An Examination of the Spectral Variability in NGC 1365 with Suzaku

We present jointly analyzed data from three deep Suzaku observations of NGC 1365. These high signal-to-noise spectra enable us to examine the nature of this variable, obscured AGN in unprecedented detail on timescales ranging from hours to years. We find that, in addition to the power-law continuum and absorption from ionized gas seen in most AGN, inner disk reflection and variable absorption from neutral gas within the Broad Emission Line Region are both necessary components in all three observations. We confirm the clumpy nature of the cold absorbing gas, though we note that occultations of the inner disk and corona are much more pronounced in the high-flux state (2008) than in the low-flux state (2010) of the source. The onset and duration of the "dips" in the X-ray light curve in 2010 are both significantly longer than in 2008, however, indicating that either the distance to the gas from the black hole is larger, or that the nature of the gas has changed between epochs. We also note significant variations in the power-law flux over timescales similar to the cold absorber, both within and between the three observations. The warm absorber does not vary significantly within observations, but does show variations in column density of a factor of more than 10 on timescales less than 2 weeks that seem unrelated to the changes in the continuum, reflection or cold absorber. By assuming a uniform iron abundance for the reflection and absorption, we have also established that an iron abundance of roughly 3.5 times the solar value is sufficient to model the broad-band spectrum without invoking an additional partial-covering absorber. Such a measurement is consistent with previous published constraints from the 2008 Suzaku observation alone, and with results from other Seyfert AGN in the literature.Comment: 19 pages, 11 figures, accepted for publication in MNRA

Kinetic theory for non-equilibrium stationary states in long-range interacting systems

We study long-range interacting systems perturbed by external stochastic forces. Unlike the case of short-range systems, where stochastic forces usually act locally on each particle, here we consider perturbations by external stochastic fields. The system reaches stationary states where external forces balance dissipation on average. These states do not respect detailed balance and support non-vanishing fluxes of conserved quantities. We generalize the kinetic theory of isolated long-range systems to describe the dynamics of this non-equilibrium problem. The kinetic equation that we obtain applies to plasmas, self-gravitating systems, and to a broad class of other systems. Our theoretical results hold for homogeneous states, but may also be generalized to apply to inhomogeneous states. We obtain an excellent agreement between our theoretical predictions and numerical simulations. We discuss possible applications to describe non-equilibrium phase transitions.Comment: 11 pages, 2 figures; v2: small changes, close to the published versio

Numerical solution of the two-dimensional Helmholtz equation with variable coefficients by the radial integration boundary integral and integro-differential equation methods

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 Taylor & Francis.This paper presents new formulations of the boundary–domain integral equation (BDIE) and the boundary–domain integro-differential equation (BDIDE) methods for the numerical solution of the two-dimensional Helmholtz equation with variable coefficients. When the material parameters are variable (with constant or variable wave number), a parametrix is adopted to reduce the Helmholtz equation to a BDIE or BDIDE. However, when material parameters are constant (with variable wave number), the standard fundamental solution for the Laplace equation is used in the formulation. The radial integration method is then employed to convert the domain integrals arising in both BDIE and BDIDE methods into equivalent boundary integrals. The resulting formulations lead to pure boundary integral and integro-differential equations with no domain integrals. Numerical examples are presented for several simple problems, for which exact solutions are available, to demonstrate the efficiency of the proposed methods

Numerical solution of the two-dimensional Helmholtz equation with variable coefficients by the radial integration boundary integral and integro-differential equation methods

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 Taylor & Francis.This paper presents new formulations of the boundary–domain integral equation (BDIE) and the boundary–domain integro-differential equation (BDIDE) methods for the numerical solution of the two-dimensional Helmholtz equation with variable coefficients. When the material parameters are variable (with constant or variable wave number), a parametrix is adopted to reduce the Helmholtz equation to a BDIE or BDIDE. However, when material parameters are constant (with variable wave number), the standard fundamental solution for the Laplace equation is used in the formulation. The radial integration method is then employed to convert the domain integrals arising in both BDIE and BDIDE methods into equivalent boundary integrals. The resulting formulations lead to pure boundary integral and integro-differential equations with no domain integrals. Numerical examples are presented for several simple problems, for which exact solutions are available, to demonstrate the efficiency of the proposed methods

Canonical Expansion of PT-Symmetric Operators and Perturbation Theory

Let $H$ be any \PT symmetric Schr\"odinger operator of the type $-\hbar^2\Delta+(x_1^2+...+x_d^2)+igW(x_1,...,x_d)$ on $L^2(\R^d)$, where $W$ is any odd homogeneous polynomial and $g\in\R$. It is proved that $\P H$ is self-adjoint and that its eigenvalues coincide (up to a sign) with the singular values of $H$, i.e. the eigenvalues of $\sqrt{H^\ast H}$. Moreover we explicitly construct the canonical expansion of $H$ and determine the singular values $\mu_j$ of $H$ through the Borel summability of their divergent perturbation theory. The singular values yield estimates of the location of the eigenvalues \l_j of $H$ by Weyl's inequalities.Comment: 20 page

GRB 091029: At the limit of the fireball scenario

Using high-quality, broad-band afterglow data for GRB 091029, we test the validity of the forward-shock model for gamma-ray burst afterglows. We used multi-wavelength (NIR to X-ray) follow-up observations obtained with the GROND, BOOTES-3/YA and Stardome optical ground-based telescopes, and the UVOT and the XRT onboard the Swift satellite. To explain the almost totally decoupled light curves in the X-ray and optical/NIR domains, a two-component outflow is proposed. Several models are tested, including continuous energy injection, components with different electron energy indices and components in two different stages of spectral evolution. Only the last model can explain both the decoupled light curves with asynchronous peaks and the peculiar SED evolution. However, this model has so many unknown free parameters that we are unable to reliably confirm or disprove its validity, making the afterglow of GRB 091029 difficult to explain in the framework of the simplest fireball model.Comment: Accepted to A&

GRB 070518: A Gamma-ray Burst with Optically Dim Luminosity

We present our optical observations of {\em Swift} GRB 070518 afterglow obtained at the 0.8-m Tsinghua University-National Astronomical Observatory of China telescope (TNT) at Xinglong Observatory. Our follow-up observations were performed from 512 sec after the burst trigger. With the upper limit of redshift $\sim$0.7, GRB 070518 is found to be an optically dim burst. The spectra indices $\beta_{ox}$ of optical to X-ray are slightly larger than 0.5, which implies the burst might be a dark burst. The extinction $A_{V}$ of the host galaxy is 3.2 mag inferred from the X-ray hydrogen column density with Galactic extinction law, and 0.3 mag with SMC extinction law. Also, it is similar to three other low-redshift optically dim bursts, which belong to XRR or XRF, and mid-term duration($T_{90}<10$, except for GRB 070419A, $T_{90}$=116s). Moreover, its $R$ band afterglow flux is well fitted by a single power-law with an index of 0.87. The optical afterglow and the X-ray afterglow in the normal segment might have the same mechanism, as they are consistent with the prediction of the classical external shock model. Besides, GRB 070518 agrees with Amati relation under reasonable assumptions. The Ghirlanda relation is also tested with the burst.Comment: 8 pages, 4 figures, MNRAS accepte

Coevolution of Glauber-like Ising dynamics on typical networks

We consider coevolution of site status and link structures from two different initial networks: a one dimensional Ising chain and a scale free network. The dynamics is governed by a preassigned stability parameter $S$, and a rewiring factor $\phi$, that determines whether the Ising spin at the chosen site flips or whether the node gets rewired to another node in the system. This dynamics has also been studied with Ising spins distributed randomly among nodes which lie on a network with preferential attachment. We have observed the steady state average stability and magnetisation for both kinds of systems to have an idea about the effect of initial network topology. Although the average stability shows almost similar behaviour, the magnetisation depends on the initial condition we start from. Apart from the local dynamics, the global effect on the dynamics has also been studied. These parameters show interesting variations for different values of $S$ and $\phi$, which helps in determining the steady-state condition for a given substrate.Comment: 8 pages, 10 figure

A statistical study of gamma-ray burst afterglows measured by the Swift Ultra-violet Optical Telescope

We present the first statistical analysis of 27 UVOT optical/ultra-violet lightcurves of GRB afterglows. We have found, through analysis of the lightcurves in the observer's frame, that a significant fraction rise in the first 500s after the GRB trigger, that all lightcurves decay after 500s, typically as a power-law with a relatively narrow distribution of decay indices, and that the brightest optical afterglows tend to decay the quickest. We find that the rise could either be produced physically by the start of the forward shock, when the jet begins to plough into the external medium, or geometrically where an off-axis observer sees a rising lightcurve as an increasing amount of emission enters the observers line of sight, which occurs as the jet slows. We find that at 99.8% confidence, there is a correlation, in the observed frame, between the apparent magnitude of the lightcurves at 400s and the rate of decay after 500s. However, in the rest frame a Spearman Rank test shows only a weak correlation of low statistical significance between luminosity and decay rate. A correlation should be expected if the afterglows were produced by off-axis jets, suggesting that the jet is viewed from within the half-opening angle theta or within a core of uniform energy density theta_c. We also produced logarithmic luminosity distributions for three rest frame epochs. We find no evidence for bimodality in any of the distributions. Finally, we compare our sample of UVOT lightcurves with the XRT lightcurve canonical model. The range in decay indices seen in UVOT lightcurves at any epoch is most similar to the range in decay of the shallow decay segment of the XRT canonical model. However, in the XRT canonical model there is no indication of the rising behaviour observed in the UVOT lightcurves.Comment: 16 pages, 9 figures, accepted MNRA

Rest-frame properties of 32 gamma-ray bursts observed by the Fermi Gamma-Ray Burst Monitor

Aims: In this paper we study the main spectral and temporal properties of gamma-ray bursts (GRBs) observed by Fermi/GBM. We investigate these key properties of GRBs in the rest-frame of the progenitor and test for possible intra-parameter correlations to better understand the intrinsic nature of these events. Methods: Our sample comprises 32 GRBs with measured redshift that were observed by GBM until August 2010. 28 of them belong to the long-duration population and 4 events were classified as short/hard bursts. For all of these events we derive, where possible, the intrinsic peak energy in the $\nu F_{\nu}$ spectrum (\eprest), the duration in the rest-frame, defined as the time in which 90% of the burst fluence was observed (\tninetyrest) and the isotropic equivalent bolometric energy (\eiso). Results: The distribution of \eprest has mean and median values of 1.1 MeV and 750 keV, respectively. A log-normal fit to the sample of long bursts peaks at ~800 keV. No high-\ep population is found but the distribution is biased against low \ep values. We find the lowest possible \ep that GBM can recover to be ~ 15 keV. The \tninetyrest distribution of long GRBs peaks at ~10 s. The distribution of \eiso has mean and median values of $8.9\times 10^{52}$ erg and $8.2 \times 10^{52}$ erg, respectively. We confirm the tight correlation between \eprest and \eiso (Amati relation) and the one between \eprest and the 1-s peak luminosity ($L_p$) (Yonetoku relation). Additionally, we observe a parameter reconstruction effect, i.e. the low-energy power law index $\alpha$ gets softer when \ep is located at the lower end of the detector energy range. Moreover, we do not find any significant cosmic evolution of neither \eprest nor \tninetyrest.Comment: accepted by A&