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 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

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 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

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

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 = 3.26 ly (light years) Large enough to measure interstellar & intergallactic distances

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 the inverse square of the distance 10 times the distance means 10-2 (1 / 100) the brightness

The Inverse-Square Law of Intensity

The Number of Stars of Any Luminosity Bright Dim

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 = 1000.2 = 2.511886432 @ 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

The Apparent Magnitude Scale

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

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

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 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

Willamina Fleming Classifying Spectra Harvard College Observatory

Principal Types of Stellar Spectra

The Strength of Some Absorption Lines

The Spectral Sequence (Table 19-2)

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

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

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

Star Sizes Graphed on an H-R Diagram

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

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

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 These data are used to produce mass-luminosity graphs

Binary Star Orbits: One Held Stationary

Binary Star Orbits: The Center of Mass

The Mass-Luminosity Relationship

The Main Sequence & Stellar Masses

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

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

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