Large Scale 3D Image Reconstruction in Optical Interferometry

Astronomical optical interferometers (OI) sample the Fourier transform of the intensity distribution of a source at the observation wavelength. Because of rapid atmospheric perturbations, the phases of the complex Fourier samples (visibilities) cannot be directly exploited , and instead linear relationships between the phases are used (phase closures and differential phases). Consequently, specific image reconstruction methods have been devised in the last few decades. Modern polychromatic OI instruments are now paving the way to multiwavelength imaging. This paper presents the derivation of a spatio-spectral ("3D") image reconstruction algorithm called PAINTER (Polychromatic opticAl INTErferometric Reconstruction software). The algorithm is able to solve large scale problems. It relies on an iterative process, which alternates estimation of polychromatic images and of complex visibilities. The complex visibilities are not only estimated from squared moduli and closure phases, but also from differential phases, which help to better constrain the polychromatic reconstruction. Simulations on synthetic data illustrate the efficiency of the algorithm.Comment: EUSIPCO, Aug 2015, NICE, Franc

Gravitational radiation from a particle in circular orbit around a black hole. VI. Accuracy of the post-Newtonian expansion

A particle of mass $\mu$ moves on a circular orbit around a nonrotating black hole of mass $M$. Under the assumption $\mu \ll M$ the gravitational waves emitted by such a binary system can be calculated exactly numerically using black-hole perturbation theory. If, further, the particle is slowly moving, then the waves can be calculated approximately analytically, and expressed in the form of a post-Newtonian expansion. We determine the accuracy of this expansion in a quantitative way by calculating the reduction in signal-to-noise ratio incurred when matched filtering the exact signal with a nonoptimal, post-Newtonian filter.Comment: 5 pages, ReVTeX, 1 figure. A typographical error was discovered in the computer code used to generate the results presented in the paper. The corrected results are presented in an Erratum, which also incorporates new results, obtained using the recently improved post-Newtonian calculations of Tanaka, Tagoshi, and Sasak

Gravitational waves from inspiralling compact binaries: Parameter estimation using second-post-Newtonian waveforms

The parameters of inspiralling compact binaries can be estimated using matched filtering of gravitational-waveform templates against the output of laser-interferometric gravitational-wave detectors. Using a recently calculated formula, accurate to second post-Newtonian (2PN) order [order $(v/c)^4$, where $v$ is the orbital velocity], for the frequency sweep ($dF/dt$) induced by gravitational radiation damping, we study the statistical errors in the determination of such source parameters as the ``chirp mass'' $\cal M$, reduced mass $\mu$, and spin parameters $\beta$ and $\sigma$ (related to spin-orbit and spin-spin effects, respectively). We find that previous results using template phasing accurate to 1.5PN order actually underestimated the errors in $\cal M$, $\mu$, and $\beta$. For two inspiralling neutron stars, the measurement errors increase by less than 16 percent.Comment: 14 pages, ReVTe

Gravitational waves from inspiraling compact binaries: Validity of the stationary-phase approximation to the Fourier transform

We prove that the oft-used stationary-phase method gives a very accurate expression for the Fourier transform of the gravitational-wave signal produced by an inspiraling compact binary. We give three arguments. First, we analytically calculate the next-order correction to the stationary-phase approximation, and show that it is small. This calculation is essentially an application of the steepest-descent method to evaluate integrals. Second, we numerically compare the stationary-phase expression to the results obtained by Fast Fourier Transform. We show that the differences can be fully attributed to the windowing of the time series, and that they have nothing to do with an intrinsic failure of the stationary-phase method. And third, we show that these differences are negligible for the practical application of matched filtering.Comment: 8 pages, ReVTeX, 4 figure

AntiRetroviral Therapy In Second-line: investigating Tenofovir-lamivudine-dolutegravir (ARTIST): protocol for a randomised controlled trial

Background: Dolutegravir has superior efficacy and tolerability than lopinavir-ritonavir in second-line antiretroviral therapy after failure of a first-line non-nucleoside reverse transcriptase inhibitors-based regimen, when dolutegravir is accompanied by at least one fully active nucleoside reverse transcriptase inhibitor (NRTI). Resistance testing to select NRTIs is not feasible in low- and middle-income countries due to cost and limited laboratory capacity. Evidence suggests that recycling tenofovir plus lamivudine or emtricitabine backbone with dolutegravir could provide an effective second-line option. This study aims to determine the virologic efficacy of tenofovir-lamivudine-dolutegravir (TLD) with and without a lead-in supplementary dose of dolutegravir (to counteract the inducing effect of efavirenz) in patients failing a first-line regimen of tenofovir-emtricitabine-efavirenz (TEE). Methods: We will perform a parallel group, randomised (1:1), double blind, placebo-controlled, Phase II trial, comparing TLD fixed dose combination daily with a lead-in supplementary 50 mg dolutegravir dose versus matching placebo taken 12 hours later for the first 14 days, in patients failing a first-line TEE regimen. The trial will be set in two primary care clinics in Khayelitsha; a large, peri-urban informal settlement in Cape Town, South Africa. We will enrol 130 participants, with follow-up to 48 weeks. The primary endpoint is proportion achieving viral load <50 copies/mL at week 24 using a modified intention-to-treat analysis and the U.S. Food and Drug Administration snapshot algorithm. Secondary endpoints include virologic suppression at weeks 12 and 48, time to suppression, emergence of dolutegravir and new NRTI resistance mutations, safety, and tolerability. Discussion: Impaired viral fitness due to NRTI resistance mutations and dolutegravir’s high barrier to resistance provide rationale for switching patients from a failing TEE regimen to TLD; however, clinical evidence regarding virologic efficacy is lacking. This study provides estimates of such a strategy’s early virologic efficacy with and without a supplementary dolutegravir dosing. Registration: ClinicalTrials.gov NCT03991013 (19/06/2019)

Gravitational waves from eccentric compact binaries: Reduction in signal-to-noise ratio due to nonoptimal signal processing

Inspiraling compact binaries have been identified as one of the most promising sources of gravitational waves for interferometric detectors. Most of these binaries are expected to have circularized by the time their gravitational waves enter the instrument's frequency band. However, the possibility that some of the binaries might still possess a significant eccentricity is not excluded. We imagine a situation in which eccentric signals are received by the detector but not explicitly searched for in the data analysis, which uses exclusively circular waveforms as matched filters. We ascertain the likelihood that these filters, though not optimal, will nevertheless be successful at capturing the eccentric signals. We do this by computing the loss in signal-to-noise ratio incurred when searching for eccentric signals with those nonoptimal filters. We show that for a binary system of a given total mass, this loss increases with increasing eccentricity. We show also that for a given eccentricity, the loss decreases as the total mass is increased.Comment: 14 pages, 4 figures, ReVTeX; minor changes made after referee's comment

Gravitational radiation from a particle in circular orbit around a black hole. V. Black-hole absorption and tail corrections

A particle of mass $\mu$ moves on a circular orbit of a nonrotating black hole of mass $M$. Under the restrictions $\mu/M \ll 1$ and $v \ll 1$, where $v$ is the orbital velocity, we consider the gravitational waves emitted by such a binary system. We calculate $\dot{E}$, the rate at which the gravitational waves remove energy from the system. The total energy loss is given by $\dot{E} = \dot{E}^\infty + \dot{E}^H$, where $\dot{E}^\infty$ denotes that part of the gravitational-wave energy which is carried off to infinity, while $\dot{E}^H$ denotes the part which is absorbed by the black hole. We show that the black-hole absorption is a small effect: $\dot{E}^H/\dot{E} \simeq v^8$. We also compare the wave generation formalism which derives from perturbation theory to the post-Newtonian formalism of Blanchet and Damour. Among other things we consider the corrections to the asymptotic gravitational-wave field which are due to wave-propagation (tail) effects.Comment: ReVTeX, 17 page

Measuring black-hole parameters and testing general relativity using gravitational-wave data from space-based interferometers

Among the expected sources of gravitational waves for the Laser Interferometer Space Antenna (LISA) is the capture of solar-mass compact stars by massive black holes residing in galactic centers. We construct a simple model for such a capture, in which the compact star moves freely on a circular orbit in the equatorial plane of the massive black hole. We consider the gravitational waves emitted during the late stages of orbital evolution, shortly before the orbiting mass reaches the innermost stable circular orbit. We construct a simple model for the gravitational-wave signal, in which the phasing of the waves plays the dominant role. The signal's behavior depends on a number of parameters, including $\mu$, the mass of the orbiting star, $M$, the mass of the central black hole, and $J$, the black hole's angular momentum. We calculate, using our simplified model, and in the limit of large signal-to-noise ratio, the accuracy with which these quantities can be estimated during a gravitational-wave measurement. Our simplified model also suggests a method for experimentally testing the strong-field predictions of general relativity.Comment: ReVTeX, 16 pages, 5 postscript figure

Gravitational waves from inspiraling compact binaries: Second post-Newtonian waveforms as search templates

We ascertain the effectiveness of the second post-Newtonian approximation to the gravitational waves emitted during the adiabatic inspiral of a compact binary system as templates for signal searches with kilometer-scale interferometric detectors. The reference signal is obtained by solving the Teukolsky equation for a small mass moving on a circular orbit around a large nonrotating black hole. Fitting factors computed from this signal and these templates, for various types of binary systems, are all above the 90% mark. According to Apostolatos' criterion, second post-Newtonian waveforms should make acceptably effective search templates.Comment: LaTeX, one eps figure. Hires and color versions are available from http://jovian.physics.uoguelph.ca/~droz/uni/papers/search.htm