  Recently, an anomalous excess was found in the electronic recoil data
collected at the XENON1T experiment. The excess may be explained by an
axion-like particle (ALP) with mass of a few keV and a coupling to electron of
$g_{ae} \sim 10^{-13}$, if the ALP constitutes all or some fraction of local
dark matter (DM). In order to satisfy the X-ray constraint, the ALP coupling to
photons must be significantly suppressed compared to that to electrons. This
strongly suggests that the ALP has no anomalous couplings to photons, i.e.,
there is no U(1)$_{\rm PQ}$-U(1)$_{\rm em}$-U(1)$_{\rm em}$ anomaly. We show
that such anomaly-free ALP DM predicts an X-ray line signal with a definite
strength through the operator arising from threshold corrections, and compare
it with the projected sensitivity of the ATHENA X-ray observatory. The
abundance of ALP DM can be explained by the misalignment mechanism, or by
thermal production if it constitutes a part of DM. In particular, we find that
the anomalous excess reported by the XENON1T experiment as well as the stellar
cooling anomalies from white dwarfs and red giants can be explained
simultaneously better when the ALP constitutes about 10\% of DM. As concrete
models, we revisit the leptophilic anomaly-free ALP DM considered in
[Phys.Lett.B 734 (2014) 178-182] as well as an ALP model based on a two Higgs
doublet model in the supplemental material.
