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The Stars:
A Celestial Census
22 March 2005
AST 2010: Chapter 17
The Lives of Stars
Stars live for a very long
time, up to 100 million years
or more
No humans can possibly
observe a star this long!
How can we learn about the
stages in a star’s life?
We can perform a celestial census, getting a snapshot of
many stars at different stages of their life
We can then try to infer the
stages that a star goes
through from the data we
assemble in the census
But we can be misled if the
star sample in the census is
biased (like political surveys)
22 March 2005
AST 2010: Chapter 17
A Stellar Census (1)
We measure distances in light years (LY)
Astronomical distances are difficult to measure, to
be discussed in Ch. 18
Small stars are less luminous and, therefore,
harder to see
If not corrected for these hard-to-see stars, our
sample of stars will be biased
Careful observation reveals that small stars (brown
dwarfs) are more common than large stars
While less numerous, large stars are easier to
see at large distances
Most of the stars visible to the naked eye are large
22 March 2005
AST 2010: Chapter 17
A Stellar Census (2)
Stars that appear very bright are not
necessarily very close to us, and those
appearing faint are not necessarily very
distant from us
In fact, the brightest stars are bright mainly
because they are intrinsically very luminous
Most of them are very far away
Moreover, most of the nearest stars are
intrinsically very faint
The luminosity (L) of stars ranges from more
than 106 LSun for the most luminous stars to
10-6 LSun for brown dwarfs
22 March 2005
AST 2010: Chapter 17
Measuring Stellar Masses
Mass is one the most important characteristics of
a star
Knowing the mass can help us estimate the
behavior and life cycle of the star
Yet, a star’s mass is very difficult to measure
Indirect measurements of stellar masses can be
done for binary-star systems
Each system consists of two stars that orbit each
other, bound together by gravity
Strictly speaking,
each of the binary
stars orbits a
common point
called the center
of mass
22 March 2005
AST 2010: Chapter 17
Orbits and Masses of Binary Stars
The masses of the 2 stars can be
estimated using Kepler's third law
The orbital period P (in years) and
semimajor axis D (in AU) of the
ellipse are related to the masses
M1 and M2 (in units of the Sun’s
mass) by D3 = (M1+M2) P2
Thus, if D and P are measured, the
sum of the masses can be found
If the relative orbital speeds of the
2 stars are also measured, the mass
of each star separately can be
calculated as well
22 March 2005
AST 2010: Chapter 17
Visual Binaries
Binary-star systems in which both of the stars
can be seen with a telescope are called visual
Binary stars: Sirius A and B
22 March 2005
AST 2010: Chapter 17
Visual Binaries:
Wobbling Motion
22 March 2005
AST 2010: Chapter 17
Sirius A and B
Sirius A is normal star
Sirius B is a white dwarf companion
The orbits are drawn to scale, but the sizes of
the stars are exaggerated
Sirius A is considerably larger than the Sun,
while Sirius B is about the size of the Earth
22 March 2005
AST 2010: Chapter 17
Spectroscopic Binaries
In some binary-star
systems, only one of the
stars can be seen with a
telescope, but the presence
of the companion star is
revealed by spectroscopy
Such stars are called
spectroscopic binaries
The binary nature is
indicated in the periodic
Doppler-shift of their
spectral lines as they orbit
around each other
22 March 2005
AST 2010: Chapter 17
Doppler Effect in Binary Stars
If the line spectra of the spectroscopic
binaries can be observed, their motion
is reflected in the Doppler shifts of the
spectral lines
Radial velocities of spectroscopic binaries
22 March 2005
AST 2010: Chapter 17
Range of Stellar Masses
How large and small can stars be?
Stars with masses up to about 100 times that of the
Sun have been discovered
Some stars may have masses up to about 200 solar masses
Theoretical calculations suggest that the mass of a
true star must be at least 1/12 that of the Sun
A “true” star is one that becomes hot enough to fuse protons
to form helium (see Ch. 15)
Objects with masses between 1/100 and 1/12 that of
the Sun are called brown dwarfs
They may produce energy for a brief time by nuclear
reactions, but do not become hot enough to fuse protons
They are intermediate in mass between stars and planets
Objects with masses less than about 1/100 that of the
Sun are considered planets
22 March 2005
AST 2010: Chapter 17
Mass-Luminosity Relation
There is a correlation
between the mass and
luminosity of a star
The more massive
stars are generally
also the more
luminous (they give
off more energy)
For about 10% of the
stars, this relationship
is violated
They include the white
22 March 2005
AST 2010: Chapter 17
Diameters of Stars
The diameter of a star can be determined by
measuring the time it takes an object (the Moon, a
planet, or a companion star) to pass in front of it and
blocks its light
The blocking of the star’s light is an eclipse
The brightness of the star decreases gradually during the
The time for the brightness decrease depends on size of star
Accurate sizes for a large
number of stars come from
measurements of eclipsing
22 March 2005
AST 2010: Chapter 17
Eclipsing Binary System
Some binary stars are lined up in such a way that,
when viewed from the Earth, each star passes in front
of the other during every revolution
Thus, we can observe periodic eclipses in these
binary-star systems, which are therefore called
eclipsing binaries
22 March 2005
AST 2010: Chapter 17
22 March 2005
AST 2010: Chapter 17
H-R Diagram
There is a relationship between the temperature (color)
and luminosity of 90% of stars
They lie along a
band called the
main sequence
The plot of stars’
luminosities versus
their temperatures
is called the
diagram (H-R
22 March 2005
AST 2010: Chapter 17
H-R Diagram for Many Stars
22 March 2005
AST 2010: Chapter 17
Features of H-R Diagram
The main-sequence band
contains almost 90% of
the stars
Large blue stars
Medium yellow stars
Small red stars
About 10% of the stars lie
below the main sequence
They are the hot, but dim,
white dwarfs
No more than 1% of the
stars lie above the main
They are cool and very
They must be giants and
22 March 2005
AST 2010: Chapter 17
Characteristics of Main-Sequence Stars
The main sequence turns out to be a sequence of stellar masses
(for almost 90% of the stars)
The more massive stars have the more weight and can thus
compress their centers to the greater degree, which implies that
they are the hotter inside and the better at generating energy
from nuclear reactions deep within
22 March 2005
AST 2010: Chapter 17
The other 10% stars
About 10% of the stars
do not follow the mass-luminosity
do not lie on the main sequence
Giant and supergiant stars
lie on the upper-right section of the H-R
are very luminous because they are large
in diameter, although they are cool
make up less than 1% of the stars
White dwarfs
lie on the lower-left section of the H-R
are small in diameter (similar to Earth’s)
are hot, but dim
make up about 10% of the stars
22 March 2005
AST 2010: Chapter 17
Main Sequence: Typical Stars
The Sun lies on the middle of the main
Is the Sun an "average'' or "typical''?
The meaning of "average'' depends on how
one chooses the sample!
Compared to the nearby stars, the Sun is luminous,
hot, and big
Compared to the apparently bright stars, the Sun is
dim, cool, and small
Compared to the stars in globular clusters, the Sun
is very young
Compared to the stars in open (galactic) clusters,
the Sun is very old
22 March 2005
AST 2010: Chapter 17
The Sun is compared
to 100 apparently
brightest stars in our
sky and 100 nearest
stars (both from
Hipparchus’ survey)
Most stars that
appear bright in our
sky turn out to be
also intrinsically
Near stars are all
within about 25 LY
from the Sun
Near stars are mostly
cool and faint
22 March 2005
AST 2010: Chapter 17
More Comparisons (1)
Population percentages
of the spectral types for
bright and near stars
Most of the apparently
bright stars are the hot
and luminous A- and Btype stars
The bright-star sample
includes a few of the
very hot O-type stars
All but one of the K-type
stars in the bright-star
sample are giants or
supergiant stars
All of the M-type stars
are giants or supergiants
22 March 2005
AST 2010: Chapter 17
More Comparisons (2)
The distribution of
the near stars is very
different from that of
the bright stars
The majority of the
near stars are cool
and faint K- and Mtype stars
Only one star in the
entire near-star
sample is a giant
The rest of the nearstar sample are
main-sequence stars
22 March 2005
AST 2010: Chapter 17
Representative Sample
Which of these samples is more representative
of the entire population of stars in our galaxy?
A representative sample includes all parts of the
population of the objects your are investigating in
their proper proportions
The relative proportion of common things will be
greater than the relative proportions of rare things
In fact, the uncommon things may not be found in
a small representative sample because they are so
With better instruments, more data on stars,
even new types of stars or other objects, will
be collected, making the celestial census more
22 March 2005
AST 2010: Chapter 17