Gamma-Ray Burst Afterglows with Energy Injection: Homogeneous Versus Wind External Media

Assuming an adiabatic evolution of a gamma-ray burst (GRB) fireball interacting with an external medium, we calculate the hydrodynamics of the fireball with energy injection from a strongly magnetic millisecond pulsar through magnetic dipole radiation, and obtain the light curve of the optical afterglow from the fireball by synchrotron radiation. Results are given both for a homogeneous external medium and for a wind ejected by GRB progenitor. Our calculations are also available in both ultra-relativistic and non-relativistic phases. Furthermore, the observed R-band light curve of GRB{000301C} can be well fitted in our model, which might provide a probe of the properties of GRB progenitors.Comment: revised version for publication in Chin. Phys. Let

Constraining ΩM\Omega_M and Dark Energy with Gamma-Ray Bursts

An $E_{\gamma,{\rm jet}}\propto {E'_p}^{1.5}$ relationship with a small scatter for current $\gamma$-ray burst (GRB) data was recently reported, where $E_{\gamma,{\rm jet}}$ is the beaming-corrected $\gamma$-ray energy and $E'_p$ is the $\nu F_\nu$ peak energy in the local observer frame. By considering this relationship for a sample of 12 GRBs with known redshift, peak energy, and break time of afterglow light curves, we constrain the mass density of the universe and the nature of dark energy. We find that the mass density $\Omega_M=0.35\pm^{0.15}_{0.15}$ (at the $1\sigma$ confident level) for a flat universe with a cosmological constant, and the $w$ parameter of an assumed static dark-energy equation of state $w=-0.84\pm^{0.57}_{0.83}$ ($1\sigma$). Our results are consistent with those from type Ia supernovae. A larger sample established by the upcoming {\em Swift} satellite is expected to provide further constraints.Comment: 8 pages including 4 figures, to appear in ApJ Letters, typos correcte

Echo Emission From Dust Scattering and X-Ray Afterglows of Gamma-Ray Bursts

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.Comment: 25 pages, 3 figures, 2 tables. Accepted for publication in Ap

GRB Afterglows from Anisotropic Jets

Some progenitor models of gamma-ray bursts (GRBs) (e.g., collapsars) may produce anisotropic jets in which the energy per unit solid angle is a power-law function of the angle ($\propto\theta^{-k}$). We calculate light curves and spectra for GRB afterglows when such jets expand either in the interstellar medium or in the wind medium. In particular, we take into account two kinds of wind: one ($n\propto r^{-3/2}$) possibly from a typical red supergiant star and another ($n\propto r^{-2}$) possibly from a Wolf-Rayet star. We find that in each type of medium, one break appears in the late-time afterglow light curve for small $k$ but becomes weaker and smoother as $k$ increases. When $k\ge 2$, the break seems to disappear but the afterglow decays rapidly. Thus, one expects that the emission from expanding, highly anisotropic jets provides a plausible explanation for some rapidly fading afteglows whose light curves have no break. We also present good fits to the optical afterglow light curve of GRB 991208. Finally, we argue that this burst might arise from a highly anisotropic jet expanding in the wind ($n\propto r^{-3/2}$) from a red supergiant to interpret the observed radio-to-optical-band afterglow data (spectrum and light curve).Comment: 12 pages + 10 figures, accepted by Ap

Gamma-ray Burst Afterglow with Continuous Energy Injection: Signature of a Highly-Magnetized Millisecond Pulsar

We investigate the consequences of a continuously injecting central engine on the gamma-ray burst afterglow emission, focusing more specifically on a highly-magnetized millisecond pulsar engine. For initial pulsar parameters within a certain region of the parameter space, the afterglow lightcurves are predicted to show a distinctive achromatic bump feature, the onset and duration of which range from minutes to months, depending on the pulsar and the fireball parameters. The detection of or upper limits on such features would provide constraints on the burst progenitor and on magnetar-like central engine models. An achromatic bump such as that in GRB 000301C afterglow may be caused by a millisecond pulsar with P0=3.4 millisecond and Bp=2.7e14 Gauss.Comment: 5 pages, emulateapj style, to appear in ApJ Letters, updated with the accepted version, a few corrections are mad

Measurement of the c-axis optical reflectance of AFe2_2As2_2 (A=Ba, Sr) single crystals: Evidence of different mechanisms for the formation of two energy gaps

We present the c-axis optical reflectance measurement on single crystals of BaFe$_2$As$_2$ and SrFe$_2$As$_2$, the parent compounds of FeAs based superconductors. Different from the ab-plane optical response where two distinct energy gaps were observed in the SDW state, only the smaller energy gap could be seen clearly for \textbf{E}$\parallel$c-axis. The very pronounced energy gap structure seen at a higher energy scale for \textbf{E}$\parallel$ab-plane is almost invisible. We propose a novel picture for the band structure evolution across the SDW transition and suggest different driving mechanisms for the formation of the two energy gaps.Comment: 4 page

Variational auto-encoded deep Gaussian processes

We develop a scalable deep non-parametric generative model by augmenting deep Gaussian processes with a recognition model. Inference is performed in a novel scalable variational framework where the variational posterior distributions are reparametrized through a multilayer perceptron. The key aspect of this reformulation is that it prevents the proliferation of variational parameters which otherwise grow linearly in proportion to the sample size. We derive a new formulation of the variational lower bound that allows us to distribute most of the computation in a way that enables to handle datasets of the size of mainstream deep learning tasks. We show the efficacy of the method on a variety of challenges including deep unsupervised learning and deep Bayesian optimization

Exponential Family Estimation via Adversarial Dynamics Embedding

We present an efficient algorithm for maximum likelihood estimation (MLE) of exponential family models, with a general parametrization of the energy function that includes neural networks. We exploit the primal-dual view of the MLE with a kinetics augmented model to obtain an estimate associated with an adversarial dual sampler. To represent this sampler, we introduce a novel neural architecture, dynamics embedding, that generalizes Hamiltonian Monte-Carlo (HMC). The proposed approach inherits the flexibility of HMC while enabling tractable entropy estimation for the augmented model. By learning both a dual sampler and the primal model simultaneously, and sharing parameters between them, we obviate the requirement to design a separate sampling procedure once the model has been trained, leading to more effective learning. We show that many existing estimators, such as contrastive divergence, pseudo/composite-likelihood, score matching, minimum Stein discrepancy estimator, non-local contrastive objectives, noise-contrastive estimation, and minimum probability flow, are special cases of the proposed approach, each expressed by a different (fixed) dual sampler. An empirical investigation shows that adapting the sampler during MLE can significantly improve on state-of-the-art estimators

A conceptual framework for the future of sea-level rise and land uplift changes in the Vaasa region of Finland

This paper uses the Vaasa region of Finland as an illustrative case study to explore how the relationships between climate change, sea-level rise and land uplift may offer applications in forecasting future land uplift changes. Using a comparative literature review and analysis of open source data, a conceptual framework is developed to ex-amine causes-effect relationships between them. The sea-level rise around the world by the end of the 21st century shows dramatic effects all over the world. However, the rate of land uplift in the Vaasa region is higher than the rate of sea-level rise. This localised finding is different from global average rates for land uplift and sea-level rise. This indicates that although climate change is global, it can lead to very different regional expressions. This paper presents a first attempt to combine sea-level rise and land uplift into a single cohesive framework to sup-port future land uplift management. The results of this paper establish a conceptual framework for studies of vulnerability and adaptation to climate change that can ben-efit local, regional and global communities