Stars

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Stars

• Edward Murphy
• RARE CATS
• Summer 2001

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Stellar Luminosity

• The luminosity of a star is the rate at which it
  is giving off energy.
• Not all stars have the same luminosity.
• They range from 1/20 to 700,000 times the
  luminosity of the Sun.
• Luminosity varies with temperature.
• E s T4 (energy per square meter).
• Luminosity depends on size.
• A 4 p R2 (number of square meters).

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Apparent Brightness

• The apparent brightness depends on the luminosity
  of the star and its distance from Earth.
• Apparent brightness drops as square of distance
  (Inverse Square Law of Light).
• The apparent brightness is measured in apparent
  magnitudes.

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Magnitude System

• Around 150 B.C. the Greek astronomer Hipparchus
  compiled a catalog of nearly 1000 stars listing
  their positions and apparent brightness.
• The brightest stars were first magnitude stars.
• The next brightest were second magnitude stars.
• The faintest stars he could see were sixth
  magnitude stars.

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Magnitude System

• Today, the magnitude system is defined such that
  a difference of 5 magnitudes is exactly a factor
  of 100 times in brightness.
• One magnitude is a difference in brightness of
  about 2.5 times.
• Two magnitudes are 2.5x2.56.3 times.
• Three magnitudes are 2.5x2.5x2.515.9 times.

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Magnitude Differences
Magnitude Difference Brightness Difference
1 2.5 times
2 6.3
3 16
4 40
5 100
6 250
10 10,000 104
15 1,000,000 106
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Magnitude System

• Unfortunately, it turns out that many objects are
  brighter than first magnitude.
• These have been assigned magnitudes smaller than
  1, including negative numbers.
• Sirius, the brightest star in the sky, has an
  apparent magnitude of 1.5.

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Magnitude System
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Magnitude System

• Fainter objects have larger apparent magnitudes.
• Brighter objects have smaller apparent magnitudes.

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Magnitude System

• The Sun has a magnitude of 26.2.
• Your eye can easily see the full moon (magnitude
  about 13) and the faintest stars (magnitude 6).
  This is a difference of nearly 20 magnitudes or a
  range of 108.
• The magnitude system is only used in visual
  astronomy. All other areas of astronomy define
  brightness in terms of energy per second per area
  received here on Earth.

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Colors of Stars
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Blackbody Curves
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Spectrum of the Sun
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Formation of Stellar Spectra

• Stars do not have identical absorption line
  spectra.
• Astronomers thought this was due to the fact that
  the chemical composition of stars varied.
• However, most stars have the same composition as
  the Sun (74 H, 25 He, 1 everything else).
• Today we know that stellar spectra look different
  because different stars have different
  temperatures.

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Classification of Stellar Spectra

• Originally, the spectra of stars were classified
  based on their complexity
• A was the simplest, B was next
• Annie J. Cannon was the first to realize that
  there was a better classification scheme.
• In order from hottest to coolest the order is
  OBAFGKML
• Oh Be a Fine Girl (Guy) Kiss My Lips

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Classification of Stellar Spectra

• Class L is new.
• The 8 classes have been divided into 10
  subclasses designated by number
• A B0 is the hottest B star, a B9 is the coolest
  and is slightly hotter than an A0 star.
• The Sun is a G2 star.

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Absorption Lines

• The strengths of the absorption lines in a
  stellar spectrum depend not only on the amount of
  a given element (its abundance), but also the
  temperature of the star.

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Hydrogen Absorption Lines

• For example, lets consider hydrogen, the most
  abundant element in stars.
• In very hot stars, hydrogen is completely
  ionized. Without any electrons, the hydrogen
  cannot absorb any light hence we see no hydrogen
  lines.
• In moderately hot stars, we see both the Lyman
  (UV) and Balmer (visible) series.

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Line Series
n6
n5
n4
n3
n2
n1
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Formation of Stellar Spectra

• In cool stars, we see only the Lyman series and
  not the Balmer series. Why?
• The Balmer series is absorption from the n2
  orbit. The electron must be excited (either
  through collisions or through UV light) to be in
  n2.
• In cool stars, there is not enough UV light and
  the temperature is not high enough to keep the
  electrons excited, so very few are in n2.

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Stellar Absorption Lines
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Spectral Classification
O Violet gt28000 Relatively few absorption lines. Lines of N, Si, and lines of other highly ionized atoms.
B Blue 10000-28000 Lines of neutral He, Si, Si, O. H lines more pronounced.
A Blue 7500-10000 Strong lines of H. Lines of Mg, Si, Fe, Ti, Ca, and others. Weak lines from neutral metals.
F Blue to white 6000-7500 H lines weaker than in A stars, but still strong. Lines of Ca, Fe and neutral Fe. More neutral metals.
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Spectral Classification
G White to yellow 5000-6000 Lines of Ca are strongest. Many ionized and neutral metals. H lines weaker still, CH present.
K Orange to Red 3500-5000 Lines of neutral metals dominate. CH bands still present.
M Red 2000-3500 Strong lines of neutral metals and molecular bands of TiO dominate.
L Red lt2000 Molecular lines dominate spectrum.
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Astronomical Distances

• The astronomical unit (AU) is defined as the
  average distance from the Earth to the Sun.
• 1 AU 1.496 x 1011 m
• The light year (LY) is defined as the distance
  light travels in one year
• 1 LY 9.461 x 1015 m
• 1 AU 8.3 light minutes

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Appendix 11 The Brightest Stars
Name Luminosity Sun1 Distance (LY) Spectral Type
Sirius (a CMa) 24 9 A1V
Canopus (a Car) 12,000 316 F0I
Alpha Centauri 1.50.5 4 G2V
Arcturus (a Boo) 187 37 K2III
Vega (a Lyr) 50 25 A0V
Capella (a Aur) 145 42 G8III
Rigel (b Ori) 60,000 773 B8Ia
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Appendix 11 The Brightest Stars
Name Luminosity Sun1 Distance (LY) Spectral Type
Procyon (a CMi) 7 11 F5IV-V
Betelgeuse (a Ori) 700,000 427 M2Iab
Achernar (a Eri) 2,800 144 B3V
b Centauri (Hadar) 65,000 525 B1III
Altair (a Aql) 10 17 A7IV-V
Aldebaran (a Tau) 450 65 K5III
Spica (a Vir) 12,000 262 B1V
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Appendix 11 The Brightest Stars
Name Luminosity Sun1 Distance (LY) Spectral Type
Antares (a Sco) 850,000 604 M1Ib
Pollux (b Gem) 40 34 K0III
Fomalhaut (a PsA) 16 25 A3V
Deneb (a Cyg) 240,000 3,228 A2Ia
b Crucis 160,000 352 B0.5IV
Regulus (a Leo) 230 77 B7V
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Bright Stars

• The Sun would appear as a magnitude 6.0 star
  (barely visible to the naked eye) at a distance
  of 56 LY
• A star with a luminosity 10,000 times that of
  the Sun will be visible with the naked eye up to
  100 times farther, 5600 LY (the inverse square
  law says that if we move it 100 times farther, it
  gets 100210,000 times fainter).

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Appendix 10 The Nearest Stars
Name Luminosity Sun1 Distance (LY) Spectral Type
Sun 1 - G2V
Proxima Centauri 6x10-6 4.2 M5V
Alpha Centauri A 1.5 4.4 G2V
Alpha Centauri B 0.5 4.4 K0V
Barnards Star 4x10-4 6.0 M4V
Wolf 359 2x10-5 7.8 M6V
Lalande 21185 5x10-3 8.3 M2V
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Appendix 10 The Nearest Stars
Name Luminosity Sun1 Distance (LY) Spectral Type
Sirius A 24 8.6 A1V
Sirius B 3x10-3 8.6 w.d.
Luyten 726-8 A 6x10-5 8.7 M5V
Luyten 726-8 B 4x10-5 8.7 M6V
Ross 154 5x10-4 9.7 M4V
Ross 248 1x10-4 10.3 M6V
Epsilon Eridani 0.3 10.5 K2V
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Appendix 10 The Nearest Stars
Name Luminosity Sun1 Distance (LY) Spectral Type
Lacaille 9352 1x10-2 10.7 M1V
Ross 128 3x10-4 10.9 M4V
Luyten 789-6 A 1x10-4 11.3 M5V
Luyten 789-6 B - 11.3 -
Luyten 789-6 C - 11.3 -
Procyon A 7.7 11.4 F5IV
Procyon B 6x10-4 11.4 w.d.
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Appendix 10 The Nearest Stars
Name Luminosity Sun1 Distance (LY) Spectral Type
61 Cygni A 8x10-2 11.4 K5V
61 Cygni B 4x10-2 11.4 K7V
Gleise 725 A 3x10-3 11.5 M3V
Gleise 725 B 2x10-3 11.5 M4V
Gleise 15 A 6x10-3 11.6 M1V
Gleise 15 B 4x10-4 11.6 M3V
Epsilon Indi 0.14 11.8 K5V
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Appendix 10 The Nearest Stars
Name Luminosity Sun1 Distance (LY) Spectral Type
DX Cancri 1x10-5 11.8 M7V
Tau Ceti 0.45 11.8 G8V
GJ 1061 8x10-5 11.9 M5V
Luyten 725-32 3x10-4 12.1 M5V
Luytens Star 1x10-3 12.4 M4V
Kapteyns Star 4x10-3 12.8 M1V
AX Microscopium 0.03 12.9 M0V
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Faint Stars

• The Sun would appear as a magnitude 6.0 star
  (barely visible to the naked eye) at a distance
  of 56 LY.
• A star with a luminosity 1/100 of the Sun must be
  10 times closer to have the same apparent
  magnitude (inverse square law). That is, it must
  be within 5.6 LY of the Sun to be visible with
  the naked eye.

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Density of Stars in the Solar Neighborhood

• There are 59 stars within 16 LY of the Sun.
• This is a volume of 17,157 cubic LY.
• There is 1 star for every 290 cubic LY.
• The average distance between stars is 6.6 LY
  (cube root of 290).
• The closest star to the Sun is Alpha Centauri
  system (4.4 LY).

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Density of Matter in the Solar Neighborhood

• Density of matter is expressed in g/cm3.
• Water has a density of 1 g/cm3, rocks 2.5-3.5
  g/cm3, and gold 19.3 g/cm3.
• If a typical star has a mass of 0.4 Msun, the
  average density in the solar neighborhood is
  3x10-24 g/cm3.
• This is about 1-2 hydrogen atoms per cubic
  centimeter (compare that to the 2.4x1019
  molecules per cm3 in the air in this room).

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Binary Stars

• Roughly half of all stars are in binary systems
  (some triple and quadruple).
• Visual binaries are binary star systems where
  each star can be seen with a telescope.
• Spectroscopic binaries are those in which the
  stars are too close to see individually, but the
  spectral lines show the Doppler shift due to the
  orbital motion of the stars.

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Orbit of Kruger 60
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Orbit of a Binary Star
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Spectroscopic Binary
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Ursa Major, The Big Bear (Big Dipper)
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Mizar

• Mizar is an example of a complicated system.
• If you have good eyesight, you can see a faint
  companion to Mizar called Alcor. These stars are
  an optical double, that is, they appear close
  together but do not orbit one another.
• In a telescope, Mizar does have a close
  companion. Thus, Mizar is a visual binary. The
  two visible components are Mizar A and Mizar B.

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Mizar

• In fact, Mizar was the first binary star, noticed
  in 1650 by Riccioli.
• With a spectroscope, it can be seen that both
  Mizar A and Mizar B are spectroscopic binaries.

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Mass of Sirius

• When we are dealing with binary stars, the masses
  of the two stars are often similar, and we cannot
  simply ignore the mass of the lighter object like
  we can with planets, moons or satellites.
• For example, consider the star Sirius and its
  companion (a white dwarf). The period of the
  orbit is 50 years and the distance between the
  stars is 20 AU.

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Mass of Sirius

• Therefore, the total mass of the system is

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Wobble of Sirius
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Orbits of Sirius A and B
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Binary Stars Total Mass

• Keplers Law gives us the total mass of the
  system, not the mass of each star individually.
• However, the larger star is closer to the center
  of mass and has a smaller orbit.
• Therefore, it moves more slowly than the lighter
  star.

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Binary Star Masses

• If we can measure the speed with which each star
  orbits the center of mass, we can determine the
  relative masses of the two stars.
• By watching the changing Doppler shifts of the
  two stars, we can determine the speed of each
  star and then the mass of one star compared to
  the other.
• If we know the total mass of the two stars from
  Keplers Law, then we can compute the mass of
  each star individually.

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Stellar Masses

• From the studies of masses of binary stars,
  astronomers have learned that
• Stars more massive than the Sun are rare.
• No nearby stars (within 33 LY) are more massive
  than 4 solar masses.
• There are a handful of stars with masses over 50
  solar masses.
• There may be a few stars with masses up to 100
  solar masses.

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Stellar Masses

• Stars smaller than the Sun are the most common.
• The smallest stars that can still burn H into He
  have a mass 1/12 of the Sun.

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Failed Stars

• Stars between 1/100 and 1/12 the mass of the Sun
  may be able to burn deuterium into helium for a
  short time, but cannot sustain nuclear reactions.
• Such failed stars are called brown dwarfs.
  They are similar in size to Jupiter with masses
  of 10-80 times that of Jupiter.

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Gliese 229B
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Failed Stars

• Objects below 1/100 the mass of the Sun are
  called planets.

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Diameters of Stars

• Even in the largest telescopes, stars appear as
  tiny points of light.
• The size of a star on a photograph of the sky is
  typically caused by the blurring effects of the
  Earths atmosphere.
• In only a very few cases (e.g. Betelgeuse) has
  the diameter of the star been measured directly
  by imaging.

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Betelgeuse
This is the first direct image of a star other
than the Sun and was made with the Hubble Space
Telescope. The image reveals a huge UV
atmosphere with a mysterious hotspot that is more
than 10 times the diameter of the Earth and 2000
K hotter than the rest of the surface of the star.
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Diameters of Stars

• In a few cases, the diameter can be measured by
  noting how long it takes the light to dim as the
  Moon passes in front of the star.

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Diameters of Stars

• Today, astronomers can use special telescopes
  called optical interferometers to directly
  measure the diameters of some stars.
• An optical interferometer is a series of small
  telescopes linked together which have the
  resolving power of a much larger telescope.

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Eclipsing Binary Stars

• The majority of stellar diameters have been
  measured using eclipsing binary stars.
• An eclipsing binary is a system in which one star
  passes behind the other during every revolution.
• When one stars blocks the light of the other, the
  blocked star is said to be eclipsed.

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Eclipsing Binary Light Curve
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Eclipsing Binary Stars

• The diameters of the stars can be measured from
  the time it takes for the eclipse to begin or
  end, and by measuring the duration of the
  eclipses.

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Measuring the Diameters of Eclipsing Binary Stars
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The Diameters of Stars

• Most stars have a diameter roughly the size of
  the Sun.
• A few of the very luminous stars that are red in
  color are giants or supergiants.
• Betelgeuse has a diameter of nearly 10 AU. If
  placed in our solar system, it would extend
  almost all the way to Jupiter.

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H-R Diagram

• In 1911 and 1913, two Ejnar Hertzsprung and Henry
  Norris Russell discovered that the temperature of
  a star is related to its luminosity.
• The Hertzsprung-Russell Diagram (H-R Diagram) is
  a plot of temperature (spectral class) vs.
  luminosity.

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H-R Diagram

• In an H-R Diagram, temperature increases to the
  left and luminosity toward the top.

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H-R Diagram

• The great majority of stars are found in a band
  running from the upper left (hot, blue and
  luminous) to lower right (red, cool and dim) on
  the diagram. This band is called the Main
  Sequence.
• Stars in the upper right corner (red, cool and
  luminous) are Giants or Supergiants.

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H-R Diagram

• Stars in the lower left corner (blue, hot and
  dim) are called white dwarfs.
• Overall, about 89 of stars are on the main
  sequence, about 10 are white dwarfs, and about
  1 are giants or supergiants.

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Main Sequence

• Stars on the main sequence are producing energy
  by fusing H to He.
• Stars spend about 90 of their lives on the main
  sequence.
• For stars on the main sequence, their size,
  luminosity, and temperature are determined by two
  parameters mass and composition.

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Main Sequence

• Stars with the largest masses are the hottest and
  most luminous. They are located in the upper
  left portion of the H-R Diagram.
• The least massive stars are the coolest and least
  luminous. They are in lower right.
• The main sequence is a sequence of stellar masses.

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Main-Sequence Stars
Spectral Type Mass (Sun 1) Luminosity (Sun1) Temperature (K) Radius (Sun1)
O5 40 700,000 40,000 18
B0 16 270,000 28,000 7
A0 3.3 55 10,000 2.5
F0 1.7 5 7,500 1.4
G0 1.1 1.4 6,000 1.1
K0 0.8 0.35 5,000 0.8
M0 0.4 0.05 3,500 0.6
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White Dwarfs

• White dwarfs have a very small size
• White dwarfs are very hot (typically 10,000 to
  50,000 K).
• White dwarfs are very faint.
• The typical white dwarf has a mass close to the
  mass of the Sun but a size about the same as the
  Earth.
• The density of a white dwarf is around 200,000
  g/cm3. One teaspoonful would weigh 50 tons.

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Sirius B

• Again consider the companion to Sirius, Sirius B.
• Mass 1.034 MSun
• Radius 5846 km
• Temperature 24,790 K
• Luminosity 1/425 LSun
• Surface gravity 3x108 gSun

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Sirius Optical Image
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Sirius B X-ray image