  Studying the Milky Way disk structure using stars in narrow bins of [Fe/H]
and [alpha/Fe] has recently been proposed as a powerful method to understand
the Galactic thick and thin disk formation. It has been assumed so far that
these mono-abundance populations (MAPs) are also coeval, or mono-age,
populations. Here we study this relationship for a Milky Way chemo-dynamical
model and show that equivalence between MAPs and mono-age populations exists
only for the high-[alpha/Fe] tail, where the chemical evolution curves of
different Galactic radii are far apart. At lower [alpha/Fe]-values a MAP is
composed of stars with a range in ages, even for small observational
uncertainties and a small MAP bin size. Due to the disk inside-out formation,
for these MAPs younger stars are typically located at larger radii, which
results in negative radial age gradients that can be as large as 2 Gyr/kpc.
Positive radial age gradients can result for MAPs at the lowest [alpha/Fe] and
highest [Fe/H] end. Such variations with age prevent the simple interpretation
of observations for which accurate ages are not available. Studying the
variation with radius of the stellar surface density and scale-height in our
model, we find good agreement to recent analyses of the APOGEE red-clump (RC)
sample when 1-4 Gyr old stars dominate (as expected for the RC). Our results
suggest that the APOGEE data are consistent with a Milky Way model for which
mono-age populations flare for all ages. We propose observational tests for the
validity of our predictions and argue that using accurate age measurements,
such as from asteroseismology, is crucial for putting constraints on the
Galactic formation and evolution.
