  We have conducted a photometric study of late-type members of the TW Hydrae
association (TWA) and measured the rotation periods for 16 stars in 12 systems.
For TWA stars listed by Webb et al. and Sterzik et al. (TWA 1-13; led by TW Hya
= TWA 1) we find a median period of 4.7 d. However, for stars that we measured
in the TWA 14-19 group identified by Zuckerman et al., we find a median period
of only 0.7 d. The period distributions of the two groups cannot be reconciled
at the 3-sigma significance level. Using photometric arguments supported by the
Hipparcos distance to HD 102458 (= TWA 19A), we find that TWA 14-19 reside at
an average distance of d \approx 90 pc, spatially at the near boundary of the
Lower Centaurus-Crux (LCC) subgroup of the Ophiuchus-Scorpius-Centaurus OB-star
association (OSCA). Proper motions for HD 102458, TWA 14, 18 and 19B link these
stars to the LCC subgroup. From Hertzsprung-Russell (H-R) diagram placement, we
derive an age of \approx 17 Myr for the HD 102458 system that may be the
representative age for the TWA 14-19 group. Merging various lines of evidence,
we conclude that these stars form a spatially- and rotationally-distinct
population of older pre-main sequence (PMS) stars, rather than being an
extension of the TWA beyond those stars associated with TW Hya that have an age
of \sim 10 Myr and reside at d \approx 55 pc. Instead, TWA 14-19 likely
represent the population of low-mass stars still physically associated with the
LCC subgroup.
