The Greater Taurus-Auriga Ecosystem I: There Is A Distributed Older
  Population
  The Taurus-Auriga association and its associated molecular cloud are a
benchmark population for studies of star and planet formation. The census of
Taurus-Auriga has been assembled over seven decades and has inherited the
biases, incompleteness, and systematic uncertainties of the input studies. The
notably unusual shape of the inferred IMF and the existence of several isolated
disk-bearing stars suggest that additional (likely disk-free) members might
remain to be discovered. We therefore have begun a global reassessment of the
membership of Taurus-Auriga that exploits new data and better definitions of
youth and kinematic membership. As a first step, we reconsider the membership
of all disk-free candidate members from the literature with spectral type
$\ge$F0, $3^h50^m<\alpha<5^h40^m$, and $14^{\circ}<\delta<34^{\circ}$. We
combine data from the literature with Keck/HIRES and UH88/SNIFS spectra to test
the membership of these candidates using HR diagram positions, proper motions,
RVs, H$\alpha$, lithium, and surface gravity. We find 218 confirmed or likely
Taurus members, 160 confirmed or likely interlopers, and only 18 that still
lack sufficient evidence to draw firm conclusions. A significant fraction of
these stars (81/218=37%) are not included in the most recent canonical member
lists. Intriguingly, there are few additional members in the immediate vicinity
of the molecular clouds, preserving the IMFs that have been deemed anomalous in
past work. Many of the likely Taurus members are distributed broadly across the
search area. When combined with known disk hosts, our updated census reveals
two regimes: a high-density population with a high disk fraction (indicative of
youth) that broadly traces the molecular clouds, and a low-density population
with low disk fraction (hence likely older) that most likely represents
previous generations of star formation.
