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Chapter 19 The Nature of the Stars

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Title: Chapter 19 The Nature of the Stars


1
CHAPTER 4STARS
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Careful measurements of the parallaxes of stars
reveal their distances.
  • The brightness of a star is not a good indicator
    of distance.
  • e.g., Polaris is closer than Betelgeuse but
    Betelgeuse appears brighter.
  • Distances to nearby stars can be measured using
    parallax.
  • Parallax is the apparent change in the position
    of an object do to a change in observing position.

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Distance Determination Methods
  • The angle subtended by an object
  • ?, is proportional to
  • For example, the angle subtended by the Moon is ?
    the angle subtended by the Sun.
  • Size of Object Sun gtgt Moon

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Distance Determination Methods
  • Distance to Sun gtgt Moon

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Trigonometric Parallax
Useful for relatively nearby stars
Earth
A nearby star appears to move with respect to
much more distant stars.
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  • For a skinny triangle,

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  • In trigonometric parallax,
  • distance depends only on
  • Angle measurement
  • Known value of 1 AU
  • Difficulty it currently does not work for d gtgt
    100ly (our immediate galactic neighborhood).
  • It allows us to calibrate STANDARD CANDLES
  • Suppose a star of a given type has a measured
    brightness, X, at a distance of 10ly.
  • The total brightness (or luminosity) is
  • L X4?d2

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  • Once we know L, we can find the distance to an
    identical star whose apparent brightness is Y by
    the same relationship

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Stellar Parallax As Earth moves from one side of
the Sun to the other, a nearby star will seem to
change its position relative to the distant
background stars. d 1 / p d distance to
nearby star in parsecs p parallax angle of that
star in arcseconds
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  • The current limitations to precision of
    measurement
  • Size of baseline. It would be easier to
    determine parallax
  • from Jupiter.
  • Resolving power of the telescope.
  • Example
  • Photographic plate gives uncertainty of about
    0.002 arc s.
  • If you want a precision of 10, you can only
    determine parallaxes
  • Up to 0.05 arc s, or d 1/0.02 50 pcs.

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In 1989, an astrometric satellite called
Hipparchus was launched,
with a resolving uncertainty of 0.0005 arc s.
This means that we could measure parallaxes of
0.005 arc s or, up to a distance of 1/0.005
200 pcs. About 1 million stars had their
parallaxes measured.
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FUTURE S I M PRECISION 1 MICROARC S AT 10
ACCURACY PARALLAX 10-5 DISTANCE 105
PARSECS WE WILL BE ABLE TO MEASURE PARALLAX TO
THE FAR EDGE OF OUR GALAXY
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Another direct method to determine the distances
to remote galaxies.
A relatively new method is to use Masers. Masers
are interstellar clouds that are easy to detect
because they emit intense microwave radiation.
The orbit of these masers around a galaxy can be
measured and used to calculate the distance to
the galaxy using the small-angle formula.
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If a stars distance is known, its luminosity can
be determined from its brightness.
  • As you get farther and farther away from a star,
    it appears to get dimmer.
  • Luminosity, L, doesnt change
  • Apparent brightness, b, does change following the
    inverse square law for distance.
  • b L / (4pd2)

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If a stars distance is known, its luminosity can
be determined from its brightness.
  • A stars luminosity can be determined from its
    apparent brightness if its distance is known.
  • L/L? (d/d?)2 x (b/b?)
  • Where L? the Suns luminosity

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Similarly, The distance to a star can be
determined from its apparent brightness if its
Luminosity is known. THIS IS THE BASIS FOR
DETERMINING DISTANCES BY MEANS OF
STANDARD CANDLES
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Luminosity Function As stars go, our Sun is
neither extremely luminous nor extremely dim.
It is somewhat more luminous than most nearby
stars of the 30 stars within 4 pc, only three
have a greater luminosity.
1 L? 3.86 X 1026 W
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  • For galaxies, we need appropriate standard
    candles with the properties
  • Intrinsically bright
  • Intrinsic brightness known.
  • Examples
  • Supernovae
  • Cepheid variables
  • Brightest elliptical galaxy in clusters of
    galaxies

L
P
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There are, in fact, two types of CEPHEIDS Type
I Population I found in open clusters. Type
II Population II found in globular clusters and
the central bulge of galaxies.
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  • Examples
  • Automobile headlights
  • Up to some distance ? angular separation
  • Beyond distance (when you cannot separate both
    headlights)
  • How bright do the combined headlights appear?
  • Apparent brightness ? 1/d2
  • In case 1., you need to know the distance or the
    separation between the headlights
  • In case 2., you need to know just how bright the
    headlights are.

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  • Standard Candle Method compares how bright an
    object appears to its intrinsic brightness.
  • Standard candles must be luminous and visible at
    large distances.
  • Standard candles must have known luminosities.
  • Standard candles should be easily identifiable at
    large distances.
  • Standard candles should be relatively common.

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  • Standard Candles
  • RR Lyrae variables
  • Cepheid variables
  • Tully-Fisher relation
  • Type Ia supernova
  • Tully-Fisher relationship for galaxies Tully
    and Fisher found that the broader the hydrogen
    21-cm line is for a galaxy, the more
    intrinsically luminous the galaxy is.

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Different methods of determining stellar distances
The Distance Ladder
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Magnitude(concept)
  • Apparent magnitude m? Observed
  • Absolute magnitude M
  • Apparent magnitude that a star would have if it
    were at a d 10 pc
  • Reflects intrinsic brightness or luminosity

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Historical- Hipparchus (146 B.C.E)
  • Magnitude 1 brightest
  • 6 faintest observable with naked eye
  • Divided into 5 equal intervals
  • Eyes response is logarithmic

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Astronomers often use the magnitude scale to
denote brightness.
  • Historically, the apparent magnitude scale runs
    from 1 (brightest) to 6 (dimmest).
  • Today, the apparent magnitude scale extends into
    the negative numbers for really bright objects
    and into the 20s and 30s for really dim objects.
  • Absolute magnitude, on the other hand is how
    bright a star would look if it were 10 pc away.

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Astronomers often use the magnitude scale to
denote brightness.
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Stars and Heavy Element Synthesis
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The Hertzsprung-Russell Diagram(H-R Diagram)
  • Stars tend to congregate in specific regions of
    this diagram.
  • This behavior can be explained in terms of the
    evolution of stars

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Hertzsprung-Russell (H-R) diagrams reveal the
different kinds of stars.
HR DIAGRAM Absolute magnitude vs
temperature or luminosity vs spectral type
39
There is a relationship between mass and
luminosity for main-sequence stars.
Bigger is brighter!
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The Hertzsprung-Russell Diagram(H-R Diagram)
  • Interesting points
  • Mass range (surface temperature range) ltlt
    Luminosity range
  • In fact,
  • L ? M3.5
  • Timescale (or lifetime) of stars
  • ? ? (M/L) ? (M/M3.5) (1/M2.5)
  • (massive stars lead shorter lives)

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As density of clouds increases, collisions
between atoms also increase. But as the
temperature decreases, their relative velocity
decreases. Electrical
bonds take hold and molecules
develop. ? Collis
ions between molecules sets them into rotational
and vibrational motions ? IR and
Radio emission ?
Further Cooling To date, more than
60 molecules have been detected in clouds,
including
ORGANIC molecules. We are currently
trying to detect amino acids, sugars, etc.
46
STAR FORMATION
As gravitational forces equal or begin to
dominate dispersive forces (temperature),
gravitational contraction proceeds. Angular
momentum produces flat, pancake-like
structures. The outer regions will not contract
further because of centrifugal forces. They will
be left behind, and in some instances, may
eventually end up as planets. The inner region of
the pancake continues to contract.
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Contraction Releases Gravitational Energy
  • 1/2 of the inner released gravitational energy is
    radiated away
  • 1/2 of the released gravitational energy
    increases the objects temperature
  • Even though T?, it will never be again able to
    disperse the object because during the
    contraction, energy is forever lost to the object.

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  • The object becomes opaque, and hot
  • ? proto-star
  • Energy source ? gravitational
  • - does not last too long.
  • Located to the upper (large R), right- hand
    (cool) side of the HR diagram
  • Eventually the central region reaches about 5
    million K.
  • Nuclear processing begins

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  • The released energy increases T ? increases P ?
    halts the contraction
  • The star has reached the MAIN SEQUENCE, where it
    will remain relatively unchanged as long as there
    is any H fuel left for nuclear processing

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  • The details of formation determine whether
  • A single star
  • A double or multiple system of stars
  • Or a planetary system
  • forms.

51
What determines the properties of a MAIN SEQUENCE
star?
  • Hydrostatic equilibrium
  • M ??V ? ??R
  • P(R) gt P(R?R)
  • ?P P(R?R) P(R)
  • -gM -g? ?R
  • ?P/ ?R -g?

52
What determines the properties of a MAIN SEQUENCE
star?
2. The Temperature profile (larger T inside,
lower T outside) is such that the net energy flow
exactly equals the energy produced at the stars
center. ? very stable condition
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A stars color depends on its surface temperature.
Wiens law the hotter the object, the shorter the
wavelength of its maximum emission.
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UBV photometry is the process of systematically
looking at intensity emitted by a star in three
wavelength (color band) regions. U ultraviolet,
B blue, V visual
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The spectra of stars reveal their chemical
compositions as well as surface temperatures.
  • In the late 19th Century, spectra was obtained
    for hundreds of thousands of stars.
  • These stellar spectra were grouped into a
    classification scheme of spectral types A through
    O by a team at Harvard.
  • Today we recognize the spectral types O, B, A, F,
    G, K, and M as running from hottest to coolest.

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The spectra of stars reveal their chemical
compositions as well as surface temperatures.
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The spectra of stars reveal their chemical
compositions as well as surface temperatures.
  • O B A F G K M
  • hottest to coolest
  • bluish to reddish
  • Further refined by attaching an integer, for
    example F0, F1, F2, F3 F9 where F1 is hotter
    than F3
  • An important sequence to remember
  • Our Best Astronomers Feel Good Knowing More
  • Oh Boy, An F Grade Kills Me
  • Oh Be a Fine Girl (or Guy), Kiss Me

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Strengths of absorption lines (our Sun is a G2
and has strong Fe II and Ca II lines)
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Stars come in a wide variety of sizes
  • Stefan-Boltzmann law relates a stars energy
    output, called LUMINOSITY, to its temperature and
    size.
  • LUMINOSITY 4pR2sT4
  • LUMINOSITY is measured in joules per square meter
    of a surface per second and s 5.67 X 10-8 W m-2
    K-4
  • Small stars will have low luminosities unless
    they are very hot.
  • Stars with low surface temperatures must be very
    large in order to have large luminosities.

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Hertzsprung-Russell (H-R) diagrams reveal the
different kinds of stars.
  • Main sequence stars
  • Stars in hydrostatic equilibrium found on a line
    from the upper left to the lower right.
  • Hotter is brighter
  • Cooler is dimmer
  • Red giant stars
  • Upper right hand corner (big, bright, and cool)
  • White dwarf stars
  • Lower left hand corner (small, dim, and hot)

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Determining the Sizes of Stars from an HR Diagram
  • Main sequence stars are found in a band from the
    upper left to the lower right.
  • Giant and supergiant stars are found in the upper
    right corner.
  • Tiny white dwarf stars are found in the lower
    left corner of the HR diagram.

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Details of a stars spectrum reveal whether it is
a giant, a white dwarf, or a main-sequence star.
Both of these stars are spectral class B8.
However, star a is a luminous super giant and
star b is a typical main-sequence star. Notice
how the hydrogen absorption lines for the more
luminous stars are narrower.
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Luminosity classes
Details of a stars spectrum reveal whether it is
a giant, a white dwarf, or a main-sequence star.
  • Class I includes all the supergiants.
  • Class V includes the main sequence stars.
  • e.g., the Sun is a G2 V

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Binary star systems provide crucial information
about stellar masses.
  • Double star a pair of stars located at nearly
    the same position in the night sky.
  • Optical double stars stars that lie along the
    same line of sight, but are not close to one
    another.
  • Binary stars, or binaries stars that are
    gravitationally bound and orbit one another.
  • Visual binary binaries that can be observed
  • Spectroscopic binary binaries that can only be
    detected by seeing two sets of lines in their
    spectra
  • Eclipsing binary binaries that cross one in
    front of the other.

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Binary Star Krüger 60 (upper left hand corner)
About half of the stars visible in the night sky
are part of multiple-star systems.
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There is a relationship between mass and
luminosity for main-sequence stars.
Bigger is brighter!
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There is a relationship between mass and
luminosity for main-sequence stars.
Bigger is brighter!
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Spectroscopy makes it possible to study binary
systems in which the two stars are close together.
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Light curves of eclipsing binaries provide
detailed information about the two stars.
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Light curves of eclipsing binaries provide
detailed information about the two stars.
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Light curves of eclipsing binaries provide
detailed information about the two stars.
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Light curves of eclipsing binaries provide
detailed information about the two stars.
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