Fixing the center-of-mass frame of numerical relativity waveforms using the post-Newtonian center-of-mass charge

Abstract

The Bondi--van der Burg--Metzner--Sachs (BMS) frame of gravitational waves produced by numerical relativity (NR) simulations is crucial for building accurate waveform models. A proper comparison of NR waveforms with other models requires fixing the arbitrary BMS frame. In this work we improve the center-of-mass (CoM) frame fixing for quasicircular, nonprecessing binary systems. Past work approximated the CoM motion with just a linear fit. We compute a post-Newtonian result of the boosted CoM charge to also capture its physical out-spiraling oscillations. We show that using the analytical results improves the robustness of the fit parameters -- translation and boost vectors -- to the choice of duration and time of the fitting window. Our analysis demonstrates a maximum improvement in robustness when the window is placed at the center of the inspiral. We quantified this improvement by computing the ratio of variances of fit parameters when the fit window size is varied. The largest improvement in robustness of parameters is by a factor of $\sim 25$ for the boost vector and $\sim 20$ for the translation vector. Finally, we incorporate this method into the BMS frame-fixing routine of the python package $\texttt{scri}$ for waveforms produced with Cauchy-characteristic evolution.

Figures (6)

• Figure 1: Oscillatory pattern in the amplitude of different $(\ell,m)$ modes due to waveform being in an arbitrary BMS frame for a quasicircular nonprecessing system SXS:BBH:2115. The time axis has been shifted by the common horizon time, $t_{c}$. The dark curves represent the mode amplitudes when the waveform is in an arbitrary BMS frame, while the light curves are obtained after fixing the BMS frame of the waveform. The power from the dominant $(2,\pm 2)$ modes leaks to subdominant higher order modes. Fixing the frame eliminates the oscillations.
• Figure 2: The center-of-mass charge vector $\vec{G}$ (in blue) obtained from the asymptotic data of a quasicircular nonprecessing system SXS:BBH:2115. Before frame-fixing (left panel), $\vec{G}$ starts closer to the origin and drifts away in a boosted outspiral. A fit to the boosted post-Newtonian prediction of Eq. \ref{['eq:Boosted CoM charge']} (orange, dashed) agrees well with numerical data. Notice the difference in scales after fixing the PNBMS frame (right panel). The small box near the origin in the left plot correspond to the range of CoM charge after fixing the frame. This plot includes times in the 15%--85% region between the metadata's reference_time and the time of the maximum norm of $h$ across the entire 2-sphere.
• Figure 3: Prefactor in the analytical CoM charge expression with derivative undefined at $\nu = \tfrac{1}{4}$, which is the case for equal mass ratio binaries.
• Figure 4: Different choices for varying the window sizes over the inspiral. The arrow head (in yellow) represents the direction in which the window size is increased for our analysis.
• Figure 5: Sensitivity of the boost $\vec{\beta}$ and translation $\vec{\Delta}$ fit parameters to different window sizes for fitting the boosted CoM charge for the simulation SXS:BBH:2115, which shows some of the best improvement between the old and new methods. The dashed grey curve shows the sensitivity of the previous linear fit while the navy blue curve shows the sensitivity of the new analytical PN fit from Eq. \ref{['eq:Boosted CoM charge']}. The windows for this figure were "center fixed" (see Fig. \ref{['fig:window-choices']}), but is qualitatively similar for start- and end-fixed.