Bayesian model selection for testing the no-hair theorem with black hole ringdowns

General relativity predicts that a black hole that results from the merger of two compact stars (either black holes or neutron stars) is initially highly deformed but soon settles down to a quiescent state by emitting a superposition of quasi-normal modes (QNMs). The QNMs are damped sinusoids with characteristic frequencies and decay times that depend only on the mass and spin of the black hole and no other parameter - a statement of the no-hair theorem. In this paper we have examined the extent to which QNMs could be used to test the no-hair theorem with future ground- and space-based gravitational-wave detectors. We model departures from general relativity (GR) by introducing extra parameters which change the mode frequencies or decay times from their general relativistic values. With the aid of numerical simulations and Bayesian model selection, we assess the extent to which the presence of such a parameter could be inferred, and its value estimated. We find that it is harder to decipher the departure of decay times from their GR value than it is with the mode frequencies. Einstein Telescope (ET, a third generation ground-based detector) could detect departures of <1% in the frequency of the dominant QNM mode of a 500 Msun black hole, out to a maximum range of 4 Gpc. In contrast, the New Gravitational Observatory (NGO, an ESA space mission to detect gravitational waves) can detect departures of ~ 0.1% in a 10^8 Msun black hole to a luminosity distance of 30 Gpc (z = 3.5).Comment: 9 pages, 5 figure

Stability Analysis of Optimal Velocity Model for Traffic and Granular Flow under Open Boundary Condition

We analyzed the stability of the uniform flow solution in the optimal velocity model for traffic and granular flow under the open boundary condition. It was demonstrated that, even within the linearly unstable region, there is a parameter region where the uniform solution is stable against a localized perturbation. We also found an oscillatory solution in the linearly unstable region and its period is not commensurate with the periodicity of the car index space. The oscillatory solution has some features in common with the synchronized flow observed in real traffic.Comment: 4 pages, 6 figures. Typos removed. To appear in J. Phys. Soc. Jp