Astronomy 162: Professor Barbara Ryden

Wednesday, January 8

INSIDE THE SUN

``You may as well go about to turn the Sun to ice with fanning in his face with a peacock's feather.''
- William Shakespeare, Henry V, act 4, scene 1

Key Concepts

The Sun's interior is in hydrostatic equilibrium.
Energy is carried away from the Sun's core by radiative diffusion and convection.
The Sun's interior can be probed by helioseismology.

(1) The Sun's interior is in hydrostatic equilibrium.

The Sun is fairly stable; we don't see it oscillating wildly in and out, and we don't see it flickering like a candle about to go out. Moreover, the Sun has been fairly stable for billions of years, allowing the continuous existence of life on Earth.

Gravity has a destabilizing effect. The tendency of gravity is to compress the Sun. If the Sun were to collapse inward under its own gravity, it would crunch down to a black hole in the course of a few hours. Obviously, such a catastrophe hasn't happened. What has kept the Sun from collapsing?

As it turns out, the Sun is kept stable by its internal pressure. Just as pressure increases as you dive deeper and deeper into the Earth's oceans, so pressure increases as you dive deeper and deeper into the Sun. By the time you reach the Sun's center, the pressure has reached a value equal to 340 billion times the air pressure at sea level here on Earth. It's a general rule that gas flows from regions of high pressure to regions of low pressure. (The pressure difference is what makes air leak out of a punctured tire.) Within the Sun, therefore, pressure creates an outward force, from the high-pressure core to the low-pressure surface. This is in contrast to gravity, which creates an inward force.

When the force due to pressure exactly balances the force due to gravity, a system is in hydrostatic equilibrium. The Sun's hydrostatic equilibrium is stable and self-regulating; if you tossed a little extra matter onto the Sun, the inward force of gravity would increase. However, the resulting compression would increase the pressure inside the Sun, resulting in an increase in the pressure force just sufficient to balance the increased gravitational force.

(2) Energy is carried away from the Sun's core by radiative diffusion and convection.

Energy is generated by nuclear fusion in the Sun's hot, dense, high-pressure core. However, the energy generated is ultimately radiated away from the Sun's surface, nearly 700,000 kilometers away (a distance equal to 17 times the Earth's circumference). How is the energy transported from the core to the surface?

There are three fundamental ways of transporting energy from hot regions to cooler regions:

Conduction: energy is transported by the small-scale random motions of atoms or molecules. One atom jostles the atom next to it, which in turn jostles the next atom, which in turn jostles the next atom...
Convection: energy is transported by large-scale circular `convection currents', as hot fluid rises and cold fluid sinks.
Radiative Diffusion: energy is transported by photons flowing from warm, bright regions to cool, dark regions.

Conduction works best in opaque solids (metals are particularly good heat conductors, which is why pots'n'pans are made of metal). Convection works best in opaque fluids (that is, liquids and gases). Radiative diffusion works best in media which are transparent, or at least translucent.

Inside the Sun, conduction is ineffective (the Sun is not solid). Energy is transported by convection in the outer regions of the Sun (the outer 30 percent, or so). Energy is transported by radiative diffusion in the inner regions of the Sun (the inner 70 percent).

(3) The Sun's interior can be probed by helioseismology.

The ``radiative zone'' of the Sun (the inner 70 percent, where energy is transported by photons) is by no means perfectly transparent. On average, photons in the radiative zone travel only two centimeters (about an inch) before being scattered in a random direction by an encounter with an electron. The photons stagger about on a random walk, or ``drunkard's walk'' which is staggeringly inefficient at bringing them to the convective zone. It typically takes about 170,000 years for energy generated by fusion in the Sun's core to stagger its way to the Sun's surface. (By contrast, if the Sun were totally transparent, the energy would be carried by photons straight to the Sun's surface, taking only 2.3 seconds for the trip!)

If the Sun isn't transparent (which it isn't) how can we be sure that our models of the solar interior are correct? Fortunately, theoretical models of the Sun's interior can be tested using helioseismology, the study of the Sun's vibrations. By looking at the Doppler shift of light coming from the Sun's surface, we can see the Sun vibrating in and out (a little bit like the surface of a drum). Just as studies of seismic waves tell us something about the Earth's interior, studies of the Sun's vibration tell us something about the Sun's interior.

Like a beaten drum or a ringing bell, the Sun vibrates at many frequencies simultaneously. (A musician would say the Sun has many `overtones'.) The frequencies at which the Sun vibrates depend on the sound speed within the Sun, which in turn depends on the pressure, density, and chemical composition within the Sun. Thus, if we want to test a model of the Sun, we can see whether its predicted vibrational frequencies match the observed vibrational frequencies of the Sun.

Currently, the world's top helioseismologists are banded together into the Global Oscillation Network Group, or ``GONG'' for short; they have observatories around the world so they can observe the Sun 24 hours a day.

Information about the Sun's interior can also be obtained by looking at neutrinos. Neutrinos are elementary particles which have no electric charge and very very little mass. (Their name means `little neutral one' in Italian.) Neutrinos are produced as a byproduct of the nuclear fusion reactions which convert hydrogen into helium within the Sun. Neutrinos scarcely ever interact with other particles. Thus, the Sun is transparent to neutrinos, which go zipping straight through the Sun unimpeded. Given the reluctance of neutrinos to interact with other particles, detecting them is difficult. Nevertheless, neutrinos have been detected coming from the Sun, confirming that fusion really is occurrin in the Sun's core!

Prof. Barbara Ryden (ryden@astronomy.ohio-state.edu)

Updated: 2003 Jan 8