**2.2. MIT enthusiasm**

Chia Ch'iao Lin was not an astronomer. Since the pre-war time, he had been
studying fluid flows. By the 1960s, he had had over 60 publications, a
monograph on hydrodynamic stability
(Lin 1955),
a world recognition of an
applied science expert, and a solid reputation at the department of
mathematics in the Massachusetts Institute of Technology (MIT) where he
worked since 1947. But he did feel a continual interest in astronomy, being
admired with strict analytical papers by Chandrasekhar, with M.
Schwarzschild' work on stellar structure, with Zwicky's morphological
method. In 1961 this side interest became Lin's life-long vitality. That
spring, on visit in Princeton,
^{38} he attended the
aforementioned conference on interstellar matter and, having become familiar
with the developments in galaxy research, he got captured by the problem of
the persistent spiral structure.
^{39}

Back in MIT, Lin conveyed his galactic enthusiasm to his young colleagues
Hunter and Toomre. ^{40} For
quick acquaintance with current periodicals, a `reading group' was formed;
^{41} a "friendly
back-and-forth atmosphere" (*Toomre*) warmed open discussions and
working visits of Woltjer and Lust, organized by Lin;
^{42} Lebovitz was hired in
the department.
^{43} In 1962, Shu arrived
there for doing his undergraduate course work under
Lin's guidance, ^{44} and
Hunter with Toomre,
their instructorship finished, left MIT, one back for Cambridge, UK, the
other for Princeton; their first papers appeared in 1963.

Hunter and Toomre made their debut in galaxy dynamics on a vital problem
already posed but yet unanswered very basically
(Kuzmin 1956;
Burbidge et al 1959):
How to connect the empirical rotation curves of galaxies with their
equilibrium mass distribution?
Toomre (1963)
set forth a general
mathematical method, and for a razor-thin disk model he derived a series of
solutions well known nowadays as Toomre's models of
*n*^{th} order (Binney & Tremaine 1987, p.44).
^{45}
Hunter (1963)
used a distinct thin-disk approximation and found another
series of exact solutions. The simplest there was the case of uniform
rotation and surface density *µ*_{0}(*r*)
(1 -
*r*^{2} / *R*^{2})^{1/2}. For it only
was the analytical study of equilibrium stability possible, and Hunter
did it "using only pencil, paper, and Legendre polynomials"
(Toomre 1977, p.464).
This cold disk proved *unstable* for a wide span of axisymmetric and
non-axisymmetric oscillation modes.
^{46} These papers by
Toomre and Hunter had paved the way for further works on kinematical models
and global dynamics of flat stellar systems.

^{38} Stromgren invited him for
discussions on stellar structure (*Lin*), largely in relation to
his fresh interest in hydrodynamics of liquid helium
(Lin 1959).
Back.

^{39} In his early spiral papers, Lin often
quoted Oort's statement
reproduced in Sect. 1.3.
Back.

^{40} At that time, the department of
mathematics in
MIT was vigorously enlarging its applied side. Hunter and Toomre were hired
there in 1960, just after they had got their PhD degrees in fluid dynamics
in England. Initially, they hoped to collaborate with Backus
(*Hunter*; *Toomre*), a
recognized leader in geomagnetic problems, but as he left MIT that year
already, they two "soon caught some of Lin's fever for problems in the
dynamics of galaxies". "Almost at the moment I first met him in fall 1960
I was struck with his breadth of scientific interests, his really excellent
spoken English, [...] and his genuinely gracious manner of dealing with
other people". (*Toomre*)
Back.

^{41} "[We] were all becoming interested in
astrophysical problems together. We read Martin Schwarzschild's book on
stellar structure together". (*Hunter*)
Back.

^{42} "It was a real pleasure to have such a thoughtful and
articulate theoretical astrophysicist as Woltjer so close to chat with about
this thing or that. [...] It was from his informal lectures that summer
that I learned for the first time not only how Dutch and Australian radio
astronomers working in parallel had more or less mapped the spiral arms of
this Galaxy from the velocity maps, but also how astonishingly thin - and
yet curiously bent - is our layer of 21-cm gas". (*Toomre*)
Back.

^{43} "I had just received my PhD [working with
Chandrasekhar], I wished to pursue applied mathematics, and I had received
an offer of an instructorship from one of the best applied-mathematics
departments in the country. Lin's motive I can only speculate on. He was
interested in moving in the direction of astronomy and of the
spiral-structure problem and perhaps figured I would be a useful
participant. If this is the case, I suppose my stay at MIT may have been
somewhat disappointing to him because I spent all of it in close
collaboration with Chandrasekhar on a quite different set of problems".
(*Lebovitz*)
Back.

^{44} "I began work with C.C. Lin in summer
1962 as an
undergraduate research assistant and continued through the fall and spring
1963, on the topic of spiral structure in galaxies as my undergraduate
thesis project in physics at MIT [...] I knew Lin from even earlier
because he is a close friend of my father". (*Shu*)
Back.

^{45} Toomre's model 1 reproduced the result
by Kuzmin (1956)
then unknown to Toomre
(Binney & Tremaine
1987, p.43).
Back.

^{46} The stability of differentially
rotating cold disks Hunter studied in his subsequent paper
(Hunter 1965).
Back.