Neutron Star Magnetic Fields and Implications for Pulsars and Gamma Ray Bursts.

Calculations of ohmic decay of neutron star dipolar magnetic fields which are confined to the neutron star crust are carried out. It is shown that the field does not decay exponentially as has been assumed in most analyses of pulsar observations and that if it occupies the entire crust it decays by less than a factor of order 100 in a Hubble time. Fields that are confined to the outer regions of the crust decay faster and again non-exponentially. We also show that the surface magnetic fields of young pulsars may fluctuate and even change polarities on time-scales much shorter than their secular decay time-scale. As a result the pulsar braking indices can significantly deviate from the value of 3, expected if the fields are constant. Through a detailed statistical analysis, we showed that non-exponential field decay is consistent with the current understanding of radio pulsars. Since the field decays non-exponentially and may retain a substantial fraction of its initial strength at ages $\geq 10\sp9$ years, it may also provide a natural explanation for the magnetic fields of millisecond pulsars, which are believed to be old objects. Strong magnetic fields may be present on the surface of neutron stars associated with $\gamma$-ray bursts. We examined the possibilities that the cyclotron emissions from plasmas in neutron star magnetospheres, which are heated through Compton process by high energy $\gamma$-rays, may produce observable optical flashes. Emerging spectra and luminosities are obtained for several models. We concluded that, under certain magnetospheric conditions, the model is capable of explaining the historical flashes found within modern $\gamma$-ray burst error boxes. The cyclotron radiative transfer calculations in high temperature (k$\sb{B} T \ \sim$ 100 keV) plasmas require a fast and accurate code to compute the cyclotron opacities. We have developed a numerical code based on the steepest descent path method first devised by Trubnikov. Our results are in general agreement with those obtained using Chanmugam and Dulk method, which breaks down at high temperatures, at $\sim$ 30 keV