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Black Hole Coalescence: Observation and Model Validation

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Working Toward Solutions in Fluid Dynamics and Astrophysics

Part of the book series: SpringerBriefs in History of Science and Technology ((BRIEFSHIST))

Abstract

This paper will discuss the recent LIGO-Virgo observations of gravitational waves and the binary black hole mergers that produce them. These observations rely on having prior knowledge of the dynamical behaviour of binary black hole systems, as governed by the Einstein Field Equations (EFEs). However, we currently lack any exact, analytic solutions to the EFEs describing such systems. In the absence of such solutions, a range of modelling approaches are used to mediate between the dynamical equations and the experimental data. Models based on post-Newtonian approximation, the effective one-body formalism, and numerical relativity simulations (and combinations of these) bridge the gap between theory and observations and make the LIGO-Virgo experiments possible. In particular, this paper will consider how such models are validated as accurate descriptions of real-world binary black hole mergers (and the resulting gravitational waves) in the face of an epistemic circularity problem: the validity of these models must be assumed to justify claims about gravitational wave sources, but this validity can only be established based on these same observations.

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Notes

  1. 1.

    See Kennefick (2007, 46–47) for a very clear explanation of this point.

  2. 2.

    There are distinctions between solutions that are “exact”, “elementary”, “algebraic” etc., which I do not delve into here. For discussion of these issues, see Fillion and Bangu (2015).

  3. 3.

    For a detailed introduction to matched-filtering in gravitational-wave astrophysics, see (Maggiore 2008, Sect. 7.3).

  4. 4.

    This assumes that the eccentricity of the orbit can be neglected, since the emission of gravitational radiation is expected to circularise the orbit by the time the emitted gravitational waves enter the bandwidth of the detector (Peters 1964).

  5. 5.

    For a details, see Abbott et al. (2020, 36).

  6. 6.

    For details about LALInference analyses, see Veitch et al. (2015).

  7. 7.

    See, for example, Kennefick (2007, Chap. 8) and Havas (1989, 1993) for the history of this problem.

  8. 8.

    For a detailed discussion of the post-Newtonian approach, see Maggiore (2008, Chap. 5).

  9. 9.

    Since the nPN order refers to inclusions of terms \(\mathcal {O}(1/c^{2n})\), 4PN results include terms \(\mathcal {O}(1/c^{8})\).

  10. 10.

    Here, by convention, \(m_{1} > m_{2}\).

  11. 11.

    For detailed reviews of the history of numerical relativity simulations, see e.g., Holst et al. (2016) and Sperhake (2015).

  12. 12.

    I discuss reasons for this confidence in Sect. 5.3.3.

  13. 13.

    Here the compactness parameter is defined as as the ratio M/r where \( 0 < M/r \lesssim 1 \), and \(M = m_{1} + m_{2}\).

  14. 14.

    The mass ratio is defined as \( m_{2}/m_{1} \) where, by convention, \( m_{1} \) is always the larger mass and thus \( 0 < m_{2}/m_{1} \lesssim 1\).

  15. 15.

    In other work, including Elder (2020, in preparation), I provide an account of what is meant by these descriptors, drawing connections to recent work in the philosophy of measurement (e.g., Parker 2017; Tal 2012, 2013).

  16. 16.

    For the purposes of this paper, I will mainly focus on the models used for this initial detection. However, modelling these systems is an active area of research, with new iterations of these modelling approaches incorporating more physical effects.

  17. 17.

    My focus here is on binary black hole mergers, in part because I am focused on the case of GW150914 specifically, and in part because the case is arguably slightly different for binary neutron star mergers. I discuss how the epistemic situation is changed for “multi-messenger” sources like GW170817 in Elder (2020, Chap. 4 and in preparation).

  18. 18.

    O3 has recently reported one burst candidate, given the preliminary name “S200114f”, but this candidate has not yet been confirmed.

  19. 19.

    “BICEP” stands for “Background Imaging of Cosmic Extragalactic Polarization”. They initially reported the observation of signatures of primordial gravitational waves in 2014 but were forced to retract this claim, instead attributing the observation to cosmic dust (Collins 2017, 72).

  20. 20.

    Other notions of validity can be added here. For example, see Cronbach and Meehl (1955) for a discussion of the notion of “construct validity”.

  21. 21.

    For the purposes of this paper I will not explicitly discuss the IMRPhenom models. However, given that these hybrid models use the same ingredients as EOBNR models (PN, EOB, and NR), most if not all of what I say about EOBNR should also apply to IMRPhenom.

  22. 22.

    In general, convergence studies need not always involve increasing the resolution. For example, for Monte Carlo simulation convergence studies are performed for increasing sample sizes.

  23. 23.

    For more on these codes, see Duez and Zlochower (2018), especially section II, and the references therein).

  24. 24.

    The agreement across variations in the simulation methods forms the basis for a robustness argument: the simulation outputs are considered to be robust (and hence reliable) due to the agreement across independent methods. As with other robustness arguments, such reasoning relies on the methods being genuinely independent (see e.g., Staley (2004) and Dethier (2020)). Note that while robustness arguments of this kind have been considered controversial in the context of climate modelling, the present case appears to be one where robustness arguments are considered to be uncontroversial (if fallible). However, a comparative study of these cases is beyond the scope of this paper.

  25. 25.

    Of course, from the perspective of proponents of (relativistic extensions of) Modified Newtonian Dynamics (MOND), the empirical discrepancies that are usually attributed to dark matter in order to save general relativity are instead a motivation to modify general relativity. On this view, of course, general relativity has not stood up to all the empirical tests it has faced.

  26. 26.

    Nonetheless, insofar as the models are embedded in the experimental methodology, there is a sense in which this could be understood as a kind of experimenter’s regress, spelled out in terms of models rather than detectors. There are also clear similarities here to the related “simulationist’s regress” (Gelfert 2012; Meskhidze 2017).

  27. 27.

    See Bokulich (2020) for discussion of the distinction between consilience and coherence testing.

  28. 28.

    See also Patton (2020) for an excellent discussion of a different test, based on the parameterised post-Einsteinian framework developed by Yunes and Pretorius, including how this connects to the issue of “fundamental theoretical bias”.

  29. 29.

    For further discussion of theory testing in gravitational-wave astrophysics, see Elder (in preparation).

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Acknowledgements

I would like to thank Don Howard, Nicholas Teh, Feraz Azhar, and Erik Curiel for their support and comments on an early version of this paper. I would similarly like to thank Dennis Lehmkuhl and the rest of the Lichtenberg Group at the University of Bonn—especially Juliusz Doboszewski, Niels Martens, and Christian Röken—for their helpful feedback on early drafts.

I would also like to thank audiences at SuperPAC, MS8, EPSA, the BHI and the (history and) philosophy of physics seminars at Bonn and Oxford for their questions and comments. Conversations with members of the LIGO Scientific Collaboration (especially Daniel Holz and Hsin-Yu Chen) at Seven Pines, BHI conferences, and a Sackler conference were also invaluable.

Special thanks are also due to Lydia Patton, a pioneer in the philosophy of gravitational-wave astrophysics, for ongoing support of my work in this area. And, of course, for thinking to connect this paper with the other excellent work in this volume.

This project/publication was funded in part by the Gordon and Betty Moore Foundation. It was also made possible through the support of a grant from the John Templeton Foundation. The opinions expressed in this publication are those of the author and do not necessarily reflect the views of these Foundations.

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  1. Black Hole Initiative, Harvard University, 20 Garden Street, 2nd Floor, Cambridge, MA, 02138, UK

    Jamee Elder

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  1. Department of Philosophy, Virginia Tech, Blacksburg, VA, USA

    Lydia Patton

  2. Munich Center for Mathematical Philosophy, Ludwig-Maximilians-Universität München, München, Bayern, Germany

    Erik Curiel

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Elder, J. (2023). Black Hole Coalescence: Observation and Model Validation. In: Patton, L., Curiel, E. (eds) Working Toward Solutions in Fluid Dynamics and Astrophysics. SpringerBriefs in History of Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-031-25686-8_5

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