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The Uncertain Future of Massive Binaries Obscures the Origin of LIGO/Virgo Sources

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 Publication date 2021
  fields Physics
and research's language is English




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The LIGO/Virgo gravitational--wave observatories have detected 50 BH-BH coalescences. This sample is large enough to have allowed several recent studies to draw conclusions about the branching ratios between isolated binaries versus dense stellar clusters as the origin of double BHs. It has also led to the exciting suggestion that the population is highly likely to contain primordial black holes. Here we demonstrate that such conclusions cannot yet be robust, because of the large current uncertainties in several key aspects of binary stellar evolution. These include the development and survival of a common envelope, the mass and angular momentum loss during binary interactions, mixing in stellar interiors, pair-instability mass loss and supernova outbursts. Using standard tools such as the population synthesis codes StarTrack and COMPAS and the detailed stellar evolution code MESA, we examine as a case study the possible future evolution of Melnick 34, the most massive known binary star system. We show that, despite its well-known orbital architecture, various assumptions regarding stellar and binary physics predict a wide variety of outcomes: from a close BH-BH binary (which would lead to a potentially detectable coalescence), through a wide BH-BH binary (which might be seen in microlensing observations), or a Thorne-Zytkow object, to a complete disruption of both objects by pair-instability supernovae. Thus since the future of massive binaries is inherently uncertain, sound predictions about the properties of BH-BH systems are highly challenging at this time. Consequently, drawing conclusions about the formation channels for the LIGO/Virgo BH-BH merger population is premature.



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We present a revised version of Peters (1964) time-scale for the gravitational-wave (GW) induced decay of two point masses. The new formula includes the effects of the first-order post-Newtonian perturbation and additionally provides a simple fit to account for the Newtonian self-consistent evolution of the eccentricity. The revised time-scale is found by multiplying Peters estimate by two factors, $R(e_0)= 8^{1-sqrt{1-e_0}}$ and $Q_{rm f}(p_0) = exp left(2.5 (r_{rm S}/p_0) right)$, where $e_0$ and $p_0$ are the initial eccentricity and periapsis, respectively, and $r_{rm S}$ the Schwarzschild radius of the system. Their use can correct errors of a factor of 1-10 that arise from using the original Peters formula. We apply the revised time-scales to a set of typical sources for existing ground-based laser interferometers and for the future Laser Interferometer Space Antenna (LISA), at the onset of their GW driven decay. We argue that our more accurate model for the orbital evolution will affect current event- and detection-rate estimates for mergers of compact object binaries, with stronger deviations for eccentric LISA sources, such as extreme and intermediate mass-ratio inspirals. We propose the correction factors $R$ and $Q_{rm f}$ as a simple prescription to quantify decay time-scales more accurately in future population synthesis models. We also suggest that the corrected time-scale may be used as a computationally efficient alternative to numerical integration in other applications that include the modelling of radiation reaction for eccentric sources.
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