Beyond secondorder convergence in simulations of binary neutron stars in full general relativity
Abstract
Despite the recent rapid progress in numerical relativity, a convergence order less than the second has so far plagued codes solving the EinsteinEuler system of equations. We report simulations of the inspiral of binary neutron stars in quasicircular orbits computed with a new code employing highorder, highresolution shockcapturing, finitedifferencing schemes that, for the first time, go beyond the secondorder barrier. In particular, without any tuning or alignment, we measure a convergence order above three both in the phase and in the amplitude of the gravitational waves. Because the new code is already able to calculate waveforms with very small phase errors at modest resolutions, we are able to obtain accurate estimates of tidal effects in the inspiral that are essentially free from the large numerical viscosity typical of lower order methods, and even for the challenging large compactness and smalldeformability binary considered here. We find a remarkable agreement between our Richardsonextrapolated waveform and the one from the tidally corrected postNewtonian (PN) TaylorT4 model, with a dephasing smaller than 0.4 rad during the seven orbits of the inspiral and up to the contact point. Because our results can be used reliably to assess the validity of the PN or other approximations at frequencies significantly larger than those considered so far in the literature, at these compactnesses, they seem to exclude significant tidal amplifications from next to nexttoleadingorder terms in the PN expansion.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 January 2014
 DOI:
 10.1093/mnrasl/slt137
 arXiv:
 arXiv:1306.6052
 Bibcode:
 2014MNRAS.437L..46R
 Keywords:

 gravitational waves;
 stars: neutron;
 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 Improved the alignment procedure with PN. Version accepted as a Letter on MNRAS. 5 pages, 3 figures