The effect of different eLISA-like configurations on massive black hole parameter estimation

As the theme for the future L3 Cosmic Vision mission, ESA has recently chosen the `Gravitational Wave Universe'. Within this call, a mission concept called eLISA has been proposed. This observatory has a current initial configuration consisting of 4 laser links between the three satellites, which are separated by a distance of one million kilometers, constructing a single channel Michelson interferometer. However, the final configuration for the observatory will not be fixed until the end of this decade. With this in mind, we investigate the effect of different eLISA-like configurations on massive black hole detections. This work compares the results of a Bayesian inference study of 120 massive black hole binaries out to a redshift of $z\sim13$ for a $10^6$m arm-length eLISA with four and six links, as well as a $2\times10^6$m arm-length observatory with four links. We demonstrate that the original eLISA configuration should allow us to recover the luminosity distance of the source with an error of less than 10% out to a redshift of $z\sim4$, and a sky error box of $\leq10^2\,deg^2$ out to $z\sim0.1$. In contrast, both alternative configurations suggest that we should be able to conduct the same parameter recovery with errors of less than 10% in luminosity distance out to $z\sim12$ and $\leq10^2\,deg^2$ out to $z\sim0.4$. Using the information from these studies, we also infer that if we were able to construct a 2Gm, 6-link detector, the above values would shift to $z\sim20$ for luminosity distance and $z\sim0.9$ for sky error. While the final configuration will also be dependent on both technological and financial considerations, our study suggests that increasing the size of a two arm detector is a viable alternative to the inclusion of a third arm in a smaller detector. More importantly, this work further suggests no clear scientific loss between either choice.Comment: 9 pages, 5 figure

An Overview of LISA Data Analysis Algorithms

The development of search algorithms for gravitational wave sources in the LISA data stream is currently a very active area of research. It has become clear that not only does difficulty lie in searching for the individual sources, but in the case of galactic binaries, evaluating the fidelity of resolved sources also turns out to be a major challenge in itself. In this article we review the current status of developed algorithms for galactic binary, non-spinning supermassive black hole binary and extreme mass ratio inspiral sources. While covering the vast majority of algorithms, we will highlight those that represent the state of the art in terms of speed and accuracy.Comment: 21 pages. Invited highlight article appearing in issue 01 of Gravitational Waves Notes, "GW Notes", edited by Pau Amaro-Seoane and Bernard F. Schutz at: http://brownbag.lisascience.org/lisa-gw-notes

Detecting compact galactic binaries using a hybrid swarm-based algorithm

Compact binaries in our galaxy are expected to be one of the main sources of gravitational waves for the future eLISA mission. During the mission lifetime, many thousands of galactic binaries should be individually resolved. However, the identification of the sources, and the extraction of the signal parameters in a noisy environment are real challenges for data analysis. So far, stochastic searches have proven to be the most successful for this problem. In this work we present the first application of a swarm-based algorithm combining Particle Swarm Optimization and Differential Evolution. These algorithms have been shown to converge faster to global solutions on complicated likelihood surfaces than other stochastic methods. We first demonstrate the effectiveness of the algorithm for the case of a single binary in a 1 mHz search bandwidth. This interesting problem gave the algorithm plenty of opportunity to fail, as it can be easier to find a strong noise peak rather than the signal itself. After a successful detection of a fictitious low-frequency source, as well as the verification binary RXJ0806.3+1527, we then applied the algorithm to the detection of multiple binaries, over different search bandwidths, in the cases of low and mild source confusion. In all cases, we show that we can successfully identify the sources, and recover the true parameters within a 99\% credible interval.Comment: 19 pages, 5 figure

A Hamiltonian Monte Carlo method for Bayesian Inference of Supermassive Black Hole Binaries

We investigate the use of a Hamiltonian Monte Carlo to map out the posterior density function for supermassive black hole binaries. While previous Markov Chain Monte Carlo (MCMC) methods, such as Metropolis-Hastings MCMC, have been successfully employed for a number of different gravitational wave sources, these methods are essentially random walk algorithms. The Hamiltonian Monte Carlo treats the inverse likelihood surface as a "gravitational potential" and by introducing canonical positions and momenta, dynamically evolves the Markov chain by solving Hamilton's equations of motion. We present an implementation of the Hamiltonian Markov Chain that is faster, and more efficient by a factor of approximately the dimension of the parameter space, than the standard MCMC.Comment: 16 pages, 8 figure

A Time Domain Waveform for Testing General Relativity

Gravitational-wave parameter estimation is only as good as the theory the waveform generation models are based upon. It is therefore crucial to test General Relativity (GR) once data becomes available. Many previous works, such as studies connected with the ppE framework by Yunes and Pretorius, rely on the stationary phase approximation (SPA) to model deviations from GR in the frequency domain. As Fast Fourier Transform algorithms have become considerably faster and in order to circumvent possible problems with the SPA, we test GR with corrected time domain waveforms instead of SPA waveforms. Since a considerable amount of work has been done already in the field using SPA waveforms, we establish a connection between leading-order-corrected waveforms in time and frequency domain, concentrating on phase-only corrected terms. In a Markov Chain Monte Carlo study, whose results are preliminary and will only be available later, we will assess the ability of the eLISA detector to measure deviations from GR for signals coming from supermassive black hole inspirals using these corrected waveforms.Comment: 5 pages. Proceedings of LISA Symposium X, submitted to Journal of Physics: Conference Serie

Supermassive Black Hole Tests of General Relativity with eLISA

Motivated by the parameterized post-Einsteinian (ppE) scheme devised by Yunes and Pretorius, which introduces corrections to the post-Newtonian coefficients of the frequency domain gravitational waveform in order to emulate alternative theories of gravity, we compute analytical time domain waveforms that, after a numerical Fourier transform, aim to represent (phase corrected only) ppE waveforms. In this formalism, alternative theories manifest themselves via corrections to the phase and frequency, as predicted by General Relativity (GR), at different post-Newtonian (PN) orders. In order to present a generic test of alternative theories of gravity, we assume that the coupling constant of each alternative theory is manifestly positive, allowing corrections to the GR waveforms to be either positive or negative. By exploring the capabilities of massive black hole binary GR waveforms in the detection and parameter estimation of corrected time domain ppE signals, using the current eLISA configuration (as presented for the ESA Cosmic Vision L3 mission), we demonstrate that for corrections arising at higher than 1PN order in phase and frequency, GR waveforms are sufficient for both detecting and estimating the parameters of alternative theory signals. However, for theories introducing corrections at the 0 and 0.5 PN order, GR waveforms are not capable of covering the entire parameter space, requiring the use of non-GR waveforms for detection and parameter estimation.Comment: 13 pages, 5 figure