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The H-R Diagram
• In 1913, the American astronomer Henry Russel plotted
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the luminosities of stars versus their spectra class (related
to the temperature)
Similar to work done
in 1911 by Danish
astronomer Ejnar
Hertzsprung
They found that the
luminosities and
temperatures of star are
related
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H-R Diagram
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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Features of the H-R Diagram
• Note that the luminosity is plotted on a
logarithmic scale and the temperature is plotted
backwards
• The majority of these stars are located along a
narrow sequence from the upper left (hot, bright)
to the lower right (coll, dim)
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Main sequence
Hotter stars are more luminous that cooler stars
• Stars above and to the right of the main sequence
are giants and supergiants
• Stars below and to the left of the main sequence
are white dwarfs
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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More H-R Diagram
• The previous H-R Diagram was plotted for stars
whose distances are well known
• Instead, we could plot intensities and temperatures
for all stars
• Astronomers find that
90% of all stars are
on the main sequence
• Models of stellar
evolution show that
the main sequence is
a sequence of stellar
mass
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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Extremes
• There are superluminous stars in the top left of the
H-R diagram
• The cool supergiants in the upper right corner are
as much as 10,000 times a luminous as the Sun
and are very much larger than the Sun
• The red, cool, low-luminosity stars in the lower
right hand corner are about 80 times denser than
the Sun
• The white dwarfs in the lower left have very high
densities
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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White Dwarfs
• The first white dwarf was discovered in 1862
which is a binary star with Sirius
• Hundreds of white dwarfs are now known
• A typical white dwarf is 40 Eridani B
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12,000 K temperature
L = 1/275 Lsun
1.4% the diameter of the Sun
Density = 200,000 g/cm3
1 teaspoon has a mass of 50 tons
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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Imaging of Stars using Optical Interference
• In 1996, the highest resolution picture of 2 binary
stars was taken using the Navy Prototype Optical
Interference (NPOI) (from Scientific American,
March, 2001)
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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Units of Distance
• The first sets of measurements were based on human dimensions
• The metric system of measurements was adopted in France in 1799
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and is now used by every country in the world EXCEPT the US
The basic unit of length was defined at the meter and was based on
a bar of platinum-iridium metal
In 1960, the definition of the meter was changed to be
1,650,763.73 wavelengths of an atomic transition in krypton-86
In 1983, the meter was again redefined in terms in terms of the
frequency of a cesium-133 clock and the speed of light

1 light second = 299,792,458.6 m
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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Distances in the Solar System
• Copernicus and Kepler established the relative distances of the
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planets
Absolute distances are measured with radar telescopes
• Radar measurements have been made
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of the distance to Venus, Mercury,
Mars, satellites of Jupiter, the rings of
Saturn, and several asteroids
The distance from the Earth to the Sun
is taken as 1 astronomical unit (AU)
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500 light seconds (LS)
8.3 light minutes (LM)
1.5 x 1011 m
150 million km
ISP 205 - Astronomy Gary D. Westfall
Radar Telescope
Lecture 18
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Triangulation
• Measuring the distance to stars cannot be done by radar
• A good method is triangulation
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Your brain does triangulation to get depth perception using your two eyes
• Triangulation is consists of using a baseline and two angles
• Parallax is the angle that
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lines AC and line BC
make
Measuring the angles at A
and B allow the
calculation of a triangle
and the distance to the tree
To study the distances to
stars, the baseline
becomes the diameter of
Earth’s orbit around the
Sun
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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Distance to Stars
• As the Earth travels around the Sun, it provides us with a baseline
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of 2 AU or 300 million km
Even with this baseline, the parallax for stars is still too small to
see with the naked eye
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Early (Greek) observers were confused by the lack of parallax for the stars
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They could not conceive how far way the stars are
• The first
successful
measurement of
the parallax of
stars were done
in 1838
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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Units of Stellar Distance
• We define the unit parsec as the distance a star
would be if it had a parallax of 1 arcsec and a
baseline of 1 AU
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“the distance at which we have a parallax of one
second”
pc
3.1 x 1013 km
1 pc = 3.26 LY, 1 LY = 0.31 pc
• The distance of a star is just the reciprocal of its
parallax
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R = 1/p
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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The Nearest Stars
• No star is within 1 LY or even 1 pc
• The closest stars are three stars the make up a multiple system in the
constellation of Centaurus
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Alpha Centauri
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Not visible in the northern hemisphere
A binary system
4.4 LY from Earth
Proxima Centauri
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4.3 LY
• The closest stars visible without a telescope from the US is Sirius
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8 LY
Binary system
• Even with the Hipparchus we can only measure distances out to 300 LY, which
is only 1% of the size of own galaxy and very small on the scale of the universe
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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Standard Bulbs Revisited
• Stars come in many luminosities
• If astronomers could tell what the luminosity of a star
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was, they could calculate the distance to the star knowing
the apparent brightness
Most stars shine steadily but some star have variable
brightness
The amount of light as a function of time is called the
light curve
Cepheid Light Curve
For Delta Cephei
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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Variable Stars
• There are two type of variable stars
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Cepheids
RR Lyrae
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Both types of variable stars actually change their diameters
with time
• Cepheids are large, yellow, pulsating stars
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Named for the constellation in which they were first
found, Delta Cephei (confusing!)
Several hundred cepheids are known
Polaris is a cepheid varying 10% in visual luminosity
with a period of 4 days
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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The Period-Luminosity Relationship
• The period and average luminosities of cepheid variables are
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related
The period is easy to measure and give the astronomer the
luminosity of the star
Using the luminosity and the apparent brightness, the astronomer
can calculate the distance to the star
The relationship between period and luminosity was discovered by
Henrietta Leavit in 1908
Leavit found that the brighter cepheids always had longer periods
These cepheids were all in the Large Magellanic Cloud and so
were all about the same distance
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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Cepheids in the Large Magellanic Cloud
• The cepheids that Leavit found were all in the Large Magellanic cloud
• Later the distance to the Large Magellanic cloud was measured by other means
and absolute distances were attached to the period-luminosity-apparent
brightness distances
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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Very Distant Cepheids
• Image of part
of M100
galaxy taken
with HST
• Inset shows
single
cepheid
going
through its
cycle of
brightness
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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H-R Diagram and Cosmic Distances
• Variable stars are useful but not all stars are
variable
• We can use the H-R Diagram to measure the
distance to non variable stars
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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Luminosity Classes
• Knowing the the spectra index gives the astronomer the luminosity
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and thus the distance using the variable star information
We can also get the pressure so we know whether we are dealing
with giant stars or main sequence stars
6 luminosity classes
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Ia: Brightest
supergiants
Ib: Less-luminous
supergiants
II: Bright giants
III: Giants
IV: Subgiants
V: Main-sequence
stars
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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RR Lyrae Stars
• A related group of stars is the RR Lyrae variables
• More common but less luminous than cepheids
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Thousands are known in our galaxy
Periods are less than a day
Brightness changes by less than a factor of two
• All RR Lyrae stars have the same luminosity
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50 Lsun
• RR Lyrae stars can be detected out to about 2
million LY
ISP 205 - Astronomy Gary D. Westfall
Lecture 18
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