Constraining the size, shape, and albedo of the large Trans-Neptunian Object (28978) Ixion with multi-chord stellar occultations

1. Problem Statement

Trans-Neptunian Objects (TNOs) are primitive remnants of the early Solar System, yet determining their precise physical properties (size, shape, albedo, and surface composition) remains challenging due to their vast distances. While thermal radiometry and single-chord stellar occultations have provided estimates for (28978) Ixion, a large Plutino, previous measurements suffered from large uncertainties or relied on assumptions (e.g., circular limbs) that limited the accuracy of derived diameters and albedos. Specifically, a 2021 study provided a precise diameter but assumed a circular limb, ignoring potential shape irregularities. There is a critical need for multi-chord stellar occultation data to:

• Accurately reconstruct the projected shape and size of Ixion.
• Derive a precise geometric albedo ($p_V$) by combining size with absolute magnitude ($H_V$).
• Search for atmospheric signatures or circum-object material (rings).
• Refine the astrometric position of Ixion to improve future ephemerides.

2. Methodology

The study utilized the Lucky Star collaboration to conduct a series of stellar occultation campaigns between 2020 and 2023.

• Observational Campaigns: The team organized observations across eight distinct occultation events involving 51 observations from 8 events, yielding 30 positive detections (chords) and several negative chords. Observations were conducted using a mix of professional facilities (e.g., 4.1m SOAR, 1.54m Danish, 4.3m Lowell Discovery Telescope) and amateur telescopes (20–40 cm apertures).
• Prediction and Astrometry: Predictions were generated using the NIMA (Numerical Integration of the Motion of an Asteroid) algorithm, incorporating Gaia DR3 stellar coordinates and updated orbital solutions for Ixion to achieve sub-milliarcsecond precision.
• Data Reduction:
  • Light curves were generated using the Occultation Portal and cross-verified with the PRAIA software.
  • SORA (Stellar Occultation Reduction Analysis) was used to model the light curves, accounting for Fresnel diffraction, finite stellar angular size, integration time, and CCD bandwidth.
  • Ingress and egress timings were extracted to define the limb chords.
• Shape Modeling:
  • A Global Limb Fit was performed using a Monte Carlo approach. The limb was modeled as a single projected ellipse defined by semi-axes ($a, b$) and position angle ($\phi$).
  • To prevent ephemeris biases, the astrometric center for each event was optimized independently (Per-Event Center Minimization), while the global shape parameters were fitted simultaneously.
  • Negative chords (non-detections) were incorporated to constrain the limb geometry further.
• Photometric Analysis: Archival photometric data (NTT/EMMI, VLT/FORS1, Gaia DR3) were analyzed to determine the absolute magnitude ($H_V$), phase curve slope ($\beta$), and broadband colors ($B-V, V-R, R-I$). These were combined with the occultation-derived size to calculate the geometric albedo.

3. Key Contributions

• First Multi-Chord Global Shape Constraint: This is the first study to provide a global, multi-epoch reconstruction of Ixion's projected shape using a dense network of multi-chord occultations, moving beyond single-event or single-chord assumptions.
• Precise Stellar Diameter Measurement: The study provided a rare, direct measurement of the angular diameter of the occulted star Gaia DR3 4056440205544338944 (a mid-M giant), resolving discrepancies between occultation data and Gaia's automated stellar parameter estimates.
• Comprehensive Albedo Determination: By combining the new, precise size measurement with updated photometry, the authors derived a robust geometric albedo, resolving previous ambiguities regarding Ixion's surface brightness.
• Atmospheric and Ring Constraints: The study set stringent upper limits on the presence of rings or atmospheres around Ixion.

4. Key Results

Physical Dimensions and Shape

• Projected Shape: Ixion is well-represented by a slightly elongated projected ellipse.
  • Semi-major axis ($a$): $363.42^{+3.53}_{-3.85}$ km
  • Semi-minor axis ($b$): $333.98^{+7.07}_{-4.96}$ km
  • Equivalent Diameter ($D_{equiv}$): $696.78^{+10.75}_{-8.87}$ km (Radius $R_{equiv} \approx 348.4$ km).
• Oblateness: The apparent oblateness is $\epsilon' = 0.081^{+0.004}_{-0.010}$, indicating a moderately flattened, nearly spheroidal body.
• Stability: Radial residuals of $\sim 10$ km suggest a largely stable shape across the observed epochs, though slight epoch-dependent variations hint at a mildly triaxial figure or surface heterogeneity.

Photometry and Albedo

• Absolute Magnitude: $H_V = 3.845 \pm 0.006$ mag.
• Phase Curve: Slope $\beta = 0.1301 \pm 0.0078$ mag deg$^{-1}$.
• Geometric Albedo: $p_V = 0.106^{+0.003}_{-0.003}$. This confirms Ixion is one of the brighter Plutinos, with a surface slightly darker than previously estimated but consistent with the "bright-red" TNO population.
• Colors: $B-V = 1.06 \pm 0.03$, $V-R = 0.61 \pm 0.02$, $R-I = 0.54 \pm 0.03$, consistent with moderately red surfaces typical of TNOs.

Stellar Occultation Specifics

• Stellar Diameter: The occulted star (Gaia DR3 4056440205544338944) has an angular diameter of $\theta_\star = 0.670 \pm 0.010$ mas, corresponding to a physical radius of $128 \pm 10 R_\odot$.
  • Significance: This value contradicts the "best" Gaia DR3 solution (OB-library, $\sim 56 R_\odot$) but aligns with the MARCS-library solution ($\sim 116 R_\odot$), highlighting issues with automatic library selection in Gaia's GSP-Phot module for cool giants.
• Atmosphere/Rings: No evidence of an atmosphere or circum-object material (rings) was detected down to sensitivity limits (opaque structures $> \sim$ few hundred meters; optical depth $\tau > 0.1$ at km scales).

Astrometry

• Eight high-precision astrometric positions were derived with sub-milliarcsecond accuracy, providing critical data for refining Ixion's orbit and improving future occultation predictions.

5. Significance

This work significantly advances the understanding of (28978) Ixion, a key target for comparative planetology among Plutinos.

1. Physical Characterization: It establishes Ixion as a moderately flattened, spheroidal body with a diameter of $\sim 700$ km and a moderate albedo, placing it firmly in the category of large, differentiated TNOs.
2. Methodological Validation: The study demonstrates the power of multi-chord occultations to resolve shape ambiguities that single-chord or thermal data cannot, and to independently validate stellar parameters derived from space missions like Gaia.
3. Dynamical Context: The refined astrometry aids in understanding the dynamical evolution of the Kuiper Belt and Neptune's migration history, as Ixion is locked in a 3:2 resonance with Neptune.
4. Negative Constraints: The absence of detected rings or an atmosphere provides a crucial baseline for comparative studies of ring systems in the outer Solar System (e.g., contrasting with Chariklo, Haumea, and Quaoar).

The paper concludes that while Ixion's global shape is well-constrained, future work requires improved photometric coverage to determine its rotation period and 3D shape more precisely.