Persistent Astrometric Deflections from Gravitational-Wave Memory

Gravitational waves (GWs) produce small distortions in the observable distribution of stars in the sky. We describe the characteristic pattern of astrometric deflections created by a specific gravitational waveform called a burst with memory. Memory is a permanent, residual distortion of space left in the wake of GWs. We demonstrate that the astrometric effects of GW memory are qualitatively distinct from those of more broadly considered, oscillatory GWs—distinct in ways with potentially far-reaching observational implications. We discuss some such implications pertaining to the random-walk development of memory-induced deflection signatures over cosmological time spans and how those may influence observations of the cosmic microwave background.

Figure 1

We consider astrometric deflections from waveletlike GWs (blue), memorylike GWs (orange), and superpositions thereof.

Figure 2

The norm of the deflection vector $\delta n^i$ as a function of time for a GW propagating in the positive $\widehat{\mathbf{z}}$ direction. The deflection vector is given by Eq. (5) and we have specifically analyzed GW waveforms that are combinations of Eqs. (9) and (10) (scales as dictated by the legend). The two colors correspond to sources of light in different directions (see the color-coded “star” markers in Fig. 3). The solid curves describe the influence of an equal-weight superposition of a wavelet signal and a memory signal. The dashed curves describe the influence of the memory alone. We set the distance of the light sources to $c\tau \times 10^2$. The left-hand inset details early times near $t=0$ when the GW waveform passes over Earth. The right-hand inset details times near $t_L$ for the sky direction associated with the magenta star in Fig. 3. A similar inset detailing the corresponding part of the cyan curve would look almost identical.

Figure 3

The prompt and permanent deflection patterns caused by GW memory. For the sake of visualization, we inflated the magnitude of the effect to unrealistically large levels. Over a timescale $\tau$, the time it takes for memory to grow from zero to its final value, light sources originally at the locations of the black dots are deflected to the positions of the red squares as the wavefront passes over Earth. Over a long timescale $(d_s/c)(1+\widehat{\mathbf{z}}·\widehat{\mathbf{n}})$, light sources drift along the dotted green paths, eventually arriving at the positions of the blue triangles.