Measuring neutron star radius with second and third generation gravitational wave detector networks

Abstract The next generation of ground-based interferometric gravitational wave detectors will observe mergers of black holes and neutron stars throughout cosmic time. A large number of the binary neutron star merger events will be observed with extreme high fidelity, and will provide stringent constraints on the equation of state of nuclear matter. In this paper, we investigate the systematic improvement in the measurability of the equation of state with increase in detector sensitivity by combining constraints obtained on the radius of a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:mn>1.4</mml:mn><mml:mstyle scriptlevel="0"/><mml:msub><mml:mrow><mml:mi mathvariant="normal">M</mml:mi></mml:mrow><mml:mrow><mml:mo>⊙</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math> neutron star from a simulated source population. Since the measurability of the equation of state depends on its stiffness, we consider a range of realistic equations of state that span the current observational constraints. We show that a single 40 km Cosmic Explorer detector can pin down the neutron star radius for a soft, medium and stiff equation of state with a precision of 10 m within a decade, whereas the current generation of ground-based detectors like the Advanced LIGO-Virgo network would take <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:mrow><mml:mi class="MJX-tex-calligraphic">O</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>5</mml:mn></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> years to do so for a soft equation of state.