  We performed a Bayesian analysis of pulsar timing residuals from the NANOGrav
pulsar timing array to search for a specific form of stochastic narrow-band
signal produced by oscillating gravitational potential in the Galactic halo.
Such oscillations arise in models of warm dark matter composed of an ultralight
massive scalar field (m\sim 10^{-23} eV), recently considered by Khmelnitsky
and Rubakov (2014). In the monochromatic approximation, the stringent upper
limit (95% c.l.) on the variable gravitational potential amplitude is found to
be Psi_c<1.14 10^{-15}, corresponding to the characteristic strain
h_c=2\sqrt{3}\Psi_c < 4 10^{-15} at frequency f=1.75 10^{-8} Hz. In the
narrow-band approximation, the upper limit of this background energy density is
\Omega_{GPB}<1.27 10^{-9} at frequency f=6.2 10^{-9} Hz. These limits are an
order of magnitude higher than the expected signal amplitude if the galactic
dark matter consists of the ultralight scalar field. The applied analysis of
pulsar timing residuals can be used to search for any narrow-band stochastic
signals with different correlation properties. As a by-product, parameters of
the red noise present in four NANOGrav pulsars (J1713+0747, J2145-0750,
B1855+09, J1744-1134) have been evaluated.
