4 X-ray, optical and radio afterglows

Beppo-Sax observations gave the X-ray flux for GRB afterglow on the level $\sim 10^{-13}$ ergs/s. Taking 3 days for the duration of X-ray emission we get $F_{\rm x}\sim 3\ 10^{-8}$ ergs/cm² for the X-ray fluence, which gives $\sim 1/30$ of the main GRB with total fluency $\sim 10^{-6}$ ergs/cm². Explosion on the neutron star could lead to nonradial mass ejection with a velocity between escape and Keplerian velocities. The ejected matter falls back to the neutron star forming an accretion disk due to its high angular momentum. Taking the distance $\sim 100$ pc, corresponding to the total GRB energy $E_{\gamma}\sim 10^{36}$ ergs, and $E_{\rm x} \sim 3\ 10^{34}$ ergs, we estimate the mass creating this X-ray flux during accretion into a neutron star as $10^{-19}M_{\odot}$.The spectrum of accretion with a low rate $\dot M \sim 3\ 10^{-17}M_{\odot}/{\rm yr}\approx 7\ 10^8$ g/s, consist of two approximately equal parts. The first is a relatively hard X-ray emission in the range 1-10 keV from the boundary layer. The second is the radiation from the accretion disk itself which emits a spectrum $F_{\gamma} \sim \omega^{1/3}$ with an exponential cutoff starting from $\omega\approx 2\ 10^{15}~{\rm s}^{-1}$, corresponding to a maximum temperature $2\ 10^4$ K, which color corresponds to a B star. Duration of the emission from the accretion disk is not expected to last a long time, and it is not expected to radiate much in the red and far red ranges, lasting several months (Sokolov 1998).

The extended GRB afterglows with spectra corresponding to a cold star may be explained easily if the neutron star has a low mass companion with $M_{\rm d}=(0.02-0.2) \,\,M_{\odot}$, as observed in most binary recycled pulsars. Taking a companion with a mass $0.03\ M_{\odot}$ and very low temperature (degenerate brown dwarf) with a normal composition $(R_{\rm d}\sim 5.3\ 10^9$ cm), or without hydrogen $(R_{\rm d}\sim 2.2\ 10^9$ cm), and binary separation $R_{12}\sim 10^{11}$ cm, we get a time for binary merging due to a gravitational radiation $\tau_{\rm g}=\frac{5c^5 R_{12}^4} {256 G^3 M_{\rm d} M_{\rm n} (M_{\rm d}+M_{\r... ...\ 10^{16} \frac{R_{11}^4} {(M_{\rm d} M_{\rm n} (M_{\rm d}+M_{\rm n}))_{\odot}}$ s of the order of a cosmological time. This companion absorbs $\sim(R_{\rm d}/R_{12})^2$ of the total energy flux, what is equal to $\sim 0.003$, $\sim 0.0005$ for normal composition, and hydrogen-free dwarfs relatively. To obtain an afterglow with energy comparable with the energy of the observed GRB we should imagine that efficiency of GR production in the event does not exceed $\sim 1\%$, and the main energy is radiated in the form of the kinetic energy, or relativistic particles. It corresponds to the total energy output $\sim 10^{38}$ ergs. The shock wave may heat the surface to high temperatures, leading to an X-ray flash $\sim(R_{12}/c) \approx 3$ seconds after the main GRB. For a longer GRB it means the corresponding change of the GRB spectrum with a sharp rise in the soft part. Radiation flux and ultrarelativistic particles penetrate deeper under the surface of the star heating a rather thick layer. Taking the absorption cross-section $\sim 10^{-26}$ cm², and the absorbed flux $(1-3)\ 10^{35}$ ergs, corresponding to $\sim 10^{16}$ ergs/cm², we obtain a surface temperature $\sim 10^5$ K immediately after absorption. It means that relatively strong ultraviolet source appears, accompanied by a strong mass loss feeding additionally the accretion disk around the neutron star. After a short ($\sim 10$ seconds) phase of the mass loss and UV emission the temperature drops, and a week cooling object appears with a spectrum moving into the red and IR region, which is in general accordance with the observed afterglows.