Early Afterglows of Gamma-Ray Bursts in a Stratified Medium with a Power-Law Density Distribution

A long-duration gamma-ray burst (GRB) has been widely thought to arise from the collapse of a massive star, and it has been suggested that its ambient medium is a homogenous interstellar medium (ISM) or a stellar wind. There are two shocks when an ultra-relativistic fireball that has been ejected during the prompt gamma-ray emission phase sweeps up the circumburst medium: a reverse shock that propagates into the fireball, and a forward shock that propagates into the ambient medium. In this paper, we investigate the temporal evolution of the dynamics and emission of these two shocks in an environment with a general density distribution of $n\propto R^{-k}$ (where $R$ is the radius) by considering thick-shell and thin-shell cases. A GRB afterglow with one smooth onset peak at early times is understood to result from such external shocks. Thus, we can determine the medium density distribution by fitting the onset peak appearing in the light curve of an early optical afterglow. We apply our model to 19 GRBs, and find that their $k$ values are in the range of 0.4 - 1.4, with a typical value of $k\sim1$, implying that this environment is neither a homogenous interstellar medium with $k=0$ nor a typical stellar wind with $k=2$. This shows that the progenitors of these GRBs might have undergone a new mass-loss evolution.Comment: 32 pages, 5 figures, 1 table, published in Ap

Energy Forecasting with Building Characteristics Analysis

With the installation of smart meters, high resolution building-level energy consumption data become increasingly accessible, which not only provides more accurate data for energy forecasting at the aggregated level but also enables datadriven energy forecasting for individual buildings. On the one hand, individual buildings exhibit high randomness, making the forecasting problem at the building-level more challenging. On the other hand, buildings usually have their own characteristics, therefore such valuable information needs to be considered in the forecast models at the aggregation level. In this paper we investigate how unique characteristics of buildings could affect the performance of forecasting models and aim to identify defining patterns of buildings. The usefulness of the proposed approach is demonstrated using data from three real-world buildings

Pre-merger electromagnetic counterparts of binary compact stars

We investigate emission signatures of binary compact star gravitational wave sources consisting of strongly magnetized neutron stars (NSs) and/or white dwarfs (WDs) in their late-time inspiral phase. Because of electromagnetic interactions between the magnetospheres of the two compact stars, a substantial amount of energy will be extracted, and the resultant power is expected to be $\sim 10^{38} - 10^{44}$ erg/s in the last few seconds before the two stars merge, when the binary system contains a NS with a surface magnetic field $10^{12}$ G. The induced electric field in the process can accelerate charged particles up to the EeV energy range. Synchrotron radiation is emitted from energetic electrons, with radiative energies reaching the GeV energy for binary NSs and the MeV energy for NS - WD or double WD binaries. In addition, a blackbody component is also presented and it peaks at several to hundreds keV for binary NSs and at several keV for NS - WD or double WD binaries. The strong angular dependence of the synchrotron radiation and the isotropic nature of the blackbody radiation lead to distinguishable modulation patterns between the two emission components. If coherent curvature radiation is presented, fast radio bursts could be produced. These components provide unique simultaneous electromagnetic signatures as precursors of gravitational wave events associated with magnetized compact star mergers and short gamma ray bursts (e.g., GRB 100717).Comment: 16 pages, 8 figures, 1 table. Minor corrections to match the version on Ap

Analytical treatment for the development of electromagnetic cascades in intense magnetic fields

In a strong magnetic field, a high-energy photon can be absorbed and then produce an electron-positron pair. The produced electron/positron will in turn radiate a high-energy photon via synchrotron radiation, which then initiates a cascade. We built a one-dimensional Monte-Carlo code to study the development of the cascade especially after it reaches the saturated status, when almost all the energy of the primary particles transfers to the photons. The photon spectrum in this status has a cut-off due to the absorption by magnetic fields, which is much sharper than the exponential one. Below the cut-off, the spectral energy distribution (SED) manifest itself as a broken power-law with a spectral index of $0.5$ and $0.125$, respectively, below and above the broken energy. The SED can be fitted by a simple analytical function, which is solely determined by the product of the cascade scale $R$ and the magnetic field perpendicular to the motion of the particle B_{\perp}, with an accuracy better than 96\%. The similarity of the spectrum to that from the cascade in an isotropic black-body photon field is also studied.Comment: 7 pages, 7 figures, minor changes. Version to appear in PR

Cosmology-Independent Distance Moduli of 42 Gamma-Ray Bursts between Redshift of 1.44 and 6.60

This report is an update and extension of our paper accepted for publication in ApJ (arXiv:0802.4262). Since objects at the same redshift should have the same luminosity distance and the distance moduli of type Ia supernovae (SNe Ia) obtained directly from observations are completely cosmology independent, we obtain the distance modulus of a gamma-ray burst (GRB) at a given redshift by interpolating or iterating from the Hubble diagram of SNe Ia. Then we calibrate five GRB relations without assuming a particular cosmological model, from different regression methods, and construct the GRB Hubble diagram to constrain cosmological parameters. Based upon these relations we list the cosmology-independent distance moduli of 42 GRBs between redshift of 1.44 and 6.60, with the 1-$\sigma$ uncertainties of 1-3%.Comment: 6 pages, 2 figures, 3 tables. To appear in the proceedings of "2008 Nanjing GRB conference", Nanjing, 23-27 June 200