Relativistic Stellar Pulsations With Near-Zone Boundary Conditions

A new method is presented here for evaluating approximately the pulsation modes of relativistic stellar models. This approximation relies on the fact that gravitational radiation influences these modes only on timescales that are much longer than the basic hydrodynamic timescale of the system. This makes it possible to impose the boundary conditions on the gravitational potentials at the surface of the star rather than in the asymptotic wave zone of the gravitational field. This approximation is tested here by predicting the frequencies of the outgoing non-radial hydrodynamic modes of non-rotating stars. The real parts of the frequencies are determined with an accuracy that is better than our knowledge of the exact frequencies (about 0.01%) except in the most relativistic models where it decreases to about 0.1%. The imaginary parts of the frequencies are determined with an accuracy of approximately M/R, where M is the mass and R is the radius of the star in question.Comment: 10 pages (REVTeX 3.1), 5 figs., 1 table, fixed minor typos, published in Phys. Rev. D 56, 2118 (1997

Generalized r-Modes of the Maclaurin Spheroids

Analytical solutions are presented for a class of generalized r-modes of rigidly rotating uniform density stars---the Maclaurin spheroids---with arbitrary values of the angular velocity. Our analysis is based on the work of Bryan; however, we derive the solutions using slightly different coordinates that give purely real representations of the r-modes. The class of generalized r-modes is much larger than the previously studied `classical' r-modes. In particular, for each l and m we find l-m (or l-1 for the m=0 case) distinct r-modes. Many of these previously unstudied r-modes (about 30% of those examined) are subject to a secular instability driven by gravitational radiation. The eigenfunctions of the `classical' r-modes, the l=m+1 case here, are found to have particularly simple analytical representations. These r-modes provide an interesting mathematical example of solutions to a hyperbolic eigenvalue problem.Comment: 12 pages, 3 figures; minor changes and additions as will appear in the version to be published in Physical Review D, January 199

Massive black hole remnants of the first stars II: optical and X-ray signatures in present-day galactic haloes

The first stars forming in minihaloes at redshifts greater than 20 may have been very massive and could have left behind massive black hole (MBH) remnants. In a previous paper we investigated the hierarchical merging of these MBHs and their associated haloes, using a semi-analytical approach consisting of a hierarchical merger tree algorithm and explicit prescriptions for the dynamics of merged substructure inside a larger host halo following a merger. One of the results was the prediction of a number of MBHs orbiting throughout present-day galactic haloes. In addition we determined the mass accretion rate of these MBHs assuming that they could in principle remain embedded in a gaseous core that is a remnant of the haloes with which the MBHs were associated before merging with the host system. On this basis we determine in this paper the bolometric, optical and X-ray luminosity functions for the accreting MBHs using thin disk and advection dominated accretion flow models. Our predicted MBH X-ray emissions are then compared with observations of ultra-luminous X-ray sources in galaxies. We find that the slope and normalisation of the predicted X-ray luminosity function are consistent with the observations.Comment: 14 pages, 10 figures; updated to match published versio

Rotating Stars in Relativity

Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information one could obtain about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on the equilibrium properties and on the nonaxisymmetric instabilities in f-modes and r-modes have been updated and several new sections have been added on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity.Comment: 101 pages, 18 figures. The full online-readable version of this article, including several animations, will be published in Living Reviews in Relativity at http://www.livingreviews.org

Genetic architecture of subcortical brain structures in 38,851 individuals

Subcortical brain structures are integral to motion, consciousness, emotions and learning. We identified common genetic variation related to the volumes of the nucleus accumbens, amygdala, brainstem, caudate nucleus, globus pallidus, putamen and thalamus, using genome-wide association analyses in almost 40,000 individuals from CHARGE, ENIGMA and UK Biobank. We show that variability in subcortical volumes is heritable, and identify 48 significantly associated loci (40 novel at the time of analysis). Annotation of these loci by utilizing gene expression, methylation and neuropathological data identified 199 genes putatively implicated in neurodevelopment, synaptic signaling, axonal transport, apoptosis, inflammation/infection and susceptibility to neurological disorders. This set of genes is significantly enriched for Drosophila orthologs associated with neurodevelopmental phenotypes, suggesting evolutionarily conserved mechanisms. Our findings uncover novel biology and potential drug targets underlying brain development and disease