Kilohertz gravitational waves from binary neutron star mergers. II. Inference of postmerger signals with the Einstein Telescope

Next-generation detectors are expected to be sensitive to postmerger signals from binary neutron star coalescences and, thus, to directly probe the remnant dynamics. We investigate the scientific potential of postmerger observations with the Einstein Telescope using full Bayesian analyses with the state of the art waveform model NRPMw. We show that postmerger signals with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>SNR</a:mi> <a:mo stretchy="false">∼</a:mo> <a:mn>7</a:mn> </a:mrow> </a:math> can be confidently detected with a Bayes’ factor of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>log</d:mi> <d:mtext> </d:mtext> <d:mi mathvariant="script">B</d:mi> <d:mo>≃</d:mo> <d:mn>5</d:mn> </d:math> ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi mathvariant="normal">e</g:mi> </g:math> -folded); the posterior distributions report informative measurements already at <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>SNR</j:mi> <j:mo>∼</j:mo> <j:mn>6</j:mn> </j:math> for some noise realizations. The postmerger peak frequency <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:msub> <l:mi>f</l:mi> <l:mn>2</l:mn> </l:msub> </l:math> can be confidently identified at SNR 7 with errors of <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>O</n:mi> <n:mo stretchy="false">(</n:mo> <n:mn>1</n:mn> <n:mtext> </n:mtext> <n:mtext> </n:mtext> <n:mi>kHz</n:mi> <n:mo stretchy="false">)</n:mo> </n:math> , that decrease below <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi>O</r:mi> <r:mo stretchy="false">(</r:mo> <r:mn>100</r:mn> <r:mtext> </r:mtext> <r:mtext> </r:mtext> <r:mi>Hz</r:mi> <r:mo stretchy="false">)</r:mo> </r:math> for SNR 10. The remnant’s time of collapse to black hole can be constrained to <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:mi>O</v:mi> <v:mo stretchy="false">(</v:mo> <v:mn>20</v:mn> <v:mtext> </v:mtext> <v:mtext> </v:mtext> <v:mi>ms</v:mi> <v:mo stretchy="false">)</v:mo> </v:math> at SNR 10. However, the inference can be biased by noise fluctuations if the latter exceed the signal’s amplitude before collapse. Violations of the equation of state (EOS)-insensitive relations for <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:msub> <z:mi>f</z:mi> <z:mn>2</z:mn> </z:msub> </z:math> can be detected at <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:mi>SNR</bb:mi> <bb:mo>≳</bb:mo> <bb:mn>8</bb:mn> </bb:math> if the frequency shifts are <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:mo>≳</db:mo> <db:mn>500</db:mn> <db:mtext> </db:mtext> <db:mtext> </db:mtext> <db:mi>Hz</db:mi> </db:math> . They can be smoking guns for EOS softening effects at extreme densities. However, the <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:msub> <fb:mi>f</fb:mi> <fb:mn>2</fb:mn> </fb:msub> </fb:math> measurement can be significantly biased by subdominant frequency components for short-lived remnants. In these cases, an EOS softening might be better inferred from the remnant’s earlier collapse.