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The Family of Stars Chapter 8:
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Organizing the Family of Stars: The Hertzsprung-Russell Diagram We know: Stars have different temperatures, different luminosities, and different sizes. To bring some order into that zoo of different types of stars: organize them in a diagram of: LuminosityversusTemperature (or spectral type) Luminosity Temperature Spectral type: O B A F G K M Hertzsprung-Russell Diagram or Absolute mag.
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The Hertzsprung Russell Diagram Most stars are found along the Main Sequence
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The Hertzsprung-Russell Diagram Stars spend most of their active life time on the Main Sequence. Same temperature, but much brighter than MS stars → Must be much larger → Giant Stars Same temp., but fainter → Dwarfs
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Radii of Stars in the Hertzsprung- Russell Diagram 10,000 times the sun’s radius 100 times the sun’s radius As large as the sun 100 times smaller than the sun Rigel Betelgeuze Sun Polaris
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Luminosity Classes Ia Bright Supergiants Ib: Supergiants II: Bright Giants III: Giants IV: Subgiants V: Main- Sequence Stars Ia Ib II III IV V
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Luminosity effects on the width of spectral lines Same spectral type, but different luminosity Lower gravity near the surfaces of giants smaller pressure smaller effect of pressure broadening narrower lines
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Binary Stars More than 50 % of all stars in our Milky Way are not single stars, but belong to binaries: Pairs or multiple systems of stars which orbit their common center of mass If we can measure and understand their orbital motion, we can estimate the stellar masses.
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The Center of Mass center of mass = balance point of the system Both masses equal => center of mass is in the middle, r A = r B. The more unequal the masses are, the more it shifts toward the more massive star.
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Estimating Stellar Masses Recall Kepler’s 3. Law: P y 2 = a AU 3 Valid for the Solar system: star with 1 solar mass in the center We find almost the same law for binary stars with masses M A and M B different from 1 solar mass: M A + M B = a AU 3 ____ Py2Py2 (M A and M B in units of solar masses)
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Visual Binaries The ideal case: Both stars can be seen directly, and their separation and relative motion can be followed directly.
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Spectroscopic Binaries Usually, the binary separation a can not be measured directly because the stars are too close to each other. A limit on the separation and thus the masses can be inferred in the most common case: Spectroscopic Binaries
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Spectroscopic Binaries The approaching star produces blue shifted lines; the receding star produces red shifted lines in the spectrum. Doppler shift → Measurement of radial velocities → Estimate of separation a → Estimate of masses
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Spectroscopic Binaries Time Typical sequence of spectra from a spectroscopic binary system
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Eclipsing Binaries Usually, the inclination angle of binary systems is unknown → uncertainty in mass estimates. Special case: Eclipsing Binaries Here, we know that we are looking at the system edge-on!
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Eclipsing Binaries Peculiar “double-dip” light curve Example: VW Cephei
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Eclipsing Binaries From the light curve of Algol, we can infer that the system contains two stars of very different surface temperature, orbiting in a slightly inclined plane. Example: Algol in the constellation of Perseus
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The Mass-Luminosity Relation More massive stars are more luminous. L ~ M 3.5
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Masses of Stars in the Hertzsprung- Russell Diagram Masses in units of solar masses Low masses High masses Mass The higher a star’s mass, the more luminous (brighter) it is: High-mass stars have much shorter lives than low-mass stars: Sun: ~ 10 billion yr. 10 M sun : ~ 30 million yr. 0.1 M sun : ~ 3 trillion yr. L ~ M 3.5 t life ~ M -2.5
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Surveys of Stars Ideal situation: Determine properties of all stars within a certain volume Problem: Fainter stars are hard to observe; we might be biased towards the more luminous stars.
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A Census of the Stars Faint, red dwarfs (low mass) are the most common stars. Giants and supergiants are extremely rare. Bright, hot, blue main- sequence stars (high- mass) are very rare.
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