Constraints on ultralight scalar dark matter from pulsar timing

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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 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 Psic<1.14 10⁻¹⁵, corresponding to the characteristic strain hc=2√3Ψc < 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 ΩGPB<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.