Gamma-ray bursts (GRBs) are the most violent explosions in the Universe and can be used to explore the properties of high-redshift universe. It is believed that the long GRBs are associated with the deaths of massive stars. So it is possible to use G
RBs to investigate the star formation rate (SFR). In this paper, we use Lynden-Bells $c^-$ method to study the luminosity function and rate of emph{Swift} long GRBs without any assumptions. We find that the luminosity of GRBs evolves with redshift as $L(z)propto g(z)=(1+z)^k$ with $k=2.43_{-0.38}^{+0.41}$. After correcting the redshift evolution through $L_0(z)=L(z)/g(z)$, the luminosity function can be expressed as $psi(L_0)propto L_0^{-0.14pm0.02}$ for dim GRBs and $psi(L_0)propto L_0^{-0.70pm0.03}$ for bright GRBs, with the break point $L_{0}^{b}=1.43times10^{51}~{rm erg~s^{-1}}$. We also find that the formation rate of GRBs is almost constant at $z<1.0$ for the first time, which is remarkably different from the SFR. At $z>1.0$, the formation rate of GRB is consistent with the SFR. Our results are dramatically different from previous studies. Some possible reasons for this low-redshift excess are discussed. We also test the robustness of our results with Monte Carlo simulations. The distributions of mock data (i.e., luminosity-redshift distribution, luminosity function, cumulative distribution and $log N-log S$ distribution) are in good agreement with the observations. Besides, we also find that there are remarkable difference between the mock data and the observations if long GRB are unbiased tracers of SFR at $z<1.0$.
We investigate the effect of X-ray echo emission in gamma-ray bursts (GRBs). We find that the echo emission can provide an alternative way of understanding X-ray shallow decays and jet breaks. In particular, a shallow decay followed by a normal decay
and a further rapid decay of X-ray afterglows can be together explained as being due to the echo from prompt X-ray emission scattered by dust grains in a massive wind bubble around a GRB progenitor. We also introduce an extra temporal break in the X-ray echo emission. By fitting the afterglow light curves, we can measure the locations of the massive wind bubbles, which will bring us closer to finding the mass loss rate, wind velocity, and the age of the progenitors prior to the GRB explosions.
The widely existing shallow decay phase of the X-ray afterglows of gamma-ray bursts (GRBs) is generally accepted to be due to long-lasting energy injection. The outflows carrying the injecting energy, based on the component that is dominative in ener
gy, fall into two possible types: baryon-dominated and lepton-dominated ones. The former type of outflow could be ejecta that is ejected during the prompt phase of a GRB and consists of a series of baryonic shells with a distribution of Lorentz factors, and the latter type could be an electron-positron-pair wind that is driven by the post-burst central engine. We here provide a unified description for the dynamics of fireballs based on these two types of energy injection, and calculate the corresponding high-energy photon emission by considering synchrotron radiation and inverse Compton scattering (including synchrotron self-Compton and combined inverse-Compton) of electrons. We find that, in the two energy-injection models, there is a plateau (even a hump) in high-energy light curves during the X-ray shallow decay phase. In particular, a considerable fraction of the injecting energy in the lepton-dominated model can be shared by the long-lasting reverse shock since it is relativistic. Furthermore, almost all of the energy of the reverse shock is carried by leptons, and thus the inverse-Compton emission is enhanced dramatically. Therefore, this model predicts more significant high-energy afterglow emission than the baryon-dominated model. We argue that these observational signatures would be used to discriminate between different energy-injection models in the upcoming {em Gamma-ray Large Area Space Telescope} (GLAST) era.
