English Paper Chapter 19

CHAPTER 19

THE EVOLUTION OF STARS

A typical star one like the sun lives (that is; produces nuclear energy) for about 10

billion years. This incredible length of time is greater than 100 million human lifetimes.

Observing the sun for 100 years covers about the same fraction of its lifetime as observing a

person for 20 second. This might make understanding the career of a star seem impossible.

However, by observing a great many stars, astronomers have developed a statistical picture of

the lives of typical stars. Astronomers also have observed occasional milestone transitions in

the lives of stars. These observations, combined with considerable hard thinking, have

brought us to the point where we have a reasonably good understanding of the evolution of

stars.

1. The Evolution of Stars

Stars evolve mean that it changes its appearance and internal structure, because

the fusion reaction that supply the star’s energy transform light elements into heavier

ones, changing the internal chemical composition of the stars. This is significant because

important processes going on in stars depend on the kinds of atoms and ions that make up

the stars. These processes change as the chemical composition changes. As a result, as the

internal structure of the star changes, its size, luminosity, and surface temperature may

change as well.

In stars, there are three processes that depend on chemical composition. One is

the rate at which the star produces energy. A second is the rate at which the energy flows

to the surface of the star, where it is radiated into space. The third is the generation of

pressure, which resists gravity and prevents the collapse of the star. As these processes

change, the star evolves.

a. Energy Generation

The two ways in which stars produce energy are fusion and gravitational

contraction or collapse.

Hydrogen fusion

The temperature at the center of a star first rises to about 10 million K at the end of

the star’s long contraction from a fragment of a molecular could. At this point, the

fusion of hydrogen into helium becomes the major source of energy in the star. In

the sun and in stars less massive than the sun, the fusion of hydrogen into helium

occurs by means of the proton-proton chain. In stars more massive than the sun,

however, hydrogen fusion occurs by mean of the carbon cycle, in which carbon,

nitrogen, and oxygen nuclei act as catalysts for the production of helium from

hydrogen. Shown in the figure bellow:

Figure 19.1 The nuclear reactions of the carbon cycle

For either set of reactions, hydrogen becomes less abundant and helium more

abundant as time passes. This graph show how the fractional amount of hydrogen

varies with time in a star of 1 Mʘ.

Figure 19.2 The depletion of hydrogen in the core of a one-solar-mass main

sequence star

(a) Before fusion begins,

(b) During fusion,

(c) After most central hydrogen has been consumed.

In graph (a), the hydrogen content throughout the star is uniform before hydrogen

fusion begins; the amount of the hydrogen is the same throughout the star. During

hydrogen burning, the hydrogen content drops fastest at the center of the star

because the rate of fusion reaction is greatest there; however it occurs most rapidly

at the center of the star because the temperature is highest there. The more rapidly

fusion goes on, the more rapidly the composition of the star changes, so the

amount of hydrogen decreases most rapidly at the center of the star (graph (b)). As

fusion continues over time, in graph (c), near the end of the core hydrogen

burning, the hydrogen content in the core is reduced nearly to zero. Notice that the

hydrogen content of the outer stellar layers is unaffected by hydrogen burning in

the core. More and more hydrogen is consumed in the core of the star. The number

of hydrogen nuclei (protons) drops because they are being fused into helium, so

the rate of collisions involving protons decreases. The rate of fusion would

decrease, as a result, except that the temperature increases slightly at the same

time. Collisions are more energetic at the higher temperature and are more likely

to lead to fusion. Thus, rising temperature compensates for the falling number of

protons to keep the rate of energy production high.

Eventually, however, all of the hydrogen in the core of a star is consumed. In

many stars, this happened only after the temperature in the region just outside the

core of the star has risen high enough that hydrogen fusion can occur there. Thus,

core hydrogen fusion is sometimes followed by an evolutionary phase in which

fusion and energy generations go on in a thin shell that surrounds the helium rich

core.

Other nuclear fuels

High temperatures are needed of fuse hydrogen because the hydrogen nuclei,

protons, are electrically charged and repel each other. Nuclei of elements other

than hydrogen contain even more protons, so they have even larger electrical

changes to overcome during fusion. As a result, even higher temperatures are

needed to bring these other nuclei close enough for fusion to take place.

At a temperature of 100 K, the fusion of helium into carbon becomes possible. The

pair of reactions through which helium fuses into carbon is called the triple α

process because three helium nuclei (α particles) are needed to make each carbon

nucleus. By the time the core of a star gets hot enough for the triple α process to

take place, all of the hydrogen has been fused into helium. Helium is now the most

abundant fuel and can supply the triple α process for a relatively long time. If the

temperature in a star reaches between 500 million to 1 billion K, the carbon that

result from the triple α process becomes a fuel. If the core temperature rises even

higher in a star, other nuclei can be consumed in fusion reaction. Fusion can

produce energy only from fuels less massive than iron. The fusion of iron and

more massive elements can never produce energy for the star in which those

reactions take place.

Contraction and collapse

Any time a star or a part of a star shrinks in size, gravitational energy is released.

Generally, as in the case of pre-main sequence evolution, a star shrinks slowly and

releases gravitational energy at a controlled rate. A star often contracts after a

nuclear fuel has been used up in the core of the star. The energy released during

contraction heats the core of the star, however, so contraction usually continues

only until the core temperature raises enough for another kind of nucleus to

become a nuclear fuel.

The total gravitational energy that has ever been released by a star as it shrank to a

given size is approximately given by

E=G M 2

R

where G is gravitational constant, M is the mass of the star, and R is its radius.

Because the total energy produced by gravitational contraction increases as radius

of a star decreases.

b. Opacity

The structure of a star will also be affected by how easily photons can pass

through the material in any given layer. If a layer absorbs photons, then it will be

heated with an increase in pressure that will expand the layer. Alternatively, if a layer

is transparent and allows photons to readily escape, then that layer will be cooler with

a lower gas pressure that will allow gravity to compress its material. Astronomers

actually use the reciprocal of transparency, or opacity, to measure the ability of

photons to pass through material. A low opacity means high transparency; a high

opacity means a low transparency. The opacity of the material in a given layer

depends on the chemical composition (some elements absorb light more easily than

other elements), the temperature, and the density.

c. Equation of state

The internal structure of normal stars is fairly simple because only a few physical

principles are involved in the determination of the structure of a gaseous object. This

simplicity is summed up in a simple principle, the Russel‐Vogt theorem. For stars of

like composition, the structure and observable properties depend on a single parameter

such as the star's mass. Alternatively, the Russell‐Vogt theorem may be expressed as

follows: The equilibrium structure of an ordinary star is determined uniquely by its

mass and chemical composition. This principle or theorem is not an accident of nature,

but is the direct result of how the laws of physics determine the equilibrium structure

of a normal star.

This physical law relates gas pressure P in a given layer to the number density of

particles N (particles/cm 3) and the temperature T at that radius from the center of the

star. For a perfect gas, the equation of state says where k is the Boltzman constant.

Pressure is simply proportional to the number density of particles and to the

temperature (expressed in Kelvin). The number of particles in a given volume,

however, depends upon the chemical composition of the material, because particles

are not identical. An atom of helium has four times the mass of an atom of hydrogen;

thus, a given amount of helium has only one‐fourth the number of particles as an equal

amount of hydrogen. The same total mass of these two elements in an identical

volume therefore will have different pressures. If the pressure from helium is

responsible for the balance against gravity in a stable star, then four times as much

mass in the form of helium would be necessary at the same temperature to produce the

same pressure as hydrogen.

Temperature is an additional factor. At low enough temperatures, atoms are

electrically neutral. At higher temperatures, atoms ionize, the electron becoming free

particles in addition to the nuclei. Each ionized hydrogen atom would be represented

by two particles, the nucleus (proton) and a free electron, with a corresponding change

in pressure compared to neutral hydrogen. Given the chemical composition of a gas

and the state of ionization of the atoms, then the mean atomic mass μ of the particles

may be calculated and the equation of state expressed as follows: the mass density ρ

becomes

P= ρkT/μ.

d. Models of Stars

In addition to ordinary stars like our Sun, the universe also contains other types of

stars whose structures may differ because they exist in a multiple‐star system or they

produce variable energy in their cores. Some of these different types of stars include

binary stars and variable stars.

- Binary stars

There are many single or isolated stars like the Sun, but about half of all stars in

the sky are found in multiple systems. Of the 25 nearest star systems within 4 pc

(13 ly) of the Sun, 8 actually are multiple systems (7 binaries and 1 triple system).

Binary systems are of special interest, because analysis of their orbital

characteristics by use of Kepler's Third Law yields a direct measure of stellar

masses. Such stars that are well separated are known as visual binaries, but others

may be detected only via the Doppler Effect and hence are known

as spectroscopic binaries. If the orientation of the orbit is such that the stars

alternatively pass in front of each other, then an eclipsing binary is observed;

analysis of the light curves yields information directly about stellar sizes.

Other phenomena are found in close binary systems. Very close stars may have

their spherical structures altered by the gravitational effects of their companions. If

the stars are close enough, this process may result in the near sides of the stars

touching as contact binaries. As one or the other of the stars in a pair evolves,

there may result mass exchange between the two stars that alters the course of

evolution for both stars. Given the large range of stellar properties, an extremely

great variety of pair types and interactions is possible.

- Variable stars

Stars whose luminosity changes in a periodic or non‐periodic fashion are known as

variable stars. There are dozens of different types of variables known. Among the

more important are very young stars (T Tauri variables) that are in the process of

establishing stable thermonuclear energy production as main sequence stars;

pulsating variables whose outer layers literally swell and contract; and several

types of red giant stars. The variability of any star yields clues to its internal

properties (in the same fashion that differences in vibration clearly distinguish a

small, lightweight snare drum from a large, heavy kettle drum), but specific types

of variables are of intense interest because they can be used as distance tools.

2. Evolutionary Tracks and Star Clusters

a. Changing appearance in the H-R Diagram

The path through an H-R diagram that a star follows as it evolves is called the

star’s evolutionary track. The evolutionary track of a 1 Mʘ star is shown in figure

bellow

Figure 19.4 An H-R Diagram showing the evolutionary track of a one-solar-mass

star.

As the star shrinks during that phase, it grows hotter and dimmer until fusion

begins in its core.

H-R Diagram of star clusters

Evolutionary tracks for pre-main sequence stars such as those shown in figure

bellow

Figure 19.5 Evolutionary tracks for pre-main sequence stars of different masses.

The positions of the stars in the H-R diagram would fall on an isochrones, a line

in an H-R diagram that shows the temperatures and luminosities of a collection of

stars that have the same age but different masses.

3. Main Sequence Stars

The main sequence phase in the evolution of a star is the period of time when it is

consuming hydrogen in its core. It is a period of stability during which both the

structure and appearance of the star change only very gradually.

The fact that the main sequence stars are represented by a band across the H-R

diagram that is smoothly populated from the rare O and B stars to the very common M

stars strongly suggests that these stars are physically the same type of object, though

some factor must be responsible for their range in observable properties. The Sun is a

main sequence star and thus, by implication, all other main sequence stars must share

its fundamental nature. Through theoretical modeling of the Sun and other main

sequence stars, scientists have determined that the factor that differentiates them from

the three other types of stars is the fact that their energy is generated internally by the

conversion of hydrogen to helium (giants and supergiant produce their energy by

gravitational contraction and by converting helium to even heavier elements; white

dwarfs are like dying embers in a fireplace, radiating away their store of heat energy).

Like most other stars, they also are in a state of equilibrium in which gravity is

balanced by gas pressure at each radius, and the luminosity flowing outwards at each

level is balanced by the energy generated interior to that level.

a. The variety of main sequence stars

Although all main sequence stars generate energy by the fusion of hydrogen into

helium in their cores, they differ from one another in many important respects,

such as mass, size, temperature, luminosity, and internal structure.

Mass

Main sequence stars range in mass from 0.08 Mʘ to perhaps130 Mʘ.

Size

The most massive main sequence stars are also the largest. Some of them are

much as 15 times as large as the sun. If we were located 1 AU from such a star,

it would have an angular size of about 7.5º. The least massive and smallest

main sequence stars are only about one-tenth as large as the sun.

Figure 19.6 The relative sizes of main sequence stars with spectral types.

Temperature and Luminosity

The main sequence stars of lowest mass have surface temperature of about

50,000 K and are spectral type O3. The main sequence stars of lowest mass

have temperature of only 2400 K and are spectral type M8. Brown dwarfs are

cooler and dimmer still and fall in spectral classes L and T.

Main sequence stars show an extremely wide range of luminosities. The most

luminous (and most massive) are more than a million times as bright as the

sun. If the sun were replaced by one of these stars, the temperature of the earth

would raise to about 10,000 K, so the earth and the other terrestrial planets

would quickly be vaporized. The smallest, least massive main sequence stars

are about 1000 times dimmer than the sun. If one of these stars replaced the

sun, the earth’s temperature would fall about 50 K, approximately the

temperature of Neptune.

Table 19.1 The spectral types, temperatures, radii, and luminosities for main

sequence stars.

Internal structure

The internal structure of a main sequence star depends on its mass. The more

massive main sequence stars have the highest central temperature as great as

40 million K. This is hot enough that massive main sequence stars can use the

carbon cycle to fuse hydrogen into helium. Because the rate at which fusion

reaction occur is very sensitive to temperature, the massive main sequence

stars consume their hydrogen at rates much faster than the sun, which has a

core temperature of only about 15 million K. the rapid consumption of

hydrogen in massive main sequence stars is the source of their tremendous

luminosities. Main sequence stars of low mass, in contrast, have core

temperatures below 10 million K, so nuclear fusion goes on very slowly in

their cores and produces only a relatively feeble output of energy.

The core of massive main sequence star produces far too much energy for

radiation alone to carry energy outward. Instead, the core of massive star has

vigorous convection. The convective region ends, however, far beneath and

without the mottled appearance shown by the sun. The central convective

region is largest for the most massive main sequence stars and grows smaller

with decreasing mass until it disappears for stars a little more massive than the

sun. Low-mass main sequence stars also have convective regions, but in this

case it is their surface layers that are convective, like the sun photosphere. The

sun has a shallow convective region, but for stars with lower masses, the depth

of the surface convective zone increases with decreasing mass until, for the

main sequence stars of lowest mass, it extends all the way to the core of the

star.

Figure 19.7 Internal structure for main sequence stars of several masses.

Main sequence lifetime

The overall lifespan of a star is determined by its mass. Since stars spend

roughly 90% of their lives burning hydrogen into helium on the main sequence

(MS), their ‘main sequence lifetime’ is also determined by their mass.

Massive stars need higher central temperatures and pressures to support

themselves against gravitational collapse, and for this reason, fusion reactions

in these stars precede at a faster rate than in lower mass stars. The result is that

massive stars use up their core hydrogen fuel rapidly and spend less time on

the main sequence before evolving into a red giant star.

An expression for the main sequence lifetime can be obtained as a function of

stellar mass and is usually written in relation to solar units (for a derivation of

this expression, see below):

Where:

tʘ = Sun MS lifetime = 1010

M = mass of star

Mʘ = solar mass

The lifetimes of main sequence stars therefore range from a million years for a

40 solar mass O-type star, to 560 billion years for a 0.2 solar mass M-type star.

Given that the Universe is only 13.7 billion years old, these long main

sequence lifetimes for M-type stars mean that every M star that has ever been

created is still on the main sequence! The Sun, a G-type star with a main

sequence lifetime of ~ 10 billion years, is currently 5 billion years old – about

half way through its main sequence lifetime.

The main sequence lifetimes of stars with masses between 1 and 30 Mʘ are

graph in figure below

Figure 19.8 The main sequence lifetime for stars of different masses.