Gaia-like astrometry and gravitational waves

Abstract

This paper discusses the effects of gravitational waves on high-accuracy astrometric observations such as those delivered by Gaia. Depending on the frequency of gravitational waves, two regimes for the influence of gravitational waves on astrometric data are identified: the regime when the effects of gravitational waves directly influence the derived proper motions of astrometric sources and the regime when those effects mostly appear in the residuals of the standard astrometric solution. The paper is focused on the second regime while the known results for the first regime are briefly summarized.The deflection of light due to a plane gravitational wave is then discussed. Starting from a model for the deflection we derive the corresponding partial derivatives and summarize some ideas for the search strategy of such signals in high-accuracy astrometric data. In order to reduce the dimensionality of the parameter space the use of vector spherical harmonics is suggested and explained. The explicit formulas for the VSH expansion of the astrometric signal of a plain gravitational wave are derived.Finally, potential sensitivity of Gaia astrometric data is discussed. Potential astrophysical sources of gravitational waves that can be interesting for astrometric detection are identified.PACS numbers: 95.10. Jk, 95.55.Br, 95.75.Pq, 95.85.Sz, 04.80.Nn

The Future of Astrometry in Space

“…In the regime of the ultra-low frequency primordial stochastic gravitational wave background, Gaia is expected to set an upper limit to the energy of the gravitational waves with frequencies ν < 6.410 −9 Hz at the level of GW < 0.00012h 1 00 −2 , where h 1 00 = H/(100Km/s/Mpc) and GW is the ratio of the energy density in gravitational waves to the energy density needed to close the Universe. This is a significant improvement over the best VLBI results (Mignard and Klioner, 2012;Klioner, 2018). These frequencies correspond to the stochastic background produced by the superposition many monochromatic signals, or of primordial origin.…”

“…One should distinguish the regime of ultra-low frequency gravitational waves that directly influence apparent proper motions (Pyne and Carroll, 1996;Gwinn et al, 1997;Book and Flanagan, 2011) and the regime of higher-frequency gravitation waves, the effects of which remain in the residuals of the astrometric solution (Klioner, 2018). In the regime of the ultra-low frequency primordial stochastic gravitational wave background, Gaia is expected to set an upper limit to the energy of the gravitational waves with frequencies ν < 6.410 −9 Hz at the level of GW < 0.00012h 1 00 −2 , where h 1 00 = H/(100Km/s/Mpc) and GW is the ratio of the energy density in gravitational waves to the energy density needed to close the Universe.…”

“…Recent papers have explored the astrometric detection of gravitational waves of higher frequencies in the context of Gaialike astrometric missions (Moore et al, 2017;Klioner, 2018). Assuming that all the signals with period less than 2 Gaia rotational periods will not detectable and that the period of the detectable waves should be considerably shorter than the length of the mission, one comes to the conclusion that Gaia is sensitive to wavelengths in the range 6.4 × 10 −9 Hz < ν < 3 × 10 −5 Hz (Klioner, 2018).…”

“…Assuming that all the signals with period less than 2 Gaia rotational periods will not detectable and that the period of the detectable waves should be considerably shorter than the length of the mission, one comes to the conclusion that Gaia is sensitive to wavelengths in the range 6.4 × 10 −9 Hz < ν < 3 × 10 −5 Hz (Klioner, 2018). A detailed practical algorithm to search the gravitational wave signatures in the residuals of Gaia-like astrometric solution is formulated in Klioner (2018). In this frequency range Gaia can search for signals of e.g., binary supermassive black holes.…”

Astrometric effects of gravitational wave backgrounds with nonluminal propagation speeds

“…(16a) and (16b) can be computed through eqs. (14). In the case = 0, a closed form expression can be derived, and the result is given in Appendix C I.…”