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This work conducts a Hamilton-Jacobi analysis of classical dynamical systems with internal constraints. We examine four systems, all previously analyzed by David Brown: three with familiar components (point masses, springs, rods, ropes, and pulleys) and one chosen specifically for its detailed illustration of the Dirac-Bergmann algorithm's logical steps. Including this fourth system allows for a direct and insightful comparison with the Hamilton-Jacobi formalism, thereby deepening our understanding of both methods. To provide a thorough analysis, we classify the systems based on their constraints: non-involutive, involutive, and a combination of both. We then use generalized brackets to ensure the theory's integrability, systematically remove non-involutive constraints, and derive the equations of motion. This approach effectively showcases the Hamilton-Jacobi method's ability to handle complex constraint structures. Additionally, our study includes an analysis of a gauge system, highlighting the versatility and broad applicability of the Hamilton-Jacobi formalism. By comparing our results with those from the Dirac-Bergmann and Faddeev-Jackiw algorithms, we demonstrate that the Hamilton-Jacobi approach is simpler and more efficient in its mathematical operations and offers advantages in computational implementation., Comment: 41 pages, 5 figures

Currently, our understanding of magnetic fields in exoplanets remains limited compared to those within our solar system. Planets with magnetic fields emit radio signals primarily due to the Electron Cyclotron Maser Instability mechanism. In this study, we explore the feasibility of detecting radio emissions from exoplanets using the Square Kilometre Array (SKA) radio telescope. Utilizing data from the NASA Exoplanet Archive, we compile information on confirmed exoplanets and estimate their radio emissions using the RBL model. Our analysis reveals that three exoplanets- Qatar-4 b, TOI-1278 b, and WASP-173 A b- exhibit detectable radio signals suitable for observation with the SKA telescope., Comment: 6 pages, 1 Figure, submitted to Frontiers in Astronomy and Space Sciences. This work is related to arXiv:2404.14359. arXiv admin note: text overlap with arXiv:2404.14359

Numerous numerical studies have been carried out in recent years that simulate different aspects of exoplanets' magnetosphere and stellar winds. These studies have focused primarily on hot Jupiters with sun-like stars. This study addresses the challenges inherent in utilizing existing MHD codes to model hot Jupiter-star systems. Due to the scaling of the system and the assumption of a uniformly flowing stellar wind at the outer boundary of the simulation, MHD codes necessitate a minimum distance of greater than 0.4 au for a Jupiter-like planet orbiting a sun-like star to avoid substantial violations of the code's assumptions. Additionally, employing the GAMERA (Grid Agnostic MHD for Extended Research Applications) MHD code, we simulate star-planet interactions considering various stellar types (Sun-like and M Dwarf stars) with both Jupiter-like and Earth-like planets positioned at varying orbital distances. Furthermore, we explore the impact of tidal locking on the total power within the magnetosphere-ionosphere systems., Comment: 11 pages, submitted to Frontiers in Astronomy and Space Sciences

There are several methods for indirectly detecting exoplanets, such as transit, radial velocity, astrometry, and the conventional gravitational microlensing approach. These methods rely on observing the effects of exoplanets on the emission or motion of observed stars. All these techniques have focused on the optical or infrared domains. However, an alternative method for exoplanet detection via microlensing events involves planets orbiting the source star, creating a binary source system. In this study, we explore a novel approach to detecting and studying exoplanets exclusively through their radio emissions resulting from magnetospheric processes. We propose utilizing the Roman telescope as a survey observer to detect microlensing events. Subsequently, we investigate the potential for detecting planetary radio signals through follow-up observations of these microlensing events in the radio band using the SKA telescope. This method is viable due to the comparable radio emission levels of exoplanets and their parent stars, unlike optical and infrared emissions. We conduct a Monte Carlo simulation to replicate the observations by the Nancy Roman Telescope, followed by a follow-up observation in radio frequencies using the SKA telescope. We determine that approximately 1317 exoplanets exhibit detectable signals by the SKA telescope during the 7-season observations by the Nancy Roman Telescope. This result indicates that such a method cannot only facilitate the direct detection of exoplanets but also enable the measurement of their magnetic field strength through analysis of their radio emissions., Comment: 13 pages, 4 figures, published in Frontiers in Astronomy and Space Sciences

Intense currents produced during geomagnetic storms dissipate energy in the ionosphere through Joule heating. This dissipation has significant space weather effects, and thus it is important to determine the ability of physics-based simulations to replicate real events quantitatively. Several empirical models estimate Joule heating based on ionospheric currents using the AE index. In this study, we select 11 magnetic storm simulations from the CCMC database and compare the integrated Joule heating in the simulations with the results of empirical models. We also use the SWMF global magnetohydrodynamic simulations for 12 storms to reproduce the correlation between the simulated AE index and simulated Joule heating. We find that the scale factors in the empirical models are half what is predicted by the SWMF simulations., Comment: Published in Frontiers in Astronomy and Space Sciences