Gamma-Ray Burst Afterglows: Effects of Radiative Corrections and Nonuniformity of the Surrounding Medium

The afterglow of a gamma-ray burst (GRB) is commonly thought to be due to continuous deceleration of a relativistically expanding fireball in the surrounding medium. Assuming that the expansion of the fireball is adiabatic and that the density of the medium is a power-law function of shock radius, viz., $n_{ext}\propto R^{-k}$, we analytically study the effects of the first-order radiative correction and the nonuniformity of the medium on a GRB afterglow. We first derive a new relation among the observed time, the shock radius and the fireball's Lorentz factor: $t_\oplus=R/4(4-k)\gamma^2c$, and also derive a new relation among the comoving time, the shock radius and the fireball's Lorentz factor: $t_{co}=2R/(5-k)\gamma c$. We next study the evolution of the fireball by using the analytic solution of Blandford and McKee (1976). The radiation losses may not significantly influence this evolution. We further derive new scaling laws both between the X-ray flux and observed time and between the optical flux and observed time. We use these scaling laws to discuss the afterglows of GRB 970228 and GRB 970616, and find that if the spectral index of the electron distribution is $p=2.5$, implied from the spectra of GRBs, the X-ray afterglow of GRB970616 is well fitted by assuming $k=2$.Comment: 17 pages, no figures, Latex file, MNRAS in pres

Local linear spatial quantile regression

Copyright @ 2009 International Statistical Institute / Bernoulli Society for Mathematical Statistics and Probability.Let {(Yi,Xi), i ∈ ZN} be a stationary real-valued (d + 1)-dimensional spatial processes. Denote by x → qp(x), p ∈ (0, 1), x ∈ Rd , the spatial quantile regression function of order p, characterized by P{Yi ≤ qp(x)|Xi = x} = p. Assume that the process has been observed over an N-dimensional rectangular domain of the form In := {i = (i1, . . . , iN) ∈ ZN|1 ≤ ik ≤ nk, k = 1, . . . , N}, with n = (n1, . . . , nN) ∈ ZN. We propose a local linear estimator of qp. That estimator extends to random fields with unspecified and possibly highly complex spatial dependence structure, the quantile regression methods considered in the context of independent samples or time series. Under mild regularity assumptions, we obtain a Bahadur representation for the estimators of qp and its first-order derivatives, from which we establish consistency and asymptotic normality. The spatial process is assumed to satisfy general mixing conditions, generalizing classical time series mixing concepts. The size of the rectangular domain In is allowed to tend to infinity at different rates depending on the direction in ZN (non-isotropic asymptotics). The method provides muchAustralian Research Counci

Particle simulation of lower hybrid waves in tokamak plasmas

Global particle simulations of the lower hybrid waves have been carried out using fully kinetic ions and drift kinetic electrons with a realistic electron-to-ion mass ratio. The lower hybrid wave frequency, mode structure, and electron Landau damping from the electrostatic simulations agree very well with the analytic theory. Linear simulation of the propagation of a lower hybrid wave-packet in the toroidal geometry shows that the wave propagates faster in the high field side than the low field side, in agreement with a ray tracing calculation. Electromagnetic benchmarks of lower hybrid wave dispersion relation are also carried out. Electromagnetic mode conversion are observed in toroidal geometry, slow waves are launched at the plasma boundary and converts to fast waves at the mode conversion layer, which is consistent with linear theory.Comment: 8 pages, 11 figure

Transverse spin effects of sea quarks in unpolarized nucleons

We calculate the non-zero Boer-Mulders functions of sea quarks inside the proton in a meson-baryon fluctuation model. The results show that the transverse spin effects of sea quarks in an unpolarized nucleon are sizable. Using the obtained antiquark Boer-Mulders functions, we estimate the $\cos 2 \phi$ asymmetries in the unpolarized $pp$ and $p D$ Drell-Yan processes at FNAL E866/NuSea experiments. The prediction for the $\cos 2 \phi$ asymmetries in the unpolarized $pp$ Drell-Yan process at the BNL Relativistic Heavy Ion Collider (RHIC) is also given.Comment: 7 pages, 5 figures, to appear in Physical Review

T-shaped Single-photon Router

We study the transport properties of a single photon scattered by a two-level system (TLS) in a T-shaped waveguide, which is made of two coupled-resonator waveguides (CRWs)--- an infinite CRW and a semi-infinite CRW. The spontaneous emission of the TLS directs single photons from one CRW to the other. Although the transfer rate is different for the wave incident from different CRWs, due to the boundary breaking the translational symmetry, the boundary can enhance the transfer rate found in Phys. Rev. Lett. 111, 103604 (2013) and Phys. Rev. A 89, 013805 (2014), as the transfer rate could be unity for the wave incident from the semi-infinite CRW.Comment: 8 pages, 3 figure

Application of a simplified probe feed impedance formula to the design of a dual frequency patch antenna

A simplified probe feed input impedance for a rectangular patch antenna based on the Green's function is used to design a dual frequency matched antenna. The predicted results at design frequencies of 1.9 and 2.4 GHz are in close agreement with experimental measurements

Strangeness production in heavy ion collisions at SPS and RHIC within two-source statistical model

The experimental data on hadron yields and ratios in central Pb+Pb and Au+Au collisions at SPS and RHIC energies, respectively, are analysed within a two-source statistical model of an ideal hadron gas. These two sources represent the expanding system of colliding heavy ions, where the hot central fireball is embedded in a larger but cooler fireball. The volume of the central source increases with rising bombarding energy. Results of the two-source model fit to RHIC experimental data at midrapidity coincide with the results of the one-source thermal model fit, indicating the formation of an extended fireball, which is three times larger than the corresponding core at SPS.Comment: Talk at "Strange Quarks in Matter" Conference (Strangeness'2001), September 2001, Frankfurt a.M., German

Relativistic electrons generated at Earth's quasi-parallel bow shock.

Plasma shocks are the primary means of accelerating electrons in planetary and astrophysical settings throughout the universe. Which category of shocks, quasi-perpendicular or quasi-parallel, accelerates electrons more efficiently is debated. Although quasi-perpendicular shocks are thought to be more efficient electron accelerators, relativistic electron energies recently observed at quasi-parallel shocks exceed theoretical expectations. Using in situ observations at Earth's bow shock, we show that such relativistic electrons are generated by the interaction between the quasi-parallel shock and a related nonlinear structure, a foreshock transient, through two betatron accelerations. Our observations show that foreshock transients, overlooked previously, can increase electron acceleration efficiency at a quasi-parallel shock by an order of magnitude. Thus, quasi-parallel shocks could be more important in generating relativistic electrons, such as cosmic ray electrons, than previously thought