17. The Nature of the Stars

1. 17. The Nature of the Stars • Parallax reveals stellar distance • Stellar distance reveals luminosity • Luminosity reveals total energy production • The stellar magnitude scale • Surface temperature determines stellar color • Stellar spectra reveal chemical composition • Stars vary greatly in mass & diameter • Hertzsprung-Russell [H-R] diagrams • Stellar spectra reveal stellar type • Binary stars reveal stellar mass • Binary stars & stellar spectra • Eclipsing binary stars

2. Parallax Reveals Stellar Distance • Definition • Apparent object motion caused by observer motion • Geometry between nearby & distant objects • Observer’s movement causes large shift of nearby object • Observer’s movement causes small shift of distant object • An optical illusion • The nearby object is known to be stationary • The distant object is assumed to be moving • Deduction • Required data • Linear distance to the nearby object • Linear distance the observer has moved • Required calculation • d = 1 / p

3. Parallax on Earth

4. Parallax in the Heavens

5. The Space (True) Velocity of Stars • Fundamental considerations • Motion relative to Earth is important • Evaluate the danger of being hit • Evaluate the general motion of stars in our vicinity • All celestial objects are in motion • Generally neither parallel nor perpendicular to line of sight • Velocity is a vector • Magnitude + Direction • Often represented as an arrow • Vectors can be resolved into two perpendicular directions • Any arbitrary pair of perpendicular directions will work • Parallel to & perpendicular to our of sight works best • Radial & tangential velocity are determined • Fundamental requirement • The ability to measure radial & tangential velocities

6. Measuring Radial & Tangential Velocity • Radial velocity measurement • Measure the star’s Doppler shift • Red shift The celestial object is moving away from us • Blue shift The celestial object is moving toward us • Tangential velocity measurement • Measure the star’s proper motion • Small The star is moving slowly parallel to us • Large The star is moving quickly parallel to us

7. Stellar Parallax • Precisely 1.00 AU as the measurement baseline • Essentially the radius of the Earth’s orbit • Diameter is larger but not used • Measurements required very near sunset & sunrise • The parsec (pc) is the unit of measure • 1.00 pc = Stellar parallax of 1.00 arcsecond • 1.00 pc = 3.26 ly (light years) • Can measure interstellar & intergallactic distances • Should measure distance to newest stars • This is an actual distance measurement

8. Radial & Tangential Velocity of Stars Space velocity Tangential velocity Radial velocity

9. Stellar Distance Reveals Luminosity • Luminosity Actual brightness • Actual energy output per unit time • Often compared to the Sun’s luminosity • 3.86 . 1026 Watts [Joules . sec-1] • Measured using a photometer • Crucial consideration • The farther an object is, the dimmer it appears • The relationship is inverse-squared • Brightness is proportional to inverse square of distance • 10 times the distance means 10-2 (1 / 100) the brightness

10. Inverse-Square Law of Intensity

11. Bright Dim Number of Stars of Any Luminosity

12. The Stellar Magnitude Scale • Magnitude Apparent brightness • Ancient astronomers used informal magnitude scale • Brightest stars = Magnitude 1.0 • Dimmest stars = Magnitude 6.0 • An inverse logarithmic scale • Modern astronomers use formal magnitude scale • Ancient scale has brightness difference of about 100 • Modern scale has brightness difference of exactly 100 • There are 5 magnitudes to be accommodated • 1001/5 = 1000.2 = 2.511886432 @ 2.5 • Any one-magnitude difference is a brightness difference of ~ 2.50 • Any two-magnitude difference is a brightness difference of ~ 6.25 • An extremely unusual characteristic • Mag. –10 is 108 times brighter than mag. +10

13. The Apparent Magnitude Scale

14. The Absolute Magnitude Scale • Definition • Star brightness at a standard distance of 10.0 pc • The Sun • Absolute magnitude is + 4.8 • The Sun would be a rather dim star in our sky • The Sun would not be naked-eye visible from most cities

15. Surface Temperature Determines Color • Basic physical processes • Most stars radiate almost like perfect blackbodies • They emit a continuous spectrum • Wavelength distribution determined only by TK • Wavelengths decrease as temperatures increases • The progression is from red (cool) to blue (hot) • Wood embers in a fireplace & xenon arc auto headlights • Measurement procedures • Standard U B V filters sample the blackbody curve • U Ultraviolet Near-ultraviolet Extremely hot • B Blue Violet, blue & green Hot • V Visible green & yellow Warm • Calculate the color ratio • bV / bB“Visible brightness” / “Blue” brightness

16. Star Blackbody Temperature & Color

17. Star Color: Ultraviolet, Blue & Visible

18. Star Temperature, Color & Color Ratio

19. Stellar Spectra Reveal Composition • Original spectral classes • Determined before spectral lines were understood • 15 spectral classes: A B C D E F G H I J K L M N O • Code letters assigned alphabetically • Sequence determined by hydrogen Balmer line strength • Modern spectral classes • Determined after spectral lines were understood • 7 spectral classes retained O B A F G K M • 2 spectral classes added L T • Classes L & T represent brown dwarfs, which are not true stars • Code letters retained but reordered • Sequence determined by a progression of spectral lines • Included understanding of the strength of various absorption lines • Sequence found to be a temperature progression • Hottest stars are spectral class O Blue-white • Coolest stars are spectral class M Red

20. Harvard College Observatory Willamina Fleming Classifying Spectra

21. Principal Types of Stellar Spectra

22. Strength of Some Absorption Lines

23. Spectral Sequence (Table 17-2)

24. Stars Vary Greatly in Mass & Size Mass determines every aspect of a star • Mass varies greatly • Least massive stars ~ 0.08 times MSun • Most massive stars ~ 110 times MSun • More massive a star More compressed its core • Core temperatures & pressures are higher • Core is a larger percent of the star’s diameter • More massive a star Faster it fuses hydrogen • A function of core temperature, pressure & size • Determining star diameter • Distance Parallax needed • Luminosity Apparent brightness needed • Surface temperature Spectral type needed

25. Determining the Radius of a Star

26. Hertzsprung-Russell [H-R] Diagrams • Simple Cartesian graphs • X-axis Spectral classes • Photosphere temperature • Photosphere color • Y-axis Energy output • Absolute magnitude • Solar luminosities • Absolute luminosities • Regions on an H-R diagram • Main sequence • Band from lower right to upper left Hydrogen-fusing stars • Upper right quadrant • Cool (red) & bright (big) Forming & dying stars • Lower left quadrant • Hot (white) & dim (small) Dead white dwarf stars

27. An Unusual H-R Characteristic • Normal Cartesian graphs • X-axis Low to high values from left to right • Y-axis Low to high values from bottom to top • H-R diagrams • X-axis High to low values from left to right • Y-axis Low to high values from bottom to top

28. Hot Cool Hertzsprung-Russell (H-R) Diagram

29. Star Sizes Shown on an H-R Diagram

30. Stellar Spectra Reveal Star Type • Basic physical processes • Star atmospheric pressure determines line strength • The closer atoms are, the more often they interact • Star pressure is determined by status • Main sequence Hydrogen fuses into helium • Giant/SupergiantHelium fuses into heavier elements • White dwarf White-hot core of a dead star • Basic star types • Giant stars • Very small He-fusing core & very large convective zone • Main sequence stars • Typical H-fusing core & normal convective zone • White dwarf stars • No fusion at all & no convective zone

31. Luminosity Affects Stellar Spectra Low-density photosphere: Narrow lines The B8 supergiant star Rigel (58,000 LSun) The B8 main sequence star Algol (100 LSun) High-density photosphere: Broad lines

32. Luminosity Classes of Stars

33. Binary Stars Reveal Stellar Mass • Types of double stars • Optical binary stars • True binary stars • Visual binary stars appear as two stars • Spectroscopic binary stars appear as split spectral lines • Binary stars & stellar mass • Determine the orbit size of the stars • Use Kepler’s third law to calculate M1 + M2 • The two stars actually orbit the common center of mass • Relative size of the two orbits determines M1 / M2 • Data are used to produce mass-luminosity graphs

34. Binary Star Orbits: One Held Stationary

35. Binary Stars Orbit the Center of Mass

36. The Mass-Luminosity Relationship

37. The Main Sequence & Stellar Mass

38. Stellar Spectra & Binary Stars • Spectroscopic binaries • Binaries that cannot be detected visually • Points of light whose absorption lines vary cyclically • Sometimes the lines merge into a single line • Sometimes the lines split into two lines • Possibilities • Simple case Both stars are the same spectral class • Typical case Each star is a differentspectral class • One major difficulty • Usually, the orbital plane’s tilt cannot be determined • Occasionally, the stars eclipse one another • The orbital plane is is our line of sight

39. Spectroscopic Binary Star Systems One star is moving toward the Earth, the other away Neither star is moving toward or away from the Earth

40. Eclipsing Binary Stars • Partially eclipsing • Very small brightness & color variations • Totally eclipsing • Moderate brightness & color variations • Tidal distortion • Dramatic brightness & color variations • Hot-spot reflection • Erratic brightness & color variations

41. Two Possible Eclipsing Binary Systems

42. Parallax reveals stellar distance Apparent shift due to observer’s shift Base line is 1.00 AU 1.00 parsec [pc] = 3.26 ly Space velocity of stars Vector addition gives true velocity Radial velocity Doppler shift Tangential velocity Proper motion Stellar distance reveals luminosity Luminosity is energy per unit time Inverse square intensity relationship Measure apparent brightness The stellar magnitude scale Brightest to dimmest: 1.0 to 6.0 This is an inverse logarithmic scale Bright stars have low magnitudes Negative magnitudes are possible Apparent & absolute magnitude Standard distance of 10.0 pc Surface temperature determines color Hot stars are blue-white Cool stars are red Spectral classification of stars Variations in absorption spectral lines O B A F G K M Hot to cool The H-R diagram Basics Spectral class on the X-axis Luminosity on the Y-axis Regions Main sequence Giant stars White dwarfs Binary stars reveal stellar mass Determination of orbital size Provides M1 + M2 Determination of center of mass Provides M1 / M2 Important Concepts