Analysis of the X-ray emission of nine Swift afterglows

The X-ray light curves of nine Swift XRT afterglows (050126, 050128, 050219A, 050315, 050318, 050319, 050401, 050408 and 050505) display a complex behaviour: a steep t(-3.0 +/- 0.3) decay until similar to 400 s, followed by a significantly slower t(-0.65 +/- 0.20) fall-off, which at 0.2-2 day after the burst evolves into a t(-1.7 +/- 0.5) decay. We consider three possible models for the geometry of relativistic blast-waves (spherical outflows, non-spreading jets and spreading jets), two possible dynamical regimes for the forward shock (adiabatic and fully radiative), and we take into account a possible angular structure of the outflow and delayed energy injection in the blast-wave to identify the models which reconcile the X-ray light-curve decay with the slope of the X-ray continuum for each of the above three afterglow phases. By piecing together the various models for each phase in a way that makes physical sense, we identify possible models for the entire X-ray afterglow. The major conclusion of this work is that a long-lived episode of energy injection in the blast-wave, during which the shock energy increases at t(1.0 +/- 0.5), is required for five afterglows and could be at work in the other four as well. For some afterglows, there may be other mechanisms that can explain the t < 400 s fast falling-off X-ray light curve (e.g. the large-angle gamma-ray burst emission), the 400 s to 5 h slow decay (e.g. a structured outflow), or the steepening at 0.2-2 day (e.g. a jet-break, a collimated outflow transiting from a wind with a r(-3) radial density profile to a homogeneous or outward-increasing density region). Optical observations in conjunction with the X-ray can distinguish among these various models. Our simple tests allow the determination of the location of the cooling frequency relative to the X-ray domain and, thus, of the index of the electron power-law distribution with energy in the blast-wave. The resulting indices are clearly inconsistent with a universal value.