Astrometric Search Method for Individually Resolvable Gravitational Wave Sources with Gaia

Gravitational waves (GWs) cause the apparent position of distant stars to oscillate with a characteristic pattern on the sky. Astrometric measurements (e.g., those made by Gaia) provide a new way to search for GWs. The main difficulty facing such a search is the large size of the data set; Gaia observes more than one billion stars. In this Letter the problem of searching for GWs from individually resolvable supermassive black hole binaries using astrometry is addressed for the first time; it is demonstrated how the data set can be compressed by a factor of more than $10^6$, with a loss of sensitivity of less than 1%. This technique was successfully used to recover artificially injected GW signals from mock Gaia data and to assess the GW sensitivity of Gaia. Throughout the Letter the complementarity of Gaia and pulsar timing searches for GWs is highlighted.

Figure 1

Orthographic projection of the Northern hemisphere with $10^3$ stars. A GW from the north pole (black dot) causes stars to oscillate at the GW frequency. The black (red) lines show movement tracks for a linearly plus (cross) polarized GW. For clarity, the GW has an unphysically large strain amplitude of $A=0.1$. The fourfold rotational symmetry of the transverse-traceless GWs is clearly imprinted on the sky.

Figure 2

One-dimensional marginalized posteriors on $\overline{\mathrm{\Psi }}$ (black lines indicate injected values). The injected GW was circularly polarized (i.e., ${\varphi }_{+}-{\varphi }_{\times }=\pi /2$) so the ${\varphi }_{\times }$ posterior is shifted such that it overlaps with ${\varphi }_{+}$. The Mollweide sky map is shown with the area of the 68% credible region given.

Figure 3

The horizon distance is reduced (relative to the uncompressed data) during compression onto grid $n=1,2,\dots ,10$. Shown in red is the loss estimate obtained by considering the maximum angle between deflections in the same Voronoi cell.

Figure 4

The black curves show the strain sensitivity of the final Gaia data release using different time samplings ($T_0$, solid; $T_1$, dotted; $T_2$, dashed; $T_3$ dot-dashed). The colored lines show 95% PTA upper limits: NanoGrav ([19] red), Epta ([20] blue), and Ppta ([21] green). These curves show different quantities and are only intended for approximate comparison; the NanoGrav curve is a Bayesian upper limit, the Epta and Ppta curves are frequentist upper limits, while the Gaia curves show the amplitude necessary to achieve a (conservative) threshold Bayes’ factor. It should be noted that these PTA limits are several years old and improve over time; Gaia’s sensitivity will not improve further.