Similar phenomena at different scales: Black Holes, the Sun, Gamma-ray Bursts, Supernovae, Galaxies and Galaxy Clusters

Many similar phenomena occur in astrophysical systems with spatial and mass scales different by many orders of magnitudes. For examples, collimated outflows are produced from the Sun, proto-stellar systems, gamma-ray bursts, neutron star and black hole X-ray binaries, and supermassive black holes; various kinds of flares occur from the Sun, stellar coronae, X-ray binaries and active galactic nuclei; shocks and particle acceleration exist in supernova remnants, gamma-ray bursts, clusters of galaxies, etc. In this report I summarize briefly these phenomena and possible physical mechanisms responsible for them. I emphasize the importance of using the Sun as an astrophysical laboratory in studying these physical processes, especially the roles magnetic fields play in them; it is quite likely that magnetic activities dominate the fundamental physical processes in all of these systems. As a case study, I show that X-ray lightcurves from solar flares, black hole binaries and gamma-ray bursts exhibit a common scaling law of non-linear dynamical properties, over a dynamical range of several orders of magnitudes in intensities, implying that many basic X-ray emission nodes or elements are inter-connected over multi-scales. A future high timing and imaging resolution solar X-ray instrument, aimed at isolating and resolving the fundamental elements of solar X-ray lightcurves, may shed new lights onto the fundamental physical mechanisms, which are common in astrophysical systems with vastly different mass and spatial scales. Using the Sun as an astrophysical laboratory, "Applied Solar Astrophysics" will deepen our understanding of many important astrophysical problems.Comment: 22 pages, 13 figures, invited discourse for the 26th IAU GA, Prague, Czech Republic, Aug. 2006, to be published in Vol. 14 IAU Highlights of Astronomy, Ed. K.A. van der Hucht. Revised slightly to match the final submitted version, after incorporating comments and suggestions from several colleagues. A full-resolution version is available on request from the author at [email protected]

Statistical properties of a filtered Poisson process with additive random noise: Distributions, correlations and moment estimation

Filtered Poisson processes are often used as reference models for intermittent fluc- tuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical term in a stochastic differential equation. The lowest order moments, probability density function, auto-correlation function and power spectral density are derived and used to identify and compare the effects of the two different noise terms. Monte-Carlo studies of synthetic time series are used to investigate the accuracy of model pa- rameter estimation and to identify methods for distinguishing the noise types. It is shown that the probability density function and the three lowest order moments provide accurate estimations of the parameters, but are unable to separate the noise types. The auto-correlation function and the power spectral density also provide methods for estimating the model parameters, as well as being capable of identifying the noise type. The number of times the signal crosses a prescribed threshold level in the positive direction also promises to be able to differentiate the noise type.Comment: 34 pages, 25 figure

Synchronization of uncoupled oscillators by common gamma impulses: from phase locking to noise-induced synchronization

Nonlinear oscillators can mutually synchronize when they are driven by common external impulses. Two important scenarios are (i) synchronization resulting from phase locking of each oscillator to regular periodic impulses and (ii) noise-induced synchronization caused by Poisson random impulses, but their difference has not been fully quantified. Here we analyze a pair of uncoupled oscillators subject to common random impulses with gamma-distributed intervals, which can be smoothly interpolated between regular periodic and random Poisson impulses. Their dynamics are charac- terized by phase distributions, frequency detuning, Lyapunov exponents, and information-theoretic measures, which clearly reveal the differences between the two synchronization scenarios.Comment: 18 page

Constrained BRST- BFV Lagrangian formulations for Higher Spin Fields in Minkowski Spaces

BRST-BFV method for constrained Lagrangian formulations (LFs) for (ir)reducible half-integer HS Poincare group representations in Minkowski space is suggested. The procedure is derived by 2 ways: from the unconstrained BRST-BFV method for mixed-symmetry HS fermionic fields subject to an arbitrary Young tableaux with k rows (suggested in arXiv:1211.1273[hep-th]) by extracting the second-class constraints, $\widehat{O}_\alpha=(\widehat{O}_a, \widehat{O}^+_a)$, from a total superalgebra of constraints, second, in self-consistent way by means of finding BRST-extended initial off-shell algebraic constraints, $\widehat{O}_a$. In both cases, the latter constraints supercommute on the constraint surface with constrained BRST $Q_C$ and spin operators $\sigma^i_C$. The closedness of the superalgebra $Q_C, \widehat{O}_a, \sigma^i_C$ guarantees that the final gauge-invariant LF is compatible with off-shell constraints $\widehat{O}_a$ imposed on field and gauge parameter vectors of Hilbert space not depending from the ghosts and conversion auxiliary oscillators related to $\widehat{O}_a$, in comparison with vectors for unconstrained BRST-BFV LF. The suggested constrained BRST-BFV approach is valid for both massive HS fields and integer HS fields in the second-order formulation. It is shown that the respective constrained and unconstrained LFs for (half)-integer HS fields with a given spin are equivalent. The constrained Lagrangians in ghost-independent and component (for initial spin-tensor field) are obtained and shown to coincide with Fang-Fronsdal formulation for constrained totally-symmetric HS field. The triplet and unconstrained quartet LFs for the latter field and gauge-invariant constrained Lagrangians for a massive field of spin n+1/2 are derived. A concept of BRST-invariant second-class constraints for a general dynamical system with mixed-class constraints is suggested.Comment: 55 pages, typos corrected, published version; footnote 1 added, typo in (3.15) correcte

The Overlooked Potential of Generalized Linear Models in Astronomy-III: Bayesian Negative Binomial Regression and Globular Cluster Populations

In this paper, the third in a series illustrating the power of generalized linear models (GLMs) for the astronomical community, we elucidate the potential of the class of GLMs which handles count data. The size of a galaxy's globular cluster population $N_{\rm GC}$ is a prolonged puzzle in the astronomical literature. It falls in the category of count data analysis, yet it is usually modelled as if it were a continuous response variable. We have developed a Bayesian negative binomial regression model to study the connection between $N_{\rm GC}$ and the following galaxy properties: central black hole mass, dynamical bulge mass, bulge velocity dispersion, and absolute visual magnitude. The methodology introduced herein naturally accounts for heteroscedasticity, intrinsic scatter, errors in measurements in both axes (either discrete or continuous), and allows modelling the population of globular clusters on their natural scale as a non-negative integer variable. Prediction intervals of 99% around the trend for expected $N_{\rm GC}$comfortably envelope the data, notably including the Milky Way, which has hitherto been considered a problematic outlier. Finally, we demonstrate how random intercept models can incorporate information of each particular galaxy morphological type. Bayesian variable selection methodology allows for automatically identifying galaxy types with different productions of GCs, suggesting that on average S0 galaxies have a GC population 35% smaller than other types with similar brightness.Comment: 14 pages, 12 figures. Accepted for publication in MNRA