7.1. Short GRB observations
Swift, and in smaller numbers HETE-2, have provided the first bona fide short burst X-ray afterglows followed up starting ~ 100 s after the trigger, leading to localizations and redshifts. In the first of these, GRB 050509b  the extrapolation of the prompt BAT emission into the X-ray range, and the XRT light curve from 100 s to about 1000 s (after which only upper limits exist, even with Chandra, due to the faintness of the burst) can be fitted with a single power law of ~ 1.2 (1.12 to 1.29 90% conf), or separately as BAT = 1.34 (0.27 to 2.87 90% conf) and XRT = 1.1 (0.57 to 2.36 90% conf). The X-ray coverage was sparse due to orbital constraints, the number of X-ray photons being small, and no optical transient was identified, probably due to the faintness of the source. An optical host was however identified, an elliptical galaxy . The next one, discovered by HETE-2, was GRB 050709 . Its host  is an irregular galaxy at z = 0.16 (and the observations ruled out any supernova association). Even earlier, HETE-2 reported the short GRB 040924 , with a soft gamma-ray prompt emission and a faint broken power law optical afterglow . A proposed host galaxy at z = 0.86 shows star formation, and evidence for an associated 1998bw-like SN contribution to the light curve , which suggests this is perhaps the short end of the long burst or XRF distribution. The next Swift short burst, GRB 050724, was relatively bright, and besides X-rays, it also yielded both a decaying optical and a radio afterglow . This burst, together with a significant part of other short bursts, is associated with an elliptical host galaxy. It also had a low-luminosity soft gamma-ray extension of the short hard gamma-ray component (which would have been missed by BATSE), and it had an interesting X-ray afterglow extending beyond 105 s  (Figure 9). The soft gamma-ray extension, lasting up to 200 s, when extrapolated to the X-ray range overlaps well with the beginning of the XRT afterglow, which between 100 and 300 s has ~ -2, followed by a much steeper drop ~ -5 - 7 out to ~ 600 s, then a more moderate decay ~ -1. An unexpected feature is a strong flare peaking at 5 × 104 s, whose energy is 10% of the prompt emission, while its amplitude is a 10 times increase over the preceding slow decay. Among more recent Swift short bursts, such as GRB 050813 [407, 443] had an X-ray afterglow, a possible elliptical host, and was reported to be near a galaxy cluster at z = 1.7-1.9 . GRB 051210  had an X-ray power law afterglow, with bumps or flares, and optical identifications still under consideration. GRB 051221a had X-ray and optical afterglows , and the host is a star forming galaxy at z = 0.55 .
7.2. Short GRB prompt and afterglow emission
The main challenges for an understanding of the mechanism of short bursts are the relatively long, soft tail of the prompt emission, and the strength and late occurrence of the X-ray bumps or flares. A possible explanation for the extended long soft tails (~ 100 s) may be that the compact binary progenitor is a black hole - neutron star system , for which analytical and numerical arguments (, and references therein) suggest that the disruption and swallowing by the black hole may lead to a complex and more extended accretion rate than for double neutron stars (c.f. [315, 109]). The flares, for which the simplest interpretation might be to ascribe them to refreshed shocks (compatible with a short engine duration T t ~ 2 s and a distribution of Lorentz factors), requires the energy in the slow material to be at least ten times as energetic as the fast material responsible for the prompt emission, for the GRB 050724 flare at 104 s. The rise and decay times are moderate enough for this interpretation within the errors. On the other hand, if the decay slope is -2.8, this is steeper than expected for refreshed shocks, but consistent with the high-latitude -2 - model; a time origin t0 can be determined at the beginning of the flare, and late Chandra observations indicate that the decay after the resumes where it had left off before the flare, which is more consistent with a late engine activity interpretation , requiring a factor 10 less energy budget than the refreshed shock interpretation. Another interpretation for such flares might be an accretion-induced collapse of a white dwarf in a binary, leading to a flare when the fireball created by the collapse hits the companion , which might explain moderate energy one-time flares of duration 102 s. However, for repeated, energetic flares, as also in the long bursts, the total energetics are easier to satisfy if one postulates late central engine activity (lasting at least half a day), containing ~ 10% of the prompt fluence . A possible way to produce this might be temporary choking up of an MHD outflow  (c.f. ), which might also imply a linear polarization of the X-ray flare . Such MHD effects could plausibly also explain the initial ~ 100 s soft tail. Another magnetic mechanism proposed for late X-ray flares in short bursts invokes a temporary post-merger massive neutron star . However, a justification for substantial 105 s features remains so far on rather tentative grounds.
Figure 9. The afterglow of GRB 050724 , showing the Swift results on the prompt BAT emission extrapolated to the X-ray range and the subsequent XRT emission, as well as the late Chandra follow-up.
The similarity of the X-ray afterglow light curve with those of long bursts is, in itself, an argument in favor of the prevalent view that the afterglows of both long and short bursts can be described by the same paradigm, independently of any difference in the progenitors. This impression is reinforced by the fact that the X-ray light curve temporal slope is, on average, that expected from the usual forward shock afterglow model, and that in GRB 050724 the X-ray afterglow shows what appears like an initial steep decay, a normal decay and a significant bump or flare. The identification of jet breaks in short bursts is still preliminary, and the subject of debate. In two short bursts (so far) evidence evidence has been reported for a jet break [35, 350, 59]. (However, in GRB 050724 a late Chandra observation indicates no X-ray break ). Taking these breaks as jet breaks, the average isotropic energy of these SHBs is a factor ~ 100 smaller, while the average jet opening angle (based on the two breaks) is a factor ~ 2 larger than those of typical long GRBs [131, 350]. Using standard afterglow theory, the bulk Lorentz factor decay can be expressed through (td) =6.5(no / E50)1/8 td-3/8, where td = (t / day), no is the external density in units of cm-3, and E50 is the isotropic equivalent energy in units of 1050 ergs. If the jet break occurs at (tj) = j-1, for a single-sided jet the jet opening angle and the total jet energy Ej are
For the afterglows of GRB 050709 and GRB 050724, the standard afterglow expressions for the flux level as a function of time before and after the break lead to fits  which are not completely determined, allowing for GRB 050709 either a very low or a moderately low external density, and for GRB 050724 a moderately low to large external density. The main uncertainty is in the jet break time, which is poorly sampled, and so far mainly in X-rays. A better determined case of an X-ray light curve break is that of GRB 051221a, where combined Swift XRT and Chandra observations indicate a late break at tj ~ 5 days, leading to an estimated j ~ 15 degrees . This is similar to jet angles calculated numerically for compact merger scenarios by [214, 6]. It is worth noting, however, that there are some indications that light curve breaks may not (or not always) be achromatic [113, 361]. We note that chromatic breaks have been argued for in some long bursts, e.g. GRB 030329, suggesting different beam opening angles for the optical/X-ray and the radio components (; see also ), and independently of whether this is the explanation, a similar phenomenon may be present in short bursts.
7.3. Short burst hosts and progenitors
The most dramatic impact of Swift concerning short GRB, after the discovery and characterization of the afterglows, has been in providing the first significant identifications of host galaxies, with the implications and constraints that this puts on the progenitor issue. Out of ten short bursts detected until the end 2005, four of the hosts (GRB 040924, 050509b, 050724 and 050813; [155, 26, 35]) are elliptical galaxies, one (GRB 050709, ) is a nearby irregular galaxy, and one (GRB 050906, ) is a star-forming galaxy. The number of elliptical hosts is of significant interest for the most frequently discussed progenitor of short GRB, the merger of neutron star binaries [343, 105, 26, 261], which would be relatively more abundant in old stellar population galaxies such as ellipticals. The argument partly depends on the expected long binary merger times, which in early population synthesis and merger simulations  was taken to be in excess of 108 years. More recent populations synthesis calculations  have reduced this to the point where compact mergers could be expected in substantial numbers also in young, e.g. star-forming galaxies, although statistically most mergers would be expected in old galaxies. The preponderance of claimed elliptical hosts, where star formation is absent, argues against alternative short burst origins such as short-lived outflows from massive stellar collapses . The lack of any observed supernova emission weeks after the burst [197, 130] also argues against a massive stellar collapse (where a Ib/c supernova could be expected), and also against a gravitational collapse of C/O white dwarfs to neutron stars leading to a supernova Ia .
An alternative interpretation of short bursts is that they may be the initial brief, hard spike seen in giant flares of soft gamma repeaters, or SGR [206, 349]. SGRs must be young objects, due to the fast field decay rate, and the total energy in giant SGR flares detected so far is at least two orders of magnitude too small to explain the short burst fluxes detected at z 0.2. The lack of recent star formation activity in the four mentioned elliptical hosts also indicates that at least some short bursts cannot be ascribed to SGRs. A statistical analysis indicates that the fraction of short bursts which could be due to SGRs is less than 15% (or less than 40% at 95% confidence level) . It is interesting that a correlation analysis of short bursts with X-ray selected galaxy clusters  gives a better than 2 angular cross-correlation with clusters up to z = 0.1, which compared to model predictions would indicate that most short bursts originate within ~ 270 Mpc. Any connection between alternative candidates and a possible third category of bursts, intermediate between short and long [199, 320, 296, 200] remains so far unexplored.
7.4. Short burst redshifts and progenitor lifetimes
With over a half dozen reasonably well studied short bursts (as of end of 2005), their distribution in redshift space and among host galaxy types, including both ellipticals and spiral/irregulars , is similar to that of other old population objects, and thus is compatible with neutron star binaries or black hole-neutron star binaries . This progenitor identification, however, cannot be considered secure, so far. Nonetheless, the most striking thing about short hard burst (or SHBs) hosts is that it includes a number of ellipticals, with low star formation rate (SFR), e.g. 050909b, 050724; and even for those SHBs with star forming hosts, e.g. 050709, 051221a, the SFR is lower than the median SFR for the long GRB hosts . This confirms that they are a distinct population, as indicated also by their intrinsic spectral-temporal properties versus those of long bursts [237, 336, 18]. Using the BATSE flux distribution and the observed redshifts, the SHB local rates are inferred to be at least ~ 10 Gpc-3 yr-1 [328, 187] without beaming corrections, and larger including beaming. The progenitor lifetimes lead to interesting constraints, e.g. the simple time delay distribution P(t) t-1 expected from galactic double neutron star systems appears in conflict with the low average redshift of SHBs [153, 328], although it is not ruled out . This has led to inferring a typical lifetime for the progenitors of ~ 6 Gyr, and the suggestion that they might be neutron star-black hole binaries, rather than double neutron stars. However if the redshift z 1.8 for GRB 050813 is correct, the lifetime of the progenitor would be constrained to 103 Gyr . On the other hand, consideration of the star formation history of both early and late type galaxies suggests that at least half of the SHB progenitors have lifetimes in excess of ~ 10 Gyr . Population synthesis models of double compact binaries  indicate two populations, with short (10-2 - 0.2 Myr and long (102 - 104 Myr) merger times, with NS-NS and BH-NS binaries distributed roughly 1:1 and 4:1 between these two merger time ranges, in apparent agreement with current SHB redshift and host distributions between ellipticals and SFR galaxies. The origin of a fraction of double neutron stars in globular clusters  would help to explain short bursts which are offset from their host galaxy.