The final (hooray!) chapter of my Ph.D. dissertation was a detailed and otherwise unpublished report on my progress (or lack thereof) in the study of nucleosynthesis in stars with degenerate neutron cores. It was a bit of gutsy nuclear astrophysics, quite different from my other work and highly educational for me. The results were negative — I found no viable stellar models — but at least I highlighted some issues and challenges for later researchers to address. (And I did fill pages 85 through 172 of my thesis, giving the volume a heft and credibility that it needed to get me out of grad school.)

Regular stars like the Sun generate energy by fusing hydrogen atoms. Giant and supergiant stars have exhausted their hydrogen and survive by fusing helium or heavier elements in their central regions. Those stellar cores are something like a white dwarf star, thousands of miles across, with atoms packed so closely together that the electrons are squeezed out of their normal orbits. Around the core are millions of miles of thinner gas, held up by the fierce pressure of radiation escaping from the center. One such star is Betelgeuse, a red supergiant in the constellation Orion.

But could there be stars with much denser cores? They would look almost the same as "normal" red supergiants from the outside. But in the center, instead of a white dwarf there might be a neutron star or even a black hole. Are such stars possible? To survive they would have to be incredibly hot towards the middle. Otherwise the gas would all fall down in a matter of a few years.

In the mid-1970s Kip Thorne and Anna Zytkow began an analysis of stars with neutron-star cores. They found that such objects could support themselves by slow, steady accretion onto the dense central body if the envelope was less than about 10 solar masses. More massive stars needed extra energy, from hydrogen-burning nuclear reactions, to hold themselves up. Thorne and Zytkow estimated this nucleosynthetic process, but they warned that a more detailed treatment might significantly change their results. I undertook such a calculation, building upon work by Michael J. Newman, my advisor Kip, and Anna.

Anna N. Zytkow (pronounced ZHIT-kov, more or less; there's a dot over the "Z" in the original) was a young astrophysicist from Poland. She was both brilliant and beautiful, with long black hair, dark eyes, a soft voice, and a striking profile. Anna made stars. More precisely, she created stellar models: sets of equations that specified the density, pressure, temperature, and composition of the materials that form a star. To get a successful model, those parameters have to be self-consistent. They must obey the laws of nature and match up properly at the center and the edges of the star.

Self-consistency is tricky. I started with Anna's and Kip's work and put in nuclear reactions as contributed by Mike Newman, a Caltech nuclear physicist. Using simple but plausible approximations I wrote moderate-sized FORTRAN programs, punched holes in hundreds of computer cards, and fed my decks into the reader. The bytes flowed over leased lines to Berkeley where a CDC-7600, quite a supercomputer for its time, compiled and executed my instructions.

It sounds simple enough ... but before I could create any models there were months of learning numerical methods, tracking down algorithmic errors, suppressing computational instabilities, and puzzling over reams of cryptic line printer output. When I got things to "work", the real challenge began: understanding and explaining the features of my calculations.

While I was attacking the problems of stars with neutron-star centers a fellow grad student, Richard Flammang, worked on cracking an even tougher nut. Working with Kip Thorne, Rich sought to simulate stars with black-hole cores. With a neutron star, at least there's a solid foundation on which to build. A black hole is more like a bottomless pit! The only hope for such objects would be to generate insanely high temperatures before the gas goes down the drain — hot enough that radiation pressure could counterbalance gravity. That's not trivial. If matter gets too hot it will give off not merely light (and X-rays and gamma rays) but also neutrinos ... which slip away so easily that they are almost worthless in the fight against collapse. Moreover, once gas starts to fall down rapidly it carries a lot of light with it, and there's no time to benefit from the radiation pressure.

But if it takes an unconventional grad student to make an unconventional stellar model, Rich Flammang was the man. He was almost as old as Kip, for starters — not the usual student-teacher relationship. Rich had been a Caltech physics undergrad in the 1960s who then went to Harvard to pursue a graduate degree in economics. After several unhappy years of that he returned to his first love and came back to the Caltech physics department. He was a fun companion, a strong hiker, and a native southern Californian whose parents were rather well-to-do; they owned a lovely house in the hills overlooking the Los Angeles basin. Rich himself was (or played the rôle of) a child of the '60s who balanced work and play, with the scale tipping toward play much of the time.

In spite of the creative energy that he brought to his research, however, Rich never succeeded in crafting stable models of stars with black-hole cores. I saw the same outcome in my erstwhile models of stars with neutron-star centers. One can rarely "prove a negative" — it's always conceivable that unanticipated phenomena could save the day — but the results that I got strongly suggest that such models can't exist in the universe.

Soft or hard, crunchy or squishy inside, the type of stellar candy doesn't matter: gravity is too strong. The cakes I baked always fell down for three major reasons:

  • Pollution: Stellar envelopes don't mix fresh new material into the hot central regions quickly enough. Waste products from nucleosynthesis accumulate in large amounts at the bottom of the convective zone and smother the energy-producing reactions. The star can't fuse enough hydrogen to survive.
  • Time: Key nuclear reactions to power the star all involve several slow steps — necessitating hundreds of seconds of waiting for unstable isotopes to decay before things can proceed. That's not a problem in a conventional star where there's plenty of time to burn, but it clobbers the reaction rates in these models.
  • Space: The zone within which energy production occurs is too small, and holds too little matter, to do the job. Temperature and density fall off rapidly above the neutron star core. The majority of nucleosynthesis occurs in a thin layer within a few kilometers of the center, and that's just not enough.

Any one of these reasons alone could cause a failure. With all three strikes against the star, the odds are that minor changes in the models I built won't overcome the problems. My best efforts only were able to provide a few percent of the needed luminosity to support an equilibrium supergiant.

Can stars with neutron-star cores exist, or are they doomed to fall down and go "boom" on timescales of a few years or less? Perhaps escape is possible via bizarre nuclear reactions that my models didn't include. Or maybe a star could survive by a series of small collapses and explosions, something like an internal combustion engine. But those are long shots. My bet is that Nature doesn't hide neutron stars inside ordinary-looking stellar objects.

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

Monday, May 01, 2000 at 05:46:11 (EDT) = 2000-05-01

TopicPersonalHistory - TopicProfiles - TopicScience

(correlates: TheAscent, AirFlow, LogScales, ...)

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