  Using the proposed space gravitational wave detector LISA, we will be able to
measure the geometrical configurations of $\sim 10^4$ close white dwarf
binaries in our Galaxy. The obtained data will be an entirely new resource to
examine the randomness of their orbital orientations. Partly motivated by a
recent reported on the systematic alignments of bulge planetary nebulae, we
discuss the outlook of the orientational analysis with LISA. We find that a
quadrupole pattern as small as $\sim 0.05$ can be detected for bulge white
dwarf binaries, owing to their large available number. From such a pattern
analysis, we might geometrically explore fossil records in our Galaxy billions
of years ago.
