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Chapter 10
Measuring the Stars
Star Cluster NGC 3603
20,000 light-years away
Figure 10.1
Stellar Parallax
Stellar 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
Proxima Centauri
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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
Figure 10.2
Sun’s Neighborhood
Nearest neighbor stars
• Less than 100 stars within 5 pc
• Several 1000 stars within 30 pc
Hipparcos satellite
• Can measure out to 200 pc
• Nearly a million stars
• Future satellites will measure to 25,000 pc
Stellar motion
• Radial velocity - along line of sight
• Measure using Doppler shift
• Transverse velocity - perpendicular to line of
sight
• Monitor star’s position on sky
Figure 10.3
Real Space Motion
a), b) Barnard’s Star - 22
years apart
c) Alpha Centauri
Proper motion
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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
Brightness and distance
• Luminosity or absolute brightness (intrinsic)
• Apparent brightness is how bright star looks
from earth
• Apparent brightness depends on luminosity
and distance
Figure 10.4
Inverse-Square Law
Figure 10.5
Luminosity
Apparent brightness
proportional to
luminosity/distance2
Magnitude 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
Apparent 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
Figure 10.6
Apparent Magnitude
Absolute 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)
More Precisely 10.1
More on the Magnitude Scale
Figure 10.7
Star Colors
Stellar 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
Figure 10.8
Blackbody Curves
Table 10-1
Stellar Colors and Temperatures
Stellar spectra
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Absorption spectrum
Aborption lines determine elements
Temperature determines strength of lines
Hotter stars have more ionized atoms
Coolest stars can have molecular lines
Figure 10.9
Stellar Spectra
Spectral classification
• In 1800’s letter classification used for
stellar spectra
• Later rearranged into order of
decreasing temperature
Table 10.2
Spectral Classes
OBAFGKM
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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)
Spectral 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)
Direct size measurement
• Several stars are large, bright and close
enough to measure their size directly
Figure 10.10
Betelgeuse
Indirect size measurement
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Most stars’ sizes can’t be measured directly
Use luminosity  temperature4
And luminosity  area (or radius2)
Indirectly determines radius
Figure 10.11
Stellar Sizes
Stellar sizes
• R - radius of sun
• Giants - 10X to 100X R
• Supergiants - up to 1000X R
• Dwarf - comparable to or smaller than R
Hertzsprung-Russell Diagram
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H-R diagram
Each point represents a star
Luminosity on vertical scale
Temperature (decreasing) on horizontal scale
Figure 10.12
H-R Diagram of Well-Known Stars
Stellar radii and H-R diagram
• Radius-luminosity-temperature relationship
gives radius
• Diagonal dashed lines on H-R diagrams
represent constant radius
Figure 10.13
H-R Diagram of Nearby Stars
Analogy 10.1
People along a main sequence
Main Sequence
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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
Figure 10.14
H-R Diagram of Brightest Stars
More Precisely 10.2
Estimating Stellar Radii
Non-Main Sequence
• 90% of stars on main sequence
• 9% of stars are white dwarfs (bottom left)
• 1% of stars are red giants (upper right)
Figure 10.15
Hipparcos H-R Diagram
Figure 10.16
Stellar Distance
Analogy 10.2
Traffic lights further away are fainter
Main sequence or not?
• Spectral line widths affected by pressure and
density
• Determines if main sequence or not
Table 10-3
Stellar Luminosity Classes
Figure 10.17
Stellar Luminosities
Table 10.4
Variation in Stellar Properties within a Spectral Class
Sun
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Spectral class G
Subdivision 2
Luminosity class V
G2V
Binary 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)
Figure 10.18
Binary Stars
Determining stellar masses
• Measure binary properties
• Use orbital radii and period
• Universal law of gravitation
Figure 10.19
Stellar Masses
More Precisely 10.3
Measuring Stellar Masses in Binary Stars
Figure 10.20
Stellar Mass Distribution
Table 10.5
Measuring the Stars
Stellar lifetime
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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
Table 10.6
Key Properties of Some Well-Known Main-Sequence
Stars
Figure 10.21
Stellar Radii and Luminosities