Galactic Doppelganger: The chemical similarity among field stars and
  among stars with a common birth origin
  We explore to which extent stars within Galactic disk open clusters resemble
each other in the high-dimensional space of their photospheric element
abundances, and contrast this with pairs of field stars. Our analysis is based
on abundances for 20 elements, homogeneously derived from APOGEE spectra (with
carefully quantified uncertainties, with a median value of $\sim 0.03$ dex). We
consider 90 red giant stars in seven open clusters and find that most stars
within a cluster have abundances in most elements that are indistinguishable
(in a $\chi^2$-sense) from those of the other members, as expected for stellar
birth siblings. An analogous analysis among pairs of $>1000$ field stars shows
that highly significant abundance differences in the 20-dimensional space can
be established for the vast majority of these pairs, and that the APOGEE-based
abundance measurements have high discriminating power. However, pairs of field
stars whose abundances are indistinguishable even at 0.03~dex precision exist:
$\sim 0.3$ percent of all field star pairs, and $\sim 1.0$ percent of field
star pairs at the same (solar) metallicity [Fe/H] = $0 \pm 0.02$. Most of these
pairs are presumably not birth siblings from the same cluster, but rather
doppelganger. Our analysis implies that 'chemical tagging' in the strict sense,
identifying birth siblings for typical disk stars through their abundance
similarity alone, will not work with such data. However, our approach shows
that abundances have extremely valuable information for probabilistic
chemo-orbital modeling and combined with velocities, we have identified new
cluster members from the field.
