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Red Giants and White Dwarfs

Red Giants and White Dwarfs. A Field Guide to Stars. The Solar Neighborhood. Milky Way Galaxy 100 billion stars Volume of nearly 100,000 light years across Orbits Galactic Center- 25,000 light years from Earth. Stellar Parallax. Measuring Parsecs. Parallax decreases as distance increases

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Red Giants and White Dwarfs

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  1. Red Giants and White Dwarfs A Field Guide to Stars

  2. The Solar Neighborhood Milky Way Galaxy 100 billion stars Volume of nearly 100,000 light years across Orbits Galactic Center- 25,000 light years from Earth

  3. Stellar Parallax

  4. Measuring Parsecs • Parallax decreases as distance increases • Distance (in parsecs)= 1 parallax (in arc seconds) Parallax=0.5” 1/0.5= 2pc Parallax=0.1” 1/0.1=10pc One Parsec≈3.3 Light years

  5. Our Neighbors Proxima Centauri Alpha Centauri Complex 0.77” parallax 270,000 AU 4.3 Light years

  6. Interstellar Void

  7. Luminosity and apparent brightness Luminosity is intrinsic also called the absolute brightness We see apparent brightness

  8. Another Inverse Square Law Leaving a star, light travels through imaginary spheres of increasing radius surrounding the source.

  9. Inverse Square • Doubling the distance from a star makes it appear 22, or 4 times dimmer. • Tripling makes it look 32, or 9 times more dim. • Luminosity also affects brightness. • Doubling the luminosity also doubles the energy crossing any spherical shell surrounding the star. • This doubles the apparent brightness. • The apparent brightness of a star is directly proportional to the star’s luminosity and inversely proportional to the square of its distance.

  10. Okay…WHAT? Apparent brightness (energy flux)∞ luminosity distance2

  11. Determining Luminosity • Two things are needed • Determine apparent brightness • Star’s distance • Magnitude Scale • Second century Greek astronomer Hipparchus • Classified into six groups

  12. The Magnitude Scale • The use of telescopes that could measure energy shows two important facts • The 1-6 magnitude range spans a magnitude of 100 in apparent brightness • Hipparchus used his eyes

  13. Modern Magnitude Scale • Define a change of 5 in magnitude to correspond to exactly a factor of 100 • 1-6 or 7-2.. • Numbers in Hipparchus’s ranking are apparent magnitudes • Scale is no longer limited to whole numbers • Magnitudes outside of the 1-6 range are allowed

  14. Apparent Magnitude Ranges from the Sun (-26.7) to the Hubble/Keck limit ≈5x1022

  15. Absolute Magnitude • Measures apparent brightness when the star is seen at its actual distance from the sun • Absolute magnitude is apparent magnitude from 10 parsecs from the observer • Inverse Square (again) • Star @ 100pc “moved” to 10pc • Distance decreases by a factor of 10 • Apparent brightness increases 102 or 100 times • Its apparent magnitude would decrease by 5

  16. More on the Magnitude Scale • Sun’s absolute magnitude is 4.83 • Since an increase in brightness by a factor of 100 corresponds to a reduction in a star’s magnitude by 5 units, a star with a luminosity 100 times that of the Sun has an absolute magnitude of • 4.83-5=-0.17 • A star with .01 Solar luminosity has an absolute magnitude of • 4.83+5=9.83

  17. More on the Magnitude Scale • We can fill in the gaps if we realize 1 magnitude corresponds to a factor of 1001/5≈2.512, 2 magnitudes to 1002/5≈6.310 and so on. • A factor of 10 in brightness corresponds to 2.5 magnitudes.

  18. Luminosity Conversion Chart Calculate the luminosity (in solar units) of a star having absolute magnitude of M. The star’s absolute magnitude differs from the Sun by (M-4.83) magnitudes, So the luminosity, L, differs from the solar luminosity by a factor of: 100 -(M-4.83)/5 or L(solar units)= 10–((M-4.83)/2.5) From appendix 3: MSun=4.83, has L=100=1 Sirius A with M=1.45, has L=101.35=22 Solar Units

  19. More on the Magnitude Scale • Barnard’s Star with M=13.24, has L=10-3.5 = 4.3x10-4 Solar Units. • Betelgeuse has M= -5.14 and L=9,700 suns…

  20. Converting Luminosity to Absolute Magnitude • Invert the previous formula • M=4.83-2.5 log10L • Vega: L=50 • M=4.83-2.5 log(50) • M=0.58 • Eridani: M=0.3 • M=4.83-2.5 log(0.3) • M=6.2

  21. Apparent Luminosity, Absolute Magnitude, and Distance • m=M+5 log (D/10pc) • Or • D= 10pc X 10((m-M)/5) • Knowing the difference m-M between apparent and absolute magnitudes is equivalent to the objects distance from us.

  22. Apparent Luminosity, Absolute Magnitude, and Distance • The star Rigel: • m=0.18 • D=240 pc • M= 0.18-5log(24)=-6.7

  23. Stellar Temperatures • Color and the Blackbody Curve • Measure the apparent brightness at several different frequencies • Match observations to appropriate blackbody curve

  24. Blackbody Curves B and V filters admit different amounts of light for objects of different temperatures.

  25. Spectral Classification • Between 1880 and 1920 stellar spectra was collected • No firm theories on how the lines were produced • Stars were classified by their hydrogen-line intensities • Now are classified as O, B, A, F, G, K, and M.

  26. Spectral Classification • Astronomers further divided each letter into 10 subdivisions • Our sun is a G2 (cooler than a G1, but hotter than a G3) • Vega: A0 • Barnard’s Star: M5 • Betelgeuse: M2

  27. Direct and Indirect Measurements • With distance known and angular diameter measured, we can calculate actual radius. • 130pc and angular diameter of up to 0.045” • Betelgeuse’s maximum radius is 630 times that of the Sun. (Betelgeuse is a variable star). • Most stars are too distant or too small to be measured directly

  28. Radiation Laws • Stefan Boltzmann Law • Energy emitted per unit area per unit time increases as the fourth power of the star’s surface temperature. • Large bodies radiate more energy than do small bodies at the same temperature • Luminosity α radius2 X temperature4 • Radius-Luminosity-Temperature relationship: • Knowledge of a star’s luminosity and temperature can yield an estimate of the star’s radius

  29. Estimating Stellar Radii • Stefan Boltzmann law: F=σT4 • Area of a sphere: A=4πR2 • Luminosity α radius2 X temperature4 • So • Luminosity= 4π σ R2 T4 • Or • Luminosityα radius2 X temperature4

  30. Estimating Stellar Radii • Use solar units • L (in solar luminosities)= 3.9x1026W • R (in solar radii)= 696,000 Km • T (solar temperature)= 5800K • We can eliminate the constant 4π σ and rewrite the equation as • L (in solar units)= R2 (in solar radii) x T4 (in units of 5,800K)

  31. Estimating Stellar Radii • L (in solar units)= R2 (in solar radii) x T4 (in units of 5,800K) • To compute the radius, we change the formula to • R=√L/T2 • Aldebaran • Surface Temperature: 4000K • Luminosity: 1.3x1023W • So the luminosity is 330 times the Sun and temperature is 4,000/5,800= 0.69 • R=√330/0.69 • R=18/0.48 • R=39 solar radii

  32. Estimating Stellar Radii • Canopus, the second brightest star in the southern sky • Apparent magnitude of -0.62 • Parallax of 0.0104” • Distance (pc)= 1/ parallax • 1/0.0104= 96pc • M=m-5log(dist/10pc) • M=-0.62-5log(9.6) • M=-5.5

  33. Estimating Stellar Radii • M=-5.5 • L= 10 –(M-4.83)/2.5 • L= 10-(-5.5-4.83)/2.5 • L=10 -(-4.132) • L≈ 14,000 • Canopus spectral type is an F0: implying a surface temperature of 7,400 K or 1.3 solar temperature • L=R2xT4 • R=√L/T2 • R=√14,000/1.69 • R≈70 solar Radii

  34. Giants and Dwarfs • Giants are any star whose radii are between 10 and 100 solar radii. • Aldebaran is red in color, so it is classified as a Red Giant. • Stars ranging up to 1000 solar radii are known as supergiant • Betelgeuse is a supergiant

  35. Giants and Dwarfs • Sirius B • T= 27,000 K (4.5) • L= 1025W (0.025) • R=√0.025/4.52 • R=0.007 solar radii • A dwarf is any star whose radius is comparable to or smaller than the Sun (including the Sun) • Because any 27,000 K object glows blue-white, Sirius B is a white dwarf.

  36. Hertzsprung-Russell Diagram Relationship exists between stellar temperature and luminosity

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