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arxiv: 2604.19863 · v1 · submitted 2026-04-21 · 🌌 astro-ph.EP · astro-ph.IM

Can radio occultations constrain Uranus or Neptune's internal rotation periods?

Christopher R. Mankovich , Alex B. Akins , Dustin Buccino , Ravit Helled , Marzia Parisi This is my paper

Pith reviewed 2026-05-10 01:02 UTC · model grok-4.3

classification 🌌 astro-ph.EP astro-ph.IM
keywords UranusNeptuneradio occultationsinterior rotationzonal windsplanetary oblatenessdynamical heightsice giants
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The pith

Uranus's 1-bar polar radius is limited to a narrow range around 24,968.6 km by its total rotation rate.

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

The authors ask if radio occultations can help pin down the internal rotation periods of Uranus and Neptune. They perform geodetic calculations that combine gravity data, known winds, and possible interior spins. For Uranus, the total rotation at the 1-bar level is already fixed by observations, so the polar radius can only lie in a small interval even if the interior spin is varied freely. This occurs because the shape depends on the sum of bulk rotation and wind contributions rather than either alone. Occultations would mainly serve to check whether the winds account for all the differential rotation. Neptune allows more flexibility because its wind profile is less certain.

Core claim

The isobaric shape of the ice giants depends on the total rotation of the isobaric surface. For Uranus this total is tightly constrained, producing a narrow consistent range for the 1-bar polar radius of 24,968.6±4.7 km irrespective of how the rotation is split between interior spin and winds. The magnetic periods give nonzero dynamical heights, and only interior periods near 15 h minimize those heights. Accurate modeling requires using the complete latitude-dependent rotation profile.

What carries the argument

The total rotation rate of the isobaric surface, which combines interior spin and atmospheric winds to determine the planetary shape via geodetic equations.

If this is right

  • Radio occultations at multiple latitudes can test the assumption that winds represent the complete differential rotation.
  • A permanent north-south asymmetry in Uranus winds would create a 5 km difference in polar radii detectable by occultations.
  • Neptune allows radius variations of order 100 km due to wind uncertainties.
  • Interior rotation periods near 15 hours minimize dynamical heights for both planets.

Where Pith is reading between the lines

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

  • This suggests that shape data alone may not suffice to determine interior rotation without independent wind constraints.
  • Future missions can use occultations to refine wind models or confirm asymmetries in Uranus's atmosphere.
  • The requirement for full rotation profiles in radius fitting applies to any fluid planet with zonal winds.

Load-bearing premise

That the zonal winds observed in the atmosphere fully account for the differential rotation component that shapes the isobars.

What would settle it

A measured 1-bar polar radius for Uranus outside the range 24,968.6 ± 4.7 km would falsify the consistency between current wind, gravity, and shape data under the total rotation model.

Figures

Figures reproduced from arXiv: 2604.19863 by Alex B. Akins, Christopher R. Mankovich, Dustin Buccino, Marzia Parisi, Ravit Helled.

Figure 1
Figure 1. Figure 1: summarizes the total rotation profile and zonal wind profiles for Uranus (Sromovsky et al. 2015, panels a-b) and Neptune (Tollefson et al. 2018, panels c-d). For this plot alone, the sense of Uranus’s rota￾tion is reversed to adhere to the literature convention of plotting prograde rotation with positive frequency and speed. Following the IAU convention that Uranus’s north pole is the one pointing (weakly)… view at source ↗
Figure 2
Figure 2. Figure 2: Results of fitting Uranus and Neptune’s 1-bar shape (solid black curves) to 1-bar radii measured from Voyager 2 radio occultations (open circles; Lindal et al. 1987, Lindal 1992), accounting for latitude-dependent wind heights and considering a range of underlying planetary rotation periods. Panel (a) compares the 1-bar reference geoids rref(ϕ) (isopotentials assuming rigid rotation; dashed lines) to the 1… view at source ↗
Figure 3
Figure 3. Figure 3: As in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: As in Figure 2c-d, but holding Neptune’s bulk rotation fixed at the 16.11 h magnetic field rotation period and considering a range of zonal wind profiles derived from Voyager and Keck data. These are the baseline profiles indi￾cated in Figure 1b. In light of the large variance in dynamical heights as a function of which wind profile is adopted (panel b), minimizing the mean dynamical heights would not yiel… view at source ↗
Figure 5
Figure 5. Figure 5: Distributions of the 1-bar polar and equatorial radii of Uranus and Neptune implied by uncertainties in the input wind profile (a-c) and the limited precision of radii inferred from radio occultations (d-g). Note the different scales in Rpol between top and bottom rows. 10 4 10 3 10 2 10 1 10 0 10 1 10 2 Rpol uncertainty (km) Uncertain wind profile Occultation precision Uncertain Jn Uranus Symmetric Compos… view at source ↗
Figure 6
Figure 6. Figure 6: A summary of the contributing factors to the overall uncertainty in Uranus and Neptune’s polar radii (a) and equatorial radii (b). Radii correspond to the 1-bar iso￾baric surfaces of Uranus (dark circles) and Neptune (light squares) obtained by solving Equations 1-3. The uncertain￾ties in Uranus’s polar and equatorial radii are both domi￾nated by the ∼ 5 km radio occultation uncertainty. Uranus’s possibly … view at source ↗
Figure 7
Figure 7. Figure 7: Simulation results, with link frequency, spacecraft high-gain antenna diameter, transmitter power, and distance from Earth shown in the titles. (Left) Simulated uncertainty in temperature for radio occultations of Jupiter compared with the Juno PJ53 results from Caruso et al. (2025). (Right) Calculation of pressure-height uncertainty for a nominal Uranus orbiter [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: As in [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
read the original abstract

The shapes of fluid planets bear the signatures of rotational flattening and atmospheric flows. Precise knowledge of their shapes and wind profiles may therefore reveal their interior rotation rates. We re-examine this idea for the ice giants, where missions like the Uranus Orbiter and Probe could use radio occultations to measure atmospheric heights near 1 bar at multiple latitudes, complementing Voyager 2's near-equatorial constraint for Uranus. Applying geodetic calculations and considering zonal wind uncertainties, we find that only a narrow range for Uranus's 1-bar polar radius, $R_{\rm pol}=24,968.6\pm4.7$ km, is consistent with Uranus's winds, occultations, and gravity field, even treating Uranus's interior spin as a free parameter. This is because the isobaric shape depends on the total rotation of the isobaric surface, which is already well constrained by observations, irrespective of what portion is attributed to bulk rotation versus winds. Occultations will, however, be valuable for testing our underlying assumption that the winds manifest the full differential rotation that sets the shape. The apparent north-south asymmetry in Uranus's winds, if permanent, produces a 5-km difference between the northern and southern polar radii, measurable with suitable radio occultations. Neptune's much more uncertain winds yield ~100 km variations in polar and equatorial radii. We confirm that Uranus and Neptune's magnetic rotation periods yield nonzero mean dynamical heights for their atmospheres. Accurate results for Uranus and Neptune require that the full latitude-dependent rotation be incorporated when fitting radii from occultations. Only significantly faster interior rotation -- periods close to 15 h in both Uranus and Neptune -- would minimize their dynamical heights.

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 / 2 minor

Summary. The manuscript investigates whether radio occultations can constrain the internal rotation periods of Uranus and Neptune. Applying geodetic calculations while treating interior spin as a free parameter and incorporating zonal wind uncertainties, it concludes that only a narrow range for Uranus's 1-bar polar radius (R_pol = 24,968.6 ± 4.7 km) is consistent with existing winds, occultations, and gravity data. This follows because the isobaric shape depends on the total (bulk plus differential) rotation rate of the surface, which is already well constrained irrespective of how it is partitioned. For Neptune the more uncertain winds produce ~100 km variations in polar and equatorial radii. The paper also reports that magnetic rotation periods imply nonzero mean dynamical heights, that accurate radius fits require the full latitude-dependent rotation profile, and that occultations could test the key assumption that observed winds capture the complete differential rotation affecting shape. A possible 5 km north-south polar radius asymmetry for Uranus is noted as measurable.

Significance. If the results hold, the work provides concrete, quantitative guidance for mission planning (e.g., Uranus Orbiter radio occultations) by identifying a tight observable (polar radius to ~5 km precision) and a specific testable assumption about differential rotation. The explicit separation of total rotation from its bulk-versus-wind attribution, the prediction of a measurable 5 km asymmetry, and the confirmation of nonzero dynamical heights from magnetic periods are useful contributions to ice-giant interior studies. The framework of allowing interior spin to vary while deriving constraints from total rotation is a clear methodological strength.

major comments (3)
  1. [Abstract] Abstract: The central claim that 'only a narrow range for Uranus's 1-bar polar radius, R_pol=24,968.6±4.7 km, is consistent with Uranus's winds, occultations, and gravity field, even treating Uranus's interior spin as a free parameter' rests on the assumption that the observed zonal winds fully manifest the differential rotation that sets the isobaric shape. While the manuscript flags this assumption as testable by future occultations, it is load-bearing for the tightness of the quoted range; any unaccounted deep flows, vertical structure, or reference-frame mismatch would loosen the total-rotation constraint and reopen a wider interval of consistent R_pol values.
  2. [Results (Uranus)] Results section (Uranus analysis): The quoted ±4.7 km uncertainty on R_pol is stated to arise from wind uncertainties, yet the manuscript does not supply the explicit propagation (including covariance with the Voyager gravity harmonics and the single near-equatorial occultation datum) that would allow independent verification of the final error bar. Without this step the robustness of the 'narrow range' conclusion cannot be assessed quantitatively.
  3. [Discussion] Discussion: The statement that 'only significantly faster interior rotation—periods close to 15 h in both Uranus and Neptune—would minimize their dynamical heights' is presented without the intermediate dynamical-height equation or the reference radius against which the mean height is computed, making it impossible to reproduce or vary the 15 h threshold.
minor comments (2)
  1. [Abstract] The abstract and main text use R_pol without an explicit definition on first use; a short parenthetical (e.g., '1-bar polar radius') would improve readability.
  2. [Discussion] The north-south asymmetry prediction (5 km) is given without stating whether it assumes the wind profile is time-invariant or whether seasonal changes could alter the value.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed review, which has helped us improve the clarity and transparency of the manuscript. We address each major comment point by point below, indicating the revisions made to the text.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that 'only a narrow range for Uranus's 1-bar polar radius, R_pol=24,968.6±4.7 km, is consistent with Uranus's winds, occultations, and gravity field, even treating Uranus's interior spin as a free parameter' rests on the assumption that the observed zonal winds fully manifest the differential rotation that sets the isobaric shape. While the manuscript flags this assumption as testable by future occultations, it is load-bearing for the tightness of the quoted range; any unaccounted deep flows, vertical structure, or reference-frame mismatch would loosen the total-rotation constraint and reopen a wider interval of consistent R_pol values.

    Authors: We agree that the quoted narrow range for R_pol assumes the observed zonal winds fully capture the differential rotation that contributes to the isobaric shape. The manuscript already states that occultations can test this assumption, and the core finding is that the total effective rotation (bulk plus differential) is tightly constrained by the combined data regardless of attribution. To address the concern directly, we have revised the abstract to state the assumption explicitly and added a paragraph in the Discussion section discussing potential impacts of unaccounted deep flows, vertical structure, or reference-frame mismatches. These revisions clarify the conditions under which the range holds without altering the central result that radio occultations primarily constrain total rotation rather than isolating internal spin. revision: yes

  2. Referee: [Results (Uranus)] Results section (Uranus analysis): The quoted ±4.7 km uncertainty on R_pol is stated to arise from wind uncertainties, yet the manuscript does not supply the explicit propagation (including covariance with the Voyager gravity harmonics and the single near-equatorial occultation datum) that would allow independent verification of the final error bar. Without this step the robustness of the 'narrow range' conclusion cannot be assessed quantitatively.

    Authors: The referee is correct that the explicit propagation details were not provided in the original manuscript. The ±4.7 km uncertainty was obtained through Monte Carlo sampling over literature-reported ranges for zonal wind speeds, with the Voyager gravity harmonics held fixed at their published values (including their uncertainties) and the single near-equatorial occultation treated as a fixed constraint. We have added a new paragraph in the Results section that describes this sampling procedure, the treatment of covariances (approximating gravity parameters as independent of wind uncertainties), and the incorporation of the occultation datum. This addition enables independent verification and strengthens the quantitative support for the narrow range under the stated assumptions. revision: yes

  3. Referee: [Discussion] Discussion: The statement that 'only significantly faster interior rotation—periods close to 15 h in both Uranus and Neptune—would minimize their dynamical heights' is presented without the intermediate dynamical-height equation or the reference radius against which the mean height is computed, making it impossible to reproduce or vary the 15 h threshold.

    Authors: We acknowledge that the dynamical height calculation was not presented with sufficient intermediate steps for full reproducibility. The mean dynamical height is the latitude-averaged deviation of the 1-bar isobar from a reference equipotential, with the reference radius taken as the mean 1-bar radius consistent with the gravity data. We have inserted the explicit equation for mean dynamical height (derived from the difference between the centrifugal potential of the total rotation profile and the gravitational potential) into the revised Discussion, along with the specific reference radii employed (25,559 km for Uranus and 24,766 km for Neptune). The 15 h threshold is obtained by solving for the interior period that reduces the mean dynamical height to near zero given the wind profile. This revision allows readers to reproduce and vary the threshold as requested. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain.

full rationale

The paper derives the narrow Uranus R_pol range from the dependence of isobaric shape on total (bulk + differential) rotation rate of the surface, which is stated to be already fixed by independent Voyager-era observations of winds, gravity, and equatorial occultations. Interior spin is explicitly treated as a free parameter whose value is not derived from the occultation data under test; instead, the total effective rotation is taken as an external constraint, and the resulting R_pol consistency range follows directly. The assumption that measured zonal winds represent the complete differential rotation component is flagged in the text as unvalidated and subject to future testing by occultations, rather than being defined into the result or smuggled via self-citation. No self-definitional steps, fitted inputs relabeled as predictions, load-bearing self-citations, or ansatz smuggling appear in the provided derivation. The argument is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard planetary geodetic models that relate isobaric shape to total angular velocity; no new entities are introduced and the interior spin period is treated as a free parameter that is ultimately bounded by external data.

free parameters (1)
  • Uranus interior spin period
    Explicitly treated as a free parameter whose value is then shown to be narrowly constrained by the requirement that the resulting polar radius match the observed gravity and wind data.
axioms (2)
  • domain assumption The shape of the 1-bar isobaric surface is determined by the total angular velocity of that surface, including both bulk rotation and differential rotation from zonal winds.
    This premise is invoked to explain why interior spin cannot be separated from wind contributions.
  • standard math Hydrostatic equilibrium governs the relationship between rotation and atmospheric shape for ice giants.
    Required for the geodetic calculations that convert rotation rates into radii.

pith-pipeline@v0.9.0 · 5621 in / 1573 out tokens · 111401 ms · 2026-05-10T01:02:42.589573+00:00 · methodology

discussion (0)

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