We explore how thermal Rossby waves propagate within the gravitationally stratified atmosphere of a low-mass star with an outer convective envelope. Under the conditions of slow, rotationally constrained dynamics, we derive a local dispersion relation for atmospheric waves in a fully compressible stratified fluid. This dispersion relation describes the zonal and radial propagation of acoustic waves and gravito-inertial waves. Thermal Rossby waves are just one class of prograde-propagating gravito-inertial wave that manifests when the buoyancy frequency is small compared to the rotation rate of the star. From this dispersion relation, we identify the radii at which waves naturally reflect and demonstrate how thermal Rossby waves can be trapped radially in a waveguide that permits free propagation in the longitudinal direction. We explore this trapping further by presenting analytic solutions for thermal Rossby waves within an isentropically stratified atmosphere that models a zone of efficient convective heat transport. We find that, within such an atmosphere, waves of short zonal wavelength have a wave cavity that is radially thin and confined within the outer reaches of the convection zone near the star’s equator. The same behavior is evinced by the thermal Rossby waves that appear at convective onset in numerical simulations of convection within rotating spheres. Finally, we suggest that stable thermal Rossby waves could exist in the lower portion of the Sun’s convection zone, despite that region’s unstable stratification. For long wavelengths, the Sun’s rotation rate is sufficiently rapid to stabilize convective motions, and the resulting overstable convective modes are identical to thermal Rossby waves.

Whitepaper #287 in the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033. Main topics: space weather applications; basic research. Additional topics: space weather research/applications/operations pipeline; solar physics; space-based missions/projects; […]

Understanding the number of sunspots is crucial for comprehending the Sun’s magnetic-activity cycle and its influence on space weather and the Earth. Recent advancements in machine learning have significantly improved the accuracy of time-series predictions, revealing a compelling approach for sunspot forecasts. Our work takes the pioneering work by proposing a hybrid forecasting approach that combines the Seasonal Autoregressive Integrated Moving Average (SARIMA) with machine-learning algorithms like Random Forest and Support Vector Machine, delivering high prediction accuracy. Despite its high accuracy, we highlight the need for caution in deploying machine-learning-based methods for sunspot-number prediction, demonstrated through a detailed case study with only three extra time stamps leading to a dramatic change. More specifically, when making a forecast of monthly averaged sunspot numbers from 2023–2043 based on data from 1749–2023, we found that the observations in June, July, and August 2023 have a significant impact on the forecast, particularly in the long term. Given the multiseasonal and nonstationary nature of the sunspot time series, we conclude that this kind of phenomenon cannot be simply captured by a pure data-driven model, which can be highly sensitive in the forecast in the long term, and requires a more comprehensive approach, possibly with a model that includes physics.

Astronomy & Astrophysics (A&A) is an international journal which publishes papers on all aspects of astronomy and astrophysics

Astronomy & Astrophysics (A&A) is an international journal which publishes papers on all aspects of astronomy and astrophysics

Using an analytic model, we derive the eigenfrequencies for thermal Rossby waves that are trapped radially and latitudinally in an isentropically stratified atmosphere. We ignore the star’s curvature and work in an equatorial f-plane geometry. The propagation of inertial waves is found to be sensitive to the relative direction of the wavevector to the zonal direction. Prograde propagating thermal Rossby waves are naturally trapped in the radial direction for frequencies above a critical threshold, which depends on the angle of propagation. Below the threshold frequency, there exists a continuous spectrum of prograde and retrograde inertial waves that are untrapped in an isentropic atmosphere but can be trapped by gradients in the specific entropy density. Finally, we discuss the implications of these waves on recent observations of inertial oscillations in the Sun, as well as in numerical simulations.