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Chapter 10Measuring the Stars
Chapter 10Measuring the Stars
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Star Cluster NGC 360320,000 light-years away
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Figure 10.1Stellar Parallax
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Stellar parallaxStellar parallax
• Measure distance to nearest stars• Baseline is earth’s orbital diameter of 2 A.U.• Parallactic angle (or parallax) is half of total
angle• Star with parallax of 1” is 1 parsec distant• 1 parsec (1 pc) is about 3.3 light-years• Smaller parallax means more distant
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Proxima CentauriProxima Centauri
• Part of Alpha Centauri triple star system• Closest star to earth, largest parallax• 0.76” parallax (difficult to measure)• 1.3 pc or 4.3 light-years away• About 300,000X further away than sun
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Figure 10.2Sun’s Neighborhood
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Nearest neighbor starsNearest neighbor stars
• Less than 100 stars within 5 pc• Several 1000 stars within 30 pc
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Hipparcos satelliteHipparcos satellite
• Can measure out to 200 pc• Nearly a million stars
• Future satellites will measure to 25,000 pc
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Stellar motionStellar motion
• Radial velocity - along line of sight• Measure using Doppler shift
• Transverse velocity - perpendicular to line of sight
• Monitor star’s position on sky
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Figure 10.3Real Space Motion
a), b) Barnard’s Star - 22 years apart
c) Alpha Centauri
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Proper motionProper motion
• Annual movement of star across sky• Corrected for parallax• Barnard’s star moved 227” in 22 years• 10.3” per year proper motion• 1.8 pc distance - transverse velocity is 88
km/s
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Brightness and distanceBrightness and distance
• Luminosity or absolute brightness (intrinsic)• Apparent brightness is how bright star looks
from earth• Apparent brightness depends on luminosity
and distance
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Figure 10.4Inverse-Square Law
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Figure 10.5Luminosity
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Apparent brightness proportional to
luminosity/distance2
Apparent brightness proportional to
luminosity/distance2
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Magnitude scaleMagnitude scale
• Greek astronomer Hipparchus (2nd century BC)
• Ranked stars into six groups• Brightest stars are 1st magnitude• Next brightest stars are 2nd magnitude• Faintest stars (to naked eye) are 6th
magnitude• Larger magnitude means fainter star
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Apparent magnitudeApparent magnitude
• Expanded beyond stars visible to naked eye• One magnitude difference is 2.5X in
brightness• A 1st magnitude star is 2.5X brighter than a
2nd magnitude star• Full moon has an apparent magnitude of -12.5 • Faintest objects visible by Hubble or Keck
telescopes are apparent magnitude 30
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Figure 10.6Apparent Magnitude
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Absolute magnitudeAbsolute magnitude
• It is the apparent magnitude of a star viewed from a distance of 10 pc
• Measure of absolute brightness or luminosity
• Our sun has absolute magnitude of 4.8
• (If sun were 10 pc from us, its apparent magnitude would be 4.8, which is faint)
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More Precisely 10.1More on the Magnitude Scale
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Figure 10.7Star Colors
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Stellar colorStellar color
• Temperature of star determines blackbody curve
• Measurements at two wavelengths can determine blackbody curve temperature
• Use B (blue) and V (visual - green/yellow) filters
• Determines star’s color index or color
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Figure 10.8Blackbody Curves
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Table 10-1Stellar Colors and Temperatures
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Stellar spectraStellar spectra
• Absorption spectrum• Aborption lines determine elements• Temperature determines strength of lines• Hotter stars have more ionized atoms• Coolest stars can have molecular lines
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Figure 10.9Stellar Spectra
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Spectral classificationSpectral classification
• In 1800’s letter classification used for stellar spectra
• Later rearranged into order of decreasing temperature
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Table 10.2Spectral Classes
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O B A F G K MO B A F G K M
• Highest to lowest temperature• Mnemonic:• Oh, Be A Fine Girl, Kiss Me• Oh, Be A Fine Guy, Kiss Me• Oh Beastly And Fearsome Gorilla, Kill Me• (Make up your own)
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Spectral class subdivisionsSpectral class subdivisions
• Each letter has 10 subdivisions, 0 - 9• 0 is hottest, 9 is coolest, within letter class• Sun is G2 (cooler than G1, hotter than G3)
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Direct size measurementDirect size measurement
• Several stars are large, bright and close enough to measure their size directly
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Figure 10.10Betelgeuse
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Indirect size measurementIndirect size measurement
• Most stars’ sizes can’t be measured directly• Use luminosity temperature4
• And luminosity area (or radius2)• Indirectly determines radius
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Figure 10.11Stellar Sizes
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Stellar sizesStellar sizes
• R - radius of sun
• Giants - 10X to 100X R
• Supergiants - up to 1000X R
• Dwarf - comparable to or smaller than R
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Hertzsprung-Russell DiagramHertzsprung-Russell Diagram
• H-R diagram• Each point represents a star• Luminosity on vertical scale• Temperature (decreasing) on horizontal scale
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Figure 10.12H-R Diagram of Well-Known Stars
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Stellar radii and H-R diagramStellar radii and H-R diagram
• Radius-luminosity-temperature relationship gives radius
• Diagonal dashed lines on H-R diagrams represent constant radius
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Figure 10.13H-R Diagram of Nearby Stars
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Analogy 10.1People along a main sequence
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Main SequenceMain Sequence
• Most stars in H-R diagram on main sequence• Runs from top left (High luminosity and temp)• To bottom right (low luminosity and temp)• Runs from blue giants and supergiants to red
dwarfs
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Figure 10.14H-R Diagram of Brightest Stars
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More Precisely 10.2Estimating Stellar Radii
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Non-Main SequenceNon-Main Sequence
• 90% of stars on main sequence• 9% of stars are white dwarfs (bottom left)• 1% of stars are red giants (upper right)
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Figure 10.15Hipparcos H-R Diagram
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Figure 10.16Stellar Distance
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Analogy 10.2Traffic lights further away are fainter
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Main sequence or not?Main sequence or not?
• Spectral line widths affected by pressure and density
• Determines if main sequence or not
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Table 10-3Stellar Luminosity Classes
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Figure 10.17Stellar Luminosities
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Table 10.4Variation in Stellar Properties within a Spectral Class
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SunSun
• Spectral class G
• Subdivision 2
• Luminosity class V
• G2V
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Binary starsBinary stars
• Most stars are members of multiple-star systems - Binary-star systems (2) most common
• Visual binaries (see 2 stars)• Spectroscopic binaries (detect Doppler
shift from one or both orbiting stars)• Eclipsing binaries (one passes in front
of other, varying light output)
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Figure 10.18Binary Stars
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Determining stellar massesDetermining stellar masses
• Measure binary properties• Use orbital radii and period• Universal law of gravitation
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Figure 10.19Stellar Masses
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More Precisely 10.3Measuring Stellar Masses in Binary Stars
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Figure 10.20Stellar Mass Distribution
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Table 10.5Measuring the Stars
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Stellar lifetimeStellar lifetime
• Depends on mass (how much fuel) and• Luminosity (how fast fuel is consumed)• A B2V star lives 90 million years• A G2V star lives 10,000 million years (our
sun)• An M5V star lives 16,000,000 million years
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Table 10.6Key Properties of Some Well-Known Main-Sequence
Stars
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Figure 10.21Stellar Radii and Luminosities