Testing scalar dark matter clumps with pulsar timing arrays

Scalar dark matter is a viable alternative to particle dark matter models such as weakly interacting massive particles. This is particularly the case for scalars with a low mass $m\ensuremath{\gtrsim}{10}^{\ensuremath{-}21}\text{ }\text{ }\mathrm{eV}$ as required to make quantum effects macroscopic on galactic scales. We point out that by synchronizing the measurements of arrival times of pairs of pulsars, pulsar timing arrays could probe ultralight dark matter (ULDM) scenarios with a mass ${10}^{\ensuremath{-}23}\text{ }\text{ }\mathrm{eV}\ensuremath{\lesssim}m\ensuremath{\lesssim}{10}^{\ensuremath{-}19}\text{ }\text{ }\mathrm{eV}$ that is greater than the one reached in standard analysis. The upper limit on the mass $m$ is set by the time lag $\mathrm{\ensuremath{\Delta}}t$ between the observations of the two pulsars and could be pushed above ${10}^{\ensuremath{-}19}\text{ }\text{ }\mathrm{eV}$ for $\mathrm{\ensuremath{\Delta}}t$ smaller than one hour. However, for these high scalar masses only very high density dark matter clouds could be detected and the capture rate of neutron stars is too low to provide sufficient statistics. Significant detection probabilities would thus require direct dark-matter-baryon interactions that favor the formation of neutron stars within such dark matter clouds, or the discovery of black hole/pulsar binary systems, taking advantage of the dark matter spike generated by the black hole.