Search for: All records

We analyse the results of direct numerical simulations of rotating convection in spherical shell geometries with stress-free boundary conditions, which develop strong zonal flows. Both the Ekman number and the Rayleigh number are varied. We find that the asymptotic theory for rapidly rotating convection can be used to predict the Ekman number dependence of each term in the governing equations, along with the convective flow speeds and the dominant length scales. Using a balance between the Reynolds stress and the viscous stress, together with the asymptotic scaling for the convective velocity, we derive an asymptotic prediction for the scaling behaviour of the zonal flow with respect to the Ekman number, which is supported by the numerical simulations. We do not find evidence of distinct asymptotic scalings for the buoyancy and viscous forces and, in agreement with previous results from asymptotic plane layer models, we find that the ratio of the viscous force to the buoyancy force increases with Rayleigh number. Thus, viscosity remains non-negligible and we do not observe a trend towards a diffusion-free scaling behaviour within the rapidly rotating regime.

 

A numerical investigation of an asymptotically reduced model for quasigeostrophic Rayleigh-Bénard convection is conducted in which the depth-averaged flows are numerically suppressed by modifying the governing equations. At the largest accessible values of the Rayleigh number Ra, the Reynolds number and Nusselt number show evidence of approaching the diffusion-free scalings of Re ∼ RaE/Pr and Nu ∼ Pr−1/2Ra3/2E2, respectively, where E is the Ekman number and Pr is the Prandtl number. For large Ra, the presence of depth-invariant flows, such as large-scale vortices, yield heat and momentum transport scalings that exceed those of the diffusion-free scaling laws. The Taylor microscale does not vary significantly with increasing Ra, whereas the integral length scale grows weakly. The computed length scales remain O(1) with respect to the linearly unstable critical wave number; we therefore conclude that these scales remain viscously controlled. We do not find a point-wise Coriolis-inertia-Archimedean (CIA) force balance in the turbulent regime; interior dynamics are instead dominated by horizontal advection (inertia), vortex stretching (Coriolis) and the vertical pressure gradient. A secondary, subdominant balance between the Archimedean buoyancy force and the viscous force occurs in the interior and the ratio of the root mean square (rms) of these two forces is found to approach unity with increasing Ra. This secondary balance is attributed to the turbulent fluid interior acting as the dominant control on the heat transport. These findings indicate that a pointwise CIA balance does not occur in the high Rayleigh number regime of quasigeostrophic convection in the plane layer geometry. Instead, simulations are characterized by what may be termed a nonlocal CIA balance in which the buoyancy force is dominant within the thermal boundary layers and is spatially separated from the interior Coriolis and inertial forces. 

Dynamos driven by rotating convection in the plane layer geometry are investigated numerically for a range of Ekman number ( $E$ ), magnetic Prandtl number ( $Pm$ ) and Rayleigh number ( $Ra$ ). The primary purpose of the investigation is to compare results of the simulations with previously developed asymptotic theory that is applicable in the limit of rapid rotation. We find that all of the simulations are in the quasi-geostrophic regime in which the Coriolis and pressure gradient forces are approximately balanced at leading order, whereas all other forces, including the Lorentz force, act as perturbations. Agreement between simulation output and asymptotic scalings for the energetics, flow speeds, magnetic field amplitude and length scales is found. The transition from large-scale dynamos to small-scale dynamos is well described by the magnetic Reynolds number based on the small convective length scale, $\widetilde {Rm}$ , with large-scale dynamos preferred when $\widetilde {Rm} \lesssim O(1)$ . The magnitude of the large-scale magnetic field is observed to saturate and become approximately constant with increasing Rayleigh number. Energy spectra show that all length scales present in the flow field and the small-scale magnetic field are consistent with a scaling of $E^{1/3}$ , even in the turbulent regime. For a fixed value of $E$ , we find that the viscous dissipation length scale is approximately constant over a broad range of $Ra$ ; the ohmic dissipation length scale is approximately constant within the large-scale dynamo regime, but transitions to a $\widetilde {Rm}^{-1/2}$ scaling in the small-scale dynamo regime. 

Cold Jovian planets play an important role in sculpting the dynamical environment in which inner terrestrial planets form. The core accretion model predicts that giant planets cannot form around low-mass M dwarfs, although this idea has been challenged by recent planet discoveries. Here, we investigate the occurrence rate of giant planets around low-mass (0.1–0.3M_⊙) M dwarfs. We monitor a volume-complete, inactive sample of 200 such stars located within 15 pc, collecting four high-resolution spectra of each M dwarf over six years and performing intensive follow-up monitoring of two candidate radial velocity variables. We use TRES on the 1.5 m telescope at the Fred Lawrence Whipple Observatory and CHIRON on the Cerro Tololo Inter-American Observatory 1.5 m telescope for our primary campaign, and MAROON-X on Gemini-North for high-precision follow up. We place a 95% confidence upper limit of 1.5% (68% confidence limit of 0.57%) on the occurrence ofM_Psini> 1M_Jgiant planets out to the water snow line and provide additional constraints on the giant planet population as a function ofM_Psiniand period. Beyond the snow line (100 K <T_eq< 150 K), we place 95% confidence upper limits of 1.5%, 1.7%, and 4.4% (68% confidence limits of 0.58%, 0.66%, and 1.7%) for 3M_J<M_Psini< 10M_J, 0.8M_J<M_Psini< 3M_J, and 0.3M_J<M_Psini< 0.8M_Jgiant planets, respectively; i.e., Jupiter analogs are rare around low-mass M dwarfs. In contrast, surveys of Sun-like stars have found that their giant planets are most common at these Jupiter-like instellations.

 

The Kepler space telescope was responsible for the discovery of over 2700 confirmed exoplanets, more than half of the total number of exoplanets known today. These discoveries took place during both Kepler’s primary mission, when it spent 4 yr staring at the same part of the sky, and its extended K2 mission, when a mechanical failure forced it to observe different parts of the sky along the ecliptic. At the very end of the mission, when Kepler was exhausting the last of its fuel reserves, it collected a short set of observations known as K2 Campaign 19. So far, no planets have been discovered in this data set because it only yielded about a week of high-quality data. Here, we report some of the last planet discoveries made by Kepler in the Campaign 19 dataset. We conducted a visual search of the week of high-quality Campaign 19 data and identified three possible planet transits. Each planet candidate was originally identified with only one recorded transit, from which we were able to estimate the planets’ radii and estimate the semimajor axes and orbital periods. Analysis of lower-quality data collected after low fuel pressure caused the telescope’s pointing precision to suffer revealed additional transits for two of these candidates, allowing us to statistically validate them as genuine exoplanets. We also tentatively confirm the transits of one planet with TESS. These discoveries demonstrate Kepler’s exoplanet detection power, even when it was literally running on fumes.

 

We report the discovery of TOI-4641b, a warm Jupiter transiting a rapidly rotating F-type star with a stellar effective temperature of 6560 K. The planet has a radius of 0.73 RJup, a mass smaller than 3.87 MJup(3σ), and a period of 22.09 d. It is orbiting a bright star (V=7.5 mag) on a circular orbit with a radius and mass of 1.73 R⊙ and 1.41 M⊙. Follow-up ground-based photometry was obtained using the Tierras Observatory. Two transits were also observed with the Tillinghast Reflector Echelle Spectrograph, revealing the star to have a low projected spin-orbit angle (λ=$1.41^{+0.76}_{-0.76}$°). Such obliquity measurements for stars with warm Jupiters are relatively few, and may shed light on the formation of warm Jupiters. Among the known planets orbiting hot and rapidly rotating stars, TOI-4641b is one of the longest period planets to be thoroughly characterized. Unlike hot Jupiters around hot stars which are more often misaligned, the warm Jupiter TOI-4641b is found in a well-aligned orbit. Future exploration of this parameter space can add one more dimension to the star–planet orbital obliquity distribution that has been well sampled for hot Jupiters. 

ABSTRACT Numerical simulations are used to investigate large-scale (mean) magnetic field generation in rotating spherical dynamos. Beyond a certain threshold, we find that the magnitude of the mean magnetic field becomes nearly independent of the system rotation rate and buoyancy forcing. The analysis suggests that this saturation arises from the Malkus-Proctor mechanism in which a Coriolis-Lorentz force balance is achieved in the zonal component of the mean momentum equation. When based on the large-scale magnetic field, the Elsasser number is near unity in the saturated regime. The results show that the large and small magnetic field saturate via distinct mechanisms in rapidly rotating dynamos, and that only the axisymmetric component of the magnetic field appears to follow an Elsasser number scaling. 

Summary The large-scale dynamics of convection-driven dynamos in a spherical shell, as relevant to the geodynamo, is analyzed with numerical simulation data and asymptotic theory. An attempt is made to determine the asymptotic size (with the small parameter being the Ekman number, Ek) of the forces, and the associated velocity and magnetic fields. In agreement with previous work, the leading order mean force balance is shown to be thermal wind (Coriolis, pressure gradient, buoyancy) in the meridional plane and Coriolis-Lorentz in the zonal direction. The Lorentz force is observed to be weaker than the mean buoyancy force across a range of Ek and thermal forcing; the relative difference in these forces appears to be O(Ek1/6) within the parameter space investigated. We find that the thermal wind balance requires that the mean zonal velocity scales as O(Ek−1/3), whereas the meridional circulation is asymptotically smaller by a factor of O(Ek1/6). The mean temperature equation shows a balance between thermal diffusion and the divergence of the convective heat flux, indicating the presence of a mean temperature length scale of size O(Ek1/6). Neither the mean nor the fluctuating magnetic field show a strong dependence on the Ekman number, though the simulation data shows evidence of a mean magnetic field length scale of size O(Ek1/6). A consequence of the asymptotic ordering of the forces is that Taylor’s constraint is satisfied to accuracy O(Ek1/6), despite the absence of a leading-order magnetostrophic balance. Further consequences of the force balance are discussed with respect to the large-scale flows thought to be important for the geodynamo.