3.3. Sources of spiral waves
For one thing, Toomre's work T69 logically debunked the very principle of the Lin-Shu theoretical construction, having shown that for all the profundity of their core QSSS hypothesis their selfsustained-wave claim did not immediately follow from their genuinely straightforward - azimuthal-force-free - `asymptotic' dispersion relation. Yet it also made an important positive offer. The point was that wave-packet drifting and damping still did not exclude the possibility itself of really long-lived spirals, it only implied that "if such patterns are to persist, the above simply means that fresh waves (and wave energy) must somehow be created to take the place of older waves that drift away and disappear".
"Where could such fresh and relatively open spiral waves conceivably originate? The only three logical sources seem to be: (a) Such waves might result from some relatively local instability of the disk itself. (b) They may be excited by tidal forces from outside, such as from a companion or satellite galaxy. (c) Or they might be a by-product of some truly large-scale (but not necessarily spiral) distortion or instability involving an entire galaxy" (T69, p.909).
Thus Toomre simply formulated the evident - but as yet unreleased - necessity of establishing real mechanisms for maintaining spiral structure in galaxies.
At the time, Toomre's particular interest lay in the tidal mechanism. 56 It arose after his and Hunter's work on bending oscillations (modes) of finite-radius thin disks of a single gravitating material (Hunter & Toomre 1969). Among other things, that study hypothesized that the bending of our Galaxy might be due to the vertical component of tidal force during a possible close passage of the Large Magellanic Cloud (LMC). The authors reckoned that their relatively slowly evolving m = 1 retrograde responses were the only plausible candidates for the observed distortion. This made them infer a very close passage at a perigalactic distance of 20-25 kpc and, to bring estimates into appreciable consistence, even claim to favor a solar galactocentric distance RO 8 kpc instead of a little too `ineffective' 10 kpc sanctioned at the time by the IAU. But Hunter and Toomre "were blissfully unaware" of the work by Pfleiderer and Siedentopf (1961; 1963) and "also did not realize the undue sensitivity - which those German authors had already implied - of any such disk to the horizontal components of the same tidal force during a direct encounter of low inclination" (Toomre 1974, p.351). 57 In a sense, Pfleiderer became Toomre's eye-opener, and in the closing part of T69 he already proposed that much of any spiral density wave in our Galaxy might have evolved from vibrations set up during such a passage of the LMC. Providing its orbital eccentricity e 0.5, it would have spent less than one galactic year traversing the nearest 90° of galactocentric longitude, and in the direct - not retrograde - case the implied angular speed s would have roughly matched the speed of advance, - / 2, of the slow m = 2 `dispersion orbit'. "And that, coupled with the dominant m = 2 character of the tidal force in the plane, means any direct close passage of the LMC should have been very effective in exciting m = 2 oscillations of the Galaxy" at a radius where s = - / 2. "It also suggests that, even with self-gravitation taken into account, the resulting `pattern speed' should have been of the order of 10 km/sec/kpc" (T69, p.911).
Toomre (1969) supported his reasoning by computations of the perturber's action on the Galaxy disk test particles (Fig.12). Then he made a separate `progress report' at the Basel Symposium (Toomre 1970), but soon turned his tidal interests to more spectacular and controversial forms, which resulted in the famous dynamical study of `galactic bridges and tails' done jointly with his brother (Toomre & Toomre 1972). 58
Figure 12. A time history of the displacements of four rings of noninteracting test particles provoked by a simulated direct passage of the LMC. The spiral curves connect points on each ring which are at maximum distance from the Galaxy center. Point `CM' marks the location of the center of mass. Time in units of 108 years is reckoned from the perigalactic point. (The figure is reproduced from Toomre 1969)
56 By the 1960s, the version of gravitational tides as mainly causing the observed variety of `peculiar' forms of interacting galaxies had been discredited, and what was brought to the forefront were alternative considerations about magnetism, explosions, ejections, and just as-yet-unknown `forces of repulsion', all kept at a level of hopes and suspicions (the topic has been nicely reviewed in Toomre & Toomre 1973). During the decade, the tidal ideas were being gradually rehabilitated, but, Toomre noticed (Toomre & Toomre 1972, p.623], "judging from the reservations admitted by Zwicky (1963, 1967) despite his former use of words like `countertide' and `tidal extensions' - and especially from the vehement doubts expressed by Vorontsov-Velyaminov (1962, 1964), Gold and Hoyle (1959)], Burbidge, Burbidge and Hoyle (1963), Pikel'ner (1963, 1965), Zasov (1967), and most recently by Arp (1966, 1969a, b, 1971) - it has usually seemed much less obvious that the basis of also such interactions could be simply the old-fashioned gravity." Only in the early 1970s did the tides find proper treatment (Tashpulatov 1969, 1970; Kozlov et al 1972); that was a period of general recovery and renewal of interests to galaxy dynamics. Back.
57 Pfleiderer reasoned that tidal action should be much the strongest in the exposed and relatively slowly rotating outer parts of the galactic disks where the mass density is small and its self-gravity must be weak. He thus just neglected the latter and treated the disk particle dynamics as the restricted three-body problem, these three being the test particle and mass centers of the paired galaxies. Such an over-idealization greatly simplified his computer work (which still remained time-consuming since hundreds of trial encounters were required for an understanding of the effects of various mass ratios, orbital parameters and times and directions of viewing).
"These test-particle calculations can, of course, be criticized for their total neglect of any interactions between the various particles. However, this is not to say that the self-gravity of these relatively low-density parts of the disk should immediately have been of major importance, nor does it contradict our qualitative picture about the evolution of the waves: For one thing, the relatively sudden passage of the LMC should have induced roughly the same initial velocities regardless of the subsequent disturbance gravity forces from within this system. And also, it seems that the principal effect of that latter mutual attraction of the various disk particles should have been to enhance the shearing discussed above, since in effect it would have reduced the epicyclic frequency and thus caused the wave speeds - / 2 at the various radii to become more disparate." (T69, p.912) Back.
58 "The hopes of Hunter and myself that an unusually close passage of the LMC caused the well-known warp of this Galaxy proved to be sadly in error. I worked on that topic quite intensely for another year or so, and even `predicted' a long tidal stream to be torn loose from the LMC in turn [...] and probably inclined about 30 degrees to the plane of our Galaxy. I never published that, but it was well enough known hereabouts that one day in early 1972 I got a sudden phone call from Wannier or Wrixon at Bell Labs to ask whether a good chunk of what turned out to be the Magellanic Stream which they had just then spotted - about a year or two before Mathewson et al (1974) turned it into a big business from Australia - might possibly be the stream of gas that I had asked about among several of our radio astronomers. And I still remember with pride that it took me just the few minutes during that phone call, after learning this new Stream was located almost a right angles to this Galaxy, to reply sadly that such an orientation or orbit could not help Hunter and me at all, and that there apparently we had lost!
That Basel example led me soon to enlist the help of my own brother Juri, who was then affiliated with one NASA research institute in New York City that had much better computers than any that I had access to ... and that in turn eventually led to our joint paper Toomre & Toomre 1972. No, we did not even come close to explaining the warp of our Galaxy ... but we did end up explaining other nice things like NGC 4038/39 = `The Antennae', and pointing out that the implied galaxy mergers probably explain why we have the ellipticals. Quite a twist from where I began." (Toomre) Back.