To investigate the potential connection between the intense X-ray emission from young, low-mass stars and the lifetimes of their circumstellar, planet-forming disks, we have compiled the X-ray luminosities ($L_X$) of M stars in the $sim$8 Myr-old TW Hya Association (TWA) for which X-ray data are presently available. Our investigation includes analysis of archival Chandra data for the TWA binary systems TWA 8, 9, and 13. Although our study suffers from poor statistics for stars later than M3, we find a trend of decreasing $L_X/L_{bol}$ with decreasing $T_{eff}$ for TWA M stars wherein the earliest-type (M0--M2) stars cluster near $log{(L_X/L_{bol})} approx -3.0$ and then $log{(L_X/L_{bol})}$ decreases, and its distribution broadens, for types M4 and later. The fraction of TWA stars that display evidence for residual primordial disk material also sharply increases in this same (mid-M) spectral type regime. This apparent anticorrelation between the relative X-ray luminosities of low-mass TWA stars and the longevities of their circumstellar disks suggests that primordial disks orbiting early-type M stars in the TWA have dispersed rapidly as a consequence of their persistent large X-ray fluxes. Conversely, the disks orbiting the very lowest-mass pre-MS stars and pre-MS brown dwarfs in the Association may have survived because their X-ray luminosities and, hence, disk photoevaporation rates are very low to begin with, and then further decline relatively early in their pre-MS evolution.
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