Physics 110: Homework #7 Solutions

7.1

Binaries with periods less than a few years are usually only a few AU apart. This is too close together for their images to be separated so that they would be seen as a visual binary. More widely separated stars orbit each other too slowly for their Doppler shifts to be easily detected, so they are not identified as spectroscopic binaries.

7.2

Primary (deeper) minimum occurs when star B (the hotter star) is eclipsed. As discussed in the text (p. 484, see also fig. 21-9), it is the hotter star, not necessarily the bigger or brighter one, that radiates the larger amount of energy in the eclipsed area and produces the deeper minimum when eclipsed. Yes, the optical spectrum would change as a function of time. During primary eclipse it would appear to be the spectrum of the cooler star. In between eclipses it would appear to be the combined spectrum of the hotter and cooler stars. During the secondary eclipse the "effective" temperature of the combined stars would appear to be the hottest of all.

7.3

After the star fills its Roche lobe, it will spill its matter through L into the Roche lobe of the other star.

7.4

Mass exchange is the ultimate cause of a Type Ia supernova. As matter accumulates rapidly on a white dwarf the star becomes smaller and its core becomes hotter. When the core temperature reaches 10 billion K, carbon fusion begins. The energy released by carbon fusion triggers a series of nuclear reactions that blow the star apart. Mass exchange is also the cause of nova explosions. However, in this case the accreted matter remains cool and the layers of gas that build up on the surface are degenerate. When the layer of gas becomes thick enough, it starts to burn (at the base of the accreted layer) and a thermonuclear runaway consumes most of the layer. The energy released from this process blows away the accreted layer and thus the total mass of the white dwarf doesn't change.

7.5

The energy emitted is ultimately derived from the gravitational energy released as matter in the disk spirals inward.

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