Pulsar timing constraints on narrow-band stochastic signals

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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 Ψc<1.14 × 10⁻¹⁵, corresponding to the dimensionless strain amplitude hc=2√3Ψc < 4× 10⁻¹⁵ at frequency f=1.75× 10⁻⁸ Hz. In the narrow-band approximation, the upper limit on the energy density of GPB is found to be ΩGPB<1.27 × 10⁻⁹ at f=6.2× 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 10⁻²³ eV is assumed to be the galactic dark matter with a local density of 0.3 GeV cm⁻³.