J. R. Fuentes

The atmospheres of polluted white dwarfs contain information about the composition of disrupted planetary material. However, interpreting the observed abundances requires a quantitative description of the mixing processes that transport accreted material through their envelopes. In particular, the accretion of metal-rich debris drives thermohaline convection in the star’s radiative zone. Previous studies have modeled this form of turbulence as an enhanced diffusive process, often inferring mass accretion rates M ̇ acc that exceed X-ray constraints. Here we develop a time-dependent model that treats thermohaline mixing as a propagating front whose evolution is coupled self-consistently to the surface abundance of heavy elements. We perform hydrodynamical simulations which demonstrate that thermohaline mixing drives the composition gradient toward values slightly above marginal thermohaline stability. Using this condition, we derive analytic solutions for the mixed layer depth h and surface abundance X _surf , finding that both scale as t ^1/2 at early times, transitioning to h ∝ t ^4/27 and X _surf ∝ t ^10/27 at later times. Without gravitational settling, the thermohaline front never reaches a steady state, while including settling leads to an equilibrium surface abundance X surf , eq ∝ M ̇ acc 30 / 43 . Applied to G 29–38, our model matches the observed heavy-element abundance for M ̇ acc ∼ 1 × 1 0 10 –2 × 10 ¹⁰ g s ⁻¹ , comparable to previous findings using stellar evolution codes. These rates exceed the X-ray estimate by about an order of magnitude, which may point to a partially suppressed X-ray luminosity from the accretion boundary layer. We also present a practical prescription for inferring accretion rates directly from the observed surface abundance and stellar parameters for other polluted white dwarfs.

Double-diffusive convection in the “fuzzy” cores of giant planets has been widely discussed as a mechanism for redistributing heavy elements, but its efficiency in evolutionary models remains uncertain. Here we implement a prescription for transport across a double-diffusive staircase in the planetary evolution code APPLE and apply it to postformation interior models of Jupiter and Saturn that contain steep compositional gradients. We find that after evolving the models for 4.56 Gyr, the transport associated with double-diffusive convection alone cannot transform steep composition gradients and compact cores into extended, partially mixed fuzzy cores. Our results show that in both Jupiter and Saturn, double-diffusive convection redistributes ≈0.1 M _⊕ of heavy elements over the age of the solar system in our fiducial models, and at most ≈2 M _⊕ even when the effective diffusivities are enhanced by 3 orders of magnitude. We show that this inefficiency arises because the buoyancy work available to drive compositional transport is constrained by the small thermal energy budget of the deep interior, in contrast to idealized Boussinesq simulations that operate in regimes more favorable to layer merging and efficient mixing. Since the present-day interiors of Jupiter and Saturn exhibit substantially more extended heavy-element distributions, those structures must have established during formation through additional transport processes not captured by the formation models considered here.

The excitation and damping mechanisms for oscillation modes of gas giant planets are undetermined. We show that differential rotation may greatly enhance the convective viscosity in giant planets, resulting in damping times of t _damp ∼ 10 ⁵ –10 ⁶ yr for f -modes and low-order p -modes. Radiative diffusion damps p -modes on timescales of t _damp ∼ 10 ³ –10 ⁷ yr. While the lethargic convective motions cannot effectively excite f- mode or p- modes, storms driven by condensation of water and/or silicates may play a role. High-order p- modes are most effectively excited by cometary/asteroid impacts. Applying these calculations to solar system planets, water storms, rock storms, and impacts may all contribute to exciting the observed f- mode amplitudes of Saturn via ring seismology. Similar f- mode amplitudes with fractional gravitational perturbations of δ Φ/Φ ∼ 10 ⁻¹⁰ –10 ⁻⁹ are expected for Jupiter and Uranus, apart from their lowest- ℓ f- modes, which could have larger gravitational perturbations of δ Φ/Φ ∼ 10 ⁻⁷ . Rock storms may contribute to mode driving in Jupiter, while water storms are more important for Uranus. The highest-amplitude p- modes are predicted to have periods of ∼10–30 minutes, with surface velocities of ∼10 cm s ⁻¹ for Jupiter and Saturn and ∼1 cm s ⁻¹ for Uranus. These oscillation modes may be detectable with radial velocity measurements, ring seismology, or spacecraft Doppler tracking. However, both the damping and excitation physics are uncertain by orders of magnitude, so more careful examination of the relevant physics is required for robust estimates.

Thermal convection in rotating stars and planets drives anisotropic turbulence and differential rotation, both capable of feeding energy into global oscillations. Using 3D simulations of rotating convection in spherical shells, we show that inertial modes—oscillations restored by the Coriolis force—emerge naturally in rotationally constrained turbulence, without imposing any external forcing other than thermal/buoyancy driving. By varying the rotation rate at fixed Rayleigh number, we find that coherent modes appear only when the convective Rossby number, the ratio of the rotation period to the convective turnover time, falls below about one-half, where rotation dominates the dynamics. These modes are mostly retrograde in the rotating frame, equatorially symmetric, and confined to mid and high latitudes, with discrete frequencies well below twice the background rotation rate. At lower viscosities, or a smaller Prandtl number, mode excitation becomes more efficient and a broader spectrum of inertial modes emerges. While the precise excitation mechanism remains uncertain, our results suggest that the modes are driven by instabilities due to differential rotation rather than stochastic forcing by convection. We conclude that similar inertial modes are likely to exist in the interiors of giant planets and stars, though their low frequencies will make them difficult to detect.

Observations from Juno and Cassini suggest that Jupiter and Saturn may possess fuzzy cores—central regions where the abundance of heavy elements varies smoothly with depth. Such gradients pose a longstanding puzzle for models of planetary evolution and formation, which predict that vigorous convection would homogenize the interiors of gas giants within the first ∼10⁶–10⁸ yr of cooling. Previous 3D simulations and analytic predictions for the propagation of a convection zone into a stable region have demonstrated that the rapid rotation of gas giants can significantly slow convective mixing, but not enough to stop it. Another piece of the puzzle is luminosity. Gas giants cool as they age, and with that comes a declining heat flux over time. Recent ideas suggest that when this declining luminosity is combined with rotational effects, convection may stall. We explore this possibility using 3D hydrodynamic simulations that include both rotation and a surface cooling flux that decreases as 1/t. Our results demonstrate that, even without rotation, a declining luminosity can suppress mixing sufficiently to preserve an initial compositional gradient in the deep interior of gas giants. If confirmed by more realistic simulations, this may help to explain the long-term survival of fuzzy cores.

Juno and Cassini have shown that Jupiter and Saturn likely contain extended gradients of heavy elements. Yet, how these gradients can survive over billions of years remains an open question. Classical convection theories predict rapid mixing and homogenization, which would erase such gradients on timescales far shorter than the planets’ ages. To address this, we estimate the energy required to erode both dense and fuzzy cores, and compare it to what the planet can realistically supply. If the entire cooling budget is available to drive mixing, then even a compact core can, in principle, be destroyed. But if mixing is limited to the thermal energy near the core, which is another plausible scenario, the energy falls short. In that case, Jupiter can erode a fuzzy core by up to approximately 10 M _⊕, but a compact one remains intact. Saturn’s core is more robust. Even in the fuzzy case, only about 1 M _⊕ is lost, and if the core is compact, erosion is negligible. The outcome depends sensitively on the assumed initial temperature and entropy profiles. Hotter and more superadiabatic interiors are more prone to mixing. We suggest that 3D simulations of convection driven from above, with realistic stratification and enough depth (i.e., many density scale heights) would be of great interest to further constrain the energy budget for core erosion.

Semiconvection occurs in regions of stars and planets that are unstable to overturning convection according to the Schwarzschild criterion, but stable according to the Ledoux criterion. Previous simulations in Cartesian boxes have advanced our understanding of the semiconvective instability, layer formation, and transport properties. However, much less is known about semiconvection in spherical geometry and under the influence of rotation or magnetic fields. We present 3D simulations of semiconvection in the full sphere (including r = 0) and accounting for rotation. We find that the formation and evolution of semiconvective layers in nonrotating spheres occurs in a similar way to that in nonrotating Cartesian boxes, in the sense that the critical density ratio at which layers are expected to form is approximately the same in both geometries. Layers rapidly merge once they form, ultimately leading to a fully mixed convective sphere. The transport properties measured through the Nusselt numbers and the buoyancy flux ratio are also similar to results from previous studies in boxes. When rotation is added to the system, layer formation and evolution proceed in a similar fashion to the nonrotating runs. However, rotation hampers the radial transport of heat and composition, and, as a result, the time that it takes for the sphere to become fully mixed gets longer as the flow becomes more rotationally constrained. We also find that semiconvective layers exhibit spherical mixing in nonrotating cases, whereas in rotating cases the mixing becomes more cylindrical. We discuss what is needed for future work to build more realistic models.

Recent observations of volume-limited samples of magnetic white dwarfs (WD) have revealed a higher incidence of magnetism in older stars. Specifically, these studies indicate that magnetism is more prevalent in WDs with fully or partially crystallized cores than in those with entirely liquid cores. This has led to the recognition of a crystallization-driven dynamo as an important mechanism for explaining magnetism in isolated WDs. However, recent simulations have challenged the capability of this mechanism to generate surface magnetic fields with the typical strengths detected in WDs. In this Letter, we explore an alternative hypothesis for the surface emergence of magnetic fields in isolated WDs. Those with masses ≳0.55 M_⊙ are the descendants of main sequence stars with convective cores capable of generating strong dynamo magnetic fields. This idea is supported by asteroseismic evidence of strong magnetic fields buried within the interiors of red giant branch stars. Assuming that these fields are disrupted by subsequent convective zones, we estimated magnetic breakout times for WDs with carbon-oxygen (CO) cores and masses ranging from 0.57 M_⊙ to 1.3 M_⊙. Due to the significant uncertainties in breakout times stemming from the treatment of convective boundaries and mass-loss rates, we cannot provide a precise prediction for the emergence time of the main sequence dynamo field. However, we can predict that this emergence should occur during the WD phase for those objects with masses ≳0.65 M_⊙. We also find that the magnetic breakout is expected to occur earlier in more massive WDs, which is consistent with observations of volume-limited samples and the well-established fact that magnetic WDs tend to be more massive than non-magnetic ones. Moreover, within the uncertainties of stellar evolutionary models, we find that the emergence of main sequence dynamo magnetic fields can account for a significant portion of the magnetic WDs. Additionally, we estimated magnetic breakout times due to crystallization-driven dynamos in CO WDs; our results suggest that this mechanism cannot explain the majority of magnetic WDs.

Recent observational constraints on the internal structure of Jupiter and Saturn suggest that these planets have “fuzzy” cores, i.e., gradients of the concentration of heavy elements that might span a large fraction of the planet’s radius. These cores could be composed of a semiconvective staircase, i.e., multiple convective layers separated by diffusive interfaces arising from double-diffusive instabilities. However, to date, no study has demonstrated how such staircases can avoid layer mergers and persist over evolutionary timescales. In fact, previous work has found that these mergers occur rapidly, leading to only a single convective layer. Using 3D simulations, we demonstrate that rotation prolongs the lifetime of a convective staircase by increasing the timescale for both layer merger and erosion of the interface between the final two layers. We present an analytic model for the erosion phase, predicting that rotation increases the erosion time by a factor of approximately Ro^−1/2, where Ro is the Rossby number of the convective flows (the ratio of the rotation period to the convective turnover time). For Jovian conditions at early times after formation (when convection is vigorous enough to mix a large fraction of the planet), we find the erosion time to be roughly 10⁹ yr in the nonrotating case and 10¹¹ yr in the rotating case. If these timescales are confirmed with a larger suite of numerical simulations, the existence of convective staircases within the deep interiors of giant planets is a strong possibility, and rotation could be an important factor in the preservation of their fuzzy cores.

Neutron stars show a steady decrease in their rotational frequency, occasionally interrupted by sudden spin-up events called glitches. The dynamics of a neutron star after a glitch involve the transfer of angular momentum from the crust (where the glitch is presumed to originate) to the liquid core, causing the core to spin up. The crust–core coupling, which determines how quickly this spin-up proceeds, can be achieved through various physical processes, including Ekman pumping, superfluid vortex-mediated mutual friction, and magnetic fields. Although the complex nature of these mechanisms has made it difficult to study their combined effects, analytical estimations for individual processes reveal that spin-up timescales vary according to the relative strength of Coriolis, viscous, and mutual friction forces, as well as the magnetic field. However, experimental and numerical validations of those analytical predictions are limited. In this paper, we focus on viscous effects and mutual friction. We conduct nonlinear hydrodynamical simulations of the spin-up problem in a two-component fluid by solving the incompressible Hall–Vinen–Bekarevich–Khalatnikov equations in the full sphere (i.e., including r = 0) for the first time. We find that the viscous (normal) component accelerates due to Ekman pumping, although the mutual friction coupling to the superfluid component alters the spin-up dynamics compared to the single-fluid scenario. Close to the sphere’s surface, the response of the superfluid is accurately described by the mutual friction timescale irrespective of its coupling strength with the normal component. However, as we move deeper into the sphere, the superfluid accelerates on different timescales due to the slow viscous spin-up of the internal normal fluid layers. We discuss potential implications for neutron stars, and requirements for future work to build more realistic models.