An ultralight scalar field is a candidate for the dark matter .
The ultralight scalar dark matter with mass around 10 ^ { -23 } { eV } induces oscillations of the pulse arrival time in the sensitive frequency range of the pulsar timing arrays .
We search for the ultralight scalar dark matter using the North American Nanohertz Observatory for Gravitational Waves 11-year Data Set .
As a result of the Bayesian analysis , no significant evidence for the presence of the ultralight scalar dark matter is found .
Therefore , the 95 % confidence upper limit is given to the signal induced by the ultralight scalar dark matter .
In comparison with the published Bayesian upper limits on the amplitude of the ultralight scalar dark matter obtained by Bayesian analysis using the Parkes Pulsar Timing Array 12-year data set ( Porayko et al .
2018 ) , we find three times stronger upper limit in the frequency range from 10 ^ { -8.34 } to 10 ^ { -8.19 } { Hz } which corresponds to the mass range from 9.45 \times 10 ^ { -24 } to 1.34 \times 10 ^ { -23 } { eV } .
In terms of the energy density of the dark matter , we find that the energy density near the Earth is less than 7 { GeV / cm ^ { 3 } } in the range from 10 ^ { -8.55 } to 10 ^ { -8.01 } { Hz } ( from 5.83 \times 10 ^ { -24 } to 2.02 \times 10 ^ { -23 } { eV } ) .
The strongest upper limit on the the energy density is given by 2 { GeV / cm ^ { 3 } } at a frequency 10 ^ { -8.28 } { Hz } ( corresponding to a mass 1.09 \times 10 ^ { -23 } { eV } ) .
We also confirm that the existence of the signal induced by the ultralight scalar dark matter can not be excluded if the solar system ephemeris error is not included in the model of the observation data .
Moreover , if we analyze noises other than the signal of the ultralight scalar dark matter in advance , we find that the noise of the pulsar PSR J1909-3744 becomes smaller as expected but the noise of the other pulsars becomes larger .