Physics 110: Homework #4 Solutions

4.1

The birthline is the line in the Hertzsprung-Russell diagram where stars of different mass first become visible. It lies to the right of the main sequence in the HR diagram, or toward lower temperatures. The general behavior of a solar-type star as it approaches the main sequence includes periods of time when its luminosity will be both bigger and smaller than its main sequence luminosity. When an evolving protostar first becomes visible on an HR diagram it is initially much brighter than a main sequence star of the same mass, because it is so much larger in size. As the protostar contracts further its luminosity drops and its surface temperature rises. This process continues until the core becomes hot enough to initiate fusion reactions. At this point the star is only slightly larger in size than its main sequence size, while its surface temperature is somewhat less. In this case the lower temperature is more important than the slightly larger size, so the star is slightly fainter than it will be on the main sequence.

4.2

Winds, or mass loss, from young stars are important for halting the infall of matter onto the protostar. Winds and disks interact to produce bipolar outflows which provide astronomers with important views of the star formation process. At latter stages winds can sweep away all the matter around the star including the circumstellar disk. Circumstellar disks are believed to provide at least part of the collimation of the wind from young stars that produce bipolar jets of material flowing out along the star's polar axis.

4.3

The time it takes is just the distance divided by the speed: 5 pc/200 km/s = m / m/s = s = 24,600 yr. The time is just the amount of mass to be lost (a solar mass) divided by the rate of mass loss: kg / kg/s = s = yr.

4.4

All stars can generate energy from gravitational collapse. Fusion reactions are another way they generate energy. The proton-proton chain is the dominant process for solar mass or smaller stars while on the main sequence. The carbon cycle occurs in the cores of main sequence stars slightly more massive than the sun. The triple alpha reaction takes place in stars at least as massive as the sun after the hydrogen in their cores has been consumed. More massive stars can also fuse carbon, oxygen, and heavier elements, up to iron, which is the absolute limit. (Fusion of iron does not produce energy.) Note that at any particular position in a star only one fusion reaction will dominate, which is due to the strong temperature dependence of fusion reactions. However stars can and do have different reactions taking place at different places in their interiors.

4.5

One needs to refer to Figure 19-5 to answer this question. When the Sun was years old it had a luminosity of 3 times its main sequence luminosity, a surface temperature of 4,000 K, and a spectral class of approximately K2. At years old the luminosity was slightly less than the main sequence luminosity ( 0.8 ) and roughly the same surface temperature and spectral class as just given.

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