Measuring tides and binary parameters from gravitational wave data and eclipsing timings of detached white dwarf binaries

Abstract

The discovery of the most compact detached white dwarf (WD) binary SDSS J065133.33+284423.3 has been discussed in terms of probing the tidal effects in WDs. This system is also a verification source for the space-based gravitational wave (GW) detector, eLISA, or the evolved Laser Interferometer Space Antenna, which will observe short-period compact Galactic binaries with P orb ≲ 5 hr. We address the prospects of performing tidal studies using eLISA binaries by showing the fractional uncertainties in the orbital decay rate, , and the rate of that decay, expected from both the GW and electromagnetic (EM) data for some of the high-f binaries. We find that and can be measured using GW data only for the most massive WD binaries observed at high frequencies. From timing the eclipses for ∼10 yr, we find that can be known to ∼0.1% for J0651. We find that from GW data alone, measuring the effects of tides in binaries is (almost) impossible. We also investigate the improvement in the knowledge of the binary parameters by combining the GW amplitude and inclination with EM data with and without . In our previous work, we found that EM data on distance constrained the 2σ uncertainty in chirp mass to 15%-25% whereas adding reduces it to 0.11%. EM data on also constrain the 2σ uncertainty in distance to 35%-19%. EM data on primary mass constrain the secondary mass m 2 to factors of two to ∼40% whereas adding reduces this to 25%. Finally, using single-line spectroscopic data constrains 2σ uncertainties in both the m 2, d to factors of two to ∼40%. Adding EM data on reduces these 2σ uncertainties to ≤25% and 6%-19%, respectively. Thus we find that EM measurements of and radial velocity are valuable in constraining eLISA binary parameters. © 2014. The American Astronomical Society. All rights reserved..