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 \Psi _ { c } < 1.14 \times 10 ^ { -15 } , corresponding to the dimensionless strain amplitude h _ { c } = 2 \sqrt { 3 } \Psi _ { c } < 4 \times 10 ^ { -15 } at frequency f = 1.75 \times 10 ^ { -8 } \mathrm { Hz } .
In the narrow-band approximation , the upper limit on the energy density of GPB is found to be \Omega _ { \mathrm { GPB } } < 1.27 \times 10 ^ { -9 } at f = 6.2 \times 10 ^ { -9 } \mathrm { 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 0.3 GeV cm ^ { -3 } .