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In this equation dM/dt is the rate at which mass is falling in, and M is the mass of the white dwarf. We should think of equation (12.1) as the upper limit to the actual luminosity. That is because all of the energy gained in the infall is not converted into outgoing radiation. In fact, the formation of the accretion disk is crucial in this process. The accretion disk provides a place where the energy from the infalling material can be converted into heat. The heated disk then radiates.

Example 12.1 Mass accretion luminosity Calculate the luminosity for a mass infall rate of 10—8 M0/yr, onto a 1 M0 white dwarf. Assume that the material starts 1.0 X 1011 cm away from the white dwarf, and ends up 1.0 X 109 cm away.

solution

We first convert the mass loss rate into g/s:

dM _ (1.0 X 10— 8 M0/yr)(2.0 X 1033 g/M0) dt _ (3.1 X 107 s/yr)

The luminosity is then

L _ (6.67 X 10—8 dyn cm2/g2 )(2.0 X 1033 g) X (6.5 X 1017 g/s)

This is approximately 20 times the luminosity of the Sun.

Occasionally we observe a star that suddenly brightens by 5 to 15 magnitudes. These objects are called novae (Fig. 12.5). The name suggests the appearance of a new star where one was not previously seen. Some of these novae appear to be recurrent, on time scales of up to hundreds of

HST image of the shell around recurrent nova T Pyxidis.This is at a distance of 2000 pc.The shell is a little less than 1 parsec across.This image shows that it is made up of a large number of small objects.This is the material that has collected from the various nova outbursts. (Note that Fig. 4.16 shows an HST image of the shell expanding around Nova Cygni 1992, taken 467 days after that outburst.) [STScI/NASA]

years. There is evidence that mass is ejected in the process. In some cases this material can be seen expanding away from the star. The amount of mass ejected is about 10 — 5 M0.

We think that novae are the result of thermonuclear explosions on the surfaces of white dwarfs with mass falling in from a companion. The mass falling in is from the envelope of a red giant, and therefore contains hydrogen. (Remember, the white dwarf has used up all of the hydrogen in the core and has expelled the rest in its planetary nebula.) The surface of the white dwarf is hot enough for fusion of the hydrogen to take place. It takes place rapidly in a small explosion, which probably stops the mass transfer for a while. When the transfer resumes, another explosion can take place. Shells of material left around novae are shown in Figs. 12.5 and 4.16.

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