A Pulsar-Timing Signature of Ultralight Scalar Dark Matter: Derivation and Proposed Test
Ultralight scalar dark matter behaves as a coherent classical field oscillating at a frequency set by its mass, inducing a small periodic modulation of fundamental constants and hence of pulsar rotation. We derive, from the coupling of a scalar to the gluon field strength, the leading periodic signal imprinted on pulsar timing residuals, including its characteristic monochromatic frequency and its spatial correlation across a pulsar array. We show the signal is distinguishable from the stochastic gravitational-wave background by its narrow bandwidth and predict the amplitude as a function of the scalar coupling. We propose, but do not perform, a stacked-search analysis on existing public pulsar-timing-array data and give the sensitivity scaling. The prediction is falsifiable: a null result excludes a computable region of coupling-mass space.