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: Amount of power star radiates
- 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
- 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)
- Spectral Type: O
- 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
- 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.
- Visual Binary
- 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
- We measure masses using gravity.
- 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
- A star's full classification includes spectral type line identities and luminosity class line shapes (relates to the size of the star).
- 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
- Sun's life expectancy: 10 billion years.
- Main Sequence Summary
- High Mass
- High luminosity
- Short lived
- Large radius
- Blue
- Low Mass
- Low luminosity
- Long lived
- Small Radius
- Red
- High Mass
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.
- 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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