Phase-coherent mapping of gravitational-wave backgrounds using ground-based laser interferometers

Abstract

We extend the formalisms developed in Gair et al. [1] and Cornish and van Haasteren [2] to create maps of gravitational-wave backgrounds using a network of ground-based laser interferometers. We show that in contrast to pulsar timing arrays, which are insensitive to the curl modes of the background, a network of ground-based interferometers is sensitive to both the gradient and curl components. The spatial separation of a network of interferometers, or of a single interferometer at different times during its rotational and orbital motion around the Sun, allows for recovery of both components. We derive expressions for the response functions of a laser interferometer in the small-antenna limit, and use these expressions to calculate the overlap reduction function for a pair of interferometers. We also construct maximum-likelihood estimates of the + and ×-polarization modes of the gravitational-wave sky in terms of the response matrix for a network of ground-based interferometers, evaluated at discrete times during Earth's rotational and orbital motion around the Sun. We demonstrate the feasibility of this approach for some simple simulated backgrounds (a single point source and two spatially-extended distributions having only grad or curl components), calculating maximum-likelihood sky maps and uncertainty maps based on the (pseudo)inverse of the response matrix. The distinction between this approach and standard methods for mapping gravitational-wave power is also discussed.

Detection methods for stochastic gravitational-wave backgrounds: a unified treatment

“…(2014), Cornish and van Haasteren (2014) and Romano et al. (2015) regarding phase-coherent mapping. For results of actual analyses of initial LIGO data and pulsar timing data for anisotropic backgrounds, see Abadie et al.…”

“…2014; Romano et al. 2015). In some sense, it can be thought of as the “square root” of the approaches described in the previous subsections, which attempt to measure the distribution of gravitational-wave power .…”

“…This is the approach followed in Cornish and van Haasteren (2014) and Romano et al. (2015), and it leads to some interesting results regarding sky-map basis vectors , which we will describe in more detail in Sect. 7.5.4.…”

“…See Romano et al. (2015) for more details and related simulations.

Fig. 56Mollweide projections of the real parts of for grad-only and curl-only anisotropic backgrounds injected into noise and analysed using a 3-detector network of ground-based laser interferometers (Hanford–Livingston–Virgo).

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Estimating the angular power spectrum of the gravitational-wave background in the presence of shot noise

“…Since the components of CBCs are the results of stellar evolution, they should reside in galaxies, 1 and the AGWB should trace the distribution of galaxies throughout the local Universe. There has therefore been significant recent interest in AGWB anisotropies [15][16][17][18][19][20][21] and associated observational searches [22][23][24] and data-analysis methods [25][26][27][28][29][30][31], as these might provide an entirely new probe of galaxy clustering and large-scale structure (LSS).…”