# Nonlinear-in-spin effects in effective-one-body waveform models of spin-aligned, inspiralling, neutron star binaries

## TL;DR

This paper enhances the effective-one-body waveform model for spin-aligned neutron star binaries by incorporating nonlinear-in-spin effects, including EOS-dependent self-spin terms at NNLO, and compares these with post-Newtonian approximations to improve gravitational wave modeling.

## Contribution

It introduces higher-order nonlinear-in-spin effects, especially EOS-dependent self-spin terms, into the TEOBResumS model, improving the accuracy of neutron star binary inspiral waveforms.

## Key findings

- NLO and NNLO monopole-quadrupole corrections accelerate phase evolution.
- Standard TaylorF2 PN treatment overestimates self-spin effects compared to EOB.
- Adding self-spin tail effects aligns PN and EOB phasing up to certain frequencies.

## Abstract

Spinning neutron stars acquire a quadrupole moment due to their own rotation. This quadratic-in-spin, self-spin effect depends on the equation of state (EOS) and affects the orbital motion and rate of inspiral of neutron star binaries. We incorporate the EOS-dependent self-spin (or monopole-quadrupole) terms in the spin-aligned effective-one-body (EOB) waveform model TEOBResumS at next-to-next-to-leading (NNLO) order, together with other (bilinear, cubic and quartic) nonlinear-in-spin effects (at leading order, LO). The structure of the Hamiltonian of TEOBResumS is such that it already incorporates, in the binary black hole case, the recently computed quartic-in-spin LO term. Using the gauge-invariant characterization of the phasing provided by the function $Q_\omega=\omega^2/\dot{\omega}$ of $\omega=2\pi f$ , where $f$ is the gravitational wave frequency, we study the EOS dependence of the self-spin effects and show that: (i) the next-to-leading order (NLO) and NNLO monopole-quadrupole corrections yield increasingly phase-accelerating effects compared to the corresponding LO contribution; (ii) the standard TaylorF2 post-Newtonian (PN) treatment of NLO (3PN) EOS-dependent self-spin effects makes their action stronger than the corresponding EOB description; (iii) the addition to the standard 3PN TaylorF2 post-Newtonian phasing description of self-spin tail effects at LO allows one to reconcile the self-spin part of the TaylorF2 PN phasing with the corresponding TEOBResumS one up to dimensionless frequencies $M\omega\simeq 0.04-0.06$. By generating the inspiral dynamics using the post-adiabatic approximation, incorporated in a new implementation of TEOBResumS, one finds that the computational time needed to obtain a typical waveform (including all multipoles up to $\ell=8$) from 10 Hz is of the order of 0.4 sec.