Impact of updated Multipole Love numbers and f-Love Universal Relations in the context of Binary Neutron Stars

Neutron star (NS) equation of state (EoS) insensitive relations or universal relations (UR) involving neutron star bulk properties play a crucial role in gravitational-wave astronomy. Considering a wide range of equations of state originating from (i) phenomenological relativistic mean field models, (ii) realistic EoS models based on different physical motivations, and (iii) polytropic EoSs described by spectral decomposition method, we update the EoS-insensitive relations involving NS tidal deformability (Multipole Love relation) and the UR between f-mode frequency and tidal deformability (f-Love relation). We analyze the binary neutron star (BNS) event GW170817 using the frequency domain TaylorF2 waveform model with updated universal relations and find that the additional contribution of the octupolar electric tidal parameter and quadrupolar magnetic tidal parameter or the change of multipole Love relation has no significant impact on the inferred NS properties. However, adding the f-mode dynamical phase lowers the 90% upper bound on $\tilde{\Lambda}$ by 16-20% as well as lowers the upper bound of NSs radii by $\sim$500m. The combined URs (multipole Love and f-Love) developed in this work predict a higher median (also a higher 90% upper bound) for $\tilde{\Lambda}$ by 6% and also predict higher radii for the binary components of GW170817 by 200-300m compared to the URs used previously in the literature. We further perform injection and recovery studies on simulated events with different EoSs in $\rm A+$ detector configuration as well as with third generation (3G) Einstein telescope. In agreement with the literature, we find that neglecting f-mode dynamical tides can significantly bias the inferred NS properties, especially for low mass NSs. However, we also find that the impact of the URs is within statistical errors.