Search Results (89 total)

Understanding the dynamics around rotating black holes is imperative to the success of future gravitational wave observatories. Although integrable in principle, test-particle orbits in the Kerr spacetime can also be elaborate, and while they have been studied extensively, classifying their general properties has been a challenge. This is the first in a series of papers that adopts a dynamical systems approach to the study of Kerr orbits, beginning with equatorial orbits. We define a taxonomy of orbits that hinges on a correspondence between periodic orbits and rational numbers. The taxonomy defines the entire dynamics, including aperiodic motion, since every orbit is in or near the periodic set. A remarkable implication of this periodic orbit taxonomy is that the simple precessing ellipse familiar from planetary orbits is not allowed in the strong-field regime. Instead, eccentric orbits trace out precessions of multileaf clovers in the final stages of inspiral. Furthermore, for any black hole, there is some point in the strong-field regime past which zoom-whirl behavior becomes unavoidable. Finally, we sketch the potential application of the taxonomy to problems of astrophysical interest, in particular its utility for computationally intensive gravitational wave calculations.

Chaos in the orbits of black hole pairs has by now been confirmed by several independent groups. While the chaotic behavior of binary black hole orbits is no longer argued, it remains difficult to quantify the importance of chaos to the evolutionary dynamics of a pair of comparable mass black holes. None of our existing approximations are robust enough to offer convincing quantitative conclusions in the most highly nonlinear regime. It is intriguing to note that, in three different approximations to a black hole pair built of a spinning black hole and a nonspinning companion, two approximations exhibit chaos and one approximation does not. The fully relativistic scenario of a spinning test mass around a Schwarzschild black hole shows chaos, as does the post-Newtonian Lagrangian approximation. However, the approximately equivalent post-Newtonian Hamiltonian approximation does not show chaos when only one body spins. It is well known in dynamical systems theory that one system can be regular while an approximately related system is chaotic, so there is no formal conflict. However, the physical question remains: Is there chaos for comparable mass binaries when only one object spins? We are unable to answer this question given the poor convergence of the post-Newtonian approximation to the fully relativistic system. A resolution awaits better approximations that can be trusted in the highly nonlinear regime.

A topologically finite universe, smaller than the observable horizon, will have circles-in-the-sky: pairs of circles around which the temperature fluctuations in the cosmic microwave background are correlated. The circles occur along the intersection of copies of the spherical surface of last scattering. For any observer moving with respect to the microwave background, the circles will be deformed into ovals. The ovals will also be displaced relative to the direction they appear in a comoving frame. The displacement is the larger of the two effects, being proportional to the velocity. For the Earth’s motion, the effect is on the order of 0.14° at the very worst. This can affect all pattern-based searches for the topology of the universe. In particular, although the deviation is too small to impact the search for circles in the Wilkinson microwave anisotropy probe (WMAP) data, higher-resolution searches for circle pairs will need to compensate for this effect.

We report new measurements of Kr^q+ photo-ions, coincident with Kα or Kβ fluorescence as incident-photon energy is swept through the Kr K-shell threshold. From the branching ratios just above threshold, we obtain measurements of the ion charge-state probabilities for decay from the Kr [2p] and Kr [3p] states. In the threshold region, we observe both resonant enhancement and depletion of the branching ratios. By analyzing this behavior in light of theory, we extract sticking probabilities, which we feel are a useful set of parameters for investigating the general relationship between cascade decay from resonant and nonresonant hole states. A simplified theoretical model is employed to calculate these probabilities for the Kr²⁺ and Kr³⁺ cases.

Experimental data are presented from three different heavy-ion storage rings (ASTRID in Aarhus, CRYRING in Stockholm, and TSR in Heidelberg) to assess the reliability of this experimental tool for the extraction of absolute rate coefficients and cross sections for dissociative recombination (DR). The DR reaction between HD⁺ and electrons has been studied between 0 and 30 eV on a dense energy grid. HD⁺ displays two characteristic local maxima in the DR rate around 9 and 16 eV. These maxima influence the data analysis at smaller collision energies. We conclude that resonant structures in the DR cross sections are reproduced among the experiments within the collision energy resolution. The absolute cross sections agree within the systematic experimental errors of 20% related to the measurement of the ion currents. Absolute thermal rate coefficients for HD⁺ ions are given for an electron temperature range of 50–300 K. Results for the DR cross section and the thermal rate coefficients are compared to recent theoretical calculations including rotational effects, finding satisfactory agreement.

Binary systems of rapidly spinning compact objects, such as black holes or neutron stars, are prime targets for gravitational wave astronomers. The dynamics of these systems can be very complicated due to spin-orbit and spin-spin couplings. Contradictory results have been presented as to the nature of the dynamics. Here we confirm that the dynamics—as described by the second post-Newtonian approximation to general relativity—is formally chaotic, despite claims to the contrary. When dissipation due to higher order radiation reaction terms is included, the chaos is damped. The damping time scale is found to be comparable to, but shorter than, the time scale that characterizes the chaotic behavior. This result suggests that the gravitational waveforms computed to 2.5 post-Newtonian order from spinning compact binaries will not suffer from sensitive dependence on initial conditions. If the post-Newtonian approximation at this order is an adequate description, then the waves can be detected using standard hierarchical matched filtering techniques. On the other hand, the competition between chaotic decoherence and radiation induced dissipation is close enough that the merger history does retain an imprint of the chaotic behavior. Moreover, the time scales are sufficiently close, and the post-Newtonian approximation is sufficiently crude, that we cannot rule out the possibility that chaotic effects play a role in real binary systems.

Double K-shell photoionization of Ne at 5000 eV was observed by recording the KK-KLL Auger-electron hypersatellite spectrum. The measured Auger spectrum is compared with the results of multiconfiguration Dirac-Fock calculations. Shake calculations are used to identify likely multivacancy states produced by photoexcitation or ionization in addition to double-K vacancies, and their calculated Auger spectra are compared with the measured spectrum. The measured relative intensities of hypersatellite and diagram Auger lines are combined with experimental and theoretical determinations of branching ratios from single- and double-K vacancies into final states to determine the ratio of double-to-single K-shell photoionization cross sections to be 0.32(4)%. This ratio is much larger than the calculated high-energy-limit ratio and indicates a large contribution of dynamic electron correlation.

Measurements of Kr^q+ yields in coincidence with K-shell fluorescence, as incident x-ray energy is varied across the K-shell threshold, are reported. Near threshold, we observe slight variations in the branching ratios as a function of energy, which are connected with the different behaviors of the flux-normalized partial yields for each q. The lower-q yields show a resonance peak near threshold superimposed on a smoothly rising edge, whereas the higher-q yields show only a smooth rise. A simple model is developed which accounts for these features, incorporating both the threshold photoexcitation and the cascade behavior of the spectator electrons.

A typical stellar mass black hole with a lighter companion is shown to succumb to a chaotic precession of the orbital plane. The chaotic behavior is identified in the conservative system since there is no clear way to do so when dissipation is included and all binaries merge. The precession and the subsequent modulation of the gravitational radiation depend on the mass ratio, eccentricity, and spins. The smaller the mass of the companion, the more prominent the effect of the precession. The most important parameters are the spin magnitudes and misalignments. If the spins are small and nearly aligned with the orbital angular momentum, then there will be no chaotic precession, while increasing both the spin magnitudes and misalignments increases the erratic precession. A large eccentricity can be induced by large, misaligned spins but does not seem to be required for chaos. When dissipation due to gravitational radiation is included chaos is damped, but a further study is needed to determine if dissipation will erase all traces of chaos or if an imprint of irregularity survives.

The vibrational relaxation of H₃⁺ molecules from a conventional plasma ion source is studied performing Coulomb explosion imaging on the ions extracted from a storage ring after variable times of storage. Storage for 2 s is found sufficient for radiative relaxation of the breathing excitation and the fragment velocity distribution in the breathing coordinate then agrees well with simulations based on the calculated ground-state wave function. The radiative decay of the two lowest pure breathing levels (1,0⁰) and (2,0⁰) is seen to be considerably faster than expected from rotationless calculations. Assuming a high rotational excitation of the H₃⁺ ions, as suggested already in earlier experiments, the theoretical transition probabilities of the University College London line list for H₃⁺ [L. Neale, S. Miller, and J. Tennyson, Astrophys. J. 464, 516 (1996)] can explain the increase of the vibrational cooling rates and reproduce the observed decay curve for the lowest breathing-excited level, confirming the absolute transition probabilities of these line tables. The observations give evidence for a quasistable population of high-lying rotational levels in the stored ion beam, relevant for the interpretation of storage ring measurements on the rate coefficients for dissociative recombination of H₃⁺ ions with low-energy electrons.

A Comment on the Letter by J. D. Schnittman and F. A. Rasio, Phys. Rev. Lett. 87, 121101 (2001).

A statistical model serving to estimate the branching ratios in the dissociative recombination of polyatomic molecular ions is described. Simple phase-space assumptions are employed separately for the electronic capture step and the subsequent dissociation and yield predictions in good agreement with existing data on H₃⁺. Also the vibrational state populations of molecular fragments can be obtained and for H₃⁺ are found to agree well with recent measurements.

The dissociative recombination of LiH⁺ ions with low-energy electrons is observed at a storage ring and the final states are analyzed using fragment imaging and field ionization techniques. The rate coefficient is found to be larger than its estimated value used in astrophysical models. Mostly the highest energetically possible Rydberg states of the lithium atom are populated by the reaction, indicating a common trend for molecular recombination via the noncrossing mode.

Twins traveling at constant relative velocity will each see the other’s time dilate leading to the apparent paradox that each twin believes the other ages more slowly. In a finite space, the twins can both be on inertial, periodic orbits so that they have the opportunity to compare their ages when their paths cross. As we show, they will agree on their respective ages and avoid the paradox. The resolution relies on the selection of a preferred frame singled out by the topology of the space.

Fragmentation patterns for dissociative recombination of the triatomic hydrogen molecular ion H₃ ⁺ in the vibrational ground state have been measured using the storage ring technique and molecular fragment imaging. A broad distribution of vibrational states in the H₂ fragment after two-body dissociation and a large predominance of nearly linear momentum geometries after three-body dissociation are found. The fragmentation results are directly contrasted with Coulomb explosion imaging data on the initial H₃ ⁺ geometry, compared to existing wave-packet calculations, and considered in the light of a simple physical picture.

Using the Coulomb explosion imaging method, the change of the relative population for the first six vibrational states of H₂⁺ during the interaction with low-kinetic-energy electrons has been measured. A model based on rate coefficients for dissociative recombination and superelastic collision processes is developed to explain the time dependence of the relative vibrational populations. Using this model, we demonstrate that superelastic collisions with rate coefficients of (1-4)×10^-6 cm³ s^-1 (about an order of magnitude higher than available theoretical predictions) can explain the observed electron-induced vibrational deexcitation of H₂⁺.

The stability of binary orbits can significantly shape the gravity wave signal which future Earth-based interferometers hope to detect. The innermost stable circular orbit has been of interest as it marks the transition from the late inspiral to final plunge. We consider purely relativistic orbits beyond the circular assumption. Homoclinic orbits are of particular importance to the question of stability as they lie on the boundary between dynamical stability and instability. We identify these, show their rate of energy loss to gravity waves, and present their gravitational wave forms.

Spinning compact binaries are shown to be chaotic in the post-Newtonian expansion of the two-body system. Chaos by definition is the extreme sensitivity to initial conditions and a consequent inability to predict the outcome of the evolution. As a result, the spinning pair will have unpredictable gravitational waveforms during coalescence. This poses a challenge to future gravity wave observatories which rely on a match between the data and a theoretical template.

We present measurements of projectile angular differential cross sections, dσ/dθ, and mean projectile energy gain or loss, ΔE_mean, as functions of the number s of electrons stabilized on the projectile in 16- and 26.4-keV Ar⁸⁺+C₆₀→Ar^(8-s)++C₆₀^r++(r-s)e^- collisions. These results are discussed in view of two models of the electronic response of C₆₀. In the infinitely conducting sphere model the charge mobility is sufficiently high in order to average out all effects of localization of individual charge carriers. In the movable-hole model “positive holes” are assumed to be localized as point charges in their equilibrium positions on the “molecular surface” within the times (down to 10^-16 s) between sequential over-the-barrier electron transfers. The two sets of predictions for θ are close for r<~8, and for r<~5 they are also in agreement with experimental results indicating ultrafast electronic response of ionized C₆₀. For r>5, both models underestimate θ and therefore we have developed Monte Carlo calculations for close collisions with individual carbon atoms in C₆₀. The energy gain first increases with s, has a flat maximum around s=4 and yields mean energy loss ΔE_mean=-20±5 eV for s=7. The measured fragmentation spectra θ(s) and ΔE_mean(s) may be partially rationalized by combining each of the two smooth-sphere models with the Monte Carlo calculations for close collisions.

Sharp thresholds are observed in the dissociative recombination cross section of vibrationally cold HD⁺ in the energy range where new channels H(1s)+D(n) [or D(1s)+H(n)] with n>2 open. The occurrence of these thresholds, not predicted by current theoretical calculations, contradicts the current assumption that the size of the total cross section can be calculated without accounting for the detailed branching ratios. An indirect signature of ion pair production is also found in the data, suggesting a significant branching into that channel.

The relative dissociative recombination rate coefficients for specific vibrational states of HD⁺ have been measured. The method is based on using merged electron and molecular ion beams in a heavy-ion storage ring together with molecular fragment imaging techniques which allow us to probe the vibrational-state population of the stored beam as a function of time as well as the final state of the dissociation. The initial vibrational distribution of the stored ion beam (from a Penning ion source) is found to be in good agreement with a Franck-Condon model of electron impact ionization, apart from slightly larger experimental populations found for low vibrational states; its time evolution in the storage ring reflects the predicted vibrational level lifetimes. Dissociative recombination measurements were performed with the electron and ion beams at matched velocities (corresponding to average collision energies of about 10 meV), and at several well-defined collision energies in the range of 3–11 eV. The obtained vibrational-state specific recombination rate coefficients are compared with theoretical calculations and show that, although an overall agreement exists between experiment and theory, large discrepancies occur for certain vibrational states at low electron energy.

Black holes cannot be seen directly since they absorb light and emit none, the very quality which earned them their name. We suggest that black holes may be seen indirectly through a chaotic defocusing of light. A black hole can capture light from a luminous companion in chaotic orbits before scattering the light in random directions. To a distant observer, the black hole would appear to light up. If the companion were a bright radio pulsar, this estimate suggests the black hole echo could be detectable.

Hot CH₂⁺ molecular ion ensembles were prepared, accelerated, and stored for radiative cooling to room temperature. The structure of the species was measured by the Coulomb explosion imaging method at different stages of cooling. The bending angle distributions were extracted and compared with recent theories as well as a previous Coulomb explosion imaging measurement. The comparison reveals an apparent large nonadiabatic contribution to the low-lying CH₂⁺ wave functions.

In an exploratory feasibility study we have measured the angular correlation between Auger electrons that were emitted in a cascadelike decay process after resonant photoexcitation, using synchrotron radiation from the Brookhaven National Synchrotron Light Source. While the monochromator was tuned to the argon 1s→4p resonance (3203.5 eV) we recorded Ar LMM Auger electrons in coincidence with KL_2,3L_2,3,KL₁L_2,3, and KL_2,3M_1,2,3 Auger electrons. We found different nonisotropic angular correlations between distinct energy regions of the LMM group of Auger lines and the KL_2,3L_2,3 Auger electrons, while for other kinetic energies the LMM Auger electrons exhibit isotropy. Because the KLL and LMM Auger energies are so different, we believe that the nonisotropic angular correlation observed is due to an alignment effect rather than a dynamical postcollision interaction effect.

The universe displays a three-dimensional pattern of hot and cold spots in the radiation remnant from the big bang. The global geometry of the universe can be revealed in the spatial distribution of these spots. In a topologically compact universe, distinctive patterns are especially prominent in spatial correlations of the radiation temperature. Whereas these patterns are usually washed out in statistical averages, we propose a scheme which uses the universe’s spots to observe global geometry in a manner analogous to the use of multiple images of a gravitationally lensed quasar to study the geometry of the lens. To demonstrate how the geometry of space forms patterns, we develop a simple real-space approximation to estimate temperature correlations for any set of cosmological parameters and any global geometry. We present correlated spheres which clearly show topological pattern formation for compact flat universes as well as for the compact negatively curved space introduced by Weeks and another discovered by Best. These examples illustrate how future satellite-based observations of the microwave background can determine the full geometry of the universe.