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

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

CARMA Large Area Star Formation Survey: Observational Analysis of Filaments in the Serpens South Molecular Cloud

We present the N2H+(J=1-0) map of the Serpens South molecular cloud obtained as part of the CARMA Large Area Star Formation Survey (CLASSy). The observations cover 250 square arcminutes and fully sample structures from 3000 AU to 3 pc with a velocity resolution of 0.16 km/s, and they can be used to constrain the origin and evolution of molecular cloud filaments. The spatial distribution of the N2H+ emission is characterized by long filaments that resemble those observed in the dust continuum emission by Herschel. However, the gas filaments are typically narrower such that, in some cases, two or three quasi-parallel N2H+ filaments comprise a single observed dust continuum filament. The difference between the dust and gas filament widths casts doubt on Herschel ability to resolve the Serpens South filaments. Some molecular filaments show velocity gradients along their major axis, and two are characterized by a steep velocity gradient in the direction perpendicular to the filament axis. The observed velocity gradient along one of these filaments was previously postulated as evidence for mass infall toward the central cluster, but these kind of gradients can be interpreted as projection of large-scale turbulence.Comment: 12 pages, 4 figures, published in ApJL (July 2014

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

CARMA Large Area Star Formation Survey: Project Overview with Analysis of Dense Gas Structure and Kinematics in Barnard 1

We present details of the CARMA Large Area Star Formation Survey (CLASSy), while focusing on observations of Barnard 1. CLASSy is a CARMA Key Project that spectrally imaged N2H+, HCO+, and HCN (J=1-0 transitions) across over 800 square arcminutes of the Perseus and Serpens Molecular Clouds. The observations have angular resolution near 7" and spectral resolution near 0.16 km/s. We imaged ~150 square arcminutes of Barnard 1, focusing on the main core, and the B1 Ridge and clumps to its southwest. N2H+ shows the strongest emission, with morphology similar to cool dust in the region, while HCO+ and HCN trace several molecular outflows from a collection of protostars in the main core. We identify a range of kinematic complexity, with N2H+ velocity dispersions ranging from ~0.05-0.50 km/s across the field. Simultaneous continuum mapping at 3 mm reveals six compact object detections, three of which are new detections. A new non-binary dendrogram algorithm is used to analyze dense gas structures in the N2H+ position-position-velocity (PPV) cube. The projected sizes of dendrogram-identified structures range from about 0.01-0.34 pc. Size-linewidth relations using those structures show that non-thermal line-of-sight velocity dispersion varies weakly with projected size, while rms variation in the centroid velocity rises steeply with projected size. Comparing these relations, we propose that all dense gas structures in Barnard 1 have comparable depths into the sky, around 0.1-0.2 pc; this suggests that over-dense, parsec-scale regions within molecular clouds are better described as flattened structures rather than spherical collections of gas. Science-ready PPV cubes for Barnard 1 molecular emission are available for download.Comment: Accepted to The Astrophysical Journal (ApJ), 51 pages, 27 figures (some with reduced resolution in this preprint); Project website is at http://carma.astro.umd.edu/class

Nonquantum Gravity

One of the great challenges for 21st century physics is to quantize gravity and generate a theory that will unify gravity with the other three fundamental forces of nature. This paper takes the (heretical) point of view that gravity may be an inherently classical, i.e., nonquantum, phenomenon and investigates the experimental consequences of such a model. At present there is no experimental evidence of the quantum nature of gravity and the liklihood of definitive tests in the future is not at all certain. If gravity is, indeed, a nonquantum phenomenon, then it is suggested that evidence will most likely appear at mesoscopic scales.Comment: essentially the same as the version that appears in Foundations of Physics, 39, 331 (2009

Singular perturbation techniques in the gravitational self-force problem

Much of the progress in the gravitational self-force problem has involved the use of singular perturbation techniques. Yet the formalism underlying these techniques is not widely known. I remedy this situation by explicating the foundations and geometrical structure of singular perturbation theory in general relativity. Within that context, I sketch precise formulations of the methods used in the self-force problem: dual expansions (including matched asymptotic expansions), for which I identify precise matching conditions, one of which is a weak condition arising only when multiple coordinate systems are used; multiscale expansions, for which I provide a covariant formulation; and a self-consistent expansion with a fixed worldline, for which I provide a precise statement of the exact problem and its approximation. I then present a detailed analysis of matched asymptotic expansions as they have been utilized in calculating the self-force. Typically, the method has relied on a weak matching condition, which I show cannot determine a unique equation of motion. I formulate a refined condition that is sufficient to determine such an equation. However, I conclude that the method yields significantly weaker results than do alternative methods.Comment: 39 pages, 5 figures, final version to be published in Phys. Rev. D, several typos corrected, added discussion of order-reductio

Routine activities and proactive police activity: a macro-scale analysis of police searches in London and New York City

This paper explored how city-level changes in routine activities were associated with changes in frequencies of police searches using six years of police records from the London Metropolitan Police Service and the New York City Police Department. Routine activities were operationalised through selecting events that potentially impacted on (a) the street population, (b) the frequency of crime or (c) the level of police activity. OLS regression results indicated that routine activity variables (e.g. day of the week, periods of high demand for police service) can explain a large proportion of the variance in search frequency throughout the year. A complex set of results emerged, revealing cross-national dissimilarities and the differential impact of certain activities (e.g. public holidays). Importantly, temporal frequencies in searches are not reducible to associations between searches and recorded street crime, nor changes in on-street population. Based on the routine activity approach, a theoretical police-action model is proposed

Research Update on Extreme-Mass-Ratio Inspirals

The inspirals of stellar-mass mass compact objects into massive black holes in the centres of galaxies are one of the most important sources of gravitational radiation for space-based detectors like LISA or eLISA. These extreme-mass-ratio inspirals (EMRIs) will enable an ambitious research program with implications for astrophysics, cosmology, and fundamental physics. This article is a summary of the talks delivered at the plenary session on EMRIs at the 10th International LISA Symposium. It contains research updates on the following topics: astrophysics of EMRIs; EMRI science potential; and EMRI modeling.Comment: 17 pages, no figures. Proceedings of the LISA Symposium X, to be published at the Journal of Physic