Using electromagnetic observations to aid gravitational-wave parameter estimation of compact binaries observed with LISA

We present a first-stage study of the effect of using knowledge from electromagnetic (EM) observations in the gravitational wave (GW) data analysis of Galactic binaries that are predicted to be observed by the new Laser Interferometer Space Antenna in the low-frequency range, $10^{-4} \mathrm{Hz}<f<1 \mathrm{Hz}$. In particular, we examine the extent to which the accuracy of GW parameter estimation improves if we use available information from EM data. We do this by investigating whether correlations exist between the GW parameters that describe these binaries and whether some of these parameters are also available from EM observations. We used verification binaries, which are known as the guaranteed sources for eLISA and will test the functioning of the instrument. We find that of the seven parameters that characterise such a binary, only a few are correlated. The most useful result is the strong correlation between amplitude and inclination, which can be used to constrain the parameter uncertainty in amplitude by making use of the constraint of inclination from EM measurements. The improvement can be up to a factor of $\sim6.5$, but depends on the signal-to-noise ratio of the source data. Moreover, we find that this strong correlation depends on the inclination. For mildly face-on binaries ($\iota \lesssim 45^{\circ}$), EM data on inclination can improve the estimate of the GW amplitude by a significant factor. However, for edge-on binaries ($\iota \sim 90^{\circ}$), the inclination can be determined accurately from GW data alone, thus GW data can be used to select systems that will likely be eclipsing binaries for EM follow-up.