Energy-optimal steering of transitions through a fractal basin boundary.

We study fluctuational transitions in a discrete dy- namical system having two co-existing attractors in phase space, separated by a fractal basin boundary. It is shown that transitions occur via a unique ac- cessible point on the boundary. The complicated structure of the paths inside the fractal boundary is determined by a hierarchy of homoclinic original sad- dles. By exploiting an analogy between the control problem and the concept of an optimal fluctuational path, we identify the optimal deterministic control function as being equivalent to the optimal fluctu- ational force obtained from a numerical analysis of the fluctuational transitions between two states

Enlargement of a low-dimensional stochastic web

We consider an archetypal example of a low-dimensional stochastic web, arising in a 1D oscillator driven by a plane wave of a frequency equal or close to a multiple of the oscillator’s natural frequency. We show that the web can be greatly enlarged by the introduction of a slow, very weak, modulation of the wave angle. Generalizations are discussed. An application to electron transport in a nanometre-scale semiconductor superlattice in electric and magnetic fields is suggested

Precise Measurement of the Spin Parameter of the Stellar-Mass Black Hole M33 X-7

In prior work, {\it Chandra} and Gemini-North observations of the eclipsing X-ray binary M33 X-7 have yielded measurements of the mass of its black hole primary and the system's orbital inclination angle of unprecedented accuracy. Likewise, the distance to the binary is known to a few percent. In an analysis based on these precise results, fifteen {\it Chandra} and {\it XMM-Newton} X-ray spectra, and our fully relativistic accretion disk model, we find that the dimensionless spin parameter of the black hole primary is $a_* = 0.77 \pm 0.05$. The quoted 1-$\sigma$ error includes all sources of observational uncertainty. Four {\it Chandra} spectra of the highest quality, which were obtained over a span of several years, all lead to the same estimate of spin to within statistical errors (2%), and this estimate is confirmed by 11 spectra of lower quality. There are two remaining uncertainties: (1) the validity of the relativistic model used to analyze the observations, which is being addressed in ongoing theoretical work; and (2) our assumption that the black hole spin is approximately aligned with the angular momentum vector of the binary, which can be addressed by a future X-ray polarimetry mission.Comment: 14 pages, 3 figures, 1 table, published in ApJ Letters; as explained in the erratum at the end of the text, the spin parameter has been corrected upward from a*=0.77 to a*=0.84. Apart from the addition of the erratum, the paper is unchanged

X-ray Reflection Spectroscopy of the Black Hole GX 339-4: Exploring the Hard State with Unprecedented Sensitivity

We analyze {\it simultaneously} six composite {\it RXTE} spectra of GX 339--4 in the hard state comprising 77 million counts collected over 196 ks. The source spectra are ordered by luminosity and spanthe range 1.6\% to 17\% of the Eddington luminosity. Crucially, using our new tool {\tt pcacorr}, we re-calibrate the data to a precision of 0.1\%, an order of magnitude improvement over all earlier work. Using our advanced reflection model {\tt relxill}, we target the strong features in the component of emission reflected from the disk, namely, the relativistically-broadened Fe K emission line, the Fe K edge and the Compton hump. We report results for two joint fits to the six spectra: For the first fit, we fix the spin parameter to its maximal value ($a_*=0.998$) and allow the inner disk radius $R_{\rm in}$ to vary. Results include (i) precise measurements of $R_{\rm in}$, with evidence that the disk becomes slightly truncated at a few percent of Eddington; and (ii) an order-of-magnitude swing with luminosity in the high energy cutoff, which reaches $>890$ keV at our lowest luminosity. For the second fit, we make the standard assumption in estimating spin that the inner edge of the accretion disk is located at the innermost stable circular orbit ($R_\mathrm{in} = R_\mathrm{ISCO}$) and find $a_* = 0.95^{+0.03}_{-0.05}$ (90\% confidence, statistical). For both fits, and at the same level of statistical confidence, we estimate that the disk inclination is $i = 48\pm 1$ deg and that the Fe abundance is super-solar, $A_\mathrm{Fe} = 5\pm1$.Comment: Accepted for publication in ApJ, 20 pages, 13 figure

Simultaneous IUE, EXOSAT and optical observations of the unusual AM Her type variable H058+608

Simultaneous observations of the AM Her type variable H0538+608 made with IUE, EXOSAT, and a 1.3 m ground based telescope, and subsequent optical spectrophotometry at high and low resolution are discussed. The X-ray and optical data show clear evidence of a 3.30 + or - 0.03 hr period. Three SWP spectra were taken outside of eclipse and during overlapping phase intervals. The UV spectra contain strong emission lines characteristic of this class of objects and a flat continuum which appears to be deficient, given the brightness of source at optical and X-ray wavelengths. There is evidence for intensity variations in emission lines, particularly C IV. The X-ray light curves for H0538+608 reveal behavior which may be related to irregularities in its accretion flow

The Mass of the Black Hole in Cygnus X-1

Cygnus X-1 is a binary star system that is comprised of a black hole and a massive giant companion star in a tight orbit. Building on our accurate distance measurement reported in the preceding paper, we first determine the radius of the companion star, thereby constraining the scale of the binary system. To obtain a full dynamical model of the binary, we use an extensive collection of optical photometric and spectroscopic data taken from the literature. By using all of the available observational constraints, we show that the orbit is slightly eccentric (both the radial velocity and photometric data independently confirm this result) and that the companion star rotates roughly 1.4 times its pseudosynchronous value. We find a black hole mass of M =14.8\pm1.0 M_{\sun}, a companion mass of M_{opt}=19.2\pm1.9 M_{\sun}, and the angle of inclination of the orbital plane to our line of sight of i=27.1\pm0.8 deg.Comment: Paper II of three papers on Cygnus X-1; 27 pages including 5 figures and 3 tables, ApJ in pres

On Estimating the High-Energy Cutoff in the X-ray Spectra of Black Holes via Reflection Spectroscopy

The fundamental parameters describing the coronal spectrum of an accreting black hole are the slope $\Gamma$ of the power-law continuum and the energy $E_{cut}$ at which it rolls over. Remarkably, this parameter can be accurately measured for values as high as 1 MeV by modeling the spectrum of X-rays reflected from a black hole accretion disk at energies below 100 keV. This is possible because the details in the reflection spectrum, rich in fluorescent lines and other atomic features, are very sensitive to the spectral shape of the hardest coronal radiation illuminating the disk. We show that fitting simultaneous NuSTAR (3-79 keV) and low-energy (e.g., Suzaku) data with the most recent version of our reflection model RELXILL, one can obtain reasonable constraints on $E_{cut}$ at energies from tens of keV up to 1 MeV, for a source as faint as 1 mCrab in a 100 ks observation.Comment: Accepted for publication in ApJL, 6 pages, 5 figure