Magnetic Dipole and Quadrupole Interaction Fields of Neutron Star

Neutron stars (NSs) are rapidly rotating entities, spinning at approximately 10<sup>4</sup> Hz, and possess extremely strong magnetic fields, ranging from 10<sup>13</sup> to 10<sup>14</sup> Gauss. These compact objects, characterized by a radius of about 10 kilometers and a density of 10<sup>13−14</sup>, <i>gcm</i><sup>−3</sup> are formed as a result of supernova explosions that mark the end of the life cycles of massive stars. Observations of electromagnetic emissions associated with curvature radiation from well-known pulsars, such as the Crab and Vela pulsars, provide compelling evidence that the magnetic field configuration near the surfaces of these neutron stars deviates significantly from the traditionally anticipated pure dipole structure. Researchers now propose that the inclusion of non-dipolar components in the magnetic field may address this longstanding discrepancy. Furthermore, the arrangement of magnetic field lines plays a crucial role in determining the characteristics and geometry of accretion discs surrounding neutron stars in binary systems. This study has focused on elucidating the geometry of the combined dipole and quadrupole magnetic field lines. In idealized scenarios, the magnetic field lines in proximity to these compact objects are typically closed; however, they may become open at greater distances due to interactions with external magnetic fields or the stress energy generated by other sources, including the accretion discs.