1

Fig. 1.2.2 Energy-

producing nuclear

reactions occur only

within the inner 25

percent of the Sun’s

radius. The energy

produced by these

reactions is carried

outward by photons to 70

percent of the Sun’s

radius. From that distance

outward, convection

carries most of the Sun’s

energy.

1.2 Stars

A star (like our sun) is a is a massive, dense ball of gases with a surface heated to incandescence by energy released

from fusion reactions deep within. Our sun is just an ordinary star with an average brightness. Since the Sun is an

average star, it can be used as a reference for understanding all the other stars.

1.2.1 Origin of Stars

Stars are born from nebulae (swirling clouds of hydrogen gas in the deep space between other stars).

These clouds consist of random, swirling atoms of gases that have little gravitational attraction for one another because they have little mass. Complex motions of stars, however, can produce a shock wave that causes particles to move closer together and collide, making local compressions. Their mutual gravitational attraction then begins to pull them together into a cluster. The cluster grows as more atoms are pulled into it, which increases the mass and thus the gravitational attraction, and still more atoms are pulled in from farther away. Theoretical calculations indicate that on the order of 1 × 10 57 atoms are necessary, all within a distance of 3 trillion km. When these conditions occur, the cloud of gas atoms begins to condense by gravitational attraction to a protostar, an accumulation of gases that will become a star.

SAMPLE PROBLEM

Compared to the 1019 molecules/cm3 of air on Earth, an average concentration of 1000. hydrogen atoms/cm3 in the

Orion Nebula does not seem very dense. However, considering that the Orion Nebula is about 20 light-years (20 × 1018

cm) across, a sphere with a volume of 4.19 × 1057cm3 would enclose the Orion Nebula, and it would contain

1000 𝑎𝑡𝑜𝑚𝑠

𝑐𝑚3 𝑥 (4.19 𝑥 1057𝑐𝑚3) = 4.19 𝑥 1060 𝑎𝑡𝑜𝑚𝑠

This is a sufficient number of hydrogen atoms to produce

4.19 𝑥 1060

1 𝑥 1057= 4190 𝑠𝑡𝑎𝑟𝑠

Thus, there is a sufficient number of hydrogen atoms in the Orion Nebula to produce 4,190 average stars like the

Sun.

Gravitational attraction pulls the average protostar from a cloud with a diameter of trillions of kilometers down to a

dense sphere with a diameter of 2.5 million km or so. As gravitational attraction accelerates the atoms toward the

center, they gain kinetic energy, and the interior temperature increases. Over a period of some 10 million years of

contracting and heating, the temperature and density conditions at the center of the protostar are sufficient to start

nuclear fusion reactions. Pressure from hot gases and energy from increasing fusion reactions begin to balance the

gravitational attraction over the next 17 million years, and the newborn, average star begins its stable life, which will

continue for the next 10 billion years.

1.2.2 Star’s Interior and Life Span

The interior of an average star, such as the Sun, is modeled after the theoretical pressure, temperature, and density

conditions that would be necessary to produce the observed energy and light from the surface. This model describes the

interior as a set of three shells: (1) the core, (2) a radiation zone, and (3) the convection zone.

2

Core - a dense, very hot region where nuclear fusion reactions release gamma and X-ray radiation. The density

of the core is about 12 times that of solid lead. Because of the plasma conditions, however, the core

remains in a gaseous state even at this density.

Radiation zone - less dense than the core, having a density about the same as that of water. Energy in the form

of gamma and X rays from the core is absorbed and reemitted by collisions with atoms in this zone. The

radiation slowly diffuses outward because of the countless collisions over a distance comparable to the distance

between Earth and the Moon. It could take millions of years before this radiation finally escapes the radiation

zone.

Convection zone - begins about seven-tenths of the way to the surface, where the density of the gases is

about 1 percent of the density of water. Gases at the bottom of this zone are heated by radiation from the

radiation zone below, expand from the heating, and rise to the surface by convection. At the surface, the gases

emit energy in the form of visible light, ultraviolet radiation, and infrared radiation, which moves out into space.

As they lose energy, the gases contract in volume and sink back to the radiation zone to become heated again,

continuously carrying energy from the radiation zone to the surface in convection cells. The surface is

continuously heated by the convection cells as it gives off energy to space, maintaining a temperature of about

5,800 K (about 5,500°C).

As an average star, the Sun converts about 1.4 × 1017 kg of matter to energy every year as hydrogen nuclei are fused to

produce helium. The Sun was born about 5 billion years ago and has sufficient hydrogen in the core to continue shining

for another 4 or 5 billion years. Other stars, however, have masses that are much greater or much less than the mass of

the Sun, so they have different life spans. More massive stars generate higher temperatures in the core because they

have a greater gravitational contraction from their greater masses. Higher temperatures mean increased kinetic

energy, which results in increased numbers of collisions between hydrogen nuclei with the end result being an increased

number of fusion reactions. Thus, a more massive star uses up its hydrogen more rapidly than a less massive star. On

the other hand, stars that are less massive than the Sun use their hydrogen at a slower rate, so they have longer life

spans. The life spans of the stars range from a few million years for large, massive stars, to 10 billion years for average

stars like the Sun, to trillions of years for small, less massive stars.

1.2.3 Brightness of a Star

Stars generate their own light, but some stars appear brighter than others in the night sky. A classification scheme for

different levels of brightness that you see is called the apparent magnitude scale. The brightness of a star as it appears

to you in the night sky is a combination of these factors:

1. the amount of light produced by the stars,

2. the size of each star,

3. the distance to a particular star, and

4. the atmospheric condition.

The apparent magnitude scale is based on a system established by a Greek astronomer over two thousand years ago.

Hipparchus made a catalog of the stars he could see and assigned a numerical value to each to identify its relative

brightness. The brightness values ranged from 1 to 6, with the number 1 assigned to the brightest star and the

number 6 assigned to the faintest star that could be seen. Stars assigned the number 1 came to be known as first-

magnitude stars, those a little dimmer as second-magnitude stars, and so on to the faintest stars visible, the sixth-

magnitude stars.

When technological developments in the nineteenth century made it possible to measure the brightness of a

star, Hipparchus’s system of brightness values acquired a precise, quantitative meaning. Today, a first-magnitude

star is defined as one that is 100 times brighter than a sixth-magnitude star, with five uniform multiples of decreasing

brightness on a scale from the first magnitude to the sixth magnitude.

To compensate for distance differences, astronomers calculate the brightness that stars would appear to have if they

were all at a defined, standard distance (32.6 light-years) (known as absolute magnitude). The absolute magnitude is an

expression of luminosity, the total amount of energy radiated into space each second from the surface of a star. The

Sun, for example, radiates 4 × 1026 joules per second from its surface. The luminosity of stars is often compared to the

Sun’s luminosity, with the Sun considered to have a luminosity of 1 unit. When this is done, the luminosity of the stars

ranges from a low of 10–6 sun units for the dimmest stars up to a high of 105 sun units. Thus, the Sun is somewhere in

the middle of the range of star luminosity.

3

Fig. 1.2.4 The distribution of radiant energy emitted is different for stars with different surface temperatures. Note that the peak radiation of a cooler star is more toward the red part of the spectrum, and the peak radiation of a hotter star is more toward the blue part of the spectrum.

SAMPLE PROBLEM

The measured brightness of a star can be determined from its luminosity (L) and its distance (d ) from the observer. This

is so because the energy radiated into space from a star spreads equally in all directions and follows an inverse square

relationship with distance. Ignoring the effects of the atmosphere, what is the brightness (B) of the Sun, in watts per

square meter, as observed from Earth?

SOLUTION L = 4 x 1026 W d = 1.5 x 1011 m B = ?

𝐵 = 𝐿

4𝜋𝑑2

= 4 𝑥 1026 𝑊

4𝜋(1.5 𝑥 1011𝑚)2

= 1 𝑥 103 𝑤 𝑚2⁄

1.2.4 Star Temperature

If you observe the

stars on a clear night,

you will notice that

some are brighter

than others, but you

will also notice some

color differences.

Some stars have a

reddish color, others

have a bluish-white

color, and still others

have a yellowish

color. This color

difference is understood to be a result of the relationship that exists between the color and the temperature of an

incandescent object. The colors of the various stars are a result of the temperatures of the stars. You see a cooler star as

reddish and comparatively hotter stars as bluish white. Stars with in-between temperatures, such as the Sun, appear to

have a yellowish color.

Astronomers analyze starlight to measure the temperature and luminosity as well as the chemical composition of a star.

When the starlight is analyzed in a spectroscope, specific elements can be identified from the unique set of spectral lines

that each element emits. Temperature and spectra are used as the basis for a star classification scheme. Originally, the

classification scheme was based on 16 categories according to the

strength of the hydrogen line spectra. The groups were identified

alphabetically with A for the group with the strongest hydrogen line

spectrum, B for slightly weaker lines, and on to the last group with

the faintest lines. Later, astronomers realized that the star

temperature was the important variable, so they rearranged the

categories according to decreasing temperatures. The original letter

categories were retained, however, resulting in classes of stars with

the hottest temperature first and the coolest last with the sequence

O B A F G K M.

SAMPLE PROBLEM

The temperature of a star in Kelvins can be determined from the peak wavelength of the light emitted by a

relationship called Wien’s displacement law. The temperature is equal to a constant of 2.897 × 107 K∙angstroms

divided by the peak wavelength in angstroms. What is the temperature of a star emitting light with a peak wavelength of

3,500 angstroms?

=2.897 𝑥 107 K ∙ angstroms

3500 𝑎𝑛𝑔𝑠𝑡𝑟𝑜𝑚𝑠

= 8300 K

Major Stellar Spectral Types and Temperatures

Type Color Temperature

O Bluish 30,000 - 80,000

B Bluish 10,000 - 30,000

A Bluish 7,500 – 10,000

F White 6,000 – 7,500

G Yellow 5,000 – 6,000

K Orange-red 3,500 – 5,000

M Reddish 2,000 – 3,500

4

1.2.5 Star Types

Henry Russell in the United States and Ejnar

Hertzsprung in Denmark independently developed a

scheme to classify stars with a temperature-

luminosity graph (known as Hertzsprung-Russell

diagram or H-R diagram).

Each dot is a data point representing the surface

temperature and brightness of a particular star. The

Sun, for example, is a type G star with an absolute

magnitude of about +5, which places the data point

for the Sun almost in the center of the diagram. This

means that the Sun is an ordinary, average star with

respect to both surface temperature and true

brightness.

Most of the stars plotted on an H-R diagram fall in or

close to a narrow band that runs from the top left to

the lower right. This band is made up of main

sequence stars. Stars along the main sequence band

are normal, mature stars that are using their nuclear

fuel at a steady rate. Those stars on the upper left of

the main sequence are the brightest, bluest, and

most massive stars on the sequence. Those at the

lower right are the faintest, reddest, and least

massive of the stars on the main sequence. In

general, most of the main sequence stars have

masses that fall between a range from 10 times

greater than the mass of the Sun (upper left) to one-

tenth the mass of the Sun (lower right). The

extremes, or ends, of the main sequence range from

about 60 times more massive than the Sun to one-

twenty-fifth of the Sun’s mass. It is the mass of a main sequence star that determines its brightness, its temperature,

and its location on the H-R diagram. High-mass stars on the main sequence are brighter and hotter and have shorter

lives than low-mass stars. These relation-ships do not apply to the other types of stars in the H-R diagram.

There are two groups of stars that have a different set of properties than the main sequence stars. The red

giant stars are bright, but low-temperature, giants. These reddish stars are enormously bright for their temperature

because they are very large, with an enormous surface area giving off light. A red giant might be 100 times larger but

have the same mass as the Sun. These low-density red giants are located in the upper right part of the H-R diagram. The

white dwarf stars, on the other hand, are located at the lower left because they are faint, white-hot stars. A white dwarf

is faint because it is small, perhaps twice the size of Earth. It is also very dense, with a mass approximately equal to the

Sun’s. During its lifetime, a star will be found in different places on the H-R diagram as it undergoes changes. Red giants

and white dwarfs are believed to be evolutionary stages that aging stars pass through, and the path a star takes across

the diagram is called an evolutionary track. During the lifetime of the Sun, it will be a main sequence star, a red giant,

and then a white dwarf.

Stars such as the Sun emit a steady light because the force of gravitational contraction is balanced by the outward flow

of energy. Variable stars, on the other hand, are stars that change in brightness over a period of time. A Cepheid

variable is a bright variable star that is used to measure distances. There is a general relationship between the period

and the brightness: the longer the time needed for one pulse, the greater the apparent brightness of that star. The

period-brightness relationship to distance was calibrated by comparing the apparent brightness with the absolute

magnitude (true brightness) of a Cepheid at a known distance with a known period. Using the period to predict how

bright the star would appear at various distances allowed astronomers to calculate the distance to a Cepheid given its

apparent brightness.

Fig. 1.2.5 The Hertzsprung-Russell diagram. The main sequence and giant regions contain most of the stars, whereas hot underluminous stars, the white dwarfs, lie below and to the left of the main sequence.

5

Fig. 1.2.6.1 A star becomes stable when the outward forces of expansion from the energy released in nuclear fusion reactions balance the inward forces of gravity.

1.2.6 Life of a Star

A star is born in a gigantic cloud of gas and dust in interstellar space, then spends billions of years calmly shining while it

fuses hydrogen nuclei in the core. How long a star shines and what happens to it when it uses up the hydrogen in the

core depend on the mass of the star.

Protostar Stage

The first stage in the theoretical model of the life cycle of a star

is the formation of the protostar. As gravity pulls the gas of a

protostar together, the density, pressure, and temperature

increase from the surface down to the center. Eventually, the

conditions are right for nuclear fusion reactions to begin in the

core, which requires a temperature of 10 million kelvins. The

initial fusion reaction essentially combines four hydrogen nuclei

to form a helium nucleus with the release of much energy. This

energy heats the core beyond the temperature reached by

gravitational contraction, eventually to 16 million kelvins. Since

the star is a gas, the increased temperature expands the volume

of the star. The outward pressure of expansion balances the

inward pressure from gravitational collapse, and the star settles

down to a balanced condition of calmly converting hydrogen to

helium in the core, radiating the energy released into space.

The theoretical time elapsed from the initial formation and

collapse of the protostar to the main sequence is about 50 million years for a star of a solar mass.

Main Sequence Stage

Where the star is located on the main sequence and what happens to it next depend only on how massive it is. The

more massive stars have higher core temperatures and use up their hydrogen more rapidly as they shine at higher

surface temperatures (O-type stars). Less massive stars shine at lower surface temperatures (M-type stars) as they use

their fuel at a slower rate. The overall life span on the main sequence ranges from millions of years for O-type stars to

trillions of years for M-type stars. An average one-solar-mass star will last about 10 billion years.

Red Giant Stage

The next stage in the theoretical life of a star begins when the hydrogen in the core has been fused into helium. With

fewer hydrogen fusion reactions, less energy is released and less outward balancing pressure is produced, so the star

begins to collapse. The collapse heats the core, which now is composed primarily of helium, and the surrounding shell

where hydrogen still exists. The increased temperature causes the hydrogen in the shell to undergo fusion, and the

increased release of energy causes the outer layers of the star to expand. With an increased surface area, the amount of

radiation emitted per unit area is less, and the star acquires the properties of a brilliant red giant.

Back Toward Main Sequence

After about 500 million years as a red giant, the star now has a surface temperature of about 4,000 kelvins compared to

its main sequence surface temperature of 6,000 kelvins. The radius of the red giant is now 1,000 times greater, a

distance that will engulf Earth when the Sun reaches this stage, assuming Earth is in the same position as today. Even

though the surface temperature has decreased from the expansion, the helium core is continually heating and

eventually reaches a temperature of 100 million kelvins, the critical temperature necessary for the helium nuclei to

undergo fusion to produce carbon. The red giant now has helium fusion reactions in the core and hydrogen fusion

reactions in a shell around the core. This changes the radius, the surface temperature, and the luminosity, with the

overall result depending on the composition of the star. In general, the radius and luminosity decrease when this stage is

reached, moving the star back toward the main sequence.

6

Fig. 1.2.6.2 The blown-off outer layers of stars form ringlike structures called planetary nebulae.

Beginning of the End for Less Massive Stars

After millions of years of helium fusion reactions, the core is gradually converted to a carbon core, and helium fusion

begins in the shell surrounding the core. The core reactions decrease as the star now has a helium fusing shell

surrounded by a second hydrogen fusing shell. This releases additional energy, and the star again expands to a red giant

for the second time. A star the size of the Sun or less massive may cool enough at this point that nuclei at the surface

become neutral atoms rather than a plasma. As neutral atoms, they can absorb radiant energy coming from within the

star, heating the outer layers. Changes in temperature produce changes in pressure, which change the balance

among the temperature, pressure, and the internal

energy generation rate. The star begins to expand

outward from heating. The expanded gases are cooled by

the expansion process, however, and are pulled back to

the star by gravity, only to be heated and expand outward

again. In other words, the outer layers of the star begin to

pulsate in and out. Finally, a violent expansion blows off the

outer layers of the star, leaving the hot core. Such blown-off

outer layers of a star form circular nebulae called planetary

nebulae. The nebulae continue moving away from the core,

eventually adding to the dust and gases between the stars.

The remaining carbon core and helium-fusing shell begin

gravitationally to contract to a small, dense white dwarf

star. A star with the original mass of the Sun or less slowly

cools from white, to red, then to a black lump of carbon in

space.

Beginning of the End for Massive Stars

A more massive star will have a different theoretical ending than the slow cooling of a white dwarf. A massive star will

contract, just as the less massive stars do, after blowing off its outer shells. In a more massive star, however, heat from

the contraction may reach the critical temperature of 600 million kelvins to begin carbon fusion reactions. Thus, a more

massive star may go through a carbon fusing stage and other fusion reaction stages that will continue to produce new

elements until the element iron is reached. After iron, energy is no longer released by the fusion process, and the star

has used up all of its energy sources. Lacking an energy source, the star is no longer able to maintain its internal

temperature. The star loses the outward pressure of expansion from the high temperature, which had previously

balanced the inward pressure from gravitational attraction. The star thus collapses, then rebounds like a compressed

spring into a catastrophic explosion called a supernova. A supernova produces a brilliant light in the sky that may last for

months before it begins to dim as the new elements that were created during the life of the star diffuse into space.

These include all the elements up to iron that were produced by fusion reactions during the life of the star and heavier

elements that were created during the instant of the explosion. All the elements heavier than iron were created as some

less massive nuclei disintegrated in the explosion, joining with one another and with lighter nuclei to produce the nuclei

of the elements from iron to uranium,. These newly produced, scattered elements will later become the building blocks

for new stars and planets such as the Sun and Earth.

If the core of a supernova has a remaining mass greater than 1.4 solar masses, the gravitational forces on the

remaining matter, together with the compressional forces of the supernova explosion, are great enough to collapse

nuclei, forcing protons and electrons together into neutrons, forming the core of a neutron star. A neutron star is

the very small (10 to 20 km diameter), superdense (1011 kg/cm3 or greater) remains of a supernova with a center core of

pure neutrons.

Because it is a superdense form of matter, the neutron star also has an extremely powerful magnetic field,

capable of becoming a pulsar (Fig. 1.2.6.3). A pulsar is a very strongly magnetized neutron star that emits a uniform

series of equally spaced electromagnetic pulses. Evidently, the magnetic field of a rotating neutron star makes it a

powerful electric generator, capable of accelerating charged particles to very high energies. These accelerated charges

are responsible for emitting a beam of electromagnetic radiation, which sweeps through space with amazing regularity).

The pulsating radio signals from a pulsar were a big mystery when first discovered. For a time, extraterrestrial life was

7

Fig. 1.2.6.3 The magnetic axis of the pulsar is inclined with respect to the rotation axis. Rapidly moving electrons in the regions near the magnetic poles emit radiation in a beam pointed outward. When the beam sweeps past Earth, a pulse is detected.

considered as the source of the signals, so they were jokingly identified as LGM (for “little green men”). Over 300 pulsars

have been identified, and most emit radiation in the form of radio waves. Two, however, emit visible light, two emit

beams of gamma radiation, and one emits X-ray pulses.

Another theoretical limit occurs if the remaining core has a mass

of about 3 solar masses or more. At this limit, the force of gravity

overwhelms all nucleon forces, including the repulsive forces

between like charged particles. If this theoretical limit is reached,

nothing can stop the collapse, and the collapsed star will become

so dense that even light cannot escape. The star is now a black

hole in space. Since nothing can stop the collapsing star,

theoretically a black hole would continue to collapse to a

pinpoint and then to a zero radius called a singularity. This event

seems contrary to anything that can be directly observed in the

physical universe, but it does agree with the general theory of

relativity and concepts about the curvature of space produced by

such massively dense objects. Black holes are theoretical and

none has been seen, of course, because a black hole theoretically

pulls in radiation of all wavelengths and emits nothing. Evidence

for the existence of a black hole is sought by studying X rays that

would be given off by matter as it is accelerated into a black

hole.

Evidence of the existence of a black hole has been provided by

photographs from the Hubble Space Telescope. Hubble pictured

a disk of gas only about 60 light-years out from the center of a

galaxy (M87), moving at more than 1.6 million km/h. The only known possible explanation for such a massive disk of gas

moving with this velocity at the distance observed would require the presence of a 1 to 2 billion solar-mass black hole.

This gas disk could only be resolved by the Hubble Space Telescope, so this telescope has provided the first

observational evidence of a black hole.

Fig. 1.2.6.4 This flowchart shows some of the possible stages in the birth and aging of a star. The differences are determined by the mass of the star