Chapter 10 Measuring the Stars

Star Cluster NGC ,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 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 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/distance 2

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 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 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

O 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 subdivisions Each letter has 10 subdivisions, 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 Betelgeuse

Indirect size measurement Most stars’ sizes can’t be measured directly Use luminosity  temperature 4 And luminosity  area (or radius 2 ) Indirectly determines radius

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

Figure 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 H-R Diagram of Nearby Stars

Analogy 10.1 People along a main sequence

Main 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 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 Hipparcos H-R Diagram

Figure 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 Stellar Luminosities

Table 10.4 Variation in Stellar Properties within a Spectral Class

Sun 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 Binary Stars

Determining stellar masses Measure binary properties Use orbital radii and period Universal law of gravitation

Figure Stellar Masses

More Precisely 10.3 Measuring Stellar Masses in Binary Stars

Figure Stellar Mass Distribution

Table 10.5 Measuring the Stars

Stellar 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 10.6 Key Properties of Some Well-Known Main-Sequence Stars

Figure Stellar Radii and Luminosities