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 are determined Fundamental requirement The ability to measure radial & tangential velocities Measuring Radial & Tangential Velocity Radial 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 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 Space Tangential Radial 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 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 100 1/5 = 100 0.2 = 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 10 8 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 T K 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 Willamina Fleming Classifying Spectra Original spectral classes Determined before spectral lines were understood 15 spectral classes: ABCDEFGHIJKLMNO Code letters assigned alphabetically Sequence determined by hydrogen Balmer line strength Modern spectral classes Determined after spectral lines were understood 7 spectral classes retained 2 spectral classes added OBAFGKM LT 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 Coolest stars are spectral class M Blue-white Red 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 Most massive stars More massive a star ~ 0.08 times MSun ~ 110 times MSun 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 Luminosity Surface temperature Parallax needed Apparent brightness needed 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) Diagram Hot 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 Luminosity Classes of Stars 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 Binary Stars Reveal Stellar Mass Binary Star Orbits: One Held Stationary Types of double stars Optical binary stars True Visual binary stars 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 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 into a single line Sometimes the lines split into two lines Possibilities Simple case Typical case Both stars are the same spectral class 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 Eclipsing Binary Stars Partially eclipsing One star is moving toward the Earth, the other away Very small brightness & color variations Totally eclipsing Moderate brightness & color variations Tidal distortion Dramatic brightness & color variations Hot-spot reflection Neither star is moving toward or away from the Earth Erratic brightness & color variations Important Concepts Two Possible Eclipsing Binary Systems Parallax reveals stellar distance Apparent shift due to observer s shift Hot stars are blue-white Base line is 1.00 AU Cool stars are 1.00 parsec [pc] = 3.26 ly Space of stars Tangential Doppler shift OBAFGKM Proper motion Spectral class on the X-axis Luminosity Inverse square intensity relationship Measure apparent brightness This is an inverse logarithmic scale Bright stars have low magnitudes Negative magnitudes are possible Apparent & absolute magnitude Standard distance of 10.0 pc on the Y-axis Regions Main sequence Giant stars The stellar magnitude scale Brightest to dimmest: 1.0 to 6.0 Hot to cool The H-R diagram Basics Stellar distance reveals luminosity Luminosity is energy per unit time red Spectral classification of stars Variations in absorption spectral lines Vector addition gives true Radial Surface temperature determines color White dwarfs Binary stars reveal stellar mass Determination of orbital size Provides M1 + M2 Determination of center of mass Provides M1 / M2