  An ultralight scalar field is a candidate for the dark matter. The ultralight
scalar dark matter with mass around $10^{-23}\,{\rm eV}$ 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. We
give the 95% confidence upper limit for 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 $10^{-8.19}\,{ \rm Hz}$ which corresponds to the mass range
from $9.45\times10^{-24}$ to $1.34\times10^{-23}\,{\rm eV}$. In terms of the
energy density of the dark matter, we find that the energy density near the
Earth is less than $7\,{\rm GeV/cm^3}$ in the range from $10^{-8.55}$ to
$10^{-8.01}\,{ \rm Hz}$ (from $5.83\times10^{-24}$ to $2.02\times10^{-23}\,{\rm
eV}$). The strongest upper limit on the the energy density is given by $2\,{\rm
GeV/cm^3}$ at a frequency $10^{-8.28}\,{ \rm Hz}$ (corresponding to a mass
$1.09\times10^{-23}\,{\rm eV}$). We find that the signal of the ultralight
scalar dark matter can be explained by the solar system ephemeris effect. Also,
we reveal that the model of the solar system ephemeris effect prefers
parameters which are contrary to the expectation that noise will be reduced on
all pulsars.
