C H A P T E R
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STELLAR EVOLUTION
ANSWERS TO REVIEW QUESTIONS
1.
The main sequence marks the onset of a comparatively stable long-lived energy source in what was
previously a collapsing protostar (fusion of H atoms into He plus energy). The star now stays pretty
much the same in energy output per second and surface temperature. This stability is because the stars
balance in their cores the weight of the overlying layers via gas pressure from heat generated by the
fusion of H atoms.
2.
A star must at some time undergo thermonuclear fusion of hydrogen in its core. This requires that the
core temperature reach at least 10 million K. Objects with masses less than 0.085 M cannot squeeze
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the core hard enough to reach temperatures of 10 million K, never ignite hydrogen fusion, and thus
never become stars.
3.
A brown dwarf is an object that is not massive enough to initiate thermonuclear fusion of hydrogen to
form helium in its core, but it is generally massive enough to initiate the fusion of deuterium in it core.
4.
A mass-luminosity relation exists because massive stars must produce more energy to support the outer
layers. Since they produce more energy, they will also have a greater luminosity. Therefore, there is a
relationship between the mass of a star and the energy it must produce to be in hydrostatic equilibrium.
The energy produced is the luminosity of the star, so there is a relation between a star’s mass and its
luminosity.
5.
The star's life expectancy is determined by its mass because the mass determines the extent to which
the core can be squeezed. The more massive the star is the greater the pressure in its core and the
greater the temperature in its core. The rate at which nuclear reactions occur depends on the
temperature of the core, and the hotter the temperature the faster the reactions occur. The massive stars
possess more fuel than the low mass stars, but they burn that fuel at a much faster rate.
6.
The outer layers of a star will cool as it expands because much of the energy produced goes into
expanding the outer layers and not into the thermal motions of the gas; therefore, the star cools as it
expands. The luminosity increases because more energy flows to the outer layers during the times of
expansion. Recall that the luminosity of an object depends on both its diameter and surface
temperature. As a star expands, its surface area increases rapidly while its temperature decreases rather
slowly. The result is that the luminosity increases as the star expands.
7.
Helium flash is caused by the ignition of helium fusion in a core that contains degenerate electrons.
The degenerate electrons control the pressure of the core and because they are degenerate, do not
readily expand with an increase in temperature. Therefore, the temperature pressure thermostat does
not operate in the cores of these objects.
Helium flash makes later stages of stellar evolution difficult to understand because helium flash occurs
so rapidly and violently that computers cannot model it. Assumptions must be made as to what
happens. This uncertainty during helium flash means that there is an uncertainty in the structure of the
star at the end of helium flash, which makes the rest of the models uncertain.
8.
Helium flash is avoided in two ways. Low mass stars avoid it because their cores never become hot
enough to initiate the fusion of helium. More massive stars avoid helium flash because their cores are
hot enough that the electrons do not become degenerate before helium fusion begins.
9.
Giant stars are expanded main sequence stars. This means that if we take a main sequence star like the
sun and increase its radius by 10 to 100 times, we would end up with a star that is a giant. However, if
its radius increased 10 to 100 fold, then its volume has increased by 1000 to 106 fold, and its density
will have dropped by an equal amount.
10. Lower mass stars are not able to ignite more massive fuels because these fuels require greater
temperatures before fusion will occur, and the lower mass stars do not have the mass to develop
significant pressure in the core to achieve the needed temperatures.
11. We can estimate the age of a star cluster by determining the temperature, or color index, of the stars
that are just leaving the main sequence (i.e., the main sequence turnoff point). This temperature is
directly related to the star’s luminosity, which depends on its mass. The mass can be used to calculate
the star’s lifetime on the main sequence. In this way we can determine the age of the stars at the
turnoff point, and since all stars in the cluster formed at the same time, we obtain an estimate of the age
of the cluster.
12. Star clusters contain many stars of different masses but of nearly the same age. The stars must be of
the same age because the ignition of fusion by massive stars sweeps material out of the cloud and halts
star formation. Each cluster presents the stage of evolution of stars of different masses at a given time
from formation. In this way we have a snapshot of stellar evolution as a function of mass.
13. Cepheid and RR Lyrae variables can show that stars evolve by revealing changes in their pulsation
periods. These stars’ pulsation periods depend on the radii of the stars. As a star evolves it will
expand or contract depending on where it is in its evolution. Therefore, any of these pulsating stars
that show long term variations in their periods indicate that the mean radius of the star is changing, and
hence, the star is evolving.
14. How Do We Know? – Mathematical models use physical laws to explain and predict behavior. This is
important to be able to mimic the behavior of a physical system that is not visible to us or must only be
viewed by indirect means. Since the mathematical models are using the same physical laws that matter
obeys we can be sure that if the theory is generally accurate then the results from the mathematical
explanations will be correct.
ANSWERS TO DISCUSSION QUESTIONS
1.
Even though a helium flash cannot be directly observed it can be indirectly inferred from other
observations. Shortly after the helium flash the star should increase dramatically in radius. Also there
are several observational pieces of evidence before the event occurs that suggest that a helium flash is
eminent. In many cases the process of cause and effect can suggest certain events must occur even
though we are not able to observe them.
ANSWERS TO LEARNING TO LOOK
1.
In the first few years of this cluster there were likely some bright red stars that were supergiants. The
supergiants were evolved massive O stars that have since died. Now only slightly lower mass B and A
stars remain in the cluster. Those hot stars are the brightest in the cluster and their high temperatures
correspond to a bright blue color.
2.
There are no bright-blue stars in M67 because the cluster is too old for any of those types of stars to
still exist. Bright-blue stars normally have a high mass and therefore don’t live for a very long period
of time (million of years).