Thursday, April 11, 2013

Chapter 11 Notes: Olivia Ward

Surveying the Stars
11.1 Properties of Stars
How do we measure stellar luminosities?

  • Brightness of a star depends on its distance and how much light it actually emits.
    • Luminosity: Amount of power star radiates
      • Watts: Energy per second
    • Apparent brightness: Amount of starlight that reaches Earth
      • Energy per second, per square meter
  • Luminosity passing through each sphere is the same.
  • The relationship between luminosity and apparent brightness depends on distance:
    • Brightness = Luminosity / 4π (distance) ^2
  • We can determine a star's luminosity:
    • Luminosity = 4π (distance)^2 X Brightness
  • Parallax is the apparent shift in position of a nearby object against a background of more distant objects.
    • Apparent positions of the nearest stars shift by about an arcsecond as Earth orbits the Sun.
    • The parallax angle depends on distance.
    • Parallax is measured by comparing snapshots taken at different times and measuring the shift in angle to star.
  • Most luminous stars: 10^6 L Sun
  • Least luminous stars: 10^-4 L Sun
    • L Sun is the luminosity of the Sun.
  • The Magnitude Scale
    • m: apparent magnitude
    • M: absolute magnitude
How do we measure stellar temperatures?
  • Lines in a star's spectrum correspond to a spectral type that reveals its temperature: (hottest) OBAFGKM (coolest)
    • Spectral Type: O
      • Example: Stars of Orion's Belt
      • Temperature Range: > 30,000 K
      • Key Absorption Line Features: Lines of ionized helium, weak hydrogen lines
      • Brightest Wavelength: > 97 nm (ultraviolet)
    • Spectral Type: B
      • Example: Rigel
      • Temperature Range: 30,000 K - 10,000 K
      • Key Absorption Line Features: Lines of neutral helium, moderate hydrogen lines
      • Brightest Wavelength: 97-290 nm (ultraviolet)
    • Spectral Type: A
      • Example: Sirius
      • Temperature Range: 10,000 K - 7,500 K
      • Key Absorption Line Features: Very strong hydrogen lines
      • Brightest Wavelength: 290-390 nm (violet)
    • Spectral Type: F
      • Example: Polaris
      • Temperature Range: 7,500 K - 6,000 K
      • Key Absorption Line Features: Moderate hydrogen lines, moderate lines of ionized calcium
      • Brightest Wavelength: 390-480 nm (blue)
    • Spectral Type: G
      • Examples: Sun, Alpha Centauri A
      • Temperature Range: 6,000 K - 5,000 K
      • Key Absorption Line Features: Weak hydrogen lines, strong lines of ionized calcium
      • Brightest Wavelength: 480-580 nm (yellow)
    • Spectral Type: K
      • Example: Arcturus
      • Temperature Range: 5,000 K - 3,500 K
      • Key Absorption Line Features: Lines of neutral and singly ionized metals, some molecules
      • Brightest Wavelength: 580-830 nm (red)
    • Spectral Type: M
      • Examples: Betelgeuse, Proxima Centauri
      • Temperature Range: < 3,500 K
      • Key Absorption Line Features: Strong molecular lines
      • Brightest Wavelength: > 830 nm (infrared)
  • Every object emits thermal radiation with a spectrum that depends on its temperature.
    • An object of fixed size grows more luminous as its temperature rises.
  • Properties of Thermal Radiation
    • Hotter objects emit more light per unit area at all frequencies.
    • Hotter objects emit photons with a higher average energy.
  • Hottest stars: 50,000 K
  • Coolest stars: 3,000 K
  • Sun's surface: 5,800 K
  • Level of ionization also reveals a star's temperature.
    • Absorption lines in a star's spectrum tell us its ionization level.
  • Pioneers of Stellar Classification
    • Annie Jump Cannon and the "calculators" at Harvard laid the foundation of modern stellar classification
How do we measure stellar masses?
  • Binary Star Orbits
    • Orbits of a binary star system depends on the strength of gravity.
    • Types of Binary Star Systems:
      • Visual Binary
        • We can directly observe the orbital motions of these stars.
      • Eclipsing Binary
        • We can measure periodic eclipses.
      • Spectroscopic Binary
        • We determine the orbit by measuring Doppler Shift.
    • About half of all stars are in binary systems.
  • Newton's Version of Kepler's Law
    • We measure masses using gravity.
      • Direct mass measurements are possibly only for stars in binary star systems.
      • Need 2 out of 3 observables to measure mass:
        • Orbital period (p)
        • Orbital separation (a or r = radius)
        • Orbital velocity
  • Most massive stars: 100 M Sun
  • Least massive stars: 0.08 M Sun
    • M Sun is the mass of the Sun
    • Some very rare stars have the mass of > 100 M Sun

11.2 Nuclear Fusion in the Sun
What is a Hertzsprung-Russell diagram?
  • An H-R diagram plots the luminosities and temperatures of stars.
    • Most stars fall somewhere on the main sequence of the H-R diagram.
  • Stars with lower temperatures and higher luminosities than main-sequence stars must have larger radii:
    • Giants and Super Giants
  • Stars with lower luminosities and higher temperatures than main-sequence stars must have smaller radii:
    • White Dwarfs
  • Stellar Luminosity Classes
    • A star's full classification includes spectral type line identities and luminosity class line shapes (relates to the size of the star).
      • I: Super Giant
      • II: Bright Giant
      • III: Giant
      • IV: Sub-Giant
      • V: Main Sequence
  • H-R diagram depicts temperature, color, spectral types, luminosity, and radius.

What is the significance of the main sequence?
  • Main sequence stars are fusing H into He in their cores like the Sun.
  • Mass measurements of main sequence stars show that the hot, blue stars are much more massive than the cool, red ones.
  • The mass of a normal, hydrogen-fusing star determines its luminosity and spectral type.
  • Hydrostatic Equilibrium
    • The core temperature of a higher-mass star needs to be higher in order to balance gravity.
    • A higher core temperature boosts the fusion rate, leading to greater luminosity.
  • Mass and Lifetime
    • Sun's life expectancy: 10 billion years.
      • Until core H (1% of total) is used up
    • Life expectancy of a 10 M Sun star:
      • 10 times as much fuel, it uses 104 times as fast.
      • 10 million years ~ 10 billion years X 10/10^4
    • Life expectancy of a 0.1 M Sun star:
      • 0.1 times as much fuel, uses it 0.01 times as fast.
      • 100 billion years ~ 10 billion years X 0.1/0.01
  • Main Sequence Summary
    • High Mass
      • High luminosity
      • Short lived
      • Large radius
      • Blue
    • Low Mass
      • Low luminosity
      • Long lived
      • Small Radius
      • Red

What are giants, super giants, and white dwarfs?
  • Off the Main Sequence
    • Stellar properties depend on both mass and age: those have finished fusing H to He in their cores are no longer on the main sequence.
    • All stars become larger and redder after exhausting their core hydrogen: giants and supergiants
  • Giants and super giants are far larger than main sequence stars and white dwarfs.
    • Most stars end up as white dwarfs once fusion is done.

11.3 Star Clusters
What are the two types of star clusters?
  • Open cluster: A few thousand loosely packed stars
  • Globular cluster: Up to a million or more stars in a dense ball bound together by gravity.
How do we measure the age of a star cluster?
  • Massive blue stares die first, followed by white, yellow, orange, and red.
  • Pleidaes now has no stars with a life expectancy less than around 100 million years.
  • The main sequence turnoff point of a cluster tell us its age (Using the H-R diagram to determine the age of a star cluster).
  • To determine accurate ages, we compare models of stellar evolution to the cluster data.
    • Detailed modeling of the oldest globular clusters reveals that they are about 13 billion years old (age of the universe).

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