3.2 How the mass of a star affects its luminosity

Last week, in understanding the structure and energy source of the Sun, you learned that nuclear reactions take place in the core of the Sun and that as the energy from these reactions makes its way out from the core to the surface it exerts a pressure that helps to support the Sun against the force of gravity, preventing collapse and keeping it stable over a long period of time.

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Figure 6 A section of the Sun. Energy from nuclear reactions in the core flows out to the surface, supporting the Sun against the inward force of gravity. Other stars on the main sequence are supported in the same way, making them stable..

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Diagram showing radiation transport in the Sun. A segment of the Sun is shown in cross-section (rather like a pizza slice). Labelling indicates the core, where nuclear reactions are taking place, surrounded first by the radiative zone, and then the outer convective zone just below the photosphere. Zigzag red lines in the core and radiative zone indicate the path of photons as they progress outwards through multiple collisions with charged particles. In the convective zone, coloured loops indicate the circulation of hot plasma in convective cells. Above the photosphere, arrows indicate energy radiated out into space. Labelling below the diagram indicates the main energy transport process in each zone – radiation in the core and radiative zone, convection in the convective zone, and radiation again beyond the photosphere.

Figure 6 A section of the Sun. Energy from nuclear reactions in the core flows out to the surface, supporting the Sun against the inward ...

Figure 6 shows a slice through the Sun. Because of the extremely high temperatures, the hydrogen and helium in the Sun exist in an ionised state called plasma, in which electrons and nuclei are split apart.

The energy produced by the nuclear reactions in the core supports the Sun against gravity in two ways. The first of these is kinetic pressure, which is simply the pressure caused by the high temperatures and dense material. The second type of pressure is radiation pressure. This is pressure exerted by energy travelling outwards towards the surface. The zigzag line in the inner layers shows the radiation colliding many times with charged particles in the plasma, resulting in an outward force.

The same processes in other stars keep them stable throughout their main-sequence lifetimes, maintaining an equilibrium between the inward pressure of gravity and the outward kinetic and radiation pressure as long as energy continues to be produced at a constant rate.

This helps us to understand the role of mass in determining the overall luminosity of a star. Stars on the main sequence are stable. For such a star to remain in equilibrium, with a constant temperature and luminosity, the rate at which energy is radiated from its surface has to be equal to the rate at which energy is being produced in the core (otherwise it would heat up or cool down). The luminosity therefore depends on conditions in the core, which in turn depend on the mass of the star.

In more massive stars the greater inward force of gravity produces higher temperatures and pressures, requiring a higher rate of energy production to support the star. The nuclear reactions of the ppI chain are extremely sensitive to conditions in the core, running faster as the temperature and pressure increase. This means that stars of different masses can be stable, with more massive stars having a higher luminosity and consuming nuclear fuel at a higher rate in order to be supported against the extra gravity.

The increase in luminosity is striking (as Figure 4 shows). Stars of just a few solar masses can have luminosities hundreds or even thousands of times more than the Sun. In addition to higher temperatures at the surface, more massive stars are also larger, and both of these factors contribute to the overall luminosity. At the top end of the scale, extreme conditions in the cores of heavy stars enable additional types of nuclear reaction to take place, converting hydrogen to helium at an even higher rate, meaning that stars of 30 solar masses have energy outputs of around 100 000 times that of the Sun.