Limit Theorems and Governing Equations for Levy Walks

The Levy Walk is the process with continuous sample paths which arises from consecutive linear motions of i.i.d. lengths with i.i.d. directions. Assuming speed 1 and motions in the domain of beta-stable attraction, we prove functional limit theorems and derive governing pseudo-differential equations for the law of the walker's position. Both Levy Walk and its limit process are continuous and ballistic in the case beta in (0,1). In the case beta in (1,2), the scaling limit of the process is beta-stable and hence discontinuous. This case exhibits an interesting situation in which scaling exponent 1/beta on the process level is seemingly unrelated to the scaling exponent 3-beta of the second moment. For beta = 2, the scaling limit is Brownian motion

Subdiffusive transport in intergranular lanes on the Sun. The Leighton model revisited

In this paper we consider a random motion of magnetic bright points (MBP) associated with magnetic fields at the solar photosphere. The MBP transport in the short time range [0-20 minutes] has a subdiffusive character as the magnetic flux tends to accumulate at sinks of the flow field. Such a behavior can be rigorously described in the framework of a continuous time random walk leading to the fractional Fokker-Planck dynamics. This formalism, applied for the analysis of the solar subdiffusion of magnetic fields, generalizes the Leighton's model.Comment: 7 page

Relativistic X-ray Lines from the Inner Accretion Disks Around Black Holes

Relativistic X-ray emission lines from the inner accretion disk around black holes are reviewed. Recent observations with the Chandra X-ray Observatory, X-ray Multi-Mirror Mission-Newton, and Suzaku are revealing these lines to be good probes of strong gravitational effects. A number of important observational and theoretical developments are highlighted, including evidence of black hole spin and effects such as gravitational light bending, the detection of relativistic lines in stellar-mass black holes, and evidence of orbital-timescale line flux variability. In addition, the robustness of the relativistic disk lines against absorption, scattering, and continuum effects is discussed. Finally, prospects for improved measures of black hole spin and understanding the spin history of supermassive black holes in the context of black hole-galaxy co-evolution are presented. The best data and most rigorous results strongly suggest that relativistic X-ray disk lines can drive future explorations of General Relativity and disk physics.Comment: 40 pages, includes color figures, to appear in ARAA, vol 45, in pres

The Complex X-ray Spectrum of the Sefyert 1.5 Source NGC 6860

The X-ray spectrum of the Seyfert 1.5 source NGC 6860 is among the most complex of the sources detected in the Swift Burst Alert Telescope all-sky survey. A short XMM-Newton follow-up observation of the source revealed a flat spectrum both above and below 2 keV. To uncover the complexity of the source, in this paper we analyze both a 40 ks Suzaku and a 100 ks XMM-Newton observation of NGC 6860. While the spectral state of the source changed between the newer observations presented here and the earlier short XMM-Newton spectrum - showing a higher flux and steeper power law component - the spectrum of NGC 6860 is still complex with clearly detected warm absorption signatures. We find that a two component warm ionized absorber is present in the soft spectrum, with column densities of about 10^20 and 10^21 cm$^-2, ionization parameters of xi = 180 and 45 ergs cm s^-1, and outflow velocities for each component in the range of 0-300 km s^-1. Additionally, in the hard spectrum we find a broad (approx 11000 km s^-1) Fe K-alpha emission line, redshifted by approx 2800 km s^-1.Comment: 35 pages, 9 figures, Accepted to Ap

A fit to the simultaneous broadband spectrum of Cygnus X-1 using the transition disk model

We have used the transition disk model to fit the simultaneous broad band ($2-500$ keV) spectrum of Cygnus X-1 from OSSE and Ginga observations. In this model, the spectrum is produced by saturated Comptonization within the inner region of the accretion disk, where the temperature varies rapidly with radius. In an earlier attempt, we demonstrated the viability of this model by fitting the data from EXOSAT, XMPC balloon and OSSE observations, though these were not made simultaneously. Since the source is known to be variable, however, the results of this fit were not conclusive. In addition, since only once set of observations was used, the good agreement with the data could have been a chance occurrence. Here, we improve considerably upon our earlier analysis by considering four sets of simultaneous observations of Cygnus X-1, using an empirical model to obtain the disk temperature profile. The vertical structure is then obtained using this profile and we show that the analysis is self- consistent. We demonstrate conclusively that the transition disk spectrum is a better fit to the observations than that predicted by the soft photon Comptonization model. Since the temperature profile is obtained by fitting the data, the unknown viscosity mechanism need not be specified. The disk structure can then be used to infer the viscosity parameter $\alpha$, which appears to vary with radius and luminosity. This behavior can be understood if $\alpha$ depends intrinsically on the local parameters such as density, height and temperature. However, due to uncertainties in the radiative transfer, quantitative statements regarding the variation of $\alpha$ cannot yet be made.Comment: 8 figures. uses aasms4.sty, accepted by ApJ (Mar 98

X-ray properties of an Unbiased Hard X-ray Detected Sample of AGN

The SWIFT gamma ray observatory's Burst Alert Telescope (BAT) has detected a sample of active galactic nuclei (AGN) based solely on their hard X-ray flux (14-195 keV). In this paper, we present for the first time {\it XMM-Newton} X-ray spectra for 22 BAT AGNs with no previously analyzed X-ray spectra. If our sources are a representative sample of the BAT AGN, as we claim, our results present for the first time global X-ray properties of an unbiased towards absorption (n$_H = 0.03$), AGN sample. We find 9/22 low absorption (n$_H < 10^{23}$ cm$^{-2}$), simple power law model sources, where 4 of these sources have a statistically significant soft component. Among these sources, we find the presence of a warm absorber statistically significant for only one Seyfert 1 source, contrasting with the ASCA results of \citet{rey97} and \citet{geo98}, who find signatures of warm absorption in half or more of their Seyfert 1 samples at similar redshifts. Additionally, the remaining sources (14/22) have more complex spectra, well-fit by an absorbed power law at $E > 2.0$ keV. Five of the complex sources are classified as Compton-thick candidates. Further, we find four more sources with properties consistent with the hidden/buried AGN reported by Ueda {\it et al.} (2007). Finally, we include a comparison of the {\it XMM-Newton} EPIC spectra with available SWIFT X-ray Telescope (XRT) observations. From these comparisons, we find 6/16 sources with varying column densities, 6/16 sources with varying power law indices, and 13/16 sources with varying fluxes, over periods of hours to months. Flux and power law index are correlated for objects where both parameters vary.Comment: 39 pages, 16 figures, accepted to Ap

Possible X-ray diagnostic for jet/disk dominance in Type 1 AGN

Using Rossi X-ray Timing Explorer Seyfert 1 and 1.2 data spanning 9 years, we study correlations between X-ray spectral features. The sample consists of 350 time-resolved spectra from 12 Seyfert 1 and 1.2 galaxies. Each spectrum is fitted to a model with an intrinsic powerlaw X-ray spectrum produced close to the central black hole that is reprocessed and absorbed by material around the black hole. To test the robustness of our results, we performed Monte Carlo simulations of the spectral sample. We find a complex relationship between the iron line equivalent width (EW) and the underlying power law index (Gamma). The data reveal a correlation between Gamma and EW which turns over at Gamma <~ 2, but finds a weak anti-correlation for steeper photon indices. We propose that this relationship is driven by dilution of a disk spectrum (which includes the narrow iron line) by a beamed jet component and, hence, could be used as a diagnostic of jet-dominance. In addition, our sample shows a strong correlation between the reflection fraction (R) and Gamma, but we find that it is likely the result of modeling degeneracies. We also see the X-ray Baldwin effect (an anti-correlation between the 2-10 keV X-ray luminosity and EW) for the sample as a whole, but not for the individual galaxies and galaxy types.Comment: Accepted for publication in ApJ, 14 page

The average X-ray/gamma-ray spectrum of radio-quiet Seyfert 1s

We have obtained the average 1--500 keV spectrum of radio-quiet Seyfert 1s using data from EXOSAT, Ginga, HEAO, and GRO/OSSE. The spectral fit to the combined average EXOSAT and OSSE data is fully consistent with that for Ginga and OSSE, confirming results from an earlier Ginga/OSSE sample. The average spectrum is well-fitted by a power-law X-ray continuum with an energy spectral index of $\alpha \simeq 0.9$ moderately absorbed by an ionized medium and with a Compton reflection component. A high-energy cutoff (or a break) in the the power-law component at a few hundred keV or more is required by the data. We also show that the corresponding average spectrum from HEAO A1 and A4 is fully compatible with that obtained from EXOSAT, Ginga and OSSE. These results confirm that the apparent discrepancy between the results of Ginga (with $\alpha \simeq 0.9$) and the previous results of EXOSAT and HEAO (with $\alpha \simeq 0.7$) is indeed due to ionized absorption and Compton reflection first taken into account for Ginga but not for the previous missions. Also, our results confirm that the Seyfert-1 spectra are on average cut off in gamma-rays at energies of at least a few hundred keV, not at $\sim 40$ keV (as suggested earlier by OSSE data alone). The average spectrum is compatible with emission from either an optically-thin relativistic thermal plasma in a disk corona, or with a nonthermal plasma with a power-law injection of relativistic electrons.Comment: 7 pages, 3 Postscript figures, MNRAS accepte