Pulsar timing constraints on narrow-band stochastic signals

We consider the sensitivity of the pulsar timing array (PTA) technique to specific kind of narrow-band stochastic signals in nano-Hz frequency range. Specifically, we examine the narrow-band signal produced by oscillating gravitational scalar potentials in the Galaxy (Gravitational Potential Background), which arise if an ultralight massive scalar field is the galactic dark matter. We have performed a Bayesian analysis of publicly available data on 12 pulsars obtained by the NANOGrav project. In the monochromatic approximation, the upper limit on the variable gravitational potential amplitude is ${\mathrm{\Psi }}_c<1.14\times {10}^{-15}$, corresponding to the dimensionless strain amplitude $h_c=2\sqrt{3}{\mathrm{\Psi }}_c<4\times {10}^{-15}$ at frequency $f=1.75\times {10}^{-8}Hz$. In the narrow-band approximation, the upper limit on the energy density of GPB is found to be ${\mathrm{\Omega }}_{GPB}<1.27\times {10}^{-9}$ at $f=6.2\times {10}^{-9}Hz$. These limits are an order of magnitude higher than the theoretically expected values, if the ultralight scalar field with a mass of $\sim {10}^{-23}eV$ is assumed to be the galactic dark matter with a local density of $\sim 0.3GeVc{m}^{-3}$.