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

Molecular excitation in the Eagle nebula's fingers

Context: The M16 nebula is a relatively nearby Hii region, powered by O stars from the open cluster NGC 6611, which borders to a Giant Molecular Cloud. Radiation from these hot stars has sculpted columns of dense obscuring material on a few arcmin scales. The interface between these pillars and the hot ionised medium provides a textbook example of a Photodissociation Region (PDR). Aims: To constrain the physical conditions of the atomic and molecular material with submillimeter spectroscopic observations. Methods: We used the APEX submillimeter telescope to map a ~3'x3' region in the CO J=3-2, 4-3 and 7-6 rotational lines, and a subregion in atomic carbon lines. We also observed C18O(3-2) and CO(7-6) with longer integrations on five peaks found in the CO(3-2) map. The large scale structure of the pillars is derived from the molecular lines' emission distribution. We estimate the magnitude of the velocity gradient at the tips of the pillars and use LVG modelling to constrain their densities and temperatures. Excitation temperatures and carbon column densities are derived from the atomic carbon lines. Results: The atomic carbon lines are optically thin and excitation temperatures are of order 60 K to 100 K, well consistent with observations of other Hii region-molecular cloud interfaces. We derive somewhat lower temperatures from the CO line ratios, of order 40 K. The Ci/CO ratio is around 0.1 at the fingers tips.Comment: 4 pages, APEX A&A special issue, accepte

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

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

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

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

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

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