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Evolution off the main sequence

10.1.1 Low mass stars

We first look at stars whose mass is less than about 5 M0. Eventually a star will reach the point where all the hydrogen in the core has been converted to helium. For a low mass star, the central temperature will not be high enough for the helium to fuse into heavier elements. There is still a lot of hydrogen outside the core, but the temperature is not high enough for nuclear reactions to take place. The core begins to contract, converting gravitational potential energy into kinetic energy, resulting in a heating of the core. The hydrogen just outside the core is heated to the point where it can fuse to form helium, and this takes place in a shell at the outer edge of the core (Fig. 10.1). We refer to this as a hydrogen-burning shell, where the word "burning" refers to nuclear reactions, rather then chemical burning. As the core contracts, the rate of energy generation in the shell increases. The shell can easily give off energy at a greater rate than the core did during the star's normal lifetime.

While all of this is happening in the interior, the outer layers of the star are changing. Energy transport from the core is radiative, and is limited by the rate at which photons can diffuse through the star. The outer layers of the star become hotter and expand. As the gas expands, it cools. The star's radius has increased, but its temperature has decreased, so the luminosity increases slightly. The behavior of the star's track on the HR diagram is shown in Fig. 10.2. The track moves to the right (cooler), and the star appears as a subgiant.

There is a mechanism that keeps the surface temperature from becoming too low. The rate of photon diffusion increases as the absolute value of dT/dr increases. Remember, dT/dr is negative, so we are saying that the greater the temperature difference between some point on the inside and the surface, the greater the energy flow between those two points. (In winter, the larger temperature difference between the inside and outside of your house results in a faster heat loss, and higher fuel bills.) If the surface temperature of the star falls too much, the photon diffusion is faster, delivering more energy to the surface, raising the surface temperature. Therefore, as the radius continues to increase, the surface temperature remains approximately constant. The luminosity

H Envelope

H Envelope

H Envelope

H Envelope

I I Regions of

Nuclear I I "Burning"

I I Regions of

Nuclear I I "Burning"

Star with an H-burning shell. (a) The temperature in the star is not hot enough to fuse the helium in the center, but is hot enough to keep the H in the shell burning. (b) In this star, the temperature is hot enough to keep both burning. (Remember, by "burning" we are talking about nuclear reactions.)

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