Binary black hole initial data from matched asymptotic expansions

We present an approximate metric for a binary black hole spacetime to construct initial data for numerical relativity. This metric is obtained by asymptotically matching a post-Newtonian metric for a binary system to a perturbed Schwarzschild metric for each hole. In the inner zone near each hole, the metric is given by the Schwarzschild solution plus a quadrupolar perturbation corresponding to an external tidal gravitational field. In the near zone, well outside each black hole but less than a reduced wavelength from the center of mass of the binary, the metric is given by a post-Newtonian expansion including the lowest-order deviations from flat spacetime. When the near zone overlaps each inner zone in a buffer zone, the post-Newtonian and perturbed Schwarzschild metrics can be asymptotically matched to each other. By demanding matching (over a 4-volume in the buffer zone) rather than patching (choosing a particular 2-surface in the buffer zone), we guarantee that the errors are small in all zones. The resulting piecewise metric is made formally $C^\infty$ with smooth transition functions so as to obtain the finite extrinsic curvature of a 3-slice. In addition to the metric and extrinsic curvature, we present explicit results for the lapse and the shift, which can be used as initial data for numerical simulations. This initial data is not accurate all the way to the asymptotically flat ends inside each hole, and therefore must be used with evolution codes which employ black hole excision rather than puncture methods. This paper lays the foundations of a method that can be sraightforwardly iterated to obtain initial data to higher perturbative order.Comment: 24 pages, 15 figures. Replaced with published version. Major editing of text, no major change to the physic

Gravitational waves from inspiraling compact binaries: Validity of the stationary-phase approximation to the Fourier transform

We prove that the oft-used stationary-phase method gives a very accurate expression for the Fourier transform of the gravitational-wave signal produced by an inspiraling compact binary. We give three arguments. First, we analytically calculate the next-order correction to the stationary-phase approximation, and show that it is small. This calculation is essentially an application of the steepest-descent method to evaluate integrals. Second, we numerically compare the stationary-phase expression to the results obtained by Fast Fourier Transform. We show that the differences can be fully attributed to the windowing of the time series, and that they have nothing to do with an intrinsic failure of the stationary-phase method. And third, we show that these differences are negligible for the practical application of matched filtering.Comment: 8 pages, ReVTeX, 4 figure

Particles versus fields in PT-symmetrically deformed integrable systems

We review some recent results on how PT-symmetry, that is a simultaneous time-reversal and parity transformation, can be used to construct new integrable models. Some complex valued multi-particle systems, such as deformations of the Calogero-Moser-Sutherland models, are shown to arise naturally from real valued field equations of non-linear integrable systems. Deformations of complex non-linear integrable field equations, some of them even allowing for compacton solutions, are also investigated. The integrabilty of various systems is established by means of the Painleve testComment: Conference Proceeding PHHQP VIII (Mumbai, 2009

Irreversibility of the renormalization group flow in non-unitary quantum field theory

We show irreversibility of the renormalization group flow in non-unitary but PT -invariant quantum field theory in two space-time dimensions. In addition to unbroken PT -symmetry and a positive energy spectrum, we assume standard properties of quantum field theory including a local energy-momentum tensor and relativistic invariance. This generalizes Zamolodchikov’s ctheorem to PT -symmetric hamiltonians. Our proof follows closely Zamolodchikov’s arguments. We show that a function ceff(s) of the renormalization group parameter s exists which is nonnegative and monotonically decreasing along renormalization group flows. Its value at a critical point is the “effective central charge” entering the specific free energy. At least in rational models, this equals ceff = c − 24∆, where c is the central charge and ∆ is the lowest primary field dimension in the conformal field theory which describes the critical point

Modulational and Parametric Instabilities of the Discrete Nonlinear Schr\"odinger Equation

We examine the modulational and parametric instabilities arising in a non-autonomous, discrete nonlinear Schr{\"o}dinger equation setting. The principal motivation for our study stems from the dynamics of Bose-Einstein condensates trapped in a deep optical lattice. We find that under periodic variations of the heights of the interwell barriers (or equivalently of the scattering length), additionally to the modulational instability, a window of parametric instability becomes available to the system. We explore this instability through multiple-scale analysis and identify it numerically. Its principal dynamical characteristic is that, typically, it develops over much larger times than the modulational instability, a feature that is qualitatively justified by comparison of the corresponding instability growth rates

The PTF Orion Project: a Possible Planet Transiting a T-Tauri Star

We report observations of a possible young transiting planet orbiting a previously known weak-lined T-Tauri star in the 7-10 Myr old Orion-OB1a/25-Ori region. The candidate was found as part of the Palomar Transient Factory (PTF) Orion project. It has a photometric transit period of 0.448413 +- 0.000040 days, and appears in both 2009 and 2010 PTF data. Follow-up low-precision radial velocity (RV) observations and adaptive optics imaging suggest that the star is not an eclipsing binary, and that it is unlikely that a background source is blended with the target and mimicking the observed transit. RV observations with the Hobby-Eberly and Keck telescopes yield an RV that has the same period as the photometric event, but is offset in phase from the transit center by approximately -0.22 periods. The amplitude (half range) of the RV variations is 2.4 km/s and is comparable with the expected RV amplitude that stellar spots could induce. The RV curve is likely dominated by stellar spot modulation and provides an upper limit to the projected companion mass of M_p sin i_orb < 4.8 +- 1.2 M_Jup; when combined with the orbital inclination, i orb, of the candidate planet from modeling of the transit light curve, we find an upper limit on the mass of the planetary candidate of M_p < 5.5 +- 1.4 M_Jup. This limit implies that the planet is orbiting close to, if not inside, its Roche limiting orbital radius, so that it may be undergoing active mass loss and evaporation.Comment: Corrected typos, minor clarifications; minor updates/corrections to affiliations and bibliography. 35 pages, 10 figures, 3 tables. Accepted to Ap

Very Low-Mass Stellar and Substellar Companions to Solar-Like Stars from MARVELS I: A Low Mass Ratio Stellar Companion to TYC 4110-01037-1 in a 79-day Orbit

TYC 4110-01037-1 has a low-mass stellar companion, whose small mass ratio and short orbital period are atypical amongst solar-like (Teff ~< 6000 K) binary systems. Our analysis of TYC 4110-01037-1 reveals it to be a moderately aged (~<5 Gyr) solar-like star having a mass of 1.07 +/- 0.08 MSun and radius of 0.99 +/- 0.18 RSun. We analyze 32 radial velocity measurements from the SDSS-III MARVELS survey as well as 6 supporting radial velocity measurements from the SARG spectrograph on the 3.6m TNG telescope obtained over a period of ~2 years. The best Keplerian orbital fit parameters were found to have a period of 78.994 +/- 0.012 days, an eccentricity of 0.1095 +/- 0.0023, and a semi-amplitude of 4199 +/- 11 m/s. We determine the minimum companion mass (if sin i = 1) to be 97.7 +/- 5.8 MJup. The system's companion to host star mass ratio, >0.087 +/- 0.003, places it at the lowest end of observed values for short period stellar companions to solar-like (Teff ~< 6000 K) stars. One possible way to create such a system would be if a triple-component stellar multiple broke up into a short period, low q binary during the cluster dispersal phase of its lifetime. A candidate tertiary body has been identified in the system via single-epoch, high contrast imagery. If this object is confirmed to be co-moving, we estimate it would be a dM4 star. We present these results in the context of our larger-scale effort to constrain the statistics of low mass stellar and brown dwarf companions to FGK-type stars via the MARVELS survey.Comment: 22 pages; accepted in A

Light Art, Perception, and Sensation

In this article, I focus on how four artists working with light can reveal the different capacities of illumination and darkness in shaping human apprehension of the world. These artists, I contend, foreground the very particular human ways in which the visual system operates in making sense of the world, for their work explores the different ways in which we sense space at various scales, from the body to the landscape. In Kielder Forest, Northumberland, a Skyspace, created by James Turrell isolates the qualities of daylight and focuses attention on the impact of the sky’s light on the landscape. Carlos Cruz-Diez’sChromosaturation highlights the ocular perception and emotional experience of colour, while Olafur Eliasson’s Model for a Timeless Garden highlights the temporality of visual perception as well as the persistence of notions about the sublime to appreciation of landscape. Both works underscore the partialities of specifically human ways of perception. Finally, Tino Seghal’s This Variation investigates the impact of darkness on the perception of space and its potential for fostering conviviality and sociality

Cryptic carbon and sulfur cycling between surface ocean plankton

Author Posting. © The Author(s), 2014. This is the author's version of the work. It is posted here by permission of National Academy of Sciences for personal use, not for redistribution. The definitive version was published in Proceedings of the National Academy of Sciences of the United States of America 112 (2015): 453-457, doi:10.1073/pnas.1413137112 .About half the carbon fixed by phytoplankton in the ocean is taken up and metabolized by marine bacteria, a transfer that is mediated through the seawater dissolved organic carbon (DOC) pool. The chemical complexity of marine DOC, along with a poor understanding of which compounds form the basis of trophic interactions between bacteria and phytoplankton, have impeded efforts to identify key currencies of this carbon cycle link. Here, we used transcriptional patterns in a bacterial-diatom model system based on vitamin B12 auxotrophy as a sensitive assay for metabolite exchange between marine plankton. The most highly upregulated genes (up to 374-fold) by a marine Roseobacter clade bacterium when co-cultured with the diatom Thalassiosira pseudonana were those encoding the transport and catabolism of 2,3- dihydroxypropane-1-sulfonate (DHPS). This compound has no currently recognized role in the marine microbial food web. As the genes for DHPS catabolism have limited distribution among bacterial taxa, T. pseudonana may use this novel sulfonate for targeted feeding of beneficial associates. Indeed, DHPS was both a major component of the T. pseudonana cytosol and an abundant microbial metabolite in a diatom bloom in the eastern North Pacific Ocean. Moreover, transcript analysis of the North Pacific samples provided evidence of DHPS catabolism by Roseobacter populations. Other such biogeochemically important metabolites may be common in the ocean but difficult to discriminate against the complex chemical background of seawater. Bacterial transformation of this diatom-derived sulfonate represents a new and likely sizeable link in both the marine carbon and sulfur cycles.This research was partially funded by NSF grants OCE-1356010 to M.A.M., OCE-1205233 to E.V.A., OCE-0928424 to E.B.K., and OCE-1233964 to S.R.C., and by the Gordon and Betty Moore Foundation grants 538.01 to M.A.M. and 537.01 to E.V.A.2015-06-2