Evidence for eccentricity in the population of binary black holes observed by LIGO-Virgo-KAGRA

Binary black holes (BBHs) in eccentric orbits produce distinct modulations in the emitted gravitational waves (GWs). The measurement of orbital eccentricity can provide robust evidence for dynamical binary formation channels. We analyze 57 GW events from the first, second, and third observing runs of the Laser Interferometer Gravitational-Wave Observatory (LIGO)-Virgo-Kamioka Gravitational Wave Detector (KAGRA) (LVK) Collaboration using a multipolar aligned-spin inspiral-merger-ringdown waveform model with two eccentric parameters: eccentricity and relativistic anomaly (assuming a quasicircular merger-ringdown). This is made computationally feasible with the machine-learning code ingo, which accelerates inference by 2–3 orders of magnitude compared to traditional inference techniques. First, when using a uniform prior on the eccentricity, we find eccentric aligned-spin against quasicircular aligned-spin <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>log</a:mi> <a:mn>10</a:mn> </a:msub> </a:math> Bayes factors of 1.84 to 4.75 (depending on the glitch mitigation) for GW200129, 3.0 for GW190701 and 1.77 for GW200208_22. We infer <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:msub> <c:mrow> <c:mi>e</c:mi> </c:mrow> <c:mrow> <c:mi>gw</c:mi> <c:mo>,</c:mo> <c:mn>10</c:mn> <c:mtext> </c:mtext> <c:mtext> </c:mtext> <c:mi>Hz</c:mi> </c:mrow> </c:msub> </c:mrow> </c:math> <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mo stretchy="false">(</e:mo> <e:msub> <e:mi>e</e:mi> <e:mrow> <e:mi>gw</e:mi> <e:mo>,</e:mo> <e:mn>20</e:mn> <e:mtext> </e:mtext> <e:mtext> </e:mtext> <e:mi>Hz</e:mi> </e:mrow> </e:msub> <e:mo stretchy="false">)</e:mo> </e:math> to be <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msubsup> <i:mn>0.27</i:mn> <i:mrow> <i:mo>−</i:mo> <i:mn>0.12</i:mn> </i:mrow> <i:mrow> <i:mo>+</i:mo> <i:mn>0.10</i:mn> </i:mrow> </i:msubsup> </i:math> ( <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msubsup> <k:mn>0.16</k:mn> <k:mrow> <k:mo>−</k:mo> <k:mn>0.05</k:mn> </k:mrow> <k:mrow> <k:mo>+</k:mo> <k:mn>0.04</k:mn> </k:mrow> </k:msubsup> </k:math> ) to <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msubsup> <m:mn>0.17</m:mn> <m:mrow> <m:mo>−</m:mo> <m:mn>0.13</m:mn> </m:mrow> <m:mrow> <m:mo>+</m:mo> <m:mn>0.14</m:mn> </m:mrow> </m:msubsup> </m:math> ( <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msubsup> <o:mn>0.1</o:mn> <o:mrow> <o:mo>−</o:mo> <o:mn>0.04</o:mn> </o:mrow> <o:mrow> <o:mo>+</o:mo> <o:mn>0.05</o:mn> </o:mrow> </o:msubsup> </o:math> ) for GW200129, <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msubsup> <q:mn>0.54</q:mn> <q:mrow> <q:mo>−</q:mo> <q:mn>0.30</q:mn> </q:mrow> <q:mrow> <q:mo>+</q:mo> <q:mn>0.12</q:mn> </q:mrow> </q:msubsup> </q:math> ( <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msubsup> <s:mn>0.31</s:mn> <s:mrow> <s:mo>−</s:mo> <s:mn>0.13</s:mn> </s:mrow> <s:mrow> <s:mo>+</s:mo> <s:mn>0.12</s:mn> </s:mrow> </s:msubsup> </s:math> ) for GW190701 and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msubsup> <u:mn>0.39</u:mn> <u:mrow> <u:mo>−</u:mo> <u:mn>0.23</u:mn> </u:mrow> <u:mrow> <u:mo>+</u:mo> <u:mn>0.23</u:mn> </u:mrow> </u:msubsup> </u:math> ( <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mrow> <w:msubsup> <w:mrow> <w:mn>0.21</w:mn> </w:mrow> <w:mrow> <w:mo>−</w:mo> <w:mn>0.08</w:mn> </w:mrow> <w:mrow> <w:mo>+</w:mo> <w:mn>0.08</w:mn> </w:mrow> </w:msubsup> </w:mrow> </w:math> ) for GW200208_22. Second, we find <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msub> <y:mi>log</y:mi> <y:mn>10</y:mn> </y:msub> </y:math> Bayes factors between the eccentric aligned-spin versus quasicircular precessing-spin hypothesis between 1.43 and 4.92 for GW200129, 2.61 for GW190701 and 1.23 for GW200208_22. Third, our analysis does not show evidence for eccentricity in GW190521, which has an eccentric aligned-spin against quasicircular aligned-spin <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msub> <ab:mi>log</ab:mi> <ab:mn>10</ab:mn> </ab:msub> </ab:math> Bayes factor of 0.04. Fourth, we estimate that if we neglect the spin-precession and use an astrophysically motivated prior on the rate of eccentric BBHs, the probability of one out of the 57 events being eccentric is greater than 99.5% or <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mrow> <cb:mo stretchy="false">(</cb:mo> <cb:mn>100</cb:mn> <cb:mo>−</cb:mo> <cb:mn>8.4</cb:mn> <cb:mo>×</cb:mo> <cb:msup> <cb:mrow> <cb:mn>10</cb:mn> </cb:mrow> <cb:mrow> <cb:mo>−</cb:mo> <cb:mn>4</cb:mn> </cb:mrow> </cb:msup> <cb:mo stretchy="false">)</cb:mo> <cb:mo>%</cb:mo> </cb:mrow> </cb:math> (depending on the glitch mitigation). Fifth, we study the impact on parameter estimation when neglecting either eccentricity in quasicircular models or higher modes in eccentric models for GW events. These results underscore the importance of including eccentric parameters in the characterization of BBHs for the upcoming observing runs of the LVK Collaboration and for future detectors on the ground and in space, which will probe a more diverse BBH population.