The afterglow of GRB 081029 showed unusual behavior, with a signifi- cant rebrightening being observed at the optical wavelength at about 3000 s after the burst. One possible explanation is that the rebrightening resulted from an energy in- jection. Here we present a detailed numerical study of the energy injection process and interpret the X-ray and optical afterglow light curves of GRB 081029. In our model, we have assumed two periods of energy injection, each with a constant injec- tion power. One injection starts at 2.8 × 10^3 s and lasts for about 2500 s, with a power of 7.0 × 10^47 erg s-1. This energy injection mainly accounts for the rapid rebrighten- ing at about 3000 s. The other injection starts at 8.0 × 10^3 s and lasts for about 5000 s. The injection power is 3.5 × 10^47 erg s-1. This energy injection can help to explain the slight rebrightening at about 10 000 s. It is shown that the observed optical after- glow, especially the marked rebrightening at about 3000 s, can be reproduced well. In the X-ray band, the predicted amplitude of the rebrightening is much shallower, which is also consistent with the observed X-ray afterglow light curve. It is argued that the two periods of energy injection can be produced by clumpy materials falling onto the central compact object of the burster, which leads to an enhancement of accretion and gives rise to a strong temporary outflow.
We propose a consistency test for some recent X-ray gas mass fraction （fgas） measurements in galaxy clusters, using the cosmic distance-duality relation, Ttneory = DL（1 ＋ Z）-2/DA, with luminosity distance （DL） data from the Union2 compilation of type Ia supernovae. We set Z/theory = 1, instead of assigning any red- shift parameterizations to it, and constrain the cosmological information preferred by fga8 data along with supernova observations. We adopt a new binning method in the reduction of the Union2 data, in order to minimize the statistical errors. Four data sets of X-ray gas mass fraction, which are reported by Allen et al. （two samples）, LaRoque et al. and Ettori et al., are analyzed in detail in the context of two theoretical models of fgas. The results from the analysis of Alien et al.＇s samples demonstrate the feasibility of our method. It is found that the preferred cosmology by LaRoque et al.＇s sample is consistent with its reference cosmology within the 1σ confidence level. However, for Ettori et al.＇s fgas sample, the inconsistency can reach more than a 3σ confidence level and this dataset shows special preference to an ΩA = 0 cosmology.
