4 GRB afterglows

In the plasmoid rest frame, the synchrotron emission from the decelerating plasmoid/jet can be modeled (e.g., Chiang & Dermer 1998) by convolving the typical electron energy spectrum (E^-p at low energies up to some "break energy'' where it steepens to E^-p-1 and cuts off exponentially at some higher energy due to synchrotron losses in magnetic acceleration) with the synchrotron Green's function (see, e.g., Meisenheimer et al. 1989). In the observer frame the beamed afterglow has a temporal and spectral behavior which can be interpolated by

$$I_\nu\sim \nu^{-\alpha}(t/t_0)^{-\beta}/[1+(t/t_0)^{\beta'-\beta}]$$ (5)

where t₀ is the time when the jet begins to spread, $\alpha \approx (p-1)/2$, $\beta\approx (p+5)/6$ and $\beta'\approx p$. For magnetic Fermi acceleration $p=2.5\pm 0.5$ and (Dar 1998a,b) $\alpha=0.75\pm 0.25$, $\beta=1.25\pm 0.08$,and $\beta'\approx 2.5\pm 0.5$. The mildly relativistic spherical ejecta from the NS collapse produces additional unbeamed supernova-like afterglow, like that of GRB 980425/SN1998bw (many planetary nebulae and some SNRs appear to eject antiparallel jets from a spherical explosion). It is observable only if the jet is dim enough. A power-law afterglow + SN 1998bw like light curve better explains GRB afterglows like that of GRB 970228. Moreover, the glows of microquasar plasmoids and radio quasar jets after ejection and of blazar jets after flaring show behavior similar to that observed in GRBs afterglows. For instance, the glows of the ejected plasmoids from GRS 1915+105 on April 16, 1994 near the source had $\alpha=0.8\pm 0.1$ and $\beta= 1.3\pm 0.2$ (Rodriguez & Mirabel 1998) identical to those observed for SS 433 (Hjellming & Johnston 1988) and for the inner regions of jets of some radio galaxies (e.g., Bridle & Perley 1984). When jets/plasmoids are attenuated and spread they decline with $\beta'\sim 2.4\pm 0.3$ (Rodriguez & Mirabel 1998). Such a fast decline has been observed in the late afterglow of some GRBs.