^z 25th March 2024 at 5:11pm

In 1976 I was talking with Roger Blandford, a brilliant young astrophysicist whose British accent combined with his appearance to give him a charm that well befitted his personal modesty. (He looked like King Arthur, straight out of Camelot!) Standing at Roger's blackboard, I sketched out some work that I was doing to estimate gravitational wave production by rotating and precessing neutron stars. I thought I knew what was going on.

Roger gently pointed out to me that, contrary to my na've mental model, a spinning mass might not merely give off gravitational radiation at twice its rotation frequency. Rather, Roger suggested, there could be emissions at lower frequencies, and maybe even more complicated signals that would give valuable information about the system to a distant observer. He argued by analogy with the electromagnetic case, for which he had strong classical instincts.

Roger was right! Free rotation in empty space is simple only for a simple body like a dumbbell twirling about one of its principal axes. Off-axis motion — especially for an asymmetric object — causes precession, nutation, and other messy phenomena (involving in the general case elliptic functions, about which I knew next to nothing). Such might well be the case for a rapidly spinning neutron star.

The calculations to prove this were quite ugly and stressful to perform; they took me a few months of steady work. I used a symbolic math program called MACSYMA to simplify the equations and check my algebra. The MACSYMA software at that time only ran on a weird computer at MIT, and so to access it I learned to use the ARPAnet — an early experience on the Internet's ancestor.

Eugene Szedenits, Jr. helped me with much of the analysis. Gene was a good-naturedly eccentric grad student who came to Caltech in 1975 and stayed for only a couple of years before moving to Michigan to write compilers for computer-controlled numerical machine tools. He was born in Hungary and grew up in Cleveland, where he attended Case-Western Reserve University. His uniform was a white shirt, black pants, and a scarlet sports coat — which could be seen at great distances as he scooted around campus, and which helped him become invisible when he uncharacteristically failed to wear it. Gene's wicked sense of humor made him a great late-night studying companion. He was honest, hard-working, a bit shy, and earnest in his insistence on the "Junior" suffix to his name.

I wrote up our results as the paper "Gravitational waves from rotating and precessing rigid bodies: Simple models and applications to pulsars", with Eugene Szedenits, Jr. as co-author. (Gene derived the major equations independently of me, checked my results, and kindly and continuously prodded me to get the research finished, written, and published. Thanks, fellow!) The article appeared in Physical Review, part D, the section subtitled "Particles and Fields". Phys Rev didn't allow me to call it "Part I", probably because the journal had already been burned too often by authors who meant well but never got around to writing their promised "Part II". In the original draft of the paper I used feminine pronouns throughout, as a tiny blow against English's default gender discrimination. Alas, an anonymous referee objected — he (you can bet it was he!) found the usage distracting, and the editors agreed. Kip Thorne (my thesis advisor) was willing to fight, bless him, but I was conflict-averse and gave in to speed publication. Too bad....

My paper with Eugene appeared in mid-1979. As far as we were able to determine, all previous work assumed that gravitational waves from mechanical systems came at twice the spin frequency. Roger Blandford's insight (plus a lot of hard work!) proved that assumption wrong. Our weak-field, slow-motion, small-stress, quadrupole-moment analysis derived the explicit waveforms radiated by two special cases of freely precessing rigid bodies. The first case was that of an axisymmetric object; the second was that of an arbitrarily-shaped body with a very small wobble angle.

Three new, important, unexpected ideas emerged:

  • gravitational waves come out at two frequencies, the spin rate and twice that;
  • when the wobble angle is small, radiation at the spin frequency is much stronger than that at double the rate; and
  • electromagnetic waves emitted by a point fixed on the surface of the body are seen to arrive in pulses at a frequency different from the gravitational waves (by plus or minus the precession rate).

These three surprising facts may (someday!) have important consequences for gravitational astronomers who observe pulsars. The experimenters' task is made harder by the splitting between the radio and the gravitational pulse frequencies, since it is not clear precisely where to "listen". On the other hand, when waves are detected they will give extensive information about their sources — information which is difficult or impossible to derive from electromagnetic observations.

I did eventually write the "Part II" paper, titled "Gravitational waves from rotating and precessing rigid bodies: General solutions and computationally useful formul'". It was published in Phys Rev D in 1980 (and as Chapter III of my dissertation). In the article, I dotted the i's and crossed the t's of the earlier piece by extending the analysis to the case of an object with arbitrary moment-of-inertia tensor (arbitrarily great deviations from axisymmetry). I gave plug-in-and-grind algorithms for computing the gravitational power radiated and waveforms produced by an arbitrary source. Those exact results confirmed the approximations and special cases calculated in Part I.

It was rather a dull paper in my opinion, without any fundamental or exciting new insights. Boring work, but somebody had to do it. Science is like that sometimes. So is life.

(see KipTheDragon, RelativityPlusAstrophysics, CherishedBeliefs, NiAndMe, PulsarWaves, and SoftOutsideCrunchyCenter, for other ^z thesis work)

(see also QpoLmxb)

Tuesday, April 11, 2000 at 06:10:53 (EDT) = 2000-04-11

TopicPersonalHistory - TopicScience - TopicProfiles

(correlates: QpoLmxb, PulsarWaves, RevolutionsOfAnIrregularSolid, ...)