# Gravitational-wave data analysis with high-precision numerical relativity
simulations of boson star mergers

Tamara Evstafyeva  0000-0002-2818-701X<EMAIL_ADDRESS>DAMTP, Centre for
Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge
CB3 0WA, UK  Ulrich Sperhake  0000-0002-3134-7088<EMAIL_ADDRESS>DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce
Road, Cambridge CB3 0WA, UK  Department of Physics and Astronomy, Johns
Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA
TAPIR 350-17, Caltech, 1200 E. California Boulevard, Pasadena, California
91125, USA  Isobel Romero-Shaw  0000-0002-4181-8090<EMAIL_ADDRESS>DAMTP,
Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road,
Cambridge CB3 0WA, UK  Kavli Institute for Cosmology Cambridge, Madingley Road
Cambridge CB3 0HA, United Kingdom  Michalis Agathos  0000-0002-9072-1121
<EMAIL_ADDRESS>DAMTP, Centre for Mathematical Sciences, University of
Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK  Kavli Institute for
Cosmology Cambridge, Madingley Road Cambridge CB3 0HA, United Kingdom

###### Abstract

Gravitational-wave signals detected to date are commonly interpreted under the
paradigm that they originate from pairs of black holes or neutron stars. Here,
we explore the alternative scenario of boson-star signals being present in the
data stream. We perform accurate and long ($\sim 20$ orbits) numerical
simulations of boson-star binaries and inject the resulting strain into LIGO
noise. Our Bayesian inference reveals that some boson-star signals are
degenerate with current approximants, albeit with biased parameters, while
others exhibit smoking-gun signatures leaving behind conspicuous residuals.

††preprint: APS/123-QED

Introduction— Following the Nobel-Prize winning detection of GW150914 [1],
about 100 further gravitational-wave (GW) events have been confidently
detected by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and
Virgo [2, 3, 4]. This ever-increasing ensemble of GW events provides ample
opportunities to explore some of the deepest mysteries of the cosmos and test
the nature of compact objects: black holes (BHs), neutron stars (NSs) and
exotic compact objects (ECOs) [5]. A research programme targeting such tests,
however, faces several crucial challenges: (i) Given a candidate class of
ECOs, can we generate gravitational waveforms of sufficient longevity and
accuracy? (ii) Supposing ECO coalescences occur in the Universe, can we detect
them with our current search pipelines? (iii) If yes, can we distinguish them
from traditional binary BH (BBH) or NS events? (iv) Can we generate
comprehensive GW template banks suitable as alternatives to BH and NS
approximants for parameter estimation (PE)? The main goal of this Letter is to
explore the answers to these questions for the case of scalar-field boson
stars (BSs), which are self-gravitating equilibrium solutions to the Einstein-
Klein-Gordon equations [6, 7, 8].

BSs have attracted a great deal of interest over the years. BSs may account
for part of the enigmatic dark-matter content of the Universe [9, 10]. BS
solutions cover a wide range of compactness, thus forming a theoretical
laboratory for exploring extreme-gravity effects beyond BHs such as the
geometry of BS shadows [11, 12] or light rings [13, 14, 15]. BSs are an ideal
proxy for a wide class of compact binaries systematically deviating from BH
systems, e.g. through finite tidal deformability [16]. Combined with their
high amenability to numerical modelling, this makes BS binaries particularly
suitable for high-precision gravitational-wave (GW) source modelling and
template construction beyond BHs. Numerical studies of BS binaries have made
tremendous progress in the last decade, focusing in particular on the merger
remnants [17, 18, 19, 20, 21, 22], and analytic approximations have been
employed for performing PE of BS binary signals [23, 24, 25] (see also Refs.
[26, 27] for searches of Proca-star head-on collisions in GW data). Here, we
numerically compute the first high-precision $\sim 20$ orbit inspiral-merger-
ringdown (IMR) waveforms for quasi-circular BS binaries and inject them into
LIGO detector noise. We perform PE using Bayesian inference and assess the
ability of present BBH and binary NS waveform templates to recover the
injected signals. We use natural units $c=1=\hbar$, i.e. $G=M_{\rm Pl}^{-2}$.
Our data and animations are publicly available [28, 29, 30].

Theory— BSs in general relativity are described by the action of a complex
scalar field $\varphi$ minimally coupled to gravity,

$S=\int\frac{\sqrt{-g}}{2}\left\\{\frac{R}{8\pi
G}-\left[g^{\mu\nu}\nabla_{\mu}\bar{\varphi}\nabla_{\nu}\varphi+V(\varphi)\right]\right\\}\mathrm{d}^{4}x,$
(1)

where $V(\varphi)$ is the potential, which we choose to be of solitonic type
[31, 32], $V_{\rm
sol}=\mu^{2}|\varphi|^{2}(1-2|\varphi|^{2}/\sigma_{0}^{2})^{2}$ with
$\sigma_{0}=0.2$. Through appropriate re-scaling of the variables [33], the
mass of the scalar can be set to $\mu=1$ which, henceforth, sets the length
scale of our units. Varying the action (1) yields the Einstein-Klein-Gordon
equations and spherically symmetric solutions are obtained by decomposing the
scalar field into amplitude $A$ and frequency $\omega$,
$\varphi(t,r)=A(r)e^{\mathrm{i}\mkern 1.0mu(\epsilon\omega t+\delta\phi)}$
[34]. Here we introduce the parameter $\epsilon=\pm 1$, determining the
rotation of the scalar field in the complex plane, and a phase offset
$\delta\phi$. Our primary BS always has $\epsilon=1,~{}\delta\phi=0$ and we
refer to configurations with secondary parameters
$(\delta\phi=0,~{}\epsilon=1)$, $(\delta\phi=\tfrac{\pi}{2},~{}\epsilon=1)$,
$(\delta\phi=\pi,~{}\epsilon=1)$, $(\delta\phi=0,~{}\epsilon=-1)$ as in-phase,
dephased, anti-phase and anti-BS binaries respectively. Given the central
amplitude $A_{\rm{ctr}}=A(0)$, we obtain a BS solution via a shooting
algorithm described in Ref. [34]. In this work, we consider two models: a
compact “A17” star with $\sqrt{G}A_{\rm{ctr}}=0.17$, dimensionless tidal
deformability $\Lambda\sim 10$ [16] and compactness $\mathcal{C}=0.2$
containing $0.99$ of its total mass $m$ within a radius $r_{99}=3.97$, and a
less compact “A147” star with $\sqrt{G}A_{\rm{ctr}}=0.147$, $\Lambda\sim
1000$, $\mathcal{C}=0.1$ and $r_{99}=4.48$.

NR Simulations— Our simulations have been performed using two codes, GRChombo

Table 1:  Summary of the BS binaries evolved in the centre-of-mass frame with initial boost velocity $v_{x,\rm{ini}}$ in the $x$-direction, impact parameter $b$ in the $y$-direction and separation $d$ in the $x$-direction. The dephased, anti-phase and anti-BS binaries are labelled as p090, p180, e1. $E_{l=2}$ is the GW energy contained in the $l=2$ modes.  Simulation |  $v_{x,\rm{ini}}$ |  $b/M$ |  $d/M$ |  $E_{l=2}/M$
---|---|---|---|---
A17-d17 | 0.1671 | 17.5 | 0.32 | 0.0333
A17-d17-p180 | 0.1671 | 17.5 | 0.32 | 0.0353
A17-d17-e1 | 0.1671 | 17.5 | 0.32 | 0.0299
A17-d20 | 0.1533 | 20 | 0.3 | 0.0346
A17-d21 | 0.14625 | 21.5 | 0.29 | 0.0367
A17-d21-p090 | 0.14625 | 21.5 | 0.29 | 0.0377
A17-d21-p180 | 0.14625 | 21.5 | 0.29 | 0.0387
A17-d21-e1 | 0.14625 | 21.5 | 0.29 | 0.0352
A147-d12 | 0.1389 | 12 | 0.05 | 0.0589
A147-d14 | 0.1256 | 14 | 0.08 | 0.0691

[35, 36, 37] and Lean [38]. Both codes evolve the Einstein equations through
fourth-order finite-differencing of the CCZ4 formulation [39], employing the
moving puncture gauge [40, 41]. Whilst GRChombo is based on adaptive-mesh-
refinement provided by Chombo [42], the Lean code, based on the cactus
computational toolkit [43], utilises mesh refinement via carpet [44]. Apparent
horizons are computed using ahfinderdirect [45]. We use a computational domain
of length $L=1024$ with bitant symmetry, 8 nested refinement levels with
resolutions $\Delta x=1/40$ to $1/48$ on the innermost level and extract GWs
at $R_{\rm ex}\in[140,240]$.

Figure 1: Plus polarizations of the $22$ IMR mode for the A17-d20 and A147-d14
binaries of Table 1.

We focus on equal-mass non-spinning BS binaries of total mass $M=2m$, listed
in Table 1, starting from initial data constructed as in Refs. [34, 46]. By
tuning the initial velocities, we reduce their orbital eccentricity, estimated
according to Eq.(17) of Ref. [47], as $0.002-0.005$. By verifying convergence
of the A17 and A147 BS binaries and extrapolating GW signals to infinity, we
obtain an error budget of $(0.1,~{}4\,\%)$ for the GW phase and amplitude for
A17 binaries and $(0.2,~{}4\,\%)$ for A147 binaries, similar to finite
differencing production runs for BH inspirals reported in Ref. [48]; see the
supplementary material for details.

In physical terms, the most conspicuous difference between the A17 and A147
binary families of Table 1 is their ultimate fate. The compact A17
coalescences ubiquitously result in the formation of a BH remnant with
dimensionless final spin $a_{\rm fin}\sim 0.7$, similar to the end-product of
non-spinning equal-mass BH mergers. By eye, the resulting GW form looks
indistinguishable from a BH signal; cf. Fig. 1. In contrast, the “fluffy” A147
binaries merge into a more compact, highly distorted BS remnant with an
oscillating central amplitude $0.156\leq\sqrt{G}A_{\rm{ctr}}\leq 0.164$. The
GW signal emitted by these fluffy binaries is characterised by a lower-
amplitude inspiral part followed by an immense GW burst at merger and a
prolonged, rapidly pulsating ringdown; cf. Fig. 1.

For the A17 family of stars we consider additional configurations with non-
zero phase-offsets, $\delta\phi=\pi/2,\pi$ and anti-BS binaries. All A17
binaries produce identical signals in the early inspiral, but as the BSs get
closer, the scalar-field interaction [49, 50] leads to delayed mergers for
$\delta\phi\neq 0$, $\epsilon=-1$ and, especially, for $\delta\phi=\pi$. A
comparison with BH waveforms [36] furthermore suggests that the A17 anti-BS
signal resembles most closely that from a non-spinning, equal-mass BH binary
in terms of the GW amplitude in the late inspiral and its phase evolution
close to merger; cf. Fig. 3 in the supplementary material.

Parameter Estimation— We inject our numerically computed GW signals into
Gaussian noise coloured by the O4 design sensitivities of the LIGO Hanford
(H1) and Livingston (L1) detectors [2] and perform Bayesian inference using
bilby [51, 52]. We focus on the dominant $l=2$ modes and consider systems of
total masses $M^{\rm{inj}}_{\rm tot}\in[5,105]\,M_{\odot}$ in the source
frame, corresponding to scalar-field masses
$\mu\in[10^{-13},10^{-12}]\,\rm{eV}$. We choose luminosity distances $d_{\rm
L}$ corresponding to (zero-noise) optimal injected signal-to-noise ratios
(SNRs) $\rho^{\rm H1}\in[15,60]$, $\rho^{\rm L1}\in[10,45]$. We recover
injected BS signals using standard waveform approximants, including effects of
asymmetric mass ratio, spin, orbital precession and tides, as used routinely
by the LIGO-Virgo-KAGRA Collaboration [3]: IMRPhenomD [53, 54], IMRPhenomPv3
[55], IMRPhenomXP, IMRPhenomXPHM [56], TaylorF2 [57], IMRPhenomPv2_NRTidal
[58, 59] and TEOBResumS [60]. We obtain comparable results for the various
approximants, as reviewed in more detail in the supplementary material, and
focus the following discussion on IMRPhenomXP and IMRPhenomPv2_NRTidal. We
report the mass values in the source frame; quantities in the detector frame
will be denoted by ’det’.

We perform our inference using two sets of BBH-like spin priors: (i) we fix
the spins in the recovery templates to their zero injected values; (ii) we
explore the complete spin prior with all parameters being free. In the
process, we compute for each detector the optimal SNR $\rho$ of the recovered
and injected signals. For each recovery we compute the Bayes factor
$\mathcal{B}^{\rm{S}}_{\rm{N}}$, quantifying the evidence ratio between a
signal being present in the data relative to the hypothesis of pure Gaussian
noise. To asses the quality of the recovery we additionally compute the
residual
$r\mathrel{\vbox{\hbox{\scriptsize.}\hbox{\scriptsize.}}}=d-h_{\rm{max}}$ from
the data stream $d$ and the approximant’s strain $h_{\rm max}$ evaluated at
the maximum-joint-log-likelihood source parameters across H1/L1. Specifically,
we construct a null distribution of the white-noise optimal SNR for a signal
duration $D$ by generating random noise realizations via

$n_{\rm{w}}\mathrel{\vbox{\hbox{\scriptsize.}\hbox{\scriptsize.}}}=\frac{\tilde{n}(f)}{\sqrt{S_{n}(f)}}\sim\mathcal{N}\big{(}0,\tfrac{1}{2}\sqrt{D}\,\big{)}\,,$
(2)

where $S_{n}(f)$ is the detector’s noise power-spectral density. If the
residual’s SNR falls above the 99th percentile of the noise SNR, we regard the
residual as incompatible with Gaussian noise.

Table 2: Recovery results for a range of BS injections from Table 1 using the IMRPhenomXP approximant with spins fixed to zero. We contrast the injected ($\rho_{\rm{net}}^{\rm{inj}}$) and recovered ($\rho_{\rm{net}}^{\rm{rec}}$) network SNRs and report the recovered chirp-masses $\mathcal{M}_{\rm{c}}^{\rm{rec}}$, mass-ratios $q^{\rm{rec}}$ at maximum-joint-log-likelihood.  Run |  $\rm{log}(\mathcal{B}^{\rm{S}}_{\rm{N}})$ |  $\rho_{\rm{net}}^{\rm inj}$ |  $\rho_{\rm net}^{\rm rec}$ |  $\mathcal{M}_{\rm{c}}^{\rm rec}$ |  $q^{\rm rec}$
---|---|---|---|---|---
$M^{\rm{inj}}_{\rm{tot}}=72.4M_{\odot}$,
$\mathcal{M}^{\rm{inj}}_{\rm{c}}=31.5$, $d^{\rm{inj}}_{L}=500\,{\rm Mpc}$
A17-d17 |  717 |  40.37 |  38.63 |  26.60 |  0.32
A17-d21-p090 |  1019 |  45.17 |  46.74 |  31.63 |  0.65
A17-d17-p180 |  792 |  43.84 |  36.62 |  25.07 |  0.97
A17-d17-e1 |  820 |  41.12 |  41.91 |  27.13 |  0.71
A17-d20 |  678 |  41.41 |  38.26 |  26.72 |  0.30
A147-d14 |  555 |  57.75 |  32.16 |  40.02 |  1.00
$M^{\rm{inj}}_{\rm{tot}}=9.9M_{\odot}$, $\mathcal{M}^{\rm{inj}}_{\rm{c}}=4.3$,
$d^{\rm{inj}}_{L}=62.5\,{\rm Mpc}$
A17-d17 |  406 |  29.69 |  30.60 |  3.89 |  0.39
A17-d21-p090 |  698 |  39.15 |  38.73 |  4.07 |  0.93
A17-d17-p180 |  328 |  30.91 |  28.28 |  3.94 |  1.00
A17-d17-e1 |  407 |  30.13 |  29.07 |  4.03 |  0.92
A17-d20 |  536 |  34.13 |  34.24 |  3.92 |  0.40
A147-d14 |  286 |  37.73 |  24.45 |  4.41 |  0.13

Results (A17 families) — For the compact A17 binaries, which form a BH post-
merger, all waveform approximants enable confident recovery of the signals
with a residual compatible with Gaussian noise, regardless of the analysis
type; see Table 2 for a representative set of examples. Approximants including
tidal effects furthermore infer tidal deformability parameters consistent with
the injected $\Lambda_{1,2}\sim\mathcal{O}(10)$, albeit with poor constraints
on $\Lambda_{2}$. This corresponds to a well measured tidal deformability
$\tilde{\Lambda}$ of the binary, but a poorly constrained
$\delta\tilde{\Lambda}$ [61]. All waveform approximants, however, fail to
correctly infer some other injected parameters (component masses, spins and/or
luminosity distance) within the $90\%$ credible region; cf. Fig. 2 for a
typical example. Provided the inspiral contributes significantly to the SNR,
i.e. for $M^{\rm inj}_{\rm tot}\lesssim 80\,M_{\odot}$ in our case, however,
these deviations are not random but exhibit clear systematics which we
illustrate in Fig. 3 for a wide range of injections and now discuss in more
detail.

A17, $\delta\phi=0$, $\epsilon=1$: We obtain consistent results for using
either of the three waveform lengths employed, d17, d20 and d21, indicating
that they are sufficiently long for the mass range considered. In general, the
recovered luminosity distance is overestimated, likely compensating for
amplitude effects arising from biases in the other parameters. Next, the
posteriors from BH approximants employed with spins fixed to zero
systematically peak at total mass values within $\sim 10\,\%$ of the injected
$M^{\rm{inj}}_{\rm tot}$. For $M_{\rm tot}^{\rm inj}\lesssim 80\,M_{\odot}$,
mass ratios are recovered with peaks in the range $0.3\lesssim
q\mathrel{\vbox{\hbox{\scriptsize.}\hbox{\scriptsize.}}}=m_{2}/m_{1}\lesssim
0.7$, with no posteriors supporting the injected $q=1$ at $90\,\%$ confidence.
This picture changes considerably when we allow the spins to be sampled over
in the prior. Then we obtain more accurate estimates for the primary mass
$m_{1}$, often supporting the injected mass inside the $90\,\%$ confidence
interval, and larger mass ratios $0.5\lesssim q\lesssim 0.85$, albeit still
well below the injected $q=1$. We furthermore infer significant spin
magnitudes peaking at $0.3\leq a_{1,2}\leq 0.98$ with clear preference for
negatively aligned spins, i.e. $\chi_{\rm eff}<0$.

Figure 2: Comparison of key PE results for A17-d17 and A17-d17-e1 injections.
We use IMRPhenomXP for recovery of a BS binary with $M^{\rm{inj}}_{\rm
tot}=72.4M_{\odot},~{}d_{\rm{L}}=500\rm{Mpc}$ and allow all binary parameters
to be sampled over. The 1, 1.5, 2-sigma contours are shown.

A17-p180, $\delta\phi=\pi$, $\epsilon=1$: As for $\delta\phi=0$, the recovered
luminosity distance is often overestimated. Quite remarkably, however, these
anti-phase binaries result in nearly opposite behaviour in PE results in every
other regard. For $M_{\rm tot}^{\rm inj}\lesssim 80\,M_{\odot}$, we obtain
good estimates for the primary mass $m_{1}$ and large mass ratios $q\geq 0.8$
when the spins are fixed to their injected values. Allowing the spins to vary,
now results in significant overestimates of $m_{1}$ and more unequal mass
ratios $0.3\leq q\leq 0.8$. We typically obtain large spin magnitudes
$a_{1,2}\geq 0.5$ but preferably exhibiting partial alignment with the orbital
angular momentum, $0.1\leq\chi_{\rm eff}\leq 0.5$.

A17-d090, $\delta\phi=\pi/2$, $\epsilon=1$: This family of BS injections
yields qualitatively similar behaviour as A17-p180, but with generally smaller
departure from the injected parameters.

A17-e1, $\delta\phi=0$, $\epsilon=-1$: The anti-BS family is the best
recovered of all our injections, supporting our conjecture that these binaries
most closely resemble waveforms from non-spinning BHs. We typically obtain
mass ratios $q\gtrsim 0.75$, where the primary mass $m_{1}$ is either
contained inside the $90\,\%$ confidence interval or close by, and, for
$M_{\rm tot}^{\rm inj}\gtrsim 20M_{\odot}$, spin values close to zero. We
illustrate this behavior by comparing in Fig. 2 a representative $M_{\rm
tot}^{\rm inj}=72.4\,M_{\odot}$ example of this family with its less
accurately recovered A17-d17 counterpart.

Figure 3:  PE results obtained for four BS families and injections with total
mass $M_{\rm tot}^{\rm inj}\in[5,105]M_{\odot}$ and luminosity distance
$d_{L}=(M^{\rm{det}}_{\rm tot}/80\,M_{\odot})500\,{\rm Mpc}$. For each
injection, we display the median values of the recovered component masses
$m_{1},\,m_{2}$ normalized by their injected values (large and small circles)
and the effective spin (crosses with $90\,\%$ confidence interval). The
recoveries are obtained for fixed (blue) or variable spins (red symbols). The
dashed lines mark the injected values, 1 for the masses and 0 for $\chi_{\rm
eff}$. The recovered parameters deviate from these values non-randomly; cf.
the main text. By repeating selected injections with different $d_{\rm L}$, we
have verified that the displayed trends are robust under variations of the
SNR.

Interpretation: The most pronounced difference between $\delta\phi=0$ BS
binary signals, compared to their anti-phase counterparts, is the steep
increase of the GW amplitude in the late inspiral and merger whereas for
$\delta\phi=\pi$, this chirp is shallower; cf. Fig. 3 in the supplemental
material. A closer inspection of GW signals from non-spinning BH binaries in
the frequency domain similarly yields a steeper increase in the GW amplitude
close to merger for unequal masses relative to $q=1$. Unequal-mass BH chirps
therefore resemble more closely those from $\delta\phi=0$ BS binaries while
$\delta\phi=\pi$ BS chirps are better approximated by equal-mass BH binaries.

The inclusion of spins allows for an additional adjustment of the chirp’s
steepness, typically boosting $\log(\mathcal{B}^{\rm{S}}_{\rm{N}})$ by $\sim
10\,\%$. BH binaries with aligned spins have an enhanced yet shallower
inspiral than those with anti-aligned spins; see e.g. Figs. 1 and 3 in [62].
The shallow inspiral-merger transition of $\delta\phi=\pi$ binaries,
therefore, favors the “hang-up” of aligned spins whereas the more abrupt
transition of $\delta\phi=0$ BS binaries favors partially anti-aligned spins.
This effect also sheds light on the mass-ratio drifts when we allow the spins
to vary. For spins fixed at zero, the steep chirp of $\delta\phi=0$ BS
binaries can only be reproduced through an unequal mass ratio in the BBH
approximant. For variable spins, in contrast, it can at least partly be
accommodated through anti-aligned spins (the anti-hang-up effect);
statistically we then expect a drift towards $q=1$. For $\delta\phi=\pi$ BS
binaries, in turn, the inclusion of spins enables bilby to reproduce the
shallow chirp in the BS signal through aligned spins rather than resorting
exclusively to a high ($q\approx 1$) mass ratio; this results in a drift
towards smaller $q$.

Figure 4: Top: The recovery of a high-mass A147-d14 binary injection using
IMRPhenomXP results in $m_{1}\sim 70M_{\odot}$, $m_{2}\sim 65M_{\odot}$,
$a_{1}\sim 0.98$ and $a_{2}\sim 0.60$. Bottom: The recovery of a low-mass
A147-d14 binary injection using IMRPhenomPv2_NRTidal yields maximum-joint-log-
likelihood estimates $m_{1}\sim 3.7M_{\odot}$, $m_{2}\sim 1.3M_{\odot}$,
$a_{1}\sim 0.96$, $a_{2}\sim 0.63$, $\Lambda_{1}\sim 3000$ and
$\Lambda_{2}\sim 11000$.

Results (A147 family) — As illustrated in Fig. 1, GW signals from our less
compact A147 family of BS binaries differ more pronouncedly from BH waveforms,
especially around merger and ringdown. These differences manifest themselves
not only in the form of PE biases, but also an incomplete recovery of the
injected signals. In particular, for high (low) total mass $M_{\rm tot}^{\rm
inj}$, the approximants are able to match the merger (inspiral) part of the
signals but never both and never the ringdown; cf. Fig.4. Overall, this leads
to a reduction in the recovered optimal SNR compared to the injection; cf.
Table 2. For injections with $\rho_{\rm inj}\lesssim 30$, the residual is
still consistent with noise but for $\rho_{\rm inj}\gtrsim 30$ we often obtain
significant residuals.

Furthermore, the late inspiral of less compact BS binaries occurs at lower
frequencies than that of compact ones, so that BBH approximants systematically
overestimate the total mass; cf. Fig. 3. The addition of tidal effects
improves the approximant’s ability to capture features in the inspiral portion
of the signal for small $M_{\rm tot}^{\rm inj}$; we thus obtain large tidal
parameters $\Lambda_{1,2}\sim 10^{3}$ to $10^{4}$ consistent with the BS
binary, albeit with large uncertainties in $\Lambda_{2}$. Similar to the
compact BS injections, overall the inclusion of tidal effects does not improve
the estimation of other injection parameters.

Conclusions— By performing high-precision NR simulations of inspiralling and
merging BS binaries, we have investigated the capability of current waveform
models to recover BS GW signals with the following key results. (i) Most BS
systems considered here are detectable with current GW analysis pipelines
although current waveform templates systematically infer incorrect source
parameters. (ii) BS binaries can be numerically modelled with accuracy
comparable to BH binaries. (iii) BSs are excellent candidate sources for
constructing GW template banks alternative to BHs and NSs.

Our study suggests that, from the viewpoint of current GW detectors, BS
signals exhibit significant degeneracy with BBH waveforms obstructing the
distinction between BS binaries, especially those forming a BH upon merger,
and NS or BH systems. The most notable exception from this degeneracy consists
in the exceptionally strong inspiral-merger transition and a long-lived
ringdown in binaries forming a BS post-merger; both these features are
generally poorly matched by present approximants leaving behind non-Gaussian
residuals.

###### Acknowledgements.

We thank Priscilla Canizares and Christopher J. Moore for fruitful discussions
on GW analysis and the GRTL collaboration
111https://github.com/GRTLCollaboration. T.E. is supported by the Centre for
Doctoral Training at the University of Cambridge funded through STFC.
I.M.R.-S. acknowledges support from the Herchel Smith Postdoctoral Fellowship
Fund. This work has been supported by STFC Research Grant No. ST/V005669/1. We
acknowledge support by the NSF Grant Nos. PHY-090003, PHY-1626190 and
PHY-2110594, DiRAC projects ACTP284 and ACTP238, STFC capital Grants Nos.
ST/P002307/1, ST/R002452/1, ST/I006285/1 and ST/V005618/1, STFC operations
Grant No. ST/R00689X/1. Computations were done on the CSD3 and Fawcett
(Cambridge), Cosma (Durham), Hawk (Cardiff), CIT LIGO Lab (Pasadena),
Stampede2 (TACC) and Expanse (SDSC) clusters.

## References

  * Abbott  _et al._ [2016] B. P. Abbott _et al._ , Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116, 061102 (2016), arXiv:1602.03837 [gr-qc] .
  * Abbott  _et al._ [2018] B. P. Abbott _et al._ (KAGRA, LIGO Scientific, VIRGO), Prospects for Observing and Localizing Gravitational-Wave Transients with Advanced LIGO, Advanced Virgo and KAGRA, Living Rev. Rel. 21, 3 (2018), arXiv:1304.0670 [gr-qc] .
  * Abbott  _et al._ [2023] R. Abbott _et al._ (KAGRA, VIRGO, LIGO Scientific), GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the Third Observing Run, Phys. Rev. X 13, 041039 (2023), arXiv:2111.03606 [gr-qc] .
  * Nitz  _et al._ [2023] A. H. Nitz, S. Kumar, Y.-F. Wang, S. Kastha, S. Wu, M. Schäfer, R. Dhurkunde, and C. D. Capano, 4-OGC: Catalog of Gravitational Waves from Compact Binary Mergers, Astrophys. J. 946, 59 (2023), arXiv:2112.06878 [astro-ph.HE] .
  * Cardoso and Pani [2019] V. Cardoso and P. Pani, Testing the nature of dark compact objects: a status report, Living Rev. Rel. 22, 4 (2019), arXiv:1904.05363 [gr-qc] .
  * Kaup [1968] D. J. Kaup, Klein-Gordon Geon, Phys. Rev. 172, 1331 (1968).
  * Ruffini and Bonazzola [1969] R. Ruffini and S. Bonazzola, Systems of selfgravitating particles in general relativity and the concept of an equation of state, Phys. Rev. 187, 1767 (1969).
  * Liebling and Palenzuela [2023] S. L. Liebling and C. Palenzuela, Dynamical boson stars, Living Rev. Rel. 26, 1 (2023), arXiv:1202.5809 [gr-qc] .
  * Sharma  _et al._ [2008] R. Sharma, S. Karmakar, and S. Mukherjee, Boson star and dark matter, (2008), arXiv:0812.3470 [gr-qc] .
  * Marsh [2016] D. J. E. Marsh, Axion Cosmology, Phys. Rept. 643, 1 (2016), arXiv:1510.07633 [astro-ph.CO] .
  * Vincent  _et al._ [2016] F. H. Vincent, Z. Meliani, P. Grandclement, E. Gourgoulhon, and O. Straub, Imaging a boson star at the Galactic center, Class. Quant. Grav. 33, 105015 (2016), arXiv:1510.04170 [gr-qc] .
  * Rosa and Rubiera-Garcia [2022] J. L. Rosa and D. Rubiera-Garcia, Shadows of boson and Proca stars with thin accretion disks, Phys. Rev. D 106, 084004 (2022), arXiv:2204.12949 [gr-qc] .
  * Grandclément [2017] P. Grandclément, Light rings and light points of boson stars, Phys. Rev. D 95, 084011 (2017), arXiv:1612.07507 [gr-qc] .
  * Cunha  _et al._ [2017] P. V. P. Cunha, E. Berti, and C. A. R. Herdeiro, Light-Ring Stability for Ultracompact Objects, Phys. Rev. Lett. 119, 251102 (2017), arXiv:1708.04211 [gr-qc] .
  * Cunha  _et al._ [2023] P. V. P. Cunha, C. Herdeiro, E. Radu, and N. Sanchis-Gual, Exotic Compact Objects and the Fate of the Light-Ring Instability, Phys. Rev. Lett. 130, 061401 (2023), arXiv:2207.13713 [gr-qc] .
  * Sennett  _et al._ [2017] N. Sennett, T. Hinderer, J. Steinhoff, A. Buonanno, and S. Ossokine, Distinguishing Boson Stars from Black Holes and Neutron Stars from Tidal Interactions in Inspiraling Binary Systems, Phys. Rev. D 96, 024002 (2017), arXiv:1704.08651 [gr-qc] .
  * Palenzuela  _et al._ [2017] C. Palenzuela, P. Pani, M. Bezares, V. Cardoso, L. Lehner, and S. Liebling, Gravitational Wave Signatures of Highly Compact Boson Star Binaries, Phys. Rev. D 96, 104058 (2017), arXiv:1710.09432 [gr-qc] .
  * Bezares  _et al._ [2022] M. Bezares, M. Bošković, S. Liebling, C. Palenzuela, P. Pani, and E. Barausse, Gravitational waves and kicks from the merger of unequal mass, highly compact boson stars, Phys. Rev. D 105, 064067 (2022), arXiv:2201.06113 [gr-qc] .
  * Croft  _et al._ [2023] R. Croft, T. Helfer, B.-X. Ge, M. Radia, T. Evstafyeva, E. A. Lim, U. Sperhake, and K. Clough, The gravitational afterglow of boson stars, Class. Quant. Grav. 40, 065001 (2023), arXiv:2207.05690 [gr-qc] .
  * Siemonsen and East [2023a] N. Siemonsen and W. E. East, Generic initial data for binary boson stars, Phys. Rev. D 108, 124015 (2023a), arXiv:2306.17265 [gr-qc] .
  * Siemonsen and East [2023b] N. Siemonsen and W. E. East, Binary boson stars: Merger dynamics and formation of rotating remnant stars, Phys. Rev. D 107, 124018 (2023b), arXiv:2302.06627 [gr-qc] .
  * Siemonsen [2024] N. Siemonsen, Nonlinear treatment of a black hole mimicker ringdown, (2024), arXiv:2404.14536 [gr-qc] .
  * Pacilio  _et al._ [2020] C. Pacilio, M. Vaglio, A. Maselli, and P. Pani, Gravitational-wave detectors as particle-physics laboratories: Constraining scalar interactions with a coherent inspiral model of boson-star binaries, Phys. Rev. D 102, 083002 (2020), arXiv:2007.05264 [gr-qc] .
  * Vaglio  _et al._ [2023] M. Vaglio, C. Pacilio, A. Maselli, and P. Pani, Bayesian parameter estimation on boson-star binary signals with a coherent inspiral template and spin-dependent quadrupolar corrections, Phys. Rev. D 108, 023021 (2023), arXiv:2302.13954 [gr-qc] .
  * Guo  _et al._ [2019] H.-K. Guo, K. Sinha, and C. Sun, Probing Boson Stars with Extreme Mass Ratio Inspirals, JCAP 09, 032, arXiv:1904.07871 [hep-ph] .
  * Calderón Bustillo  _et al._ [2021] J. Calderón Bustillo, N. Sanchis-Gual, A. Torres-Forné, J. A. Font, A. Vajpeyi, R. Smith, C. Herdeiro, E. Radu, and S. H. W. Leong, GW190521 as a Merger of Proca Stars: A Potential New Vector Boson of $8.7\times 10^{-13}$ eV, Phys. Rev. Lett. 126, 081101 (2021), arXiv:2009.05376 [gr-qc] .
  * Calderon Bustillo  _et al._ [2023] J. Calderon Bustillo, N. Sanchis-Gual, S. H. W. Leong, K. Chandra, A. Torres-Forne, J. A. Font, C. Herdeiro, E. Radu, I. C. F. Wong, and T. G. F. Li, Searching for vector boson-star mergers within LIGO-Virgo intermediate-mass black-hole merger candidates, Phys. Rev. D 108, 123020 (2023), arXiv:2206.02551 [gr-qc] .
  * [28] T. Evstafyeva and U. Sperhake, Boson star waveforms.
  * Evstafyeva  _et al._ [2024a] T. Evstafyeva, U. Sperhake, I. Romero-Shaw, and M. Agathos, Inspiral and merger of equal-mass boson star binary forming a black hole post-merger (2024a).
  * Evstafyeva  _et al._ [2024b] T. Evstafyeva, U. Sperhake, I. Romero-Shaw, and M. Agathos, Inspiral and merger of equal-mass boson star binary forming a boson star post-merger (2024b).
  * Lee and Pang [1992] T. D. Lee and Y. Pang, Nontopological solitons, Phys. Rept. 221, 251 (1992).
  * Lee [1987] T. D. Lee, Soliton Stars and the Critical Masses of Black Holes, Phys. Rev. D 35, 3637 (1987).
  * Evstafyeva  _et al._ [2023a] T. Evstafyeva, R. Rosca-Mead, U. Sperhake, and B. Brugmann, Boson stars in massless and massive scalar-tensor gravity, Phys. Rev. D 108, 104064 (2023a), arXiv:2310.05200 [gr-qc] .
  * Helfer  _et al._ [2022] T. Helfer, U. Sperhake, R. Croft, M. Radia, B.-X. Ge, and E. A. Lim, Malaise and remedy of binary boson-star initial data, Class. Quant. Grav. 39, 074001 (2022), arXiv:2108.11995 [gr-qc] .
  * Clough  _et al._ [2015] K. Clough, P. Figueras, H. Finkel, M. Kunesch, E. A. Lim, and S. Tunyasuvunakool, GRChombo : Numerical Relativity with Adaptive Mesh Refinement, Class. Quant. Grav. 32, 245011 (2015), arXiv:1503.03436 [gr-qc] .
  * Radia  _et al._ [2022] M. Radia, U. Sperhake, A. Drew, K. Clough, P. Figueras, E. A. Lim, J. L. Ripley, J. C. Aurrekoetxea, T. França, and T. Helfer, Lessons for adaptive mesh refinement in numerical relativity, Class. Quant. Grav. 39, 135006 (2022), arXiv:2112.10567 [gr-qc] .
  * Andrade  _et al._ [2021] T. Andrade _et al._ , GRChombo: An adaptable numerical relativity code for fundamental physics, J. Open Source Softw. 6, 3703 (2021), arXiv:2201.03458 [gr-qc] .
  * Sperhake [2007] U. Sperhake, Binary black-hole evolutions of excision and puncture data, Phys. Rev. D 76, 104015 (2007), gr-qc/0606079.
  * Alic  _et al._ [2012] D. Alic, C. Bona-Casas, C. Bona, L. Rezzolla, and C. Palenzuela, Conformal and covariant formulation of the Z4 system with constraint-violation damping, Phys. Rev. D 85, 064040 (2012), arXiv:1106.2254 [gr-qc] .
  * Campanelli  _et al._ [2006a] M. Campanelli, C. O. Lousto, P. Marronetti, and Y. Zlochower, Accurate evolutions of orbiting black-hole binaries without excision, Phys. Rev. Lett. 96, 111101 (2006a), arXiv:gr-qc/0511048 .
  * Baker  _et al._ [2006] J. G. Baker, J. Centrella, D.-I. Choi, M. Koppitz, and J. van Meter, Gravitational wave extraction from an inspiraling configuration of merging black holes, Phys. Rev. Lett. 96, 111102 (2006), arXiv:gr-qc/0511103 .
  * Adams  _et al._ [2019] M. Adams _et al._ ,  _Chombo Software Package for AMR Applications - Design Document_ , Tech. Rep. LBNL-6616E (Lawrence Berkeley National Laboratory, 2019).
  * Allen, G. and Goodale, T. and Massó, J. and Seidel, E. [1999] Allen, G. and Goodale, T. and Massó, J. and Seidel, E., The Cactus Computational Toolkit and Using Distributed Computing to Collide Neutron Stars, in  _Proceedings of Eighth IEEE International Symposium on High Performance Distributed Computing, HPDC-8, Redondo Beach, 1999_ (IEEE Press, Piscataway, New Jersey, United States, 1999).
  * Schnetter  _et al._ [2004] E. Schnetter, S. H. Hawley, and I. Hawke, Evolutions in 3-D numerical relativity using fixed mesh refinement, Class. Quant. Grav. 21, 1465 (2004), arXiv:gr-qc/0310042 .
  * Thornburg [2004] J. Thornburg, A Fast apparent horizon finder for three-dimensional Cartesian grids in numerical relativity, Class. Quant. Grav. 21, 743 (2004), gr-qc/0306056.
  * Evstafyeva  _et al._ [2023b] T. Evstafyeva, U. Sperhake, T. Helfer, R. Croft, M. Radia, B.-X. Ge, and E. A. Lim, Unequal-mass boson-star binaries: initial data and merger dynamics, Class. Quant. Grav. 40, 085009 (2023b), arXiv:2212.08023 [gr-qc] .
  * Mroue  _et al._ [2010] A. H. Mroue, H. P. Pfeiffer, L. E. Kidder, and S. A. Teukolsky, Measuring orbital eccentricity and periastron advance in quasi-circular black hole simulations, Phys. Rev. D 82, 124016 (2010), arXiv:1004.4697 [gr-qc] .
  * Hinder  _et al._ [2014] I. Hinder _et al._ , Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration, Class. Quant. Grav. 31, 025012 (2014), arXiv:1307.5307 [gr-qc].
  * Palenzuela  _et al._ [2007] C. Palenzuela, I. Olabarrieta, L. Lehner, and S. L. Liebling, Head-on collisions of boson stars, Phys. Rev. D 75, 064005 (2007), arXiv:gr-qc/0612067 .
  * Sanchis-Gual  _et al._ [2022] N. Sanchis-Gual, J. Calderón Bustillo, C. Herdeiro, E. Radu, J. A. Font, S. H. W. Leong, and A. Torres-Forné, Impact of the wavelike nature of Proca stars on their gravitational-wave emission, Phys. Rev. D 106, 124011 (2022), arXiv:2208.11717 [gr-qc] .
  * Ashton  _et al._ [2019] G. Ashton _et al._ , BILBY: A user-friendly Bayesian inference library for gravitational-wave astronomy, Astrophys. J. Suppl. 241, 27 (2019), arXiv:1811.02042 [astro-ph.IM] .
  * Romero-Shaw  _et al._ [2020] I. M. Romero-Shaw _et al._ , Bayesian inference for compact binary coalescences with bilby: validation and application to the first LIGO–Virgo gravitational-wave transient catalogue, Mon. Not. Roy. Astron. Soc. 499, 3295 (2020), arXiv:2006.00714 [astro-ph.IM] .
  * Husa  _et al._ [2016] S. Husa, S. Khan, M. Hannam, M. Pürrer, F. Ohme, X. Jiménez Forteza, and A. Bohé, Frequency-domain gravitational waves from nonprecessing black-hole binaries. I. New numerical waveforms and anatomy of the signal, Phys. Rev. D 93, 044006 (2016), arXiv:1508.07250 [gr-qc] .
  * Khan  _et al._ [2016] S. Khan, S. Husa, M. Hannam, F. Ohme, M. Pürrer, X. Jiménez Forteza, and A. Bohé, Frequency-domain gravitational waves from nonprecessing black-hole binaries. II. A phenomenological model for the advanced detector era, Phys. Rev. D 93, 044007 (2016), arXiv:1508.07253 [gr-qc] .
  * Khan  _et al._ [2019] S. Khan, K. Chatziioannou, M. Hannam, and F. Ohme, Phenomenological model for the gravitational-wave signal from precessing binary black holes with two-spin effects, Phys. Rev. D 100, 024059 (2019), arXiv:1809.10113 [gr-qc] .
  * Pratten  _et al._ [2021] G. Pratten _et al._ , Computationally efficient models for the dominant and subdominant harmonic modes of precessing binary black holes, Phys. Rev. D 103, 104056 (2021), arXiv:2004.06503 [gr-qc] .
  * Messina and Nagar [2017] F. Messina and A. Nagar, Parametrized-4.5PN TaylorF2 approximants and tail effects to quartic nonlinear order from the effective one body formalism, Phys. Rev. D 95, 124001 (2017), [Erratum: Phys.Rev.D 96, 049907(E) (2017)], arXiv:1703.08107 [gr-qc] .
  * Dietrich  _et al._ [2017] T. Dietrich, S. Bernuzzi, and W. Tichy, Closed-form tidal approximants for binary neutron star gravitational waveforms constructed from high-resolution numerical relativity simulations, Phys. Rev. D 96, 121501(R) (2017), arXiv:1706.02969 [gr-qc] .
  * Dietrich  _et al._ [2019] T. Dietrich, A. Samajdar, S. Khan, N. K. Johnson-McDaniel, R. Dudi, and W. Tichy, Improving the NRTidal model for binary neutron star systems, Phys. Rev. D 100, 044003 (2019), arXiv:1905.06011 [gr-qc] .
  * Nagar  _et al._ [2018] A. Nagar _et al._ , Time-domain effective-one-body gravitational waveforms for coalescing compact binaries with nonprecessing spins, tides and self-spin effects, Phys. Rev. D 98, 104052 (2018), arXiv:1806.01772 [gr-qc] .
  * Wade  _et al._ [2014] L. Wade, J. D. E. Creighton, E. Ochsner, B. D. Lackey, B. F. Farr, T. B. Littenberg, and V. Raymond, Systematic and statistical errors in a bayesian approach to the estimation of the neutron-star equation of state using advanced gravitational wave detectors, Phys. Rev. D 89, 103012 (2014), arXiv:1402.5156 [gr-qc] .
  * Campanelli  _et al._ [2006b] M. Campanelli, C. O. Lousto, and Y. Zlochower, Spinning-black-hole binaries: The orbital hang up, Phys. Rev. D 74, 041501(R) (2006b), gr-qc/0604012.
  * Note [1] https://github.com/GRTLCollaboration.

Supplementary Material

.

## Convergence tests

Figure S1: Convergence test of the compact configurations A17-d17 and A17-d20
of Table II in the main document. The difference between high and medium
resolutions has been re-scaled by factors $Q_{2}$ to $Q_{4}$, corresponding to
convergence of second to fourth order.

To evaluate the numerical error incurred in our simulations, we analyze their
convergence properties for three representative configurations. We start with
the GRChombo simulations of binaries from the compact families A17-d17 and

Figure S2: Convergence test of the configuration A147-d14 of Table II in the
main document for the GW strain (upper) and phase (lower panel). The
difference between high and medium resolutions has been scaled by factors
$Q_{4}$ and $Q_{7}$, corresponding to fourth- and seventh-order convergence.

A17-d20. Here we use $\Delta x_{\rm{low}}=1/28$, $\Delta x_{\rm{med}}=1/32$,
$\Delta x_{\rm{high}}=1/40$ for the low, medium and high resolutions,
respectively. The resulting convergence analysis for the GW signals extracted
at $R_{\rm ex}=140$ is shown in Fig. S1 and yields convergence between third
and fourth order. For the shorter A17-d17 configuration, Richardson
extrapolation yields an amplitude error of 2.5% and a phase error of 0.03
while we obtain 3% in the amplitude and 0.04 in the phase for the longer
A17-d20 binary. We quantify the error due to finite radius extraction through
extrapolation to infinity and thus find a phase error of $0.06$ and an
amplitude error of $1\%$. Overall, this brings the total numerical error
budget for the A17 family of runs to 4% in the amplitude and 0.1 in the phase.

For the less compact A147-d14 configuration, we display in Fig. S2 the
convergence properties obtained with the Lean code for the GW multipole
$h_{22}$ extracted at $R_{\rm ex}=240$ for resolutions $\Delta x_{\rm
low}=1/32$, $\Delta x_{\rm med}=1/36$ and $\Delta x_{\rm high}=1/40$. We
obtain fourth-order convergence for the amplitude and, during most of the
inspiral, for the phase. In the late inspiral and merger, the phase evolution
exhibits over convergence up to about seventh order, likely due to fortuitous
cancellations of different error contributions. We conservatively estimate the
numerical uncertainties for this configuration assuming exclusively fourth-
order convergence. For the amplitude, we obtain $0.5\,\%$ in the early
inspiral slowly increasing to about $3\,\%$ around merger. The phase error
peaks at about $0.09$ during the mid inspiral. The uncertainty due to finite
extraction radius is about $0.15$ or less in the GW phase and decreases from
$4\,\%$ (in the early inspiral) to $1\,\%$ (around merger) in the amplitude.
This results in an overall error budget of $0.2$ in the phase and $4\,\%$ in
the amplitude.

## Inference set-up

In this Section, we outline the injection and analysis set-up employed in our
parameter estimation in bilby.

Injections: We utilise LALsuite [1, 2] to perform reconstruction of our NR
signals. Prior to injecting, we remove junk radiation at the beginning of our
waveforms and prepare the NR data in line with the Format 1 standards of LIGO
Algorithms Library injections [3]. Unless otherwise stated all of our
injections use the same extrinsic parameters. In particular, we use a right
ascension $\alpha=1.375$, declination $\delta=-1.2108$, inclination angle
$\iota=\tfrac{\pi}{3}=60\degree$ and polarisation angle
$\psi=\tfrac{\pi}{2}=90\degree$. The total binary masses $M^{\rm
inj}_{\rm{tot}}\in[5,105]M_{\odot}$ in the source frame considered in this
work correspond to $M^{\rm{det}}_{\rm{tot}}\in[5,120]M_{\odot}$ in the
detector frame.

Parameter estimation: In all analyses, we use a sampling frequency of $4096$
Hz, a reference frequency of $50$ Hz and a minimum frequency set by the
starting frequency of our NR waveforms. When the starting frequency of our
injected waveforms drops below 20 Hz, we set the minimum frequency to 20 Hz.
The NR signals are injected into the Hanford and Livingston detectors,
assuming noise curves from the 4th observing run (O4) [4]. For all of the PE
runs reported in the main text, we initialise the sampler with 1000 points –
for some test runs included in Table 1 below, we have used 500 points instead
– and marginalise over time and luminosity distance. For approximants
including only the $(22)$-mode, we additionally marginalise over the phase. We
have used a range of nested samplers, such as dynesty [5], cpnest [6] and
nessai [7, 8, 9], and have found good agreement between them. The sampling
space is determined by bilby’s default BBH and BNS priors (cf. Tables 1 and 2
of Ashton  _et al._ [10]). However, we increase the spin magnitude ($a_{1}$,
$a_{2}$) upper limits to $0.99$. When using non-precessing models, the prior
on the spin magnitudes is a uniform distribution $\chi_{1},\chi_{2}\in[-1,1]$,
where $\chi_{1},\chi_{2}$ denote the dimensionless spin projections onto the
orbital angular momentum. This range includes binaries with anti-aligned
spins. For BNS models, we additionally increase the upper limits in the prior
of the dimensionless tidal deformability parameters ($\Lambda_{1}$,
$\Lambda_{2}$) to $20000$. We find this choice necessary for injections of the
less compact A147 family in order to circumvent one of the tidal deformability
numbers railing against the upper prior bound.

We have tested the quality of our parameter estimation using injections from
different resolutions and extraction radii, and have found consistent results.

## Black-hole and boson-star signals

In this section, we compare the IMR signals of our BS families with those from
equal-mass non-spinning BH binaries and discuss the varying degrees of
deviation from the BH case which we observe. We start this discussion by
exploring first what behaviour we would expect theoretically. For this
purpose, we follow the analysis of the scalar-field interaction outlined in
Appendix B of Ref. [11] and in particular consider the energy density of a
scalar field $\varphi$ in the flat-space limit,

$\rho=\frac{1}{2}\left(|\Pi|^{2}+|\partial_{i}\varphi|^{2}+V(\varphi)\right)\,.$
(S1)

During the plunge and merger phase of

Figure S3: Comparison of amplitude (left) and phase (right) of the dominant
(22)-modes obtained for the in-phase BS (A17-d21), dephased (A17-d21-p090),
anti-phase (A17-d21-p180), anti-BS (A17-d21-e1) and BH binaries. Both
amplitude and phase have been aligned such that the peak amplitudes coincide
in time. The anti-BS signal exhibits the best agreement with the BH waveform,
whereas the in-phase and anti-phase configurations result in the largest
deviations from the BH signal.

a binary the two BSs’ scalar fields overlap and we can approximate the
resulting field and its time derivative as a superposition given by
$\varphi=\varphi_{1}+\varphi_{2}$ and $\Pi=\Pi_{1}+\Pi_{2}$. This results in a
combined energy density

$\rho=\rho_{1}+\rho_{2}+\Delta,$ (S2)

where $\rho_{1},\rho_{2}$ are the individual energy densities of the stars as
in Eq. (S1) and $\Delta$ is the interaction potential; cf. Eq.(B3) of Ref
[11]. This interaction term is composed of mixed products of the scalar field,
such as $\varphi_{1}\bar{\varphi}_{2}$ or $\Pi_{1}\bar{\Pi}_{2}$, and
therefore vanishes in the limit of large separations. We next recall that the
two BS scalar fields’ phase offset and relative rotation in the complex plane
are determined by the parameters $\delta\phi$ and $\epsilon$, respectively.
For an equal-mass binary system, the scalar field profiles of the two stars
forming a binary thus acquire the following forms,

$\displaystyle\varphi_{1}$ $\displaystyle=A(t,r)e^{\mathrm{i}\mkern
1.0mu\omega t},$ (S3) $\displaystyle\varphi_{2}$
$\displaystyle=A(t,r)e^{\mathrm{i}\mkern 1.0mu(\epsilon\omega t+\delta\phi)}.$
(S4)

We assume that the scalar field amplitude is a slowly varying function of time
so that the dynamical part is dominated by the exponential factor
$e^{\mathrm{i}\mkern 1.0mu\omega t}$. Evaluating the interaction potential
$\Delta$ for the equal-mass (i) $\epsilon=1$, $\delta\phi=0$ (in-phase), (ii)
$\epsilon=1$, $\delta\phi=\pi/2$ (dephased), (iii) $\epsilon=1$,
$\delta\phi=\pi$ (anti-phase), and (iv) $\epsilon=-1$, $\delta\phi=0$ (anti-
BS) configurations, we then find

$\displaystyle\Delta_{\rm{BS}}$ $\displaystyle=\Delta_{0},$ (S5)
$\displaystyle\Delta_{\delta\phi=\frac{\pi}{2}}$ $\displaystyle=0,$ (S6)
$\displaystyle\Delta_{\delta\phi=\pi}$ $\displaystyle=-\Delta_{0},$ (S7)
$\displaystyle\Delta_{\rm{anti-BS}}$ $\displaystyle=\Delta_{0}\rm{cos}(2\omega
t),$ (S8)

where $\Delta_{0}$ is strictly non-negative. Note that the anti-BS
configuration results in an interaction potential with explicitly harmonic
time dependence that oscillates between the $\Delta$ values of the in-phase
and anti-phase binaries. If the time-scale of the late inspiral and plunge is
much longer than the scalar oscillation period of individual BSs, the
interaction contribution to the energy density averages out to zero. The
interaction potential for the $\delta\phi=\pi/2$ binary, in turn, vanishes
completely without any oscillating behaviour. Therefore, we may expect that
the anti-BS and $\delta\phi=\pi/2$ configurations will bear closest
resemblance to the BH case, where scalar self-interactions are absent by
construction. As we will see next, this expectation is largely, but not
completely, borne out by the empirical results.

For testing this hypothesis, we compare in Fig. S3 the aligned GW amplitude
and phase obtained for the different BS configurations with those obtained in
Ref. [12] for an equal-mass non-spinning BH binary. In accordance with our
above discussion, the anti-BS binary exhibits excellent agreement with the BH
results and displays an oscillatory pattern in the GW amplitude commensurate
with the expected oscillation of the interaction term $\Delta_{\rm anti-BS}$.
Its amplitude and phase furthermore fall into the range between the in-phase
and anti-phase binaries. The $\delta\phi=\pi/2$ binary, however, does not
quite fulfill the expectations from our theoretical analysis; even though its
amplitude and phase match the BH signal better than the in-phase and anti-
phase binaries do, its deviations exceed those of the (averaged) anti-BS
signal. This feature may simply mark the limitations of the above flat-space
analysis; and yet there remains the question why the prediction works so well
for the anti-BS configuration but not for the $\delta\phi=\pi/2$ case. At
present, we do not have a fully satisfactory answer to this question. A more
comprehensive exploration of the BS model parameter space may shed more light
on this puzzle.

## Injections

We present in Table 1 a list of injections of boson-star (BS) waveforms
together with the recovered parameters and consistency checks of the recovered
signals. We sort this table by the different families of non-spinning BS
binaries listed in Table III of the main document. The varying injected
parameters, namely the component masses $m_{1}$, $m_{2}$ in the source frame
and the luminosity distance $d_{\rm L}$, are listed along with the resulting
injected optimal SNR values for the Hanford and Livingston detectors,
$\rho^{\rm H1}$ and $\rho^{\rm L1}$. Each injection is analyzed using a
waveform approximant abbreviated as follows.

D | = | IMRPhenomD
---|---|---
F2 | = | TaylorF2
Pv2T | = | IMRPhenomPv2_NRTidal
Pv3 | = | IMRPhenomPv3
TEOB | = | TEOBResumS
XP | = | IMRPhenomXP
XPHM | = | IMRPhenomXPHM

The recovery is performed using the listed samplers with $N_{s}$ points. Next,
we report the recovered parameters which are obtained from the posterior
distributions with $90\,\%$ confidence intervals: the component masses $m_{1}$
and $m_{2}$, the luminosity distance $d_{L}$, the dimensionless spins 222For
non-precessing models, we report projections of the dimensionless spins onto
the orbital angular momentum, $\chi_{1}$, $\chi_{2}$, which are allowed to be
negative. $a_{1}$ and $a_{2}$, the effective spin $\chi_{\rm eff}$, the
precession spin parameter $\chi_{p}$ and the tidal deformation parameters
$\Lambda_{1}$ and $\Lambda_{2}$. The recovered SNR is given for the two
detectors as $\rho^{\rm H1}$ and $\rho^{\rm L1}$ and calculated from the
inferred parameters maximising the joint-log-likelihood. We flag with ticks or
crosses whether the residual is compatible with Gaussian noise and quantify
the significance of a detection with the Bayes factor
$\log(\mathcal{B}^{\rm{S}}_{\rm{N}})$.

Table 1:  List of all our injections for the BS families listed in Table I of the main document. We report the injected component masses, $m_{1}$ and $m_{2}$, luminosity distance $d_{L}$ and the corresponding SNR values for the H1 and L1 detectors. The recovery is performed using the specified approximants and samplers initialised with $N_{s}$ sampling points. The recovered values for the masses, luminosity distance, the dimensionless spins $a_{1}$ and $a_{2}$, the effective and precession spin parameters $\chi_{\rm eff}$, $\chi_{\rm p}$ and the tidal deformability parameters $\Lambda_{1}$, $\Lambda_{2}$ are given in the form of median values with $90\,\%$ confidence intervals. We additionally list the recovered optimal SNR and Bayes evidence factors $\log(\mathcal{B}^{\rm{S}}_{\rm{N}})$ and mark residuals consistent (inconsistent) with Gaussian noise by a ✓(✗) symbol.  | Injection | Analysis | Recovery | Consistency
---|---|---|---|---
Family | $\frac{m_{1}}{M_{\odot}}$ | $\frac{m_{2}}{M_{\odot}}$ | $\frac{d_{L}}{\rm Mpc}$ | $\rho^{\rm H1}$ | $\rho^{\rm L1}$ | Appr. | Sampler | $N_{s}$ | $\frac{m_{1}}{M_{\odot}}$ | $\frac{m_{2}}{M_{\odot}}$ | $\frac{d_{L}}{\rm Mpc}$ | $a_{1}$ | $a_{2}$ | $\chi_{\rm eff}$ | $\chi_{\rm p}$ | $\Lambda_{1}$ | $\Lambda_{2}$ | $\rho^{\rm H1}$ | $\rho^{\rm L1}$ | Res.(H,L) | $\log(\mathcal{B}^{\rm{S}}_{\rm{N}})$
A147-d14 | 2.48 | 2.48 | 30 | 24.5 | 17.4 | Pv2T | nessai | 1000 | $3.70^{+0.12}_{-0.10}$ | $1.75^{+0.05}_{-0.06}$ | $51.2^{+24.3}_{-16.9}$ | – | – | – | – | $10407^{+1915}_{-1795}$ | $10002^{+8973}_{-8897}$ | 21.7 | 14.7 | (✗,✗) | 316
A147-d14 | 2.48 | 2.48 | 30 | 24.5 | 17.4 | Pv2T | nessai | 1000 | $3.64^{+0.15}_{-0.13}$ | $1.70^{+0.15}_{-0.21}$ | $49.8^{+9.9}_{-11.3}$ | $0.78^{+0.18}_{-0.29}$ | $0.47^{+0.44}_{-0.41}$ | $-0.33^{+0.27}_{-0.28}$ | $0.53^{+0.26}_{-0.20}$ | $6102^{+2519}_{-2352}$ | $10302^{+8602}_{-8881}$ | 22.1 | 17.0 | (✓,✓) | 341
A147-d14 | 2.48 | 2.48 | 31.25 | 23.8 | 17.1 | Pv2T | nessai | 1000 | $3.57_{-0.11}^{+0.20}$ | $1.59_{-0.19}^{+0.16}$ | $54.3_{-13.1}^{+8.6}$ | $0.79_{-0.38}^{+0.18}$ | $0.52_{-0.46}^{+0.42}$ | $-0.40_{-0.25}^{+0.34}$ | $0.47_{-0.22}^{+0.30}$ | $7894_{-3089}^{+2791}$ | $9998_{-8867}^{+8902}$ | 22.5 | 16.0 | (✓,✓) | 350
A147-d14 | 2.48 | 2.48 | 31.25 | 23.8 | 17.1 | XP | nessai | 1000 | $6.92^{+0.56}_{-0.33}$ | $1.07^{+0.07}_{-0.08}$ | $74.0^{+23.9}_{-28.5}$ | – | – | – | – | – | – | 17.2 | 12.6 | (✓,✓) | 214
A147-d14 | 2.48 | 2.48 | 31.25 | 23.8 | 17.1 | XP | nessai | 1000 | $5.31^{+1.23}_{-0.72}$ | $1.37^{+0.18}_{-0.21}$ | $432^{+63}_{-368}$ | $0.69^{+0.16}_{-0.16}$ | $0.80^{+0.17}_{-0.51}$ | $0.00^{+0.14}_{-0.12}$ | $0.68^{+0.13}_{-0.16}$ | – | – | 3.14 | 1.66 | (✗,✗) | 237
A147-d14 | 4.98 | 4.98 | 20 | 96.2 | 68.1 | XP | nessai | 1000 | $13.7_{-0.06}^{+0.05}$ | $1.72_{-0.01}^{+0.01}$ | $26.0_{-0.84}^{+0.96}$ | $0.86_{-0.01}^{+0.01}$ | $0.98_{-0.05}^{+0.01}$ | $-0.74_{-0.02}^{+0.02}$ | $0.46_{-0.01}^{+0.01}$ | – | – | 75.6 | 51.6 | (✗,✗) | 4221
A147-d14 | 4.94 | 4.94 | 50 | 38.5 | 27.2 | XP | nessai | 1000 | $15.0_{-0.4}^{+0.2}$ | $1.90_{-0.02}^{+0.06}$ | $56.1_{-3.8}^{+8.2}$ | $0.90_{-0.02}^{+0.04}$ | $0.87_{-0.39}^{+0.11}$ | $-0.57_{-0.03}^{+0.05}$ | $0.71_{-0.02}^{+0.03}$ | – | – | 26.6 | 17.3 | (✓,✓) | 674
A147-d14 | 4.93 | 4.93 | 62.5 | 30.8 | 21.8 | XP | nessai | 1000 | $15.8_{-0.2}^{+0.2}$ | $1.99_{-0.02}^{+0.03}$ | $140_{-68}^{+35}$ | – | – | – | – | – | – | 19.9 | 14.2 | (✓,✓) | 286
A147-d14 | 4.93 | 4.93 | 62.5 | 30.8 | 21.8 | XP | nessai | 1000 | $16.1^{+0.2}_{-0.7}$ | $2.04^{+0.04}_{-0.07}$ | $110^{+190}_{-47}$ | – | – | – | – | – | – | 18.8 | 14.1 | (✓,✓) | 253
A147-d14 | 4.93 | 4.93 | 62.5 | 30.8 | 21.8 | XP | nessai | 1000 | $13.1^{+0.1}_{-0.1}$ | $1.65^{+0.02}_{-0.02}$ | $75.4^{+17.3}_{-10.0}$ | $0.99^{+0.00}_{-0.01}$ | $0.87^{+0.11}_{-0.39}$ | $-0.91^{+0.06}_{-0.03}$ | $0.32^{+0.05}_{-0.08}$ | – | – | 25.2 | 14.7 | (✓,✓) | 378
A147-d14 | 4.93 | 4.93 | 62.5 | 30.8 | 21.8 | F2 | nessai | 1000 | $9.83_{-1.13}^{+3.11}$ | $2.06_{-0.29}^{+0.23}$ | $171_{-59}^{+42}$ | $-0.83_{-0.11}^{+0.31}$ | $-0.05_{-0.52}^{+0.41}$ | $-0.69_{-0.11}^{+0.23}$ | – | $511_{-279}^{+235}$ | $2544_{-2221}^{+2136}$ | 21.4 | 15.6 | (✓,✓) | 342
A147-d14 | 4.93 | 4.93 | 62.5 | 30.8 | 21.8 | TEOB | nessai | 1000 | $12.9_{-0.13}^{+0.14}$ | $1.62_{-0.02}^{+0.02}$ | $98.4_{-40.6}^{+37.2}$ | $-0.98_{-0.01}^{+0.02}$ | $-0.84_{-0.12}^{+0.27}$ | $-0.96_{-0.02}^{+0.03}$ | – | – | – | 21.0 | 14.1 | (✓,✓) | 337
A147-d14 | 4.89 | 4.89 | 100 | 19.2 | 13.6 | F2 | nessai | 1000 | $13.2^{+1.0}_{-1.3}$ | $1.93^{+0.20}_{-0.15}$ | $273^{+113}_{-101}$ | – | – | – | – | $1666^{+601}_{-344}$ | $2514^{+2161}_{-2201}$ | 14.1 | 11.6 | (✓,✓) | 111
A147-d14 | 4.89 | 4.89 | 100 | 19.2 | 13.6 | F2 | nessai | 1000 | $10.2^{+2.9}_{-2.3}$ | $2.18^{+0.50}_{-0.39}$ | $294^{+89}_{-110}$ | $-0.61^{+0.22}_{-0.25}$ | $-0.03^{+0.39}_{-0.50}$ | $-0.51^{+0.16}_{-0.17}$ | – | $688^{+724}_{-356}$ | $2518^{+2186}_{-2192}$ | 14.8 | 10.6 | (✓,✓) | 114
A147-d14 | 9.73 | 9.73 | 125 | 38.7 | 27.2 | XPHM | cpnest | 1000 | $23.6^{+0.8}_{-1.0}$ | $4.60^{+0.41}_{-0.11}$ | $477^{+112}_{-166}$ | – | – | – | – | – | – | 18.0 | 12.1 | (✗,✓) | 193
A147-d14 | 9.73 | 9.73 | 125 | 38.7 | 27.2 | XPHM | cpnest | 1000 | $20.3^{+1.4}_{-3.6}$ | $4.97^{+0.86}_{-0.20}$ | $227^{+32}_{-31}$ | $0.70^{+0.25}_{-0.14}$ | $0.63^{+0.34}_{-0.56}$ | $-0.55^{+0.15}_{-0.22}$ | $0.37^{+0.11}_{-0.06}$ | – | – | 22.6 | 15.1 | (✗,✗) | 318
A147-d14 | 9.73 | 9.73 | 125 | 38.7 | 27.2 | XP | nessai | 1000 | $25.3^{+1.8}_{-0.9}$ | $4.62^{+0.20}_{-0.15}$ | $473^{+156}_{-184}$ | – | – | – | – | – | – | 18.6 | 11.6 | (✓,✓) | 181
A147-d14 | 9.73 | 9.73 | 125 | 38.7 | 27.2 | XP | nessai | 1000 | $19.4^{+0.8}_{-3.1}$ | $4.79^{+1.31}_{-0.06}$ | $247^{+28}_{-46}$ | $0.96^{+0.03}_{-0.21}$ | $0.84^{+0.14}_{-0.37}$ | . $-0.76^{+0.16}_{-0.08}$ | $0.38^{+0.10}_{-0.06}$ | – | – | 22.6 | 16.1 | (✗,✓) | 340
A147-d14 | 19.0 | 19.0 | 250 | 43.4 | 30.4 | XP | nessai | 1000 | $26.5^{+2.5}_{-1.6}$ | $24.7^{+2.1}_{-1.7}$ | $1119^{+324}_{-463}$ | – | – | – | – | – | – | 21.0 | 15.1 | (✗,✓) | 284
A147-d14 | 19.0 | 19.0 | 250 | 43.4 | 30.4 | XP | nessai | 1000 | $42.6^{+1.3}_{-1.3}$ | $19.3^{+0.7}_{-0.7}$ | $101^{+4}_{-1}$ | $0.33^{+0.05}_{-0.05}$ | $0.66^{+0.15}_{-0.12}$ | $0.03^{+0.07}_{-0.08}$ | $0.06^{+0.01}_{-0.01}$ | – | – | 32.3 | 19.7 | (✓,✓) | 660
A147-d14 | 28.2 | 28.2 | 300 | 57.0 | 39.9 | XP | nessai | 1000 | $39.4^{+3.0}_{-2.5}$ | $37.0^{+2.7}_{-2.8}$ | $889^{+376}_{-362}$ | – | – | – | – | – | – | 30.2 | 21.2 | (✗,✗) | 642
A147-d14 | 28.2 | 28.2 | 300 | 57.0 | 39.9 | XP | nessai | 1000 | $68.1^{+2.7}_{-2.4}$ | $47.5^{+1.1}_{-1.7}$ | $103^{+9}_{-3}$ | $0.96^{+0.02}_{-0.07}$ | $0.65^{+0.05}_{-0.04}$ | $0.59^{+0.03}_{-0.03}$ | $0.42^{+0.03}_{-0.03}$ | – | – | 42.8 | 25.4 | (✓,✓) | 1243
A147-d14 | 37.9 | 37.9 | 250 | 94.7 | 66.2 | XP | nessai | 1000 | $53.9_{-2.4}^{+3.4}$ | $51.4_{-2.6}^{+3.2}$ | $721_{-300}^{+198}$ | – | – | – | – | – | – | 52.6 | 35.7 | (✗,✗) | 2002
A147-d14 | 37.9 | 37.9 | 250 | 94.7 | 66.2 | XP | nessai | 1000 | $67.4_{-0.38}^{+0.42}$ | $60.2_{-0.33}^{+0.35}$ | $124_{-6}^{+5}$ | $0.83_{-0.01}^{+0.00}$ | $0.99_{-0.01}^{+0.00}$ | $-0.02_{-0.00}^{+0.00}$ | $0.71_{-0.01}^{+0.01}$ | – | – | 78.0 | 44.9 | (✗,✗) | 4041
A147-d14 | 36.9 | 36.9 | 400 | 61.0 | 42.3 | XPHM | cpnest | 500 | $83.9^{+3.5}_{-2.7}$ | $57.6^{+4.2}_{-3.5}$ | $103^{+10}_{-2}$ | $0.57^{+0.10}_{-0.09}$ | $0.98^{+0.01}_{-0.02}$ | $0.49^{+0.06}_{-0.05}$ | $0.47^{+0.06}_{-0.05}$ | – | – | 47.6 | 26.8 | (✓,✓) | 1560
A147-d14 | 36.2 | 36.2 | 500 | 47.3 | 33.1 | XP | nessai | 1000 | $50.2_{-3.9}^{+5.6}$ | $44.8_{-4.8}^{+4.6}$ | $1350_{-533}^{+373}$ | – | – | – | – | – | – | 26.5 | 18.2 | (✗,✓) | 457
A147-d14 | 36.2 | 36.2 | 500 | 47.3 | 33.1 | XP | nessai | 1000 | $69.1_{-0.9}^{+0.8}$ | $64.7_{-0.9}^{+0.8}$ | $116_{-12}^{+15}$ | $0.97_{-0.05}^{+0.02}$ | $0.59_{-0.03}^{+0.02}$ | $0.22_{-0.01}^{+0.01}$ | $0.80_{-0.05}^{+0.04}$ | – | – | 38.1 | 23.7 | (✓,✓) | 919
A147-d14 | 36.2 | 36.2 | 500 | 47.3 | 33.1 | D | nessai | 1000 | $45.6_{-2.3}^{+3.3}$ | $43.2_{-2.4}^{+3.0}$ | $826_{-358}^{+245}$ | $-0.97_{-0.01}^{+0.03}$ | $-0.97_{-0.02}^{+0.03}$ | $-0.97_{-0.01}^{+0.02}$ | – | – | – | 31.5 | 19.8 | (✓,✓) | 671
A147-d14 | 36.2 | 36.2 | 500 | 47.3 | 33.1 | XPHM | cpnest | 1000 | $64.7^{+1.0}_{-1.0}$ | $36.8^{+1.7}_{-1.6}$ | $247^{+35}_{-36}$ | $0.98^{+0.01}_{-0.02}$ | $0.96^{+0.02}_{-0.08}$ | $-0.42^{+0.04}_{-0.05}$ | $0.41^{+0.06}_{-0.06}$ | – | – | 41.0 | 21.7 | (✓,✓) | 955
A147-d14 | 44.3 | 44.3 | 625 | 48.4 | 33.8 | XP | nessai | 1000 | $64.2^{+6.4}_{-5.0}$ | $59.2^{+5.6}_{-5.2}$ | $1345^{+509}_{-539}$ | – | – | – | – | – | – | 30.5 | 21.0 | (✓,✓) | 644
A147-d14 | 44.3 | 44.3 | 625 | 48.4 | 33.8 | XP | nessai | 1000 | $96.1^{+1.4}_{-2.4}$ | $45.5^{+2.4}_{-1.8}$ | $106^{+13}_{-6}$ | $0.98^{+0.01}_{-0.04}$ | $0.96^{+0.02}_{-0.07}$ | $-0.64^{0.03}_{-0.03}$ | $0.53^{+0.06}_{-0.06}$ | – | – | 41.0 | 20.7 | (✓,✓) | 1017
A147-d14 | 52.1 | 52.1 | 750 | 48.6 | 34.0 | XP | nessai | 1000 | $76.7^{+6.6}_{-5.8}$ | $71.6^{+6.3}_{-5.6}$ | $1305^{+560}_{-492}$ | – | – | – | – | – | – | 33.1 | 23.0 | (✓,✓) | 753
A147-d14 | 52.1 | 52.1 | 750 | 48.6 | 34.0 | XP | nessai | 1000 | $96.9^{+0.8}_{-1.3}$ | $86.3^{+1.1}_{-1.3}$ | $102^{+6}_{-2}$ | $0.98^{+0.01}_{-0.04}$ | $0.97^{+0.02}_{-0.04}$ | $-0.51^{0.02}_{-0.03}$ | $0.85^{+0.02}_{-0.03}$ | – | – | 40.5 | 24.1 | (✓,✓) | 1047

| Injection | Analysis | Recovery | Consistency
---|---|---|---|---
Family | $\frac{m_{1}}{M_{\odot}}$ | $\frac{m_{2}}{M_{\odot}}$ | $\frac{d_{L}}{\rm Mpc}$ | $\rho^{\rm H1}$ | $\rho^{\rm L1}$ | Appr. | Sampler | $N_{s}$ | $\frac{m_{1}}{M_{\odot}}$ | $\frac{m_{2}}{M_{\odot}}$ | $\frac{d_{L}}{\rm Mpc}$ | $a_{1}$ | $a_{2}$ | $\chi_{\rm eff}$ | $\chi_{\rm p}$ | $\Lambda_{1}$ | $\Lambda_{2}$ | $\rho^{\rm H1}$ | $\rho^{\rm L1}$ | Res.(H,L) | $\log(\mathcal{B}^{\rm{S}}_{\rm{N}})$
A17-d17 | 2.48 | 2.48 | 31.25 | 16.5 | 11.8 | Pv2T | nessai | 1000 | $2.75_{-0.31}^{+0.67}$ | $2.19_{-0.41}^{+0.25}$ | $55.0_{-21.6}^{+20.2}$ | $0.57_{-0.48}^{+0.37}$ | $0.53_{-0.47}^{+0.41}$ | $0.30_{-0.24}^{+0.23}$ | $0.44_{-0.29}^{+0.34}$ | $79.8_{-73.2}^{+257}$ | $175_{-158}^{+357}$ | 16.3 | 12.9 | (✓,✓) | 154
A17-d17 | 2.48 | 2.48 | 31.25 | 16.3 | 11.5 | XP | nessai | 1000 | $2.80_{-0.39}^{+0.70}$ | $1.98_{-0.46}^{+0.35}$ | $52.2_{-22.2}^{+17.0}$ | – | – | – | – | – | – | 16.4 | 11.2 | (✓,✓) | 151
A17-d17 | 2.48 | 2.48 | 31.25 | 16.3 | 11.5 | XP | nessai | 1000 | $3.33_{-0.85}^{+1.48}$ | $1.76_{-0.49}^{+0.58}$ | $48.2_{-16.9}^{+19.4}$ | $0.52_{-0.43}^{+0.41}$ | $0.52_{-0.45}^{+0.42}$ | $0.13_{-0.20}^{+0.22}$ | $0.49_{-0.34}^{+0.41}$ | – | – | 15.2 | 10.4 | (✓,✓) | 153
A17-d17 | 4.93 | 4.93 | 62.5 | 24.2 | 17.2 | F2 | nessai | 1000 | $10.7_{-4.9}^{+3.0}$ | $2.44_{-0.56}^{+2.01}$ | $126_{-41}^{+35}$ | $0.41_{-0.09}^{+0.17}$ | $0.04_{-0.45}^{+0.54}$ | $0.35_{-0.06}^{+0.07}$ | – | $0.80_{-0.75}^{+11.3}$ | $94.0_{-88.2}^{+618}$ | 22.3 | 17.7 | (✓,✓) | 357
A17-d17 | 4.93 | 4.93 | 62.5 | 24.2 | 17.2 | XP | nessai | 1000 | $7.08_{-0.79}^{+0.59}$ | $3.00_{-0.31}^{+0.48}$ | $98.7_{-38.8}^{+24.4}$ | – | – | – | – | – | – | 24.6 | 18.2 | (✓,✓) | 406
A17-d17 | 4.93 | 4.93 | 62.5 | 24.2 | 17.2 | XP | nessai | 1000 | $6.24_{-1.55}^{+1.84}$ | $3.34_{-0.69}^{+0.95}$ | $103.6_{-33.7}^{+19.9}$ | $0.21_{-0.19}^{+0.38}$ | $0.42_{-0.37}^{+0.46}$ | $-0.08_{-0.17}^{+0.18}$ | $0.23_{-0.17}^{+0.32}$ | – | – | 21.6 | 16.2 | (✓,✓) | 406
A17-d17 | 9.73 | 9.73 | 125 | 31.0 | 22.0 | XP | nessai | 1000 | $14.7_{-0.9}^{+0.9}$ | $5.43_{-0.42}^{+0.49}$ | $197_{-74}^{+45}$ | – | – | – | – | – | – | 31.7 | 22.2 | (✓,✓) | 685
A17-d17 | 9.73 | 9.73 | 125 | 31.0 | 22.0 | XP | nessai | 1000 | $10.8_{-1.2}^{+1.0}$ | $7.09_{-0.59}^{+0.84}$ | $125_{-40}^{+84}$ | $0.51_{-0.22}^{+0.26}$ | $0.57_{-0.36}^{+0.26}$ | $-0.20_{-0.07}^{+0.07}$ | $0.40_{-0.16}^{+0.18}$ | – | – | 33.1 | 21.4 | (✓,✓) | 697
A17-d17 | 19.0 | 19.0 | 250 | 35.0 | 24.8 | TEOB | nessai | 1000 | $17.7_{-1.5}^{+2.3}$ | $14.8_{-1.8}^{+1.3}$ | $376_{-166}^{+95}$ | $-0.41_{-0.36}^{+0.41}$ | $-0.31_{-0.51}^{+0.41}$ | $-0.37_{-0.06}^{+0.06}$ | – | – | – | 34.1 | 22.8 | (✓,✓) | 806
A17-d17 | 19.0 | 19.0 | 250 | 35.0 | 24.8 | D | nessai | 1000 | $17.7_{-1.6}^{+2.5}$ | $14.5_{-1.8}^{+1.4}$ | $373_{-168}^{+101}$ | $-0.41_{-0.37}^{+0.37}$ | $-0.39_{-0.44}^{+0.43}$ | $-0.40_{-0.06}^{+0.06}$ | – | – | – | 33.5 | 22.3 | (✓,✓) | 792
A17-d17 | 19.0 | 19.0 | 250 | 35.0 | 24.8 | F2 | nessai | 1000 | $50.9_{-4.6}^{+3.1}$ | $6.86_{-0.37}^{+0.64}$ | $523_{-243}^{+152}$ | $0.39_{-0.03}^{+0.04}$ | $-0.01_{-0.48}^{+0.46}$ | $0.34_{-0.03}^{+0.03}$ | – | $0.20_{-0.18}^{+0.35}$ | $203_{-180}^{+401}$ | 34.1 | 22.5 | (✓,✓) | 765
A17-d17 | 19.0 | 19.0 | 250 | 35.0 | 24.8 | XP | nessai | 1000 | $29.9_{-4.1}^{+1.9}$ | $9.57_{-1.34}^{+0.92}$ | $410_{-213}^{+917}$ | – | – | – | – | – | – | 32.2 | 21.7 | (✓,✓) | 762
A17-d17 | 19.0 | 19.0 | 250 | 35.0 | 24.8 | XP | nessai | 1000 | $18.9_{-5.85}^{+2.04}$ | $13.7_{-4.4}^{+1.5}$ | $302_{-125}^{+3203}$ | $0.56_{-0.24}^{+0.28}$ | $0.56_{-0.33}^{+0.28}$ | $-0.35_{-0.08}^{+0.07}$ | $0.35_{-0.15}^{+0.16}$ | – | – | 33.5 | 23.5 | (✓,✓) | 796
A17-d17 | 29.5 | 29.5 | 75 | 171.6 | 122.0 | XPHM | dynesty | 500 | $30.5_{-0.07}^{+0.06}$ | $26.4_{-0.05}^{+0.08}$ | $58.9_{-2.7}^{+2.9}$ | $0.63_{-0.01}^{+0.01}$ | $0.98_{-0.02}^{+0.01}$ | $-0.12_{-0.00}^{+0.00}$ | $0.15_{-0.01}^{+0.01}$ | – | – | 170.0 | 115.9 | (✓,✓) | 21637
A17-d17 | 29.0 | 29.0 | 150 | 85.8 | 61.0 | XP | nessai | 1000 | $30.2_{-0.14}^{+0.13}$ | $26.0_{-0.09}^{+0.14}$ | $116_{-10}^{+11}$ | $0.61_{-0.02}^{+0.02}$ | $0.97_{-0.04}^{+0.02}$ | $-0.12_{-0.01}^{+0.01}$ | $0.15_{-0.01}^{+0.02}$ | – | – | 86.2 | 60.5 | (✓,✓) | 5413
A17-d17 | 28.7 | 28.7 | 200 | 64.3 | 45.7 | XP | nessai | 1000 | $30.0_{-0.23}^{+0.24}$ | $25.9_{-0.18}^{+0.25}$ | $147_{-23}^{+25}$ | $0.61_{-0.03}^{+0.02}$ | $0.96_{-0.06}^{+0.02}$ | $-0.12_{-0.01}^{+0.01}$ | $0.15_{-0.02}^{+0.02}$ | – | – | 64.0 | 45.2 | (✓,✓) | 3032
A17-d17 | 27.8 | 27.8 | 375 | 34.3 | 24.4 | XP | nessai | 1000 | $33.5_{-3.5}^{+1.9}$ | $19.6_{-1.0}^{+2.9}$ | $665_{-237}^{+159}$ | – | – | – | – | – | – | 32.9 | 23.7 | (✓,✓) | 794
A17-d17 | 27.8 | 27.8 | 375 | 34.3 | 24.4 | XP | nessai | 1000 | $28.3_{-0.9}^{+1.1}$ | $23.8_{-1.02}^{+0.87}$ | $525_{-128}^{+185}$ | $0.81_{-0.19}^{+0.15}$ | $0.91_{-0.17}^{+0.07}$ | $-0.09_{-0.02}^{+0.02}$ | $0.74_{-0.11}^{+0.12}$ | – | – | 33.8 | 24.4 | (✓,✓) | 834
A17-d17 | 27.8 | 27.8 | 375 | 34.3 | 24.4 | XPHM | dynesty | 500 | $32.8_{-2.2}^{+1.5}$ | $19.8_{-1.2}^{+2.2}$ | $690_{-154}^{+122}$ | – | – | – | – | – | – | 32.5 | 23.2 | (✓,✓) | 794
A17-d17 | 27.8 | 27.8 | 375 | 34.3 | 24.4 | XPHM | dynesty | 500 | $28.8_{-0.8}^{+0.8}$ | $24.5_{-0.8}^{+0.8}$ | $403_{-84}^{+117}$ | $0.86_{-0.21}^{+0.12}$ | $0.89_{-0.19}^{+0.09}$ | $-0.12_{-0.03}^{+0.03}$ | $0.70_{-0.13}^{+0.13}$ | – | – | 32.3 | 23.2 | (✓,✓) | 738
A17-d17 | 27.2 | 27.2 | 500 | 25.7 | 18.3 | XP | nessai | 1000 | $27.9_{-1.5}^{+1.5}$ | $23.4_{-1.4}^{+1.3}$ | $633_{-224}^{+304}$ | $0.72_{-0.18}^{+0.23}$ | $0.89_{-0.26}^{+0.09}$ | $-0.09_{-0.03}^{+0.04}$ | $0.61_{-0.39}^{+0.26}$ | – | – | 24.7 | 17.4 | (✓,✓) | 459
A17-d17 | 26.2 | 26.2 | 700 | 18.4 | 13.1 | XP | nessai | 1000 | $26.1_{-2.2}^{+3.6}$ | $22.3_{-2.6}^{+2.1}$ | $985_{-310}^{+435}$ | $0.67_{-0.54}^{+0.29}$ | $0.61_{-0.51}^{+0.34}$ | $-0.07_{-0.04}^{+0.05}$ | $0.67_{-0.35}^{+0.25}$ | – | – | 19.4 | 15.1 | (✓,✓) | 224
A17-d17 | 25.8 | 25.8 | 800 | 16.1 | 11.4 | XP | nessai | 1000 | $25.5_{-3.0}^{+3.9}$ | $21.7_{-3.4}^{+2.2}$ | $1176_{-381}^{+719}$ | $0.61_{-0.51}^{+0.34}$ | $0.52_{-0.46}^{+0.41}$ | $-0.07_{-0.05}^{+0.06}$ | $0.64_{-0.36}^{+0.28}$ | – | – | 15.6 | 11.2 | (✓,✓) | 167
A17-d17 | 36.2 | 36.2 | 500 | 32.9 | 23.4 | XPHM | cpnest | 1000 | $53.2_{-8.7}^{+5.1}$ | $19.1_{-2.6}^{+6.4}$ | $896_{-123}^{+138}$ | – | – | – | – | – | – | 28.7 | 20.8 | (✓,✓) | 692
A17-d17 | 36.2 | 36.2 | 500 | 32.9 | 23.4 | XPHM | cpnest | 500 | $34.3_{-4.5}^{+3.6}$ | $24.5_{-3.3}^{+3.9}$ | $692_{-290}^{+142}$ | $0.77_{-0.34}^{+0.20}$ | $0.64_{-0.53}^{+0.32}$ | $-0.53_{-0.13}^{+0.12}$ | $0.37_{-0.24}^{+0.25}$ | – | – | 32.8 | 24.0 | (✓,✓) | 764
A17-d17 | 36.2 | 36.2 | 500 | 32.9 | 23.4 | XP | nessai | 1000 | $56.6_{-3.8}^{+3.9}$ | $18.4_{-1.4}^{+1.9}$ | $740_{-281}^{+188}$ | – | – | – | – | – | – | 31.4 | 22.5 | (✓,✓) | 717
A17-d17 | 36.2 | 36.2 | 500 | 32.9 | 23.4 | XP | nessai | 1000 | $35.5^{+2.8}_{-3.0}$ | $25.5^{+2.3}_{-2.0}$ | $838_{-240}^{+113}$ | $0.33_{-0.18}^{+0.26}$ | $0.78_{-0.24}^{+0.14}$ | $-0.27_{-0.11}^{+0.09}$ | $0.46_{-0.18}^{+0.15}$ | – | – | 32.7 | 22.5 | (✓,✓) | 792
A17-d17 | 36.2 | 36.2 | 500 | 32.9 | 23.4 | Pv3 | nessai | 1000 | $58.3_{-3.7}^{+3.9}$ | $17.8_{-1.4}^{+1.7}$ | $736_{-284}^{+185}$ | – | – | – | – | – | – | 31.4 | 21.9 | (✓,✓) | 706
A17-d17 | 36.2 | 36.2 | 500 | 32.9 | 23.4 | Pv3 | nessai | 1000 | $35.3_{-2.5}^{+2.8}$ | $26.3_{-2.0}^{+2.1}$ | $811_{-214}^{+119}$ | $0.29_{-0.14}^{+0.22}$ | $0.42_{-0.25}^{+0.38}$ | $-0.21_{-0.14}^{+0.07}$ | $0.27_{-0.17}^{+0.23}$ | – | – | 34.8 | 24.1 | (✓,✓) | 792
A17-d17 | 44.3 | 44.3 | 625 | 30.9 | 22.1 | XP | nessai | 1000 | $44.3_{-3.1}^{+4.7}$ | $40.0_{-3.8}^{+3.6}$ | $1192_{-469}^{+303}$ | – | – | – | – | – | – | 27.2 | 19.6 | (✓,✓) | 625
A17-d17 | 44.3 | 44.3 | 625 | 30.9 | 22.1 | XP | nessai | 1000 | $44.7_{-5.3}^{+3.9}$ | $25.6_{-4.1}^{+7.2}$ | $780_{-250}^{+199}$ | $0.88_{-0.29}^{+0.10}$ | $0.60_{-0.54}^{+0.37}$ | $-0.60_{-0.14}^{+0.15}$ | $0.26_{-0.18}^{+0.34}$ | – | – | 29.2 | 22.2 | (✓,✓) | 680
A17-d17 | 44.3 | 44.3 | 625 | 30.9 | 22.1 | XPHM | dynesty | 500 | $50.4_{-3.6}^{+3.5}$ | $35.5_{-3.2}^{+3.5}$ | $1041_{-257}^{+253}$ | – | – | – | – | – | – | 27.2 | 19.6 | (✓,✓) | 633
A17-d17 | 44.3 | 44.3 | 625 | 30.9 | 22.1 | XPHM | dynesty | 500 | $44.3_{-3.1}^{+3.3}$ | $26.1_{-2.9}^{+4.0}$ | $830_{-152}^{+146}$ | $0.88_{-0.22}^{+0.10}$ | $0.33_{-0.30}^{+0.59}$ | $-0.56_{-0.11}^{+0.11}$ | $0.28_{-0.19}^{+0.32}$ | – | – | 28.8 | 20.4 | (✓,✓) | 681
A17-d17 | 52.1 | 52.1 | 750 | 29.3 | 20.9 | XP | nessai | 1000 | $61.0_{-2.9}^{+4.6}$ | $55.6_{-4.8}^{+2.8}$ | $398_{-81}^{+79}$ | – | – | – | – | – | – | 28.1 | 21.7 | (✓,✓) | 543
A17-d17 | 52.1 | 52.1 | 750 | 29.3 | 20.9 | XP | nessai | 1000 | $54.9_{-6.0}^{+5.6}$ | $39.3_{-7.5}^{+6.6}$ | $260_{-56}^{+61}$ | $0.81_{-0.37}^{+0.16}$ | $0.45_{-0.38}^{+0.41}$ | $-0.52_{-0.17}^{+0.15}$ | $0.26_{-0.17}^{+0.23}$ | – | – | 28.4 | 22.4 | (✓,✓) | 592
A17-d20 | 2.48 | 2.48 | 31.25 | 19.6 | 13.9 | Pv2T | nessai | 1000 | $2.68_{-0.31}^{+0.73}$ | $2.05_{-0.42}^{+0.27}$ | $54.3_{-17.7}^{+15.0}$ | $0.44_{-0.39}^{+0.45}$ | $0.52_{-0.46}^{+0.41}$ | $0.12_{-0.17}^{+0.19}$ | $0.48_{-0.30}^{+0.36}$ | $84.8_{-78.9}^{+296}$ | $233_{-210}^{+482}$ | 17.9 | 13.4 | (✓,✓) | 205
A17-d20 | 4.93 | 4.93 | 62.5 | 27.8 | 19.8 | F2 | nessai | 1000 | $11.2_{-3.3}^{+1.7}$ | $2.27_{-0.29}^{+0.88}$ | $111_{-34}^{+31}$ | $0.38_{-0.07}^{+0.06}$ | $0.02_{-0.43}^{+0.50}$ | $0.32_{-0.06}^{+0.05}$ | – | $0.39_{-0.35}^{+1.28}$ | $74.9_{-70.4}^{+239.9}$ | 26.1 | 21.4 | (✓,✓) | 528
A17-d20 | 4.93 | 4.93 | 62.5 | 27.8 | 19.8 | XP | nessai | 1000 | $7.19_{-0.44}^{+0.42}$ | $2.98_{-0.21}^{+0.24}$ | $95.9_{-33.6}^{+23.5}$ | – | – | – | – | – | – | 27.5 | 20.4 | (✓,✓) | 536
A17-d20 | 4.93 | 4.93 | 62.5 | 27.8 | 19.8 | XP | nessai | 1000 | $5.00_{-0.30}^{+1.45}$ | $4.15_{-0.89}^{+0.20}$ | $97.0_{-22.6}^{+27.7}$ | $0.61_{-0.47}^{+0.30}$ | $0.83_{-0.71}^{+0.15}$ | $-0.19_{-0.07}^{+0.12}$ | $0.66_{-0.51}^{+0.16}$ | – | – | 22.0 | 17.7 | (✓,✓) | 532
A17-d20 | 19.0 | 19.0 | 250 | 37.8 | 27.0 | F2 | nessai | 1000 | $49.1_{-2.1}^{+2.4}$ | $7.09_{-0.35}^{+0.34}$ | $479_{-146}^{+109}$ | $0.37_{-0.04}^{+0.04}$ | $0.01_{-0.51}^{+0.55}$ | $0.32_{-0.03}^{+0.04}$ | – | $0.03_{-0.03}^{+0.05}$ | $21.0_{-18.7}^{+48.2}$ | 36.7 | 27.5 | (✓,✓) | 1004
A17-d20 | 19.0 | 19.0 | 250 | 37.8 | 27.0 | XP | nessai | 1000 | $29.8_{-1.1}^{+1.1}$ | $10.1_{-0.4}^{+0.5}$ | $362_{-120}^{+85}$ | – | – | – | – | – | – | 34.5 | 26.7 | (✓,✓) | 994
A17-d20 | 19.0 | 19.0 | 250 | 37.8 | 27.0 | XP | nessai | 1000 | $18.3_{-2.4}^{+1.0}$ | $15.4_{-0.8}^{+2.0}$ | $415_{-61}^{+48}$ | $0.33_{-0.16}^{+0.30}$ | $0.65_{-0.32}^{+0.27}$ | $-0.20_{-0.08}^{+0.04}$ | $0.49_{-0.24}^{+0.24}$ | – | – | 36.8 | 28.0 | (✓,✓) | 1038
A17-d20 | 36.2 | 36.2 | 500 | 33.6 | 24.2 | XPHM | dynesty | 750 | $51.2_{-3.8}^{+3.9}$ | $21.0_{-2.3}^{+2.6}$ | $884_{-113}^{+100}$ | – | – | – | – | – | – | 32.5 | 22.7 | (✓,✓) | 737
A17-d20 | 36.2 | 36.2 | 500 | 33.6 | 24.2 | XPHM | dynesty | 750 | $37.0_{-2.6}^{+2.9}$ | $22.3_{-2.3}^{+2.8}$ | $698_{-100}^{+85}$ | $0.88_{-0.20}^{+0.10}$ | $0.53_{-0.49}^{+0.44}$ | $-0.53_{-0.09}^{+0.10}$ | $0.33_{-0.23}^{+0.24}$ | – | – | 34.3 | 24.1 | (✓,✓) | 805
A17-d20 | 36.2 | 36.2 | 500 | 33.6 | 24.2 | XP | nessai | 1000 | $58.8_{-8.1}^{+4.9}$ | $17.8_{-2.0}^{+4.2}$ | $710_{-255}^{+208}$ | – | – | – | – | – | – | 30.5 | 23.1 | (✓,✓) | 678
A17-d20 | 36.2 | 36.2 | 500 | 33.6 | 24.2 | XP | nessai | 1000 | $35.3_{-2.7}^{+2.3}$ | $25.7_{-1.9}^{+2.3}$ | $727_{-218}^{+116}$ | $0.5_{-0.21}^{+0.24}$ | $0.72_{-0.30}^{+0.23}$ | $-0.33_{-0.13}^{+0.08}$ | $0.47_{-0.21}^{+0.18}$ | – | – | 34.1 | 24.2 | (✓,✓) | 866
A17-d20 | 36.2 | 36.2 | 500 | 33.9 | 23.7 | TEOB | nessai | 1000 | $35.6_{-3.9}^{+3.3}$ | $24.0_{-2.3}^{+3.5}$ | $662_{-235}^{+150}$ | $-0.73_{-0.19}^{+0.36}$ | $-0.24_{-0.56}^{+0.29}$ | $-0.53_{-0.05}^{+0.06}$ | – | – | – | 34.1 | 24.2 | (✓,✓) | 808

| Injection | Analysis | Recovery | Consistency
---|---|---|---|---
Family | $\frac{m_{1}}{M_{\odot}}$ | $\frac{m_{2}}{M_{\odot}}$ | $\frac{d_{L}}{\rm Mpc}$ | $\rho^{\rm H1}$ | $\rho^{\rm L1}$ | Appr. | Sampler | $N_{s}$ | $\frac{m_{1}}{M_{\odot}}$ | $\frac{m_{2}}{M_{\odot}}$ | $\frac{d_{L}}{\rm Mpc}$ | $a_{1}$ | $a_{2}$ | $\chi_{\rm eff}$ | $\chi_{\rm p}$ | $\Lambda_{1}$ | $\Lambda_{2}$ | $\rho^{\rm H1}$ | $\rho^{\rm L1}$ | Res.(H,L) | $\log(\mathcal{B}^{\rm{S}}_{\rm{N}})$
A17-d21 | 4.94 | 4.94 | 50 | 39.2 | 27.8 | F2 | nessai | 1000 | $4.76^{+0.33}_{-0.15}$ | $4.44^{+0.15}_{-0.29}$ | $71.9^{+34.6}_{-23.5}$ | – | – | – | – | $1.77^{+17.93}_{-1.63}$ | $2.20^{+26.27}_{-2.02}$ | 36.6 | 29.2 | (✓,✓) | 1023
A17-d21 | 4.94 | 4.94 | 50 | 38.0 | 27.8 | F2 | nessai | 1000 | $13.8^{+0.2}_{-0.5}$ | $1.77^{+0.07}_{-0.03}$ | $95.5^{+18.1}_{-31.2}$ | $0.36^{+0.04}_{-0.03}$ | $-0.04^{+0.47}_{-0.56}$ | $0.31^{+0.03}_{-0.03}$ | – | $0.10^{+0.26}_{-0.09}$ | $107^{+302}_{-99}$ | 37.4 | 26.4 | (✓,✓) | 977
A17-d21 | 4.89 | 4.89 | 100 | 19.6 | 13.9 | F2 | dynesty | 500 | $4.65^{+0.17}_{-0.17}$ | $4.30^{+0.17}_{-0.15}$ | $158^{+63}_{-57}$ | – | – | – | – | $168^{+153}_{-151}$ | $208^{+206}_{-186}$ | 20.1 | 13.1 | (✓,✓) | 235
A17-d21 | 4.89 | 4.89 | 100 | 19.6 | 13.9 | F2 | dynesty | 500 | $11.7^{+1.8}_{-6.0}$ | $1.96^{+1.70}_{-0.24}$ | $182^{+44}_{-66}$ | $0.34^{+0.06}_{-0.25}$ | $0.01^{+0.48}_{-0.45}$ | $0.29^{+0.06}_{-0.20}$ | – | $1.29^{+5.97}_{-1.17}$ | $352^{+1581}_{-340}$ | 19.4 | 14.0 | (✓,✓) | 235
A17-d21 | 4.89 | 4.89 | 100 | 19.6 | 13.9 | F2 | nessai | 1000 | $4.80^{+0.68}_{-0.29}$ | $4.18^{+0.28}_{-0.53}$ | $171^{+55}_{-65}$ | – | – | – | – | $11.4^{+50.9}_{-10.5}$ | $19.6^{+86.6}_{-18.0}$ | 18.3 | 14.8 | (✓,✓) | 225
A17-d21 | 19.0 | 19.0 | 250 | 40.8 | 28.9 | XPHM | cpnest | 500 | $17.9^{+2.4}_{-1.5}$ | $14.4^{+1.5}_{-1.8}$ | $342^{+82}_{-118}$ | $0.75^{+0.21}_{-0.45}$ | $0.51^{+0.44}_{-0.44}$ | $-0.45^{+0.08}_{-0.06}$ | $0.34^{+0.33}_{-0.21}$ | – | – | 38.8 | 28.5 | (✓,✓) | 1103
A17-d21 | 39.1 | 39.1 | 100 | 172 | 123 | XPHM | cpnest | 1000 | $38.9^{+1.2}_{-1.3}$ | $25.4^{+1.6}_{-1.2}$ | $135^{+7}_{-10}$ | $0.97^{+0.02}_{-0.10}$ | $0.94^{+0.05}_{-0.88}$ | $-0.62^{+0.04}_{-0.03}$ | $0.52^{+0.12}_{-0.46}$ | – | – | 172 | 123 | (✓,✓) | 22229
A17-d21 | 38.3 | 38.3 | 200 | 86.1 | 61.6 | XPHM | cpnest | 1000 | $37.8^{+1.1}_{-1.1}$ | $25.4^{+1.1}_{-1.2}$ | $236^{+23}_{-22}$ | $0.95^{+0.03}_{-0.13}$ | $0.13^{+0.72}_{-0.12}$ | $-0.59^{+0.04}_{-0.05}$ | $0.14^{+0.32}_{-0.08}$ | – | – | 83.1 | 64.0 | (✓,✓) | 5392
A17-d21 | 37.6 | 37.6 | 300 | 57.4 | 41.1 | XPHM | cpnest | 1000 | $36.5^{+2.1}_{-1.8}$ | $26.3^{+3.5}_{-2.2}$ | $393^{+48}_{-52}$ | $0.87^{+0.10}_{-0.23}$ | $0.57^{+0.39}_{-0.50}$ | $-0.51^{+0.12}_{-0.08}$ | $0.46^{+0.33}_{-0.29}$ | – | – | 54.2 | 42.7 | (✓,✓) | 2356
A17-d21 | 36.9 | 36.9 | 400 | 43.0 | 30.8 | XPHM | cpnest | 500 | $35.6^{+3.3}_{-3.4}$ | $24.7^{+3.5}_{-2.9}$ | $515^{+90}_{-127}$ | $0.86^{+0.12}_{-0.30}$ | $0.55^{+0.39}_{-0.51}$ | $-0.57^{+0.09}_{-0.11}$ | $0.33^{+0.27}_{-0.22}$ | – | – | 42.9 | 31.3 | (✓,✓) | 1294
A17-d21 | 36.9 | 36.9 | 400 | 43.0 | 30.8 | XPHM | cpnest | 1000 | $36.8^{+1.9}_{-2.1}$ | $23.9^{+2.4}_{-1.9}$ | $473^{+62}_{-93}$ | $0.90^{+0.08}_{-0.21}$ | $0.45^{+0.49}_{-0.41}$ | $-0.60^{+0.08}_{-0.09}$ | $0.25^{+0.30}_{-0.18}$ | – | – | 43.8 | 30.3 | (✓,✓) | 1402
A17-d21 | 36.2 | 36.2 | 500 | 35.6 | 25.1 | XPHM | cpnest | 500 | $35.1^{+2.9}_{-2.9}$ | $26.0^{+3.5}_{-3.4}$ | $538^{+207}_{-172}$ | $0.77^{+0.19}_{-0.35}$ | $0.57^{+0.37}_{-0.50}$ | $-0.54^{+0.10}_{-0.10}$ | $0.32^{+0.30}_{-0.21}$ | – | – | 34.7 | 25.7 | (✓,✓) | 896
A17-d21 | 36.2 | 36.2 | 500 | 35.6 | 25.1 | XPHM | cpnest | 1000 | $37.7^{+4.2}_{-3.5}$ | $26.2^{+4.4}_{-5.2}$ | $507^{+215}_{-229}$ | $0.80^{+0.17}_{-0.29}$ | $0.56^{+0.40}_{-0.50}$ | $-0.44^{+0.11}_{-0.14}$ | $0.43^{+0.35}_{-0.27}$ | – | – | 37.3 | 27.5 | (✓,✓) | 895
A17-d21 | 29.3 | 29.3 | 2000 | 8.61 | 6.16 | XPHM | cpnest | 1000 | $31.1^{+12.9}_{-5.8}$ | $22.8^{+6.0}_{-7.6}$ | $2689^{+1372}_{-1247}$ | $0.50^{+0.44}_{-0.45}$ | $0.52^{+0.42}_{-0.47}$ | $-0.15^{+0.23}_{-0.31}$ | $0.48^{+0.40}_{-0.36}$ | – | – | 8.44 | 7.66 | (✓,✓) | 32
A17-d17-p180 | 2.48 | 2.48 | 31.25 | 16.8 | 11.8 | Pv2T | nessai | 1000 | $2.68_{-0.30}^{+0.77}$ | $2.14_{-0.41}^{+0.24}$ | $63.0_{-25.1}^{+19.1}$ | $0.74_{-0.50}^{+0.23}$ | $0.65_{-0.55}^{+0.31}$ | $0.45_{-0.25}^{+0.23}$ | $0.48_{-0.30}^{+0.32}$ | $109_{-101}^{+397}$ | $283_{-255}^{+574}$ | 17.9 | 11.1 | (✓,✓) | 146
A17-d17-p180 | 4.93 | 4.93 | 62.5 | 24.1 | 17.7 | F2 | nessai | 1000 | $14.3_{-3.0}^{+1.0}$ | $2.07_{-0.15}^{+0.57}$ | $125_{-42}^{+30}$ | $0.55_{-0.05}^{+0.10}$ | $0.00_{-0.52}^{+0.49}$ | $0.48_{-0.04}^{+0.06}$ | – | $1.22_{-1.05}^{+1.20}$ | $632_{-577}^{+1211}$ | 22.6 | 17.0 | (✓,✓) | 450
A17-d17-p180 | 4.93 | 4.93 | 62.5 | 25.2 | 17.9 | XP | nessai | 1000 | $4.73_{-0.18}^{+0.39}$ | $4.35_{-0.35}^{+0.17}$ | $85.1_{-26.9}^{+13.7}$ | – | – | – | – | – | – | 22.6 | 17.0 | (✓,✓) | 328
A17-d17-p180 | 4.93 | 4.93 | 62.5 | 25.2 | 17.9 | XP | nessai | 1000 | $7.43_{-0.99}^{+1.82}$ | $4.11_{-0.76}^{+0.62}$ | $76.3_{-24.6}^{+20.5}$ | $0.87_{-0.14}^{+0.10}$ | $0.86_{-0.29}^{+0.12}$ | $0.68_{-0.07}^{+0.07}$ | $0.45_{-0.20}^{+0.18}$ | – | – | 24.5 | 17.9 | (✓,✓) | 405
A17-d17-p180 | 36.2 | 36.2 | 500 | 35.8 | 25.3 | XP | nessai | 1000 | $31.6_{-1.9}^{+3.2}$ | $28.3_{-2.6}^{+2.1}$ | $756_{-300}^{+195}$ | – | – | – | – | – | – | 29.2 | 22.1 | (✓,✓) | 792
A17-d17-p180 | 36.2 | 36.2 | 500 | 35.8 | 25.3 | XP | nessai | 1000 | $45.3_{-4.9}^{+7.0}$ | $29.4_{-5.2}^{+4.4}$ | $808_{-257}^{+272}$ | $0.81_{-0.25}^{+0.16}$ | $0.75_{-0.51}^{+0.21}$ | $0.51_{-0.06}^{+0.06}$ | $0.44_{-0.27}^{+0.20}$ | – | – | 34.5 | 25.2 | (✓,✓) | 906
A17-d17-p180 | 36.2 | 36.2 | 500 | 35.8 | 25.3 | XPHM | dynesty | 500 | $32.9_{-2.7}^{+2.5}$ | $28.8_{-2.6}^{+2.0}$ | $623_{-239}^{+325}$ | – | – | – | – | – | – | 29.9 | 21.9 | (✓,✓) | 744
A17-d17-p180 | 36.2 | 36.2 | 500 | 35.8 | 25.3 | XPHM | dynesty | 500 | $46.7_{-4.7}^{+4.2}$ | $24.8_{-2.2}^{+3.7}$ | $1168_{-154}^{+119}$ | $0.65_{-0.21}^{+0.17}$ | $0.63_{-0.55}^{+0.33}$ | $0.48_{-0.06}^{+0.06}$ | $0.32_{-0.19}^{+0.21}$ | – | – | 33.6 | 24.8 | (✓,✓) | 885
A17-d21-p180 | 2.48 | 2.48 | 30 | 23.7 | 16.8 | XP | nessai | 1000 | $2.52^{+0.38}_{-0.20}$ | $2.11^{+0.18}_{-0.29}$ | $42.6^{+7.0}_{-14.8}$ | – | – | – | – | – | – | 21.9 | 16.4 | (✓,✓) | 348
A17-d21-p180 | 2.48 | 2.48 | 30 | 23.7 | 16.8 | XP | nessai | 1000 | $2.94^{+0.83}_{-0.52}$ | $1.86^{+0.36}_{-0.35}$ | $41.7^{+7.9}_{-13.4}$ | $0.27^{+0.28}_{-0.23}$ | $0.55^{+0.39}_{-0.48}$ | $0.09^{+0.15}_{-0.11}$ | $0.32^{+0.27}_{-0.23}$ | – | – | 23.9 | 14.4 | (✓,✓) | 347
A17-d21-p180 | 4.93 | 4.93 | 60 | 33.3 | 23.6 | XP | nessai | 1000 | $4.77^{+0.40}_{-0.20}$ | $4.34^{+0.19}_{-0.35}$ | $97.6^{+22.1}_{-38.5}$ | – | – | – | – | – | – | 31.9 | 21.1 | (✓,✓) | 697
A17-d21-p180 | 4.93 | 4.93 | 60 | 33.3 | 23.6 | XP | nessai | 1000 | $7.77^{+1.72}_{-0.92}$ | $3.05^{+0.36}_{-0.44}$ | $95.8^{+13.0}_{-26.3}$ | $0.75^{+0.16}_{-0.12}$ | $0.84^{+0.14}_{-0.43}$ | $0.31^{+0.10}_{-0.07}$ | $0.55^{+0.24}_{-0.21}$ | – | – | 31.6 | 24.5 | (✓,✓) | 800
A17-d21-p180 | 9.73 | 9.73 | 125 | 39.5 | 28.0 | XP | nessai | 1000 | $9.03^{+0.41}_{-0.20}$ | $8.66^{+0.21}_{-0.36}$ | $201^{+43}_{-73}$ | – | – | – | – | – | – | 36.8 | 28.3 | (✓,✓) | 949
A17-d21-p180 | 9.73 | 9.73 | 125 | 39.5 | 28.0 | XP | nessai | 1000 | $13.6^{+1.8}_{-2.0}$ | $6.84^{+1.08}_{-0.90}$ | $127^{+81}_{-14}$ | $0.60^{+0.17}_{-0.18}$ | $0.30^{+0.55}_{-0.26}$ | $0.29^{+0.05}_{-0.05}$ | $0.40^{+0.22}_{-0.19}$ | – | – | 36.9 | 28.4 | (✓,✓) | 1070
A17-d21-p180 | 19.0 | 19.0 | 250 | 42.3 | 30.0 | XP | nessai | 1000 | $17.3^{+0.7}_{-0.5}$ | $16.6^{+0.6}_{-0.6}$ | $406^{+87}_{-166}$ | – | – | – | – | – | – | 39.3 | 26.3 | (✓,✓) | 1054
A17-d21-p180 | 19.0 | 19.0 | 250 | 42.3 | 30.0 | XP | nessai | 1000 | $20.0^{+0.5}_{-0.4}$ | $16.4^{+0.5}_{-0.6}$ | $452^{+38}_{-54}$ | $0.97^{+0.02}_{-0.08}$ | $0.88^{+0.10}_{-0.21}$ | $0.27^{+0.04}_{-0.05}$ | $0.72^{+0.15}_{-0.15}$ | – | – | 43.6 | 30.6 | (✓,✓) | 1322
A17-d21-p180 | 28.2 | 28.2 | 300 | 50.4 | 35.8 | XP | nessai | 1000 | $25.4^{+1.2}_{-0.8}$ | $24.3^{+1.0}_{-1.0}$ | $474^{+103}_{-187}$ | – | – | – | – | – | – | 45.6 | 33.5 | (✓,✓) | 1523
A17-d21-p180 | 28.2 | 28.2 | 300 | 50.4 | 35.8 | XP | nessai | 1000 | $37.2^{+2.4}_{-2.6}$ | $20.4^{+1.9}_{-1.8}$ | $589^{+44}_{-122}$ | $0.68^{+0.15}_{-0.13}$ | $0.42^{+0.52}_{-0.37}$ | $0.38^{+0.04}_{-0.12}$ | $0.22^{+0.21}_{-0.13}$ | – | – | 50.2 | 35.1 | (✓,✓) | 1860
A17-d21-p180 | 36.2 | 36.2 | 500 | 37.6 | 26.7 | XP | nessai | 1000 | $33.7^{+4.2}_{-3.1}$ | $27.8^{+2.9}_{-3.2}$ | $718^{+212}_{-298}$ | – | – | – | – | – | – | 34.2 | 23.9 | (✓,✓) | 850
A17-d21-p180 | 36.2 | 36.2 | 500 | 37.6 | 26.7 | XP | nessai | 1000 | $49.5^{+3.6}_{-3.8}$ | $30.9^{+2.7}_{-2.5}$ | $446^{+193}_{-101}$ | $0.91^{+0.07}_{-0.13}$ | $0.73^{+0.22}_{-0.26}$ | $0.47^{+0.04}_{-0.04}$ | $0.41^{+0.14}_{-0.13}$ | – | – | 38.9 | 28.0 | (✓,✓) | 1045
A17-d21-p180 | 44.3 | 44.3 | 625 | 35.5 | 25.2 | XP | nessai | 1000 | $53.9^{+3.7}_{-3.1}$ | $23.4^{+2.0}_{-1.6}$ | $762^{+180}_{-295}$ | – | – | – | – | – | – | 34.5 | 24.2 | (✓,✓) | 870
A17-d21-p180 | 44.3 | 44.3 | 625 | 35.5 | 25.2 | XP | nessai | 1000 | $60.3^{+5.4}_{-6.7}$ | $32.7^{+5.8}_{-3.4}$ | $875^{+307}_{-242}$ | $0.71^{+0.17}_{-0.17}$ | $0.83^{+0.15}_{-0.41}$ | $0.43^{+0.08}_{-0.06}$ | $0.39^{+0.17}_{-0.19}$ | – | – | 37.1 | 22.8 | (✓,✓) | 940
A17-d21-p180 | 52.1 | 52.1 | 750 | 33.7 | 24.0 | XP | nessai | 1000 | $68.9^{+4.9}_{-4.1}$ | $22.4^{+2.0}_{-1.7}$ | $808^{+203}_{-326}$ | – | – | – | – | – | – | 32.6 | 23.1 | (✓,✓) | 758
A17-d21-p180 | 52.1 | 52.1 | 750 | 33.7 | 24.0 | XP | nessai | 1000 | $69.3^{+5.7}_{-5.7}$ | $32.5^{+4.9}_{-3.6}$ | $1112^{+238}_{-358}$ | $0.49^{+0.18}_{-0.20}$ | $0.57^{+0.37}_{-0.48}$ | $0.33^{+0.08}_{-0.08}$ | $0.27^{+0.19}_{-0.17}$ | – | – | 34.8 | 25.1 | (✓,✓) | 884

| Injection | Analysis | Recovery | Consistency
---|---|---|---|---
Family | $\frac{m_{1}}{M_{\odot}}$ | $\frac{m_{2}}{M_{\odot}}$ | $\frac{d_{L}}{\rm Mpc}$ | $\rho^{\rm H1}$ | $\rho^{\rm L1}$ | Appr. | Sampler | $N_{s}$ | $\frac{m_{1}}{M_{\odot}}$ | $\frac{m_{2}}{M_{\odot}}$ | $\frac{d_{L}}{\rm Mpc}$ | $a_{1}$ | $a_{2}$ | $\chi_{\rm eff}$ | $\chi_{\rm p}$ | $\Lambda_{1}$ | $\Lambda_{2}$ | $\rho^{\rm H1}$ | $\rho^{\rm L1}$ | Res.(H,L) | $\log(\mathcal{B}^{\rm{S}}_{\rm{N}})$
A17-d21-p090 | 2.48 | 2.48 | 30 | 23.8 | 16.9 | XP | nessai | 1000 | $2.69^{+0.47}_{-0.33}$ | $2.00^{+0.29}_{-0.32}$ | $43.3^{+6.5}_{-14.3}$ | – | – | – | – | – | – | 22.3 | 15.7 | (✓,✓) | 342
A17-d21-p090 | 2.48 | 2.48 | 30 | 23.8 | 16.9 | XP | nessai | 1000 | $3.00^{+0.57}_{-0.29}$ | $1.82^{+0.16}_{-0.26}$ | $33.6^{+12.3}_{-8.5}$ | $0.43^{+0.14}_{-0.12}$ | $0.79^{+0.17}_{-0.32}$ | $0.06^{+0.10}_{-0.08}$ | $0.45^{+0.14}_{-0.15}$ | – | — | 22.9 | 18.1 | (✓,✓) | 420
A17-d21-p090 | 2.48 | 2.48 | 31.25 | 22.8 | 16.2 | Pv2T | nessai | 1000 | $2.53_{-0.15}^{+0.37}$ | $2.21_{-0.31}^{+0.15}$ | $53.6_{-19.2}^{+11.0}$ | $0.40_{-0.36}^{+0.48}$ | $0.48_{-0.42}^{+0.43}$ | $0.22_{-0.18}^{+0.22}$ | $0.40_{-0.27}^{+0.35}$ | $114_{-110}^{+288}$ | $190_{-175}^{+366}$ | 21.6 | 16.7 | (✓,✓) | 342
A17-d21-p090 | 4.93 | 4.93 | 60 | 33.2 | 23.6 | XP | nessai | 1000 | $4.77^{+0.33}_{-0.16}$ | $4.41^{+0.16}_{-0.29}$ | $96.1^{+21.6}_{-34.9}$ | – | – | – | – | – | – | 31.6 | 22.4 | (✓,✓) | 722
A17-d21-p090 | 4.93 | 4.93 | 60 | 33.2 | 23.6 | XP | nessai | 1000 | $5.04^{+1.38}_{-0.11}$ | $4.28^{+0.09}_{-0.90}$ | $99.6^{+17.1}_{-24.3}$ | $0.86^{+0.10}_{-0.34}$ | $0.92^{+0.07}_{-0.24}$ | $0.04^{+0.06}_{-0.05}$ | $0.83^{+0.12}_{-0.37}$ | – | – | 32.4 | 22.3 | (✓,✓) | 750
A17-d21-p090 | 4.93 | 4.93 | 62.5 | 31.9 | 22.7 | F2 | nessai | 1000 | $14.1_{-0.6}^{+0.2}$ | $1.82_{-0.03}^{+0.08}$ | $104_{-32}^{+24}$ | $0.42_{-0.03}^{+0.04}$ | $-0.04_{-0.57}^{+0.44}$ | $0.37_{-0.03}^{+0.03}$ | – | $0.13_{-0.12}^{+0.29}$ | $146_{-131}^{+338}$ | 31.0 | 24.3 | (✓,✓) | 730
A17-d21-p090 | 4.93 | 4.93 | 62.5 | 31.9 | 22.7 | XP | nessai | 1000 | $4.82^{+0.42}_{-0.21}$ | $4.35^{+0.21}_{-0.36}$ | $100^{+23}_{-36}$ | – | – | – | – | – | – | 31.6 | 22.4 | . (✓,✓) | 698
A17-d21-p090 | 9.73 | 9.73 | 125 | 39.1 | 27.8 | XP | nessai | 1000 | $9.26^{+0.57}_{-0.31}$ | $8.66^{+0.31}_{-0.50}$ | $208^{+46}_{-85}$ | – | – | . – | – | – | – | 38.6 | 26.4 | (✓,✓) | 1037
A17-d21-p090 | 9.73 | 9.73 | 125 | 39.1 | 27.8 | XP | nessai | 1000 | $9.87^{+2.56}_{-0.26}$ | $8.45^{+0.28}_{-1.60}$ | $206^{+26}_{-41}$ | $0.76^{+0.14}_{-0.25}$ | $0.77^{+0.18}_{-0.33}$ | $0.09^{+0.06}_{-0.03}$ | $0.74^{+0.15}_{-0.29}$ | – | – | 38.6 | 29.5 | (✓,✓) | 1174
A17-d21-p090 | 19.0 | 19.0 | 250 | 41.8 | 29.7 | XP | nessai | 1000 | $17.9^{+1.2}_{-0.7}$ | $16.7^{+0.8}_{-1.0}$ | $387^{+96}_{-174}$ | – | – | – | – | – | – | 41.0 | 28.0 | (✓,✓) | 1200
A17-d21-p090 | 19.0 | 19.0 | 250 | 41.8 | 29.7 | XP | nessai | 1000 | $24.4^{+1.9}_{-2.3}$ | $13.0^{+1.4}_{-0.9}$ | $389^{+49}_{-93}$ | $0.38^{+0.28}_{-0.19}$ | $0.56^{+0.37}_{-0.45}$ | $0.12^{+0.05}_{-0.05}$ | $0.32^{+0.25}_{-0.17}$ | – | – | 39.8 | 31.6 | (✓,✓) | 1309
A17-d21-p090 | 28.2 | 28.2 | 300 | 49.3 | 35.0 | XP | nessai | 1000 | $26.4^{+1.7}_{-1.1}$ | $24.7^{+1.2}_{-1.5}$ | $445^{+115}_{-201}$ | – | – | – | – | – | – | 48.5 | 34.9 | (✓,✓) | 1698
A17-d21-p090 | 28.2 | 28.2 | 300 | 49.3 | 35.0 | XP | nessai | 1000 | $38.3^{+2.9}_{-3.1}$ | $18.0^{+1.7}_{-1.4}$ | $529^{+58}_{-131}$ | $0.28^{+0.19}_{-0.19}$ | $0.63^{+0.32}_{-0.52}$ | $0.19^{+0.05}_{-0.05}$ | $0.26^{+0.16}_{-0.15}$ | – | – | 46.0 | 34.2 | (✓,✓) | 1599
A17-d21-p090 | 36.2 | 36.2 | 500 | 36.8 | 26.2 | XP | nessai | 1000 | $39.1^{+3.4}_{-4.4}$ | $26.3^{+3.7}_{-2.3}$ | $710^{+156}_{-291}$ | – | – | – | – | – | – | 37.8 | 27.5 | (✓,✓) | 1019
A17-d21-p090 | 36.2 | 36.2 | 500 | 36.8 | 26.2 | XP | nessai | 1000 | $40.6^{+5.4}_{-5.0}$ | $30.1^{+4.6}_{-4.0}$ | $935^{+111}_{-275}$ | $0.47^{+0.32}_{-0.39}$ | $0.49^{+0.42}_{-0.43}$ | $0.29^{+0.05}_{-0.05}$ | $0.34^{+0.31}_{-0.21}$ | – | – | 37.4 | 27.6 | (✓,✓) | 1010
A17-d21-p090 | 36.2 | 36.2 | 500 | 36.8 | 26.2 | XPHM | cpnest | 500 | $38.9^{+7.5}_{-3.1}$ | $33.2^{+4.1}_{-8.6}$ | $851^{+292}_{-382}$ | $0.43^{+0.38}_{-0.37}$ | $0.55^{+0.38}_{-0.44}$ | $0.30^{+0.06}_{-0.09}$ | $0.34^{+0.40}_{-0.20}$ | – | – | 34.6 | 23.9 | (✓,✓) | 952
A17-d21-p090 | 36.2 | 36.2 | 500 | 36.8 | 26.2 | XPHM | cpnest | 1000 | $41.2^{+7.0}_{-5.8}$ | $29.0^{+6.4}_{-5.4}$ | $818^{+215}_{-285}$ | $0.41^{+0.36}_{-0.35}$ | $0.54^{+0.38}_{-0.42}$ | $0.24^{+0.09}_{-0.08}$ | $0.36^{+0.30}_{-0.23}$ | – | – | 39.5 | 29.7 | (✓,✓) | 1047
A17-d21-p090 | 44.3 | 44.3 | 625 | 34.7 | 24.7 | XP | nessai | 1000 | $54.0^{+4.1}_{-4.0}$ | $26.1^{+2.6}_{-2.1}$ | $824^{+202}_{-307}$ | – | – | – | – | – | – | 34.0 | 23.2 | (✓,✓) | 802
A17-d21-p090 | 44.3 | 44.3 | 625 | 34.7 | 24.7 | XP | nessai | 1000 | $50.0^{+6.3}_{-6.0}$ | $37.3^{+5.2}_{-5.4}$ | $932^{+255}_{-322}$ | $0.54^{+0.32}_{-0.39}$ | $0.56^{+0.37}_{-0.46}$ | $0.27^{+0.07}_{-0.07}$ | $0.43^{+0.29}_{-0.26}$ | – | – | 34.7 | 25.8 | (✓,✓) | 936
A17-d21-p090 | 52.1 | 52.1 | 750 | 33.0 | 23.5 | XP | nessai | 1000 | $69.1^{+4.7}_{-3.9}$ | $26.0^{+2.4}_{-2.0}$ | $844^{+203}_{-323}$ | – | – | – | – | – | – | 33.8 | 24.2 | (✓,✓) | 817
A17-d21-p090 | 52.1 | 52.1 | 750 | 33.0 | 23.5 | XP | nessai | 1000 | $59.1^{+7.1}_{-8.5}$ | $36.5^{+9.1}_{-6.0}$ | $1230^{+269}_{-423}$ | $0.40^{+0.34}_{-0.32}$ | $0.47^{+0.44}_{-0.42}$ | . $0.21^{+0.09}_{-0.10}$ | $0.32^{+0.31}_{-0.21}$ | – | – | 32.2 | 24.3 | (✓,✓) | 759
A17-d17-e1 | 2.48 | 2.48 | 31.25 | 16.4 | 11.6 | Pv2T | nessai | 1000 | $2.62_{-0.19}^{+0.36}$ | $2.32_{-0.30}^{+0.18}$ | $61.0_{-24}^{+14}$ | $0.47_{-0.41}^{+0.43}$ | $0.49_{-0.43}^{+0.43}$ | $0.26_{-0.19}^{+0.18}$ | $0.41_{-0.28}^{+0.37}$ | $25.1_{-23.0}^{+76.0}$ | $39.1_{-35.4}^{+100.0}$ | 16.9 | 11.1 | (✓,✓) | 177
A17-d17-e1 | 2.49 | 2.49 | 17.0 | 30.2 | 21.4 | XP | nessai | 1000 | $3.28_{-0.65}^{+1.25}$ | $1.94_{-0.43}^{+0.45}$ | $30.3_{-10.2}^{+7.0}$ | $0.60_{-0.37}^{+0.29}$ | $0.63_{-0.51}^{+0.31}$ | $0.30_{-0.13}^{+0.15}$ | $0.49_{-0.25}^{+0.32}$ | – | – | 30.1 | 21.7 | (✓,✓) | 646
A17-d17-e1 | 2.48 | 2.48 | 31.25 | 16.4 | 11.6 | XP | nessai | 1000 | $2.66_{-0.26}^{+0.49}$ | $2.07_{-0.35}^{+0.23}$ | $49.0_{-21.2}^{+15.6}$ | – | – | – | – | – | – | 16.5 | 11.9 | (✓,✓) | 174
A17-d17-e1 | 2.48 | 2.48 | 31.25 | 16.4 | 11.6 | XP | nessai | 1000 | $3.32_{-0.79}^{+2.24}$ | $1.88_{-0.62}^{+0.52}$ | $54.5_{-19.8}^{+14.5}$ | $0.68_{-0.51}^{+0.27}$ | $0.52_{-0.46}^{+0.42}$ | $0.29_{-0.23}^{+0.24}$ | $0.52_{-0.31}^{+0.34}$ | – | – | 17.1 | 12.1 | (✓,✓) | 177
A17-d17-e1 | 4.93 | 4.93 | 62.5 | 24.6 | 17.4 | F2 | nessai | 1000 | $13.4_{-2.2}^{+0.9}$ | $1.95_{-0.14}^{+0.40}$ | $118_{-44}^{+34}$ | $0.43_{-0.04}^{+0.06}$ | $0.00_{-0.52}^{+0.53}$ | $0.37_{-0.04}^{+0.04}$ | – | $0.31_{-0.28}^{+0.60}$ | $205_{-187}^{+593}$ | 23.4 | 18.1 | (✓,✓) | 376
A17-d17-e1 | 4.93 | 4.93 | 62.5 | 24.6 | 17.4 | XP | nessai | 1000 | $4.98_{-0.30}^{+0.65}$ | $4.33_{-0.53}^{+0.28}$ | $81.8_{-29.0}^{+16.4}$ | – | – | – | – | – | – | 24.4 | 15.8 | (✓,✓) | 407
A17-d17-e1 | 4.93 | 4.93 | 62.5 | 24.6 | 17.4 | XP | nessai | 1000 | $5.65_{-0.71}^{+1.46}$ | $4.19_{-0.82}^{+0.60}$ | $117_{-47}^{+22}$ | $0.49_{-0.39}^{+0.40}$ | $0.48_{-0.42}^{+0.44}$ | $0.19_{-0.10}^{+0.10}$ | $0.44_{-0.29}^{+0.41}$ | – | – | 24.8 | 15.6 | (✓,✓) | 409
A17-d17-e1 | 9.73 | 9.73 | 125 | 31.6 | 22.4 | XP | nessai | 1000 | $9.63_{-0.52}^{+1.04}$ | $8.54_{-0.88}^{+0.49}$ | $202_{-95}^{+52}$ | – | – | – | – | – | – | 31.7 | 23.5 | (✓,✓) | 724
A17-d17-e1 | 9.73 | 9.73 | 125 | 31.6 | 22.4 | XP | nessai | 1000 | $11.7_{-1.8}^{+1.5}$ | $7.65_{-0.89}^{+1.23}$ | $178_{-64}^{+66}$ | $0.36_{-0.20}^{+0.24}$ | $0.48_{-0.40}^{+0.37}$ | $0.15_{-0.07}^{+0.07}$ | $0.34_{-0.17}^{+0.24}$ | – | – | 32.9 | 24.0 | (✓,✓) | 729
A17-d17-e1 | 19.0 | 19.0 | 250 | 35.9 | 25.5 | XP | nessai | 1000 | $19.8_{-1.1}^{+2.1}$ | $17.3_{-1.8}^{+1.1}$ | $87.8_{-16.1}^{+10.8}$ | – | – | – | – | – | – | 37.7 | 23.8 | (✓,✓) | 915
A17-d17-e1 | 19.0 | 19.0 | 250 | 35.9 | 25.5 | XP | nessai | 1000 | $20.9_{-2.3}^{+2.3}$ | $16.0_{-1.7}^{+1.9}$ | $180_{-39}^{+17}$ | $0.17_{-0.15}^{+0.25}$ | $0.23_{-0.21}^{+0.39}$ | $0.04_{-0.05}^{+0.06}$ | $0.16_{-0.13}^{+0.24}$ | – | – | 36.6 | 22.8 | (✓,✓) | 914
A17-d17-e1 | 27.8 | 27.8 | 375 | 35.6 | 25.2 | XP | nessai | 1000 | $29.5_{-3.0}^{+3.2}$ | $22.7_{-2.5}^{+2.7}$ | $431_{-117}^{+62}$ | – | – | – | – | – | – | 36.8 | 26.9 | (✓,✓) | 957
A17-d17-e1 | 27.8 | 27.8 | 375 | 35.6 | 25.2 | XP | nessai | 1000 | $31.2_{-3.9}^{+3.0}$ | $22.1_{-2.01}^{+3.12}$ | $422_{-98}^{+70}$ | $0.20_{-0.18}^{+0.40}$ | $0.28_{-0.25}^{+0.55}$ | $0.05_{-0.05}^{+0.06}$ | $0.21_{-0.16}^{+0.37}$ | – | – | 32.1 | 21.6 | (✓,✓) | 955
A17-d17-e1 | 36.2 | 36.2 | 500 | 33.6 | 23.7 | XPHM | dynesty | 500 | $35.8_{-3.5}^{+4.8}$ | $27.8_{-4.5}^{+4.4}$ | $971_{-307}^{+156}$ | – | – | – | – | – | – | 32.4 | 23.3 | (✓,✓) | 817
A17-d17-e1 | 36.2 | 36.2 | 500 | 33.6 | 23.7 | XPHM | dynesty | 500 | $37.1_{-4.1}^{+4.5}$ | $27.2_{-3.9}^{+4.8}$ | $999_{-247}^{+129}$ | $0.21_{-0.19}^{+0.43}$ | $0.31_{-0.28}^{+0.56}$ | $0.04_{-0.07}^{+0.07}$ | $0.26_{-0.21}^{+0.36}$ | – | – | 33.1 | 24.8 | (✓,✓) | 816
A17-d17-e1 | 36.2 | 36.2 | 500 | 33.6 | 23.7 | XP | nessai | 1000 | $38.1_{-5.02}^{+4.59}$ | $27.2_{-3.14}^{+4.38}$ | $826_{-306}^{+204}$ | – | – | – | – | – | – | 34.0 | 24.5 | (✓,✓) | 820
A17-d17-e1 | 36.2 | 36.2 | 500 | 33.2 | 23.8 | XP | nessai | 500 | $38.2_{-4.86}^{+4.54}$ | $27.1_{-3.3}^{+4.4}$ | $901_{-317}^{+168}$ | $0.15_{-0.13}^{+0.32}$ | $0.23_{-0.20}^{+0.51}$ | $0.02_{-0.06}^{+0.07}$ | $0.19_{-0.15}^{+0.32}$ | – | – | 33.1 | 24.8 | (✓,✓) | 817
A17-d17-e1 | 44.3 | 44.3 | 625 | 31.7 | 22.3 | XP | nessai | 1000 | $54.6_{-6.4}^{+4.6}$ | $33.2_{-3.5}^{+5.6}$ | $411_{-127}^{+81}$ | – | – | – | – | – | – | 31.3 | 23.1 | (✓,✓) | 725
A17-d17-e1 | 44.3 | 44.3 | 625 | 31.7 | 22.3 | XP | nessai | 500 | $53.1_{-6.6}^{+5.3}$ | $35.0_{-5.0}^{+7.0}$ | $434_{-119}^{+60}$ | $0.13_{-0.11}^{+0.27}$ | $0.23_{-0.20}^{+0.42}$ | $0.03_{-0.07}^{+0.08}$ | $0.16_{-0.11}^{+0.27}$ | – | – | 30.6 | 23.4 | (✓,✓) | 722
A17-d17-e1 | 52.1 | 52.1 | 750 | 30.0 | 21.2 | XP | nessai | 1000 | $67.0_{-8.6}^{+6.0}$ | $39.2_{-4.8}^{+8.2}$ | $449_{-155}^{+47}$ | – | – | – | – | – | – | 29.9 | 21.6 | (✓,✓) | 652
A17-d17-e1 | 52.1 | 52.1 | 750 | 30.0 | 21.2 | XP | nessai | 500 | $68.1_{-6.2}^{+5.3}$ | $34.5_{-6.5}^{+8.3}$ | $455_{-109}^{+40}$ | $0.16_{-0.14}^{+0.26}$ | $0.27_{-0.24}^{+0.48}$ | $-0.05_{-0.13}^{+0.11}$ | $0.17_{-0.12}^{+0.22}$ | – | – | 30.1 | 22.3 | (✓,✓) | 652

## References

  * LIGO Scientific Collaboration  _et al._ [2018] LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration, LVK Algorithm Library - LALSuite, Free software (GPL) (2018).
  * Wette [2020] K. Wette, SWIGLAL: Python and Octave interfaces to the LALSuite gravitational-wave data analysis libraries, SoftwareX 12, 100634 (2020).
  * Schmidt  _et al._ [2017] P. Schmidt, I. W. Harry, and H. P. Pfeiffer, Numerical relativity injection infrastructure (2017), arXiv:1703.01076 [gr-qc] .
  * Abbott  _et al._ [2018] B. P. Abbott _et al._ (KAGRA, LIGO Scientific, VIRGO), Prospects for Observing and Localizing Gravitational-Wave Transients with Advanced LIGO, Advanced Virgo and KAGRA, Living Rev. Rel. 21, 3 (2018), arXiv:1304.0670 [gr-qc] .
  * Speagle [2020] J. S. Speagle, dynesty: a dynamic nested sampling package for estimating Bayesian posteriors and evidences, Monthly Notices of the Royal Astronomical Society 493, 3132–3158 (2020).
  * Del Pozzo and Veitch [2022] W. Del Pozzo and J. Veitch, CPNest: Parallel nested sampling, Astrophysics Source Code Library, record ascl:2205.021 (2022).
  * Williams [2021] M. J. Williams, nessai: Nested sampling with artificial intelligence (2021).
  * Williams  _et al._ [2021] M. J. Williams, J. Veitch, and C. Messenger, Nested sampling with normalizing flows for gravitational-wave inference, Phys. Rev. D 103, 103006 (2021), arXiv:2102.11056 [gr-qc] .
  * Williams  _et al._ [2023] M. J. Williams, J. Veitch, and C. Messenger, Importance nested sampling with normalising flows, Mach. Learn. Sci. Tech. 4, 035011 (2023), arXiv:2302.08526 [astro-ph.IM] .
  * Ashton  _et al._ [2019] G. Ashton _et al._ , BILBY: A user-friendly Bayesian inference library for gravitational-wave astronomy, Astrophys. J. Suppl. 241, 27 (2019), arXiv:1811.02042 [astro-ph.IM] .
  * Palenzuela  _et al._ [2007] C. Palenzuela, I. Olabarrieta, L. Lehner, and S. L. Liebling, Head-on collisions of boson stars, Phys. Rev. D 75, 064005 (2007), arXiv:gr-qc/0612067 .
  * Radia  _et al._ [2022] M. Radia, U. Sperhake, A. Drew, K. Clough, P. Figueras, E. A. Lim, J. L. Ripley, J. C. Aurrekoetxea, T. França, and T. Helfer, Lessons for adaptive mesh refinement in numerical relativity, Class. Quant. Grav. 39, 135006 (2022), arXiv:2112.10567 [gr-qc] .
  * Note [2] For non-precessing models, we report projections of the dimensionless spins onto the orbital angular momentum, $\chi_{1}$, $\chi_{2}$, which are allowed to be negative.