Tidal interactions of a Maclaurin spheroid. I: Properties of free oscillation modes

We review the work of Bryan (1889) on the normal modes of a Maclaurin spheroid, carrying out numerical calculations of the frequencies and spatial forms of these modes that have not been previously published. We study all modes of degree $l \le 4$, which includes both inertial modes and surface gravity modes, with the aim of better understanding the effect of rapid rotation on tidal interactions. The inclusion of these higher degree modes greatly increases the number of frequencies at which tidal resonances may occur. We derive an expression for the decay rates of these modes to first order in viscosity and explicitly plot these for modes. We see that the equatorial bulge of the spheroid has a significant effect on the decay rates (changing some of these by a factor of 2 between an eccentricity of $e=0$ and $0.5$), and a more modest effect on the mode frequencies. This suggests that models of tidal interaction between rapidly rotating stars and giant planets that model the Coriolis force while neglecting the centrifugal distortion of the body may be in error by an order unity factor. In a subsequent paper we shall examine the case of a forced flow in this spheroid, and complete the model by considering how the tides raised by the orbiting companion change the orbital elements.Comment: 27 pages, 39 figures, 1 table, accepted for publication in MNRA

Continuation and stability deduction of resonant periodic orbits in three dimensional systems

In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the classical three body problem in three dimensions and use its dynamics to assess the long-term evolution of extrasolar systems. We compute periodic orbits, which correspond to exact resonant motion, and determine their linear stability. By computing maps of dynamical stability we show that stable periodic orbits are surrounded in phase space with regular motion even in systems with more than two degrees of freedom, while chaos is apparent close to unstable ones. Therefore, families of stable periodic orbits, indeed, consist backbones of the stability domains in phase space.Comment: Proceedings of the 6th International Conference on Numerical Analysis (NumAn 2014). Published by the Applied Mathematics and Computers Lab, Technical University of Crete (AMCL/TUC), Greec

My Own Kathlyne: My Sweet Romantic Queen

https://digitalcommons.library.umaine.edu/mmb-vp/2219/thumbnail.jp

Induced matter: Curved N-manifolds encapsulated in Riemann-flat N+1 dimensional space

Liko and Wesson have recently introduced a new 5-dimensional induced matter solution of the Einstein equations, a negative curvature Robertson-Walker space embedded in a Riemann flat 5-dimensional manifold. We show that this solution is a special case of a more general theorem prescribing the structure of certain N+1-dimensional Riemann flat spaces which are all solutions of the Einstein equations. These solutions encapsulate N-dimensional curved manifolds. Such spaces are said to "induce matter" in the sub-manifolds by virtue of their geometric structure alone. We prove that the N-manifold can be any maximally symmetric space.Comment: 3 page

A fully-coherent all-sky search for gravitational-waves from compact binary coalescences

We introduce a fully-coherent method for searching for gravitational wave signals generated by the merger of black hole and/or neutron star binaries. This extends the coherent analysis previously developed and used for targeted gravitational wave searches to an all-sky, all-time search. We apply the search to one month of data taken during the fifth science run of the LIGO detectors. We demonstrate an increase in sensitivity of 25% over the coincidence search, which is commensurate with expectations. Finally, we discuss prospects for implementing and running a coherent search for gravitational wave signals from binary coalescence in the advanced gravitational wave detector data.Comment: 17 pages, 12 figure

A CANDELS WFC3 Grism Study of Emission-Line Galaxies at z ~ 2: A Mix of Nuclear Activity and Low-Metallicity Star Formation

We present Hubble Space Telescope Wide Field Camera 3 (WFC3) slitless grism spectroscopy of 28 emission-line galaxies at z ~ 2, in the GOODS-S region of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey. The high sensitivity of these grism observations, with >1σ detections of emission lines to f > 2.5 × 10^(–18) erg s^(–1) cm^(–2), means that the galaxies in the sample are typically ~7 times less massive (median M_* = 10^(9.5) M_☉) than previously studied z ~ 2 emission-line galaxies. Despite their lower mass, the galaxies have [O III]/Hβ ratios which are very similar to previously studied z ~ 2 galaxies and much higher than the typical emission-line ratios of local galaxies. The WFC3 grism allows for unique studies of spatial gradients in emission lines, and we stack the two-dimensional spectra of the galaxies for this purpose. In the stacked data the [O III] emission line is more spatially concentrated than the Hβ emission line with 98.1% confidence. We additionally stack the X-ray data (all sources are individually undetected), and find that the average L_([O III])/L_(0.5-10keV) ratio is intermediate between typical z ~ 0 obscured active galaxies and star-forming galaxies. Together the compactness of the stacked [O III] spatial profile and the stacked X-ray data suggest that at least some of these low-mass, low-metallicity galaxies harbor weak active galactic nuclei

Rest Frame Optical Spectra of Lyman Break Galaxies: Other Lensing Arcs around MS1512-cB58

We have obtained near-infrared spectra of two images of the galaxy at z=2.72 which is gravitationally lensed by the foreground cluster MS1512+36. The brighter arc, cB58, is an image of only the nucleus and the southern half of the background galaxy, while the fainter image, A2, encompasses the entire background galaxy. Thus the gravitational lensing provides spatial resolution on a smaller scale than is routinely available by other methods. Our observations indicate no evidence for any systematic rotational velocity gradient across the face of this galaxy. The nucleus and outer regions of the galaxy do not differ in their gas reddening or excitation level, based on the identical Hα/5007 ratios. cB58 (which is more dominated by the nucleus) has relatively stronger continuum emission, perhaps because of a higher ratio of old to young stars, compared to the outer parts of the galaxy. A second emission line source, denoted as K1, at a slightly lower redshift was serendipitously detected in the slit. It appears to be the gravitationally lensed image of another background galaxy in the same group as cB58