  The XENON1T collaboration has found an excess of electron recoil events in
their Science Run 1 data below ~7 keV with a spectral shape consistent with
that expected from a solar-axion-induced signal. The claimed statistical
significance of the solar-axion model over the null hypothesis is 3.5$\sigma$.
In this work we provide evidence for mismodeling in the electron recoil data
that may decrease the local significance of the axion model to as low as $p
\approx 0.1$. To reach this conclusion, we search for a signal with the
spectral template of the solar axion model, but shifted to higher (unphysical)
energies above ~7 keV. We find that the distribution of significances found
from this side-band analysis does not follow the expected chi-square
distribution, which allows us to quantify the extent to which mismodeling may
be affecting the interpretation of the data at energies below ~7 keV. For
example, we find that there is an even higher-significance fit to the data when
the solar axion model is shifted upwards in energy by ~15 keV and allowed to
have a negative normalization.
