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

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

Parallax on Earth

Parallax in the Heavens

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

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

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

Radial & Tangential Velocity of Stars

Radial velocity

Tangential velocity

Space velocity

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

Inverse-Square Law of Intensity

Number of Stars of Any Luminosity

Bright Dim

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

The Apparent Magnitude Scale

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

Surface Temperature Determines Color• Basic physical processes

– Most stars radiate like almost 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

Star Blackbody Temperature & Color

Star Color: Ultraviolet, Blue & Visible

Star Temperature, Color & Color Ratio

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

Willamina Fleming Classifying Spectra

Harvard College Observatory

Principal Types of Stellar Spectra

Strength of Some Absorption Lines

Spectral Sequence (Table 17-2)

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

Determining the Radius of a Star

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

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

Hertzsprung-Russell (H-R) DiagramHot Cool

Star Sizes Shown on an H-R Diagram

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/Supergiant Helium fuses into heavier

elements• White dwarf White-hot exposed 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

Luminosity Affects Stellar Spectra

Low-density photosphere: Narrow linesThe B8 supergiant star Rigel (58,000 LSun)

The B8 main sequence star Algol (100 LSun)High-density photosphere: Broad lines

Luminosity Classes of Stars

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

Binary Star Orbits: One Held Stationary

Binary Stars Orbit the Center of Mass

The Mass-Luminosity Relationship

The Main Sequence & Stellar Mass

Stellar Spectra & Binary Stars• Spectroscopic binaries

– Binaries that cannot be detected visually– Points of light whose absorption lines vary cyclically

• Sometimes the lines merge intoa single line• Sometimes the lines split intotwo 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 in our line of sight

Spectroscopic Binary Star Systems

One star is moving toward the Earth, the other away

Neither star is moving toward or away from the Earth

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

Two Possible Eclipsing Binary Systems

• 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 velocityDoppler shift

• Tangential velocityProper 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