Chapter 11 Surveying the Stars

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Chapter 11Surveying the Stars

• Chapter Outline
• Properties of Stars
• Classifying Stars
• Star Clusters

3/30/2006 1104 AM
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11.1 Properties of Stars

• How luminous are stars?
• How hot are stars?
• How massive are stars?

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Is knowing the distance to stars important in
understanding stars? If so, why?

• Yes, the distance permits us to determine the
  absolute properties of stars, such as luminosity,
  radius, and mass.
• Otherwise, we are restricted to relative values,
  which is a much weaker understanding of stars.

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Stellar Parallax
Parallax - annual apparent shift in position of
nearby star relative to very distant stars due
to Earth's orbital motion Ground-based limited to
about 0.01 arcseconds Satellite limit is about
0.001 arcseconds
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Distance Units

• Light Year - distance light travels in one year
  at the rate of 300,000 km/s (186,000 miles/s)
• 1 ly 9.46 x 1012 km
• Example - Proxima Centauri, nearest star, is 4.2
  ly
• Parsec - (parallax of one second of arc) the
  distance at which one AU subtends an angle of one
  second of arc
• 1 pc 3.26 ly 3.09 x
  1013 km
• Example - Proxima Centauri is 1.3 pc from the
  Solar System
• Formula d (in parsecs) 1 / p (in arcseconds)

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Parallax Angle Depends on Distance
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106 K
105 K
Ionized Gas (Plasma)
State of Matter is Determined by Temperature
(Energy Density)
104 K
103 K
Neutral Gas
Molecules (Liquid)
102 K
10 K
Solid
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Thermal Sources of Radiation
An object of fixed size grows more luminous as
its temperature rises.
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Relationship between a stars luminosity, radius,
and surface temperature

• Stars come in a wide variety of sizes

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Luminosity for Stars

• Luminosity - amount of electromagnetic radiation
  over all wavelengths emitted by stars entire
  photosphere per unit of time
• Measure in watts ( joule/s) or erg/s
• Formula L (4pR2)(sT4)
• Luminosities known for several hundred stars
• Examples Lsun 3.8 x 1026 watts
• LProxima Centauri
  0.0006Lsun
• LBetelgeuse 38,000Lsun
• Apparent brightness (luminosity-distance formula)
• bstar Lstar / (4pdistance2)

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Inverse-Square Law

• Must know true brightness of class of stars
  stars membership in a class can be based on
• Spectral type
• Luminosity type
• Variability
• Association, etc.
• Calculate distance from observed apparent
  brightness by inverse-square law

Two stars of same intrinsic brightness 1st star 2
times more distant than 2nd star, observed
brightness of 1st star compared to 2nd reduced by
factor of 22 4 (inversely as square of 2 times
distance) 1st star 3 times more distant,
reduction 32 9 1st star 4 times more distant,
reduction 42 16
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Variable Stars

• Variable stars - vary in luminosity either
  periodically, semi-periodically, or in sudden
  outbursts
• Pulsating variables - stars that undergo regular
  expansion and contraction of radius, L ? R2T4
• Explosive variables - stars that expel material
  in an eruptive outburst either once or several
  times
• Less than 1 of stars are conspicuously variable,
  larger percentage possess very small variability

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Magnitude System of Brightness

• Hipparchus (2nd century BC) measured (naked eye)
  apparent brightness of stars assigning them to 1
  of 6 magnitude categories
• Bright stars - 1st magnitude
• Faintest stars - 6th magnitude
• Apparent magnitude - logarithmic measure of
  apparent brightness
• Ratio of apparent brightness of 1st to 6th
  magnitude defined to be 1001
• Formula b1st/b6th 100 2.5125 2.512(6-1)

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Magnitude Scale

• Apparent scale is an inverted scale
• Bright stars are algebraically small numbers
  (mlt0)
• Faint stars are algebraically large numbers (mgt0)
• Formula b1/b2 2.512(m2-m1)

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Apparent Magnitudes for Bright Stars in Orion
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Absolute Magnitude

• Absolute magnitude - apparent magnitude star
  would have at distance of 10 pc or 32.6 ly
• Formula B/b (d/10 pc)2 2.512(m-M)

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Stars of Different Colors
Hubble Space Telescope view along the plane of
our Galaxy showing that stars come in many
different colors.
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Does a stars color depend on temperature? If
so, the temperature of what?

• Yes
• Temperature of its photosphere.
• Stars are thermal sources of radiation.

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Color Indices - Temperature

• Slope of thermal radiation curve through the
  visual depends on temperature
• Ratio of brightness in one part of spectrum, such
  as blue, to that in another part, such as green,
  depends on temperature
• Ratio of brightness is called a color index or
  just a color

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11.2 Classifying Stars

• How do we classify stars?
• Why is a stars mass its most important property?
• What is a Hertzsprung-Russell diagram?

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Can temperature be determined by the photospheric
absorption spectrum of a star?

• Yes, the ability of any atom or ion to absorb
  radiation at selected wavelengths depends on the
  temperature and density of the matter in which
  the atom or ion is located (the photosphere of
  the star).

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Hydrogen versus Temperature
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Spectral Classification

• Spectral classification - grouping stars
  according to similarities in violet, blue, and
  green portions of visible spectrum
• Seven spectral classes - O, B, A, F, G, K, M
• Each spectral class subdivided into 10 spectral
  types
• Spectral class A subdivided into spectral types
• A0, A1, A2, A3, A4, A5, A6, A7, A8,
  A9
• Spectral class O is exception, subdivided into
  O4, O5, O6, O7, O8, O9

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Stellar Spectral Types
H?
H?
H?
H?
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Stellar Spectral Sequence
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Elements, Spectral Type and Temperature
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Meaning of Spectral Classification

• Terminology for direction along spectral sequence
• Early-type stars - toward spectral classes O, B,
  A
• Late-type stars - toward spectral classes G, K, M
• Spectral classification grades stars according to
  photospheric temperature (66 bins).
• Not chemical composition
• Spectral appearance of star depends on
  temperature and density of the photosphere.

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Some Nearby Stars (lt12 ly)
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Some Bright Stars
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How is the mass of a star determined? Are there
any restrictions in determining mass?

• The only method for determining mass is through
  the motion in which stars exert significant
  gravitational influence on other stars, such as
  in a binary system.
• Restrictions
• Must be able to determine orbits or path.
• Sum of the masses of both stars in a binary are
  determined.

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Binary Stars

• Binary system - two (or more) stars held by
  mutual gravitational attraction

Sirius
Center of Mass
ds
Ms
White Dwarf
dwd
Mwd
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Binary Star Orbits
Star 1
Center of Mass
Star 2
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Binary Star Classification

• Visual binaries - two or more stars observed
• Widely separated in general
• Fairly close to Solar System in general
• Spectroscopic binaries - appears as single star,
  Doppler shifts reveal binary nature
• Double-line systems - absorption spectrum of both
  stars visible
• In general, not widely separated pair of stars
• Single-line systems - absorption spectrum of only
  brighter star visible and undergoing Doppler
  shifts second star too faint
• Eclipsing binaries - systems in which one star
  passes in front of other star
• Orbit plane contains line of sight
• Relative few systems, but important for amount of
  information obtainable on star properties

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Orbit of 70 Ophiuchi

• Visual binary
• Orbit is that of fainter star relative to
  brighter
• Keplers third law yields sum of masses for system

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Spectroscopic Binary Systems
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Eclipsing Binary Systems
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Occurance of Binary Systems

• Percentage of all stars that are part of binary
  system may be as high as 50 or higher
• Probable that all stars form in companion
  relation with and/or
• Other stars
• Brown dwarfs
• Jovian-like planets
• Terrestrial-like planets
• Even smaller bodies

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H-R Diagram

• 1911-13, Hertzsprung and Russell develop H-R
  diagram
• H-R diagram - luminosity verses surface
  temperature
• Horizontal axis - photospheric (surface)
  temperature
• Spectral type
• Color index
• Vertical axis luminosity
• Absolute visual magnitude
• Stars group to define definite regions
• Suggests common set of physical processes applies
  to all stars in particular region
• Each region represents a stage in the evolution
  of stars

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The correlation in the H-R diagram between
luminosity and temperature is due to what
physical law?

• Stars radiate like blackbodies.
• L 4?R2?T4 ? R2T4
• R radius
• T photospheric temperature (K)

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Radii for Various Stars
Largest red stars 1000 Rsun Smallest red
stars 0.1 RSun
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Luminosity Classes

• Luminosity class - luminosity classification that
  is obtained from the spectra of stars (more
  subtle than temperature effects).
• Nomenclature for luminosity classes
• I Supergiants
• II Bright giants
• III Giants (red giants)
• IV Subgiants
• V Main-sequence (dwarf stars)

B8 supergiant Rigel, 70000 Lsun
B8 main sequence Algol, 100 Lsun
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Two different types of star classes

• Spectral class
• O, B, A, F, G, K, M, L, T
• Os and Bs are very hot, Blue white stars
• M, L, T are much cooler and radiate in red light
• Luminosity class
• Ia and Ib are supergiants
• II, III, and IV are giants and subgiants
• V are main sequence stars

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• On the H-R diagram, giant and supergiant stars
  lie above the main sequence, while white dwarfs
  are below the main sequence

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Hertzsprung-Russell (HR) Diagram
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Mass-Luminosity Relation for Main-Sequence Stars

• Observation - masses increase from spectral class
  M to O for main-sequence stars
• Mass-luminosity relation - plot of mass against
  luminosity (where possible)
• Luminosity proportional to approximately fourth
  power of mass
• Equation L ? M3.5
• Fundamental property which distinguishes one star
  from another is mass

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Main Sequence Lifetime

• Main sequence is defined by hydrogen burning all
  stars on the main sequence derive energy through
  hydrogen burning
• Time star spends on main sequence is proportional
  to mass divided by luminosity
• Equation tmain sequence ? M/L
• Substituting mass-luminosity relation for
  main-sequence stars
• tmain sequence ? M/(M3.5)
  ? 1/M2.5
• How long H-burning lasts depends on stars mass
• High-mass stars ? short main-sequence life
• Low-mass stars ? long main-sequence life

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Main-Sequence Lifetime Estimates
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Main-Sequence Star Summary
High Mass High Luminosity Short-Lived
Large Radius Blue Low Mass Low
Luminosity Long-Lived Small Radius Red
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High-Mass Stars
What is the significance of the main-sequence?
Normal hydrogen- burning stars reside on the main
sequence of the H-R diagram.
Low-Mass Stars
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11.3 Star Clusters

• What are the two types of star cluster?
• How do we measure the age of a star cluster?

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Stellar Clusters

• Stellar cluster - many stars, greater than about
  100, held together by mutual gravitational
  attraction
• Star orbits in cluster unstable
• Motion like a random walk
• Categories
• Open (galactic) clusters
• Globular clusters
• OB Associations

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Open Clusters
Pleiades Cluster in Taurus M45

• Typical separation - ? 2-3 ly
• Field stars (Sun) - ? 5-6 ly
• Typical size - 10s of ly
• Roughly spherical shape
• Typical numbers of stars - 10s to 1000s
• Brightest stars
• Either blue main sequence, giants, and
  supergiants
• Or, red giants and supergiants
• Number of clusters gt 20,000
• Located in spiral arms and disk

Praesepe Cluster in CancerM44
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PleiadesHR Diagram
No Red Giants

• Number of stars - about 500
• Diameter - about 5 ly
• Age - about 100 million years
• Main sequence stars
• No red giant stars

Each dot represents luminosity and surface
temperature of a star in open cluster Pleiades
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How might one track the course of stellar
evolution using star clusters?

• Stellar evolution proceeds according to the mass
  of the star.
• According to our theoretical understanding of
  stellar evolution, massive stars evolve faster
  than low mass stars.
• Star clusters are collections of different mass
  stars, but they formed at the same time and from
  the same material.

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Main Sequence Turnoff Point

• Main-sequence turnoff point - most massive main
  sequence star that has not reached hydrogen
  exhaustion line
• Indicates age of cluster from model calculations

Turnoff point
Exhaustion of core hydrogen
L
Zero-age main sequence
T
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O
A
F
G
M
B
K
NGC 2362
h ? Persei
h ? Persei
-6
-4
107
Pleiades
-2
M 41
M 41
M 11
M 11
108
Mv
0
Coma
H P
Hyades
M 67
Praesepe
109
2
NGC 752
Age in years at turnoff point
M 67
4
Sun
1010
6
-0.4
0.0
0.4
0.8
1.2
1.6
B - V (color index)
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To determine accurate ages, we compare models of
stellar evolution to the cluster data.
Cluster Evolution
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Globular Clusterstend to be very old

• Typical separation - ? 0.2 ly
• Typical size - 100s ly
• Nearly spherical shape
• Typical number of stars - 10,000s to 100,000s
• Brightest stars
• Always red giants and red supergiants
• No bright blue stars
• Number of globular clusters - ? 150
• Located in halo and near nucleus
• Are among the oldest stars in our Galaxy

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Globular Clusters M13 and M80
M80 is more than 12 billion years old. The
prominent red stars are red giants nearing the
end of their lives. The central region is about
15 ly across.
M13 is roughly 23,000 ly from Earth with a
diameter of about 150 ly giving an average
density about 100 times greater than solar
neighborhood.
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Globular Cluster H-R Diagram
Each dot represents apparent magnitude and
surface temperature of a star in globular cluster
M55
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C
B
Which star is the hottest?
D
Luminosity
A
Temperature
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C
C
B
Which star is the hottest?
B
D
Luminosity
D
A
A
A
Temperature
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C
B
Which star is the most luminous?
D
Luminosity
A
Temperature
65
C
B
Which star is the most luminous?
D
Luminosity
A
C
Temperature
66
C
B
Which star is a main-sequence star?
D
Luminosity
A
Temperature
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C
B
Which star is a main-sequence star?
D
Luminosity
A
D
Temperature
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C
B
Which star has the largest radius?
D
Luminosity
A
Temperature
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C
B
Which star has the largest radius?
D
Luminosity
A
C
Temperature
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A
Which star is most like our Sun?
D
Luminosity
B
C
Temperature
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A
Which star is most like our Sun?
D
Luminosity
B
B
C
Temperature
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A
Which of these stars will have changed the least
10 billion years from now?
D
Luminosity
B
C
Temperature
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Which of these stars will have changed the least
10 billion years from now?
A
D
Luminosity
B
C
C
Temperature
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A
Which of these stars can be no more than 10
million years old?
D
Luminosity
B
C
Temperature
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A
Which of these stars can be no more than 10
million years old?
D
Luminosity
B
C
A
Temperature
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Range of Stellar Properties
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The Big Picture

• Mass and age determine differences among stars
  stars are hydrogen and helium structures at
  birth.
• Hertzsprung-Russell (H-R) diagram summarizes
  properties of stars and their evolution.
• Stars spend most of their lives as main-sequence
  stars replacing the luminosity by converting
  hydrogen to helium masses of stars increases up
  the main sequence the more massive the star the
  shorter its main-sequence lifetime will be.
• Star clusters provide a validation of our
  theoretical studies of stellar structure and
  evolution.