Constraining black hole mimickers with gravitational wave observations

Nathan K. Johnson-McDaniel, Arunava Mukherjee, Rahul Kashyap, Parameswaran Ajith, Walter Del Pozzo, and Salvatore Vitale

Phys. Rev. D 102, 123010 – Published 7 December 2020

Abstract

LIGO and Virgo have recently observed a number of gravitational wave (GW) signals that are fully consistent with being emitted by binary black holes described by general relativity. However, there are theoretical proposals of exotic objects that can be massive and compact enough to be easily confused with black holes. Nevertheless, these objects differ from black holes in having nonzero tidal deformabilities, which can allow one to distinguish binaries containing such objects from binary black holes using GW observations. Using full Bayesian parameter estimation, we investigate the possibility of constraining the parameter space of such “black hole mimickers” with upcoming GW observations. Employing perfect fluid stars with a polytropic equation of state as a simple model that can encompass a variety of possible black hole mimickers, we show how the observed masses and tidal deformabilities of a binary constrain the equation of state. We also show how such constraints can be used to rule out binaries of some simple models of boson stars as possible sources of the simulated events we consider.

Received 11 May 2018
Accepted 28 October 2020

DOI:https://doi.org/10.1103/PhysRevD.102.123010

Physics Subject Headings (PhySH)

Gravitational waves

Astronomical black holes Binary stars

Composition of astronomical objects

Interdisciplinary PhysicsGravitation, Cosmology & AstrophysicsGeneral Physics

Authors & Affiliations

Nathan K. Johnson-McDaniel ^1,2,*, Arunava Mukherjee ^1,3,4,5,6, Rahul Kashyap ^1,7, Parameswaran Ajith ^1,8, Walter Del Pozzo^9,10,11, and Salvatore Vitale ¹²

¹International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
²Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
³Astroparticle Physics and Cosmology Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India
⁴SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
⁵Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, Callinstr. 38, D-30167 Hannover, Germany
⁶Leibniz Universität Hannover, D-30167 Hannover, Germany
⁷Institute for Gravitation and the Cosmos, Center for Multimessenger Astrophysics, Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
⁸Canadian Institute for Advanced Research, CIFAR Azrieli Global Scholar, MaRS Centre, West Tower, 661 University Ave., Suite 505, Toronto, ON M5G 1M1, Canada
⁹School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
¹⁰Universitá di Pisa, I-56127 Pisa, Italy
¹¹INFN, Sezione di Pisa, I-56127 Pisa, Italy
¹²LIGO Laboratory and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

^*Present address: 149 Oak Avenue, Jefferson, Georgia 30549, USA

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Vol. 102, Iss. 12 — 15 December 2020

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Images

Figure 1
The quadrupolar and octupolar tidal deformabilities for polytropic stars as well as those for boson stars with a quartic self-interaction computed by [21]. Both of these are plotted versus the star’s mass $M_{⋆}$ , scaled by the maximum mass of a stable star with a given EOS, $M_{\max}$ . Here $n$ is the polytropic index and ${\tilde{λ}}_{B} ≔ λ_{B} (M_{Pl} / m_{B})^{2}$ , where $m_{B}$ and $λ_{B}$ are the boson mass and coupling constant and $M_{Pl}$ is the Planck mass.
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Figure 2
Posterior distributions of the (source frame) mass $m_{1}$ and tidal deformability $Λ_{1}$ of the more massive object (marginalized over all other parameters), obtained from the simulated observation with detector frame masses $m_{1}^{z} = 39.5 M_{⊙}$ and $m_{2}^{z} = 31.7 M_{⊙}$ . The middle panel shows the 90% credible regions in the marginalized posterior distribution $P (m_{1}, Λ_{1})$ , while top/side panels show the marginalized one-dimensional posteriors $P (m_{1})$ and $P (Λ_{1})$ . The distributions are computed from the posterior samples using Gaussian kernel density estimates. The legend shows the cutoff frequencies employed in the calculation of these posteriors, the mean SNR of the posterior samples, and the fraction of posterior samples with contact frequency (computed using $n = 0.9$ ) larger than the cutoff frequency employed. The vertical lines on the top panel show the 90% credible lower bounds on $m_{1}$ , while the horizontal lines on the side panel show the 90% credible upper bounds on $Λ_{1}$ .
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Figure 3
Left panel: the dashed line shows the minimum value $Λ_{\min}$ of the dimensionless tidal deformability parameter allowed by the polytropic EOS [Eq. (1)], plotted against the polytropic index $n$ . The violin plots (yellow) show the marginalized posterior distribution of $Λ_{1}$ for each value of $n$ (thus the individual violin plots’ extent in the horizontal direction indicates probability, on an arbitrary scale, not values of $n$ ), while the red triangles show the 90% credible upper bounds $Λ_{UL}$ . These are both computed from a simulated event with (detector frame) masses of 39.5 and $31.7 M_{⊙}$ . The shaded region shows the values of $n$ for which the observed upper bounds $Λ_{UL}$ are lower than the theoretical minimum $Λ_{\min}$ for the EOS and hence can be ruled out. In all panels, the values of $n$ for which there are no points for a given event are those values for which there are not enough posterior samples satisfying the selection criteria discussed in the text (i.e., contact frequency $>$ cutoff frequency used in the parameter estimation or $Λ_{1} < Λ_{\min}$ ). Middle panel: same as the left panel, except that we show the upper bounds obtained from all four simulated events (masses shown in legend). We show the largest exclusion region, corresponding to the most massive system considered (the same one as in the left panel). Right panel: the maximum value of the polytropic constant $K$ (for a given polytropic index $n$ ) that is unconstrained by the observed lower limit $m_{LL}$ on the mass of the compact object for all four simulated events. The pink shaded region is the largest region excluded by such an observation and corresponds to the most massive system considered (the same one as in the left panel). The gray shaded region corresponds to the $Λ_{\min}$ constraint from the same system.
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Figure 4
Top panels: posterior distributions of the tidal deformabilities of the two objects, $Λ_{1}$ and $Λ_{2}$ (marginalized over all other parameters), obtained from simulated observations of two binaries with nonzero tidal deformabilities, one (left) with GW150914-like masses and distance and $Λ_{1} = Λ_{2} = 200$ created with the same waveform model used in this analysis and one (right) that is equal mass with $Λ_{1} = Λ_{2} = 246$ and obtained by scaling a numerical binary neutron star waveform to a total mass similar to GW150914. These results are both obtained with a cutoff frequency of 74 Hz, the highest frequency we use in our analysis of these simulated observations. In each set of figures, the center panel shows the two-dimensional distribution of $Λ_{1}$ and $Λ_{2}$ (darker shading indicates larger probability density), while the panels to its top and right show the marginalized one-dimensional posteriors for these quantities and the bottom panel shows this for the mass ratio $q$ . For $Λ_{1, 2}$ , we show the 90% upper bounds, while for $q$ we show the 90% credible interval around the median. We see significant waveform systematics in the right-hand figure. Bottom panels: the posterior distributions of the effective tidal deformability $\tilde{Λ}$ of the binary with a variety of different cutoff frequencies, reweighted to a uniform prior in $\tilde{Λ}$ , for the same two simulated observations as the upper plots. The vertical lines show the 90% bounds on $\tilde{Λ}$ for the case with the highest cutoff frequency, again illustrating the waveform systematics observed for the scaled BNS simulated observation.
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Figure 5
Constraints on the parameter space of a boson star with quartic self-interaction from the simulated observation of the 15.5, $8.2 M_{⊙}$ (detector frame) binary black hole using the fits in Eq. (4) applied to the $n \geq 1.4$ results. Here $m_{B}$ is the boson mass and $λ_{B}$ is the coupling strength. The solid and dashed cyan curves correspond to the observed lower limit of $m_{1} \geq 10.5 M_{⊙}$ and upper limit of $Λ \leq 298$ (both at the 95% credible level), respectively. The gray region is excluded at the 95% credible level. The purple line shows the parameters corresponding to a self-interaction cross section per unit mass of $0.1 - 1 {cm}^{2} / g$ , as suggested for dark matter by various astronomical observations (discussed in, e.g., [18]).
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