Gravitational waves and stalled satellites from massive galaxy mergers at z <= 1

We present a model for merger-driven evolution of the mass function for massive galaxies and their central supermassive black holes at late times. We discuss the current observational evidence in favor of merger-driven massive galaxy evolution during this epoch, and demonstrate that the observed evolution of the mass function can be reproduced by evolving an initial mass function under the assumption of negligible star formation. We calculate the stochastic gravitational wave signal from the resulting black-hole binary mergers in the low redshift universe (z <= 1) implied by this model, and find that this population has a signal-to-noise ratio as much as ~5x larger than previous estimates for pulsar timing arrays, with an expectation value for the characteristic strain h_c (f=1 yr^{-1}) = 4.1 x 10^{-15} that may already be in tension with observational constraints, and a {2-sigma, 3-sigma} lower limit within this model of h_c (f=1 yr^{-1}) = {1.1 x 10^{-15}, 6.8 x 10^{-16}}. The strength of this signal is sufficient to make it detectable with high probability under conservative assumptions within the next several years, if the principle assumption of merger-driven galaxy evolution since z = 1 holds true. For cases where a galaxy merger fails to lead to a black hole merger, we estimate the probability for a given number of satellite unmerged black holes to remain within a massive host galaxy, and interpret the result in light of ULX observations. In particular, we find that the brightest cluster galaxies should have 1-2 such sources with luminosities above 10^{39} erg/s, which is consistent with the statistics of observed ULXs.Comment: 11 pages, 5 figures, submitted to ApJ, v2 includes the referee's requested change

Stability of exact force-free electrodynamic solutions and scattering from spacetime curvature

Recently, a family of exact force-free electrodynamic (FFE) solutions was given by Brennan, Gralla and Jacobson, which generalizes earlier solutions by Michel, Menon and Dermer, and other authors. These solutions have been proposed as useful models for describing the outer magnetosphere of conducting stars. As with any exact analytical solution that aspires to describe actual physical systems, it is vitally important that the solution possess the necessary stability. In this paper, we show via fully nonlinear numerical simulations that the aforementioned FFE solutions, despite being highly special in their properties, are nonetheless stable under small perturbations. Through this study, we also introduce a three-dimensional pseudospectral relativistic FFE code that achieves exponential convergence for smooth test cases, as well as two additional well-posed FFE evolution systems in the appendix that have desirable mathematical properties. Furthermore, we provide an explicit analysis that demonstrates how propagation along degenerate principal null directions of the spacetime curvature tensor simplifies scattering, thereby providing an intuitive understanding of why these exact solutions are tractable, i.e. why they are not backscattered by spacetime curvature.Comment: 33 pages, 21 figures; V2 updated to match published versio

Experimental Measurements of Phase Space

Direct measurements of integrated phase-space densities, e.g., f(x,vy,t), have been made in an experiment. Using spectroscopically active ions, measurements in a plasma show the ion response, fi(x,v,t), to linear and nonlinear waves and phase-space particle bunching. Time-resolved measurements show coherent and incoherent phase-space density changes in the presence of waves, indicating that transitions to turbulence and chaos may be studied. The time, space, and velocity-space resolution may allow experimental tests of predictions from the Boltzmann equation

Laboratory Simulations of Suprauroral Mechanisms Leading to Perpendicular Ion Heating and Conic Formation

Laboratory experiments are presented simulating aspects of perpendicular ion heating and conic formation that are observed or hypothesized to occur in the terrestrial ionosphere and magnetosphere. Previous laboratory observations of ion conics in the presence of the current‐driven electrostatic ion cyclotron wave are reviewed. Field‐aligned ion beams, accompanied by beam‐generated electrostatic ion cyclotron modes, resulted in perpendicular energization of beam ions and also the heating of background plasma ions. Antenna‐launched broadband and narrow‐band lower hybrid waves produced considerable perpendicular ion heating and non‐Maxwellian “tail” formation. Laboratory results are discussed in light of in situ measurements by the S3‐3 satellite and the MARIE sounding rocket

Random Projections For Large-Scale Regression

Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool in machine learning and statistics. We discuss the applications of random projections in linear regression problems, developed to decrease computational costs, and give an overview of the theoretical guarantees of the generalization error. It can be shown that the combination of random projections with least squares regression leads to similar recovery as ridge regression and principal component regression. We also discuss possible improvements when averaging over multiple random projections, an approach that lends itself easily to parallel implementation.Comment: 13 pages, 3 Figure