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2.4. Extremely satisfactory comparisons?

J.H. Oort asks: What are Lin's further plans for numerical model computations [of spiral structure]?

Lin answers: At present, we have no immediate plans to extend our work much further...In the meantime, we are collaborating with Stromgren on the problem of the migration of stars, to gain a more definite picture of the spiral structure within a few kpc of the Sun.
Discussion: Noordwijk 1966, p.334

Being in 1966 on the wave of his first success in astronomy, Lin spoke of "three levels of discussion in dealing with the structure of the Theory of Spiral Structure" (Lin 1966b, p.6). Two of them - physical and mathematical - he saw already mastered to a degree, 43 so that more opportune and vital for the day he recognized the third level that discussed "the agreement of the theory with detailed checks with observations" (Lin 1966b, p.6).

"In view of the difficulty of the theoretical problem, it is fortunate that, from the beginning, we have placed great emphasis on working out the consequences of the QSSS hypothesis" (Lin 1975, p.120). "In the absence of a complete theory for the mechanism of density waves, the need for observational support is urgent" (Lin et al 1969, p.722). "Indeed, our theory can be used as a tool to connect several seemingly unrelated observations. [...] Even without the discussion of the detailed mechanisms, the mere assertion of the existence of a density wave with a spiral structure, propagating around the galactic center, leads to implications which can be checked against observations." (Lin 1968, p.36, 49)

Deliberately avoiding mathematical difficulties as "the challenge for future investigations", Lin did not seem embarrassed in the face of empirical difficulties due to apparent incompleteness and inaccuracy of observational data, and he went and led his associates along the way that was in fact no lesser challenge. There he saw an urgent interest in problems of systematic noncircular gas motions and star migration (Lin 1966b; 1967b; 1968). The famous 1969 paper by Lin, Yuan and Shu "On the structure of disk galaxies. III. Comparison with observations" (Lin et al 1969, hereinafter LYS) gave a summary of all of Lin's "levels of discussion".

Systematic noncircular gas motions in the Galaxy were under discussion already, 44 still - LYS noticed - no one spoke of their producing dynamical mechanism, although "it is easy to see this from considerations of angular momentum". Indeed, the spiral gravity causes additional along-arm gas motion which must be with the general rotation on the outside edge of the arm and against it on the inside edge, and which is "to maintain conservation of matter" (LYS, p.731). Starting from the well-known data on wavelike velocity variations in the Galaxy rotation curve, 45 LYS determined radial and azimuthal components of noncircular motion to be of the desired, for linear analysis, order of 10 km/sec, and assured (Lin 1966b; Yuan 1970) that the observed three-to-five-fold gas compression in the arms just corresponds to such a motion, so that "there is good agreement in major features" (LYS, p.732). But at their accepted pitch angle i cong 5° WKBJ equations associated those motions with a rather strong, knowingly nonlinear density response that was the business of a theory yet not in the authors' hands. Thus more correct would be their simpler inference that the observed noncircular motions indeed "in major features" are due to a certain spiral density wave.

Mentioned by Lin at Noordwijk, the problem of young star migration arose in relation to Stromgren-initiated studies of star ages, claimed to be accurate within 15% (Crawford & Stromgren 1966; Stromgren 1966a; 1967)]. Contopoulos and Stromgren (1965) set this migration problem as based on the idea that time reversion of star motions and their countdown in the hold of the axisymmetric gravity field of the Galaxy could / would show the stars' birthplaces and check if they fall inside the arms. With their tables of plane galactic orbits, Stromgren traced back the migration history of about sixty late B stars aged between 100 and 200 million years and placed within 200 pc from our Sun. Those "showed a definite separation into two [velocity] groups", and their birthplaces took a nearly tangent-to-circle extended area connecting those regions of two nearest to us outer arms where the `points' were grouped more closely. Stromgren concluded that "the present location of the arms favors the picture formed by the theory of density waves, providing one takes the pattern frequency Omegap to be about 20 km/sec/kpc" and that this "offers possibilities of testing the theory developed by C.C. Lin" and "forms a definite test" for it (Stromgren 1966b, pp.3- 4; Stromgren 1967, pp.325, 329).

In response, Lin executed some "preliminary explorations" accounting for the spiral component of galactic gravity, and found that "even a small spiral field [...] could be quite significant" (LYS, p.734). He then urged Chi Yuan to check "whether there exist a pattern speed and a strength of the spiral gravitational field (or a range for it) such that the stars considered are found to have been formed in the gaseous arm as expected" (Yuan 1969b, p.890). Experimenting with different choices of the parameters, Yuan preferred a pattern speed of about 13.5 km/sec/kpc and a spiral field strength of about 5%, with which he calculated time-reversed motions of 25 stars from the Stromgren sample, their ages being `optimized', or arbitrarily shifted within 15 percent in the desired sense. With these (and several other) corrections Yuan succeeded in improving Stromgren's picture and taking out of the interarm space all his stars that fell there but one. LYS proclaimed this result as offering an "impressive agreement" and "also extremely satisfactory comparison between theory and observation" (LYS, p.736). That was an overestimate, as was soon shown to the authors (Contopoulos 1972; Kalnajs 1973) and as they conceded in turn. 46

43 All the same, Lin conceded that "as one can see upon a little reflection, the problem of the origin of the spiral structure is mathematically more difficult", so that "these studies remain a challenge for future investigations" (Lin et al 1969, p.722). Back.

44 Kerr (1962) was likely the first to point out systematic motions as a possible source for differences in the northern and southern observations. Considering such motions near the outer edge of the Sagittarius arm, Burton (1966) suggested that an along-arm hydrogen flow might explain the high-velocity stream. Shane and Bieger-Smith (1966) considerably contributed to the discussion. Back.

45 "These variations have long been observed, but they were thought to be possibly the consequence of missing gas over interarm regions. A detailed study by Yuan (1969a) has conclusively shown that the latter effect does not give significant contributions to the variation in velocity." (LYS, p.731) Back.

46 Contopoulos gave two reasons why he did "not consider this test as crucial". First, he calculated the uncertainty in the birthplaces, assuming an uncertainty in the ages of 10-15 percent, and found that that was large enough "so that most of the stars found by Yuan as born between the spiral arms may well have originated in a spiral arm, without considering the attraction of the arm". Secondly, he noticed, in any case and any spiral galaxy the stars spend on the average more time in the arms than between them. "Therefore, finding that the perturbed orbits give the places of origin in the spiral arms does not provide a good test for the particular model chosen. [...] Similar results were found by Kalnajs (private communication) after a more detailed analysis". (Contopoulos 1972, p.91)

Indeed, Kalnajs (1973) reproduced all of Yuan's calculations and determined their statistical significance. He found that even when correcting star ages following Yuan in a most advantageous manner, one to three stars from the latter's sample should anyway be expected to be `bad' and not to leave the interarm territory. Yuan had one such star at least. (Stromgren's initial sample included 26, not 25 stars; the omitted 26th proved `bad', too.) Therefore, Kalnajs concluded, Yuan's "calculated birthplaces of the stars, while in agreement with the expectations of the density wave theory, do not provide a test for the presence of the spiral field" (Kalnajs 1973, p.40). "Perhaps C.C. thought this was a stringent test of the theory, but as I discovered, the truth is quite the opposite: nothing really could have gone wrong, and what little did go wrong was hushed up by the omission of the errant star #26." (Kalnajs)

"I never responded to Kalnajs' article, Yuan comments. The reason was he stressed the point, if I am not mistaken, that we have not proven the density wave theory to be correct by star formation study. We did not want to challenge that point. In fact, we agree with it. We only demonstrated the consistency between the theory and the observations (not only star migration but all other studies, e.g., streaming motions, vertex deviation, etc). I believe that his Observatory article was written to respond to some of the strong claims of the density wave theory made by C.C. in early days. [...]

My early contribution to the density wave theory is to piece together all the relevant observations to show the consistency of the theory. One aspect in agreement is not enough, but the agreements with all observations are impressive. The most significant early work for me was the doubly periodic solution of the MHD density waves (Roberts and Yuan 1970; that paper was alphabetic order in authorship; I made the crucial assumption and formulated the problem and solved it in parallel to Roberts). That work was shortly confirmed by Mathewson in observation of synchrotron radiation of M51. It produced a strong support of the density wave theory. That MHD model is still the best model for the Milky Way." (Yuan) Back.

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