41,857 research outputs found
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 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
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 and has the same
normalized Jones-like vector. The angle between the fixed unit
vector and the propagation axis acts as a parameter that describes the
vectorial property of the beam. The impact of 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
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