Your PhD in 1975 dealt with equilibrium states of interstellar gas with magnetic and gravitational fields. How did you choose this topic and who were mentors during your formative years?
As a physics graduate student, I wanted to pursue research in plasma physics applied to astrophysics. So, when I talked with George Field about a possible Ph.D.-thesis problem and he said “if you want to become famous quickly in astrophysics, you should do something with magnetic fields”, I did not give it a second thought. Little did I know what I was getting into!
I had very little background in astrophysics at the time, so I asked George if I could spend a quarter doing reading under his supervision before starting on a research project. He liked the idea and asked me to prepare a reading list. My naivete and ignorance must have been obvious to him when I presented him with a list which, among other articles, included Spitzer's book, Diffuse Matter in Space, Pikelner's book on the Interstellar Medium, Parker's review on cosmic rays, Zeldovich's review on cosmology, Parker's papers on what is today known as the Parker instability, Shklovsky's book on supernovae, and at least half a dozen other articles or books. He approved my list with a grin on his face. I started with Spitzer's book, and it did not take long to understand that grin. Any one of the items on my reading list would have been enough for a quarter's reading! During our weekly meetings, I came to admire his keen intellect and how, without looking at the many pages of calculations I had, he would give a physical reason as to why a conclusion I had reached did not make sense. From those meetings, I realized how important it was to be able to translate mathematical formalism into intuitive understanding and vice versa (i.e., ideas into tractable mathematical formulations).
Unfortunately (for me), George left Berkeley for Harvard soon thereafter — but continued to support me (with Harvard funds) and be my thesis advisor.
Frank Shu came to Berkeley at about that time. Very quickly we developed a strong friendship, although we disagreed on the role of magnetic fields in interstellar gas dynamics and star formation. Each morning, after spending all night at the Lawrence Berkeley Lab working on my thesis project using the supercomputers of the time and before I would go to sleep, I would stop by Frank's office and tell him what new results I had. Our arguments were vigorous, but we both knew the rules of scientific debate and we never personalized them or offended each other. Through those, I learnt to defend my work against as fierce a criticism as one could possibly receive. I cannot imagine a better training for a graduate student than those interactions I had with Frank. Even when, to my surprise, he stood up after my talk at the Kitt Peak workshop (organized by Steve Strom) and said “Oh, come on Telemachos, everybody knows, certainly nature does, that magnetic fields have nothing to do with star formation”, to which I replied with equal vigor “Frank Shu, I'll prove you wrong even if it takes the rest of my life to do that”, we maintained the strong friendship and respect for each other's work for many years.
E. N. Parker was another strong influence on me. When in 1974 I nervously submitted my first paper as a single-author graduate student on final equilibrium states of the Parker instability, after he had claimed that such states do not exist, not only did he not criticize my work, but he also praised it. It taught me early on that one should not let his/her ego get caught in one's work, and that one should be supportive of younger scientists.
Lyman Spitzer, as my postdoctoral supervisor and while he was immersed in the Copernicus data, recognized where my strength was and gave me the freedom to pursue my interests (on the role of magnetic fields in star formation through magnetic braking and ambipolar diffusion), although he was skeptical that anything of substance would come out of it, given Mestel's work based on the virial theorem. I had already shown during my Ph.D.-thesis project that the virial theorem is inadequate for studying even the equilibria of clouds, much less their dynamical evolution. I had to use the magnetohydrostatic equations, supplemented by a new equation, which accounts for mass and magnetic-flux conservation in a static problem. (These two concepts are lost in going from the MHD to the MHS equations because time derivatives and velocities vanish identically.) Lyman appreciated the potential of that approach, but had reservations as to whether one could formulate mathematically tractable problems that would not be so idealized as to lose physical significance. Nevertheless, he encouraged me to pursue that kind of work.
The year after, you wrote a very influential paper on nonhomologous contraction of self-gravitating, magnetic clouds embedded in a hot and tenuous medium. What were the key new insights?
From a basic physics point of view, the key advance was in the formulation of the problem, i.e., closing the system of the inherently open magnetohydrostatic equations in a self-consistent manner, by accounting for mass and magnetic-flux conservation, as I mentioned in response to your first question. The numerical results showed for the first time the detailed structure (density and magnetic-field strength) of self-gravitating clouds, the hour-glass shape of the fieldlines, the flattening of the clouds along fieldlines, and, coupled with analytical arguments, the scaling of the magnetic-field strength with gas density in the central part of model clouds, which for isothermal contraction gives an exponent of 1/2. This exponent is unavoidable as long as balance of forces is maintained along fieldlines (regardless of the force opposing gravity, be it thermal pressure or turbulence) and contraction perpendicular to the fieldlines takes place as rapidly or as slowly as magnetic forces allow. (Seventeen years later, with Fiedler, we used numerical simulations and a moving grid to study the formation and contraction of fragments due to ambipolar diffusion. We found that an exponent of 0.47 is established, independent of initial conditions, after fragments enter the dynamical stage of contraction.)
About the same time you and Lyman Spitzer published a two-page note in ApJ on the collapse of magnetic interstellar clouds, which is your most cited paper. What accounts for the major impact of this brief note?
That short paper used the virial theorem as an interpolation formula to obtain a best fit to equilibrium states of clouds on the verge of collapse, which I had calculated in my Ph.D.-thesis work. That way, we obtained a reliable critical mass-to-flux ratio, based on nonlinear calculations, instead of relying on the virial theorem and its necessary idealizations or on linear stability analyses.
In the January 1, 1977 issue of ApJ, I noticed a paper with a very long title. What is that all about?
Oh, you are right about the long title. I still remember it: A Connection between the Rate of Rotation of Interstellar Clouds, Magnetic Fields, Ambipolar Diffusion, and the Periods of Binary Stars. It's the paper that put together all my basic ideas and preliminary analytical results arguing for the importance of magnetic fields in cloud dynamics and star formation. It's the one that opened up the field. It argued that (1) Magnetic fields, through magnetic braking, would keep clouds in synchronous galactocentric orbits, as they try to contract — with the implication that the nasty angular momentum problem of star formation would be resolved that way. (2) Ambipolar diffusion would come into play at a later stage, but at much lower densities (about 1,000 particles per cc) than those obtained by equating Spitzer's estimate of the ambipolar-diffusion timescale and the free-fall time — by the latter argument, nuclear reactions in stars would not be important because, for example, the free-fall time of the Sun is smaller than 1 hour, while the p-p reaction timescale exceeds 1 billion years. (3) A single stage of fragmentation in self-gravitating clouds would lead to stellar-mass size fragments and star formation, in contrast to Hoyle's hierarchical fragmentation. The existence of such fragments (or cores) were later observed by Myers and collaborators. (4) Based on the above, the prediction was made that the period distribution of binary stars should have a single maximum, contrary to observations, which showed two maxima (corresponding to short-period spectroscopic binaries and wide visual pairs).
This paper was rejected by an anonymous referee as being speculative. However, Helmut Abt (then editor of ApJ), in sending me the referee's report he also informed me that the paper was accepted for publication! He included in the same envelope a preprint by himself and Levy, which showed that, indeed, the two maxima in the period distribution of binary stars were the result of observational selection, and that the data showed a single maximum.
A year later I recognized that, unlike the prevailing notion that the onset of ambipolar diffusion renders magnetic braking ineffective, it is the onset of dynamical contraction (after the critical mass-to-flux ratio is exceeded in fragments) which leads to trapping of angular momentum (and magnetic flux) in contracting fragments/cores. Magnetic braking still operates during the ambipolar-diffusion controlled phase of contraction.
In 1979, you published an ApJ paper on ambipolar diffusion. How did that differ from Spitzer's earlier work?
There is a fundamental difference in the assumed model cloud, which leads to an important quantitative difference in the ambipolar-diffusion timescale, and to an even more important conceptual difference in the effect of ambipolar diffusion in cloud evolution and star formation. Spitzer assumed a uniform-density cloud model. Since the timescale for (gravitationally-driven) ambipolar diffusion turns out to be proportional to the degree of ionization and since cosmic rays with energy greater than 100 MeV penetrate most clouds, the degree of ionization is the same everywhere in the model cloud's interior. This leads to the incorrect conclusion that ambipolar diffusion gets rid of a cloud's magnetic flux.
The model cloud I used was one in exact magnetohydrostatic equilibrium. Both the density and magnetic-field strength decrease from the core to the envelope. As a result, the degree of ionization is a few orders of magnitude smaller in the cloud core than in its envelope, implying a much more rapid ambipolar diffusion there. In fact, ambipolar diffusion in the envelopes of typical clouds was found to be insignificant. This had two important implications: (1) A cloud does not lose any magnetic flux to the external medium. (2) The essence of ambipolar diffusion is a redistribution of magnetic flux in a cloud's deep interior (on a typical timescale of 1 Myr or less), thereby leading to fragmentation and star formation there.
Around 1980 you and Efthimios Paleologou published several papers dealing with magnetic braking during star formation. What did you learn?
As it was the case in my thesis project and everything else I worked on since then, the proper formulation of a problem is more than half of its solution. With Makis, we showed in 1979 that magnetic braking resolves the angular momentum problem for perpendicular rotators, and in 1980 for aligned rotators. In the latter case, we included the propagation of torsional Alfvén waves inside model clouds and their numerous partial internal reflections and transmissions. Moreover, if one is only interested in the timescale for magnetic braking, instead of the detailed solution, one can obtain an exact value on the basis of freshman mechanics — by answering the question of how long it takes for the torsional waves to affect a moment of inertia of the external medium (cloud envelope or intercloud medium) equal to that of the model fragment or cloud. We later confirmed those analytical conclusions with Shantanu Basu for his thesis work, using numerical dynamical simulations, and obtained numerous new results amenable to observational tests.
You returned to this subject in 1991 in a highly cited paper discussing the role of magnetic braking and ambipolar diffusion in the determination of stellar masses.
I originally published those results in a review paper in 1987, but, because those papers are not available online, hardly anybody noticed; hence the 1991 ApJ paper. Contrary to the then prevailing view that the collapse of fragments is a process free of any lengthscale, I showed that it is actually characterized by at least three lengthscales, whose relative magnitudes and evolution determine protostellar masses. Much later, in 2009 with Matt Kunz, we extended that work and used our ambipolar-diffusion based theory of star formation to obtain an initial Core Mass Function, which is the same as the stellar IMF. It fitted beautifully the observations of more than 300 cores in the Orion molecular cloud, including for the first time their low-mass end. Incidentally, in a review paper at the Zermatt meeting in 1988, I predicted that, if ambipolar diffusion is also important in primordial star formation, the first stars should be massive.
Early on, you were also concerned with the “magnetic-flux problem of star formation”. Is that problem resolved and, if it is, what is responsible for its resolution?
Observed magnetic fluxes of stars are smaller than those of parent fragments by a few orders of magnitude. With Desch in 2001, Tassis in mid-to-late 2000s, and Kunz in 2010, we built on the earlier work we had done with Ciolek, which accounted for grains. We showed that ambipolar diffusion reawakens when a contracting fragment enters the nonisothermal phase, and it almost resolves the problem by a density ≃ 1013 cm-3, beyond which Ohmic dissipation takes over and completes the task by a density ≃ 1015 cm-3.
Fifteen years later you revisited the problem of the star formation timescale and the ages of molecular clouds in terms of ambipolar-diffusion-controlled vs turbulence-induced star formation. What were your conclusions?
That paper, with Tassis and Kunz, reached four main conclusions: (1) The claims that molecular clouds are short-lived and star formation is a rapid process (about 1 Myr) are incompatible with each other and also contradicted by observations. (2) The ages of molecular clouds (at least 10 Myr) in our and in other galaxies are consistent with the ambipolar-diffusion theory. (3) The linewidth—size relation for objects for which the magnetic field is also measured is an almost scatter diagram; however, when the same data are replotted according to an equation I obtained in 1987, which involves the linewidth, the size, and the magnetic-field strength (under the assumption that the linewidths are due to nonlinear MHD waves), the data fall on an almost perfect straight line in accordance with the theoretical prediction. (4) SuperAlfvénic turbulence, usually assumed in numerical simulations, is contradicted by both observations and basic theoretical considerations.
What is the state of ambipolar diffusion theory today?
Despite the formidable initial resistance to the theory, hardly anybody who works on star formation today doubts its importance. The controversy has shifted to tangled vs. ordered magnetic fieldlines. This shows an unfamiliarity with the two distinct kinds of ambipolar diffusion; namely, magnetically-driven and gravitationally-driven. The former straightens out the fieldlines on timescales much smaller than the free-fall time on lengthscales comparable to observed core sizes. The latter leads to fragmentation, through an increase of the mass-to-flux ratio, and to star formation. This unnecessary controversy will end, too, after it is understood that the requisite energy sources for keeping the fieldlines tangled do not exist in molecular clouds.
What are you currently working on?
I am writing two books. The first is a textbook at the introductory graduate level, on astrophysical MHD and the physics of star formation. The second is on the same subject, but at a more advanced, research level.