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 actual 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 our line of sight
Velocity is a vector
Magnitude + Direction
Often represented as an arrow
Vectors can be resolved into two perpendicular directions
Generally, any arbitrary pair of perpendicular directions will work
In astronomy, parallel to & perpendicular to our of sight works best
In astronomy, 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 star is moving away from us
Blue shift The star 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
This is essentially the radius of the Earth’s orbit
The diameter is larger but not used
Measurements would be required very near sunset & sunrise
The parsec is the unit of measure
1.00 parsec (pc) means stellar parallax of 1.00 arcseconds
1.00 pc = ly (light years)
Large enough to measure interstellar & intergallactic distances

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

9. Stellar Distance Reveals Luminosity
Luminosity Actual brightness
Actual energy output per unit time
Often compared to the Sun’s luminosity
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 the inverse square of the distance
10 times the distance means 10-2 (1 / 100) the brightness

10. The Inverse-Square Law of Intensity

11. The Number of Stars of Any Luminosity
Bright
Dim

12. The Stellar Magnitude Scale
Magnitude Apparent brightness
Ancient astronomers used an informal magnitude scale
Brightest stars = Magnitude 1.0
Dimmest stars = Magnitude 6.0
An inverse logarithmic scale
Modern astronomers use a formal magnitude scale
The ancient scale has brightness difference of about 100
The modern scale has brightness difference of exactly 100
There are 5 magnitudes to be accommodated
1001/5 = = 2.5
Any one-magnitude difference is a brightness difference of ~ 2.5
Magnitude 1.7 is ~ 2.5 times brighter than magnitude 2.7
Any two-magnitude difference is a brightness difference of ~ 6.25
Magnitude 1.7 is ~ 6.25 times brighter than magnitude 3.7
An extremely unusual characteristic
Magnitude –10 is 108 times brighter than magnitude +10

13. The Apparent Magnitude Scale

14. The Absolute Magnitude Scale
Definition
Any star’s 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 is determined entirely by temperature
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 well understood
15 spectral classes named A B C D E F G H I J K L M N O
Code letters assigned alphabetically
Sequence determined by strength of hydrogen’s Balmer lines
Modern spectral classes
Determined after spectral lines were well 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 determined to be a temperature progression
Hottest stars are spectral class O Blue-white
Coolest stars are spectral class M Red

20. Willamina Fleming Classifying Spectra
Harvard College Observatory

21. Principal Types of Stellar Spectra

22. The Strength of Some Absorption Lines

23. The Spectral Sequence (Table 19-2)

24. Stars Vary Greatly in Mass & Diameter
Mass determines every important aspect of a star
Mass varies greatly
Least massive stars ~ 0.08 times MSun
Most massive stars ~ 110 times MSun
The more massive a star, the more compressed its core
Core temperatures & pressures are higher
Core is a larger percent of the star’s diameter
The more massive a star, the 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

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

29. Star Sizes Graphed on an H-R Diagram

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

31. Luminosity Affects a Star’s Spectrum
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
These data are used to produce mass-luminosity graphs

34. Binary Star Orbits: One Held Stationary

35. Binary Star Orbits: The Center of Mass

36. The Mass-Luminosity Relationship

37. The Main Sequence & Stellar Masses

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 different spectral 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. Important Concepts 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