Astrometric and timing effects of gravitational waves from localized sources

Abstract

Localized astronomical sources like a double stellar system, rotating neutron star, or a massive black hole at the center of the Milky Way emit periodic gravitational waves. For a long time only a far-zone contribution of gravitational fields of the localized sources (plane-wave-front approximation) were a matter of theoretical analysis. We demonstrate how this analysis can be extended to take into account near-zone and intermediate-zone contributions as well. The formalism is used to calculate gravitational-wave corrections to the Shapiro time delay in binary pulsars and low-frequency (LF) pulsar timing noise produced by an ensemble of double stars in our galaxy.c We note that variables r0 and θ0 are not independent and can be expressed through r and θ d Function F (ν) is nomalized to unity, and n(r) = n(θ, r) is normalized to the total number of double stars in the ensemble.

Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

“…The second important observation is that the class of the harmonic coordinates is actually much more generic than physicists used to think. In particular, we have shown [2,61,62] that the standard Arnowitt-Deser-Misner gauge [63] widely used for dynamic formulation of general relativity, may be viewed as a subclass of the harmonic gauge suitable for the description of the gravitational field of an isolated astronomical system in vacuum. A final remark is that we always work in this paper with solutions of the gravity-field wave equation (11) in terms of an observable quantity that is the deflection angle of a light ray referred to asymptotically flat space-time.…”

“…The planet has equal equatorial moments of inertia A B, and the axial moment of inertia C Þ A. The dynamic oblateness of the planet is denoted as J 2 C ÿ A =A [48,65]. This definition yields the intrinsic quadrupole moment represented as an STF tensor of the second rank [65] …”

“…Preliminary calculations [5] reveal that the major planets of the solar system are sufficiently massive to pull photons by their gravitational fields, which have significant multipolar structures [6], in contrast with the Sun whose quadrupole moment is only J 2 2:3 10 ÿ7 [7,8]. Moreover, in the case of a photon propagating near the planet the interaction between the gravitational field and the photon can no longer be considered static, because the planet moves around the Sun as the photon traverses through the solar system [9,10].…”

“…Beyond the microarcsecond threshold, one will be able to observe a new range of celestial physical phenomena caused by gravitational waves from the early universe and various localized astronomical sources, space-time topological defects, moving gravitational lenses, time variability of gravitational fields of supermassive binary black holes located in quasars, and many others [1][2][3]. Furthermore, this will allow us to test the general theory of relativity in the solar system in a dynamic regime, that is when the velocity-dependent and accelerationdependent components of the gravitational field (the metric tensor) of the Sun and planets bring about observable relativistic effects in the light deflection, time delay, and frequency [4], to an unparalleled degree of precision.…”

Gaia-like astrometry and gravitational waves

“…The first subject of these studies was the effect of stochastic background of ultra-low-frequency primordial gravitational waves on the propagation of light as seen in astrometry, pulsar timing and other observational techniques. Then, triggered by some false claims in the literature, astrometric effects of gravitational waves from localized sources have been studied in great details [1,6,28,42, and references therein]. Starting from the very beginning of the space astrometry project Gaia it was clear that Gaia can potentially put an interesting limit on the energy flux of primordial gravitational waves [7,22,36].…”