X-ray interferometry with transmissive beam combiners for ultra-high angular resolution astronomy

Interferometry provides one of the possible routes to ultra-high angular resolution for X-ray and gamma-ray astronomy. Sub-micro-arc-second angular resolution, necessary to achieve objectives such as imaging the regions around the event horizon of a super-massive black hole at the center of an active galaxy, can be achieved if beams from parts of the incoming wavefront separated by 100s of meters can be stably and accurately brought together at small angles. One way of achieving this is by using grazing incidence mirrors. We here investigate an alternative approach in which the beams are recombined by optical elements working in transmission. It is shown that the use of diffractive elements is a particularly attractive option. We report experimental results from a simple 2-beam interferometer using a low-cost commercially available profiled film as the diffractive elements. A rotationally symmetric filled (or mostly filled) aperture variant of such an interferometer, equivalent to an X-ray axicon, is shown to offer a much wider bandpass than either a Phase Fresnel Lens (PFL) or a PFL with a refractive lens in an achromatic pair. Simulations of an example system are presented.Comment: To be published in "Experimental Astronomy

A simple variational method for calculating energy and quantum capacitance of an electron gas with screened interactions

We describe a variational procedure for calculating the energy of an electron gas in which the long-range Coulomb interaction is truncated by the screening effect of a nearby metallic gate. We use this procedure to compute the quantum capacitance of the system as a function of electron density and spin polarization. The accuracy of the method is verified against published Monte-Carlo data. The results compare favorably with a recent experiment.Comment: 4 pages, 3 figure

On the high coherence of kilo-Hz Quasi-Periodic Oscillations

We have carried out a systematic study of the properties of the kilo-Hertz quasi-periodic oscillations (QPO) observed in the X-ray emission of the neutron star low-mass X-ray binary 4U1608-52, using archival data obtained with the Rossi X-ray Timing Explorer. We have investigated the quality factor, Q, of the oscillations (defined as the ratio of the frequency of the QPO peak to its full width at half maximum). In order to minimise the effect of long-term frequency drifts, power spectra were computed over the shortest times permitted by the data statistics. We show that the high Q of ~200 reported by Berger et al. (1996) for the lower frequency kilo-Hz QPO in one of their observations is by no means exceptional, as we observe a mean Q value in excess of 150 in 14 out of the 21 observations analysed and Q can remain above 200 for thousands of seconds. The frequency of the QPO varies over the wide range 560--890 Hz and we find a systematic trend for the coherence time of the QPO, estimated as tau=Q /(pi nu), to increase with the frequency, up to a maximum level at ~ 800 Hz, beyond which it appears to decrease, at frequencies where the QPO weakens. There is a more complex relationship between tau and the QPO root mean squared amplitude (RMS), in which positive and negative correlations can be found. A higher-frequency QPO, revealed by correcting for the frequency drift of the 560-890 Hz one, has a much lower Q (~10) which does not follow the same pattern. We discuss these results in the framework of competing QPO models and show that those involving clumps orbiting within or above the accretion disk are ruled out.Comment: Accepted for publication in MNRAS, 8 pages, 6 figures, 3 Table

A Persistent High-Energy Flux from the Heart of the Milky Way : Integral's view of the Galactic Center

The Ibis/Isgri imager on Integral detected for the first time a hard X-ray source, IGR J17456-2901, located within 1' of Sgr A* over the energy range 20-100 keV. Here we present the results of a detailed analysis of ~7 Ms of Integral observations of the GC. With an effective exposure of 4.7 Ms we have obtained more stringent positional constraints on this HE source and constructed its spectrum in the range 20-400 keV. Furthermore, by combining the Isgri spectrum with the total X-ray spectrum corresponding to the same physical region around SgrA* from XMM data, and collected during part of the Integral observations, we constructed and present the first accurate wide band HE spectrum for the central arcmins of the Galaxy. Our complete analysis of the emission properties of IGR shows that it is faint but persistent with no variability above 3 sigma contrary to what was alluded to in our first paper. This result, in conjunction with the spectral characteristics of the X-ray emission from this region, suggests that the source is most likely not point-like but, rather, that it is a compact, yet diffuse, non-thermal emission region. The centroid of IGR is estimated to be R.A.=17h45m42.5, decl.=-28deg59'28'', offset by 1' from the radio position of Sgr A* and with a positional uncertainty of 1'. Its 20-400 keV luminosity at 8 kpc is L=5.4x10^35 erg/sec. Very recently, Hess detected of a source of ~TeV g-rays also located within 1' of Sgr A*. We present arguments in favor of an interpretation according to which the photons detected by Integral and Hess arise from the same compact region of diffuse emission near the central BH and that the supernova remnant Sgr A East could play an important role as a contributor of very HE g-rays to the overall spectrum from this region.Comment: 14 pages, 11 figures, Accepted for publication in Ap

The problem of shot selection in basketball

In basketball, every time the offense produces a shot opportunity the player with the ball must decide whether the shot is worth taking. In this paper, I explore the question of when a team should shoot and when they should pass up the shot by considering a simple theoretical model of the shot selection process, in which the quality of shot opportunities generated by the offense is assumed to fall randomly within a uniform distribution. I derive an answer to the question "how likely must the shot be to go in before the player should take it?", and show that this "lower cutoff" for shot quality $f$ depends crucially on the number $n$ of shot opportunities remaining (say, before the shot clock expires), with larger $n$ demanding that only higher-quality shots should be taken. The function $f(n)$ is also derived in the presence of a finite turnover rate and used to predict the shooting rate of an optimal-shooting team as a function of time. This prediction is compared to observed shooting rates from the National Basketball Association (NBA), and the comparison suggests that NBA players tend to wait too long before shooting and undervalue the probability of committing a turnover.Comment: 7 pages, 2 figures; comparison to NBA data adde

Spiral Waves in Chaotic Systems

Spiral waves are investigated in chemical systems whose underlying spatially-homogeneous dynamics is governed by a deterministic chaotic attractor. We show how the local periodic behavior in the vicinity of a spiral defect is transformed to chaotic dynamics far from the defect. The transformation occurs by a type of period doubling as the distance from the defect increases. The change in character of the dynamics is described in terms of the phase space flow on closed curves surrounding the defect.Comment: latex file with three postscript figures to appear in Physical review Letter

Troubles with Bayesianism: An introduction to the psychological immune system

A Bayesian mind is, at its core, a rational mind. Bayesianism is thus well-suited to predict and explain mental processes that best exemplify our ability to be rational. However, evidence from belief acquisition and change appears to show that we do not acquire and update information in a Bayesian way. Instead, the principles of belief acquisition and updating seem grounded in maintaining a psychological immune system rather than in approximating a Bayesian processor

EXIST: The Ultimate Spatial/Temporal Hard X-ray Survey

The Energetic X-ray Imaging Survey Telescope (EXIST) is a proposed mission to conduct an all-sky imaging hard x-ray (HX) survey (~5–600 keV) with ~0.05mCrab sensitivity (5σ; 6mo.; ~5–100keV) comparable to the ROSAT soft x-ray survey, and to provide the maximum sensitivity and resolution (spatial and temporal) HX imager as the Next Generation GRB mission. Its primary science goals are to i) identify and measure obscured AGN and constrain the accretion luminosity of the universe as well as the cosmic IR background from Blazar spectra coincident with GeV-TeV observations, ii) measure spectra, variability and locations for the faintest GRBs to study the most energetic events in the universe and the earliest epoch of star formation, and iii) study black holes on all scales, from x-ray transients to luminous AGN. EXIST would incorporate a very large area (~8m^2) imaging Cd-Zn-Te detector and coded aperture telescope array with nearly half-sky instantaneous view which images the full sky each orbit. With fixed zenith pointing, it could be mounted on the ISS or a free flyer and would complement both GLAST and Constellation-X science if launched before 2010, as recommended by the Astronomy and Astrophysics Decadal Survey