ASTR 1230 (Whittle) Lecture Notes
Topic 6. STELLAR ASTRONOMY
Young star cluster NGC 1818 in
the Large Magellanic Cloud (HST)
Human beings have wondered about the stars for probably a million
years, but only in the 20th century did we achieve a real understanding
of their physical nature and their life cycles. This can fairly be
said to be the main accomplishment of astronomy since 1900. We now
understand the stars in almost all their essentials, and only details
remain to be worked out.
The astrophysical study of the stars has provided many crucial insights:
With a small telescope, you can explore many facets of stellar
evolution. In fact, much of the basic evidence on stellar
astrophysics was gathered historically with quite modest telescopes.
This lecture introduces these subjects.
- The Sun is a star, with properties typical of those of
billions of other stars in our Galaxy.
This recognition resolved thousands of years of religious,
philosophical, and scientific debate. To learn the fate of the
Sun, on which we absolutely depend for survival, we must look to
- Stars generate their energy by burning hydrogen in nuclear
fusion reactions. The hydrogen supply is large but
nonetheless finite, so this implies that all stars must
evolve---i.e. change their properties with time.
- Among other
things, this means that the favorable conditions in the Earth's
biosphere cannot exist for ever and that humans, or their
descendents, will have to leave Earth at a predictable (if very
distant) time in the future to survive.
understanding of stellar evolution allows us to age-date the stars and
thus establishes the basic time scale of the universe. The
universe must be at least as old as the oldest stars.
- The age of the Sun is 5 billion years. The oldest
objects yet dated (globular star clusters---see below) are 13 billion
years old. No identifications of significantly older stars
have been made. The universe is therefore very ancient but had a
- All of the elements heavier than helium have been
synthesized by nuclear reactions inside stars during
their evolution. The Earth and all its inhabitants are made of atoms
which passed through stars now long dead.
- Stars continuously form out of interstellar gas. Although
the Sun is middle-aged, there are many "young" stars with ages of
less than 10 million years within easy reach of your telescopes.
- The Earth lies inside the Sun's (extended) atmosphere,
so all forms of atmospheric activity on the Sun can potentially affect us.
B. PROPERTIES OF THE STARS
APPARENT BRIGHTNESSES (MAGNITUDES)
Here is a list of the 50 brightest stars.
- Astronomers measure brightnesses of stars using a refined version
of the magnitude system introduced by the Greek astronomer
Hipparchus about 130 BC. Hipparchus ranked the visible stars from
first to sixth magnitude, with first being brightest.
- The magnitude system was
elaborated and made quantitative after it became possible to measure
accurate relative brightnesses of stars with telescopes and auxiliary
instruments. The system is logarithmic because
biological systems like the eye respond in proportion to the logarithm
of the stimulus.
- The modern magnitude system is defined by the following expression:
where f is the flux of electromagnetic radiation received from
a source. Flux is conventionally measured in units of EM energy received
per second per unit area in a given spectral band. The constant C is
adjusted, depending on the waveband being observed, in order to make
the values of m conform to adopted values for a set of calibrator stars.
- As a result of this definition, a 1 magnitude difference
in brightness corresponds to a factor of 2.51 in flux.
instance, a star with m = 4 produces 2.51 times less flux
than a star with m = 3.
- A factor of 10 in flux corresponds
to 2.5 magnitudes; a factor of 100 corresponds to 5.0 magnitudes.
- Smaller magnitudes correspond to brighter stars. The modern
magnitude scale extends well past the sixth magnitude limit of
Hipparchus and to negative values as well (for very bright
objects). Here is a
graphic illustrating the magnitude scale.
- The chart below shows some familiar objects on the magnitude system.
With your 8-in telescopes, you could see stars up to mag 12-13.
INTRINSIC BRIGHTNESSES (ABSOLUTE MAGNITUDES OR LUMINOSITIES)
- The magnitude scale just discussed measures the apparent
brightness of stars---i.e. how they appear from the Earth. It does
not refer to their intrinsic brightnesses. The apparent brightness
depends on the intrinsic brightness but also on the distance to the
- In the 19th century, astronomers obtained the first accurate
measures of stellar distances (using the geometrical
method). This enabled us to determined the intrinsic
luminosity of stars---i.e. their total energy output per second,
measured in units like watts (energy output per unit time).
The luminosity of the Sun, a middling star, is 4 x 1026
- Even the nearest stars turn out to be very distant, at
least by the expectations of early astronomers (and certainly by
- Alpha Centauri (in the southern hemisphere) is
the nearest star. It is at a distance of 1.3 parsecs.
- A parsec is a unit of distance which is defined in terms
of the size of the Earth's orbit. It is 3.1 x 1013 km(!),
206,000 times the distance to the Sun, or about 3.25 light
years (one light year is the distance light travels in a year).
- Here is a perspective
plot of the stars within 50 light years (15.4 parsecs) of the Sun.
- Here is a list of the 50 nearest stars to the Sun.
Most of the names will be unfamiliar, because these objects are mostly
quite faint (despite their proximity).
- Because of uncertainties in the flux scales which weren't
resolved until late in the 20th century, astronomers established a
convenient, but arbitrary, version of the magnitude system to measure
luminosities. This is the absolute magnitude, which
is defined to be the apparent magnitude that a star would have if
it were at a distance of 10 parsecs.
- Since most stars lie at distances far greater than 10 parsecs, their
absolute magnitudes are much brighter than their apparent magnitudes.
- It turns out that the easily visible stars, which have an apparent brightness
range of only about 100:1, have a luminosity range of
- Although the Sun dominates our sky, this is only a proximity
effect. Intrinsically, the Sun is a relatively faint star. If placed
at 10 parsecs distance, the Sun would appear only as a star of 4.8
magnitude (barely visible under typical viewing conditions), whereas
Antares (Alpha Sco) would be at -5.2 magnitudes, brighter than Venus.
- Here is magnitude and distance information for some familiar stars.
Barnard's Star is typical of the very faint "red dwarf" stars which
Magnitudes and Distances For Some
*Magnitudes in the ``V'' filter. Original table by
|Star ||App.Mag. ||Distance (pc) ||Abs.Mag. ||Luminosity/Sun
|Sun ||-26.7 ||4.84813×10-6 ||4.8 ||1
|Sirius (Alpha CnMaj) ||-1.4 ||2.64 ||1.5 ||22.5
|Arcturus (Alpha Boo) ||-0.05 ||11.25 ||-0.31 ||114
|Vega (Alpha Lyr) ||0.03 ||7.76 ||0.58 ||50.1
|Spica (Alpha Vir) ||0.98 ||80.5 ||-3.6 ||2250
|Deneb (Alpha Cyg) ||1.3 ||3230 ||-8.7 ||250,000
|Barnard's Star ||9.5 ||1.82 ||13.2 ||1/2310
- We have learned to measure the surface temperatures of stars using
their electromagnetic spectra, following
experiments first done by the physicist Kirchhoff in the 19th century.
Bad Philosophy Footnote: Click
here for a description of one of the worst, but not one of
the last, faulty prognostications about science by a philosopher,
in this case the claim that we could never know the temperatures
of the stars.
- The EM spectrum of any star depends on its temperature.
Hotter objects emit more energy at shorter
wavelengths; cooler objects emit more energy at longer wavelengths.
Hence, hot stars will look blue-white to the eye while cool stars look
- The diagram above shows the gross EM spectra of 3 stars with different
temperatures. It illustrates how temperature affects the wavelength at
which the energy output of a star peaks. (500 nm on this wavelength
scale corresponds to 5000 Å.) The higher the temperature, the
shorter the wavelength of the peak. The visible band is shown in color
in the diagram.
- The Sun, with a surface temperature of 6000o
Kelvin, has a spectrum which peaks at about 5000 Å---i.e. in
(Does this fact, combined with the principle of
natural biological selection, suggest a reason why our eyes are most
sensitive to yellow-green light?).
- Vega, Sirius, and Rigel, with temperatures near 10000o
K, look blue-white. Arcturus or Pollux, with temperatures near
4500o K, are yellowish. Cooler stars, like Aldebaran,
Antares, and Betelgeuse are orange-red. The image at right shows
Orion in color, contrasting Betelgeuse (upper left) with the
other bright blue-white stars in the constellation, including Rigel (lower
here for an image of the Southern Cross in dispersed color. Only
unusual objects, like carbon stars, look "stoplight red."
- Colors are more apparent in telescopes or binoculars, because your
eye requires more flux to distinguish color than simply brightness.
- For a Java demo of the effects of temperature on EM radiation, see
Davidson Webphysics applet..
- [Note: the colors of stars reflect only their surface temperatures.
The deep interiors of stars have much higher temperatures, 15 million degrees
in the case of the Sun.]
- The mass of a star turns out to be the key to determining its life
Masses of stars are measured mainly by applying
Newton's laws of motion and gravitation to stars which
are in orbit around one another, i.e. binary or "double"
Newton showed that the time taken to complete one orbit (the
"period") by any object in a gravitational orbit around another is
related to the combined mass of the two objects. By measuring the
orbital sizes and periods of binary stars (and also their
distances from us), we can therefore determine their masses. During
the 19th and early 20th centuries, small telescopes were often used
for this kind of study.
You can find lists of brighter binary stars in each constellation at
the Peoria Astronomical Society website.
- The masses of normal stars have a smaller range than do their
intrinsic brightnesses. The lowest mass, self-sustaining stars
are about 0.1 solar mass, while the most massive are in the range
20-50 solar masses.
C. STELLAR EVOLUTION
THE HERTZSPRUNG-RUSSELL DIAGRAM
- The basic observational insight to understanding the structure & evolution
of stars is the correlation between the luminosities and temperatures of
stars found in the Hertzsprung-Russell (HR) diagram, which was
discovered independently by two astronomers ca. 1910. Their work depended
on the painstaking accumulation of measures of accurate distances to stars.
A modern version for stars in the vicinity of the Sun is shown below:
- In the HRD, stellar luminosity increases upwards while
temperature increases to the left (an artifact of
tradition). Bluer stars hence are at the left side of the
diagram, redder stars to the right.
- The important point is that stars are not randomly scattered in
the diagram but instead confined to well-defined sequences.
- Most stars fall on the main sequence (MS), which runs
diagonally across the HRD. Brighter MS stars are also hotter. The
Sun is an MS star (lying at T = 6000 and AbsMag = 4.8).
- A second
concentration of the so-called red giants and
supergiants falls in the upper right hand quadrant of
the HRD (luminous but cool). These are "giants" both in luminosity
and in diameter (can be over 100 times the size of the Sun). Finally,
the white dwarfs are very faint stars lying beneath the MS.
- A key discovery for interpreting the HRD was that the
masses of stars on the main sequence are systematically
higher at brighter magnitudes (higher luminosities) and higher
- The structure present in the HRD and the mass-luminosity relation
are basic clues to stellar physics. This was enough information to
allow astrophysicists like Eddington and Bethe to analyze the basic
structure of stars and then, in the late 1930's, to discover the
prodigious energy source that maintains them: nuclear fusion
- If its interior is not kept hot, a star like the Sun would
collapse under its own gravity in only 15 minutes. But nuclear
reactions in the core of a star release enough energy to keep its
interior hot enough (15 million degrees) to produce pressure
sufficient to resist collapse.
- The nuclear reactions which sustain a star involve the fusion of
light elements like hydrogen (H) and helium (He) to make heavier
elements, with the release of energy. The most important reactions during the MS
phase fuse four H nuclei (protons) to form one He nucleus. Click on
the thumbnail at right for a more detailed illustration of the
- There is obviously a tremendous amount of nuclear fuel in a star
like the Sun. Hence, it can stay in the MS phase burning hydrogen for
a very long period of time. The MS lifetime for a star like the Sun
is 10 billion years. The Sun is now 5 billion years old---therefore
halfway through its MS phase.
- More massive stars have more fuel but
also burn it more quickly, so that the MS lifetime for a star which is
15 times the mass of the sun is "only" 10 million years.
- As efficient as are nuclear reactions, however, stars have only a
finite supply of fuel. They can remain on the MS burning
hydrogen for a long time, but the accumulation of nuclear "ashes" in
their centers means that eventually nuclear burning will cease there.
Stars must readjust to avoid collapse. This is the reason that stars
must evolve and consequently change their locations in the HRD.
- The late stages of evolution involve a complex series of switches
to other fuel sources (e.g. He and carbon) and gross changes in the
structure of the stars. The most important of these is an enormous
inflation of their outer envelopes, which produces the red
giants. Red giants are therefore not a different species of stars;
instead, they are normal stars in the late stages of evolution.
- The diagram at the right shows evolutionary tracks in the HRD for
stars of different initial masses. Ages are marked on the tracks.
Note that stars like the Sun become much more luminous but cooler as
evolution proceeds. More massive stars undergo the whole process much
more rapidly than lower mass stars.
D. STELLAR EVOLUTION IN THE SKY
With binoculars and small telescopes you can observe many aspects of
stellar evolution, including individual stars, binary stars, and star
clusters. The most interesting phenomena involve the initial and
final phases of stellar evolution: star birth and death.
Apart from individual stars and binaries, the brighter objects
relevant to stellar evolution are mostly listed in the Messier
Catalog: This catalog was compiled by the 18th
century astronomer Charles Messier. It contains star clusters,
nebulae, and galaxies. Messier compiled it not because of an interest
in these kinds of objects but so he would not mistake them for comets,
which were his passion. The web site listed at the bottom of this
page contains lists and descriptions of the Messier objects. Here is a mosaic of
images of the 110 Messier objects. An updated version of the Messier
Catalog is the The Caldwell
(1) Early phases of stellar evolution
(2) Mid-phases of stellar evolution
- Star formation occurs inside clouds of interstellar
gas which are shielded and refrigerated by dust grains
(tiny, solid particles like smoke) and have become dense and cold
enough to form molecules.
Because the dust absorbs and scatters light
at optical wavelengths, dust clouds look like dark blotches when
seen in projection against more distant nebulae or star fields.
Starbirth begins when interstellar clouds begin to collapse under
their own gravity. Most of this process is hidden from easy
view at optical wavelengths by the dust and can only be observed with
infrared telescopes. (Infrared light more easiliy penetrates
the dust clouds.)
However, once stars form, they disrupt the surrounding clouds, blowing
away the gas and dust and often causing it to glow by virtue of
ionization from hot stars. (In an ionized gas, one or more
electrons are stripped from its atoms.)
A visible signature of an ionized nebula is a "pinkish" glow, produced
by concentrated emission from hydrogen gas. Many spectacular examples
of this nebular phase can be seen in the sky, including the
Eagle, Triffid, and Lagoon nebulae. The Orion Nebula is the easiest
example to observe.
Overall, in our Galaxy, about 1 solar mass of material is converted to
new stars each year. Rates up to about 1000 times higher are observed
in some very gas-rich environments in other galaxies.
Starbirth region in the Eagle Nebula, a beautiful mixture
of cold dust pillars (dark lanes) surrounded by hot gas. At left
is a wide-field view of the whole Nebula. At right is the HST closeup
of the central dust pillars. Click for
The Orion Nebula surrounds the (multiple) central
star of Orion's "sword." Stars are continuously forming in a dark molecular
cloud (not visible) behind the Nebula; the Nebula is only a small part
of the cloud where hot stars have begun to blow out and ionize the
- Stars often form in clusters---compact groups of a few hundred
up to hundreds of thousands of stars, all with the same age.
The youngest, still-forming star clusters are usually enshrouded
by dust. But clusters can stay together for long times, so we can see
many mature clusters easily in small telescopes. Good descriptions of
the brighter clusters are given in the SEDS Messier pages.
Star clusters are essential diagnostics of stellar evolution, since
their constituent stars differ only in mass, and one can use them to
trace the rate of evolution with mass.
Younger bright star clusters include
h and Chi
Persei, the Pleiades,
the Praesepe, and the Hyades. Their estimated ages are 15, 100,
700, and 800 million years, respectively. These are of the "open"
type---not highly concentrated and containing only a few hundred up to
a few thousand stars.
The most spectacular clusters are the "globular" type, such
as Messier 13, Messier 4, and Messier 15. These are spherical, dense,
and very massive (100,000 or more stars). They are also very
old (10-13 billion years) and are keys to age-dating the
universe. Below is a view of the globular cluster Messier 13.
Imagine that the Sun were situated in the middle of a globular cluster
like M13. There would be over 1000 stars brighter than Sirius!
(3) Late phases of stellar evolution
- Many of the familiar bright stars are in the main sequence
phase. This is the longest-lived phase of evolution, fueled by
hydrogen burning, and relatively quiescent.
The Sun, Vega, Sirius, and Spica are all MS stars; their
intrinsic brightness and temperature depends only on their masses.
- Other bright stars are in the giant phase of evolution.
They are evolving relatively rapidly, burning He in their cores and H
in a shell surrounding the core. They have swollen to
enormous volumes. Bright giants include Arcturus and Aldebaran.
Betelgeuse and Antares are red supergiants. Deneb is a white
- Especially in the giant phase, but also in other phases, stars
can become variable. The most common cause of variability is
pulsation of the stellar surface, which changes its luminosity and
temperature. Cepheids (named after Delta Ceph) and RR Lyrae stars are two
important types of pulsational variables. These types are widely used
to estimate distances to star clusters and galaxies.
- Binary stars are widely observed by amateur astronomers.
They can present nice color contrasts (Albireo is shown at the right).
Observers like to test the quality of their equipment by trying to
resolve very close binaries.
The orbits of binary components around one another
are often determined with small telescopes, though this, of course,
may take years of observations.
Some binaries, like Algol, can vary in brightness because of
one star by the other or gravitational interactions between the two
companions. Amateur astronomers have made enormous contributions to
the study of variable stars and binaries.
- The final phases of evolution depend on a star's mass. Lower
mass stars like the Sun become very distended and eject their outer
The remaining core collapses and heats up, ionizing the
expanding shell, on its way to becoming a white dwarf. The
ejected material can produce a "planetary" nebula, so called
because of their often round shapes. Planetaries are nice targets for
small telescopes. The Ring Nebula (Messier 57) and the Dumbbell Nebula
(Messier 27) are bright planetaries. HST images of two other examples
are shown below:
- More massive stars undergo a tremendous supernova
explosion, leaving behind a compact neutron star or black
hole. The Crab Nebula (Messier 1) is a remnant of such an event
(image below). Most of the heavy elements found on the Earth,
including those in your body, were created during supernova explosions
and recycled back to the interstellar medium through nebulae like
NASA recently released some remarkable
time-lapse X-ray and optical movies of the Crab Nebula which show
waves of energy being injected into the nebula from the central
spinning neutron star.
Download, print, and read the webnotes for this lecture.
Take the Review Quiz for week 6 on Collab
Supplementary reading: The best resource for this material is a good
ASTR 121/124 textbook.
You should start Lab 3 at the first opportunity.
October 2008 by rwo
Apparent magnitude diagram, table, HR diagram, Eagle and
Orion images copyright © 2000 by Nick Strobel. Plots of stars
within 50 LY copyright © by R. Powell. Color
image of EM spectra and plot of evolutionary tracks copyright ©
2000 Harcourt, Inc.. Nuclear reaction drawing copyright © 1999 by
Univ. of Tennessee. M13 picture by Bill Keel. Color photo of
Orion copyright by Bill & Sally Fletcher. Color photo of Albireo
copyright by M. de Regt. Text copyright © 2000-2008 Robert W.
O'Connell. All rights reserved. These notes are intended for the
private, noncommercial use of students enrolled in Astronomy 130 at
the University of Virginia.