Fixing the Solar Model

Over the past few years, I have been following a minor controversy about the current model for the Sun. It seems that advances in computational power and numerical techniques have allowed astrophysicists to improve their estimates of the relative amounts of each element in the Sun, and that this has broken our best model for the structure of the Sun.

Active Region 1002 on an Unusually Quiet Sun.

Active Region 1002 on an Unusually Quiet Sun.

Our understanding of the structures of stars (like the Sun) is detailed, but contains a lot of necessary approximations. One starts with three relationships that are well-understood: (1) the balance between a star’s gravity and the pressure of its plasma (hydrostatic balance), (2) a relationship between density and mass (a continuity equation), and (3) a relationship between density, pressure, and temperature (for instance, the ideal gas law).

Next, one needs to know (4) the rate at which energy is generated by thermonuclear fusion within stars. In the Sun, four atoms of hydrogen are built into a helium atom through a process that also produces, for brief periods before they decay, unstable isotopes of berylium, boron, and lithium (these reactions are important in understanding the Solar neutrino problem). In stars that are more massive and hotter than the Sun, hydrogen is burned into helium through a catalytic cycle involving carbon, nitrogen, and oxygen.

Finally, one needs to model how heat generated in the core of a star reaches its surface. There are two possibilities: (5a) heat is carried by light diffusing outward, or (5b) heat is transported by gas moving that rises buoyantly, cools, and then descends back into the star (convection). These two effects are important in different regions of each star. The key to determining where they are important is to determine how far light can travel through the star before it interacts with an ion in the plasma (the opacity of the plasma). For many elements, both calculating the opacity from first principles and determining it from experiments turns out to be exceedingly difficult. Moreover, once the calculations are done for each element, one needs to know to what fraction of the star is made up of each element. This is also hard to measure with high precision. This is where the controversy starts.

Astrophysicists have a lot of data that they have to explain when they try to model the abundances of elements in the Sun. Looking at the atmosphere of the sun, they have to explain the change in apparent brightness of the solar disk as one moves from the center to the edges (limb darkening). They need to explain the depths of the absorption lines from various ions, which is related to both the temperature in the atmosphere and the abundances of each element. They have to explain how the shapes of hydrogen lines vary across the face of the disk, which is related to how the pressure of the atmosphere changes with height. Finally, they need to explain why the surface of the Sun is speckled. This last feature, in particular, has led astrophysicists to develop three-dimensional models of the Solar atmosphere.

While they were at it, several groups incorporated the most recently calculated and measured values for the opacities of each element, and dropped the assumption that everything would locally be in equilibrium.

The new models seem to do the best job yet of explaining the appearance of the surface of the Sun. The models also imply that the abundances of carbon, nitrogen, oxygen, and neon in the Sun are lower than astrophysicists previously thought. The abundances of many of the elements are more consistent with measurements of elemental abundances in meteors and in interstellar space.

At first glance, this wouldn’t seem like it could cause much of a problem for modeling the Sun, because each of these elements is about 10,000 times less abundant than hydrogen. However, changing the assumed abundances of these elements changes the assumed density and opacity of the Sun, and it turns out that both of these things affect another important set of calculations.

In the 1960s and 1970s, it was realized that the Sun was continually pulsingat a barely-perceptible level. The pulsations are caused by sound waves propagating through the Sun. The set of characteristic frequencies at which the Sun pulses tells us about its interior, much like how seismic waves on Earth can be used to study the Earth’s core. As a result of their analogous usefulness, the Solar pulsations are called helioseismic (although the physical mechanism causing “seismic” disturbances on the Earth and Sun are very different).

Constructing a model of helioseismic waves requires knowing the speed of sound throughout the star. This in turn depends upon the density of the plasma, and the locations at which energy is transported by radiation or convection. It turns out that using the new elemental abundances, the models for the pulsations of the Sun no longer work.

Currently, the astrophysicists involved are hopeful that other changes can be made to the Solar model so that everything will be consistent again. Over the past few years, refinements of the model have improved its agreement with the helioseismic data. Perhaps this problem will go away with better calculations of the opacities of various elements. However, the changes needed are up to 15% at some temperatures, which might have other observable consequences.

There is even a small chance that the discrepancy could be a piece in a bigger puzzle. Already, the Sun has provided us with a big hint as to what might be found beyond the Standard Model for particle physics. We see fewer neutrinos from the Sun than we expect given the nuclear reactions that are occurring in its core. This is taken as evidence that the electron neutrinos we are looking for are changing into other types of neutrinos, which in turn implies that neutrinos have mass (see the page by the late John Bachall for more detail). Could the mismatch between helioseismology and the standard solar model that was introduced with the new abundances be another clue? I don’t know. However, the best place to look for progress in science is where there is something significant we can’t yet explain.