Two stellar astrophysicists are arguing about the virtues of the mixing length approximation at an open air reception held on a clear night in Edmonton. They are approached by a Macclean’s magazine journalist. The journalist points to the second brightest star in the Big Dipper and fires a series of hard-hitting questions at the pair: "Is that a planet?", "What is its name?", "How old is it?", "How big is it?", "Can you make money on it?" To which the astrophysicists reply, respectively (but not very respectfully) "It’s not a planet, it’s a star.", "It’s called alpha Ursae Majoris A, the ‘pointer star.’", "We don’t know.", "We don’t know.", and "We don’t know." Exit journalist mumbling something sarcastic about how out-of-touch today’s educators are with the real world.

The first two "We don’t know" questions will soon be answered by Canadian astronomers.

Before a stellar modeller can produce a model of a star, the modeller needs to know a few things about the star. Ideally, the stellar modeller would like to know the star’s mass, chemical composition, surface temperature, age, and luminosity. In the real world, though, the only things we are likely to know about a star are its heavy element composition relative to hydrogen, its parallax, its visual brightness, and its colour. If the star has a companion then we might also know the mass ratio of the two stars. Rarely will the stellar modeller be given enough information to calculate a unique model of the star.

In general, to construct a model of a star, and even given every observable currently available for stars, the stellar modeller still must assume, without any direct observational constraints, the helium abundance and the efficiency of convection near the surface. We cannot directly determine the abundance of helium in a star, especially in the central regions, where it matters most. And we have no way to test our model of convective energy transport in stars (the mixing length approximation), much less calibrate its efficiency.

We are forced to assume values for these two parameters. The values we assume and the confidence we have in these assumptions depends on the type (i.e., population) of the star. For stars similar in composition and evolutionary phase to the Sun, we are confident in using values obtained from calibrated models of the Sun (since the solar age, radius, composition, luminosity, and mass are well established). For other types of stars, there does not exist a formal method of directly calibrating these parameters to the same level of accuracy as we do the Sun. Needless to say, as a consequence, there is some debate among stellar modellers on how best to carry out the calibrations.

The outcome of all this is that, if we do not know the primordial helium abundance in the nuclear burning core of a star then we cannot determine the rate of nuclear burning, hence, even for a star with a well determined luminosity we cannot accurately estimate its age. Furthermore, if we do not know the efficiency of convective energy transport for a star (intermediate to low mass) then we cannot determine the radius of the star.

The data to be obtained from the MOST satellite (described in a separate article by Jaymie Matthews (UBC)) is going to change they way we model stars. MOST is designed to observe the minute luminosity variations that are associated with the nonradial acoustic oscillations that exist in many types of stars, including stars like our Sun. The stellar oscillation data obtained from MOST will be used, among other things, to accurately calibrate the helium abundance and convective efficiency in a variety of stars.

Indeed, we expect stellar seismology observations to lead to the first other-than-Sun tests of the mixing length approximation. Furthermore, two groups (one at The University of Aarhus, Denmark, and the other split between Yale University, New Haven, and Saint Mary’s University, Halifax) in anticipation of the first stellar seismology data are already producing three-dimensional hydrodynamical simulations of stellar convection that will soon (within the next five to ten years) be used to replace the mixing length approximation.

It is well known that p-modes are sensitive to the surface layers, which is why they are extremely useful in testing models of convection. In order to probe into deeper layers it is necessary to cancel out the effects of the surface layers. Thanks in part to the work of Monique Tassoul (Montreal), we know there is an easy way to do this. By forming specific arithmetic combinations of oscillation mode frequencies one can effectively subtract out the portion of the frequency being influenced by the surface layers. The most popular combination, referred to as the small spacing, is formed by taking the difference of two nearly commensurable eigenfrequencies. Because the small spacing frequency is sensitive to the structure of the central regions of a star, small changes in the ratio of the abundance of helium to hydrogen in the core are easily identified. This makes the small spacing an excellent diagnostic of stellar evolutionary age.

Helioseismology has already had a tremendous impact on stellar astrophysics, from confirming basic stellar structure theory to stimulating the development of improved stellar model physics. Asteroseismology has the potential to have an even greater impact through the diversity of stellar objects that can be observed. Whether as laboratories for studying turbulent convection, serving as tracers of the dynamical and chemical evolution of our Galaxy, or setting upper limits on the age of the Universe, stellar modelling boosted by the advent of asteroseismology, remains a subject of fundamental importance to astrophysics.