Exploring the Orbital Alignments of Galactic Close White Dwarf Binaries with LISA

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.