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Constraints on Bose-Einstein-condensed Axion Dark Matter from The HI Nearby Galaxy Survey data

One of the leading candidates for dark matter is axion or axion-like particle in a form of Bose-Einstein condensate (BEC). In this paper, we present an analysis of 17 high-resolution galactic rotation curves from "The H{\footnotesize I} Nearby Galaxy Survey (THINGS)" data [F. Walter et al., Astron. J. 136, 2563 (2008)] in the context of the axionic Bose-Einstein condensed dark matter model. Assuming a repulsive two-body interaction, we solve the non-relativistic Gross-Pitaevskii equation for $N$ gravitationally trapped bosons in the Thomas-Fermi approximation. We obtain the maximum possible radius $R$ and the mass profile $M(r)$ of a dilute axionic Bose-Einstein condensed gas cloud. A standard least-$χ^2$ method is employed to find the best-fit values of the total mass $M$ of the axion BEC and its radius $R$. The local mass density of BEC axion dark-matter is $ρ_{a}\simeq 0.02~{\rm GeV/cm}^3$, which agrees with that presented by Beck [C. Beck, Phys. Rev. Lett. 111, 231801 (2013)]. The axion mass $m_a$ we obtain depends not only on the best-fit value of $R$ but also on the $s$-wave scattering length $a$ ($m_a \propto a^{1/3}$). The transition temperature $T_a$ of axion BEC on galactic scales is also estimated. Comparing the calculated $T_a$ with the ambient temperature of galaxies and galaxy clusters implies that $a\sim 10^{-3}$ fm. The corresponding axion mass is $m_a\simeq 0.58$ meV. We compare our results with others.