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. 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 $10^{-8.19}\,{ \rm Hz}$ 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 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.

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使用 NANOGrav 脉冲星计时阵列寻找超轻标量暗物质

超轻标量场是暗物质的候选者。质量约为 $10^{-23}\,{\rm eV}$ 的超轻标量暗物质在脉冲星定时阵列的敏感频率范围内引起脉冲到达时间的振荡。我们使用北美纳赫兹引力波天文台 11 年数据集搜索超轻标量暗物质。作为贝叶斯分析的结果，没有发现超轻标量暗物质存在的重要证据。因此，超轻标量暗物质诱发的信号具有95%的置信度上限。与使用 Parkes Pulsar Timing Array 12-year 数据集（Porayko et al. 2018）通过贝叶斯分析获得的超轻标量暗物质振幅的已发表贝叶斯上限相比，我们发现在 $10^{-8.34}$ 到 $10^{-8.19}\,{ \rm Hz}$ 的频率范围内强三倍的上限，对应于 $9.45\times10^{-24}$ 的质量范围到 $1.34\times10^{-23}\,{\rm eV}$。在暗物质的能量密度方面，我们发现地球附近的能量密度小于$7\，{\rm GeV/cm^3}$ 范围从$10^{-8.55}$到$10^ {-8.01}\,{ \rm Hz}$（从 $5.83\times10^{-24}$ 到 $2.02\times10^{-23}\,{\rm eV}$）。能量密度的最强上限由 $2\,{\rm GeV/cm^3}$ 给出，频率 $10^{-8.28}\,{ \rm Hz}$（对应于质量 $1.09\times10 ^{-23}\,{\rm eV}$)。我们还确认，如果观测数据模型中不包含太阳系星历误差，则不能排除超轻标量暗物质诱发信号的存在。而且，