Gravitational wave sources as timing references for LISA data

In the mHz gravitational-wave band, galactic ultracompact binaries (UCBs) are continuous sources emitting at near-constant frequency. The signals from many of these galactic binaries will be sufficiently strong to be detectable by the Laser Interferometer Space Antenna (LISA) after $\sim \mathcal{O}(1\mathrm{week})$ of observing. In addition to their astrophysical value, these UCBs can be used to monitor the data quality of the observatory. This paper demonstrates the capabilities of galactic UCBs to be used as calibration sources for LISA by demanding signal coherence between adjacent week-long data segments separated by a gap in time of a priori unknown duration. A parameter for the gap duration is added to the UCB waveform model and used in a Markov-chain Monte Carlo algorithm simultaneously fitting for the astrophysical source parameters. Results from measurements of several UCBs are combined to produce a joint posterior on the gap duration. The measurement accuracy’s dependence on how much is known about the UCBs through prior observing, and seasonal variations due to the LISA orbital motion, is quantified. The duration of data gaps in a two-week segment of data can be constrained to within $\sim 0.2\mathrm{s}$ using $\mathcal{O}(10)$ UCBs after one month of observing. The timing accuracy from UCBs improves to $\lesssim 0.1\mathrm{s}$ after 1 year of mission operations. These results are robust to within a factor of $\sim 2$ when taking into account seasonal variations.

Figure 1

Circles show locations of the UCBs in frequency-amplitude space colored by their S/N after two weeks of observing. The black line is the LISA noise amplitude spectral density curve, including the contribution from the unresolved foreground of low-frequency UCBs in the galaxy (dashed line). The foreground is the residual signal from UCBs after all resolvable signals have been identified and subtracted. This example is from the expected residual after one year of LISA operations. For this study, only binaries with frequencies above the confusion noise were selected to avoid complexities due to seasonal variations of the foreground and source overlap.

Figure 2

Two-dimensional marginalized posterior distribution function for $f_0$ and gap duration $\delta t$ (shifted so that 0 is the true value) from analyzing two weeks of data without assuming any prior knowledge of the source, demonstrating the covariance between source frequency $f_0$ and gap duration. Horizontal lines enclose the 90% credible region after one month (light blue, solid line) and twelve months (dark green, dot-dashed line) of prior observing. The black dotted line is the true value of $f_0$ for the simulated source. Priors constructed from pilot runs on UCBs will propagate to improved constraints on the gap duration.

Figure 3

Example Gaussian fit (black, dashed line) to the marginalized posterior distribution function for $\delta t$ (green, solid histogram). The posterior is shifted in time so that the true value is at 0. Fitting the posterior to a Gaussian is a satisfactory approximation for this study. This demonstration used a $\sim 7\mathrm{mHz}$ source after two months of prior observing.

Figure 4

Left panel: $2\sigma$ intervals of the joint posterior on the gap duration $\delta t$ separating two 1-week segments of data as a function of the number of sources in the fit. The joint posterior $p(\delta t|\mathbf{d})$ converges towards the true value of $\delta t-\delta t_0=0$ as the number of sources increases. Different color bands correspond to priors built from one month (light blue) two months (dark blue), six months (light green) and twelve months (dark green) of observing. Right panel: The same results now showing the standard deviation ${\sigma }_{\delta t}$ of the joint posterior as a function of the number of sources, reaching 0.2 s (0.1 s) for 1 month (12 months) of prior observing.

Figure 5

Demonstration of the seasonal variation in the joint posterior of $\delta t$ using the 25 brightest UCBs after one (top left), two (top right), six (bottom left), and twelve (bottom right) months of prior observing. The different distributions are the results from simulating data during each quarter of the LISA constellation’s yearly orbit. While the seasonal variation is evident, the constraints on $\delta t$ are of similar scale.