Magnetic-distortion-induced ellipticity and gravitational wave radiation of neutron stars: millisecond magnetars in short GRBs, Galactic pulsars, and magnetars

Neutron stars may sustain a non-axisymmetric deformation due to magnetic distortion and are potential sources of continuous gravitational waves (GWs) for ground-based interferometric detectors. With decades of searches using available GW detectors, no evidence of a GW signal from any pulsar has been observed. Progressively stringent upper limits of ellipticity have been placed on Galactic pulsars. In this work, we use the ellipticity inferred from the putative millisecond magnetars in short gamma-ray bursts (SGRBs) to estimate their detectability by current and future GW detectors. For $\sim 1$ ms magnetars inferred from the SGRB data, the detection horizon is $\sim 30$ Mpc and $\sim 600$ Mpc for advanced LIGO (aLIGO) and Einstein Telescope (ET), respectively. Using the ellipticity of SGRB millisecond magnetars as calibration, we estimate the ellipticity and gravitational wave strain of Galactic pulsars and magnetars assuming that the ellipticity is magnetic-distortion-induced. We find that the results are consistent with the null detection results of Galactic pulsars and magnetars with the aLIGO O1. We further predict that the GW signals from these pulsars/magnetars may not be detectable by the currently designed aLIGO detector. The ET detector may be able to detect some relatively low frequency signals ($<50$ Hz) from some of these pulsars. Limited by its design sensitivity, the eLISA detector seems not suitable for detecting the signals from Galactic pulsars and magnetars.Comment: Accepted for publication in Ap

Dynamical Processes of Gravity Waves Propagation and Dissipation, and Statistical Characteristics of Their Momentum Flux in the Mesosphere and Lower Thermosphere

The mesosphere and lower thermosphere (MLT) (⇠80–110 km) is dominated by abundant atmospheric waves, of which gravity waves are one of the least understood due to large varieties in wave characteristics as well as potential sources. Gravity waves play an important role in the atmosphere by influencing the thermal balance and helping to drive the global circulation. But due to their sub-grid scale, the effects of gravity waves in General Circulation Models (GCMs) are mostly parameterized. The investigations of gravity waves in this dissertation are from two perspectives: the dynamical processes of gravity wave propagation and dissipation in the MLT region, and the climatology and statistical characteristics of gravity waves as physical basics of gravity wave parameterization. The studies are based on the data acquired from an airglow imager and a sodium lidar, with the assistance of some simulation data from a meso-scale numerical model and GCMs. To understand the dynamical processes in gravity wave propagation and dissipation, a gravity wave should be resolved as fully as possible. The first topic of this dissertation is motivated by the fact that most observational instruments can only capture part of the gravity waves spectrum, either horizontal or vertical structures. Observations from multiple complementary instruments are used to study gravity waves in 3-D space. There are two cases included in this topic. In case 1, a co-located sodium lidar and an airglow imager were used to depict a comprehensive picture of a wave event at altitude between 95–105 km. Thus, the horizontal and vertical gravity waves structures and their ambient atmosphere states were fully characterized, which suggests that a gravity wave undergoes reflection at two different altitudes and near-critical layer filtering in-between. All the retrieved parameters were then applied to a 2-D numerical model whose outputs help to interpret the observations. In case 2, the lidar system is configured in a 5-direction mode, whose laser beams were pointed to zenith and 30! o↵-zenith at four cardinal directions. Thus, there is a ⇠50 km separation at ⇠90 km altitude between zenith and any o↵-zenith directions. Besides the vertical information from traditional lidar measurement profiles, horizontal wavelength and propagation direction are derived from the phase differences among measurements in different directions. With a full set of wave and background parameters, multiple dispersion and polarization relations are examined and the results validate the goodness of different assumptions involved in linear gravity wave theory. Better knowledge of gravity waves from observational and numerical, as well as theoretical studies directly contribute to the development of physically-based parameterizations. The second topic of this dissertation is about long-term climatology and statistical characteristics of gravity waves observed by an airglow imager. The results provide some insights on how the source spectrum can be specified and tuning factors are constrained in the parameterization. Results from two sites are compared, one is in the middle of the Pacific Ocean, and the other above the Andes Mountains. The difference and similarity provide some clues to the effects of wave sources and background flow on the gravity wave climatology and intermittency in the mesopause region. Firstly, the long-term climatology of intrinsic wave parameters and propagation direction preferences for high-frequency quasi-monochromatic gravity waves observed by an airglow imager is presented. Wave occurrence and propagation direction are related to convective activities nearby and local background winds. The preferential wave propagation during austral summer is poleward and equatorward during winter. The estimated momentum fluxes show a clear anti-correlation with background winds. Secondly, intermittency of gravity waves near mesopause region is studied. The concept of intermittency is originally from the factors used in wave parameterization schemes to describe the fractional coverage of waves within a large spatial grid and/or temporal period in order to accurately quantify the forcing on the atmosphere by dissipating gravity waves. Intermittency of gravity waves was described by the probability density functions of absolute momentum flux and some diagnostic parameters. An explicit probability function that is a piecewise function of lognormal and power law functions is obtained from airglow data. The relative importance of abundant waves with smaller amplitudes and rare waves with dramatically large amplitudes were compared. Lastly, the duration of gravity waves in the airglow layer is studied. The observed gravity waves duration in the airglow layer is exponentially distributed. Several mechanisms that could lead to such a distribution are put forward from the perspective of wave breaking due to instabilities and blocking due to evanescent regions. Ducted propagation is also a possible factor. Through individual cases and statistical studies, this dissertation investigates the dynamical processes and statistical characteristics of gravity waves in the MLT region. The results are expected to provide more insight in both observational and modeling research on gravity waves

On Neutralization of Charged Black Holes

For non-spinning, charged (Reissner–Nordström) black holes, the particles with an opposite sign of charge with respect to that of the black hole will be pulled into the black hole by the extra electromagnetic force. Such a hole will be quickly neutralized so that there should not exist significantly charged, non-spinning black holes in the universe. The case of spinning, charged (Kerr–Newmann, KN) black holes is more complicated. For a given initial position and initial velocity of the particle, an oppositely charged particle does not always more easily fall into the black hole than a neutral particle. The possible existence of a magnetosphere further complicate the picture. One therefore cannot straightforwardly conclude that a charged spinning black hole will be neutralized. In this paper, we make the first step to investigate the neutralization of KN black holes without introducing a magnetosphere. We track the particle trajectories under the influence of the curved space–time and the electromagnetic field carried by the spinning, charged black hole. A statistical method is used to investigate the neutralization problem. We find a universal dependence of the falling probability into the black hole on the charge of the test particle, with the oppositely charged particles having a higher probability of falling. We therefore conclude that charged, spinning black holes without a magnetosphere should be quickly neutralized, consistent with people’s intuition. The neutralization problem of KN black holes with a corotating force-free magnetosphere is subject to further studies

Ricci flow on compact K\"ahler manifolds of positive bisectional curvature

We announce a new proof of the uniform estimate on the curvature of solutions to the Ricci flow on a compact K\"ahler manifold $M^n$ with positive bisectional curvature. In contrast to the recent work of X. Chen and G. Tian, our proof of the uniform estimate does not rely on the exsitence of K\"ahler-Einstein metrics on $M^n$, but instead on the first author's Harnack inequality for the K\"ahler-Ricc flow, and a very recent local injectivity radius estimate of Perelman for the Ricci flow.Comment: 4 page

Fear of the Unknown: Familiarity and Economic Decisions

Evidence indicates that people fear change and the unknown. We offer a model of familiarity bias in which individuals focus on adverse scenarios in evaluating defections from the status quo. The model explains the endowment effect, portfolio underdiversification, home and local biases. Equilibrium stock prices reflect an unfamiliarity premium. In an international setting, our model implies that the absolute pricing error of the standard CAPM is positively correlated with the amount of home bias. It also predicts that a modified CAPM holds wherein the market portfolio is replaced with a portfolio of the stock holdings of investors not subject to familiarity bias.

Double pion production in NNNN and NˉN\bar{N}N collisions

With an effective Lagrangian approach, we give a full analysis on the $NN \to NN\pi\pi$ and $\bar{N}N\to \bar{N}N\pi\pi$ reactions by exploring the roles of various resonances with mass up to 1.72 GeV. We find large contributions from $\Delta$, $N^*(1440)$, $\Delta(1600)$ and $\Delta(1620)$ resonances. Our calculations also indicate sizeable contributions from nucleon poles for the energies close to the threshold. A good description to the existing data of different isospin channels of $NN\to NN\pi\pi$ and $\bar{N}N\to \bar{N}N\pi\pi$ for beam energies up to 2.2 GeV is reached. Our results provide important implications to the ABC effect and guildlines to the future experimental projects at COSY, HADES and HIRFL-CSR. We point out that the \={P}ANDA at FAIR could be an essential place for studying the properties of baryon resonances and the data with baryon and anti-baryon in final states are worth analyzing.Comment: Invited plenary talk at the 11th International Workshop on Meson Production, Properties and Interaction (MESON2010), 10-15 June, 2010, Krakow, Polan