Relativistic reflection from accretion disks in the population of Active Galactic Nuclei at z=0.5-4

We report the detection of relativistically broadened iron K alpha emission in the X-ray spectra of AGN detected in the 4Ms CDF-S. Using the Bayesian X-ray analysis (BXA) package, we fit 199 hard band (2-7 keV) selected sources in the redshift range z=0.5--4 with three models: (i) an absorbed power-law, (ii) the first model plus a narrow reflection component, and (iii) the second model with an additional relativistic broadened reflection. The Bayesian evidence for the full sample of sources selects the model with the additional broad component as being 10^5 times more probable to describe the data better than the second model. For the two brightest sources in our sample, CID 190 (z=0.734) and CID 104 (z=0.543), BXA reveals the relativistic signatures in the individual spectra. We estimate the fraction of sources containing a broad component to be 54^{+35}_{-37}% (107/199 sources). Considering that the low signal-to-noise ratio of some spectra prevents the detection of the broad iron K alpha line, we infer an intrinsic fraction with broad emission of around two thirds. The detection of relativistic signatures in the X-ray spectra of these sources suggests that they are powered by a radiatively efficient accretion disk. Preliminary evidence is found that the spin of the black hole is high, with a maximally spinning Kerr BH model (a=1) providing a significantly better fit than a Schwarzschild model (a=0). Our analysis demonstrate the potential of X-ray spectroscopy to measure this key parameter in typical SMBH systems at the peak of BH growth.Comment: 10 pages, 5 figures, accepted for publication in MNRA

Acoustic Emission from crumpling paper

From magnetic systems to the crust of the earth, many physical systems that exibit a multiplicty of metastable states emit pulses with a broad power law distribution in energy. Digital audio recordings reveal that paper being crumpled, a system that can be easily held in hand, is such a system. Crumpling paper both using the traditional hand method and a novel cylindrical geometry uncovered a power law distribution of pulse energies spanning at least two decades: (exponent 1.3 - 1.6) Crumpling initally flat sheets into a compact ball (strong crumpling), we found little or no evidence that the energy distribution varied systematically over time or the size of the sheet. When we applied repetitive small deformations (weak crumpling) to sheets which had been previously folded along a regular grid, we found no systematic dependence on the grid spacing. Our results suggest that the pulse energy depends only weakly on the size of the paper regions responsible for sound production.Comment: 12 pages of text, 9 figures, submitted to Phys. Rev. E, additional information availible at http://www.msc.cornell.edu/~houle/crumpling

Comment: The Constitutionality of Local Anti-Pollution Ordinances

Local governments have recently expanded their efforts to abate pollution problems. The constitutionality of such local ordinances under both federal and state law, however, has not yet been adequately determined. In order to clarify the constitutional limits of local environmental laws, it is necessary to examine the relevant questions raised by both the United States Constitution and the various state constitutions. Part I of this comment will deal with the federal-local conflicts and Part II will discuss the state-local conflicts. In each of the two sections, relevant legislation in the environmental field will be discussed. Finally, a model statute will be offered as an example of the wide range of powers a locality can constitutionally exercise

Can AGN and galaxy clusters explain the surface brightness fluctuations of the cosmic X-ray background?

Fluctuations of the surface brightness of cosmic X-ray background (CXB) carry unique information about faint and low luminosity source populations, which is inaccessible for conventional large-scale structure (LSS) studies based on resolved sources. We used Chandra data of the XBOOTES field ($\sim9\,\mathrm{deg^2}$) to conduct the most accurate measurement to date of the power spectrum of fluctuations of the unresolved CXB on the angular scales of $\sim3\,$arcsec $-$ $\sim17\,$arcmin. We find that at sub-arcmin angular scales, the power spectrum is consistent with the AGN shot noise, without much need for any significant contribution from their one-halo term. This is consistent with the theoretical expectation that low-luminosity AGN reside alone in their dark matter halos. However, at larger angular scales we detect a significant LSS signal above the AGN shot noise. Its power spectrum, obtained after subtracting the AGN shot noise, follows a power law with the slope of $-0.8\pm0.1$ and its amplitude is much larger than what can be plausibly explained by the two-halo term of AGN. We demonstrate that the detected LSS signal is produced by unresolved clusters and groups of galaxies. For the flux limit of the XBOOTES survey, their flux-weighted mean redshift equals \left\sim0.3, and the mean temperature of their intracluster medium (ICM), \left\approx 1.4 keV, corresponds to the mass of $M_{500} \sim 10^{13.5}\,\mathrm{M}_\odot$. The power spectrum of CXB fluctuations carries information about the redshift distribution of these objects and the spatial structure of their ICM on the linear scales of up to $\sim$Mpc, i.e. of the order of the virial radius.Comment: 25 pages, 20 figures, submitted to MNRAS, comments welcom

Drip Paintings and Fractal Analysis

It has been claimed [1-6] that fractal analysis can be applied to unambiguously characterize works of art such as the drip paintings of Jackson Pollock. This academic issue has become of more general interest following the recent discovery of a cache of disputed Pollock paintings. We definitively demonstrate here, by analyzing paintings by Pollock and others, that fractal criteria provide no information about artistic authenticity. This work has also led to two new results in fractal analysis of more general scientific significance. First, the composite of two fractals is not generally scale invariant and exhibits complex multifractal scaling in the small distance asymptotic limit. Second the statistics of box-counting and related staircases provide a new way to characterize geometry and distinguish fractals from Euclidean objects

Shell Model for Time-correlated Random Advection of Passive Scalars

We study a minimal shell model for the advection of a passive scalar by a Gaussian time correlated velocity field. The anomalous scaling properties of the white noise limit are studied analytically. The effect of the time correlations are investigated using perturbation theory around the white noise limit and non-perturbatively by numerical integration. The time correlation of the velocity field is seen to enhance the intermittency of the passive scalar.Comment: Replaced with final version + updated figure

Zipf's law, 1/f noise, and fractal hierarchy

Fractals, 1/f noise, Zipf's law, and the occurrence of large catastrophic events are typical ubiquitous general empirical observations across the individual sciences which cannot be understood within the set of references developed within the specific scientific domains. All these observations are associated with scaling laws and have caused a broad research interest in the scientific circle. However, the inherent relationships between these scaling phenomena are still pending questions remaining to be researched. In this paper, theoretical derivation and mathematical experiments are employed to reveal the analogy between fractal patterns, 1/f noise, and the Zipf distribution. First, the multifractal process follows the generalized Zipf's law empirically. Second, a 1/f spectrum is identical in mathematical form to Zipf's law. Third, both 1/f spectra and Zipf's law can be converted into a self-similar hierarchy. Fourth, fractals, 1/f spectra, Zipf's law, and the occurrence of large catastrophic events can be described with similar exponential laws and power laws. The self-similar hierarchy is a more general framework or structure which can be used to encompass or unify different scaling phenomena and rules in both physical and social systems such as cities, rivers, earthquakes, fractals, 1/f noise, and rank-size distributions. The mathematical laws on the hierarchical structure can provide us with a holistic perspective of looking at complexity such as self-organized criticality (SOC).Comment: 20 pages, 9 figures, 3 table