Constraining parameters of white-dwarf binaries using gravitational-wave and electromagnetic observations

TL;DR

This paper evaluates how combining gravitational-wave data from eLISA with electromagnetic observations can significantly improve the measurement of physical parameters of white-dwarf binaries, such as masses and distances.

Contribution

It quantifies the parameter constraints achievable by integrating EM measurements with GW data for white-dwarf binaries, highlighting the most effective observational combinations.

Findings

EM distance measurements constrain chirp mass to 15-25%.

Single-lined spectroscopic data constrains secondary mass and distance to 40%.

Double-lined spectroscopic data constrains distance to 30%.

Abstract

The space-based gravitational wave (GW) detector, \emph{evolved Laser Interferometer Space Antenna} (eLISA) is expected to observe millions of compact Galactic binaries that populate our Milky Way. GW measurements obtained from the eLISA detector are in many cases complimentary to possible electro-magnetic (EM) data. In our previous papers, we have shown that the EM data can significantly enhance our knowledge of the astrophysically relevant GW parameters of the Galactic binaries, such as the amplitude and inclination. This is possible due to the presence of some strong correlations between GW parameters that are measurable by both EM and GW observations, for example the inclination and sky position. In this paper, we quantify the constraints in the physical parameters of the white-dwarf binaries, i.e. the individual masses, chirp mass and the distance to the source that can be obtained by combining the full set of EM measurements such as the inclination, radial velocities, distances and/or individual masses with the GW measurements. We find the following $2-\sigma$ fractional uncertainties in the parameters of interest. The EM observations of distance constrains the the chirp mass to $\sim 15-25 %$, whereas EM data of a single-lined spectroscopic binary constrains the secondary mass and the distance with factors of 2 to $\sim 40 %$. The single-line spectroscopic data complemented with distance constrains the secondary mass to $\sim 25-30%$. Finally EM data on double-lined spectroscopic binary constrains the distance to $\sim 30%$. All of these constraints depend on the inclination and the signal strength of the binary systems. We also find that the EM information on distance and/or the radial velocity are the most useful in improving the estimate of the secondary mass,inclination and/or distance.