Peering inside of a star...
and astronomy's startling success story

This is a short discussion of the observational evidence supporting our understanding of the structure of stars and their evolution. We cannot ``see'' further into a star than its photosphere, so how do we know what goes on inside?

As we have discussed in class, the structure of a star (i.e., how the quantities temperature, density, and pressure vary through the star) is determined by setting the force of gravity at each layer equal to the available pressure distributed over the surface area of that layer. The sources of pressure inside normal stars are gas (proportional to density and temperature) and radiation (proportional to T4), though the latter is important only in stars much hotter inside than our Sun. Gravity bears inward, pressure pushes outward, and in this struggle an equilibrium arises, setting up the structure of the star. Well, except for one thing....

The resulting conditions at the very centers of stars are such that the fusion of lighter elements into heavier ones occurs naturally, releasing energy through Einstein's most famous equation E = mc2. This energy must be transported to the surface, either by radiation (photons) or convection (upward bulk motion of buoyant gas), and when the energy produced in the core is exactly balanced by the energy lost at the surface as light (the stars's luminosity, proportional to R2xTs4), then the star can come into full equilibrium. Go here for a summary.

``That's all very well and good,'' you say, ``but that's all based upon theoretical constructs, even if each of them have been tested observationally/experimentally on their own. What is the evidence that this is what's really happening inside a star?''

Good question. Until recently, we had only indirect evidence. That is, we could build a computer model of a star (or a whole series of model stars for a star cluster) and compare their outward characteristics (luminosity, surface temperature, radius, spectrum) with what we could derive from measurements of a star of a given mass and composition. We could also let our models progress in time, as their cores consumed one fuel and fused it into another, and in this way we could track the evolution of a star, or a whole cluster of stars, and compare the resulting distributions of the model stars on the H-R diagram with what is observed. All such comparisons between model and observation have met with spectacular success. Here is another startling success: the observed abundances of the elements on the periodic table are reproduced to good accuracy by models of galactic evolution, which describe how multiple generations of billions of stars produce and recycle the elements heavier than helium. That is, we know WHY carbon, nitrogen, oxygen and iron (for example) are found in concentrations of 3.5 x 10-4, 9.3 x 10-5, 7.4 x10-4, and 3.2 x 10-5 by number relative to hydrogen in our Sun, in stars with ages similar to our Sun's, and in gas clouds in this part of our Milky Way Galaxy. That having been said, the galactic chemical evolution models remain a work in progress.

Are there any more direct measurements that give us confidence that we understand the workings of stars? Recently, improvements in experiment, observation, and technology have allowed us a closer, more direct peak at the inside of at least 1 star - our Sun. In two words: helioseismology and neutrinos.

What in the world am I talking about?

Helioseismology - Due to the convective motions of gases in the outer 30% of the Sun's radius, observed as bubbling granulation cells in the Sun's photosphere (see also this gif movie) our Sun rings like a bell - though very gently. Acoustic (sound) waves of 10 million modes of oscillation propagate through our Sun, with periods of typically several minutes. Detailed analyses of the measurements of these ultra-low amplitude oscillations (with surface velocities of less than 10 cm/s) allow astronomers to determine how temperature, density, and composition vary through the Sun's interior. These vibrations are detected as tiny Doppler shifts in the light emanating at the photosphere.This is similar to how geologists determine the Earth's interior structure and state through the study of earthquake waves, or loosely analogous to an ultrasound sonogram revealing the interior structure of a human.

In this picture showing a model representing the observed oscillations in our Sun, the blue areas are approaching, while red areas are receding. The density, temperature, and even changes in composition may all be measured through an analysis of the millions of modes of oscillation. This page has some further explanations and animations. The latest results show that the best theoretical models predict a structure of our Sun (pressure, temperature, density, relative fractions of hydrogen, helium, heavy elements as functions of distance from the Sun's center) that differs by 0.1%-0.3% from that determined from helioseismology observations. Not bad, eh? Astronomers are now trying to understand the causes of this small deficiency in their models of the Sun.

In addition the boundary between radiation energy transport and convective energy transport that is predicted by the standard solar model to occur at 71.3% of the Sun's full radius is also measured. So is the standard model's prediction that the center of the Sun's core contains just 34% hydrogen and 64% helium (with the hydrogen fraction increasing outward through the hydrogen-fusing core), compared to 70.1% and 27.9% respectively for the bulk of the Sun. In 4.57 +/- 0.11 billion years our Sun has fused about half of its hydrogen inside the core into helium. This age matches the measured ages of solar system meteorites of 4.57 +/- 0.02 billion years, and this match is expected from the theoretical models that describe the formation of solar systems and the cooling of its planets over time. This agreement in measured age is striking, especially when you consider that the physics involved in each case is totally different.

Astronomers are already conducting "seismology" measurements of bright nearby stars (e.g., Alpha Centauri A & B) using telescopes from the ground. Next step: Sun-orbiting telescopes (first mission named Kepler) will do "seismology" measurements of many nearby stars to probe their inner structures to compare to our theoretical models of stars.

Solar Neutrinos - Many of the thermonuclear fusion reactions predicted to occur in the core of our Sun produce a sub-atomic particle, known as a neutrino. As its name implies, it has no charge, and its main property is that it does not interact with other matter very much (doing so through the weak nuclear force). Until very recently, we did not know if it had any mass (without mass, like a photon, it would travel at the speed of light). Because it interacts very little with other matter, it was known that most neutrinos should "fly" out of the Sun, and that with gargantuan vats of certain liquid compounds we might be able to detect a miniscule (but predictable) fraction of them here on Earth. Since 1968, various experiments have tried but  failed to measure the predicted numbers of neutrinos from the fusion reactions expected to go on in the core of our Sun.

So what's up? Is there something wrong with the Solar Model? Or  is there something about the neutrino that we don't understand? Well, helioseismology has given us confidence that we understand the structure of our Sun, and we know quite a bit about thermonuclear fusion (think hydrogen bomb). Could there be something about the neutrino we hadn't yet grasped?

It turns out there was. Theoretical and experimental particle physics show that neutrinos come in three types, but only one of them is produced in the fusion reactions inside our Sun, and it is that type that these experiments were set-up to measure. A  non-standard version of particle theory predicts that the neutrino could morph itself from one type to another as it moved through dense matter (like the Sun and Earth), but only if the neutrino has mass. The most recent experiment, the Sudbury Neutrino Observatory (SNO) in Canada, announced in 2001 June that their results in conjunction with those from a different experiment in Japan (1998), represent strong evidence that neutrinos do indeed change types (and so have mass). Confirmation with much higher levels of confidence were announced by SNO in July 2002. When this "morphing" is taken into account, Earth's neutrino detectors are finding just the right numbers of neutrinos produced in the Sun's core as the astrophysical theory of the Sun predicts.

For astrophysicists this was a victory long in coming - 33 years. Ray Davis, the pioneer of solar neutrino detection won the 2002 Nobel Prize in Physics in recognition of that life long work. As for particle physicists, while it was they who have now solved the long standing "solar neutrino problem", they've got their work cut out for them in coming up with a significant revision to the standard model of fundamental particles to understand why neutrinos have tiny but non-zero (rest) mass.

The solar experiment at Sudbury will continue for a few more years, and there are long-range plans for more elaborate and sensitive neutrino telescopes, for studying exploding stars (that also emit scads of neurtrinos) and to search for the cosmic neutrino background that is predicted to have been produced during the first second of the Big Bang. Ain't science cool?

Kirk Korista
Professor of Astronomy
Department of Physics
Western Michigan University