Orbits of particles with magnetic dipole moment around magnetized Schwarzschild black holes: Applications to S2 star orbit

TL;DR

This paper analytically investigates the motion of magnetized particles around a magnetized Schwarzschild black hole, compares findings with the S2 star orbit, and estimates the star's magnetic dipole moment.

Contribution

It provides a comprehensive analytical framework for particle orbits in a magnetized black hole environment, including applications to real stellar observations and magnetic dipole estimations.

Findings

Maximum and minimum magnetic interaction parameters identified.

Estimated magnetic dipole moment of S2 star around 10^6 G·cm^3.

Derived solutions involve elliptic integrals and Jacobi functions.

Abstract

This study provides a comprehensive analytical investigation of the bound and unbound motion of magnetized particles orbiting a Schwarzschild black hole immersed in an external asymptotically uniform magnetic field, which includes all conceivable types of bounded and unbounded orbits. In particular, for planetary orbits, we perform a comparative analysis of our findings with the observed position of the S2 star carrying magnetic dipole moment around Sagittarius A* (Sgr A*). We found maximum and minimum values for the parameter of magnetic interaction between the magnetic dipole of the star and the external magnetic field, as well as the energy and angular momentum of the S2 star. As a result, we obtain estimations of the magnetic dipole of the star in order of $10^6 \rm \ G\cdot cm^{3}$. Additionally, we explore deflecting trajectories akin to gravitational Rutherford scattering. In obtaining the solutions for the orbital equations, we articulate the elliptic integrals and Jacobi elliptic functions, and our study is augmented by illustrative figures and simulations.