CHAPTER 14
The Lives and Deaths of Low-Mass Stars
CHAPTER OUTLINE
14-1 Brown Dwarfs
1. The maximum mass that a star can have is about 150 solar masses, since otherwise the
internal pressure and huge amounts of energy generated in the core would overwhelm
gravity and blow the star apart.
2. The minimum mass that a star can have is about 0.08 solar masses, since otherwise its
core cannot become hot and dense enough for nuclear reactions to begin.
3. A brown dwarf is a star-like object whose mass is too small to sustain nuclear fusion.
Probable limits of mass for brown dwarfs are from 0.013 to 0.08 solar masses. (Jupiter’s
mass is about 0.001 solar masses.) After a brief initial phase where some deuterium is
burned, brown dwarfs continue to cool.
4. A brown dwarf (GL229B) was first seen in 1994. Its mass is between 20 and 50 times
that of Jupiter.
5. Most known brown dwarfs are isolated. Their formation is most likely similar to that
of a normal isolated star but they could also be the byproduct of a chaotic star formation
process during which they are ejected from a new-born stellar group.
6. A brown dwarf is not a star because it cannot sustain nuclear reactions in its core.
14-2 Stellar Maturity
Stellar Nuclear Fusion
1. In stars of low mass (less than 1.5 solar masses), the predominant energy-generating
series of reactions is the proton-proton (p-p) chain.
2. In stars of mass greater than 1.5 solar masses, the core temperatures are greater and
thus a different chain of nuclear reactions (the CNO cycle) dominates. This series of reactions involves hydrogen, carbon, nitrogen, and oxygen.
3. The carbon or CNO cycle is a series of nuclear reactions that results in the fusion of
four hydrogen nuclei into a helium nucleus (just like the p-p chain), using carbon-12 as a
catalyst in the process.
The Stellar Thermostat
1. The core of a main sequence star has a regulating mechanism (just like a thermostat)
that controls the rate of consumption of hydrogen fuel.
2. The overall effect of the mechanism is that the star remains in hydrostatic equilibrium.
Main Sequence Life
1. In the core of a main sequence star, the following sequence of events occurs: the number of nuclei decrease due to fusion, the core shrinks, gravitational energy heats the core,
the fusion rate increases, additional energy is released by the core, the star becomes more
luminous, the outer layers of the star expand, and as a result the star’s surface cools.
2. As a star ages on the main sequence, it becomes more luminous, its radius increases,
and its surface (effective) temperature decreases. The star’s position on the H-R diagram
moves to the up and right of the main sequence.
3. Massive stars have a greater fusion rate and thus are more luminous. As a result, they
can use up the hydrogen in their cores in a few million years. The least massive stars can
sustain hydrogen fusion for hundreds of billions of years.
4. Observational evidence for the shorter lifetimes of massive stars comes from galactic
clusters. Assuming that the stars in a cluster formed at about the same time, the older the
cluster, the farther its most massive stars have moved to the right from the zero-age main
sequence.
5. The main sequence lifetime of the stars at the turnoff point (the point on the H-R diagram of a cluster of stars where the stars are just leaving the main sequence) is equal to
the cluster’s age.
Tools of Astronomy: Lifetimes on the Main Sequence
1. The amount of time a star spends on the main sequence depends on the amount of hydrogen in its core and its rate of hydrogen consumption.
2. The lifetime (t) of a star on the main sequence is given by the expression: t = tSun / M2.5,
where M is the star’s mass in solar units and tSun is the Sun’s main sequence lifetime
(about 10 billion years).
14-3 Star Death
1. Until their lives end on the main sequence, the main difference between the evolution
of stars of various masses is the amount of time they spend as protostars and main sequence stars.
2. After this point, the star’s mass determines which of several different paths its life will
take.
3. Stars can be grouped by mass as very low mass (< 0.4 M solar masses), moderately low
mass (0.4–4 M solar masses), moderately massive (4–8 M solar masses), and very massive (> 8
M solar masses).
14-4 Very Low Mass Stars (< 0.4 M solar masses)
1. In stars with a mass of less than about 0.4 solar masses, convection occurs throughout
most or all of the star’s volume. Hydrogen from throughout the star is cycled through the
core, and the entire star runs low on hydrogen at the same time.
2. As the rate of fusion decreases in the core, the star contracts and heats up. The position
of the star on the H-R diagram moves toward the lower left, and the star becomes a white
dwarf.
3. A very low mass star will take more than 20 billion years to completely burn its hydrogen.
4. Since the lifetime of a very low mass star is more than the age of the universe, white
dwarfs currently observed must have originated in a different manner.
14-5 Beyond the Very Low Mass Stars: The Red Giant Stage
1. About 90% of the stars in the sky are on the main sequence. This implies that a typical
star spends 90% of its luminous lifetime on the main sequence.
2. For most of these stars the next step after leaving the main sequence is to become red
giants.
3. A typical star begins to contract once its core is depleted of hydrogen. This gravitational contraction causes the star to heat up.
4. Energy from the contraction of the core then heats a shell surrounding the core to temperatures that permit fusion of hydrogen to begin.
5. These two sources of energy cause the outer portions of the star to expand and cool.
6. The position of the star on the H-R diagram moves to the right and upward (due to increasing luminosity).
7. A red giant can have a lower surface temperature (less radiation per square meter) but
a higher luminosity because its diameter will have expanded by a large factor (200 times
for a “typical” red giant).
14-6 Moderately Low Mass Stars (0.4 – 4 M solar masses)
Electron Degeneracy and the Helium Flash
1. The core of a red giant consists of helium nuclei intermingled with electrons, a mixture
that has properties similar to a regular gas.
2. The core of a red giant will not continue to contract indefinitely because of electron
degeneracy.
3. Electron degeneracy is the state of a gas in which its electrons are packed as densely as
nature permits. The temperature of such a high-density gas is not dependent on the pres-
sure as it is in a “normal” gas.
4. In the case of the degenerate core of a red giant, the more massive the core is, the
smaller is its radius.
5. As the red giant evolves and hydrogen burning takes place in its outer layers, the helium “ashes” are dumped back onto the degenerate core, raising the temperature of the
core.
6. When the core temperature reaches 100 million Kelvin, helium nuclei begin to combine, forming carbon.
7. Because of degeneracy, the core cannot cool by expanding and thus helium fusion reactions occur faster and faster. Helium flash is the process of runaway helium fusion reactions that occurs during the evolution of a red giant.
8. The end result of the helium flash is that the core heats up, the degeneracy is destroyed,
the stellar thermostat is restored, and some mass from the star’s surface may be lost.
9. Following the helium flash, the star contracts slightly and its surface temperature increases.
10. The by-products of helium fusion reactions are carbon and oxygen. When a red giant
reaches the stage where it has a carbon core, the heat from the shrinking core ignites helium fusion in a shell around it, while hydrogen is fusing in a second shell beyond the first.
11. The star slowly enters a new red giant phase and its position on the H-R diagram
moves to the right and upward.
12. Stars more massive than 2 solar masses do not experience a helium flash. Their cores
make a smooth transition to helium burning without becoming degenerate. When their
helium supply is exhausted, however, their internal structure is similar to that of Sun-like
stars.
Stellar Pulsations
1. During its evolution, a star continuously tries to remain in equilibrium. The changes
occurring in its core are often periodic.
2. Two types of pulsating stars are especially important to astronomers because they can
be used as distance indicators: the Cepheid variables (with periods between 1 and 100
days) and the RR Lyrae variables (with periods shorter than one day).
3. The oscillations of the star’s outer layers result from the ionization of helium in the
outer layers when it gets compressed. The resulting gas is opaque, trapping heat from inside the star. This results in an increase of the pressure under the layers, an expansion and
subsequent cooling of the layers. The layers then become transparent, the trapped energy
is released, the layers fall inward and the cycle repeats itself.
4. The conditions necessary for such pulsations occur in a narrow strip on the H-r diagram called the instability strip.
5. Cepheid variables result from massive stars in the instability strip, while RR Lyrae variables result from low mass stars.
6. In some cases stellar pulsations can be so large that the star loses its outer layers to
outer space.
Mass Loss from Red Giants
1. Observations show that other main sequence stars shed material just like our Sun does
as the solar wind.
2. The solar wind carries away about 10–14 of the Sun’s mass each year. Over the course
of 10 billion years, the Sun will lose only 0.01% of its mass this way.
3. In red giant stars it is thought that core instabilities and pulsations are responsible for
the large mass loss. A typical red giant loses 10–7 solar masses a year.
Planetary Nebulae
1. A planetary nebula is a spherical shell of gas that is expelled by a low mass red giant
near the end of its life.
2. Planetary nebulae have nothing to do with planets. They were named so decades ago
because their colors resemble the colors of Neptune and Uranus when seen through a
small telescope.
3. The material in the shell glows because UV radiation from the central hot star causes it
to fluoresce.
4. Pulsations in the core of the red giant and/or stellar winds emitted from the dying star
(and which occur in definite stages) are thought to cause planetary nebulae.
5. Not all planetary nebulae appear as rings. Some show hints of spherical structure while
others are bipolar. Their shapes depend on how the outflows interact with each other and
with the star’s magnetic field.
6. Planetary nebulae do not last long. Their material quickly dissipates into space and becomes part of the interstellar medium.
7. The proto-planetary nebula phase lasts between a few hundred to 1000 years. (This
phase corresponds to the transition between the last stages of a red giant star’s life and the
late stages of a planetary nebula after the star ejected most of its mass.)
8. Observations show that proto-planetary nebulae are huge organic chemical factories.
9. The core left behind after the nebula dissipates becomes a white dwarf.
14-7 White Dwarfs
1. Sirius B was the first white dwarf observed (in 1862); it has about the same mass as
Sirius A, but is small and hard to see.
2. Astronomers estimate that 10% of all stars are white dwarfs.
3. White dwarfs are the cores of red giants that remain after the outer parts of the original
stars have blown away.
The Chandrasekhar Limit
1. Even though electron degeneracy supports the white dwarf against collapsing completely, there is a limit to the amount of pressure degenerate electrons can withstand.
2. This limit to the mass of a white dwarf above which it cannot be supported by electron
degeneracy and cannot exist as a white dwarf is known as the Chandrasekhar limit. It is
about 1.4 solar masses.
3. Main sequence stars with masses up to 4 solar masses can end up as white dwarfs only
if they lose mass during the red giant and planetary nebula phases.
Characteristics of White Dwarfs
1. White dwarfs that formed from low mass stars are composed of helium and carbon.
White dwarfs that formed from more massive stars contain nuclei of oxygen, neon, sodium, and even iron.
2. White dwarfs have observed surface temperatures between 4,000 K and 85,000 K.
Their masses range from perhaps 0.02 solar masses up to 1.4 solar masses.
3. A typical white dwarf will have 0.8 solar masses, a diameter of 10,000 km (3/4 of
Earth’s), and a density of 106 g/cm3. A teaspoon of white dwarf material would weigh
two tons.
4. To get to the white dwarf stage, a low-mass star will have gone through these stages:
protostar, main sequence star, red giant, planetary nebula.
5. White dwarfs do not produce energy. They radiate away their leftover energy and
simply fade away and become black dwarfs.
6. Black dwarf is the theorized final state of a star with a main sequence mass less than
about 8 solar masses, in which all of its energy sources have been depleted so that it emits
no radiation.
Novae
1. A binary system of a white dwarf and a newly formed red giant will result in the formation of an accretion disk around the white dwarf. The material in the disk comes from
the red giant and is mostly hydrogen.
2. An accretion disk is a rotating disk of gas orbiting a star, formed by material falling
toward the star.
3. The hydrogen builds up on the surface of the white dwarf, becomes denser and hotter
and can ignite in an explosive fusion reaction when the temperature reaches 10 million K.
4. This surface explosion blows off the outer layers of the white dwarf. Though this shell
contains a tiny amount of mass (0.0001 M solar masses) it can cause the white dwarf to
brighten by 10 to 20 magnitudes (10,000 to 100 million times brighter) in a few days.
5. A nova is a star that suddenly and temporarily brightens, thought to be due to new material being deposited on the surface of a white dwarf.
6. Because so little mass is blown off during a nova, the explosion does not disrupt the
binary system. Ignition of the infalling hydrogen can recur again with periods ranging
from months to thousands of years.
14-8 Type I Supernovae
1. If accretion brings the mass of a white dwarf above the Chandrasekhar limit, electron
degeneracy can no longer support the star, and it collapses. The collapse raises the core
temperature and runaway carbon fusion begins, which ultimately leads to the star exploding completely.
2. Such an exploding white dwarf is called a supernova.
3. While a nova may reach an absolute magnitude of –8 (about 100,000 Suns), a supernova attains a magnitude of –19 (10 billion Suns).
4. There are two types of supernovae:
(a) Type I: their spectrum has no hydrogen lines.
(b) Type II: their spectrum contains prominent hydrogen lines; they originate from the
explosion of a single star.
5. Type I supernovae are divided into three subclasses:
(a) Type Ib, and Ic are caused by massive stars that have lost different proportions of their
outer layers before exploding.
(b) Type Ia result from white dwarfs.
6. A Type Ia supernova reaches maximum brightness in a few days, fades quickly for
about a month, and then declines in brightness more gradually until it dissipates in about
a year.
7. Models indicate that the energy of a Type Ia supernova (following the explosion)
comes from radioactive decay of nuclei produced in the explosion.
8. The light curves and spectra of all Type Ia supernovae are very similar. This similarity
is a powerful tool that astronomers use to trace the history of the expansion of the universe.