The minimum and maximum gravitational-wave background from supermassive binary black holes

Xing Jiang Zhu, Weiguang Cui, Eric Thrane

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18 Citations (Scopus)


The gravitational-wave background from supermassive binary black holes (SMBBHs) has yet to be detected. This has led to speculations as to whether current pulsar timing array limits are in tension with theoretical predictions. In this paper, we use electromagnetic observations to constrain the SMBBH background from above and below. To derive the maximum amplitude of the background, we suppose that equal-mass SMBBH mergers fully account for the local black hole number density. This yields a maximum characteristic signal amplitude at a period of one year Ayr < 2.4 × 10−15, which is comparable to the pulsar timing limits. To derive the minimum amplitude requires an electromagnetic observation of an SMBBH. While a number of candidates have been put forward, there are no universally accepted electromagnetic detections in the nanohertz band. We show the candidate 3C 66B implies a lower limit, which is inconsistent with limits from pulsar timing, casting doubt on its binary nature. Alternatively, if the parameters of OJ 287 are known accurately, then Ayr > 6.1 × 10−17 at 95 per cent confidence level. If one of the current candidates can be established as a bona fide SMBBH, it will immediately imply an astrophysically interesting lower limit.

Original languageEnglish
Pages (from-to)2588-2596
Number of pages9
JournalMonthly Notices of the Royal Astronomical Society
Issue number2
Publication statusPublished - 11 Jan 2019


  • Black hole physics
  • Galaxies: evolution
  • Galaxies: individual (3C 66B)
  • Gravitational waves
  • Pulsars: general
  • Quasars: individual (OJ 287)

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