Unraveling High Magnetic Field Pulsars: Neutrino and Photon Emissions from the Swift Era

In this paper, We delve into the Unraveling decay of high magnetic fields in pulsars, assessing the influential roles of neutrino and photon emissions in high magnetic field scenarios, particularly for gamma-ray pulsars during the Swift era. How do these emissions shape the life cycle of these enigmatic celestial objects? Our modeling reveals cooling curves that yield pulsar surface magnetic fields strikingly consistent with observational data. We propose that the gamma-ray cooling curve adheres to a single power-law decay, defined by $\textrm{B} \propto \textrm{t}^{\alpha}$ where $\alpha$ is the decay index $\alpha = -1/6$ for neutrino emissions and $\alpha = -3/2$ for photon emissions. Importantly, We show that the magnetic field evolves as $\textrm{B} \propto \textrm{t}^{\-1/6}$ during the early stages, encompassing the first $10^4-10^5$ \textrm{yrs}. Following this period, a dramatic transition occurs, driven by strong surface fields leading to enhanced photon cooling and a much faster decay rate. This intricate interplay between emission mechanisms not only shapes the evolution of pulsar magnetic fields but also deepens our understanding of their complex nature.