  We report the discovery of LEHPM 2-59 as the coolest extreme M subdwarf
(esdM) found to date. Optical and near infrared spectroscopy demonstrate that
this source is of later spectral type than the esdM7 APMPM 0559-2903, with the
presence of strong alkali lines (including Rb I), VO absorption at 7400 A and
H2O absorption at 1.4 microns. Current optical classification schemes yield a
spectral type of esdM8, making LEHPM 2-59 one of only two ultracool esdMs
known. The substantial space velocity of this object (V_galactic ~ -180 km/s)
identifies it as a halo star. Spectral model fits to the optical and near
infrared spectral data for this and four other late-type esdMs indicate that
LEHPM 2-59 is the coolest esdM currently known, with Teff = 2800-3000 K and
-1.5 <~ [M/H] <~ -2.0. Comparison of Teff determinations for M dwarfs and esdMs
based on spectral model fits from this study and the literature demonstrate a
divergence in Teff scales beyond spectral types M5/esdM5, as large as 600-800 K
by types M8/esdM8. While this divergence is likely an artifact of the
underlying classification scheme, it may lead to systematic errors in the
derived properties of intermediate metallicity subdwarfs. We comment on the
future of ultracool subdwarf classification, and suggest several ideas for
addressing shortcomings in current (largely extrapolated) schemes.
