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 Space velocity Tangential velocity Radial velocity Stellar Distance Reveals Luminosity Luminosity Actual brightness Actual energy output per unit time Often compared to the Sun s luminosity 3.86. 10 26 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 100 1/5 = 100 0.2 = 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 10 8 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 b V / b B 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 Coolest stars are spectral class M Blue-white 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 M Sun Most massive stars ~ 110 times M Sun 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 Upper right quadrant Cool (red) & bright (big) Lower left quadrant Hot (white) & dim (small) Hydrogen-fusing stars Forming & dying stars 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 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 Luminosity Classes of Stars Low-density photosphere: Narrow lines The B8 supergiant star Rigel (58,000 L Sun ) The B8 main sequence star Algol (100 L Sun ) High-density photosphere: Broad lines 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 Binary Star Orbits: One Held Stationary Use Kepler s third law to calculate M 1 + M 2 The two stars actually orbit the common center of mass Relative size of the two orbits determines M 1 / M 2 These data are used to produce mass-luminosity graphs 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 Typical case One major difficulty Both stars are the same spectral class Each star is a different spectral class 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 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 Important Concepts 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 M 1 + M 2 Determination of center of mass Provides M 1 / M 2