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Methods and prospects for gravitational-wave searches targeting ultralight vector-boson clouds around known black holes

Dana Jones, Ling Sun, Nils Siemonsen, William E. East, Susan M. Scott, and Karl Wette
Phys. Rev. D 108, 064001 – Published 1 September 2023
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  • INTRODUCTION
  • VECTOR-BOSON CLOUDS
  • DIRECTED SEARCHES
  • SEARCH SENSITIVITY AND HORIZON DISTANCE
  • SOURCES AND SKY LOCALIZATION
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    Ultralight bosons are predicted in many extensions to the Standard Model and are popular dark matter candidates. The black hole superradiance mechanism allows for these particles to be probed using only their gravitational interaction. In this scenario, an ultralight boson cloud may form spontaneously around a spinning black hole and extract a non-negligible fraction of the black hole’s mass. These oscillating clouds produce quasi-monochromatic, long-duration gravitational waves that may be detectable by ground-based or space-based gravitational wave detectors. We discuss the capability of a new long-duration signal tracking method, based on a hidden Markov model, to detect gravitational wave signals generated by ultralight vector-boson clouds, including cases where the signal frequency evolution timescale is much shorter than that of a typical continuous wave signal. We quantify the detection horizon distances for vector-boson clouds with current- and next-generation ground-based detectors. We demonstrate that vector clouds hosted by black holes with mass ≳60M⊙ and spin ≳0.6 are within the reach of current-generation detectors up to a luminosity distance of ∼1  Gpc. This search method enables one to target vector-boson clouds around remnant black holes from compact binary mergers detected by gravitational-wave detectors. We discuss the impact of the sky localization of the merger events and demonstrate that a typical remnant black hole reasonably well-localized by the current generation detector network is accessible in a follow-up search.

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    • Received 30 April 2023
    • Accepted 10 August 2023

    DOI:https://doi.org/10.1103/PhysRevD.108.064001

    © 2023 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    General relativityGravitational wavesParticle dark matter
    1. Physical Systems
    Quantum aspects of black holes
    1. Techniques
    Gravitational wave detectionNumerical relativity
    Gravitation, Cosmology & Astrophysics

    Authors & Affiliations

    Dana Jones1,*, Ling Sun1, Nils Siemonsen2,3,4, William E. East2, Susan M. Scott1, and Karl Wette1

    • 1OzGrav-ANU, Centre for Gravitational Astrophysics, College of Science, The Australian National University, Australian Capital Territory 2601, Australia
    • 2Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
    • 3Arthur B. McDonald Canadian Astroparticle Physics Research Institute, 64 Bader Lane, Queen’s University, Kingston, ON K7L 3N6, Canada
    • 4Department of Physics & Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada

    • *Corresponding author: dana.jones@anu.edu.au

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    Vol. 108, Iss. 6 — 15 September 2023

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    Images

    • Figure 1
      Figure 1

      Strain amplitude at the cloud’s saturation h0peak as a function of fGWpeak for five different black holes with Mi=5, 10, 20, 50, and 100M⊙ for χi=0.7 and d=100  Mpc. The color corresponds to α. For all five black holes, the optimally matched scenario (i.e., maximum h0peak) occurs at αopt=0.176.

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    • Figure 2
      Figure 2

      Boson mass mVopt=αoptℏ/rg in units of eV (top), h0peak (for d=100  Mpc) (middle), and fGWpeak (bottom) as a function of initial black hole mass Mi. In all three panels, we use the optimally matched α as defined in Eq. (20). The colored lines in each panel correspond to different values of initial black hole spin.

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    • Figure 3
      Figure 3

      GW emission timescale τGW as a function of initial black hole mass Mi and spin χi for αopt as defined in Eq. (20).

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    • Figure 4
      Figure 4

      Cloud growth (top) and GW emission timescales (bottom) as a function of initial black hole mass Mi and α with initial black hole spin χi=0.7. The dashed white line marks α=αopt=0.176 corresponding to the optimally matched boson mass for each black hole mass, as defined in Eq. (20).

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    • Figure 5
      Figure 5

      First time derivative of the GW frequency f˙GW (at saturation) as a function of initial black hole mass Mi and spin χi, assuming α=αopt as defined in Eq. (20).

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    • Figure 6
      Figure 6

      L¯th as a function of NT for Tcoh=30  min (data points are taken at NT=25, 50, 100, 200, 300, 400, and 500 steps). The solid curve is an exponential decay fit: L¯th=ae−bNT+c with fit parameters a=2.99, b=0.0168, and c=6.66.

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    • Figure 7
      Figure 7

      Viterbi tracking (solid orange curve) for a synthetic vector boson signal (dashed blue curve) injected into Gaussian noise with Sh1/2=4×10−24  Hz−1/2 for two aLIGO detectors (system parameters: Mi=200M⊙, χi=0.6, αopt=0.141, and d=500  Mpc). We use Tcoh=207  min=3.45  h and run the search for a total duration of ∼26  d (NT=181 steps). The detection statistic is L¯=57.43>L¯th=6.73.

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    • Figure 8
      Figure 8

      Viterbi tracking (solid orange curve) for a synthetic vector boson signal (dashed blue curve) injected into Gaussian noise with Sh1/2=4×10−24  Hz−1/2 for two aLIGO detectors (system parameters: Mi=60M⊙, χi=0.7, αopt=0.176, and d=500  Mpc). We use Tcoh=11.6  min and run the search for (a) 23 steps, (b) 46 steps, (c) 92 steps, and (d) 184 steps, corresponding to Tobs=0.25τGW, 0.5τGW, τGW, and 2τGW, respectively (τGW=0.74  days). In panels (b), (c), and (d), L¯ is above the corresponding threshold, whereas in panel (a), L¯<L¯th, which is a nondetection.

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    • Figure 9
      Figure 9

      Horizon distance (colored contour) as a function of the initial black hole mass Mi and initial spin χi for two aLIGO detectors at design sensitivity. The gray region marks the parameter space where the signal is evolving too quickly to be tracked using the method in this paper (f˙det>1.39×10−4  Hz s−1). The white contours mark the optimally matched boson masses [as defined in Eq. (20)] in eV.

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    • Figure 10
      Figure 10

      Horizon distance (colored contour) as a function of the initial black hole mass Mi and initial spin χi for two aLIGO detectors at design sensitivity (top), one Cosmic Explorer (middle), and one Einstein Telescope with three identical observatories at the same triangular site (bottom). The gray region marks the parameter space where the signal is evolving too quickly to be tracked using the method in this paper (f˙det>1.39×10−4  Hz s−1). The white contours mark the optimally matched [as defined in Eq. (20)] boson masses (in eV), roughly indicating the parameter space that can be probed with these ground-based detectors.

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    • Figure 11
      Figure 11

      Horizon distance (colored contour) as a function of Mi and α (at χi=0.7) for two aLIGO detectors at design sensitivity. The dashed white line marks αopt=0.176, the α-value corresponding to the optimally matched boson mass for each black hole mass.

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    • Figure 12
      Figure 12

      Colored contour of L¯/L¯th as a function of the offset in RA and Dec for a short-duration signal (left) and a long-duration signal (right). See Table 2 for the injection parameters. Left: We have L>L¯th in the whole panel. Right: The bright EPSF enclosed within the white contour marks the region of the sky with L¯>L¯th where the signal is successfully recovered.

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