An interview with George Field

Interview by Bo Reipurth, SFN #338 - February 2021

On the occasion of your recent 90th anniversary, I would like to talk with you about your work in the field of the interstellar medium and of star formation. Your 1956 thesis with Lyman Spitzer was on plasma oscillations induced by shock waves in the solar corona. Did that work plant the seed for your later interest in the interstellar medium?

No, not directly because solar physics is far removed from the interstellar medium. However, it drew me into plasma physics, a complex field whose simplest manifestation is magnetohydrodynamics, on which I then focused.

In 1965 you published a very influential paper, so far cited 1300 times, on thermal instability, in which you discuss the two-phase model of the HI interstellar medium. How did that concept emerge?

My thesis advisor, Lyman Spitzer, was observing interstellar absorption line spectra at Mt Wilson. He interpreted the sharp lines at various velocities as due to absorption by discrete clouds along the line of sight. He found that the velocity dispersions within the clouds are of the order of km/s, so he wondered why the clouds don't simply expand, thereby losing their identities. Maybe there is something that confines them. I think Spitzer ruled out self gravitation as the confining agent. In the same period, a Dutch group was studying the large scale distribution of HI, and the concept of HI clouds embedded in some medium seemed natural. We both started thinking of an intercloud medium that would exert a confining pressure. But what is that stuff? It had to be hydrogen, either neutral or ionized. If I recall, HII was ruled out observationally, so it had to be HI. Because it is widely distributed it had to have lower densities to avoid upper limits on the 21 cm intensity. To exert the needed pressure it had to be hot. I did not consider turbulence at the time. So I wondered if there are conditions when HI would be hot. Spitzer had worked out the cooling mechanisms - which are mainly radiation by ionized carbon which has been excited by electron collisions - and had suggested that the heating could be cosmic rays. Cooling goes like n² and heating like n. That might work because low-density gas would be hot and therefore possibly at the same pressure as the cold but dense gas in the clouds. I realized gas at intermediate densities would have the strange property that its pressure would decrease as the density increases. Instability! At least three other authors had considered such an instability, but no one had calculated its growth rate. I studied the behavior of a small amplitude perturbation as a function of its scale and found that the growth rate is the solution to a cubic equation, reflecting the fact that sound waves provide two degrees of freedom, and the cooling and heating a third one. If the perturbation has a large scale, sound takes a while to cross it and bring the pressure to equilibrium, so cooling and heating have time to come into balance. But at small scales, while there is time to establish pressure equilibrium, thermal equilibrium takes longer. So the thermal balance takes place at constant pressure, a new feature. As a result, low-density regions in the perturbations get hotter, thus providing a pressure to confine clouds of cold gas. The result is two phases in pressure equilibrium. Recently the instability has been carried numerically into the nonlinear regime and clouds are observed to form. The fact that I provided several examples of the instability working in different astronomical situations may explain the many citations to my paper.

A few years later you, with Don Goldsmith and Harm Habing, worked out a model in which cool clouds are in pressure equilibrium with a warm intercloud medium.

All of this occurred while I was a professor at Princeton, where I was Carl Heiles's thesis advisor. On the observational side, I suggested that he look for additional clouds at 21 cm, which he found. But I had trouble in attracting theory students, given that both Spitzer and Schwarzschild were leaders in their fields, so I accepted a position at Berkeley. There I hit it off with Don Goldsmith, who for his thesis computed the pressure vs. electron density p(n) curve that became familiar. To fit the observations we had to settle on a specific ionization rate for cosmic rays in an energy range not observable on Earth; that in turn predicted the ratio n_e /n_H in HI clouds. That prediction languished in the literature until recently, when McCall found that a certain value is necessary to understand observations of H₃+ (McCall, Geballe, Hinkle 1998, Science 279, 1910). Their value agrees with ours, for what that is worth.

You and your student Bill Saslaw presented in 1965 a statistical model of the formation of stars and interstellar clouds, developing on earlier ideas by Lyman Spitzer and Jan Oort. What are the main ingredients?

Saslaw was an undergraduate looking for a thesis problem. I suggested that he study a model of cloud formation posed by Jan Oort, in which clouds grow in mass by collisions with other clouds. He came up with a nonlinear equation for the cloud mass distribution which he solved numerically. The result seemed simple, so I attacked it analytically using Laplace transforms, a technique I had learned as an MIT undergraduate, My solution agreed with Saslaw's. This pleasant result gave me unwarranted preference for analytic solutions. Unwarranted, because, if the analytic result is a Bessel function, someone has to tabulate its value numerically. Later Spitzer looked at the problem and found a solution just by looking at it long enough. I have not followed further developments in this field.

You have had a long-term interest in the question of intergalactic matter and wrote an Annual Reviews article on this subject in 1972. What are the key developments in this field since you wrote that article?

It all started when I got a postdoc at Harvard. Bart Bok had gotten a dish for 21 cm observations of the ISM. Dave Heeschen was in charge. As I had spent a summer at DTM working on a 21 cm project, I knew Dave. Hagan and Lilley had found absorption in the 21 cm spectrum of a quasar, so it occurred to me that there might also be a widespread IGM of HI. So as a postdoc at Harvard I compared the intensity of Cyg A, a quasar, to that of Cas A, a galactic supernova remnant, covering all redshifted 21 cm frequencies between zero and that of Cyg A. It took some theory to quantify the resulting upper limit, which led me to calculate the spin temperature of intergalactic HI. One driver of the spin temperature is the Wouthuysen effect, in which Lyman α photons from galaxies excite the n=2 level, which subsequently decays to one of the hyperfine levels of the ground state. The effect of all of this on the spin temperature depends on the shape of the Lyman α line, which in turn depends on the scattering of photons within the line by Doppler shifts. I was able to solve that problem for the Doppler core of the line analytically. When I described this at a recent meeting on cosmology, the crowd was amused, because of course nowadays it is done numerically. Interestingly my paper in the '50s was long forgotten until there became interest in detecting emission from such high redshifts that the stars that would ionize it had not yet been born. Later, Penzias and Wilson tightened the upper limit by searching for redshifted emission. We now know that there is a lot of ionized IGM. Of course, we knew that might be the case. When the x-ray background was discovered, Dick Henry and I fit the spectrum with thermal bremsstrahlung at 500 million degrees and a density important for cosmology. I worked on that model for a few years, but Riccardo Giacconi thought all along that the background is unresolved, which was finally proved to be the case.

More recently you and your colleagues Eric Keto and Eric Blackman have written a series of papers dealing with the fundamental problem of how gravity transforms a molecular cloud into stars across 20 orders of magnitude in density. More generally, what are your thoughts about star formation?

Like everyone else, I believe that all stars form from interstellar molecular clouds, with self gravitation playing a crucial role. The key issue is what prevents all the gas from condensing at once. The thermal pressure in the clouds is too weak by orders of magnitude. Since the observed line widths are supersonic, supersonic turbulence is probably the answer. Such turbulence must contain shock waves, and it is hard to visualize that situation, so we take the word 'turbulence' to be a fact that we don't completely understand. I think everyone agrees that a good theory must explain Larson's three laws. Instead of discussing the recent paper by Keto, me, and Blackman in detail, I'll outline a scheme for star formation. It is plausible, but it is by no means a theory that deserves formal publication.

1. It is known that molecular clouds of 10⁶ M_☉ are common. I assume that is because they are supported by supersonic turbulence, which is Larson's 1st law.

2. The spectrum of the turbulence is different from Kolmogoroff's -5/3 because it is compressible. Recent simulations confirm that it is -2, as predicted by Burgers long ago.

3. When integrated over wavenumber k, this means that the velocity dispersion sigma squared is proportional to the spatial scale R, thus explaining Larson's 2nd law. Larson's 3rd law follows from 1 and 2.

4. Eventually, the turbulence dissipates, leading to a new instability in which the molecular cloud starts to collapse.

5. Keto, Field & Blackman (2020) followed the instability into the nonlinear regime, calculating the ratio of the Jeans mass to that of the molecular cloud. When that ratio reached 1/2, fragmentation into two offspring molecular clouds takes place.

6. This process continues until sigma equals the thermal speed at 10 K.

7. A little arithmetic shows that in 20 such steps the 10⁶ M_☉ cloud becomes 1 M_☉, a protostar.

8. What observers see is a snapshot of this cascade. Blackman and I showed some time ago that the observations are consistent with such a scheme.