Theories of Early Afterglow

The rapid follow-up of gamma-ray burst (GRB) afterglows made possible by the multiwavelength satellite Swift, launched in November 2004, has put under a microscope the GRB early post-burst behavior, This is leading to a significant reappraisal and expansion of the standard view of the GRB early afterglow behavior, and its connection to the prompt gamma-ray emission. In addition to opening up the previously poorly known behavior on minutes to hours timescales, two other new pieces in the GRB puzzle being filled in are the the discovery and follow-up of short GRB afterglows, and the opening up of the z> ∼ redshift range. We review some of the current theoretical interpretations of these new phenomena. CHALLENGES POSED BY NEW SWIFT OBSERVATIONS Compared to previous satellites, Swift has made a large difference on two main accounts. First, the sensitivity of the Burst Alert Detector (BAT, in the range 20-150 keV) is a factor ∼ 5 higher than for the corresponding instruments in the predecessor CGROBATSE, BeppoSAX and HETE-2. Second, Swift can slew in less then 100 seconds in the direction determined by the BAT instrument, positioning its much higher angular resolution X-ray (XRT) and UV-Optical (UVOT) detectors on the burst [1] As of December 2005, at an average rate of 2 bursts detected per week, over 100 bursts had been detected by BAT, of which 90% were followed promptly with the XRT within 350 s from the trigger, and about half within 100 s [2], while ∼ 30% were detected with the UVOT [3]. Of these, over 23 resulted in redshift determinations. Ten short GRB were detected, of which five had detected X-ray afterglows, three had optical, and one had a radio afterglow, and five had a redshift determination. The new observations brings the total redshift determinations to over 50 since 1997 when BeppoSAX enabled the first one. The redshifts based on Swift have a median z> ∼2, which is a factor ∼ 2 higher than the median of those previously culled via BeppoSAX and HETE-2, [5]. This can be ascribed to the higher sensitivity of BAT and the prompt accurate positions from XRT and UVOT, making possible ground-based detection at a stage when the afterglow is much brighter. The highest Swift-enabled redshift so far is in GRB 050904, obtained with Subaru, z = 6.29 [6], the second highest being GRB 050814 at z=5.3, whereas the previous Beppo-SAX era record was z=4.5. The relative paucity of UVOT detections versus XRT detections may be ascribed in part to this higher median redshift, and in part to the higher dust extinction at the implied shorter rest-frame wavelenghts for a given observed frequency [3], although additional effects may be at work too. The BAT light curves show that in some of the bursts which fall in the Theories of Early Afterglow February 5, 2008 1 “long" category (tγ > ∼2 s) faint soft gamma-ray tails can be followed which extend the duration by a factor up to two beyond what BATSE could have detected [1]. A rich trove of information on the burst and afterglow physics has come from detailed XRT light curves, starting on average 100 seconds after the trigger, together with the corresponding BAT light curves and spectra. This suggests a canonical X-ray afterglow [18] with one or more of the following: 1) an initial steep decay FX ∝ t1 with a temporal index 3< ∼α1 < ∼5, and an energy spectrum Fν ∝ ν1 with energy spectral index 1< ∼β1 < ∼2 (or photon number index 2< ∼Γ = α + 1< ∼3), extending up to a time 300s< ∼t1 < ∼500s; 2) a flatter decay FX ∝ t2 with 0.2< ∼α2 < ∼0.8 and energy index 0.7< ∼β2 < ∼1.2, at times 10s< ∼t2 < ∼10 s; 3) a “normal" decay FX ∝ t3 with 1.1< ∼α3 < ∼1.7 and 0.7< ∼β2 < ∼1.2 (generally unchanged the previous stage), up to a time t3 ∼ 10s, or in some cases longer; 4) In some cases, a steeper decay FX ∝ t4 with 2< ∼α4 < ∼3, after t4 ∼ 10 s; 5) In about half the afterglows, one or more X-ray flares are observed, sometimes starting as early as 100 s after trigger, and sometimes as late as 10s. The energy in these flares ranges from a percent up to a value comparable to the prompt emission (in GRB 050502b). The rise and decay times of these flares is unusually steep, depending on the reference time t0, behaving as (t− t0)fl with 3< ∼αfl < ∼6, and energy indices which can be also steeper than during the smooth decay portions. The flux level after the flare usually decays to the value extrapolated from the value before the flare rise. FIGURE 1. Schematic features seen by the XRT in bursts detected by Swift [16] (see text). Another major advance achieved by Swift was the detection of the long burst GRB 050904, which broke through the astrophysically and psychologically important redshift barrier of z ∼ 6. This burst was very bright, both in its prompt γ-ray emission (Eγ,iso ∼ 10 erg) and in its X-ray afterglow. Prompt ground-based optical/IR upper limits and a J-band detection suggested a photometric redshift z > 6 [4]. Spectroscopic confirmation with the 8.2 m Subaru telescope gave a z = 6.29 [6]. There are several striking features to this burst. One is the enormous X-ray brightness, exceeding for a full day the X-ray brightness of the most distant X-ray quasar know to-date, SDSS J0130+0524, by up to Theories of Early Afterglow February 5, 2008 2 a factor 10 in the first minutes [7]. The implications as a tool for probing the IGM are thought-provoking. Another feature is the extremely variable X-ray light curve, showing many large amplitude flares extending up to at least a day. A third exciting feature is the report of a brief, very bright IR flash [8], comparable in brightness to the famous mV ∼ 9 optical flash in GRB 990123. The third major advance from Swift was the discovery and localization of short GRB afterglows. As of December 2005 nine short bursts had been localized by Swift, while in the same period HETE-2 discovered two, and one was identified with the IPN network. In five of the Swift short bursts an X-ray afterglow was measured and followed up, with GRB 050709, 050724 and 051221a showing an optical afterglow, and 050724 also a radio afterglow, while 040924 had an optical afterglow but not an X-ray one [46]. These are the first afterglows detected for short bursts. Also, for the first time, host galaxies were identified for these short bursts, which in four cases are early type (ellipticals) and in two cases are irregular galaxies. The redshifts of four of them are in the range z ∼ 0.15− 0.5, while another one was initially given as z = 0.8 but more recently has been reported as z ≃ 1.8 [49]. The median z is < ∼1/3− 1/2 that of the long bursts. There is no evidence for significant star formation in any of these host environments, which corresponds to what one would expect for neutron star mergers or neutron starblack hole mergers, the most often discussed progenitor candidates (it would also be compatible with other progenitors involving old compact stars). The first short burst seen by Swift, GRB 05059b, was a low luminosity (Eiso ∼ 2× 10 erg) burst with a simple power-law X-ray afterglow which could only be followed for ∼ 10 s [36]. The third one, GRB 050724, was brighter, Eiso ∼ 3× 10 erg, and could be followed in X-rays for at least 10 s [37]. The remarkable thing about this burst’s X-ray afterglow is that it resembles the typical X-ray light curves described above for long GRB – except for the lack of a slow-decay phase, and for the short prompt emission which places it the the category of short bursts, as well as the elliptical host galaxy candidate. It also has X-ray flares, at 100 s and another one at 3×10 s. The first flare has the same fluence as the prompt emission, while the late flare has ∼ 10% of that. The interpretation of these pose interesting challenges, as discussed below. MODELS OF EARLY AFTERGLOWS IN LIGHT OF SWIFT The afterglow is expected to become important after a time tag =Max[(3/4)(rdec/2cΓ )(1+ z) , T ] = Max[102(E52/n0) Γ −8/3 2 (1+ z)|s , T ] , (1) where the deceleration time is tdec ∼ (3/4)(rdec/2cΓ) and T is the duration of the prompt outflow, tag marking the beginning of the self-similar blast wave regime. Denoting the frequency and time dependence of the afterglow spectral energy flux as Fν(t)∝ ν t, the late X-ray afterglow phases (3) and (4) described above are similar to those known previously from Beppo-SAX. (For a review of this earlier behavior and its modeling see e.g. [9]). The “normal" decay phase (3), with temporal decay indices α ∼ 1.1− 1.5 and spectral energy indices β ∼ 0.7− 1.0, is what is expected from the Theories of Early Afterglow February 5, 2008 3 evolution of the forward shock in the Blandford-McKee self-similar late time regime, under the assumption of synchrotron emission. The late steep decay decay phase (4) of §, occasionally seen in Swift bursts, is naturally explained as a jet break, when the decrease of the ejecta Lorentz factor leads to the light-cone angle becoming larger than the jet angular extent, Γj(t) ∼1/θj (e.g. [9]). It is noteworthy, however, that this final steepening has been seen in less than ∼ 10% of the Swift afterglows, and then with reasonable confidence mainly in X-rays. The corresponding optical light curve breaks have been few, and not well constrained. This is unlike the case with the ∼ 20 Beppo-SAX bursts, for which an achromatic break was reported in the optical [10], while in some of the rare cases where an X-ray or radio break was reported it occurred at a different time [11]. The relative paucity of optical breaks in Swift afterglows may be an observational selection effect due to the larger median redshift, and hence fainter and redder optical afterglow at the same observer epoch, as well as perhaps reluctance to commit large telescope time on more frequently reported bursts (an average, roughly, of 2/month with Beppo-SAX versus 2/week with Swift).