Different kinds of long-term variability from Cygnus X-1

We present a study of the long-term variability of Cyg X-1 using data from the RXTE/ASM and the RXTE/PCA during the time between the two soft states of 1996 and 2001/2002. This period has been characterized by many short ASM flaring episodes which we have identified as "failed state transitions". The 150 d period which has been seen before and shortly after the 1996 soft state is not obviously present in the ASM rate during most of this time. Applying selection criteria from our pointed RXTE/PCA observations to exclude the flaring episodes we show that the 150 d period can indeed still be significantly detected in the hard state. Furthermore, while the ~420 d timescale associated with the flaring is reduced in the selected hard state count rate, it is still pronounced in the temporal evolution of the corresponding hardness ratios. The Ryle radio flux is also consistent with the 150 d period being present but distorted during this time.Comment: 4 pages, 6 figures, to appear in Proceedings of "X-ray Timing 2003: Rossi and Beyond", ed. P. Kaaret, F.K. Lamb, & J.H. Swan

Universality class of the depinning transition in the two-dimensional Ising model with quenched disorder

With Monte Carlo methods, we investigate the universality class of the depinning transition in the two-dimensional Ising model with quenched random fields. Based on the short-time dynamic approach, we accurately determine the depinning transition field and both static and dynamic critical exponents. The critical exponents vary significantly with the form and strength of the random fields, but exhibit independence on the updating schemes of the Monte Carlo algorithm. From the roughness exponents $\zeta, \zeta_{loc}$ and $\zeta_s$, one may judge that the depinning transition of the random-field Ising model belongs to the new dynamic universality class with $\zeta \neq \zeta_{loc}\neq \zeta_s$ and $\zeta_{loc} \neq 1$. The crossover from the second-order phase transition to the first-order one is observed for the uniform distribution of the random fields, but it is not present for the Gaussian distribution.Comment: 16 pages, 16 figures, 3 table

Statistical mechanics of spatial evolutionary games

We discuss the long-run behavior of stochastic dynamics of many interacting players in spatial evolutionary games. In particular, we investigate the effect of the number of players and the noise level on the stochastic stability of Nash equilibria. We discuss similarities and differences between systems of interacting players maximizing their individual payoffs and particles minimizing their interaction energy. We use concepts and techniques of statistical mechanics to study game-theoretic models. In order to obtain results in the case of the so-called potential games, we analyze the thermodynamic limit of the appropriate models of interacting particles.Comment: 19 pages, to appear in J. Phys.

Disordered Environments in Spatial Games

The Prisoner's dilemma is the main game theoretical framework in which the onset and maintainance of cooperation in biological populations is studied. In the spatial version of the model, we study the robustness of cooperation in heterogeneous ecosystems in spatial evolutionary games by considering site diluted lattices. The main result is that due to disorder, the fraction of cooperators in the population is enhanced. Moreover, the system presents a dynamical transition at $\rho^*$, separating a region with spatial chaos from one with localized, stable groups of cooperators.Comment: 6 pages, 5 figure

Field theory on κ\kappa--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry

This paper is devoted to detailed investigations of free scalar field theory on $\kappa$-Minkowski space. After reviewing necessary mathematical tools we discuss in depth the Lagrangian and solutions of field equations. We analyze the spacetime symmetries of the model and construct the conserved charges associated with translational and Lorentz symmetry. We show that the version of the theory usually studied breaks Lorentz invariance in a subtle way: There is an additional trans-Planckian mode present, and an associated conserved charge (the number of such modes) is not a Lorentz scalar.Comment: 22 pages, 1 figure, formulas in sect. III correcte

Beyond XSPEC: Towards Highly Configurable Analysis

We present a quantitative comparison between software features of the defacto standard X-ray spectral analysis tool, XSPEC, and ISIS, the Interactive Spectral Interpretation System. Our emphasis is on customized analysis, with ISIS offered as a strong example of configurable software. While noting that XSPEC has been of immense value to astronomers, and that its scientific core is moderately extensible--most commonly via the inclusion of user contributed "local models"--we identify a series of limitations with its use beyond conventional spectral modeling. We argue that from the viewpoint of the astronomical user, the XSPEC internal structure presents a Black Box Problem, with many of its important features hidden from the top-level interface, thus discouraging user customization. Drawing from examples in custom modeling, numerical analysis, parallel computation, visualization, data management, and automated code generation, we show how a numerically scriptable, modular, and extensible analysis platform such as ISIS facilitates many forms of advanced astrophysical inquiry.Comment: Accepted by PASP, for July 2008 (15 pages

Spectro-timing analysis of Cygnus X-1 during a fast state transition

We present the analysis of two long, quasi-uninterrupted RXTE observations of Cygnus X-1 that span several days within a 10 d interval. The spectral characteristics during this observation cover the region where previous observations have shown the source to be most dynamic. Despite that the source behavior on time scales of hours and days is remarkably similar to that on year time scales. This includes a variety of spectral/temporal correlations that previously had only been observed over Cyg X-1's long-term evolution. Furthermore, we observe a full transition from a hard to a soft spectral state that occurs within less than 2.5 hours - shorter than previously reported for any other similar Cyg X-1 transition. We describe the spectra with a phenomenological model dominated by a broken power law, and we fit the X-ray variability power spectra with a combination of a cutoff power law and Lorentzian components. The spectral and timing properties are correlated: the power spectrum Lorentzian components have an energy-dependent amplitude, and their peak frequencies increase with photon spectral index. Averaged over 3.2-10 Hz, the time lag between the variability in the 4.5-5.7 keV and 9.5-15 keV bands increases with decreasing hardness when the variability is dominated by the Lorentzian components during the hard state. The lag is small when there is a large power law noise contribution, shortly after the transition to the soft state. Interestingly, the soft state not only shows the shortest lags, but also the longest lags when the spectrum is at its softest and faintest. We discuss our results in terms of emission models for black hole binaries.Comment: 13 pages, 15 figures, accepted for publication in Astronomy and Astrophysic

The Rest-Frame Instant Form of Relativistic Perfect Fluids and of Non-Dissipative Elastic Materials

For perfect fluids with equation of state $\rho = \rho (n,s)$, Brown gave an action principle depending only on their Lagrange coordinates $\alpha^i(x)$ without Clebsch potentials. After a reformulation on arbitrary spacelike hypersurfaces in Minkowski spacetime, the Wigner-covariant rest-frame instant form of these perfect fluids is given. Their Hamiltonian invariant mass can be given in closed form for the dust and the photon gas. The action for the coupling to tetrad gravity is given. Dixon's multipoles for the perfect fluids are studied on the rest-frame Wigner hyperplane. It is also shown that the same formalism can be applied to non-dissipative relativistic elastic materials described in terms of Lagrangian coordinates.Comment: revtex file, 70 page

On the determination of the spin of the black hole in Cyg X-1 from X-ray reflection spectra

The spin of Cygnus X-1 is measured by fitting reflection models to Suzaku data covering the energy band 0.9-400 keV. The inner radius of the accretion disc is found to lie within 2 gravitational radii (r_g=GM/c^2) and a value for the dimensionless black hole spin is obtained of 0.97^{+0.014}_{-0.02}. This agrees with recent measurements using the continuum fitting method by Gou et al. and of the broad iron line by Duro et al. The disc inclination is measured at 23.7^{+6.7}_{-5.4} deg, which is consistent with the recent optical measurement of the binary system inclination by Orosz et al of 27+/-0.8 deg. We pay special attention to the emissivity profile caused by irradiation of the inner disc by the hard power-law source. The X-ray observations and simulations show that the index q of that profile deviates from the commonly used, Newtonian, value of 3 within 3r_g, steepening considerably within 2r_g, as expected in the strong gravity regime.Comment: 7 pages, 10 figures, MNRAS in pres