Second Order Gravitational Self-Force

The second-order gravitational self-force on a small body is an important problem for gravitational-wave astronomy of extreme mass-ratio inspirals. We give a first-principles derivation of a prescription for computing the first and second perturbed metric and motion of a small body moving through a vacuum background spacetime. The procedure involves solving for a "regular field" with a specified (sufficiently smooth) "effective source", and may be applied in any gauge that produces a sufficiently smooth regular field

Electromagnetic self-forces and generalized Killing fields

Building upon previous results in scalar field theory, a formalism is developed that uses generalized Killing fields to understand the behavior of extended charges interacting with their own electromagnetic fields. New notions of effective linear and angular momenta are identified, and their evolution equations are derived exactly in arbitrary (but fixed) curved spacetimes. A slightly modified form of the Detweiler-Whiting axiom that a charge's motion should only be influenced by the so-called "regular" component of its self-field is shown to follow very easily. It is exact in some interesting cases, and approximate in most others. Explicit equations describing the center-of-mass motion, spin angular momentum, and changes in mass of a small charge are also derived in a particular limit. The chosen approximations -- although standard -- incorporate dipole and spin forces that do not appear in the traditional Abraham-Lorentz-Dirac or Dewitt-Brehme equations. They have, however, been previously identified in the test body limit.Comment: 20 pages, minor typos correcte

Effective source approach to self-force calculations

Numerical evaluation of the self-force on a point particle is made difficult by the use of delta functions as sources. Recent methods for self-force calculations avoid delta functions altogether, using instead a finite and extended "effective source" for a point particle. We provide a review of the general principles underlying this strategy, using the specific example of a scalar point charge moving in a black hole spacetime. We also report on two new developments: (i) the construction and evaluation of an effective source for a scalar charge moving along a generic orbit of an arbitrary spacetime, and (ii) the successful implementation of hyperboloidal slicing that significantly improves on previous treatments of boundary conditions used for effective-source-based self-force calculations. Finally, we identify some of the key issues related to the effective source approach that will need to be addressed by future work.Comment: Invited review for NRDA/Capra 2010 (Theory Meets Data Analysis at Comparable and Extreme Mass Ratios), Perimeter Institute, June 2010, CQG special issue - 22 pages, 8 figure

The Atacama Cosmology Telescope: Physical Properties of Sunyaev-Zel'dovich Effect Clusters on the Celestial Equator

We present the optical and X-ray properties of 68 galaxy clusters selected via the Sunyaev-Zel'dovich Effect at 148 GHz by the Atacama Cosmology Telescope (ACT). Our sample, from an area of 504 square degrees centered on the celestial equator, is divided into two regions. The main region uses 270 square degrees of the ACT survey that overlaps with the co-added ugriz imaging from the Sloan Digital Sky Survey (SDSS) over Stripe 82 plus additional near-infrared pointed observations with the Apache Point Observatory 3.5-meter telescope. We confirm a total of 49 clusters to z~1.3, of which 22 (all at z>0.55) are new discoveries. For the second region the regular-depth SDSS imaging allows us to confirm 19 more clusters up to z~0.7, of which 10 systems are new. We present the optical richness, photometric redshifts, and separation between the SZ position and the brightest cluster galaxy (BCG). We find no significant offset between the cluster SZ centroid and BCG location and a weak correlation between optical richness and SZ-derived mass. We also present X-ray fluxes and luminosities from the ROSAT All Sky Survey which confirm that this is a massive sample. One of the newly discovered clusters, ACT-CL J0044.4+0113 at z=1.1 (photometric), has an integrated XMM-Newton X-ray temperature of kT_x=7.9+/-1.0 keV and combined mass of M_200a=8.2(-2.5,+3.3)x10^14 M_sun/h70 placing it among the most massive and X-ray-hot clusters known at redshifts beyond z=1. We also highlight the optically-rich cluster ACT-CL J2327.4-0204 (RCS2 2327) at z=0.705 (spectroscopic) as the most significant detection of the whole equatorial sample with a Chandra-derived mass of M_200a=1.9(-0.4,+0.6)x10^15 M_sun/h70, comparable to some of the most massive known clusters like "El Gordo" and the Bullet Cluster.Comment: 18 pages, 12 figures. Accepted to the Astrophysical Journal. New version includes minor changes in the accepted pape

Spin–orbit precession for eccentric black hole binaries at first order in the mass ratio

We consider spin–orbit ('geodetic') precession for a compact binary in strong-field gravity. Specifically, we compute ψ, the ratio of the accumulated spin-precession and orbital angles over one radial period, for a spinning compact body of mass m 1 and spin s 1, with ${{s}_{1}}\ll Gm_{1}^{2}/c$ , orbiting a non-rotating black hole. We show that ψ can be computed for eccentric orbits in both the gravitational self-force and post-Newtonian frameworks, and that the results appear to be consistent. We present a post-Newtonian expansion for ψ at next-to-next-to-leading order, and a Lorenz-gauge gravitational self-force calculation for ψ at first order in the mass ratio. The latter provides new numerical data in the strong-field regime to inform the effective one-body model of the gravitational two-body problem. We conclude that ψ complements the Detweiler redshift z as a key invariant quantity characterizing eccentric orbits in the gravitational two-body problem

The Atacama Cosmology Telescope: CO(J = 3 - 2) mapping and lens modeling of an ACT-selected dusty star-forming galaxy

We report Northern Extended Millimeter Array (NOEMA) CO($J = 3 - 2$) observations of the dusty star-forming galaxy ACT-S\,J020941+001557 at $z = 2.5528$, which was detected as an unresolved source in the Atacama Cosmology Telescope (ACT) equatorial survey. Our spatially resolved spectral line data support the derivation of a gravitational lens model from 37 independent velocity channel maps using a pixel-based algorithm, from which we infer a velocity-dependent magnification factor $\mu \approx 7-22$ with a luminosity-weighted mean \left\approx 13. The resulting source-plane reconstruction is consistent with a rotating disk, although other scenarios cannot be ruled out by our data. After correction for lensing, we derive a line luminosity $L^{\prime}_{\rm CO(3-2)}= (5.53\pm 0.69) \times 10^{10}\,{\rm \,K\,km\,s^{-1}\,pc^{2}}$, a cold gas mass $M_{{\rm gas}}= (3.86 \pm 0.33) \times 10^{10}\,M_{\odot}$, a dynamical mass $M_{\rm dyn}\,{\rm sin}^2\,i = 3.9^{+1.8}_{-1.5} \times 10^{10}\,M_{\odot}$, and a gas mass fraction $f_{\rm gas}\,{\rm csc}^2\,i = 1.0^{+0.8}_{-0.4}$. The line brightness temperature ratio of $r_{3,1}\approx 1.6$ relative to a Green Bank Telescope CO($J=1-0$) detection may be elevated by a combination of external heating of molecular clouds, differential lensing, and/or pointing errors.Comment: 8 pages, 5 figures, accepted to Ap

Mechanics of extended masses in general relativity

The "external" or "bulk" motion of extended bodies is studied in general relativity. Compact material objects of essentially arbitrary shape, spin, internal composition, and velocity are allowed as long as there is no direct (non-gravitational) contact with other sources of stress-energy. Physically reasonable linear and angular momenta are proposed for such bodies and exact equations describing their evolution are derived. Changes in the momenta depend on a certain "effective metric" that is closely related to a non-perturbative generalization of the Detweiler-Whiting R-field originally introduced in the self-force literature. If the effective metric inside a self-gravitating body can be adequately approximated by an appropriate power series, the instantaneous gravitational force and torque exerted on it is shown to be identical to the force and torque exerted on an appropriate test body moving in the effective metric. This result holds to all multipole orders. The only instantaneous effect of a body's self-field is to finitely renormalize the "bare" multipole moments of its stress-energy tensor. The MiSaTaQuWa expression for the gravitational self-force is recovered as a simple application. A gravitational self-torque is obtained as well. Lastly, it is shown that the effective metric in which objects appear to move is approximately a solution to the vacuum Einstein equation if the physical metric is an approximate solution to Einstein's equation linearized about a vacuum background.Comment: 39 pages, 2 figures; fixed equation satisfied by the Green function used to construct the effective metri

Multiwavelength characterisation of an ACT-selected, lensed dusty star-forming galaxy at z=2.64

We present \ci\,(2--1) and multi-transition $^{12}$CO observations of a dusty star-forming galaxy, ACT\,J2029+0120, which we spectroscopically confirm to lie at $z$\,=\,2.64. We detect CO(3--2), CO(5--4), CO(7--6), CO(8--7), and \ci\,(2--1) at high significance, tentatively detect HCO$^{+}$(4--3), and place strong upper limits on the integrated strength of dense gas tracers (HCN(4--3) and CS(7--6)). Multi-transition CO observations and dense gas tracers can provide valuable constraints on the molecular gas content and excitation conditions in high-redshift galaxies. We therefore use this unique data set to construct a CO spectral line energy distribution (SLED) of the source, which is most consistent with that of a ULIRG/Seyfert or QSO host object in the taxonomy of the \textit{Herschel} Comprehensive ULIRG Emission Survey. We employ RADEX models to fit the peak of the CO SLED, inferring a temperature of T$\sim$117 K and $n_{\text{H}_2}\sim10^5$ cm$^{-3}$, most consistent with a ULIRG/QSO object and the presence of high density tracers. We also find that the velocity width of the \ci\ line is potentially larger than seen in all CO transitions for this object, and that the $L'_{\rm C\,I(2-1)}/L'_{\rm CO(3-2)}$ ratio is also larger than seen in other lensed and unlensed submillimeter galaxies and QSO hosts; if confirmed, this anomaly could be an effect of differential lensing of a shocked molecular outflow.Comment: Accepted for publication in Ap

A Multi-Wavelength Mass Analysis of RCS2 J232727.6-020437, a ~3x1015^{15}M⊙_{\odot} Galaxy Cluster at z=0.7

We present an initial study of the mass and evolutionary state of a massive and distant cluster, RCS2 J232727.6-020437. This cluster, at z=0.6986, is the richest cluster discovered in the RCS2 project. The mass measurements presented in this paper are derived from all possible mass proxies: X-ray measurements, weak-lensing shear, strong lensing, Sunyaev Zel'dovich effect decrement, the velocity distribution of cluster member galaxies, and galaxy richness. While each of these observables probe the mass of the cluster at a different radius, they all indicate that RCS2 J232727.6-020437 is among the most massive clusters at this redshift, with an estimated mass of M_200 ~3 x10^15 h^-1 Msun. In this paper, we demonstrate that the various observables are all reasonably consistent with each other to within their uncertainties. RCS2 J232727.6-020437 appears to be well relaxed -- with circular and concentric X-ray isophotes, with a cool core, and no indication of significant substructure in extensive galaxy velocity data.Comment: 19 pages, 15 figures, submitted to ApJ on March 5, 2015; in press. Manuscript revised following the referee revie