Gravitational waves from eccentric intermediate mass binary black hole mergers

Owing to the difficulty of direct observation, mergers of intermediate-mass black hole binaries are relatively less understood compared to stellar-mass binaries; however, the gravitational waves from their last few orbits and ringdown fall in the band of ground-based detectors. Because the typical source is expected to circularize prior to entering LIGO or VIRGO's range, inspiral searches concentrate on circularized binaries. It is possible that events will be missed if there are sources with residual eccentricity. We study the variation of the signal to noise present in the dominant mode of the eccentric evolutions as a function of mass and eccentricity and also the relative contribution of the signal in the various spherical harmonic modes. The energy radiated in gravitational waves increases with eccentricity until the eccentricity becomes too high, leading to plunging trajectories, at which point the energy radiated decreases. This enhancement of the energy for initial eccentricities near the transition value translates into larger signal-to-noise ratios. Consequently despite the anticipated loss in the signal-to-noise ratio due to the use of quasi-circular detection templates, some eccentric signals potentially may be seen farther out than others

Numerical stability for finite difference approximations of Einstein's equations

We extend the notion of numerical stability of finite difference approximations to include hyperbolic systems that are first order in time and second order in space, such as those that appear in Numerical Relativity. By analyzing the symbol of the second order system, we obtain necessary and sufficient conditions for stability in a discrete norm containing one-sided difference operators. We prove stability for certain toy models and the linearized Nagy-Ortiz-Reula formulation of Einstein's equations. We also find that, unlike in the fully first order case, standard discretizations of some well-posed problems lead to unstable schemes and that the Courant limits are not always simply related to the characteristic speeds of the continuum problem. Finally, we propose methods for testing stability for second order in space hyperbolic systems.Comment: 18 pages, 9 figure

Binary Black Hole Encounters, Gravitational Bursts and Maximum Final Spin

The spin of the final black hole in the coalescence of nonspinning black holes is determined by the ``residual'' orbital angular momentum of the binary. This residual momentum consists of the orbital angular momentum that the binary is not able to shed in the process of merging. We study the angular momentum radiated, the spin of the final black hole and the gravitational bursts in a series of orbits ranging from almost direct infall to numerous orbits before infall that exhibit multiple bursts of radiation in the merger process. We show that the final black hole gets a maximum spin parameter $a/M_h \le 0.78$, and this maximum occurs for initial orbital angular momentum $L \approx M^2_h$.Comment: Replaced with version to appear in PR

Age-Specific Effects of Mirror-Muscle Activity on Cross-Limb Adaptations Under Mirror and Non-Mirror Visual Feedback Conditions

Cross-limb transfer (CLT) describes the observation of bilateral performance gains due to unilateral motor practice. Previous research has suggested that CLT may be reduced, or absent, in older adults, possibly due to age-related structural and functional brain changes. Based on research showing increases in CLT due to the provision of mirror visual feedback (MVF) during task execution in young adults, our study aimed to investigate whether MVF can facilitate CLT in older adults, who are known to be more reliant on visual feedback for accurate motor performance. Participants (N = 53) engaged in a short-term training regime (300 movements) involving a ballistic finger task using their dominant hand, while being provided with either visual feedback of their active limb, or a mirror reflection of their active limb (superimposed over the quiescent limb). Performance in both limbs was examined before, during and following the unilateral training. Furthermore, we measured corticospinal excitability (using TMS) at these time points, and assessed muscle activity bilaterally during the task via EMG; these parameters were used to investigate the mechanisms mediating and predicting CLT. Training resulted in significant bilateral performance gains that did not differ as a result of age or visual feedback (both p > 0.1). Training also elicited bilateral increases in corticospinal excitability (p < 0.05). For younger adults, CLT was significantly predicted by performance gains in the trained hand (β = 0.47), whereas for older adults it was significantly predicted by mirror activity in the untrained hand during training (β = 0.60). The present study suggests that older adults are capable of exhibiting CLT to a similar degree to younger adults. The prominent role of mirror activity in the untrained hand for CLT in older adults indicates that bilateral cortical activity during unilateral motor tasks is a compensatory mechanism. In this particular task, MVF did not facilitate the extent of CLT

Implementation of standard testbeds for numerical relativity

We discuss results that have been obtained from the implementation of the initial round of testbeds for numerical relativity which was proposed in the first paper of the Apples with Apples Alliance. We present benchmark results for various codes which provide templates for analyzing the testbeds and to draw conclusions about various features of the codes. This allows us to sharpen the initial test specifications, design a new test and add theoretical insight.Comment: Corrected versio

Dyslipidemia impairs mitochondrial trafficking and function in sensory neurons

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154247/1/fsb2fj201700206r.pd

Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem

We study gravitational perturbations of Schwarzschild spacetime by solving a hyperboloidal initial value problem for the Bardeen-Press equation. Compactification along hyperboloidal surfaces in a scri-fixing gauge allows us to have access to the gravitational waveform at null infinity in a general setup. We argue that this hyperboloidal approach leads to a more accurate and efficient calculation of the radiation signal than the common approach where a timelike outer boundary is introduced. The method can be generalized to study perturbations of Kerr spacetime using the Teukolsky equation.Comment: 14 pages, 9 figure

The Influence of Mirror-Visual Feedback on Training-Induced Motor Performance Gains in the Untrained Hand

The well-documented observation of bilateral performance gains following unilateral motor training, a phenomenon known as cross-limb transfer, has important implications for rehabilitation. It has recently been shown that provision of a mirror image of the active hand during unilateral motor training has the capacity to enhance the efficacy of this phenomenon when compared to training without augmented visual feedback (i.e., watching the passive hand), possibly via action observation effects [1]. The current experiment was designed to confirm whether mirror-visual feedback (MVF) during motor training can indeed elicit greater performance gains in the untrained hand compared to more standard visual feedback (i.e., watching the active hand). Furthermore, discussing the mechanisms underlying any such MVF-induced behavioural effects, we suggest that action observation and the cross-activation hypothesis may both play important roles in eliciting cross-limb transfer. Eighty participants practiced a fast-as-possible two-ball rotation task with their dominant hand. During training, three different groups were provided with concurrent visual feedback of the active hand, inactive hand or a mirror image of the active hand with a fourth control group receiving no training. Pre- and post-training performance was measured in both hands. MVF did not increase the extent of training-induced performance changes in the untrained hand following unilateral training above and beyond those observed for other types of feedback. The data are consistent with the notion that cross-limb transfer, when combined with MVF, is mediated by cross-activation with action observation playing a less unique role than previously suggested. Further research is needed to replicate the current and previous studies to determine the clinical relevance and potential benefits of MVF for cases that, due to the severity of impairment, rely on unilateral training programmes of the unaffected limb to drive changes in the contralateral affected limb

Implementation of higher-order absorbing boundary conditions for the Einstein equations

We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer boundary, which is taken to be a coordinate sphere. We reformulate the boundary conditions as conditions on the gauge-invariant Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated by rewriting the boundary conditions as a system of ODEs for a set of auxiliary variables intrinsic to the boundary. From these we construct boundary data for a set of well-posed constraint-preserving boundary conditions for the Einstein equations in a first-order generalized harmonic formulation. This construction has direct applications to outer boundary conditions in simulations of isolated systems (e.g., binary black holes) as well as to the problem of Cauchy-perturbative matching. As a test problem for our numerical implementation, we consider linearized multipolar gravitational waves in TT gauge, with angular momentum numbers l=2 (Teukolsky waves), 3 and 4. We demonstrate that the perfectly absorbing boundary condition B_L of order L=l yields no spurious reflections to linear order in perturbation theory. This is in contrast to the lower-order absorbing boundary conditions B_L with L<l, which include the widely used freezing-Psi_0 boundary condition that imposes the vanishing of the Newman-Penrose scalar Psi_0.Comment: 25 pages, 9 figures. Minor clarifications. Final version to appear in Class. Quantum Grav

Exact boundary conditions in numerical relativity using multiple grids: scalar field tests

Cauchy-Characteristic Matching (CCM), the combination of a central 3+1 Cauchy code with an exterior characteristic code connected across a time-like interface, is a promising technique for the generation and extraction of gravitational waves. While it provides a tool for the exact specification of boundary conditions for the Cauchy evolution, it also allows to follow gravitational radiation all the way to infinity, where it is unambiguously defined. We present a new fourth order accurate finite difference CCM scheme for a first order reduction of the wave equation around a Schwarzschild black hole in axisymmetry. The matching at the interface between the Cauchy and the characteristic regions is done by transfering appropriate characteristic/null variables. Numerical experiments indicate that the algorithm is fourth order convergent. As an application we reproduce the expected late-time tail decay for the scalar field.Comment: 14 pages, 5 figures. Included changes suggested by referee