3 Main results

For GRB with the energy 10⁵² erg we considered the following densities of the surrounding interstellar medium: $10^5\, \mbox{cm}^{-3},\ 300 \,\mbox{cm}^{-3},\ 0.25 \,\mbox{cm}^{-3},\ 1.6\ 10^{-3}\, \mbox{cm}^{-3}$. The main results of calculations in optically thin approximation are presented in our publications Timokhin & Bisnovatyi- Kogan ([1995,1996]). According to these calculations, a counterpart of cosmological GRB due to the influence of GRB on the surrounding medium could be observed if density of the medium is greater then $300 \,\mbox{cm}^{-3}$. For such dense interstellar clouds optically thin approximation is not valid because of large optical depth in main emission lines.

Then we considered a simplified picture of conversion of UV photons into optical ones in optically thick regions, which allowed us to get optical and UV light curves of counterparts (see details in Bisnovatyi-Kogan & Timokhin [1997]). We considered GRBs with energies 10⁵², 10⁵¹ ergs and following initial conditions in a gaseous cloud of radius R:

1

$n_0 =10^5\,\mbox{cm}^{-3}, T_0 = 20\,\mbox{K}, R = 1.5\, \mbox{pc}$

2

$n_0 =10^4\,\mbox{cm}^{-3}, T_0 = 20\,\mbox{K}, R = 5\, \mbox{pc}$.

The results of these calculations are presented in Fig. 1. Dashed lines give the lower boundary for luminosity, and solid lines - the upper one. For GRB with total energy output 10⁵¹ and 10⁵² ergs, maximal luminosities of counterparts differ by one order of magnitude too. This means that relative maximum brightness of the counterparts depends weakly on the total energy output. The total duration of the counterpart radiation decreases 2 times when the total output decreases 10 times. A more detailed description of the results is given in Bisnovatyi-Kogan & Timokhin ([1997]).