Recognizing Axionic Dark Matter by Compton and de Broglie Scale Modulation of Pulsar Timing

Light axionic dark matter, motivated by string theory, is increasingly favored for the no weakly interacting massive particle era. Galaxy formation is suppressed below a Jeans scale of similar or equal to 10(8) M-circle dot by setting the axion mass to m(B) similar to 10(-22) eV, and the large dark cores of dwarf galaxies are explained as solitons on the de Broglie scale. This is persuasive, but detection of the inherent scalar field oscillation at the Compton frequency omega(B) = (2.5 months)(-1) (m(B)/10(-22) eV) would be definitive. By evolving the coupled Schrdinger-Poisson equation for a Bose-Einstein condensate, we predict the dark matter is fully modulated by de Broglie interference, with a dense soliton core of size similar or equal to 150 pc, at the Galactic center. The oscillating field pressure induces general relativistic time dilation in proportion to the local dark matter density and pulsars within this dense core have detectably large timing residuals of similar or equal to 400 nsec/(m(B)/10(-22) eV). This is encouraging as many new pulsars should be discovered near the Galactic center with planned radio surveys. More generally, over the whole Galaxy, differences in dark matter density between pairs of pulsars imprints a pairwise Galactocentric signature that can be distinguished from an isotropic gravitational wave background.