Systematic Parameter Errors in Inspiraling Neutron Star Binaries

The coalescence of two neutron stars is an important gravitational wave source for LIGO and other detectors. Numerous studies have considered the precision with which binary parameters (masses, spins, Love numbers) can be measured. Here I consider the accuracy with which these parameters can be determined in the presence of systematic errors due to waveform approximations. These approximations include truncation of the post-Newtonian (PN) series and neglect of neutron star (NS) spin, tidal deformation, or orbital eccentricity. All of these effects can yield systematic errors that exceed statistical errors for plausible parameter values. In particular, neglecting spin, eccentricity, or high-order PN terms causes a significant bias in the NS Love number. Tidal effects will not be measurable with PN inspiral waveforms if these systematic errors are not controlled.

Figure 1

Contribution of the last four terms in Eq. (1) to the number of wave cycles in the phase of the Fourier transform $\tilde{h}(f)$. Parameter values are as indicated; $t_c$ and ${\varphi }_c$ are chosen such that $\mathrm{\Delta }{N}_{\text{cyc}}$ and its frequency derivative vanish at a reference frequency $f_0=10\mathrm{Hz}$: i.e., for each term $X$, $2\pi \mathrm{\Delta }{N}_{\text{cyc}}^X=\mathrm{\Delta }{\psi }^X(f)-\mathrm{\Delta }{\psi }^X(f_0)+(f-f_0)d\mathrm{\Delta }{\psi }^X/d{f}_0$, where $\mathrm{\Delta }{\psi }^X\equiv 3\mathrm{\Delta }{\mathrm{\Psi }}^X/(128\eta v^5)$.

Figure 2

aLIGO and ET statistical and systematic parameter errors for different waveform approximations. (a) Fractional errors in $\eta$ due to neglecting high PN-order terms as a function of the relative PN order in ${\mathrm{\Psi }}_{\mathrm{AP}}$. (b) The corresponding error due to neglecting spin effects. (c) The error from neglecting orbital eccentricity. (d) The ratio of systematic to statistical errors in the reduced tidal deformation parameter $\tilde{\mathrm{\Lambda }}$ as a function of ${\widehat{\lambda }}_i$ and for different waveform errors (neglecting spin, eccentricity, or high PN terms). All plots are for a $m_1=m_2=1.4M_{\odot }$ BNS at 100 Mpc. Angle-averaged SNRs are 14.5 for aLIGO and 175 for ET. These results are relatively insensitive to small changes in $\eta$ that keep $M$ constant.