The Second Swift BAT Gamma-Ray Burst Catalog

We present the second Swift Burst Alert Telescope (BAT) catalog of gamma-ray bursts (GRBs), which contains 476 bursts detected by the BAT between 2004 December 19 and 2009 December 21. This catalog (hereafter the BAT2 catalog) presents burst trigger time, location, 90% error radius, duration, fluence, peak flux, time-averaged spectral parameters and time-resolved spectral parameters measured by the BAT. In the correlation study of various observed parameters extracted from the BAT prompt emission data, we distinguish among long-duration GRBs (L-GRBs), short-duration GRBs (S-GRBs), and short-duration GRBs with extended emission (S-GRBs with E.E.) to investigate differences in the prompt emission properties. The fraction of L-GRBs, S-GRBs and S-GRBs with E.E. in the catalog are 89%, 8% and 2% respectively. We compare the BAT prompt emission properties with the BATSE, BeppoSAX and HETE-2 GRB samples. We also correlate the observed prompt emission properties with the redshifts for the GRBs with known redshift. The BAT T90 and T50 durations peak at 70 s and 30 s, respectively. We confirm that the spectra of the BAT S-GRBs are generally harder than those of the L-GRBs. The time-averaged spectra of the BAT S-GRBs with E.E. are similar to those of the L-GRBs. Whereas, the spectra of the initial short spikes of the S-GRBs with E.E. are similar to those of the S-GRBs. We show that the BAT GRB samples are significantly softer than the BATSE bright GRBs, and that the time-averaged Epeak of the BAT GRBs peaks at 80 keV which is significantly lower energy than those of the BATSE sample which peak at 320 keV. The time-averaged spectral properties of the BAT GRB sample are similar to those of the HETE-2 GRB samples. By time-resolved spectral analysis, we find that only 10% of the BAT observed photon indices are outside the allowed region of the synchrotron shock model.Comment: 65 pages, 33 figures, 13 tables, Accepted in ApJS, Nine machine-readable tables are available at http://swift.gsfc.nasa.gov/docs/swift/results/bat2_catalog

Self-Consistent Velocity Dependent Effective Interactions

The theory of self-consistent effective interactions in nuclei is extended for a system with a velocity dependent mean potential. By means of the field coupling method, we present a general prescription to derive effective interactions which are consistent with the mean potential. For a deformed system with the conventional pairing field, the velocity dependent effective interactions are derived as the multipole pairing interactions in doubly-stretched coordinates. They are applied to the microscopic analysis of the giant dipole resonances (GDR's) of ${}^{148,154}Sm$, the first excited $2^+$ states of Sn isotopes and the first excited $3^-$ states of Mo isotopes. It is clarified that the interactions play crucial roles in describing the splitting and structure of GDR peaks, in restoring the energy weighted sum rule, and in reducing the values of $B(E\lambda)$.Comment: 35 pages, RevTeX, 7 figures (available upon request), to appear in Phys.Rev.

Generalized sine-Gordon/massive Thirring models and soliton/particle correspondences

We consider a real Lagrangian off-critical submodel describing the soliton sector of the so-called conformal affine $sl(3)^{(1)}$ Toda model coupled to matter fields (CATM). The theory is treated as a constrained system in the context of Faddeev-Jackiw and the symplectic schemes. We exhibit the parent Lagrangian nature of the model from which generalizations of the sine-Gordon (GSG) or the massive Thirring (GMT) models are derivable. The dual description of the model is further emphasized by providing the relationships between bilinears of GMT spinors and relevant expressions of the GSG fields. In this way we exhibit the strong/weak coupling phases and the (generalized) soliton/particle correspondences of the model. The $sl(n)^{(1)}$ case is also outlined.Comment: 22 pages, LaTex, some comments and references added, conclusions unchanged, to appear in J. Math. Phy

A year in the life of GW170817: the rise and fall of a structured jet from a binary neutron star merger

We present the results of our year-long afterglow monitoring of GW170817, the first binary neutron star (NS) merger detected by advanced LIGO and advanced Virgo. New observations with the Australian Telescope Compact Array (ATCA) and the Chandra X-ray Telescope were used to constrain its late-time behavior. The broadband emission, from radio to X-rays, is well-described by a simple power-law spectrum with index ~0.585 at all epochs. After an initial shallow rise ~t^0.9, the afterglow displayed a smooth turn-over, reaching a peak X-ray luminosity of ~5e39 erg/s at 160 d, and has now entered a phase of rapid decline ~t^(-2). The latest temporal trend challenges most models of choked jet/cocoon systems, and is instead consistent with the emergence of a relativistic structured jet seen at an angle of ~22 deg from its axis. Within such model, the properties of the explosion (such as its blastwave energy E_K~2E50 erg, jet width theta_c~4 deg, and ambient density n~3E-3 cm^(-3)) fit well within the range of properties of cosmological short GRBs.Comment: 11 pages, 8 figures, 2 tables, MNRAS, in press. Final version, minor changes only relative to original submission dated 21 August 201

Magnetic translation groups in an n-dimensional torus

A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. We show that the MTG on an n-dimensional torus is isomorphic to a central extension of a cyclic group Z_{nu_1} x ... x Z_{nu_{2l}} x T^m by U(1) with 2l+m=n. We construct and classify irreducible unitary representations of the MTG on a three-torus and apply the representation theory to three examples. We shortly describe a representation theory for a general n-torus. The MTG on an n-torus can be regarded as a generalization of the so-called noncommutative torus.Comment: 29 pages, LaTeX2e, title changed, re-organized, to be published in Journal of Mathematical Physic

Galerkin FEM for fractional order parabolic equations with initial data in H−s, 0<s≤1H^{-s},~0 < s \le 1

We investigate semi-discrete numerical schemes based on the standard Galerkin and lumped mass Galerkin finite element methods for an initial-boundary value problem for homogeneous fractional diffusion problems with non-smooth initial data. We assume that $\Omega\subset \mathbb{R}^d$, $d=1,2,3$ is a convex polygonal (polyhedral) domain. We theoretically justify optimal order error estimates in $L_2$- and $H^1$-norms for initial data in $H^{-s}(\Omega),~0\le s \le 1$. We confirm our theoretical findings with a number of numerical tests that include initial data $v$ being a Dirac $\delta$-function supported on a $(d-1)$-dimensional manifold.Comment: 13 pages, 3 figure

Linkage mapping reveals sex-dimorphic map distances in a passerine bird

Linkage maps are lacking for many highly influential model organisms in evolutionary research, including all passerine birds. Consequently, their full potential as research models is severely hampered. Here, we provide a partial linkage map and give novel estimates of sex-specific recombination rates in a passerine bird, the great reed warbler (Acrocephalus arundinaceus). Linkage analysis of genotypic data at 51 autosomal microsatellites and seven markers on the Z-chromosome (one of the sex chromosomes) from an extended pedigree resulted in 12 linkage groups with 2–8 loci. A striking feature of the map was the pronounced sex-dimorphism: males had a substantially lower recombination rate than females, which resulted in a suppressed autosomal map in males (sum of linkage groups: 110.2cM) compared to females (237.2cM; female/male map ratio: 2.15). The sex-specific recombination rates will facilitate the building of a denser linkage map and cast light on hypotheses about sex-specific recombination rates

Epeak estimator for Gamma-Ray Bursts Observed by the Swift Burst Alert Telescope

We report a correlation based on a spectral simulation study of the prompt emission spectra of gamma-ray bursts (GRBs) detected by the Swift Burst Alert Telescope (BAT). The correlation is between the Epeak energy, which is the peak energy in the \nu F_\nu spectrum, and the photon index (\Gamma) derived from a simple power-law model. The Epeak - \Gamma relation, assuming the typical smoothly broken power-law spectrum of GRBs, is \log Epeak = 3.258 - 0.829\Gamma (1.3 < \Gamma < 2.3). We take into account not only a range of Epeak energies and fluences, but also distributions for both the low-energy photon index and the high-energy photon index in the smoothly broken power-law model. The distribution of burst durations in the BAT GRB sample is also included in the simulation. Our correlation is consistent with the index observed by BAT and Epeak measured by the BAT, and by other GRB instruments. Since about 85% of GRBs observed by the BAT are acceptably fit with the simple power-law model because of the relatively narrow energy range of the BAT, this relationship can be used to estimate Epeak when it is located within the BAT energy range.Comment: 27 pages, 31 figures, accepted for publication in Ap

Bar-driven Transport of Molecular Gas to Galactic Centers and Its Consequences

We study the characteristics of molecular gas in the central regions of spiral galaxies on the basis of our CO(J=1-0) imaging survey of 20 nearby spiral galaxies using the NRO and OVRO millimeter arrays. Condensations of molecular gas at galactic centers with sizescales < 1 kpc and CO-derived masses M_gas(R<500pc) = 10^8 - 10^9 M_sun are found to be prevalent in the gas-rich L^* galaxies. Moreover, the degree of gas concentration to the central kpc is found to be higher in barred systems than in unbarred galaxies. This is the first statistical evidence for the higher central concentration of molecular gas in barred galaxies, and it strongly supports the theory of bar-driven gas transport. It is most likely that more than half of molecular gas within the central kpc of a barred galaxy was transported there from outside by the bar. The supply of gas has exceeded the consumption of gas by star formation in the central kpc, resulting in the excess gas in the centers of barred systems. The mean rate of gas inflow is statistically estimated to be larger than 0.1 - 1 M_sun/yr. The correlation between gas properties in the central kpc and the type of nuclear spectrum (HII, LINER, or Seyfert) is investigated. A correlation is found in which galaxies with larger gas-to-dynamical mass ratios tend to have HII nuclear spectra, while galaxies with smaller ratios show spectra indicating AGN. Also, the theoretical prediction of bar-dissolution by condensation of gas to galactic centers is observationally tested. It is suggested that the timescale for bar dissolution is larger than 10^8 - 10^10 yr, or a bar in a L^* galaxy is not destroyed by a condensation of 10^8 - 10^9 M_sun gas in the central kpc.Comment: AASTeX, 20 pages, 8 eps figs, ApJ in press (10 Nov. 1999 issue

A luminous blue kilonova and an off-axis jet from a compact binary merger at z=0.1341

The recent discovery of a faint gamma-ray burst (GRB) coincident with the gravitational wave (GW) event GW 170817 revealed the existence of a population of low-luminosity short duration gamma-ray transients produced by neutron star mergers in the nearby Universe. These events could be routinely detected by existing gamma-ray monitors, yet previous observations failed to identify them without the aid of GW triggers. Here we show that GRB150101B was an analogue of GRB170817A located at a cosmological distance. GRB 150101B was a faint short duration GRB characterized by a bright optical counterpart and a long-lived X-ray afterglow. These properties are unusual for standard short GRBs and are instead consistent with an explosion viewed off-axis: the optical light is produced by a luminous kilonova component, while the observed X-rays trace the GRB afterglow viewed at an angle of ~13 degrees. Our findings suggest that these properties could be common among future electromagnetic counterparts of GW sources.Comment: 28 pages, 8 figures, 2 tables. Accepted for publicatio