Chapter 10Measuring the Stars

Chapter 10Measuring the Stars

Star Cluster NGC 360320,000 light-years away

Figure 10.1Stellar Parallax

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

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

Figure 10.2Sun’s Neighborhood

Nearest neighbor starsNearest neighbor stars

• Less than 100 stars within 5 pc• Several 1000 stars within 30 pc

Hipparcos satelliteHipparcos satellite

• Can measure out to 200 pc• Nearly a million stars

• Future satellites will measure to 25,000 pc

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

Figure 10.3Real Space Motion

a), b) Barnard’s Star - 22 years apart

c) Alpha Centauri

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

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

Figure 10.4Inverse-Square Law

Figure 10.5Luminosity

Apparent brightness proportional to

luminosity/distance2

Apparent brightness proportional to

luminosity/distance2

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

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

Figure 10.6Apparent Magnitude

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)

More Precisely 10.1More on the Magnitude Scale

Figure 10.7Star Colors

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

Figure 10.8Blackbody Curves

Table 10-1Stellar Colors and Temperatures

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

Figure 10.9Stellar Spectra

Spectral classificationSpectral classification

• In 1800’s letter classification used for stellar spectra

• Later rearranged into order of decreasing temperature

Table 10.2Spectral Classes

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)

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)

Direct size measurementDirect size measurement

• Several stars are large, bright and close enough to measure their size directly

Figure 10.10Betelgeuse

Indirect size measurementIndirect size measurement

• Most stars’ sizes can’t be measured directly• Use luminosity temperature4

• And luminosity area (or radius2)• Indirectly determines radius

Figure 10.11Stellar Sizes

Stellar sizesStellar sizes

• R - radius of sun

• Giants - 10X to 100X R

• Supergiants - up to 1000X R

• Dwarf - comparable to or smaller than R

Hertzsprung-Russell DiagramHertzsprung-Russell Diagram

• H-R diagram• Each point represents a star• Luminosity on vertical scale• Temperature (decreasing) on horizontal scale

Figure 10.12H-R Diagram of Well-Known Stars

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

Figure 10.13H-R Diagram of Nearby Stars

Analogy 10.1People along a main sequence

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

Figure 10.14H-R Diagram of Brightest Stars

More Precisely 10.2Estimating Stellar Radii

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)

Figure 10.15Hipparcos H-R Diagram

Figure 10.16Stellar Distance

Analogy 10.2Traffic lights further away are fainter

Main sequence or not?Main sequence or not?

• Spectral line widths affected by pressure and density

• Determines if main sequence or not

Table 10-3Stellar Luminosity Classes

Figure 10.17Stellar Luminosities

Table 10.4Variation in Stellar Properties within a Spectral Class

SunSun

• Spectral class G

• Subdivision 2

• Luminosity class V

• G2V

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)

Figure 10.18Binary Stars

Determining stellar massesDetermining stellar masses

• Measure binary properties• Use orbital radii and period• Universal law of gravitation

Figure 10.19Stellar Masses

More Precisely 10.3Measuring Stellar Masses in Binary Stars

Figure 10.20Stellar Mass Distribution

Table 10.5Measuring the Stars

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

Table 10.6Key Properties of Some Well-Known Main-Sequence

Stars

Figure 10.21Stellar Radii and Luminosities