A more effective coordinate system for parameter estimation of precessing compact binaries from gravitational waves

Benjamin Farr, Evan Ochsner, Will M. Farr, and Richard O’Shaughnessy

Phys. Rev. D 90, 024018 – Published 7 July 2014

Abstract

Ground-based gravitational wave detectors are sensitive to a narrow range of frequencies, effectively taking a snapshot of merging compact-object binary dynamics just before merger. We demonstrate that by adopting analysis parameters that naturally characterize this “picture,” the physical parameters of the system can be extracted more efficiently from the gravitational wave data and interpreted more easily. We assess the performance of Markov chain Monte Carlo parameter estimation in this physically intuitive coordinate system, defined by (a) a frame anchored on the binary’s spins and orbital angular momentum and (b) a time at which the detectors are most sensitive to the binary’s gravitational wave emission. Using anticipated noise curves for the advanced-generation LIGO and Virgo gravitational wave detectors, we find that this careful choice of reference frame and reference time significantly improves parameter estimation efficiency for binary neutron stars, neutron star–black hole, and binary black hole signals.

Received 29 April 2014

DOI:https://doi.org/10.1103/PhysRevD.90.024018

Authors & Affiliations

Benjamin Farr^1,2,*, Evan Ochsner^3,†, Will M. Farr^2,‡, and Richard O’Shaughnessy³

¹Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) & Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA
²School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
³Center for Gravitation and Cosmology, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, USA

^*bfarr@u.northwestern.edu
^†evano@gravity.phys.uwm.edu
^‡w.farr@bham.ac.uk

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 90, Iss. 2 — 15 July 2014

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Fiducial binary orientation: We plot the evolution of angles describing the orientation of our fiducial NS-BH and BBH binaries versus time to coalescence. For both the NS-BH (top left) and the BBH (top right) binaries, the radiation-frame angle $ι$ evolves significantly, while the system-frame angles $ψ_{J}, θ_{J L}, θ_{J N}$ evolve slowly. For the single-spin NS-BH binary the spin maintains a constant tilt relative to $\hat{L}$ (not shown). For the double-spin BBH binary, the tilts of the component spins relative to $\hat{L}$ do vary by a few tenths of a radian (lower left panel). In the lower right panel we plot the azimuthal angles $ϕ_{J L}$ describing the motion of $\hat{L}$ moving in its cone about $\hat{J}$ , and $ϕ_{12}$ , the azimuthal separation of component spins measured relative to $\hat{L}$ for the BBH binary.
Reuse & Permissions
Figure 2
Autocorrelation times: Cumulative histogram of the largest intrinsic parameter ACT of each MCMC chain, for signals analyzed using the radiation frame (with parameters defined at 40 Hz) and precessing system frame (parameters defined at 100 Hz). Left panel: Results for the 15 BNS signals; using the system frame reduces ACTs by a median factor of 7.6. Center panel: Results for each analysis of the NS-BH binary described in Table 1. The system frame is found to have a median improvement of a factor of 11 in efficiency over the radiation frame. Right panel: Results for each analysis of the BBH binary described in Table 1. The system frame is found to have a median improvement of a factor of 3.7 in efficiency over the radiation frame.
Reuse & Permissions
Figure 3
Left panel: MCMC samples from the posterior of a simulated BNS signal. The region where both spins have a negative $\hat{L_{z}}$ component is excluded. This information is easily described, and sampled, in the system frame. Right panel: Posterior samples from the analyses of an NS-BH injection, centered on the mean. $θ$ and $ϕ$ correspond to $θ_{{NS}_{1}}$ and $ϕ_{1}$ in the radiation frame, and $θ_{{LS}_{1}}$ and $ϕ_{JL}$ in the system frame. The strong, nonlinear correlation between spin parameters in the radiation frame is difficult to sample, resulting in large ACTs. The system frame parametrization eliminates this correlation, allowing for more efficient MCMC sampling.
Reuse & Permissions
Figure 4
The 95% posterior credible regions from analyses of a BBH injection. $θ$ and $ϕ$ correspond to $θ_{{NS}_{1}}$ and $ϕ_{1}$ in the radiation frame, and $θ_{{LS}_{1}}$ and $ϕ_{JL}$ in the system frame. The posterior in the radiation frame parametrization has significant structure. In the system frame parameters, support is largely confined to a single uncorrelated mode that crosses the cyclic boundary of $ϕ_{JL}$ , proving much more efficient to sample.
Reuse & Permissions
Figure 5
Left panel: Box-and-whisker plots summarizing the distributions of maximum intrinsic-parameter ACTs for the fiducial NS-BH and BBH systems for the 11 tested reference frequencies. Boxes indicate the first and third quartiles, with interior lines indicating medians, whiskers showing the range of data within 1.5 inner-quartile widths, and $+$ ’s indicating points outside this range. Right panel: The standard deviations and correlation of the $θ_{{LS}_{1}}$ and $ϕ_{JL}$ distributions of the NS-BH fiducial system over the evolution of the waveform. $θ_{{LS}_{1}}$ is found to have a relatively stationary distribution, while $ϕ_{JL}$ is best constrained at $\sim 70 Hz$ . The correlation between parameters, though highly variable, has a minimum near 140 Hz.
Reuse & Permissions

Physical Review D

covering particles, fields, gravitation, and cosmology