Analytic Light-Curves of Gamma-Ray Burst Afterglows: Homogeneous versus Wind External Media

Assuming an adiabatic evolution of a Gamma-Ray Burst (GRB) remnant interacting with an external medium, we calculate the injection, cooling, and absorption break frequencies, and the afterglow flux for plausible orderings of the break and observing frequencies. The analytical calculations are restricted to a relativistic remnant and, in the case of collimated ejecta, to the phase where there is an insignificant lateral expansion. Results are given for both a homogeneous external medium and for a wind ejected by the GRB progenitor. We compare the afterglow emission at different observing frequencies, for each type of external medium. It is found that observations at sub-millimeter frequencies during the first day provide the best way of discriminating between the two models. By taking into account the effect of inverse Compton scatterings on the electron cooling, a new possible time-dependence of the cooling break is identified. The signature of the up-scattering losses could be seen in the optical synchrotron emission from a GRB remnant interacting with a pre-ejected wind, as a temporary mild flattening of the afterglow decay. The up-scattered radiation itself should be detected in the soft X-ray emission from GRB remnants running into denser external media, starting few hours after the main event.Comment: 11 pages, to be published in the ApJ, vol 54

Gamma-Ray Bursts from Up-Scattered Self-Absorbed Synchrotron Emission

We calculate the synchrotron self-Compton emission from internal shocks occurring in relativistic winds as a source of gamma-ray bursts, with allowance for self-absorption. For plausible model parameters most pulses within a Gamma-Ray Burst (GRB) are optically thick to synchrotron self-absorption at the frequency at which most electrons radiate. Up-scattering of photon number spectra harder than $\nu^0$ (such as the self-absorbed emission) yields inverse Compton photon number spectra that are flat, therefore our model has the potential of explaining the low-energy indices harder than $\nu^{-2/3}$ (the optically thin synchrotron limit) that have been observed in some bursts. The optical counterparts of the model bursts are sufficiently bright to be detected by such experiments as LOTIS, unless the magnetic field is well below equipartition.Comment: to be published in ApJL, 5 pages, 3 color figure

Power Density Spectra of Gamma-Ray Bursts in the Internal Shock Model

We simulate Gamma-Ray Bursts arising from internal shocks in relativistic winds, calculate their power density spectrum (PDS), and identify the factors to which the PDS is most sensitive: the wind ejection features, which determine the wind dynamics and its optical thickness, and the energy release parameters, which give the pulse 50-300 keV radiative efficiency. For certain combinations of ejection features and wind parameters the resulting PDS exhibits the features observed in real bursts. We found that the upper limit on the efficiency of conversion of wind kinetic energy into 50-300 keV photons is $\sim$ 1%. Winds with a modulated Lorentz factor distribution of the ejecta yield PDSs in accord with current observations and have efficiencies closer to $10^{-3}$, while winds with a random, uniform Lorentz factor ejection must be optically thick to the short duration pulses to produce correct PDSs, and have an overall efficiency around $10^{-4}$.Comment: 6 pages, 4 figures, Latex, submitted to The Astrophysical Journal (05/04/99

Creation of Electron--Positron Wind in Gamma-Ray Bursts and Its Effect on the Early Afterglow Emission

We calculate the creation of electron--positron pairs in Gamma-Ray Bursts (GRBs) resulting from the collision between scattered and outward moving gamma-ray photons. The number of pairs exceeds the number of ambient medium electrons encountered by the GRB ejecta up to ~ 10^{16} cm from the center of explosion. The shock resulting from the interaction of the ejecta with the pair-wind may brighten the afterglow synchrotron emission during the first few minutes. Even without this effect, the peak intensity of the optical afterglow increases with the density of the surrounding medium. Therefore, observations of the optical flux at early times constrain the density of the circumburst medium. If the electron and magnetic field energies behind the forward shock sweeping-up the pair-wind and the circumburst medium are as inferred from fits to the broadband afterglow emission at 0.5-100 days, then the current upper limits on the optical counterpart emission, set by the ROTSE and LOTIS experiments, indicate that the circumburst medium within 0.01 pc is less dense than 100 cm^{-3} or, if a wind, corresponds to a progenitor mass-loss to wind speed ratio below 10^{-6} M_sun/yr/(1000 km/s).Comment: 9 pages, submitted to MNRAS in 200