Constraining fast radio burst progenitors with gravitational lensing

Fast Radio Bursts (FRBs) are new transient radio sources discovered recently. Because of the angular resolution restriction in radio surveys, no optical counter part has been identified yet so it is hard to determine the progenitor of FRBs. In this paper we propose to use radio lensing survey to constrain FRB progenitors. We show that, different types of progenitors lead to different probabilities for a FRB to be gravitationally lensed by dark matter halos in foreground galaxies, since different type progenitors result in different redshift distributions of FRBs. For example, the redshift distribution of FRBs arising from double stars shifts toward lower redshift than of the FRBs arising from single stars, because double stars and single stars have different evolution timescales. With detailed calculations, we predict that the FRB sample size for producing one lensing event varies significantly for different FRB progenitor models. We argue that this fact can be used to distinguish different FRB models and also discuss the practical possibility of using lensing observation in radio surveys to constrain FRB progenitors.Comment: 14 pages, including 6 figures and 1 tabl

Search for strong gravitational lensing effect in the current GRB data of BATSE

Because gamma-ray bursts (GRBs) trace the high-z Universe, there is an appreciable probability for a GRB to be gravitational lensed by galaxies in the universe. Herein we consider the gravitational lensing effect of GRBs contributed by the dark matter halos in galaxies. Assuming that all halos have the singular isothermal sphere (SIS) mass profile in the mass range $10^{10} h^{-1} M_\odot < M < 2\times 10^{13} h^{-1}M_\odot$ and all GRB samples follow the intrinsic redshift distribution and luminosity function derived from the Swift LGRBs sample, we calculated the gravitational lensing probability in BATSE, Swift/BAT and Fermi/GBM GRBs, respectively. With an derived probability result in BATSE GRBs, we searched for lensed GRB pairs in the BATSE 5B GRB Spectral catalog. The search did not find any convincing gravitationally lensed events. We discuss our result and future observations for GRB lensing observation.Comment: 18 pages, 8 figure

Representation theory for vector electromagnetic beams

A representation theory of finite electromagnetic beams in free space is formulated by factorizing the field vector of the plane-wave component into a $3 \times 2$ mapping matrix and a 2-component Jones-like vector. The mapping matrix has one degree of freedom that can be described by the azimuthal angle of a fixed unit vector with respect to the wave vector. This degree of freedom allows us to find out such a beam solution in which every plane-wave component is specified by the same fixed unit vector $\mathbf{I}$ and has the same normalized Jones-like vector. The angle $\theta_I$ between the fixed unit vector and the propagation axis acts as a parameter that describes the vectorial property of the beam. The impact of $\theta_I$ is investigated on a beam of angular-spectrum field scalar that is independent of the azimuthal angle. The field vector in position space is calculated in the first-order approximation under the paraxial condition. A transverse effect is found that a beam of elliptically-polarized angular spectrum is displaced from the center in the direction that is perpendicular to the plane formed by the fixed unit vector and the propagation axis. The expression of the transverse displacement is obtained. Its paraxial approximation is also given.Comment: 16 pages. The final version appears in the Phys. Rev.

Generalised regression estimation given imperfectly matched auxiliary data

Generalised regression estimation allows one to make use of available auxiliary information in survey sampling. We develop three types of generalised regression estimator when the auxiliary data cannot be matched perfectly to the sample units, so that the standard estimator is inapplicable. The inference remains design-based. Consistency of the proposed estimators is either given by construction or else can be tested given the observed sample and links. Mean square errors can be estimated. A simulation study is used to explore the potentials of the proposed estimators