Size, Shape, and Geometric Albedo of Dwarf Planet Quaoar's Largest Satellite Weywot

The gist Weywot’s volume-equivalent radius to be req = 73 ± 5 km, with principal axes a = 82+5−3, b = 73+5−3, c = 65+8−12 km, indicating a triaxial shape

Size and Shape Determination

The study focused on Quaoar’s small primary satellite Weywot to determine its size, shape, and geometric albedo. Weywot’s rotational lightcurve was constrained along with its independent photometric phase curve, which was used to obtain more robust measurements of Weywot’s size, shape, and geometric albedo. The resulting volume-equivalent radius for Weywot is req = 73 ± 5 km. This triaxial shape is consistent with a Roche-ellipsoid rubble-pile interpretation requiring only moderate internal friction at Weywot’s current semimajor axis, and Weywot can retain this shape down to Quaoar’s co-rotation radius. The derived 3D shape parameters are: Long axis (km) a = 82+5−3, Intermediate axis (km) b = 73+5−3, Polar axis (km) c = 65+8−12 km. The ratio of the intermediate axis to the long axis is b/a = 0.88 ± 0.04.

Surface Properties and Formation Interpretation

Weywot’s geometric albedo was found to be quite low, pV = 0.036+0.010−- - - ◦, akin to that of Eris’s satellite Dysnomia, but over an order of magnitude lower than Pluto’s minor satellites and Haumea’s satellites. This suggests that Weywot’s ice-mass fraction fice < 100%, and that Weywot is not sourced from the water-ice mantle of a differentiated pre-impact progenitor as suggested for Pluto’s minor satellites and Haumea’s satellites. The low geometric albedo and H2O spectral type support previous work that associated the H2O spectral type with relatively darker surfaces. The dichotomy between Weywot’s dark surface (pV ≤ 0.05) and Quaoar’s surface (pV = 0.124 ± 0.006) may represent different bulk ice-mass fractions fice < 100%.

Rotational Dynamics and Tidal State

The analysis of Weywot’s rotational lightcurve supports the assumption that Weywot’s spin is synchronized with its orbit, as evidenced by the lightcurve being nearly inphase with its angular separation from Quaoar. The timescale for Weywot’s spin to synchronize with its orbit as the result of tidal torques was estimated to be < 150 Myr. This implies that it is safe to assume Weywot’s spin to be synchronized with the orbit period of Pf ≃ 12.43 days. The derived lightcurve parameters are used in Section 4.2 to derive Weywot’s 3D shape, which was measured to be moderately prolate and significantly oblate, with an intermediate axis ratio b/a = 0.88 ± 0.04 and polar axis ratio c/a = 0.78+ - - -.

Mass Constraints and Ring System Influence

An upper limit to Weywot’s mass was derived to be 5.0×1018 kg, much lower than previous results. This small mass for Weywot further weakens the hypothesis that it induces bending waves in the outer ring due to its inclination relative to the ring system (∼ 5◦). The nominal solution for Weywot’s shape is inconsistent with a fluid Roche equilibrium figure at Weywot’s current semimajor axis, implying Weywot’s interior resists self-gravity’s attempt to make its shape that of a fluid Roche ellipsoid. Under the assumption that Weywot is a rubble-pile satellite potentially formed out of circum-Quaoar material, such that it has no tensile strength, internal friction between aggregates allows it to access a wider variety of triaxial ellipsoidal shapes.

Conclusion on Origin

Weywot likely formed as the result of a massive collision in Quaoar’s past, potentially forming from the same material making up the ring system. Alternatively, Weywot may be the source of ring material. The low geometric albedo and measured phase curve reinforce this dichotomy between the surfaces of Quaoar and Weywot. Weywot’s low albedo and H2O spectral type support previous work that associated the H2O spectral type with relatively darker surfaces. This suggests Weywot may have formed from the debris of an undifferentiated dwarf-planet progenitor, or is a surviving collisional fragment of a smaller TNO whose surface was depleted in volatiles.

Summary

The paper uses 11 orbits of Hubble Space Telescope data to constrain the size, 3D shape and geometric albedo of Quaoar’s largest satellite Weywot. Weywot likely formed as the result of a massive collision in Quaoar’s past, potentially forming from the same material making up the ring system. The timescale for Weywot’s spin to synchronize with its orbit as the result of tidal torques was estimated to be < 150 Myr. Weywot’s lightcurve also oscillates in-phase with its apparent angular separation from Quaoar, supporting synchronous rotation as well as a triaxial shape for Weywot. The derived 3D shape parameters are: Long axis (km) a = 82+5−3, Intermediate axis (km) b = 73+5−3, Polar axis (km) c = 65+8−12 km. The volume-equivalent radius was estimated to be req = 73 ± 5 km. An upper limit to Weywot’s mass was derived to be 5.0×1018 kg. The low geometric albedo of Weywot, pV = 0.036+ - - -, places Weywot’s surface among the darkest known for TNOs. This suggests Weywot’s ice-mass fraction fice < 100%, and that Weywot is not sourced from the water-ice mantle of a differentiated pre-impact progenitor as suggested for Pluto’s minor satellites and Haumea’s satellites. Weywot may have formed from the debris of an undifferentiated dwarf-planet progenitor, or is a surviving collisional fragment of a smaller TNO whose surface was depleted in volatiles. The paper provides new constraints on Weywot’s tidal state and 3D shape through lightcurve and occultation analysis.

How it works

The researchers built upon previous work by re-analyzing the June 2023 stellar occultation by Weywot using results from 11 orbits of HST imaging with the Wide Field Camera 3. They constrained Weywot’s rotational lightcurve along with its independent photometric phase curve, which they used to obtain more robust measurements of Weywot’s size, shape, and geometric albedo. To improve photometry, they created residual background frames by combining residual frames from Quaoar-removed frames where no contaminating sources were nearby. They employed the ‘Popand-Drop’ method of PSF resampling to test whether Weywot’s measured flux variations were only due to imperfect PSF subtraction. This process allowed them to determine in which regions their PSF photometry methods could be trusted.

Lightcurve Modeling and Shape Derivation

The lightcurve model for Weywot was based on a simple sinusoid, assuming a linear relationship between reduced magnitude and phase angle. The two lightcurve models were Eqs. 7 and 10, where Eq. 7 is nested in Eq. 10. This indicates that Weywot’s shape is prolate, though the small lightcurve amplitude measured at an aspect angle of ψ = - - - rules out Weywot being a contact binary. The occultation analysis used occult3d to derive triaxial ellipsoid shape models by combining occultations, lightcurves, and other external constraints. The best fit shape model provides excellent agreement with the reported chords during the June 2023 occultation (Figure 4).

Photometric Conversion

The V-band geometric albedo of Weywot was updated using the formula pV = 10- - - R squared / (HV −V⊙), where R is in units of au and V⊙ = -26.74 mag. The rotationally averaged absolute magnitude is HV = 8.484 ± 0.042 mag. This calculation yielded pV = 0.

1. The AI system can now accurately constrain a body's physical properties by fitting observed photometric data to a lightcurve model, as demonstrated by Weywot’s rotational lightcurve was constrained along with its independent photometric phase curve, which we used to obtain more robust measurements of Weywot’s size, shape, and geometric albedo. This allows for the determination of parameters like req = 73 ± 5 km and the triaxial shape axes a = 82+5 −3, b = 73+5 −3, c = 65+8 −12 km.

2. The system can distinguish between different formation scenarios for small satellites by analyzing surface properties, as it "propose[s] this may indicate that Weywot’s ice-mass fraction fice < 100%, and that Weywot is not sourced from the water-ice mantle of a differentiated pre-impact progenitor as suggested for Pluto’s minor satellites and Haumea’s satellites. It can also quantify this by comparing the geometric albedo, noting Weywot’s low geometric albedo to be quite low, pV = 0.036+0.010 −0.006."

3. The AI system can perform Bayesian inference on complex observational data to determine physical states, such as spin synchronization and shape models, by employing MCMC sampling to constrain Weywot’s rotational lightcurve from the resolved HST observations. This enables the determination that Weywot’s 3D shape was measured to be moderately prolate and significantly oblate, with an intermediate axis ratio b/a = 0.88 ± 0.04 and polar axis ratio c/a = 0.78+0.08 −0.13.

4. The system can evaluate the dynamical relevance of potential satellite influences on ring systems, as it can derive an upper bound on Weywot’s mass using our shape model, yielding a value of 5.0 × 1018 kg, which is used to assess the effect of Weywot on Quaoar’s ring system.

5. The AI system can infer internal structure characteristics based on external constraints, as it can conclude that Weywot’s triaxial shape at its current semimajor axis can be explained by a moderate internal friction angle of 5−10◦, and thus is fully consistent with the rubble pile interpretation.

The small satellites of dwarf-planet size worlds in trans-Neptunian space are thought to be produced through giant impacts, and are typically observed to have bright water-ice-dominated surfaces. Here we focus on Quaoar's small primary satellite, Weywot. We build on previous work by re-analyzing the June 2023 stellar occultation by Weywot using results from 11 orbits of HST imaging with the Wide Field Camera 3. Weywot's rotational lightcurve was constrained along with its independent photometric phase curve, which we used to obtain more robust measurements of Weywot's size, shape, and geometric albedo. We found Weywot's volume-equivalent radius to be req = 73+-5 km, with principal axes a = 82+5-3 , b = 73+5-3, c = 65+8-12 km, indicating a triaxial shape. This shape is consistent with a Roche-ellipsoid rubble-pile interpretation requiring only moderate internal friction at Weywot's current semimajor axis, and Weywot can retain this shape down to Quaoar's co-rotation radius. We also found Weywot's geometric albedo to be quite low, pV = 0.036+0.010-0.006, akin to that of Eris's satellite Dysnomia, but over an order of magnitude lower than Pluto's minor satellites and Haumea's satellites. We propose this may indicate that Weywot's ice-mass fraction < 100%, and that Weywot is not sourced from the water-ice mantle of a differentiated pre-impact progenitor as suggested for Pluto's minor satellites and Haumea's satellites.