  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-$\chi^2$ 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 $\rho_{a}\simeq
0.02~{\rm GeV/cm}^3$, 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.
