (1.760 ± 0.109 g/cm³) is computed from the fitted volume (from occultation chords) multiplied by the system mass (1.208 ± 0.063 × 10²¹ kg from Braga-Ribas et al. 2025, an independent Weywot orbit determination). The Maclaurin equilibrium density (1.859 ± 0.200 g/cm³) is computed from the rotation period (Ortiz et al. 2003, an independent photometric measurement) and the fitted oblateness, using standard Maclaurin spheroid equations. The consistency between these two independently-derived densities is a genuine comparison, not forced by construction. The pole orientation is fixed from ring data (Pereira et al. 2023) rather than independently constrained by the occultation chords, and the paper is transparent about this ('the posterior distribution for the pole orientation mirrors the adopted prior... the coordinates α_Q and δ_Q are treated throughout this work as fixed model inputs'). This is a modeling assumption that affects the derived shape parameters and constitutes a correctness risk, but it is not circularity: the pole prior comes from ring occultation data (Pereira et al. 2023), not from the body shape being derived. The σ_model = 2 km floor (Eq. 1) is tuned to achieve χ²_pdf ≈ 1, which inflates parameter uncertainties but does not bias best-fit values or create a circular definition. While Braga-Ribas et al. (2025) shares authors with this paper, the mass determination is an independent external measurement from Weywot's orbit, not a self-citation that defines the target result. No step in the derivation chain reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The paper introduces no new physical entities, particles, or forces. The free parameters are standard geometric model parameters fitted to data. The axioms are domain assumptions standard in TNO occultation analysis, though the pole alignment and hydrostatic equilibrium assumptions are load-bearing for the central claim.

free parameters (4)
  • σ_model = 2 km
    Systematic uncertainty floor iteratively estimated to force χ²_pdf close to 1. Acts as an empirical weighting factor across the observation network.
  • a, b (equatorial semi-axes) = 566.1 km
    Fitted via MCMC to occultation chord data. Constrained to a=b for oblate model.
  • c (polar semi-axis) = 511.2 km
    Fitted via MCMC to occultation chord data.
  • f_i, g_i (projected centers) = varies per event
    70 local parameters (2 per occultation event) for the projected center of the ellipsoid on the tangent plane for each of 36 events.
axioms (4)
  • domain assumption Quaoar's rotational pole is aligned with its ring pole (α_Q = α_QR = 259.82°, δ_Q = δ_QR = 53.45°)
    Section 3.2: 'we first assumed that Quaoar's pole orientation is aligned with that of its rings.' The paper confirms the occultation data alone do not independently constrain the pole.
  • domain assumption Quaoar is in hydrostatic equilibrium and thus takes the shape of a Maclaurin spheroid
    Section 3.2: 'it is reasonable to assume that it is in hydrostatic equilibrium, and the simplest equilibrium figure is that of an oblate spheroid.' This is the model assumption that the data are fitted to.
  • domain assumption Quaoar's rotation period is 8.8394±0.0002 hours (single-peaked)
    Section 4: Uses Ortiz et al. (2003) single-peaked period for Maclaurin density calculation. The double-peaked alternative (17.6788h, triaxial) is acknowledged but not adopted.
  • domain assumption Thermal profile T(r) for atmosphere modeling: surface T=42K, gradient 5.7 K/km, isothermal at 102K above 10km
    Section 3.3: Uses the same thermal profile as Braga-Ribas et al. (2013) and Morgado et al. (2022) for the atmospheric upper limit calculation.

pith-pipeline@v1.1.0-glm · 49950 in / 3097 out tokens · 454922 ms · 2026-07-08T05:11:49.246869+00:00 · methodology

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Works this paper leans on

48 extracted references · 48 canonical work pages · 1 internal anchor

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