Published online by Cambridge University Press: 30 March 2016
My contribution to this Joint Discussion can hardly be termed very novel or original. Rather, I just want to call your attention here to two headaches - one perhaps only a hangover, but the other a real migraine. Sooner or later these two headaches beset anyone who persists in asking how the random motions of stars in the only vicinity where we tolerably observe them can possibly jibe with the sensible presumption that not only our neighborhood but this entire Galaxy should by now be reasonably stable.
There is of course nothing strictly ‘local’ about any problem involving the far-reaching gravity. Yet if some conceivable instability of our collection of nearby stars comes even close to deserving such a label, it is surely the Jeans instability or tendency toward gravitational collapse. After all it is not difficult to estimate (e.g., Toomre, 1964) that the most troublesome of such incipient clumpings ought to have significant dimensions (such as half-wavelengths) of the order of 3 or 4 kpc. Even the latter scale is probably not too large a fraction of our distance from the galactic center for ‘local’ analyses in the WKBJ spirit to remain coarsely trustworthy.