Angular power spectra of anisotropic stochastic gravitational wave background: Developing statistical methods and analyzing data from ground-based detectors

Deepali Agarwal, Jishnu Suresh, Sanjit Mitra, and Anirban Ain

Phys. Rev. D 108, 023011 – Published 13 July 2023

Abstract

Unresolved sources of gravitational waves can create a stochastic gravitational wave background (SGWB) which may have intrinsic or extrinsic anisotropies. The angular power spectrum is a well-suited estimator for characterizing diffuse anisotropic distributions in the sky. Here we estimate the first model-independent all-sky all-frequency SGWB angular power spectra in the 20–1726 Hz frequency range from the third observing run (O3) of the Advanced LIGO and Advanced Virgo detectors. We develop a method to use the spectrum’s signal-to-noise ratio as the detection statistic and show that the shape of the distribution of the statistic obtained from the data agrees with the analytical model with a modified value of the parameter. Since we find the data to be consistent with noise, 95% confidence Bayesian upper limits are set on the angular power spectra, ranging from $C_{ℓ}^{1 / 2} \leq (3.0 \times 10^{- 9} - 0.73) {sr}^{- 1}$ . We also introduce a method to combine the narrow band angular power spectra to obtain estimators for broadband SGWB. These results can directly constrain theoretical models that predict the SGWB angular power spectra and for estimating or constraining the corresponding parameters. In addition, the results and the techniques introduced in this work can be useful for performing correlation-based searches, for instance, with electromagnetic observations.

Received 1 March 2023
Accepted 20 June 2023

DOI:https://doi.org/10.1103/PhysRevD.108.023011

Physics Subject Headings (PhySH)

Gravitation Gravitational waves

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Deepali Agarwal ^1,*, Jishnu Suresh ^2,†, Sanjit Mitra ^1,‡, and Anirban Ain^3,§

¹Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune 411007, India
²Centre for Cosmology, Particle Physics and Phenomenology (CP3), Université catholique de Louvain, Louvain-la-Neuve B-1348, Belgium
³Istituto Nazionale di Fisica Nucleare (INFN) sezione Pisa, 56126 Pisa, Italy

^*deepali@iucaa.in
^†jishnu.suresh@uclouvain.be
^‡sanjit@iucaa.in
^§anirban.ain@pi.infn.it

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Issue

Vol. 108, Iss. 2 — 15 July 2023

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Images

Figure 1
The ML estimator of monopole (ASAF-SpH; $ℓ_{\max} = 0$ ) as a function of frequency (green line) and its uncertainty compared with the error bars (orange scatter) of the estimator obtained from O3 isotropic analysis (red line) [40] using the HL baseline.
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Figure 2
The matrix plots on the left present the measure of the detector response, $A$ , and the expected correlation between the SpH modes measured using HL baseline at frequencies 40.5 and 200.5 Hz, respectively. The correlation is quantified by the ratio $r_{ℓ ℓ^{'}} = \frac{A_{ℓ ℓ^{'}}}{\sqrt{A_{ℓ ℓ} A_{ℓ^{'} ℓ^{'}}}}$ . The correlation and detector response is found to be a function of frequency. The right plot depicts the singular value spectrum for the Fisher matrix, $Γ$ , obtained with the HL and HLV baselines. It shows that including the Virgo baseline slightly improves the ill-conditioned nature of the matrix.
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Figure 3
Histogram of SNRs obtained using the zero-lag (blue) and time-shifted (pink) data from the third observing run of Advanced LIGO and Advanced Virgo (HLV) detectors. Here, for each harmonic mode, the frequency samples are treated as independent samples for the statistic. The solid black line represents the approximate PDF with effective DOF $k_{eff} = 2 ℓ_{eff} + 1$ best fitted to the samples obtained by the time-shifted run. The zero-lag and time-shifted data is broadly consistent with the approximated distribution of SNRs within three-sigma (yellow color) Poisson error bars for lower harmonic modes but deviate at higher modes. The frequencies for maximum SNR in the zero-lag run are indicated in the histogram. The black dashed line depicts the SNR threshold for the global $p$ value 0.05 given approximated PDF.
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Figure 4
Left: joint histogram of the SNR samples obtained using the zero-lag (ZL; blue) and time-shifted (TS; pink) data from the third observing run of Advanced LIGO and Advanced Virgo (HLV) detectors. The solid black line represents a fitted approximated PDF with $ℓ_{eff} = 1.82$ . The vertical dashed lines show the SNR threshold for the global $p$ value 5% and 1%, respectively. Right panel: 95% confidence Bayesian upper limits set on the angular power spectrum $(C_{ℓ}^{95 %})^{1 / 2}$ with units ${sr}^{- 1}$ for all frequencies and all harmonic modes are shown. The horizontal gaps are the notched frequencies.
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Figure 5
The ML estimators and their uncertainties (two sigma) for the broadband angular power spectrum with $f_{ref} = 25 Hz$ and spectral index $α = 0, 2 / 3$ , 3 obtained from combining the narrow band angular power spectrum (orange) and compared with the standard method (blue) of combing the dirty maps for the SpH coefficients.
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