Second-order gravitational self-force

Using a rigorous method of matched asymptotic expansions, I derive the equation of motion of a small, compact body in an external vacuum spacetime through second order in the body's mass (neglecting effects of internal structure). The motion is found to be geodesic in a certain locally defined regular geometry satisfying Einstein's equation at second order. I outline a method of numerically obtaining both the metric of that regular geometry and the complete second-order metric perturbation produced by the body.Comment: 5 pages, added clarifications in response to referee comments, accepted for publication in PR

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

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

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

TADPOL: A 1.3 mm Survey of Dust Polarization in Star-forming Cores and Regions

We present {\lambda}1.3 mm CARMA observations of dust polarization toward 30 star-forming cores and 8 star-forming regions from the TADPOL survey. We show maps of all sources, and compare the ~2.5" resolution TADPOL maps with ~20" resolution polarization maps from single-dish submillimeter telescopes. Here we do not attempt to interpret the detailed B-field morphology of each object. Rather, we use average B-field orientations to derive conclusions in a statistical sense from the ensemble of sources, bearing in mind that these average orientations can be quite uncertain. We discuss three main findings: (1) A subset of the sources have consistent magnetic field (B-field) orientations between large (~20") and small (~2.5") scales. Those same sources also tend to have higher fractional polarizations than the sources with inconsistent large-to-small-scale fields. We interpret this to mean that in at least some cases B-fields play a role in regulating the infall of material all the way down to the ~1000 AU scales of protostellar envelopes. (2) Outflows appear to be randomly aligned with B-fields; although, in sources with low polarization fractions there is a hint that outflows are preferentially perpendicular to small-scale B-fields, which suggests that in these sources the fields have been wrapped up by envelope rotation. (3) Finally, even at ~2.5" resolution we see the so-called "polarization hole" effect, where the fractional polarization drops significantly near the total intensity peak. All data are publicly available in the electronic edition of this article.Comment: 53 pages, 37 figures -- main body (13 pp., 3 figures), source maps (32 pp., 34 figures), source descriptions (8 pp.). Accepted by the Astrophysical Journal Supplemen

Dynamically Driven Evolution of the Interstellar Medium in M51

Massive star formation occurs in giant molecular clouds (GMCs); an understanding of the evolution of GMCs is a prerequisite to develop theories of star formation and galaxy evolution. We report the highest-fidelity observations of the grand-design spiral galaxy M51 in carbon monoxide (CO) emission, revealing the evolution of GMCs vis-a-vis the large-scale galactic structure and dynamics. The most massive GMCs (giant molecular associations (GMAs)) are first assembled and then broken up as the gas flow through the spiral arms. The GMAs and their H_2 molecules are not fully dissociated into atomic gas as predicted in stellar feedback scenarios, but are fragmented into smaller GMCs upon leaving the spiral arms. The remnants of GMAs are detected as the chains of GMCs that emerge from the spiral arms into interarm regions. The kinematic shear within the spiral arms is sufficient to unbind the GMAs against self-gravity. We conclude that the evolution of GMCs is driven by large-scale galactic dynamics—their coagulation into GMAs is due to spiral arm streaming motions upon entering the arms, followed by fragmentation due to shear as they leave the arms on the downstream side. In M51, the majority of the gas remains molecular from arm entry through the interarm region and into the next spiral arm passage

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

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