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BINARIES

BINARIES. Read Your Textbook: Foundations of Astronomy Chapter 10 Homework Problems Chapter 9 Review Questions: 1, 4, 5, 7 Review Problems: 1-5 Web Inquiries: 1 Homework Problems Chapter 10 Review Questions: 1, 2, 4, 6-8 Review Problems: 1-4, 8 Web Inquiries: 2. Binary Center of Mass.

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BINARIES

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  1. BINARIES • Read Your Textbook: Foundations of Astronomy • Chapter 10 • Homework Problems Chapter 9 • Review Questions: 1, 4, 5, 7 • Review Problems: 1-5 • Web Inquiries: 1 • Homework Problems Chapter 10 • Review Questions: 1, 2, 4, 6-8 • Review Problems: 1-4, 8 • Web Inquiries: 2

  2. Binary Center of Mass Balance point

  3. Binary Separation a = rA + rB Visual Binary Star

  4. SpectroscopicBinary From Doppler Shift

  5. Spectroscopic Orbit This represents the orbit of the star that is farthest from the center of mass. Its velocity amplitude is higher. It is the lower mass star. Velocity Time

  6. Spectroscopic Orbit This represents the orbit of the star that is closest to the center of mass. Its velocity amplitude is smaller. It is the higher mass star. Velocity Time

  7. Spectroscopic Parameters Center of Mass Low Mass Star Velocity Amplitude High Mass Star Velocity Amplitude Velocity Time

  8. Inclination K velocity = amplitude of radial velocity (m/s) Doppler effect is maximized for an “edge-on” system; non-existent for a “pole-on” system. Inclination ~ 90o Inclination ~ 0o

  9. Inclination K velocity = amplitude of radial velocities v sin(i) v = velocity i = 90 degrees, edge on i = 0 degrees, pole face

  10. Spectroscopic Parameters g velocity = velocity of Center of Mass (CoM) K velocity = amplitude of radial velocity (v sin i) P = period Mass ratio M2/M1 = K1/K2 Smaller star orbits farther from the CoM, Larger star is closer from the CoM. Smaller star has large K velocity.

  11. Spectroscopic Orbit Center of Mass Velocity?

  12. Spectroscopic Orbit Orbital Period?

  13. Spectroscopic Orbit

  14. Spectroscopic Orbit K velocities?

  15. Spectroscopic Orbit K2 = 115 - 40 = 75

  16. Spectroscopic Orbit K1 = 65 - 40 = 25

  17. K2/K1= M1/M2 = 75/25 = 3 One Star is 3 times more massive than the other. Spectroscopic Orbit

  18. Eclipsing Binary Light Intensity variations are observed because of blocking of light by each of the stars in the system if inclination is large enough. Systems are edge-on or nearly edge-on as seen from earth. (i.e. inclinations are ~ 90 degrees)

  19. Algol (b Perseus) Light Curve Light Intensity versus Time

  20. Eclipsing Binary Light Curve B A

  21. Eclipsing Binary Light Curve B A LA + LB LA + LB LB+ f LA LA Only

  22. Eclipsing Binary Light Curve B A LA + LB LA + LB LB+ f LA LA Only

  23. Eclipsing Binary Light Curve B A LA + LB LA + LB LB+ f LA LA Only

  24. Eclipsing Binary Light Curve B A LA + LB LA + LB LB+ f LA LA Only

  25. Simple Eclipsing Binary

  26. Unequal Temperature and Size

  27. Star Spots

  28. Light Curve Fit

  29. Light Curve Varieties

  30. Light Curve Contacts

  31. Light Curve Contacts Time interval (t2 - t1) ~ size of “orange” star t1 t2 t3 t4

  32. Light Curve Contacts Time interval (t3 - t1) ~ size of “yellow” star t1 t2 t3 t4

  33. Size Determinations 2 RA = (VA+VB) ( t2 - t1 ) 2 RB = (VA+VB) ( t3 - t1 ) Velocities obtained from spectroscopic orbit. Contact times obtained from eclipse light curve. The radii of the stars are then calculated to yield their size.

  34. Determining Radii

  35. Intrinsic Luminosity L = 4pR2sT4 Radius obtained from spectroscopic orbit with eclipse light curve. Temperature obtained from observations of spectrum.

  36. Fundamental Stellar Parameters • Spectra • Distance • Temperature • Chemical Composition • Luminosity (if distance is known) • Velocity • Binaries • Orbital Velocities • Sizes • Masses • Luminosity

  37. Fundamental Stellar Parameters

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