Gamma-ray bursts from magnetospheric plasma oscillations. II. model spectra

Several mechanisms for the primary release of energy in gamma-ray bursts (GRBs) may result in the excitation of relativistic, magnetospheric plasma oscillations above the polar cap of a neutron star. In this paper, we report on detailed calculations of the inverse Compton scattering interaction between the sinusoidally accelerated particles in the plasma and the thermal radiation from the stellar surface, which we determine self-consistently by means of a Monte Carlo simulation for the upscattered photons and the deposition of γ-ray energy below the photosphere. In order to avoid complications arising from the quantizing effects of a teragauss magnetic field on the Compton scattering cross section, we restrict the value of the surface magnetic field such that B_s ≲ 10¹²(γ_max/100)(l_osc/3R*) ³ G where R* is the stellar radius, γ_max is the particle Lorentz factor, and l_os is the scale length of the oscillating region above the polar cap. We find that the overall spectrum is comprised of essentially four main components: (1) once-scattered radiation, which is generally highly beamed in the direction of the magnetic field B₀ within the oscillating region because γ_max must lie in the range 10 ≲ γ_max≲ 10^2-3 in order to account for the observation of 1-100 MeV photons in some bursts; (2) multiply-scattered radiation (mostly second-order), which is also (at least partially) beamed. This component extends to higher frequencies than the first because photons gain energy with each subsequent scattering; (3) photons that are upscattered within the oscillating region and are then reflected by the stellar surface. Due to frequency redistribution within the star, this component contributes primarily in the ∼ 10-100 keV energy range and is generally more isotropic than components (1) and (2), and (4) thermal emission from the polar cap region due to the reprocessing of γ-rays scattered toward the star. Although we do not optimize our parameters to model individual GRBs, the qualitative agreement between the theoretical spectra and those observed during bursts such as GB720427 lead us to the following interpretation: (1) the turn-up at photon energy ≳1 MeV is probably due to multiply-scattered radiation, (2) the central, broad hump near ∼0.1-1 MeV arises from first-order scatterings and/or the reflected γ-rays, and (3) the component below ∼10 keV is likely due to thermal emission. We also show that the viability of this model may be tested through several of its robust predictions. First, γ-ray bursts should also be associated with emission at UV/soft X-ray energies, but the power in this component relative to that in γ-rays is a function of the aspect angle θ measured with respect to B₀. Bursts from distant sources, which because of beaming would presumably be of the small-θ variety in order to have fluxes above the detection limit, should generally show a slight excess above the extrapolation of the spectrum from higher frequencies. Bursts originating nearby should be detectable over a wide range of θ, and the UV/soft X-ray emission in some of these might be more prominent relative to the γ-rays. Second, the low-energy absorption features should be evident only in bursts detected at θ ≳ 30^○40^○, for which the reflected component dominates the spectrum in the ∼ 10-100 keV range. Detailed calculations of the cyclotron line formation should therefore deduce large viewing angles (i.e., θ ≳ 30^○-40^○) with respect to B₀. One might also expect that the presence of absorption lines might be correlated to the strength of the UV/soft X-ray excess and that spectra of bursts that display these lines should generally have lower values of the high-energy cutoff than those of the GRB population as a whole because the high-frequency component is preferentially beamed along B₀, Third, the low-energy features should be evident in ≳ 18% of all bursts if the burst energy function is flat and γ_max is distributed uniformly over the range 10-200. This seems to be consistent with the KONUS data.