We study the dynamical instability against bar-mode deformation of differentially rotating stars. We performed numerical simulation and linear perturbation analysis adopting polytropic equations of state with the polytropic index $n=1$. It is found that rotating stars of a high degree of differential rotation are dynamically unstable even for the ratio of the kinetic energy to the gravitational potential energy of $O(0.01)$. Gravitational waves from the final nonaxisymmetric quasistationary states are calculated in the quadrupole formula. For rotating stars of mass $1.4M_{\odot}$ and radius several 10 km, gravitational waves have frequency several 100 Hz and effective amplitude $\sim 5 \times 10^{-22}$ at a distance of $\sim 100$ Mpc.Comment: 5 pages, 7 figures, accepted for publication in MNRA

As an extension of our previous work, we investigate the dynamical instability against non‐axisymmetric bar‐mode deformations of differentially rotating stars in Newtonian gravity by varying the equations of state and velocity profiles. We performed the numerical simulation and the follow‐up linear stability analysis by adopting polytropic equations of state with polytropic indices n= 1, 3/2 and 5/2, and with two types of angular velocity profiles (the so‐called j‐constant‐like and Kepler‐like laws). It is confirmed that rotating stars with a high degree of differential rotation are dynamically unstable against bar‐mode deformation, even when the ratio of the kinetic energy to the gravitational potential energy β is of order 0.01. The criterion for the onset of bar‐mode dynamical instability depends weakly on the polytropic index n and the angular velocity profile, as long as the degree of differential rotation is high. Gravitational waves from the final non‐axisymmetric quasi‐stationary states are calculated using the quadrupole formula. For proto‐neutron stars of mass 1.4 M⊙, radius ∼30 km and β≲ 0.1, such gravitational waves have a frequency of ∼600–1400 Hz, and the effective amplitude is larger than 10−22 at a distance of about 100 Mpc, irrespective of n and the angular velocity profile.

The dichotic presentation of two sinusoids with a slight difference in frequency elicits subjective fluctuations called binaural beat (BB). BBs provide a classic example of binaural interaction considered to result from neural interaction in the central auditory pathway that receives input from both ears. To explore the cortical representation of the fluctuation of BB, we recorded magnetic fields evoked by slow BB of 4.00 or 6.66 Hz in nine normal subjects. The fields showed small amplitudes; however, they were strong enough to be distinguished from the noise accompanying the recordings. Spectral analyses of the magnetic fields recorded on single channels revealed that the responses evoked by BBs contained a specific spectral component of BB frequency, and the magnetic fields were confirmed to represent an auditory steady-state response (ASSR) to BB. The analyses of spatial distribution of BB-synchronized responses and minimum-norm current estimates revealed multiple BB ASSR sources in the parietal and frontal cortices in addition to the temporal areas, including auditory cortices. The phase of synchronized waveforms showed great variability, suggesting that BB ASSR does not represent changing interaural phase differences (IPD) per se, but instead it reflects a higher-order cognitive process corresponding to subjective fluctuations of BB. Our findings confirm that the activity of the human cerebral cortex can be synchronized with slow BB by using information on the IPD.

No abstract

In models of temporal processing, time delays incurred by axonal propagation of action potentials play a prominent role. A preeminent model of temporal processing in audition is the binaural model of Jeffress (1948), which has dominated theories regarding our acute sensitivity to interaural time differences (ITDs). In Jeffress’ model a binaural cell is maximally active when the ITD is compensated by an internal delay, which brings the inputs from left and right ears in coincidence, and which would arise from axonal branching patterns of monaural input fibers. By arranging these patterns in systematic and opposite ways for the ipsi- and contralateral inputs, a range of length differences, and thereby of internal delays, is created so that ITD is transformed into a spatial activation pattern along the binaural nucleus. We reanalyze single, labeled and physiologically characterized, axons of spherical bushy cells of the cat anteroventral cochlear nucleus (AVCN) which project to binaural coincidence detectors in the medial superior olive (MSO). The reconstructions largely confirm the observations of two previous reports, but several features are observed which are inconsistent with Jeffress’ model. We found that ipsilateral projections can also form a caudally-directed delay line pattern, which would counteract delays incurred by caudally-directed contralateral projections. Comparisons of estimated axonal delays with binaural physiological data indicate that the suggestive anatomical patterns cannot account for the frequency-dependent distribution of best delays in the cat. Surprisingly, the tonotopic distribution of the afferents endings indicate that low CFs are under- rather than overrepresented in the MSO.

For the analysis of the r-mode oscillation of hot young neutron stars, it is necessary to consider the effect of differential rotation, because viscosity is not strong enough for differentially rotating young neutron stars to be lead to uniformly rotating configurations on a very short time scale after their birth. In this paper, we have developed a numerical scheme to solve r-mode oscillations of differentially rotating polytropic inviscid stars. This is the extended version of the method which was applied to compute r-mode oscillations of uniformly rotating Newtonian polytropic stars. By using this new method, we have succeeded in obtaining eigenvalues and eigenfunctions of r-mode oscillations of differentially rotating polytropic stars.Our numerical results show that as the degree of differential rotation is increased, it becomes more difficult to solve r-mode oscillations for slightly deformed configurations from sphere compared to solving r-mode oscillations of considerably deformed stars. One reason for it seems that for slightly deformed stars corotation points appear near the surface region if the degree of differential rotation is strong enough. This is similar to the situation that the perturbational approach of r-mode oscillations for slowly rotating stars in general relativity results in a singular eigenvalue problem.

The evolution of a nonaxisymmetric bar-mode perturbation of rapidly rotating stars due to a secular instability induced by gravitational wave emission is studied in post-Newtonian simulations taking into account gravitational radiation reaction. A polytropic equation of state with the polytropic index n = 1 is adopted. The ratio of the rotational kinetic energy to the gravitational potential energy T /|W | is chosen in the range between 0.2 and 0.26. Numerical simulations were performed until the perturbation grows to the nonlinear regime, and illustrate that the outcome after the secular instability sets in is an ellipsoidal star of a moderately large ellipticity > ∼ 0.7. A rapidly rotating protoneutron star may form such an ellipsoid, which is a candidate for strong emitter of gravitational waves for ground-based laser interferometric detectors. A possibility that effects of magnetic fields neglected in this work may modify the growth of the secular instability is also mentioned.04.25. Dm, 04.40.Dg

The RWN visibility and the preoperative HRCT findings showed a high correlation. Drawing the prediction line is a simple and useful way for preoperatively predicting the RWN visibility in cochlear implant surgery.