  Observations show an almost ubiquitous presence of extra mixing in low-mass
upper giant branch stars. The most commonly invoked explanation for this is
thermohaline mixing. One-dimensional stellar evolution models include various
prescriptions for thermohaline mixing, but the use of observational data
directly to discriminate between thermohaline prescriptions has thus far been
limited. Here, we propose a new framework to facilitate direct comparison:
Using carbon-to-nitrogen measurements from the SDSS-IV APOGEE survey as a probe
of mixing and a fluid parameter known as the reduced density ratio from
one-dimensional stellar evolution programs, we compare the observed amount of
extra mixing on the upper giant branch to predicted trends from
three-dimensional fluid dynamics simulations. Using this method, we are able to
empirically constrain how mixing efficiency should vary with the reduced
density ratio. We find the observed amount of extra mixing is strongly
correlated with the reduced density ratio and that trends between reduced
density ratio and fundamental stellar parameters are robust across choices for
modeling prescription. We show that stars with available mixing data tend to
have relatively low density ratios, which should inform the regimes selected
for future simulation efforts. Finally, we show that there is increased mixing
at low reduced density ratios, which is consistent with current hydrodynamical
models of thermohaline mixing. The introduction of this framework sets a new
standard for theoretical modeling efforts, as validation for not only the
amount of extra mixing, but trends between the degree of extra mixing and
fundamental stellar parameters is now possible.
