Search for eccentric NSBH and BNS mergers in the third observing run of Advanced LIGO and Virgo

The possible formation histories of neutron star binaries remain unresolved by current gravitational-wave catalogs. The detection of an eccentric binary system could be vital in constraining compact binary formation models. We present the first search for aligned spin eccentric neutron star-black hole binaries (NSBH) and the most sensitive search for aligned-spin eccentric binary neutron star (BNS) systems using data from the third observing run of the advanced LIGO and advanced Virgo detectors. No new statistically significant candidates are found; we constrain the local merger rate for specific astrophysical models to be less than <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>150</a:mn><a:mtext> </a:mtext><a:mtext> </a:mtext><a:msup><a:mrow><a:mi>Gpc</a:mi></a:mrow><a:mrow><a:mo>−</a:mo><a:mn>3</a:mn></a:mrow></a:msup><a:mtext> </a:mtext><a:msup><a:mrow><a:mi>yr</a:mi></a:mrow><a:mrow><a:mo>−</a:mo><a:mn>1</a:mn></a:mrow></a:msup></a:mrow></a:math> for binary neutron stars in the field, and, 50, 100, and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>70</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:msup><c:mrow><c:mi>Gpc</c:mi></c:mrow><c:mrow><c:mo>−</c:mo><c:mn>3</c:mn></c:mrow></c:msup><c:mtext> </c:mtext><c:msup><c:mrow><c:mi>yr</c:mi></c:mrow><c:mrow><c:mo>−</c:mo><c:mn>1</c:mn></c:mrow></c:msup></c:mrow></c:math> for neutron star-black hole binaries in globular clusters, hierarchical triples and nuclear clusters, respectively, at the 90% confidence level if we assume that no sources have been observed from these populations. We predict the capabilities of upcoming and next-generation observatory networks; we investigate the ability of three LIGO (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi mathvariant="normal">A</e:mi><e:mo>#</e:mo></e:msup></e:math>) detectors and Cosmic Explorer <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:mi>CE</h:mi><h:mtext> </h:mtext><h:mo stretchy="false">(</h:mo><h:mn>20</h:mn><h:mtext> </h:mtext><h:mi>km</h:mi><h:mo stretchy="false">)</h:mo><h:mo>+</h:mo><h:mi>CE</h:mi><h:mtext> </h:mtext><h:mo stretchy="false">(</h:mo><h:mn>40</h:mn><h:mtext> </h:mtext><h:mi>km</h:mi><h:mo stretchy="false">)</h:mo></h:mrow></h:math> to use eccentric binary observations for determining the formation history of neutron star binaries. We find that 2–100 years of observation with three <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msup><n:mi mathvariant="normal">A</n:mi><n:mo>#</n:mo></n:msup></n:math> observatories are required before we observe clearly eccentric NSBH binaries; this reduces to only 10 days–1 year with the CE detector network. CE will observe tens to hundreds of measurably eccentric binaries from each of the formation models we consider.