Abstract We study the relationship of zonal gravity coefficients, J 2 n , zonal winds, and axial moment of inertia (MoI) by constructing models for the interiors of giant planets. We employ the nonperturbative concentric Maclaurin spheroid method to construct both physical (realistic equation of state and barotropes) and abstract (small number of constant-density spheroids) interior models. We find that accurate gravity measurements of Jupiter’s and Saturn’s J 2 , J 4 , and J 6 by the Juno and Cassini spacecraft do not uniquely determine the MoI of either planet but do constrain it to better than 1%. Zonal winds (or differential rotation (DR)) then emerge as the leading source of uncertainty. For Saturn they are predicted to decrease the MoI by 0.4% because they reach a depth of ∼9000 km, while on Jupiter they appear to reach only ∼3000 km. We thus predict DR to affect Jupiter’s MoI by only 0.01%, too small by one order of magnitude to be detectable by the Juno spacecraft. We find that winds primarily affect the MoI indirectly via the gravity harmonic J 6 , while direct contributions are much smaller because the effects of pro- and retrograde winds cancel. DR contributes +6% and −0.8% to Saturn’s and Jupiter’s J 6 value, respectively. This changes the J 6 contribution that comes from the uniformly rotating bulk of the planet that correlates most strongly with the predicted MoI. With our physical models, we predict Jupiter’s MoI to be 0.26393 ± 0.00001. For Saturn, we predict 0.2181 ± 0.0002, assuming a rotation period of 10:33:34 hr that matches the observed polar radius.
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The Promise and Limitations of Precision Gravity: Application to the Interior Structure of Uranus and Neptune
We study the constraining power of a high-precision measurement of the gravity field for Uranus and Neptune, as could be delivered by a low-periapse orbiter. Our study is practical, assessing the possible deliverables and limitations of such a mission with respect to the structure of the planets. Our study is also academic, assessing in a general way the relative importance of the low-order gravity, high-order gravity, rotation rate, and moment of inertia (MOI) in constraining planetary structure. We attempt to explore all possible interior density structures of a planet that are consistent with hypothetical gravity data via MCMC sampling of parameterized density profiles. When the gravity field is poorly known, as it is today, uncertainties in the rotation rate on the order of 10 minutes are unimportant, as they are interchangeable with uncertainties in the gravity coefficients. By the same token, when the gravity field is precisely determined, the rotation rate must be known to comparable precision. When gravity and rotation are well known, the MOI becomes well constrained, limiting the usefulness of independent MOI determinations unless they are extraordinarily precise. For Uranus and Neptune, density profiles can be well constrained. However, the nonuniqueness of the relative roles of H/He, watery volatiles, and rock in the deep interior will still persist with high-precision gravity data. Nevertheless, the locations and magnitudes (in pressure space) of any large-scale composition gradient regions can likely be identified, offering a crucially better picture of the interiors of Uranus or Neptune.
more » « less- Award ID(s):
- 1908615
- NSF-PAR ID:
- 10484961
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Planetary Science Journal
- Volume:
- 3
- Issue:
- 4
- ISSN:
- 2632-3338
- Format(s):
- Medium: X Size: Article No. 88
- Size(s):
- ["Article No. 88"]
- Sponsoring Org:
- National Science Foundation
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Abstract The contrasting internal luminosity of Uranus and Neptune present a challenge to our understanding of the origin and evolution of these bodies, as well as extra-solar ice giants. The thermal evolution of Neptune is known to be nearly consistent with an entirely fluid interior, but this is not a unique solution, and does not account for the tidal dissipation required by the migration of its moons. We examine a model that has been previously shown to explain the thermal and tidal evolution of Uranus: one that features a growing, frozen core. The core traps heat in the interior, affecting the cooling time scale, and provides a source of tidal dissipation. We review the growing, frozen core model, and the computation of thermal and tidal evolution. We then apply this model to Neptune. We find that the growing frozen core model can account for the observed internal luminosity of Neptune and the migration of its moons, in the form of resonances that were either encountered or avoided in the past. We discuss prospects for observational tests of the growing frozen core model and possible implications for understanding the gas giants.
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There are no existing experimental studies of flame spread rate trends for ultra-thin solid samples. Previous theory has predicted that for concurrent flame in kinetic regime, the flame spread rate decreases as the sample thickness decreases and there is a critical thickness below which burning is not possible. To test this hypothesis, a series of microgravity experiments of concurrent-flow flame spread over samples of ultra-low area densities are conducted using NASA Glenn Research Center’s Zero Gravity Research Facility (the 5.18 s drop tower). The tested samples are cellulose-based materials of various area densities, ranging from 0.2 mg/cm2 to 13 mg/cm2, as low as one order of magnitude less than those ever tested before. Each sample is 30 cm long by 5 cm wide and is burned in a low-speed concurrent air flow (5 to 30 cm/s). The results show that the concurrent flame spread rate is proportional to the flow velocity relative to the flame and is inversely proportional to the sample area density. A theoretical formulation, provided in this work, suggests that the flame length has a linear relationship with the relative flow speed and has no direct dependency on the sample area density. The experimental data supports this conclusion. From the images recorded in the experiments, a unique flame base tubular structure directed upstream away from the burnout zone is observed for thin samples. This structure is suspected to be due to flame stretching and localized blowoff caused by the oxidative pyrolysis Stefan flows at the sample burnout. This can be an indication that the chemical time becomes comparable to the flow time of the Stefan flow and the tested samples are approaching the kinetically-limited thickness. For the thinnest tested sample (0.2 mg/cm2), flames with concurrent and opposed dual natures are observed when the air flow rate is low (< 20 cm/s). At the lowest tested flow rate (5 cm/s), the flame spread rate exceeds the air flow rate and the flame transits to an opposed flame in the concurrent flow. The dual nature and flame transition are presented and discussed. This study provides detailed examination through high-resolution images of the transition between the concurrent to opposed flame spread modes.more » « less
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Aims. We present a detailed visible and near-infrared spectro-interferometric analysis of the Be-shell star o Aquarii from quasi-contemporaneous CHARA/VEGA and VLTI/AMBER observations. Methods. We analyzed spectro-interferometric data in the H α (VEGA) and Br γ (AMBER) lines using models of increasing complexity: simple geometric models, kinematic models, and radiative transfer models computed with the 3D non-LTE code HDUST. Results. We measured the stellar radius of o Aquarii in the visible with a precision of 8%: 4.0 ± 0.3 R ⊙ . We constrained the circumstellar disk geometry and kinematics using a kinematic model and a MCMC fitting procedure. The emitting disk sizes in the H α and Br γ lines were found to be similar, at ~10–12 stellar diameters, which is uncommon since most results for Be stars indicate a larger extension in H α than in Br γ . We found that the inclination angle i derived from H α is significantly lower (~15°) than the one derived from Br γ : i ~ 61.2° and 75.9°, respectively. While the two lines originate from a similar region of the disk, the disk kinematics were found to be near to the Keplerian rotation (i.e., β = −0.5) in Br γ ( β ~ −0.43), but not in H α ( β ~ −0.30). After analyzing all our data using a grid of HDUST models (BeAtlas), we found a common physical description for the circumstellar disk in both lines: a base disk surface density Σ 0 = 0.12 g cm −2 and a radial density law exponent m = 3.0. The same kind of discrepancy, as with the kinematic model, is found in the determination of i using the BeAtlas grid. The stellar rotational rate was found to be very close (~96%) to the critical value. Despite being derived purely from the fit to interferometric data, our best-fit HDUST model provides a very reasonable match to non-interferometric observables of o Aquarii: the observed spectral energy distribution, H α and Br γ line profiles, and polarimetric quantities. Finally, our analysis of multi-epoch H α profiles and imaging polarimetry indicates that the disk structure has been (globally) stable for at least 20 yr. Conclusions. Looking at the visible continuum and Br γ emission line only, o Aquarii fits in the global scheme of Be stars and their circumstellar disk: a (nearly) Keplerian rotating disk well described by the viscous decretion disk (VDD) model. However, the data in the H α line shows a substantially different picture that cannot fully be understood using the current generation of physical models of Be star disks. The Be star o Aquarii presents a stable disk (close to the steady-state), but, as in previous analyses, the measured m is lower than the standard value in the VDD model for the steady-state regime ( m = 3.5). This suggests that some assumptions of this model should be reconsidered. Also, such long-term disk stability could be understood in terms of the high rotational rate that we measured for this star, the rate being a main source for the mass injection in the disk. Our results on the stellar rotation and disk stability are consistent with results in the literature showing that late-type Be stars are more likely to be fast rotators and have stable disks.more » « less
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