Stellar Structure

232-235

How does the temperature, or pressure or density vary in a star as you plunge from the surface into the interior? Where, in the star does nuclear fusion begin? How does the energy generated in the core of the star find its way to the surface? Answering questions like these are all part of what goes into understanding the structure of stars.

Stellar Modeling

Modern astronomy (and most sciences) operates through a continuous interplay among 3 inter-linked processes: theory, observation or experiment and modeling. The last process of modeling works by applying physical laws and theories to create plausible representations of phenomena in an attempt to reproduce observations. In the case of understanding stars, an astronomer creates a mathematical model that provides testable predictions about the structure, composition and observable features of a star. A few of the ideas that are incorporated into constructing a model of a star are:

• gravity always pulls inward in a precise and predictable way
• gravity is balanced by outward gas pressure
• if temperature in the core drops the pressure drops and the star contracts
• if a star contracts this releases energy and the star heats until it can stop further contraction
• stars convert - via fusion - light elements into heavy elements
• energy created in the core of a star must eventually each the surface so that the rate at which energy leaves the star equals the rate at which it is produced
• heavy elements accumulate in the core - cause slow changes in structure of the star

So what does a mathematical model of a star look like?

Figure 9.22 shows a model star consisting of layers of concentric shells. A stellar model would provide temperature, pressure, composition etc information for each layer in the star. In Table 9.5 a small portion of a 1-solar mass stellar model is shown. This suggests that deep in the star (roughly the inner 10%) the density is more than 60 g/cm3 (60 times denser than water) and a temperature greater than 10 million degrees Kelvin.

Figure 9.22 Concentric shells in a stellar model

Although many other ideas are also incorporated into a successful model of a star, there are only 4 broad principles at work which collectively can be called the "laws of stellar structure". These 4 laws are:

The Laws of Stellar Structure and How Energy Moves in Stars

The first two "laws of stellar structure" are actually statements of two of the most fundamental conservation laws in science and help provide important constraints when writing and solving the mathematical equations of stellar models. The law of Hydrostatic Equilibrium was introduced in the previous section and reflects an important link between the physics of gravitational forces and the laws of gases. How energy moves from the core to the surface is the focus of the fourth law and is the most complex of the four. In general, heat (energy) moves via three processes: Conduction, Convection and Radiation. Let's consider how each of these contribute to the transport of energy in a star:

Conduction

Anytime you have accidentally burned your hand on a hot pot lid or frozen your tongue to a metal pole on a cold January day you have had a graphic illustration of the transport of heat via conduction. Conduction occurs through collisions of atoms making up a substance and transports heat from hotter to cooler regions through these collisions. In the case of metals conduction is a very effective method of moving energy. In normal gases, however, conduction is very in-effective. In normal stars conduction plays a negligible role in the transport of energy. However, you will see a few notable exceptions to this when you consider some of the more exotic states that some stars can find themselves in.

Convection

A bubbling pot of oatmeal on a stove provides an every-day example of convection. Another would be the billowing thunderhead that towers above a Canadian prairie landscape on a hot summer afternoon. Both examples illustrate the wholesale motion of a fluid moving from a hot region to a cooler one and in so doing transporting large amounts of energy. Convection is a extremely important energy transport mechanism in stars. Convection is usually most effective when the temperature in the star changes rapidly. As we will see in the next section, convection occurs in most stars and also plays an important role in moving hydrogen fuel from cooler regions of the star into the core of the star.

Example 9.7 Explain how convection could affect nuclear fusion in a star.

Figure 9.23 Convective energy transport in the interior of a star. Hot gases from the core rise and deposit large amounts of energy to the outer layers.

Solution As fusion progresses in the core of a star the concentration of Helium increases. Helium fusion requires extremely high temperatures and if it does fuse will only do so much later in the lifetime of the star. Convection, however, can not only transport heat outward but the the convective cycle will also draw cool, fresh Hydrogen down into the core. This will enhance the energy generation of the star by providing more nuclear fuel.

Radiation

The third way in which energy can move in a star is through radiation. The intense nuclear reactions in the core of a star produce a flood of high energy photons that radiate outward and undergo a series of absorption and re-radiation as they make their way to the surface of the star. Radiation is an important energy transport mechanism for most stars and especially so in the most massive of stars.

Exploring Stellar Models

The following applet allows you to explore stellar models to see how they can tell you about the internal workings of a star. The models used in this applet were generated with a computer model originally based on the work of the astronomer Peter Eggleton.

Asteroseismology - Peering into the Cores of Stars with MOST

How do we test stellar models? As you saw in a previous unit, our sun undergoes subtle "non-radial" pulsations. Other stars do the same thing and the Canadian Space Telescope MOSTwhich stands for the Microvariability and Oscillation of STars satellite is designed to monitor the subtle flickering of light from stars that betrays such pulsations. By measuring the frequencies at which stars vibrate extremely tight constraints are imposed on stellar models. This provides an extremely important link between models and observation and is helping refine our understanding of how stars work. Figure 9.24 shows Professor Jaymie Matthews of the University of British Columbia who is the project scientist for the MOST mission with the MOST satellite prior to launch in June 2003.

Figure 9.24 Dr Jaymie Matthews next to the MOST satellite prior to launch in 2003.

Practice

1. At what position in the sun (measured as a fraction of solar radius) does the temperature exceed 5 million K?
2. How does the core density of a 20 Mo star compare with the core density of a star like our sun?
3. The graph given below shows the fractional abundance of helium and hydrogen in the core of the Sun over 10 billion years of the Sun's history. Explain why the one abundance drops while the other abundance rises?

To understand the internal structure of stars

Chp 11.3

Photons created in the centre of a star like the sun take nearly a million years to make their way to the surface. As they radiate outward they undergo absorption and re-emission. THe re-emission can occur in any direction so a photon is almost as likely to head back into the star than out. Astronomers call this a "random walk" process.