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ASTRO 101

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Title: ASTRO 101


1
ASTRO 101
  • Principles of Astronomy

2
Instructor Jerome A. Orosz
(rhymes with boris)Contact
  • Telephone 594-7118
  • E-mail orosz_at_sciences.sdsu.edu
  • WWW http//mintaka.sdsu.edu/faculty/orosz/web/
  • Office Physics 241, hours T TH 330-500

3
Text Perspectives on Astronomy First
Editionby Michael A. Seeds Dana Milbank.
4
Astronomy Help Room Hours
  • Monday 1200-1300, 1700-1800
  • Tuesday 1700-1800
  • Wednesday 1200-1400, 1700-1800
  • Thursday 1400-1800, 1700-1800
  • Friday 900-1000, 1200-1400
  • Help room is located in PA 215

5
Coming Up
  • November 3 In-class review
  • November 5 Exam 2
  • November 10 Furlough day class cancelled
  • Extra review session Wednesday, November 4 at
    330 pm in PA 216

6
Review
  • Thursday Exam 2 Chapters 5-8
  • Bring the Scantron No. F-288-PAR-L

7
Breakdown
  • There will be three types of questions
  • multiple choice questions (2 pts each)
  • long answer (5 pts each)
  • fill in the blank (1 pt each)

8
Highlights
  • The Sun and Stars
  • Basic properties
  • Spectral type
  • Temperature
  • Mass and radius
  • Luminosity
  • Internal Structure

9
Highlights
  • Stellar Evolution
  • Observational aspects
  • lifetime depends on initial mass
  • Observations of star clusters
  • Theory, using stellar models
  • outline of phases of stellar evolution, details
    depend on initial mass
  • Formation in clouds of gas and dust
  • Main sequence
  • Expansion into a red giant
  • Mass loss
  • Planetary nebula (low mass stars)
  • Supernova explosion (high mass stars)
  • Remnant
  • White dwarf (low mass stars)
  • Neutron star (massive stars)
  • Black hole (most massive stars)

10
Review Questions Chapter 5
  • 6. Why cant you see deeper in the Sun than the
    photosphere?
  • 7. What evidence can you give that granulation
    is caused by convection?
  • 20. How are astronomers able to explore the
    layers of the Sun below the photosphere?
  • 24. How can solar flares affect Earth?

11
Review Questions Chapter 6
  • 1. Why are Earth-based parallax measurements
    limited to the nearest stars?
  • 5. Why are hydrogen Balmer line strong in the
    spectra of medium-temperature stars and weak in
    the spectra of hot and cool stars?
  • 7. Why does the luminosity of a star depend on
    both its radius and its temperature?
  • 8. How can you be sure that giant stars really
    are larger than main-sequence stars?
  • 9. Why do astronomers conclude that white
    dwarfs must be very small?

12
Review Questions Chapter 6
  • 12. What observations would you make to study an
    eclipsing binary star?
  • 13. Why dont astronomers know the inclination of
    a spectroscopic binary? How do they know the
    inclination of an eclipsing binary?

17. If all of the stars in the photo here
are members of the same star cluster, then they
all have about the same distance. Then why are
three of the brightest stars much redder than the
rest? What kind of star are they?
13
Review Questions Chapter 7
  • 1. What opposing forces are balanced in a
    stable star?
  • 3. How does the pressure-temperature thermostat
    control the nuclear reactions inside stars?
  • 6. Why is there a lower limit to the mass of a
    main sequence star?
  • 7. Why does a stars life expectancy depend on
    its mass?

14
Review Questions Chapter 7
  • What evidence can you cite that the space between
    the stars is not empty?
  • Why would an emission nebula near a hot star look
    red, while a reflection nebula near its star look
    blue?
  • 10. Why do astronomers rely heavily on infrared
    observations to study star formation?

15
Review Questions Chapter 8
  • 4. How can star clusters confirm astronomers
    theories of stellar evolution?
  • Why cant a white dwarf star contract as it
    cools?
  • How are neutron stars and white dwarfs similar?
    How do they differ?
  • If neutron stars are hot, why arent they very
    luminous?
  • 23. How can a black hole emit X-rays?

16
Review Questions Chapter 5
  • 6. Why cant you see deeper in the Sun than the
    photosphere?
  • 7. What evidence can you give that granulation
    is caused by convection?
  • 20. How are astronomers able to explore the
    layers of the Sun below the photosphere?
  • 24. How can solar flares affect Earth?

17
The Sun and the Stars
  • The Sun is the nearest example of a star.
  • Basic questions to ask
  • What do stars look like on their surfaces? Look
    at the Sun since it is so close.
  • How do stars work on their insides? Look at both
    the Sun and the stars to get many examples.
  • What will happen to the Sun? Look at other stars
    that are in other stages of development.

18
The Sun
  • There are two broad areas of solar research
  • The study of the overall structure of the Sun.
  • The study of its detailed surface features.
  • Think of the distinction of climate and
    weather on Earth
  • Climate refers to global trends.
  • Weather refers to local conditions.

19
The Surface of the Sun
  • The surface of the Sun can be complex.
  • Surprisingly, observing the Sun can be quite
    difficult, owing to the immense heat.
  • The study of the solar surface is usually done
    using many different wavelengths, from the X-rays
    to radio. Different features show up well in
    certain wavelengths.

20
The Solar Surface
  • The Sun has no solid surface. The part we see is
    called the photosphere.
  • A visual light image captures different features
    than an ultraviolet light image.

21
The Solar Surface
  • The Sun has no solid surface. The part we see is
    called the photosphere.
  • High resolution images of the photosphere show
    granulation.

22
Granulation
  • From the measurement of Doppler shifts, we know
    that the granules are blobs of gas that are
    rising and falling.
  • The granules are similar to what one sees in
    boiling water on Earth.
  • Energy from the interior is being transported
    outwards by motions in the gas. This type of
    energy transport is called convection.

23
Solar Oscillations
  • By detailed analysis of the Doppler shifts of
    different parts of the photosphere, we know that
    the photosphere oscillates (i.e. it vibrates much
    like a bell).
  • These vibrations are somewhat similar to sound
    waves in the air on Earth.
  • Since the speed of sound in a gas depends on the
    temperature and density of the gas, the study of
    solar oscillations can reveal details about the
    solar interior.

24
Sunspots
  • Sunspots are darker regions on the Suns surface.
  • They can be observed in the optical, and were
    first discovered by Galileo in 1610.

25
Sunspots
  • Note the complex structure in the spot and its
    surroundings.

26
The Solar Cycle
  • In the mid 1800s, a Swiss astronomer made
    detailed observations of sunspots in order to
    search for transits of a possible planet interior
    to Mercury.

27
The Solar Cycle
  • No planets were found, but it was discovered that
    the number of sunspots varies with an 11 year
    cycle.
  • This is not fully understood.

28
Sunspots
  • Galileo used sunspots to track the rotation of
    the Suns surface

29
Sunspots
  • Galileo was the first to sunspots to track the
    rotation of the Suns surface.

30
Sunspots
  • Galileo was the first to sunspots to track the
    rotation of the Suns surface.
  • The Sun does not rotate as a solid body. The
    equator rotates once every 25 days. At 45o
    latitude, it takes 27.8 days.

31
The Sun and Space Weather
  • Violent activity can occur in regions near
    sunspots.
  • A solar flare is a giant eruption of particles
    and radiation.
  • The radiation and particles can interact with the
    Earths upper atmosphere, disrupting satellite
    communications and power grids.

32
The Sun and Space Weather
  • Violent activity can occur in regions near
    sunspots.
  • A solar flare is a giant eruption of particles
    and radiation.
  • The cause of these giant flares is not
    understood, although magnetic fields are thought
    to play a role.

33
Review Questions Chapter 5
  • 6. Why cant you see deeper in the Sun than the
    photosphere?
  • 7. What evidence can you give that granulation
    is caused by convection?
  • 20. How are astronomers able to explore the
    layers of the Sun below the photosphere?
  • 24. How can solar flares affect Earth?

34
Review Questions Chapter 6
  • 1. Why are Earth-based parallax measurements
    limited to the nearest stars?
  • 5. Why are hydrogen Balmer line strong in the
    spectra of medium-temperature stars and weak in
    the spectra of hot and cool stars?
  • 7. Why does the luminosity of a star depend on
    both its radius and its temperature?
  • 8. How can you be sure that giant stars really
    are larger than main-sequence stars?
  • 9. Why do astronomers conclude that white
    dwarfs must be very small?

35
Review Questions Chapter 6
  • 12. What observations would you make to study an
    eclipsing binary star?
  • 13. Why dont astronomers know the inclination of
    a spectroscopic binary? How do they know the
    inclination of an eclipsing binary?

17. If all of the stars in the photo here
are members of the same star cluster, then they
all have about the same distance. Then why are
three of the brightest stars much redder than the
rest? What kind of star are they?
36
The Distance
  • How can you measure the distance to something?
  • Direct methods, e.g. a tape measure. Not good for
    things in the sky.
  • Sonar or radar send out a signal with a know
    velocity and measure the time it takes for the
    reflected signal. Works for only relatively
    nearby objects (e.g. the Moon, certain
    asteroids).
  • Triangulation the use of parallax.

37
The Parallax
  • Parallax is basically the apparent shifting of
    nearby objects with respect to far away objects
    when the viewing angle is changes.
  • Example hold out your finger and view it with
    one eye closed, then the other eye closed. Your
    finger shifts with respect to the background.

38
The Parallax
  • Example hold out your finger and view it with
    one eye closed, then the other eye closed. Your
    finger shifts with respect to the background.

39
The Parallax
  • A better example place an object on the table
    in front of the room and look at its position
    against the back wall as you walk by. In most
    practical applications you will have to change
    your position to make use of parallax.

40
Triangulation
  • Triangulation is based on trigonometry, and is
    often used by surveyors.
  • Here is another diagram showing the technique.
    This technique can be applied to other stars!

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
41
Triangulating the Stars
  • The largest baseline one can obtain is the orbit
    of the Earth!
  • When viewed at 6 month intervals, a relatively
    nearby star will appear to shift with respect to
    distant stars.

42
Triangulating the Stars
  • The largest baseline one can obtain is the orbit
    of the Earth!
  • When viewed at 6 month intervals, a relatively
    nearby star will appear to shift with respect to
    distant stars.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
43
Triangulating the Stars
  • The largest baseline one can obtain is the orbit
    of the Earth!
  • When viewed at 6 month intervals, a relatively
    nearby star will appear to shift with respect to
    distant stars.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
44
Triangulating the Stars
  • Here are two neat Java tools demonstrating
    parallax

http//www.astro.ubc.ca/scharein/a310/Sim.htmlOn
eover
http//spiff.rit.edu/classes/phys240/lectures/para
llax/para1_jan.html
45
Triangulating the Stars
  • When viewed at 6 month intervals, a relatively
    nearby star will appear to shift with respect to
    distant stars.
  • The angle p for the nearest star is 0.77
    arcseconds. One can currently measure angles as
    small as a few thousands of an arcsecond.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
46
Triangulating the Stars
  • For very tiny angles, use the approximation that
    tan(p)p, when p is in radians.
  • Then dB/tan(p) becomes dB/p.
  • B1 astronomical unit (e.g. the Earth-Sun
    distance). Define a unit of distance such that
    d1/p, if the angle p is measured in arcseconds.
  • This unit is the parsec, which is 3.26 light
    years.

47
Stellar Distances
  • Parallax angles as small as about 1/50 of an
    arcsecond can be measured from the ground. Thus
    the distance can be measured only for stars
    closer than 50 parsecs (163 light years).
  • From space, parallax angles as small as about
    0.003 arcseconds can be measured, corresponding
    to distances closer than about 300 parsecs.

48
Review Questions Chapter 6
  • 1. Why are Earth-based parallax measurements
    limited to the nearest stars?
  • 5. Why are hydrogen Balmer line strong in the
    spectra of medium-temperature stars and weak in
    the spectra of hot and cool stars?
  • 7. Why does the luminosity of a star depend on
    both its radius and its temperature?
  • 8. How can you be sure that giant stars really
    are larger than main-sequence stars?
  • 9. Why do astronomers conclude that white
    dwarfs must be very small?

49
Observing Other Stars
  • Recall there is basically no hope of spatially
    resolving the disk of any star (apart from the
    Sun). The stars are very far away, so their
    angular size as seen from Earth is extremely
    small.
  • The light we receive from a star comes from the
    entire hemisphere that is facing us. That is, we
    see the disk-integrated light.

50
Observing Other Stars
  • To get an understanding of how a star works, the
    most useful thing to do is to measure the
    spectral energy distribution, which is a plot of
    the intensity of the photons vs. their
    wavelengths (or frequencies or energies).
  • There are two ways to do this
  • Broad band, by taking images with a camera and
    a colored filter.
  • High resolution, by using special optics to
    disperse the light and record it.

51
Broad Band Photometry
  • Despite the disadvantages, broad band photometry
    is useful.
  • For example, it is immediately evident that
    different stars have different colors (the
    image on the left is a composite of three images
    taken in different filters.

52
High Resolution Spectroscopy
  • To obtain a high resolution spectrum, light from
    a star is passed through a prism (or reflected
    off a grating), and focused and detected using
    some complicated optics.

53
High Resolution Spectroscopy
  • Using a good high resolution spectrum, you can
    get a much better measurement of the spectral
    energy distribution.
  • The disadvantage is that the efficiency is lower
    (more photons are lost in the complex optics).
    Also, it is difficult to measure more than one
    star at a time (in contrast to the direct imaging
    where several stars can be on the same image).

54
Stellar Properties
  • The Sun and the stars are similar objects.
  • In order to understand them, we want to try and
    measure as many properties about them as we can
  • Temperature at the surface
  • Power output (luminosity)
  • Radius
  • Mass
  • Chemical composition

55
Spectral Classification
  • In the early 1800s, Joseph Fraunhofer observed
    the solar spectrum. He saw dark regions, known
    as spectral lines (these tell us what elements
    are there).
  • Starting in the late 1800s, it became possible to
    take the spectra of stars with similar detail.

56
Spectral Classification
  • At first, there was no physical understanding.
  • The earliest classification scheme was based on
    the strength of the hydrogen lines, with classes
    of A, B, C, D, E, F, G, H, I, J, K, L, M, N, O.
  • Class A had the strongest hydrogen lines, class O
    the weakest.
  • Later on, only a few of these classes were kept.
    Then, subclasses were added (e.g. G2), based on
    other elements.

57
Spectral Classification
  • At first, there was no physical understanding.
  • The earliest classification scheme was based on
    the strength of the hydrogen lines, with classes
    of A, B, F, G, K, M, O.
  • Eventually, physical understanding came. It was
    discovered that the spectral type was a
    temperature indicator. As a result, a more
    natural ordering of the spectral types became O,
    B, A, F, G, K, M (the old classes were retained).

58
Spectral Type Sequence Mnemonics
  • Oh Boy, An F Grade Kills Me
  • Oh, Be A Fine Girl, Kiss Me
  • http//www.astro.sunysb.edu/fwalter/AST101/mnemoni
    c.html

59
Spectral Classification
  • Here are digital plots of representative stars in
    the spectral sequence.
  • Note the variation in the strength of the
    hydrogen lines.

60
Spectral Classification
  • This is a computer simulation of the different
    types.

61
Spectral Classification
  • Why do the spectral classes look different from
    one another?
  • The temperature. The electrons in the atoms are
    responsible for the spectral lines, and the
    energies of the electrons are change with
    changing temperature. Example an O-star is so
    hot that the hydrogen atoms have lost their
    electrons, so no lines of hydrogen are seen.

62
Spectral Classification
  • http//www.astronomynotes.com

63
Spectral Classification
  • This is a computer simulation of the different
    types.

64
Spectral Classification
  • A measurement of the spectral type gives the
    surface temperature of the star.
  • O-stars are the hottest, with surface
    temperatures of up to 60,000 K.
  • M-stars are the coolest, with temperatures of
    only 3000 K.
  • The temperature of the Sun (a G2 star) is 5770 K.

65
Review Questions Chapter 6
  • 1. Why are Earth-based parallax measurements
    limited to the nearest stars?
  • 5. Why are hydrogen Balmer line strong in the
    spectra of medium-temperature stars and weak in
    the spectra of hot and cool stars?
  • 7. Why does the luminosity of a star depend on
    both its radius and its temperature?
  • 8. How can you be sure that giant stars really
    are larger than main-sequence stars?
  • 9. Why do astronomers conclude that white
    dwarfs must be very small?

66
Stellar Properties
  • The Sun and the stars are similar objects.
  • In order to understand them, we want to try and
    measure as many properties about them as we can
  • Temperature at the surface Use the spectral
    type
  • Power output (luminosity)
  • Radius
  • Mass
  • Chemical composition

67
The Luminosity of Stars
  • An important physical characteristic of a star is
    its luminosity, which is a measure of the amount
    of energy emitted by the star at its surface per
    unit time.

68
The Luminosity of Stars
  • An important physical characteristic of a star is
    its luminosity, which is a measure of the amount
    of energy emitted by the star at its surface per
    unit time.
  • We can measure the amount of energy received from
    the star per unit time (we call this the flux).

69
The Luminosity of Stars
  • An important physical characteristic of a star is
    its luminosity, which is a measure of the amount
    of energy emitted by the star at its surface per
    unit time.
  • We can measure the amount of energy received from
    the star per unit time (we call this the flux).
  • How do we relate the luminosity to the flux?

70
The Inverse Square Law
  • The received flux from a source depend inversely
    on the square of the distance.

71
The Inverse Square Law
  • Here is a neat Java tool demonstrating the
    inverse square law

http//www.astro.ubc.ca/scharein/a310/Sim.htmlOn
eover
72
The Inverse Square Law
  • The received flux from a source depend inversely
    on the square of the distance.
  • If you want to know the intrinsic luminosity of
    your source, you must measure the flux and the
    distance.

73
Stellar Properties
  • The Sun and the stars are similar objects.
  • In order to understand them, we want to try and
    measure as many properties about them as we can
  • Temperature at the surface Use the spectral
    type
  • Power output (luminosity) Measure the flux
    distance
  • Radius
  • Mass
  • Chemical composition

74
Stellar Properties
  • We can measure the apparent brightnesses of stars
    relatively easily (e.g. broad-band photometry).
  • We can measure the color index and/or the
    spectral type of stars. This gives us the
    temperatures.
  • We can measure the distances to the relatively
    nearby stars. Thus we can compute intrinsic
    brightnesses or luminosities for these stars.
  • What do you do with these data?

75
Temperature-Luminosity Diagrams
  • When you have a large number of objects, each
    with several observed characteristics, look for
    correlations between the observed properties.

76
Correlations
  • You might plot the horsepower of a cars engine
    vs. the weight of the car.
  • Most cars would fall along a single sequence, but
    some would deviate.

77
Temperature-Luminosity Diagrams
  • When you have a large number of objects, each
    with several observed characteristics, look for
    correlations between the observed properties.
  • Henry Norris Russell and Ejnar Hertzsprung were
    the first to do this with stars in the early
    1900s.
  • Some measure of the temperature is plotted on the
    x-axis of the plot, and some measure of the
    intrinsic luminosity is plotted on the y-axis.

78
Temperature-Luminosity Diagrams
  • The stars do not fall on random locations in this
    diagram!

79
Temperature-Luminosity Diagrams
  • The stars do not fall on random locations in this
    diagram!

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
80
Temperature-Luminosity Diagrams
  • The stars do not fall on random locations in this
    diagram!
  • What does this mean?

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
81
Temperature-Luminosity Diagrams
  • The stars do not fall on random locations in this
    diagram!
  • What does this mean?
  • This diagram gives us clues to inner workings of
    stars, and how they evolve.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
82
Temperature-Luminosity Diagrams
  • The stars do not fall on random locations in this
    diagram!
  • There is some specific physical process that
    limits where a star can be on this diagram.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
83
Temperature-Luminosity Diagrams
  • The stars do not fall on random locations in this
    diagram!
  • Furthermore, the location of a star on this
    diagram is an indicator of its size.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
84
Review Black Body Radiation
  • Recall the discussion of the ideal radiator,
    aka the black body.

85
Review Black Body Radiation
  • For a given size, hotter objects give off more
    energy than cooler objects, and are bluer.

86
Black Body Radiation
  • For a given temperature, larger bodies give off
    more energy than smaller bodies, in direct
    proportion to their surface areas.

87
Black Body Radiation
  • The luminosity (energy loss per unit time) of a
    black body is proportional the surface area times
    the temperature to the 4th power

88
Black Body Radiation
  • What does this equation tell us?

89
Black Body Radiation
  • What does this equation tell us?
  • The luminosity, radius, and temperature of a
    black body are related measure any two values,
    you can compute the third one.

90
Black Body Radiation
  • The luminosity, radius, and temperature of a
    black body are related measure any two values,
    you can compute the third one.
  • Since stars are approximately black bodies, their
    location in the CMD indicates their radii.

91
Temperature-Luminosity Diagrams
  • Temperature is on the x-axis hotter stars are on
    the left, cooler ones on the right.
  • Luminosity is on the y-axis, more luminuous ones
    are at the top, the less luminuous ones are at
    the bottom.

92
Temperature-Luminosity Diagrams
  • Temperature is on the x-axis hotter stars are on
    the left, cooler ones on the right.
  • Luminosity is on the y-axis, more luminuous ones
    are at the top, the less luminuous ones are at
    the bottom.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
93
Temperature-Luminosity Diagrams
  • Lines of constant radius go something like this

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
94
Temperature-Luminosity Diagrams
  • Lines of constant radius go something like this

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
95
Temperature-Luminosity Diagrams
  • Lines of constant radius go something like this
  • Cool and luminous stars large radii.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
96
Temperature-Luminosity Diagrams
  • Lines of constant radius go something like this
  • Cool and luminous stars large radii.
  • Hot and faint stars small radii.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
97
Temperature-Luminosity Diagrams
  • Lines of constant radius go something like this
  • Cool and luminous stars large radii.
  • Hot and faint stars small radii.
  • Most stars are here, and there is not a large
    variation in radius.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
98
Temperature-Luminosity Diagrams
  • This diagram shows some well-known stars. Most
    of the bright stars you see without a telescope
    are giants.

99
Review Questions Chapter 6
  • 1. Why are Earth-based parallax measurements
    limited to the nearest stars?
  • 5. Why are hydrogen Balmer line strong in the
    spectra of medium-temperature stars and weak in
    the spectra of hot and cool stars?
  • 7. Why does the luminosity of a star depend on
    both its radius and its temperature?
  • 8. How can you be sure that giant stars really
    are larger than main-sequence stars?
  • 9. Why do astronomers conclude that white
    dwarfs must be very small?

100
Review Questions Chapter 6
  • 12. What observations would you make to study an
    eclipsing binary star?
  • 13. Why dont astronomers know the inclination of
    a spectroscopic binary? How do they know the
    inclination of an eclipsing binary?

17. If all of the stars in the photo here
are members of the same star cluster, then they
all have about the same distance. Then why are
three of the brightest stars much redder than the
rest? What kind of star are they?
101
Binary Stars
  • A binary system is when two stars are bound
    together by gravity. They orbit their common
    center of mass.

102
Detour The Two-Body Problem
  • Use Newtons Laws to describe the behavior of two
    objects under the influence of their mutual
    gravity.
  • We will apply it to binary star systems (e.g. a
    system consisting of two stars).

103
Center of Mass
  • For two point masses, the center of mass is along
    the line joining the two masses.
  • The center of mass is closer to the more massive
    body.

104
Center of Mass
  • Why is this useful? Two bodies acting under their
    mutual gravity will orbit in a plane about their
    center of mass.
  • Here is the case for equal masses.

105
Center of Mass
  • Why is this useful? Two bodies acting under their
    mutual gravity will orbit in a plane about their
    center of mass.
  • Here is the case for M1 2M2.

106
Center of Mass
  • Why is this useful? Two bodies acting under their
    mutual gravity will orbit in a plane about their
    center of mass.
  • Here is the case for M1 gtgt M2, for example
    the Sun and Earth.

107
Binary Stars
  • A binary system is when two stars are bound
    together by gravity. They orbit their common
    center of mass.
  • In some cases, you can see two stars move around
    each other on the sky.

108
Binary Stars
  • A binary system is when two stars are bound
    together by gravity. They orbit their common
    center of mass.
  • In some cases, you can see two stars move around
    each other on the sky.
  • These are visual binaries.

109
Binary Stars
  • A binary system is when two stars are bound
    together by gravity. They orbit their common
    center of mass.
  • In a visual binary, you can see two stars.
  • However, for most binary stars, their separation
    is very small compared to their distance, and
    from Earth they appear to be a single point.
  • How do you observe these types of binaries? Use
    spectroscopy!

110
Center of Mass
  • A star will appear to wobble when it is
    orbiting another body.
  • If the other body is another star, the wobble
    will be relatively large.
  • If the other body is a planet, the wobble will be
    very small.

111
Detecting the Wobble
112
Detecting the Wobble
  • In Astronomy, any motion can be broken down into
    two groups
  • Motion in the plane of the sky (e.g. east-west
    and north-south motion).

113
Detecting the Wobble
  • In Astronomy, any motion can be broken down into
    two groups
  • Motion in the plane of the sky (e.g. east-west
    and north-south motion).
  • Motion towards or away from us (e.g. radial
    velocities).

114
Detecting the Wobble
  • In Astronomy, any motion can be broken down into
    two groups
  • Motion in the plane of the sky (e.g. east-west
    and north-south motion).
  • Motion towards or away from us (e.g. radial
    velocities).
  • For a binary star, the decomposition depends on
    the orientation of the orbit

115
Detecting the Wobble
  • In Astronomy, any motion can be broken down into
    two groups
  • Motion in the plane of the sky (e.g. east-west
    and north-south motion).
  • Motion towards or away from us (e.g. radial
    velocities).
  • For a binary star, the decomposition depends on
    the orientation of the orbit
  • For an orbit seen face-on, all motion is in the
    plane of the sky.
  • For an orbit seen edge-on, the motion is also in
    the radial direction. The size of the radial
    velocity variations depend on the inclination of
    the orbit (the radial velocity is the true
    velocity times the sine of the inclination.)

116
Viewing Angle
  • The plane of the orbit is two dimensional, so
    depending on how that plane is tilted with
    respect to your line of sight you can see
    different things.

117
Detecting the Wobble
  • In Astronomy, any motion can be broken down into
    two groups
  • Motion in the plane of the sky (e.g. east-west
    and north-south motion).
  • Motion towards or away from us (e.g. radial
    velocities).
  • Motions in the plane of the sky are usually
    small, and typically one has to wait many years
    to see a relatively big shift.

118
Detecting the Wobble
  • In Astronomy, any motion can be broken down into
    two groups
  • Motion in the plane of the sky (e.g. east-west
    and north-south motion).
  • Motion towards or away from us (e.g. radial
    velocities).
  • Motions in the plane of the sky are usually
    small, and typically one has to wait many years
    to see a relatively big shift. One can see
    Sirius wobble over the course of decades (it has
    a very massive, but dark, companion).

119
Detecting the Wobble
  • In Astronomy, any motion can be broken down into
    two groups
  • Motion in the plane of the sky (e.g. east-west
    and north-south motion).
  • Motion towards or away from us (e.g. radial
    velocities).
  • Motions in the plane of the sky are usually
    small, and typically one has to wait many years
    to see a relatively big shift. We cant detect
    this motion in most binaries.

120
Detecting the Wobble
  • In Astronomy, any motion can be broken down into
    two groups
  • Motion in the plane of the sky (e.g. east-west
    and north-south motion).
  • Motion towards or away from us (e.g. radial
    velocities).
  • Motions in the plane of the sky are usually
    small, and typically one has to wait many years
    to see a relatively big shift. We cant detect
    this motion in most binaries.

121
Detecting Radial Velocities
  • Recall that radial velocities can be measured
    from Doppler shifts in the spectral lines

122
Detecting Radial Velocities
  • Recall that radial velocities can be measured
    from Doppler shifts in the spectral lines

Motion towards us gives a shorter observed
wavelength.
123
Detecting Radial Velocities
  • Recall that radial velocities can be measured
    from Doppler shifts in the spectral lines

Motion towards us gives a shorter observed
wavelength. Motion away from us gives a longer
observed wavelength.
124
Spectroscopic Binaries
  • Recall that radial velocities can be measured
    from Doppler shifts in the spectral lines
  • Here are two spectra of Castor B, taken at two
    different times. The shift in the lines due to a
    change in the radial velocity is apparent.

125
Spectroscopic Binaries
  • The radial velocity of each star changes smoothly
    as the stars orbit each other.
  • These changes in the radial velocity can be
    measured using high resolution spectra.

126
Spectroscopic Binaries
  • Recall from that radial velocities can be
    measured from Doppler shifts in the spectral
    lines

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
127
Spectroscopic Binaries
  • In some cases, you can see both stars in the
    spectrum.
  • In most cases, you can only see one star changing
    its radial velocity in a periodic way.

128
Binary Stars
  • A binary system is when two stars are bound
    together by gravity. They orbit their common
    center of mass.
  • In some cases, we can use binary stars to measure
    precise masses and radii for stars.

129
Center of Mass
  • Recall that m1r1m2r2
  • Also, note that velocity of the star is
    proportional to the distance to the center of
    mass since a star further from the COM has a
    greater distance to cover in the same amount of
    time.

130
Center of Mass
  • Recall that m1r1m2r2
  • Also, note that velocity of the star is
    proportional to the distance to the center of
    mass since a star further from the COM has a
    greater distance to cover in the same amount of
    time. This implies m1v1m2v2, or m1/m2v2/v1

131
Center of Mass
  • Recall that m1r1m2r2
  • Also, note that velocity of the star is
    proportional to the distance to the center of
    mass since a star further from the COM has a
    greater distance to cover in the same amount of
    time. This implies m1v1m2v2, or m1/m2v2/v1
  • The ratio of the velocities in inversely
    proportional to the mass ratio.

132
Center of Mass
  • Recall that m1r1m2r2
  • Also, note that velocity of the star is
    proportional to the distance to the center of
    mass since a star further from the COM has a
    greater distance to cover in the same amount of
    time. This implies m1v1m2v2, or m1/m2v2/v1
  • The ratio of the velocities in inversely
    proportional to the mass ratio. Also, the same
    is true for radial velocities.

133
Center of Mass
  • If you can see both stars in the spectrum, then
    you may be able to use Doppler shifts to measure
    the radial velocities of both stars. This gives
    you the mass ratio, regardless of the viewing
    angle (e.g. nearly face-on, nearly edge-on, etc.).

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
134
Stellar Masses
  • If you can see both stars in the spectrum, then
    you may be able to use Doppler shifts to measure
    the radial velocities of both stars. This gives
    you the mass ratio, regardless of the viewing
    angle (e.g. nearly face-on, nearly edge-on,
    etc.). This is usually useful information.

135
Stellar Masses
  • If you can see both stars in the spectrum, then
    you may be able to use Doppler shifts to measure
    the radial velocities of both stars. This gives
    you the mass ratio, regardless of the viewing
    angle (e.g. nearly face-on, nearly edge-on,
    etc.). This is usually useful information.
  • If you can find the viewing angle, then you can
    compute true orbital velocities and use Keplers
    Laws and Newtons theory to find the actual
    masses.

136
Viewing Angle
  • The plane of the orbit is two dimensional, so
    depending on how that plane is tilted with
    respect to your line of sight you can see
    different things.

137
Stellar Masses
  • If you can see both stars in the spectrum, then
    you may be able to use Doppler shifts to measure
    the radial velocities of both stars. This gives
    you the mass ratio, regardless of the viewing
    angle (e.g. nearly face-on, nearly edge-on,
    etc.). This is usually useful information.
  • If you can find the viewing angle, then you can
    compute true orbital velocities and use Keplers
    Laws and Newtons theory to find the actual
    masses. How do you find the viewing angle?

138
Stellar Masses
  • If you can see both stars in the spectrum, then
    you may be able to use Doppler shifts to measure
    the radial velocities of both stars. This gives
    you the mass ratio, regardless of the viewing
    angle (e.g. nearly face-on, nearly edge-on,
    etc.). This is usually useful information.
  • If you can find the viewing angle, then you can
    compute true orbital velocities and use Keplers
    Laws and Newtons theory to find the actual
    masses. Find eclipsing systems!

139
Definition
  • An eclipse, occultation, and transit essentially
    mean the same thing one body passes in front of
    another as seen from earth.

140
Eclipsing Systems and Stellar Radii
  • Eclipsing systems must be nearly edge-on, since
    the stars appear to pass in front of each other
    as seen from Earth.

141
Eclipsing Systems and Stellar Radii
  • The relative radii can be found by studying how
    much light is blocked, and for how long.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
142
Eclipsing Systems and Stellar Radii
  • The light curve depends on the relative sizes
    and brightnesses of the stars, and on the
    orientation.

143
Eclipsing Systems and Stellar Radii
  • The light curve depends on the relative sizes
    and brightnesses of the stars, and on the
    orientation.
  • Algol was known to be variable for a long time,
    and its periodic nature was established in 1783.

144
Accurate Masses and Radii From Binary Stars
  • The ideal binary systems are ones where both
    stars are seen in the spectrum (double-lined),
    and where eclipses are seen.

145
Accurate Masses and Radii From Binary Stars
  • The ideal binary systems are ones where both
    stars are seen in the spectrum (double-lined),
    and where eclipses are seen. Masses and radii
    accurate to a few percent can be derived from
    careful observations of these systems.

146
Accurate Masses and Radii From Binary Stars
  • The ideal binary systems are ones where both
    stars are seen in the spectrum (double-lined),
    and where eclipses are seen. Masses and radii
    accurate to a few percent can be derived from
    careful observations of these systems.
  • There are on the order of 100 such well-studied
    systems with main sequence stars. What do you
    do with this information?

147
Mass-Luminosity Relation
  • The stars form a tight sequence. This is another
    clue to the inner workings of stars!

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
148
Stellar Properties
  • The Sun and the stars are similar objects.
  • In order to understand them, we want to try and
    measure as many properties about them as we can
  • Temperature at the surface ---use spectral
    types
  • Power output (luminosity) --- flux and distance
  • Radius --- eclipsing binary stars
  • Mass --- eclipsing binary stars
  • Chemical composition

149
Review Questions Chapter 6
  • 1. Why are Earth-based parallax measurements
    limited to the nearest stars?
  • 5. Why are hydrogen Balmer line strong in the
    spectra of medium-temperature stars and weak in
    the spectra of hot and cool stars?
  • 7. Why does the luminosity of a star depend on
    both its radius and its temperature?
  • 8. How can you be sure that giant stars really
    are larger than main-sequence stars?
  • 9. Why do astronomers conclude that white
    dwarfs must be very small?

150
Review Questions Chapter 6
  • 12. What observations would you make to study an
    eclipsing binary star?
  • 13. Why dont astronomers know the inclination of
    a spectroscopic binary? How do they know the
    inclination of an eclipsing binary?

17. If all of the stars in the photo here
are members of the same star cluster, then they
all have about the same distance. Then why are
three of the brightest stars much redder than the
rest? What kind of star are they?
151
Review Questions Chapter 7
  • 1. What opposing forces are balanced in a
    stable star?
  • 3. How does the pressure-temperature thermostat
    control the nuclear reactions inside stars?
  • 6. Why is there a lower limit to the mass of a
    main sequence star?
  • 7. Why does a stars life expectancy depend on
    its mass?

152
Models of the Solar Interior
  • The interior of the Sun is relatively simple
    because it is an ideal gas, described by three
    quantities
  • Temperature
  • Pressure
  • Mass density

153
Models of the Solar Interior
  • The interior of the Sun is relatively simple
    because it is an ideal gas, described by three
    quantities
  • Temperature
  • Pressure
  • Mass density
  • The relationship between these three quantities
    is called the equation of state.

154
Ideal Gas
  • For a fixed volume, a hotter gas exerts a higher
    pressure

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
155
Hydrostatic Equilibrium
  • The Sun does not collapse on itself, nor does it
    expand rapidly.

156
Hydrostatic Equilibrium
  • The Sun does not collapse on itself, nor does it
    expand rapidly. Gravity and internal pressure
    balance

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
157
Hydrostatic Equilibrium
  • The Sun does not collapse on itself, nor does it
    expand rapidly. Gravity and internal pressure
    balance. This is true at all layers of the Sun.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
158
Hydrostatic Equilibrium
  • The Sun (and other stars) does not collapse on
    itself, nor does it expand rapidly. Gravity and
    internal pressure balance. This is true at all
    layers of the Sun.
  • The temperature increases as you go deeper and
    deeper into the Sun!

159
Models of the Solar Interior
  • The pieces so far
  • Energy generation (nuclear fusion).
  • Ideal gas law (relation between temperature,
    pressure, and volume.
  • Hydrostatic equilibrium (gravity balances
    pressure).

160
Models of the Solar Interior
  • The pieces so far
  • Energy generation (nuclear fusion).
  • Ideal gas law (relation between temperature,
    pressure, and volume.
  • Hydrostatic equilibrium (gravity balances
    pressure).
  • Continuity of mass (smooth distribution
    throughout the star).

161
Models of the Solar Interior
  • The pieces so far
  • Energy generation (nuclear fusion).
  • Ideal gas law (relation between temperature,
    pressure, and volume.
  • Hydrostatic equilibrium (gravity balances
    pressure).
  • Continuity of mass (smooth distribution
    throughout the star).
  • Continuity of energy (amount entering the bottom
    of a layer is equal to the amount leaving the
    top).

162
Models of the Solar Interior
  • The pieces so far
  • Energy generation (nuclear fusion).
  • Ideal gas law (relation between temperature,
    pressure, and volume.
  • Hydrostatic equilibrium (gravity balances
    pressure).
  • Continuity of mass (smooth distribution
    throughout the star).
  • Continuity of energy (amount entering the bottom
    of a layer is equal to the amount leaving the
    top).
  • Energy transport (how energy is moved from the
    core to the surface).

163
Models of the Solar Interior
  • Solve these equations on a computer
  • Compute the temperature and density at any layer,
    at any time.
  • Compute the size and luminosity of the star as a
    function of the initial mass.
  • Etc.

164
Stellar Models
165
Review Questions Chapter 7
  • 1. What opposing forces are balanced in a
    stable star?
  • 3. How does the pressure-temperature thermostat
    control the nuclear reactions inside stars?
  • 6. Why is there a lower limit to the mass of a
    main sequence star?
  • 7. Why does a stars life expectancy depend on
    its mass?

166
Nuclear Fusion
  • Summary 4 hydrogen nuclei (which are protons)
    combine to form 1 helium nucleus (which has two
    protons and two neutrons).
  • Why does this produce energy?
  • Before the mass of 4 protons is 4 proton masses.
  • After the mass of 2 protons and 2 neutrons is
    3.97 proton masses.
  • Einstein E mc2. The missing mass went into
    energy! 4H ---gt 1He energy

167
Controlled Fusion in the Sun
  • First, note that the rate of the p-p chain or CNO
    cycle is very sensitive to the temperature.
  • Rate (temperature)4 for p-p chain.
  • Rate (temperature)15 for the CNO cycle.
  • Small changes in the temperature lead to large
    changes in the fusion rate.
  • Suppose the fusion rate inside the Sun increased

168
Controlled Fusion in the Sun
  • First, note that the rate of the p-p chain or CNO
    cycle is very sensitive to the temperature.
  • Rate (temperature)4 for p-p chain.
  • Rate (temperature)15 for the CNO cycle.
  • Small changes in the temperature lead to large
    changes in the fusion rate.
  • Suppose the fusion rate inside the Sun increased
  • The increased energy heats the core and expands
    the star. But the expansion cools the core,
    lowering the fusion rate. The lower rate allows
    the core to shrink back to where it was before.

169
Odds and Ends
  • Why does L vary like (mass)4? E.g., why is an
    O-star about 10,000 times more luminous than the
    Sun when its mass is only 20 times the solar mass?

170
Odds and Ends
  • Why does L vary like (mass)4? E.g., why is an
    O-star about 10,000 times more luminous than the
    Sun when its mass is only 20 times the solar
    mass?
  • More massive stars need hotter interiors to be
    stable. The increased temperature leads to large
    increase in energy generation (the rate varies
    like (temperature)15.)

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
171
Odds and Ends
  • Why are there no stars more massive than about
    100 solar masses, and no stars with masses less
    than about 1/10 of a solar mass?

172
Odds and Ends
  • Why are there no stars more massive than about
    100 solar masses, and no stars with masses less
    than about 1/10 of a solar mass?
  • At the high end, the pressure rises rapidly with
    mass, and is stronger than gravity when the mass
    gets near 100 solar masses.

173
Odds and Ends
  • Why are there no stars more massive than about
    100 solar masses, and no stars with masses less
    than about 1/10 of a solar mass?
  • At the high end, the pressure rises rapidly with
    mass, and is stronger than gravity when the mass
    gets near 100 solar masses. The star is no longer
    stable!

174
Odds and Ends
  • Why are there no stars more massive than about
    100 solar masses, and no stars with masses less
    than about 1/10 of a solar mass?
  • At the low end, the core temperature does not get
    high enough to fuse hydrogen since the
    gravitational force is relatively weak.

175
Odds and Ends
  • Why are there no stars more massive than about
    100 solar masses, and no stars with masses less
    than about 1/10 of a solar mass?
  • At the low end, the core temperature does not get
    high enough to fuse hydrogen since the
    gravitational force is relatively weak. Brown
    dwarfs are such low-mass objects.

176
Review Questions Chapter 7
  • 1. What opposing forces are balanced in a
    stable star?
  • 3. How does the pressure-temperature thermostat
    control the nuclear reactions inside stars?
  • 6. Why is there a lower limit to the mass of a
    main sequence star?
  • 7. Why does a stars life expectancy depend on
    its mass?

177
Review Questions Chapter 7
  • What evidence can you cite that the space between
    the stars is not empty?
  • Why would an emission nebula near a hot star look
    red, while a reflection nebula near its star look
    blue?
  • 10. Why do astronomers rely heavily on infrared
    observations to study star formation?

178
Side Bar Observing Clouds
  • Ways to see gas
  • By reflection of a nearby light source. Blue
    light reflects better than red light, so
    reflection nebulae tend to look blue.
  • By emission at discrete wavelengths. A common
    example is emission in the Balmer-alpha line of
    hydrogen, which appears red.

179
Side Bar Observing Clouds
  • Ways to see dust
  • If the dust is warm (a few hundred degrees K)
    then it will emit light in the long-wavelength
    infrared region or in the short-wavelength radio.
  • Dust will absorb light blue visible light is
    highly absorbed red visible light is less
    absorbed, and infrared light suffers from
    relatively little absorption. Dust causes
    reddening.

180
Interstellar Dust
  • The dust is composed of tiny slivers of graphite
    and silicates, possibly coated with water ice.
  • Note that the scale on this diagram is 10-7
    meters!

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
181
Interstellar Dust
  • Light passing through an interstellar dust cloud
    will be dimmed.
  • However, the amount of dimming depends on the
    wavelength of the light blue light is scattered
    more easily than red light. The object appears
    redder.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
182
Why is the Sky Blue?
  • Blue light travels a relatively short distance
    before it is scattered by molecules in the air.
    Red light goes much further before being
    scattered.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
183
Intersteller Dust
  • Interstellar dust makes a star appear dimmer and
    redder if that star is behind a cloud of dust.

184
Interstellar Dust
  • Interstellar dust makes a star appear dimmer and
    redder if that star is behind a cloud of dust.

185
Giant Molecular Clouds
  • This nebula is in the sword of Orion. It is
    about 29 light years across and 1500 light years
    away.
  • Dark regions are apparent (obscuration by dust),
    as well as regions of glowing gas (heated by a
    nearby hot star). Image from Nick
    Strobels Astronomy Notes (http//www.astronomynot
    es.com)

186
Giant Molecular Clouds
  • This nebula is in the belt of Orion. Dark dust
    lanes and also glowing gas are evident.

187
Giant Molecular Clouds
188
Giant Molecular Clouds
  • Interstellar dust makes stars appear redder.

189
Giant Molecular Clouds
190
Review Questions Chapter 7
  • What evidence can you cite that the space between
    the stars is not empty?
  • Why would an emission nebula near a hot star look
    red, while a reflection nebula near its star look
    blue?
  • 10. Why do astronomers rely heavily on infrared
    observations to study star formation?

191
Review Questions Chapter 8
  • 4. How can star clusters confirm astronomers
    theories of stellar evolution?
  • Why cant a white dwarf star contract as it
    cools?
  • How are neutron stars and white dwarfs similar?
    How do they differ?
  • If neutron stars are hot, why arent they very
    luminous?
  • 23. How can a black hole emit X-rays?

192
Stellar Groupings
  • One way to get around sample biases is to study
    groups of stars bound by gravity. Why?
  • The distance across a group is relatively small,
    which means the stars in the group have roughly
    the same distance from us. This in turn means
    that ratios in apparent brightness are the same
    as the ratios of intrinsic luminosities.

193
Stellar Groupings
  • One way to get around sample biases is to study
    groups of stars bound by gravity. Why?
  • The groups are loosely bound, meaning that the
    stars must have formed together, rather than
    being captured after formation.

194
Stellar Groupings
  • One way to get around sample biases is to study
    groups of stars bound by gravity. Why?
  • The groups are loosely bound, meaning that the
    stars must have formed together, rather than
    being captured after formation. This means the
    stars in the group all have the same age and the
    same chemical composition.

195
Star Clusters
  • Star clusters can be roughly classified based on
    how tight they are.

196
Star Clusters
  • Star clusters can be roughly c
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