  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.
