Reconstructing the sky location of gravitational-wave detected compact binary systems: Methodology for testing and comparison

Abstract

The problem of reconstructing the sky position of compact binary coalescences detected via gravitational waves is a central one for future observations with the ground-based network of gravitational-wave laser interferometers, such as Advanced LIGO and Advanced Virgo. Different techniques for sky localization have been independently developed. They can be divided in two broad categories: fully coherent Bayesian techniques, which are high latency and aimed at in-depth studies of all the parameters of a source, including sky position, and "triangulation-based" techniques, which exploit the data products from the search stage of the analysis to provide an almost real-time approximation of the posterior probability density function of the sky location of a detection candidate. These techniques have previously been applied to data collected during the last science runs of gravitational-wave detectors operating in the so-called initial configuration. Here, we develop and analyze methods for assessing the self consistency of parameter estimation methods and carrying out fair comparisons between different algorithms, addressing issues of efficiency and optimality. These methods are general, and can be applied to parameter estimation problems other than sky localization. We apply these methods to two existing sky localization techniques representing the two above-mentioned categories, using a set of simulated inspiralonly signals from compact binary systems with a total mass of ≤ 20M ⊙ and nonspinning components. We compare the relative advantages and costs of the two techniques and show that sky location uncertainties are on average a factor ≈20 smaller for fully coherent techniques than for the specific variant of the triangulation-based technique used during the last science runs, at the expense of a factor ≈1000 longer processing time.

Measuring the distance-redshift relation with the cross-correlation of gravitational wave standard sirens and galaxies

“…The maximum multipole ℓ max should be determined from the angular resolution of GW observations. The angular resolution of the Einstein Telescope network corresponds to approximately ℓ max = 100 [22,35], which we adopt as a fiducial value. However we also consider an optimistic case ℓ max = 300 in order to check the dependence of our results on ℓ max .…”

Measuring Intermediate-Mass Black-Hole Binaries with Advanced Gravitational Wave Detectors

“…The prior on the single aligned spin χ was fixed to be flat in [−1, 0.6], the range of validity of the SEOBNRv1 [33] approximant. Since this prior distribution does not match the distribution of sources analyzed, we should anticipate that posteriors on individual injections can be centered away from the true values, despite the self-consistency of LALInference, which has been demonstrated to produce X% credible intervals that contain the true value X% of the time [38,39,43]. For example, the low a a priori probability of high-mass extreme-mass ratio injections with non-spinning components, coupled to the asymmetry in the impact of remnant spin on the well-measured central frequency of the dominant ringdown harmonic [e.g., 44], will lead to a typical over-estimate of the inferred total mass for such sources.…”

Determining the progenitors of merging black-hole binaries

“…The issue of spatial localization is complicated and has been investigated in detail, see e.g. [32][33][34][35]. The exact value of max will depend in principle on redshift, position on the sky, SNR of the event, and a variety of instrument design parameters…”