The Secular Bar-Mode Instability in Rapidly Rotating Stars Revisited

Uniformly rotating, homogeneous, incompressible Maclaurin spheroids that spin sufficiently rapidly are secularly unstable to nonaxisymmetric, bar-mode perturbations when viscosity is present. The intuitive explanation is that energy dissipation by viscosity can drive an unstable spheroid to a stable, triaxial configuration of lower energy - a Jacobi ellipsoid. But what about rapidly rotating compressible stars? Unlike incompressible stars, which contain no internal energy and therefore immediately liberate all the energy dissipated by viscosity, compressible stars have internal energy and can retain the dissipated energy as internal heat. Now compressible stars that rotate sufficiently rapidly and also manage to liberate this dissipated energy very quickly are known to be unstable to bar-mode perturbations, like their incompressible counterparts. But what is the situation for rapidly rotating compressible stars that have very long cooling timescales, so that all the energy dissipated by viscosity is retained as heat, whereby the total energy of the star remains constant on a secular (viscous) evolution timescale? Are such stars also unstable to the nonlinear growth of bar modes, or is the viscous heating sufficient to cause them to expand, drive down the ratio of rotational kinetic to gravitational potential energy T/|W| ~ 1/R, where R is the equatorial radius, and turn off the instability before it gets underway? If the instability still arises in such stars, at what rotation rate do they become unstable, and to what final state do they evolve? We provide answers to these questions in the context of the compressible ellipsoid model for rotating stars. The results should serve as useful guides for numerical simulations in 3+1 dimensions for rotating stars containing viscosity.Comment: Accepted for publication in ApJ 613, 1213-1220, 200

Parametric Manifolds I: Extrinsic Approach

A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the 1-parameter family of hypersurfaces orthogonal to the curves, each of which inherits a metric and connection from the original manifold via orthogonal projections; this is the well-known Gauss-Codazzi formalism. We generalize this formalism to the case where the foliation is not hypersurface orthogonal. Crucial to this generalization is the notion of deficiency, which measures the failure of the orthogonal tangent spaces to be surface-forming, and which behaves very much like torsion. Some applications to initial value problems in general relativity will be briefly discussed.Comment: Plain TeX, 21 pages, no figure

Early-childhood BMI trajectories: evidence from a prospective, nationally representative British cohort study

Background and Objectives: By age 5, 20% of British children are classed as overweight or obese, suggesting that early childhood is crucial for lifelong body mass index (BMI) trajectories. In this paper, we identify latent trajectories of early-childhood BMI from ages 3 to 11 years. Given the current context of growing socio-economic inequalities in childhood and adult overweight and obesity, we examine the socio-economic characteristics and mechanisms during pregnancy and infancy which underscore these trajectories.Subject and Methods: We use a nationally representative, prospective cohort study of 9699 children born in 2000–2002, living in the United Kingdom shortly after birth, with complete information on height and weight (measured by an interviewer) at ages 3, 5, 7 and 11. Trajectories of BMI are calculated using latent growth mixture models. Multinomial models characterize these trajectories by their socio-economic profiles and mechanisms during pregnancy and infancy.Results: Four trajectories were identified: two separate trajectories where BMI remains within a normal range (85% of the sample), an overweight trajectory (14.4%), and an obese trajectory (3.1%). No ‘declining BMI’ or late-onset groups were found. The obese group is already distinct from the other trajectories by age 3. The overweight group diverges from the normal groups around age 5. Strong socio-economic inequalities emerged; for the obese group, part of this disadvantage is mediated through early mechanisms such as pregnancy smoke and not initiating breastfeeding.Conclusions: This study provides strong evidence for the idea that childhood BMI trajectories develop early, especially for children who will follow an obese trajectory. Strong socio-economic patterns in these trajectories suggest that the observed trend in growing inequalities may be rooted in early life. Mediating mechanisms for the obese appear to be in the pregnancy and infant period, further research should explore mechanisms occurring around age 5 when the overweight trajectory diverges

Clonal analysis of meningococci during a 26 year period prior to the introduction of meningococcal serogroup C vaccines

Meningococcal disease remains a public health burden in the UK and elsewhere. Invasive Neisseria meningitidis, isolated in Scotland between 1972 and 1998, were characterised retrospectively to examine the serogroup and clonal structure of the circulating population. 2607 isolates causing invasive disease were available for serogroup and MLST analysis whilst 2517 were available for multilocus sequence typing (MLST) analysis only. Serogroup distribution changed from year to year but serogroups B and C were dominant throughout. Serogroup B was dominant throughout the 1970s and early 1980s until serogroup C became dominant during the mid-1980s. The increase in serogroup C was not associated with one particular sequence type (ST) but was associated with a number of STs, including ST-8, ST-11, ST-206 and ST-334. This is in contrast to the increase in serogroup C disease seen in the 1990s that was due to expansion of the ST-11 clonal complex. While there was considerable diversity among the isolates (309 different STs among the 2607 isolates), a large proportion of isolates (59.9%) were associated with only 10 STs. These data highlight meningococcal diversity over time and the need for ongoing surveillance during the introduction of new meningococcal vaccines

IllinoisGRMHD: An Open-Source, User-Friendly GRMHD Code for Dynamical Spacetimes

In the extreme violence of merger and mass accretion, compact objects like black holes and neutron stars are thought to launch some of the most luminous outbursts of electromagnetic and gravitational wave energy in the Universe. Modeling these systems realistically is a central problem in theoretical astrophysics, but has proven extremely challenging, requiring the development of numerical relativity codes that solve Einstein's equations for the spacetime, coupled to the equations of general relativistic (ideal) magnetohydrodynamics (GRMHD) for the magnetized fluids. Over the past decade, the Illinois Numerical Relativity (ILNR) Group's dynamical spacetime GRMHD code has proven itself as a robust and reliable tool for theoretical modeling of such GRMHD phenomena. However, the code was written "by experts and for experts" of the code, with a steep learning curve that would severely hinder community adoption if it were open-sourced. Here we present IllinoisGRMHD, which is an open-source, highly-extensible rewrite of the original closed-source GRMHD code of the ILNR Group. Reducing the learning curve was the primary focus of this rewrite, with the goal of facilitating community involvement in the code's use and development, as well as the minimization of human effort in generating new science. IllinoisGRMHD also saves computer time, generating roundoff-precision identical output to the original code on adaptive-mesh grids, but nearly twice as fast at scales of hundreds to thousands of cores.Comment: 37 pages, 6 figures, single column. Matches published versio

Photometric Variability in Earthshine Observations

The identification of an extrasolar planet as Earth-like will depend on the detection of atmospheric signatures or surface non-uniformities. In this paper we present spatially unresolved flux light curves of Earth for the purpose of studying a prototype extrasolar terrestrial planet. Our monitoring of the photometric variability of earthshine revealed changes of up to 23 % per hour in the brightness of Earth's scattered light at around 600 nm, due to the removal of specular reflection from the view of the Moon. This variability is accompanied by reddening of the spectrum, and results from a change in surface properties across the continental boundary between the Indian Ocean and Africa's east coast. Our results based on earthshine monitoring indicate that specular reflection should provide a useful tool in determining the presence of liquid water on extrasolar planets via photometric observations.Comment: To appear in Astrobiology 9(3). 17 pages, 3 figures, 1 tabl

Accretion disks around binary black holes of unequal mass: GRMHD simulations near decoupling

We report on simulations in general relativity of magnetized disks onto black hole binaries. We vary the binary mass ratio from 1:1 to 1:10 and evolve the systems when they orbit near the binary-disk decoupling radius. We compare (surface) density profiles, accretion rates (relative to a single, non-spinning black hole), variability, effective $\alpha$-stress levels and luminosities as functions of the mass ratio. We treat the disks in two limiting regimes: rapid radiative cooling and no radiative cooling. The magnetic field lines clearly reveal jets emerging from both black hole horizons and merging into one common jet at large distances. The magnetic fields give rise to much stronger shock heating than the pure hydrodynamic flows, completely alter the disk structure, and boost accretion rates and luminosities. Accretion streams near the horizons are among the densest structures; in fact, the 1:10 no-cooling evolution results in a refilling of the cavity. The typical effective temperature in the bulk of the disk is $\sim 10^5 (M/10^8 M_\odot)^{-1/4} (L/L_{\rm edd})^{1/4} {\rm K}$ yielding characteristic thermal frequencies $\sim 10^{15} (M/10^8 M_\odot)^{-1/4} (L/L_{\rm edd})^{1/4}(1+z)^{-1}{\rm Hz}$. These systems are thus promising targets for many extragalactic optical surveys, such as LSST, WFIRST, and PanSTARRS.Comment: 29 pages, 23 captioned figures, 3 tables, submitted to PR