The Family of Stars

1
The Family of Stars

• Chapter 8

2
Fig. 8-CO, p. 132
3
Goals
Explain how stellar distances are
determined. Discuss the motions of the stars
through space and how these motions are measured
from Earth. Distinguish between luminosity and
apparent brightness and explain how stellar
luminosity is determined. Explain the usefulness
of classifying stars according to their colors,
surface temperatures, and spectral
characteristics. Explain how physical laws are
used to estimate stellar sizes. Describe how an
HR diagram is constructed and used to identify
stellar properties.
4
Goals
Know how to calculate the distance to a star
using the astronomer's method described in this
chapter Explain the difference between absolute
visual magnitude and luminosity Interpret an H-R
diagram and know how our sun fits into such a
model List and describe the various types of
binary star systems
5
Trifid Nebula
Figure 8.1 A family portrait. Each point of
light in this photo of the Trifid Nebula is a
star, but nothing about the appearance of a star
tells us its energy output, its diameter, or its
mass. By puzzling out these properties of stars,
astronomers can understand this photo as a family
portrait. Stars of different sizes and masses
fill the image, as newborn stars are forming at
the center of the nebula. (AURA/NOAO/NSF)
Fig. 8-1, p. 133
6
8.1 Measuring the Distances to Stars
The Surveyor's Method Key terms
baseline, landmark The Astronomer's Method
Key terms stellar parallax (p), parsec
(pc) By the Numbers 8-1 Parallax and
Distance  
7
Triangulation
Figure 8.2 You can find the distance d across a
river by measuring the baseline and the angles A
and B and then constructing a scale drawing of
the triangle.
Fig. 8-2, p. 134
8
Parallax 1
Figure 8.3 We can measure the parallax of a
nearby star by photographing it from two points
along Earths orbit. For example, we might
photograph it now and again in six months. Half
of the stars total change in position from one
photograph to the other is its stellar parallax,
p.
Fig. 8-3, p. 134
9
Parallax 2
Figure 8.4 To measure the parallax of a star, we
must examine the long, thin triangle formed by
Earth, the sun, and the star. The short side of
the triangle, S, is the baseline of our
measurement, 1 AU. If we were located at the star
and looked back at Earth, the angular distance
from Earth to the sun would equal the parallax,
p. This means we can use the small-angle formula
(see By the Numbers 3-1) to find the stars
distance, d, using its parallax.
Fig. 8-4, p. 135
10
Distances to Stars
Parallax is the apparent shift of a foreground
object relative to some distant background as the
observers point of view changes. To determine
an objects parallax, we observe it from either
end of some baseline, and measure the angle
through which the line of sight to the object
shifts. In astronomical contexts, the angle is
usually obtained by comparing photographs made
from the two ends of the baseline  
11
More parallax
. If we ask at what distance a star must lie in
order for its observed parallax to be exactly 1',
we get an answer of 206,265 A.U., or 3.1 x 1016
m. (By the Numbers, p.135, Seeds) Astronomers
call this distance 1 parsec (1 pc), from
parallax in arc seconds. The parsec is
defined so as to make the conversion between
distance and parallactic angle easy. ( d
1/p). An object with a parallax of 0.5'' lies at
a distance of 1/0.5 2 pc an object with a
parallax of 0.1'' lies at 1/0.1 10 pc, and so
on. One parsec is approximately equal to 3.3
light-years.  
12
Our nearest neighbours
The closest star to Earth (besides the Sun) is
called Proxima Centauri. It has the largest known
stellar parallax, 0.76'', which means that it is
about 1/0.76 1.3 pc awayabout 270,000 A.U., or
4.3 light-years. Our next nearest neighbor to
the Sun beyond the Alpha Centauri system is
called Barnards Star. Its parallax is 0.55'', so
it lies at a distance of 1.8 pc, or 6.0
light-years.  
13
From the surface Astronomers have special
equipment that can routinely measure stellar
parallaxes of 0.03'' or less, corresponding to
stars within about 30 pc (100 light-years) of
Earth.   From space Observations made by the
European Hipparcos satellite have extended the
range of accurately measured parallaxes to over
200 pc, encompassing more than a million stars.  
14
The Trigonometric Parallax
0
Example Nearest star, a Centauri, has a
parallax of p 0.76 arc seconds
d 1/p 1.3 pc 4.3 LY
With ground-based telescopes, we can measure
parallaxes p 0.02 arc sec d 50 pc
This method does not work for stars farther away
than 50 pc.
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Stellar Motion
Barnards Star 22 years apart This stellar
motion has two components. A stars radial
velocityalong the line of sightcan be measured
using the Doppler effect. For many nearby stars,
the transverse velocityperpendicular to our line
of sightcan also be determined by careful
monitoring of the stars position on the sky.
17
The annual movement of a star across the sky, as
seen from Earth and corrected for parallax, is
called proper motion. It describes the transverse
component of a stars velocity relative to the
Sun. Like parallax, proper motion is measured in
terms of angular displacement Spectral lines
from Alpha Centauri are blueshifted by a tiny
amountabout 0.0067 percentallowing astronomers
to find the radial velocity from the Doppler
Effect
Use basic trig to find the hypotenuse.
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Luminosity and Apparent Brightness
Luminosity is an intrinsic property of a starit
does not depend in any way on the location or
motion of the observer. It is sometimes referred
to as the stars absolute brightness. However,
when we look at a star, we see not its luminosity
but rather its apparent brightness Apparent
brightness is a measure not of a stars
luminosity but of the energy flux (energy per
unit area per unit time) produced by the star, as
seen from Earth. It depends on our distance from
the star.
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Intrinsic Brightness / Absolute Visual
Magnitude(II)
0
The flux received from the light is proportional
to its intrinsic brightness or luminosity (L) and
inversely proportional to the square of the
distance (d)
L
__
F
d2
Star A
Star B
Earth
Both stars may appear equally bright, although
star A is intrinsically much brighter than star B.
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The Inverse Square Relation
Figure 8.5 A light source is surrounded by
spheres with radii of 1 unit and 2 units. The
light falling on an area of 1 m2 on the inner
sphere spreads to illuminate an area of 4 m2 on
the outer sphere. Thus, the brightness of the
light source is inversely proportional to the
square of the distance.
Fig. 8-5, p. 136
21
the energy per unit areathe stars apparent
brightness, as seen by our eye or our
telescopeis inversely proportional to the square
of the distance from the star. Doubling the
distance from a star makes it appear 22, or 4,
times dimmer  
22
We can therefore say that the apparent brightness
of a star is directly proportional to the stars
luminosity and inversely proportional to the
square of its distance Determining a stars
luminosity is a twofold task. First, the
astronomer must determine the stars apparent
brightness by measuring the amount of energy
detected through a telescope in a given amount of
time. Second, the stars distance must be
measured The luminosity can then be found using
the inverse-square law  
23
THE MAGNITUDE SCALE
The scale dates from the second century B.C.,
when the Greek astronomer Hipparchus ranked the
naked-eye stars into six groups. The brightest
stars were categorized as first magnitude. First,
the 16 magnitude range defined by Hipparchus
spans about a factor of 100 in apparent
brightnessa first-magnitude star is
approximately 100 times brighter than a
sixth-magnitude star. Second, the physiological
characteristics of the human eye are such that
each magnitude change of 1 corresponds to a
factor of about 2.5 in apparent brightness.
2.512 to the fifth power is 100
24
We now define a change of 5 in the magnitude of
an object (going from magnitude 1 to magnitude 6,
say, or from magnitude 7 to magnitude 2) to
correspond to exactly a factor of 100 in apparent
brightness. Second, because we are really talking
about apparent (rather than absolute)
brightnesses, the numbers in Hipparchuss ranking
system are called apparent magnitudes. Third, the
scale is no longer limited to whole numbers
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Looks can fool you.
Stars at greatly different distances can appear
just as bright if the more distant is much more
luminous.
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Distance and Intrinsic Brightness
0
Example
Recall
Betelgeuse
App. Magn. mV 0.41
Rigel
App. Magn. mV 0.14
For a magnitude difference of 0.41 0.14 0.27,
we find an intensity ratio of (2.512)0.27 1.28
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Distance and Intrinsic Brightness
0
Rigel appears 1.28 times brighter than Betelgeuse,
Betelgeuse
But Rigel is 1.6 times further away than
Betelgeuse
Thus, Rigel is actually (intrinsically)
1.28(1.6)2 3.3 times brighter than Betelgeuse.
Rigel
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Absolute magnitude
To compare intrinsic, or absolute, properties of
stars, however, astronomers imagine looking at
all stars from a standard distance of 10 pc
(arbitrary choice). Because the distance is fixed
in this definition, absolute magnitude is a
measure of a stars absolute brightness, or
luminosity. Knowing distance allows us to compute
its absolute magnitude. As discussed further in
By the numbers 8-2,p. 137, the numerical
difference between a stars absolute and apparent
magnitudes is a measure of the distance to the
star
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Absolute Visual Magnitude
0

• To characterize a stars intrinsic brightness,
  define absolute visual magnitude (MV)

Apparent visual magnitude that a star would have
if it were at a distance of 10 pc.
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Absolute Visual Magnitude(II)
0
Back to our example of Betelgeuse and Rigel
Betelgeuse
Rigel
Difference in absolute magnitudes 6.8 5.5
1.3 Luminosity ratio (2.512)1.3 3.3
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The Distance Modulus
0
If we know a stars absolute magnitude, we can
infer its distance by comparing absolute and
apparent magnitudes
Distance Modulus mV MV -5 5 log10(d pc)
Distance in units of parsec
Equivalent d 10(mV MV 5)/5 pc
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Well do a lab on this relationship. Bring a
calculator.
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Stellar Temperatures
Stars have color differences as well as
differences in brightness. Betelgeuse is clearly
red while Rigel has a blue white tint.
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COLOR AND THE BLACKBODY CURVE
Because the basic shape of the blackbody curve is
so well understood, astronomers can estimate a
stars temperature using as few as two
measurements at selected wavelengths. 3000K
(B-V)0
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Stellar spectra
Early workers classified stars primarily
according to their hydrogen-line intensities.
They adopted an alphabetic A, B, C, D, E. . .
scheme in which A stars, with the strongest
hydrogen lines, were thought to have more
hydrogen than did B stars, and so on. The
classification extended as far as the letter
P.  After atomic theory, classed by surface
temperature The original letters now run O, B, A,
F, G, K, M. (The other letter classes have been
dropped.) These stellar designations are called
spectral classes (or spectral types). Use the
time-honored (and politically incorrect) mnemonic
Oh, Be A Fine Girl, Kiss Me to remember them in
the correct order.
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Classifications include 0 to 9 graduations for
more accuracy. A G2 star is hotter than a G8 star.
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Automobile horsepower versus weight
Figure 8.6 We could analyze automobiles by
plotting their horsepower versus their weight and
thus reveal relationships between various models.
Most would lie somewhere along the main sequence
of normal cars.
Fig. 8-6, p. 138
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Organizing the Family of Stars The
Hertzsprung-Russell Diagram
0
We know Stars have different temperatures,
different luminosities, and different sizes.
To bring some order into that zoo of different
types of stars organize them in a diagram of
Luminosity
versus
Temperature (or spectral type)
Absolute mag.
Hertzsprung-Russell Diagram
Luminosity
or
Temperature
Spectral type O B A F G K M
42
An HR diagram
An HR diagram is a graph of luminosity versus
temperature on which stars are represented as
points. Spectral types have been added at the top
to show how they are related to temperature.
Absolute magnitude has been added at the right to
show its relationship to luminosity. Star
diameters are not to scale in this schematic
diagram.
43
An HR diagram
Fig. 8-7, p. 140
44
The Hertzsprung Russell Diagram
0
Most stars are found along the main sequence
45
The Hertzsprung-Russell Diagram (II)
0
Same temperature, but much brighter than MS stars
? Must be much larger
Stars spend most of their active life time on the
Main Sequence.
? Giant Stars
Same temp., but fainter ? Dwarfs
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Well-known stars
Figure 8.8 An HR diagram showing the luminosity
and temperature of many well-known stars. The
dashed lines are lines of constant radius.
(Individual stars that orbit each other are
designated A and B, as in Spica A and Spica B.)
Fig. 8-8, p. 141
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From your book
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Stellar Sizes
A few stars are big enough to resolve in the new
telescopes. Sizes for these can now be calculated
directly. Betleguese is 600X larger than the Sun.
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Indirect Size determinations
Using the luminosity and the temperature of a
star the area and hence the size of a star can be
determined. This is the radius-luminosity-temperat
ure relationship. E sT4 L/Area. Area
4pR2 So Area L (absolute brightness,
luminosity)/E And R is found from the surface
area See By the Numbers 8-3,p. 139 and part 7 of
Ex 30.
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The Size (Radius) of a Star
0
We already know flux increases with surface
temperature ( T4) hotter stars are brighter.
But brightness also increases with size
Star B will be brighter than star A.
A
B
Absolute brightness is proportional to radius
squared, L R2.
Quantitatively L 4 p R2 s T4
Surface flux due to a blackbody spectrum
Surface area of the star
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Example
0
Polaris has just about the same spectral type
(and thus surface temperature) as our sun, but it
is 10,000 times brighter than our sun.
Thus, Polaris is 100 times larger than the sun.
This causes its luminosity to be 1002 10,000
times more than our suns.
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Radii of Stars in the Hertzsprung-Russell Diagram
0
Rigel
Betelgeuse
10,000 times the suns radius
Polaris
100 times the suns radius
Sun
As large as the sun
100 times smaller than the sun
54
Spectral lines of supergiants, giants, and
main-sequence stars
Figure 8.9 Differences in widths and strengths
of spectral lines distinguish the spectra of
supergiants, giants, and main-sequence stars.
(Adapted from H. A. Abt, A. B. Meinel, W. W.
Morgan, and J. W. Tapscott, An Atlas of
Low-Dispersion Grating Stellar Spectra, Kitt Peak
National Observatory, 1968)
Fig. 8-9, p. 141
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Luminosity classes
Figure 8.10 The approximate location of the
luminosity classes on the HR diagram.
Fig. 8-10, p. 142
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Luminosity Classes
0
Ia Bright Supergiants
Ia
Ib
Ib Supergiants
II
II Bright Giants
III
III Giants
IV Subgiants
IV
V
V Main-Sequence Stars
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Main regions
For stars
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Luminosity effects on the width of spectral lines
0
Same spectral type, but different luminosity

• Lower gravity near the surfaces of giants
• smaller pressure
• smaller effect of pressure broadening
• narrower lines

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Star Colors M 39 Brightest stars are usually hot
and blue or cool and red.
60
Some stars often used as examples Luminosity is
brightness corrected for distance ie an
intrinsic property and surface temperature is
also independent of distance.
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To get a true picture of typical stars we need an
unbiased sample of stars.
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The most visible stars
Notice the scales are log scales. The diagonals
are lines of constant radius, from the
radius-luminosity-temperature relationship.
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Nearby Stars
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Brightest or nearby
p. 152
65
There should be nothing special about our local
neighborhood. It therefore is useful as a random
sample of stars in the galaxy. The larger our
sample size the better our conclusions. So a
complete sample out to greater distances gives a
more accurate picture of the galaxy as a
whole. I take a lot of grades.
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A random sample of stars
p. 151
67
Hipparcos H-R Diagram
20,000 stars within 1000 pc detected by
Hipparcos . Even here we need to realize these
are visible objects.
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Extending the Distance Scale
For main sequence stars we see there is a
correlation between the stars temperature and the
luminosity or absolute brightness. This
relationship based on data from stars close
enough to measure distance from parallax when
applied to more distant stars is called
spectroscopic parallax .
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F 17.17 Stellar Distances. From parallax outward
each new method is calibrated by data from the
earlier method. The methods overlap.
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Stellar Masses

• Applications of Newtons Keplers Laws to
  Binary Star Systems

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Binary Systems

• Many stars are in multiple star systems.
• CLASSES
• - visual binaries
• - spectroscopic binaries
• -eclipsing binaries

• Optical doubles are not true binary systems.
• Optical doubles are just chance superpositions,
  i.e. widely separated in r.

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Binary star system
Figure 8.11 As stars in a binary star system
revolve around each other, the line connecting
them always passes through the center of mass,
and the more massive star is always closer to the
center of mass.
Fig. 8-11, p. 143
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Visual Binaries

• Visual binaries are related. They appear within a
  few seconds of arc, and they orbit one another.
• They usually have periods a few decades long.
• Orbital motion is tracked by separation and
  position angle relative to the brighter star.

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Visual Binary
Figure 8.12 The orbital motion of Sirius A and
Sirius B can reveal their individual masses.
(Photo Lick Observatory)
Fig. 8-12a, p. 145
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Figure 17.19 Kruger 60
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VB all
Figure 8.12 The orbital motion of Sirius A and
Sirius B can reveal their individual masses.
(Photo Lick Observatory)
Fig. 8-12b, p. 145
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VB1
Fig. 8-12c, p. 145
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VB2
Fig. 8-12d, p. 145
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VB3
Fig. 8-12e, p. 145
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Visual Binaries, 2

• We track the apparent relative orbit. This orbit
  is most likely at an angle to our line of sight.
• The apparent orbit has to be corrected to find
  the true relative orbit.

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Masses from motion

• Objects orbit their common center of mass. F
  2.22, p54 CMc
• M1r1 m2r2
• For r r1 r2
• R3/p2 m1 m2 , a form of Keplers 2nd
• See By the Numbers 8-4, p.143

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Estimating Stellar Masses
0
Recall Keplers 3rd Law Py2 aAU3
Valid for the solar system star with 1 solar
mass in the center.
We find almost the same law for binary stars with
masses MA and MB different from 1 solar mass
aAU3
____
MA MB
Py2
(MA and MB in units of solar masses)
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Examples
0
a) Binary system with period of P 32 years and
separation of a 16 AU
163
____
MA MB 4 solar masses.
322
b) Any binary system with a combination of period
P and separation a that obeys Keplers 3. Law
must have a total mass of 1 solar mass.
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Visual Binaries, 3

• Only a few dozen binaries have been analyzed to
  give reliable masses. They must be close enough
  to resolve.
• New scopes increase our data base.

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Astrometric Binaries

• .. Are binaries with one star too faint to be
  seen.
• The visible star still orbits the center of mass.
  The stars proper motion is a wiggle. Revealing
  the presence of an unseen mass. ( remember
  extrasolar planet detection).

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Spectroscopic Binaries

• are too close together to be resolved
  separately.
• Position changes of the darkline spectra (Doppler
  again) reveal radial component of the stars
  orbital motion.

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Fig. 17.20 Spectroscopic Binary
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Spectroscopic Binaries,3

• If of equal brightness both spectra can be
  resolved. ( double line spectroscopic)
• a lower limit of the mass of the stars can be
  found.
• Statistical analysis of a large number of s.
  binaries allows a mass estimate of the stars by
  spectroscopic class (OBAFGKM)
• This class of binary is common.

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Eclipsing Binaries

• Rare but give important data
• To eclipse one another the orbital plane must be
  in line of sight with the earth.
• CHANGES IN THE LIGHT CURVES
• --can give the ratio of the temperatures of the
  two stars.---give an independent measure of the
  stellar diameters.

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Eclipsing Binary,2

• The light curves can give the orbital
  inclination.
• With the Doppler shifts the mass of the two stars
  can be determined.
• E.g. Algol the demons head(b Persi) eclipses
  are noticeable to the naked eye. Mv 2.1 to 3.4 in
  10 hours.

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Spectroscopic Binary
Figure 8.13 From Earth, a spectroscopic binary
looks like a single point of light, but the
Doppler shifts in its spectrum reveal the orbital
motion of the two stars.
Fig. 8-13a, p. 145
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SB2
Fig. 8-13b, p. 145
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SB3
Fig. 8-13c, p. 145
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SB4
Fig. 8-13d, p. 145
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SB5
Fig. 8-13e, p. 145
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SB intensity spectra
Figure 8.14 Fourteen spectra of the star HD80715
are shown here as graphs of intensity versus
wavelength. A single spectral line (arrow in top
spectrum) splits into a pair of spectral lines
(arrows in third spectrum), which then merge and
split apart again. These changing Doppler shifts
reveal that HD80715 is a spectroscopic binary.
(Adapted from data courtesy of Samuel C. Barden
and Harold L. Nations)
Fig. 8-14, p. 146
98
Mizar and Alcor
Figure 8.15 (a) At the bend of the handle of the
Big Dipper lies a pair of stars, Mizar and Alcor.
Through a telescope we discover that Mizar has a
fainter companion and so is a member of a visual
binary system.
Fig. 8-15a, p. 146
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Spectra of Mizar
Figure 8.15 (b) Spectra of Mizar recorded at
different times show that it is itself a
spectroscopic binary system rather than a single
star. In fact, both the faint companion to Mizar
and the nearby star Alcor are also spectroscopic
binary systems. (The Observatories of the
Carnegie Institution of Washington)
Fig. 8-15b, p. 146
100
Eclipsing Binary
Figure 8.16 Imagine a model of a binary system
with balls for stars and a disk of cardboard for
the plane of the orbits. Only if we view the
system edge-on do we see the stars cross in front
of each other.
Fig. 8-16, p. 147
101
EB1
Fig. 8-17a, p. 147
102
EB2
Fig. 8-17b, p. 147
103
EB3
Fig. 8-17c, p. 147
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EB4
Fig. 8-17d, p. 147
105
EB5
Fig. 8-17e, p. 147
106
VW Cephei light curve
Figure 8.18 The observed light curve of the
binary star VW Cephei (lower curve) shows that
the two stars are so close together their gravity
distorts their shapes. Slight distortions in the
light curve reveal the presence of dark spots at
specific places on the stars surface. The upper
curve shows what the light curve would look like
if there were no spots. (Graphics created with
Binary Maker 2.0)
Fig. 8-18a, p. 148
107
Algol
Figure 8.19 The eclipsing binary Algol consists
of a hot B star and a cooler G or K star. The
eclipses are partial, meaning that neither star
is completely hidden during eclipses. The orbit
here is drawn as if the cooler star were
stationary.
Fig. 8-19, p. 149
108
Back to Stellar Masses.

• We can add mass to the data we have on stars
  thanks to the binaries.
• We find
• Supergiants, giants and white dwarfs reveal no
  clear pattern.
• But main sequence stars show a clear trend.

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MAIN SEQUENCE STARS ONLY (a) Size and mass
relation (b) Luminosity and mass
110
Included on the HR diagram luminosity is shown to
be very sensitive to the stars mass.
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Mass on HR Diagram
Notice that the masses of main-sequence stars
decrease from top to bottom but that masses of
giants and supergiants are not arranged in any
ordered pattern.
Fig. 8-20, p. 150
113
Masses of Stars in the Hertzsprung-Russell Diagram
0
Masses in units of solar masses
The higher a stars mass, the more luminous
(brighter) it is
High masses
L M3.5
High-mass stars have much shorter lives than
low-mass stars
Mass
tlife M-2.5
Low masses
Sun 10 billion yr.
10 Msun 30 million yr.
0.1 Msun 3 trillion yr.
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Main sequence mass distribution. Most stars are
smaller than the sun.
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MassLuminosity relation
Figure 8.21 The massluminosity relation shows
that the more massive a main-sequence star is,
the more luminous it is. The open circles
represent white dwarfs, which do not obey the
relation. The red line represents the equation in
By the Numbers 8-5. L M3.5
Fig. 8-21, p. 150
117
Stellar Masses Main Sequence Stars Summary

• The more massive the star the more luminous the
  star.
• Main sequence stars vary in mass from 0.08Msun
  to 50 Msun with an
• Enormous effect on their luminosities, from 10-6
  L sun to 106 L sun a factor of 1012 !
• A small change in mass has a large effect on
  luminosity.

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A random sample of stars
p. 151
119
Our neighborhood
The most luminous stars are so rare few are close
by. There are no O stars at all within 62 pc of
Earth.
p. 151
120
0
121
Population Distribution,1D
122
A Census of the Stars
0
Faint, red dwarfs (low mass) are the most common
stars.
Bright, hot, blue main-sequence stars (high-mass)
are very rare.
Giants and supergiants are extremely rare.
123
Stellar Lifetime estimates
The radius increases proportionally to mass. The
luminosity increases much faster, almost as the
fourth power. The lifetime depends directly on
the mass available but inversely on the
luminosity (how fast it burns), Thus the stellar
lifetime is roughly inversely proportional to the
third power (2.5) of the mass.
124
This explains the observed population density of
stars by type. Hot massive stars dont last long.
Small low mass stars have very long lifetimes.
Some low mass stars formed in the first wave
after the universe began are still around.
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p. 152
126
Brightest or nearby
Although white dwarfs and red dwarfs are very
common, not a single one is bright enough to be
visible to the naked eye.
p. 152