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Chapter 11 Stars

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Title: Chapter 11 Stars


1
Chapter 11 Stars
  • Properties of Stars
  • Classifying Stars
  • Hertzsprung-Russel (H-R) Diagram
  • Star Clusters
  • Open and Globular Clusters

2
Properties of Stars
  • Mass The single most important property that
    determines other properties of the star.
  • Luminosity The total amount of energy (light)
    that a star emits into space.
  • Temperature surface temperature, closely
    related to the luminosity and color of the star.
  • Spectral type closely related to the surface
    temperature
  • Size together with temperature determine the
    luminosity

3
What can we measure directly?
  • The Easy Ones
  • Apparent brightness a well-calibrated detector.
  • Temperature spectroscopy
  • Spectral type spectroscopy
  • The Hard ones
  • Distance stellar parallax, but the stars are so
    farrrrr away
  • Size The stars are so far away. Their small
    angular size makes it really difficult to be
    measured directly.
  • Mass Newtons version of Keplers Third Law
  • Need to find the right targets

4
The Apparent Brightness
  • Apparent brightness
  • The brightness of the a star as it appears to our
    eyes (or detectors).
  • It depends on both the luminosity AND distance
    between the star and the Earth.
  • The apparent brightness of a star is related to
    its luminosity and distance by the formula
  • The total energy in this cone is fixed
  • At a larger distance from the star, the same
    amount of energy is spread into a larger area.
    Thus, the apparent brightness of a star is lower
    if we are further away from it.

5
The Magnitude System
  • Apparent magnitude describes the relative
    brightness of objects as they appears in sky.
  • A difference of 5 magnitudes is equivalent to a
    factor of 100 difference in apparent brightness.
  • ? 1st magnitude star is 100 times brighter than
    a 6th magnitude star.
  • A difference of one magnitude is a factor of 2.51
    difference in brightness.
  • The larger the magnitude, the fainter the object
  • Objects with negative magnitude appear brighter
    than objects with positive apparent magnitude.
  • Apparent magnitude mv of selected objects
  • The brightest star in the in night time sky,
    Sirius, is mv -1.4
  • The Sun mv -27
  • The full Moon is -13
  • Maximum brightness of
  • Venus mv -4.7
  • Mars mv -2.9
  • Jupiter mv -2.8
  • Large Magellantic Cloud mv 0.9
  • Andromeda galaxy mv 4.3
  • Faintest star visible to human eyes mv 6

6
The Absolute Magnitude
  • A stars absolute magnitude Mv is the apparent
    magnitude it would have if it were at a distance
    of 10 parsecs (32.6 light-years) from Earth.
  • The Suns absolute magnitude is Mv 4.8
  • Sirius Mv 1.4
  • Betelgeuse Mv -5.1
  • Apparent magnitude tells us nothing about the
    luminosity of the objects, but it tell us how
    difficult it is to see the objects in the sky.
  • Absolute magnitude, on the other hand, is
    directly related to the luminosity of the object.
    But it does not tell us how bright they appear in
    the sky.

Astronomical Distance
7
Measuring the Temperature of Stars
  • Everything with a temperature emit thermal
    radiation. We can measure the temperature of the
    stars or any object by studying the shape of
    their overall spectra.
  • Black Body
  • An idealized perfect light absorber that absorbs
    all the photons that strikes it (no reflection).
    It re-emits the absorbed energy through thermal
    radiation, with a spectrum characterized by the
    blackbody spectrum.
  • The shape of the blackbody spectrum is always the
    same, independent of its temperature.
  • The peak position (in wavelength) of the
    blackbody spectrum depends only on the
    temperature, independent of the blackbodys
    composition, or size, etc.

8
Spectral Type of Stars
  • Spectral type is closely related to temperature

9
Spectral Type and Temperature
  • The spectral features of the stars are closely
    related to the surface temperature of the star
    because the formation of ionized atoms, the
    excitation state of the atoms, and the existence
    of molecules in the stellar atmosphere strongly
    depends on the temperature
  • High temperature
  • ? Ionized atoms
  • Medium temperature
  • ? Neutral atoms
  • Low temperature
  • ? Molecules

10
Determination of Distance
  • Stellar Parallax
  • Knowledge of the distance to the stars is crucial
    for our determination of the luminosity of stars
  • Current technology allows us to determine the
    distance accurately to within a few hundred
    light-years.
  • Hipparcos mission (European Space Agency)
    measured the stellar parallax of roughly 100,000
    stars with precision of a few milli-arcseconds.
    So, it can measure distance of star up to 1,000
    light-years away

Simulation of Stellar Parallax
11
Astronomical Distance Units
  • Light-year
  • The distance light travels (in vacuum) in one
    year.
  • one light-year is 10 trillion (1013) km
  • Parsec parallax arcsecond
  • One parsec the distance to an object with a
    parallax angle of 1 arcsecond.
  • One parsec equals to 3.26 light-year.
  • kiloparsecs 1,000 parsecs.
  • megaparsecs 1,000,000 parsec.

Absolute Magnitude
12
Determination of Stellar Mass
  • Mass is the single most important property of a
    star. But it is also difficult to measure
  • The most dependable method we have for measuring
    the mass of distant stars is Newtons version of
    Keplers Third Law of orbital motion (Problem 33,
    Chapter 4).
  • Recall that
  • So, if we can find
  • two stars (binary star system) orbiting each
    other, and
  • if we can measure their
  • rotational period p, and
  • semi-axis a of the orbit,
  • then we can determine their masses.

13
Binary Star Systems
  • Binary star systems are formed by two stars that
    are gravitationally bounded, and they orbit each
    other.
  • About 50 of the stars are in binary star system.
    There are three categories of binary star
    systems
  • Visual Binary a pair of stars that we can see
    distinctly (with a telescope) as the stars orbit
    each other.
  • Eclipsing Binary is a pair of stars that orbit
    in the plane of our line of sight. The stars are
    not resolved, but we can see the effects of the
    stars blocking each other in their combined
    light-curve.
  • Spectroscopic Binary in some binary system, we
    cannot see the two stars, nor can we see their
    light curve changes, but we can see the motion of
    the stars from Doppler effect measurement of the
    spectra.

14
Binary Star Systems
Two stars appearing close to each other in the
sky do not necessarily means that they are a
binary system.
15
Visual Binary Sirius
Sirius (in constellation Canis Major) is the
brightest star in the night-time sky (magnitude
-1.4). It is a visual binary system. Sirius A
(the larger of the two) is a main sequence star
with spectral type A0, and Sirius B is a white
dwarf.
Hubble Space Telescope image of Sirius
Sirius A B time sequence
White Dwarf
16
Eclipsing Binary
  • About 50 of the stars are in binary star
    system. There are three categories of binary star
    systems
  • Eclipsing Binary is a pair of stars that orbit
    in the plane of our line of sight, (measuring the
    time curve)

Animations source http//en.wikipedia.org/wiki/S
pectroscopic_binary
17
Algol Eclipsing Binary
  • Algol (the demon star) is in the constellation
    of Perseus.
  • Algol A main sequence star, more massive.
  • Algol B subgiant, less massive.
  • The Algol Paradox
  • Why is the more massive Algol A evolve slower
    than the less massive Algol B? (Next chapter).

18
Spectroscopic Binary
  • Sometimes only the spectrum from one star is
    seen, the other star is too dim.
  • Sometimes two sets of spectra can be seen at the
    same time
  • Sometimes more than two sets of spectra can be
    seen
  • Mizar is a visual binary system in the
    constellation of Big Dipper.
  • Each star in the visual binary system is also a
    spectroscopic binary!

19
Eclipsing Binary and Stellar Mass Measurements
  • Among the three types of binary star systems,
    the eclipsing binary system is most important for
    the determination of stellar mass, because
  • Determination of the stellar mass requires
    knowledge of the orbital period and distance (in
    real distance unit, not in angular separation).
  • Orbital period is easy to measure, but distance
    between the stars is difficult to determine.
  • For visual binary, we need to know the distance
    from Earth to the stars before we can determine
    the separation between the stars in the binary
    system.
  • For spectroscopic binary, we can calculate the
    separation between the stars if we know their
    orbital speed. However, we can only determine the
    line-of-sight speed of the binary system from
    Doppler measurement. If the orbits are tilted
    with respect to our line-of-sight, then we under
    estimate the orbital speed.
  • If an eclipsing binary is also a spectroscopic
    binary, then we know its true orbital speed, and
    can determine the separation between the two
    stars. Then, the masses of the stars can be
    determined!

20
Luminosity
  • To directly measure the luminosity of a star
    (lets say, the Sun), we will need to surround
    the Sun completely with detectors, which is
    impossible.
  • We can infer the luminosity of the Sun if we know
  • the distance to the star, and
  • the stars apparent brightness
  • Further more, we need to assume that
  • the star emits energy uniformly in all direction
  • Then we can calculate its luminosity by the
    formula

d
The total area of the sphere with a radius of r
is 4?d2
21
Quiz Which Star Has Higher Luminosity?
  • The apparent brightness decrease as d 2
  • The brightness of star A is 10 1 10
  • The brightness of star B is 1 102 100 if
    observed at distance 1
  • ? Star B is 10 times more luminous than A!

The photons contained in box A are spread into an
area 4 times as large in box Y which is twice the
distance from the star as X.
X
Y
22
Luminosity of Selected Stars
23
Luminosity and Distance Chicken and Egg
Most of the time, we need measurement of distance
to calculate the luminosity. Howver, if we can
determine the luminosity of an object with other
methods (independent of distance measurement,
such as the luminosity of supernovae), then we
can derive the distance to the object from
measurement of their apparent brightness.
24
Direct Measurement of the Size of the Stars
  • Except for the Sun, all the stars in the sky
    are very far away, and their angular sizes (the
    size of the star as it appears to observers on
    Earth, not the physical size) are all very small.
    Although the theoretical resolving power of
    modern large telescopes (such as the Keck
    telescope with 10-meter aperture) is about 0.01
    arcseconds in the visible wavelength, it is
    difficult to realize the full resolution of the
    large telescopes due to atmospheric seeing
    effects.
  • Interferometry have directly measure the angular
    size of stars. Direct measurement by
    interferometry can achieve about 0.01 arcseconds
    angular resolution.
  • The angular size of Betelgeuse was first observed
    using interferometry in 19210.051 arcseconds.
  • R Doradus (in constellation Dorado in the
    southern hemisphere) is the star with the largest
    observed angular size 0.057 arcseconds.
  • 0.057 arcseconds is equal to 0.000016 degrees!
  • If we know the angular size and the distance of
    a star, we can derive its physical size
  • Size of star angular size radian ? distance

25
Optical Interferometry
  • The technique of combining images from multiple
    telescopes to obtain very high resolution
    imagesRecall that the resolving power of
    telescopes is fundamentally limited by the size
    of the telescope.
  • However, it is not necessary to build a single
    telescope with sufficient size to achieve the
    required resolution. Theoretically, multiple
    small telescopes separated by a large distance
    can achieve the same resolution of that of a
    single large telescope.
  • The two 10-meter Keck Telescopes at Mauna Kea are
    separated by 85 meters distance. When they are
    used together as an interferometer, the
    theoretical resolution is equivalent to that of a
    single 85-meter diameter telescope.
  • Interferometry is routinely used for observation
    in radio frequency.

26
Betelgeuse and R Doradus
  • The physical size of Betelgeuse (a red
    supergiant) is roughly 500 times the size of the
    Sun, or 4.6 AU (radius of 2.3 AU, or 345 million
    km).
  • The size of R Doradus (a red giant) is 370 times
    the size of the Sun, or 3.4 AU (radius of 1.7
    AU).
  • If R Doradus or Betelgeuse are placed at the
    center of our solar system, then their surface
    would extends beyond the orbit of Mars (1.5 AU,
    or 225 million km).

Image of hot spots on Betelgeuse from
http//www.mrao.cam.ac.uk/telescopes/coast/betel.
html using interferometric technique.
Giants and Supergiants
27
Indirect Determination of the Size of Stars
  • Since the stars are so far away, we can only
    directly measure the angular size of just about
    10 stars by interferometric technique so far.
    However,
  • if we know the luminosity (from apparent
    brightness and distance measurements) and the
    temperature of the stars, then we can calculate
    their physical size
  • Assuming that stars are blackbody
  • The energy output of a unit surface area on the
    surface of the star is determined by its
    temperature (Stefan-Boltzman Law)
  • The total energy output (luminosity) therefore
    depends on the temperature and its total surface
    area, which is related to its size.
  • where r is the radius of the star.
  • We can then calculate the size of the star by

28
Properties of Stars Summary
  • Mass range 0.08 Msun to 100 Msun
  • Luminosity range 0.00001 Lsun to 1,000,000 Lsun
  • Size range 0.01 Rsun for white dwarf to 1,000
    Rsun for supergiants.
  • Temperature range 3,000 K for M star to 40,000
    for O stars.

29
  • Properties of Stars
  • Classifying Stars
  • Spectral Type and Luminosity Class
  • Hertzsprung-Russel (H-R) Diagram
  • Main Sequence Stars
  • Giants and Supergiants
  • White Dwarf
  • Star Clusters
  • Open and Globular Clusters

30
Clues to Relationships Between the Properties of
Stars
  • General trends of the stars
  • Most of the very brightest stars are reddish in
    color.
  • If we ignore those relatively few bright red
    stars, theres a general trend to the
    luminosities and colors among all the rest of the
    stars
  • The brighter ones are white with a little bit of
    blue tint,
  • the more modest ones are similar to our Sun in
    color with a yellowish white tint, and
  • the dimmest ones are barely visible specks of
    red.

31
Hertzsprung-Russell Diagram
  • Since there appears to be a strong correlation
    between luminosity and color (temperature), we
    put all the stars on a Luminosity Temperature
    plot, and this is what it looks like
  • Properties of Stars shown in the H-R Diagram
  • Luminosity (log scale).
  • Temperature and spectral type
  • Size
  • Mass of the main sequence
  • Lifetime

32
Hertzsprung-Russell Diagram
  • Notice that
  • Temperature scale decreases from left to right.
  • The scale of luminosity is in power of 10 (log
    scale).
  • Mass increases from lower right to upper left
  • Size increases from lower left to upper right.

33
Classification of Stars in H-R Diagram
  • The Main Sequence stars
  • healthy stars, fusing hydrogen in the core.
  • High-mass, high-luminosity, high-temperature, and
    short-lived stars on the upper-left-hand corner
  • Low-mass, low-luminosity, low-temperature, and
    long-lived stars on the lower-right-hand corner
  • The Supergiants,
  • The Giants,
  • Supergiants and giants are dying stars, fusing
    helium and heavier elements.
  • The White Dwarfs.
  • dead stars, exposed core of dead main-sequence
    stars.

34
Classification of Stars
  • Full classification of stars includes both
    spectral type and luminosity class
  • Spectral type OBAFGKM
  • Luminosity Class in descending order
  • I Supergiants
  • II Bright giants
  • III Giants
  • IV Subgiants
  • V Main-sequence stars
  • The full classification of a star includes both a
    spectral type and a luminosity class
  • The Sun is a G2 V
  • Proxima Centauri is M5 V
  • Betelgeuse is M2 I
  • Sirius A A1 V
  • Sirius B DA2 V
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