The X -ray light-curves of 9 Swift XRT afterglows ( 050126 , 050128 , 050219A , 050315 , 050318 , 050319 , 050401 , 050408 , 050505 ) display a complex behaviour : a steep t ^ { -3.0 \pm 0.3 } decay until \sim 400 s , followed by a significantly slower t ^ { -0.65 \pm 0.20 } fall-off , which at 0.2–2 d after the burst evolves into a t ^ { -1.7 \pm 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 \pm 0.5 } , is required for 5 afterglows and could be at work in the other 4 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 GRB emission ) , the 400 s–5 h slow decay ( e.g . a structured outflow ) , or the steepening at 0.2–2d ( 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 an universal value .