The outflowing magnetized wind from a host star shapes planetary and exoplanetary magnetospheres dictating the extent of its impact. We carry out three-dimensional (3D) compressible magnetohydrodynamic (MHD) simulations of the interactions between magnetized stellar winds and planetary magnetospheres corresponding to a far-out star-planet system, with and without planetary dipole obliquity. We identify the pathways that lead to the formation of a dynamical steady-state magnetosphere and find that magnetic reconnection plays a fundamental role in the process. The magnetic energy density is found to be greater on the night-side than that on the day-side and the magnetotail is comparatively more dynamic. Magnetotail reconnection events are seen to associated with stellar wind plasma injection into the inner magnetosphere. We further study magnetospheres with extreme tilt angles keeping in perspective the examples of Uranus and Neptune. High dipole obliquities may also manifest due to polarity excursions during planetary field reversals. We find that global magnetospheric reconnection sites change for large planetary dipole obliquity and more complex current sheet structures are generated. We discuss the implications of these findings for injection of interplanetary species and energetic particles into the inner magnetosphere, auroral activity and magnetospheric radio emission. This study is relevant for exploring star planet interactions in the solar and extra-solar systems.

Normal-mode helioseismic data analysis uses observed solar oscillation spectra to infer perturbations in the solar interior due to global and local-scale flows and structural asphericity. Differential rotation, the dominant global-scale axisymmetric perturbation, has been tightly constrained primarily using measurements of frequency splittings via “a-coefficients.” However, the frequency-splitting formalism invokes the approximation that multiplets are isolated. This assumption is inaccurate for modes at high angular degrees. Analyzing eigenfunction corrections, which respect cross-coupling of modes across multiplets, is a more accurate approach. However, applying standard inversion techniques using these cross-spectral measurements yields a-coefficients with a significantly wider spread than the well-constrained results from frequency splittings. In this study, we apply Bayesian statistics to infer a-coefficients due to differential rotation from cross-spectra for both f-modes and p-modes. We demonstrate that this technique works reasonably well for modes with angular degrees ℓ = 50–291. The inferred a 3-coefficients are found to be within 1 nHz of the frequency-splitting values for ℓ > 200. We also show that the technique fails at ℓ < 50 owing to the insensitivity of the measurement to the perturbation. These results serve to further establish mode-coupling as an important helioseismic technique with which to infer internal structure and dynamics, both axisymmetric (e.g., meridional circulation) and non-axisymmetric perturbations.

Departures from standard spherically symmetric solar models, in the form of perturbations such as global and local-scale flows and structural asphericities, result in the splitting of eigenfrequencies in the observed spectrum of solar oscillations. Drawing from prevalent ideas in normal-mode-coupling theory in geophysical literature, we devise a procedure that enables the computation of sensitivity kernels for general Lorentz-stress fields in the Sun. Mode coupling due to any perturbation requires careful consideration of self- and cross coupling of multiplets. Invoking the isolated-multiplet approximation allows for limiting the treatment to purely self coupling, requiring significantly less computational resources. We identify the presence of such isolated multiplets under the effect of Lorentz stresses in the Sun. Currently, solar missions allow for precise measurements of self coupling of multiplets via “a-coefficients” and the cross-spectral correlation signal that enables the estimation of the “structure coefficients”. We demonstrate the forward problem for both self coupling (a-coefficients) and cross coupling (structure coefficients). In doing so, we plot the self-coupling kernels and estimate a-coefficients arising from a combination of deep-toroidal and surface-dipolar axisymmetric fields. We also compute the structure coefficients for an arbitrary general magnetic field (real and solenoidal) and plot the corresponding “splitting function”, a convenient way to visualize the splitting of multiplets under 3D internal perturbations. The results discussed in this paper pave the way to formally pose an inverse problem and infer solar internal magnetic fields.

The age-dependent activity of a star dictates the extent of its planetary impact. We study the interaction of the stellar wind produced by Solar-like stars with the magnetosphere of Earth-like planets using three dimensional (3D) magnetohydrodynamic (MHD) simulations. The numerical simulations reveal important features of star-planet interaction e.g. bow-shock, magnetopause, magnetotail, etc. Interesting phenomena such as particle injection into the planetary atmosphere as well as atmospheric mass loss are also observed which are instrumental in determining the atmospheric retention by the planet.