Pulsar timing residual induced by ultralight tensor dark matter

Ultralight boson fields, with a mass around $10^{-23}\text{eV}$, are promising candidates for the elusive cosmological dark matter. These fields induce a periodic oscillation of the spacetime metric in the nanohertz frequency band, which is detectable by pulsar timing arrays. In this paper, we investigate the gravitational effect of ultralight tensor dark matter on the arrival time of radio pulses from pulsars. We find that the pulsar timing signal caused by tensor dark matter exhibits a different angular dependence than that by scalar and vector dark matter, making it possible to distinguish the ultralight dark matter signal with different spins. Combining the gravitational effect and the coupling effect of ultralight tensor dark matter with standard model matter provides a complementary way to constrain the coupling parameter $\alpha$. We estimate $\alpha \lesssim 10^{-6}\sim 10^{-5}$ in the mass range $m<5\times 10^{-23}\mathrm{eV}$ with current pulsar timing array.