  A number of observations of stellar systems show a mild preference for
anomalously fast cooling compared with what predicted in the standard theory,
which leads to a speculation that there exists an additional energy loss
mechanism originated from the emission of axions in stars. We revisit the
global analysis of the stellar cooling anomalies by adopting conservative
assessments on several systematic uncertainties and find that the significance
of the cooling hints becomes weaker but still indicates a non-vanishing
axion-electron coupling at around 2.4$\,\sigma$. With the revised analysis
results, we explore the possibility that such excessive energy losses are
interpreted in the framework of variant axion models, which require two Higgs
doublets and flavor-dependent Peccei-Quinn charge assignments. These models
resolve two fundamental issues faced in the traditional KSVZ/DFSZ models by
predicting a sizable axion coupling to electrons required to explain the
cooling anomalies and at the same time providing a solution to the cosmological
domain wall problem. We also find that a specific structure of the axion
couplings to electrons and nucleons slightly relaxes the constraint from
supernova 1987A and enlarges viable parameter regions compared with the DFSZ
models. It is shown that good global fits to the observational data are
obtained for axion mass ranges of $0.45\,\mathrm{meV} \lesssim m_a \lesssim
30\,\mathrm{meV}$, and that the predicted parameter regions can be probed in
the forthcoming helioscope searches.
