Ultralight scalar dark matter versus nonadiabatic perfect fluid dark matter in pulsar timing

Recent evidence for stochastic gravitational waves reported by pulsar timing array (PTA) Collaborations might open a new window for studying cosmology and astrophysical phenomena. In addition to signals from gravitational waves, there is motivation to explore residual signals from oscillating dark matter, which might partially comprise the galactic halo. We investigate fluctuations in pulsar timing originating from the coherent oscillation of scalar dark matter up to the subleading-order correction of $\mathcal{O}(k/m)$, as well as from acoustic oscillations of nonadiabatic perfect fluid dark matter. Both types of dark matter can induce the Newtonian potential and curvature perturbations, thereby affecting pulsar timing. We show distinctive signatures in pulsar timing residuals and angular correlations in the PTA frequency band and considering the known distances of pulsars. For scalar dark matter, both the timing residuals and the angular correlation are sensitive to small variations in the distance, $\ensuremath{\delta}L$, due to the subleading-order correction of $\mathcal{O}(k/m)$. In contrast, for perfect fluid dark matter, it is insensitive to the $\ensuremath{\delta}L$. For deterministic sources from scalar dark matter, the distance of a pulsar has influence on the degree of directional dependence of timing residuals, significantly. For stochastic sources from perfect fluid dark matter, the angular correlation tends to a constant and enhances only when the pulsar pair is very close to each other. In this sense, perfect fluid dark matter is shown to be a more suitable physical origin for monopolar signals in angular correlations compared to the scalar dark matter.