Advanced LIGO and Virgo have detected ten binary black hole mergers by the end of their second observing run. These mergers have already allowed constraints to be placed on the population distribution of black holes in the Universe, which will only improve with more detections and increasing sensitivity of the detectors. In this paper we develop techniques to measure the angular distribution of black hole mergers by measuring their statistical N-point correlations through hierarchical Bayesian inference. We apply it to the special case of two-point angular correlations using a Legendre polynomial basis on the sky. Building on the mixture model formalism introduced by Smith and Thrane [Phys. Rev. X 8, 021019 (2018)PRXHAE2160-330810.1103/PhysRevX.8.021019], we show how one can measure two-point correlations with no threshold on significance, allowing us to target the ensemble of subthreshold binary black hole mergers not resolvable with the current generation of ground based detectors. We also show how one can use these methods to correlate gravitational waves with other probes of large scale angular structure like galaxy counts, and validate both techniques through simulations.
Bibliographical noteFunding Information:
We are grateful to Andrew Matas and Colm Talbot for useful discussion and comments. S. B. acknowledges support by the Doctoral Dissertation Fellowship at the University of Minnesota. S. B. and V. M. were supported by NSF Grant No. PHY-1806630. All corner plots were made with c hain c onsumer . The authors are thankful for the computing resources provided by LIGO Laboratory and supported by the National Science Foundation Grants No. PHY-0757058 and No. PHY-0823459. This paper carries the internal LIGO document number LIGO-P2000174.
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