Osculating orbits in Schwarzschild spacetime, with an application to extreme mass-ratio inspirals

We present a method to integrate the equations of motion that govern bound, accelerated orbits in Schwarzschild spacetime. At each instant the true worldline is assumed to lie tangent to a reference geodesic, called an osculating orbit, such that the worldline evolves smoothly from one such geodesic to the next. Because a geodesic is uniquely identified by a set of constant orbital elements, the transition between osculating orbits corresponds to an evolution of the elements. In this paper we derive the evolution equations for a convenient set of orbital elements, assuming that the force acts only within the orbital plane; this is the only restriction that we impose on the formalism, and we do not assume that the force must be small. As an application of our method, we analyze the relative motion of two massive bodies, assuming that one body is much smaller than the other. Using the hybrid Schwarzschild/post-Newtonian equations of motion formulated by Kidder, Will, and Wiseman, we treat the unperturbed motion as geodesic in a Schwarzschild spacetime whose mass parameter is equal to the system's total mass. The force then consists of terms that depend on the system's reduced mass. We highlight the importance of conservative terms in this force, which cause significant long-term changes in the time-dependence and phase of the relative orbit. From our results we infer some general limitations of the radiative approximation to the gravitational self-force, which uses only the dissipative terms in the force.Comment: 18 pages, 6 figures, final version to be published in Physical Review

Formation of Pillars at the Boundaries between H II Regions and Molecular Clouds

We investigate numerically the hydrodynamic instability of an ionization front (IF) accelerating into a molecular cloud, with imposed initial perturbations of different amplitudes. When the initial amplitude is small, the imposed perturbation is completely stabilized and does not grow. When the initial perturbation amplitude is large enough, roughly the ratio of the initial amplitude to wavelength is greater than 0.02, portions of the IF temporarily separate from the molecular cloud surface, locally decreasing the ablation pressure. This causes the appearance of a large, warm HI region and triggers nonlinear dynamics of the IF. The local difference of the ablation pressure and acceleration enhances the appearance and growth of a multimode perturbation. The stabilization usually seen at the IF in the linear regimes does not work due to the mismatch of the modes of the perturbations at the cloud surface and in density in HII region above the cloud surface. Molecular pillars are observed in the late stages of the large amplitude perturbation case. The velocity gradient in the pillars is in reasonably good agreement with that observed in the Eagle Nebula. The initial perturbation is imposed in three different ways: in density, in incident photon number flux, and in the surface shape. All cases show both stabilization for a small initial perturbation and large growth of the second harmonic by increasing amplitude of the initial perturbation above a critical value.Comment: 21 pages, 8 figures, accepted for publication in ApJ. high resolution figures available upon reques

The self-consistent gravitational self-force

I review the problem of motion for small bodies in General Relativity, with an emphasis on developing a self-consistent treatment of the gravitational self-force. An analysis of the various derivations extant in the literature leads me to formulate an asymptotic expansion in which the metric is expanded while a representative worldline is held fixed; I discuss the utility of this expansion for both exact point particles and asymptotically small bodies, contrasting it with a regular expansion in which both the metric and the worldline are expanded. Based on these preliminary analyses, I present a general method of deriving self-consistent equations of motion for arbitrarily structured (sufficiently compact) small bodies. My method utilizes two expansions: an inner expansion that keeps the size of the body fixed, and an outer expansion that lets the body shrink while holding its worldline fixed. By imposing the Lorenz gauge, I express the global solution to the Einstein equation in the outer expansion in terms of an integral over a worldtube of small radius surrounding the body. Appropriate boundary data on the tube are determined from a local-in-space expansion in a buffer region where both the inner and outer expansions are valid. This buffer-region expansion also results in an expression for the self-force in terms of irreducible pieces of the metric perturbation on the worldline. Based on the global solution, these pieces of the perturbation can be written in terms of a tail integral over the body's past history. This approach can be applied at any order to obtain a self-consistent approximation that is valid on long timescales, both near and far from the small body. I conclude by discussing possible extensions of my method and comparing it to alternative approaches.Comment: 44 pages, 4 figure

Waves on the surface of the Orion molecular cloud

Massive stars influence their parental molecular cloud, and it has long been suspected that the development of hydrodynamical instabilities can compress or fragment the cloud. Identifying such instabilities has proved difficult. It has been suggested that elongated structures (such as the `pillars of creation') and other shapes arise because of instabilities, but alternative explanations are available. One key signature of an instability is a wave-like structure in the gas, which has hitherto not been seen. Here we report the presence of `waves' at the surface of the Orion molecular cloud near where massive stars are forming. The waves seem to be a Kelvin-Helmholtz instability that arises during the expansion of the nebula as gas heated and ionized by massive stars is blown over pre-existing molecular gas.Comment: Preprint of publication in Natur

Gravitational redshift of galaxies in clusters as predicted by general relativity

The theoretical framework of cosmology is mainly defined by gravity, of which general relativity is the current model. Recent tests of general relativity within the \Lambda Cold Dark Matter (CDM) model have found a concordance between predictions and the observations of the growth rate and clustering of the cosmic web. General relativity has not hitherto been tested on cosmological scales independent of the assumptions of the \Lambda CDM model. Here we report observation of the gravitational redshift of light coming from galaxies in clusters at the 99 per cent confidence level, based upon archival data. The measurement agrees with the predictions of general relativity and its modification created to explain cosmic acceleration without the need for dark energy (f(R) theory), but is inconsistent with alternative models designed to avoid the presence of dark matter.Comment: Published in Nature issued on 29 September 2011. This version includes the Letter published there as well as the Supplementary Information. 23 pages, 7 figure

Sources of Sex Information Used by Young British Women Who Have Sex with Women (WSW) and Women Who Have Sex Exclusively with Men (WSEM): Evidence from the National Survey of Sexual Attitudes and Lifestyles

There is little consideration about the provision of information about sex to women who have sex with women (WSW). This study drew on data from the third National Survey of Sexual Attitudes and Lifestyle, a nationally representative survey of people in Great Britain. Logistic regression was undertaken to examine firstly the relationships between WSW and women who have sex exclusively with men (WSEM) and their main source of information about sex, and secondly between WSW/WSEM and unmet need for information about sex. Each source was included as the binary outcome indicating yes this was the main source, or no this was not the main source of information about sex. The results found that WSW had significantly lower odds of reporting lessons at schools as their main source of information, and significantly higher odds of reporting sources defined as ‘other’ (predominantly first girlfriend/boyfriend or sexual partner) as their main source of information. Reported levels of unmet need for information was also higher amongst young WSW compared with WSEM. This study provides new insights into the sex educational needs of young women and highlights the need for sex education in schools in Great Britain to include information on a full-range of sexual practices, including same-sex sexual relationships

Tracing the Bipolar Outflow from Orion Source I

Using CARMA, we imaged the 87 GHz SiO v=0 J=2-1 line toward Orion-KL with 0.45 arcsec angular resolution. The maps indicate that radio source I drives a bipolar outflow into the surrounding molecular cloud along a NE--SW axis, in agreement with the model of Greenhill et al. (2004). The extended high velocity outflow from Orion-KL appears to be a continuation of this compact outflow. High velocity gas extends farthest along a NW--SE axis, suggesting that the outflow direction changes on time scales of a few hundred years.Comment: 4 pages, 4 figures; accepted for publication in Ap J Letter

Signatures of Young Star Formation Activity Within Two Parsecs of Sgr A*

We present radio and infrared observations indicating on-going star formation activity inside the $\sim2-5$ pc circumnuclear ring at the Galactic center. Collectively these measurements suggest a continued disk-based mode of on-going star formation has taken place near Sgr A* over the last few million years. First, VLA observations with spatial resolution 2.17$"\times0.81"$ reveal 13 water masers, several of which have multiple velocity components. The presence of interstellar water masers suggests gas densities that are sufficient for self-gravity to overcome the tidal shear of the 4$\times10^6$ \msol\, black hole. Second, SED modeling of stellar sources indicate massive YSO candidates interior to the molecular ring, supporting in-situ star formation near Sgr A* and appear to show a distribution similar to that of the counter-rotating disks of $\sim$100 OB stars orbiting Sgr A*. Some YSO candidates (e.g., IRS~5) have bow shock structures suggesting that they have have gaseous disks that are phototoevaporated and photoionized by the strong radiation field. Third, we detect clumps of SiO (2-1) and (5-4) line emission in the ring based on CARMA and SMA observations. The FWHM and luminosity of the SiO emission is consistent with shocked protostellar outflows. Fourth, two linear ionized features with an extent of $\sim0.8$ pc show blue and redshifted velocities between $+50$ and $-40$ \kms, suggesting protostellar jet driven outflows with mass loss rates of $\sim5\times10^{-5}$ solar mass yr$^{-1}$. Finally, we present the imprint of radio dark clouds at 44 GHz, representing a reservoir of molecular gas that feeds star formation activity close to Sgr A*.Comment: 38 pages, 10 figures, ApJ (in press

A patch-based approach to 3D plant shoot phenotyping

The emerging discipline of plant phenomics aims to measure key plant characteristics, or traits, though as yet the set of plant traits that should be measured by automated systems is not well defined. Methods capable of recovering generic representations of the 3D structure of plant shoots from images would provide a key technology underpinning quantification of a wide range of current and future physiological and morphological traits. We present a fully automatic approach to image-based 3D plant reconstruction which represents plants as series of small planar sections that together model the complex architecture of leaf surfaces. The initial boundary of each leaf patch is refined using a level set method, optimising the model based on image information, curvature constraints and the position of neighbouring surfaces. The reconstruction process makes few assumptions about the nature of the plant material being reconstructed. As such it is applicable to a wide variety of plant species and topologies, and can be extended to canopy-scale imaging. We demonstrate the effectiveness of our approach on real images of wheat and rice plants, an artificial plant with challenging architecture, as well as a novel virtual dataset that allows us to compute distance measures of reconstruction accuracy. We also illustrate the method’s potential to support the identification of individual leaves, and so the phenotyping of plant shoots, using a spectral clustering approach