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Item Dynamical tides during the inspiral of rapidly spinning neutron stars: Solutions beyond mode resonance(American Physical Society, 2024-07) Yu, Hang; Arras, Phil; Weinberg, Nevin N.We investigate the dynamical tide in a gravitational wave (GW)-driven coalescing binary involving at least one neutron star (NS). The deformed NS is assumed to spin rapidly, with its spin axis antialigned with the orbit. Such an NS may exist if the binary forms dynamically in a dense environment, and it can lead to a particularly strong tide because the NS f-mode can be resonantly excited during the inspiral. We present a new analytical solution for the f-mode resonance by decomposing the tide into a resummed equilibrium component varying at the tidal forcing frequency and a dynamical component varying at the f-mode eigenfrequency that is excited only around mode resonance. This solution simplifies numerical implementations by avoiding the subtraction of two diverging terms as was done in previous analyses. It also extends the solution’s validity to frequencies beyond mode resonance. When the dynamical tide back reacts on the orbit, we demonstrate that the commonly adopted effective Love number is insufficient because it does not capture the tidal torque on the orbit that dominates the back reaction during mode resonance. An additional dressing factor originating from the imaginary part of the Love number is therefore introduced to model the torque. The dissipative interaction between the NS and the orbital mass multipoles is computed including the dynamical tide and shown to be subdominant compared to the conservative energy transfer from the orbit to the NS modes. Our study shows that orbital phase shifts caused by the 𝑙=3 and 𝑙=2 f-modes can reach 0.5 and 10 radians at their respective resonances if the NS has a spin rate of 850 Hz and direction antialigned with the orbit. Because of the large impact of the 𝑙=2 dynamical tide, a linearized analytical description becomes insufficient, calling for future developments to incorporate higher-order corrections. After mode excitation, the orbit cannot remain quasicircular, and the eccentricity excited by the 𝑙=2 dynamical tide can approach nearly 𝑒≃0.1, leading to nonmonotonic frequency evolution which breaks the stationary phase approximation commonly adopted by frequency domain phenomenological waveform constructions. Lastly, we demonstrate that the GW radiation from the resonantly excited f-mode alone can be detected with a signal-to-noise ratio exceeding unity at a distance of 50 Mpc with the next-generation GW detectors.Item Surface of rapidly-rotating neutron stars: Implications to neutron star parameter estimation(American Physical Society, 2021-03) Silva, Hector O.; Pappas, George; Yunes, Nicolás; Yagi, KentThe Neutron star Interior Composition Explorer (NICER) is currently observing the x-ray pulse profiles emitted by hot spots on the surface of rotating neutron stars allowing for an inference of their radii with unprecedented precision. A critical ingredient in the pulse profile model is an analytical formula for the oblate shape of the star. These formulas require a fitting over a large ensemble of neutron star solutions, which cover a wide set of equations of state, stellar compactnesses and rotational frequencies. However, this procedure introduces a source of systematic error, as (i) the fits do not describe perfectly the surface of all stars in the ensemble and (ii) neutron stars are described by a single equation of state, whose influence on the surface shape is averaged out during the fitting procedure. Here we perform a first study of this systematic error, finding evidence that it is subdominant relative to the statistical error in the radius inference by NICER. We also find evidence that the formula currently used by NICER can be used in the inference of the radii of rapidly rotating stars, outside of the formula’s domain of validity. Moreover, we employ an accurate enthalpy-based method to locate the surface of numerical solutions of rapidly rotating neutron stars and a new highly accurate formula to describe their surfaces. These results can be used in applications that require an accurate description of oblate surfaces of rapidly rotating neutron stars.