Stars

1. Stars Edward Murphy RARE CATS Summer 2001 RARE CATS

2. Stellar Luminosity • The luminosity of a star is the rate at which it is giving off energy. • Not all stars have the same luminosity. • They range from 1/20 to 700,000 times the luminosity of the Sun. • Luminosity varies with temperature. • E = s T4 (energy per square meter). • Luminosity depends on size. • A = 4 p R2 (number of square meters). RARE CATS

3. Apparent Brightness • The apparent brightness depends on the luminosity of the star and its distance from Earth. • Apparent brightness drops as square of distance (Inverse Square Law of Light). • The apparent brightness is measured in apparent magnitudes. RARE CATS

4. Magnitude System • Around 150 B.C. the Greek astronomer Hipparchus compiled a catalog of nearly 1000 stars listing their positions and apparent brightness. • The brightest stars were first magnitude stars. • The next brightest were second magnitude stars. • The faintest stars he could see were sixth magnitude stars. RARE CATS

5. Magnitude System • Today, the magnitude system is defined such that a difference of 5 magnitudes is exactly a factor of 100 times in brightness. • One magnitude is a difference in brightness of about 2.5 times. • Two magnitudes are 2.5x2.5=6.3 times. • Three magnitudes are 2.5x2.5x2.5=15.9 times. RARE CATS

6. Magnitude Differences RARE CATS

7. Magnitude System • Unfortunately, it turns out that many objects are brighter than first magnitude. • These have been assigned magnitudes smaller than 1, including negative numbers. • Sirius, the brightest star in the sky, has an apparent magnitude of –1.5. RARE CATS

8. Magnitude System RARE CATS

9. Magnitude System • Fainter objects have larger apparent magnitudes. • Brighter objects have smaller apparent magnitudes. RARE CATS

10. Magnitude System • The Sun has a magnitude of –26.2. • Your eye can easily see the full moon (magnitude about –13) and the faintest stars (magnitude 6). This is a difference of nearly 20 magnitudes or a range of 108. • The magnitude system is only used in visual astronomy. All other areas of astronomy define brightness in terms of energy per second per area received here on Earth. RARE CATS

11. Colors of Stars RARE CATS

12. Blackbody Curves RARE CATS

13. Spectrum of the Sun RARE CATS

14. Formation of Stellar Spectra • Stars do not have identical absorption line spectra. • Astronomers thought this was due to the fact that the chemical composition of stars varied. • However, most stars have the same composition as the Sun (74% H, 25% He, 1% everything else). • Today we know that stellar spectra look different because different stars have different temperatures. RARE CATS

15. Classification of Stellar Spectra • Originally, the spectra of stars were classified based on their complexity: • A was the simplest, B was next… • Annie J. Cannon was the first to realize that there was a better classification scheme. • In order from hottest to coolest the order is: OBAFGKML • Oh Be a Fine Girl (Guy) Kiss My Lips RARE CATS

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17. Classification of Stellar Spectra • Class L is new. • The 8 classes have been divided into 10 subclasses designated by number: • A B0 is the hottest B star, a B9 is the coolest and is slightly hotter than an A0 star. • The Sun is a G2 star. RARE CATS

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23. Absorption Lines • The strengths of the absorption lines in a stellar spectrum depend not only on the amount of a given element (its abundance), but also the temperature of the star. RARE CATS

24. Hydrogen Absorption Lines • For example, let’s consider hydrogen, the most abundant element in stars. • In very hot stars, hydrogen is completely ionized. Without any electrons, the hydrogen cannot absorb any light hence we see no hydrogen lines. • In moderately hot stars, we see both the Lyman (UV) and Balmer (visible) series. RARE CATS

25. Line Series n=6 n=5 n=4 n=3 n=2 n=1 RARE CATS

26. Formation of Stellar Spectra • In cool stars, we see only the Lyman series and not the Balmer series. Why? • The Balmer series is absorption from the n=2 orbit. The electron must be excited (either through collisions or through UV light) to be in n=2. • In cool stars, there is not enough UV light and the temperature is not high enough to keep the electrons excited, so very few are in n=2. RARE CATS

27. Stellar Absorption Lines RARE CATS

28. Spectral Classification RARE CATS

29. Spectral Classification RARE CATS

30. Astronomical Distances • The astronomical unit (AU) is defined as the average distance from the Earth to the Sun. • 1 AU = 1.496 x 1011 m • The light year (LY) is defined as the distance light travels in one year • 1 LY = 9.461 x 1015 m • 1 AU = 8.3 light minutes RARE CATS

31. Appendix 11: The Brightest Stars RARE CATS

32. Appendix 11: The Brightest Stars RARE CATS

33. Appendix 11: The Brightest Stars RARE CATS

34. Bright Stars • The Sun would appear as a magnitude 6.0 star (barely visible to the naked eye) at a distance of 56 LY • A star with a luminosity 10,000 times that of the Sun will be visible with the naked eye up to 100 times farther, 5600 LY (the inverse square law says that if we move it 100 times farther, it gets 1002=10,000 times fainter). RARE CATS

35. Appendix 10: The Nearest Stars RARE CATS

36. Appendix 10: The Nearest Stars RARE CATS

37. Appendix 10: The Nearest Stars RARE CATS

38. Appendix 10: The Nearest Stars RARE CATS

39. Appendix 10: The Nearest Stars RARE CATS

40. Faint Stars • The Sun would appear as a magnitude 6.0 star (barely visible to the naked eye) at a distance of 56 LY. • A star with a luminosity 1/100 of the Sun must be 10 times closer to have the same apparent magnitude (inverse square law). That is, it must be within 5.6 LY of the Sun to be visible with the naked eye. RARE CATS

41. Density of Stars in the Solar Neighborhood • There are 59 stars within 16 LY of the Sun. • This is a volume of 17,157 cubic LY. • There is 1 star for every 290 cubic LY. • The average distance between stars is 6.6 LY (cube root of 290). • The closest star to the Sun is Alpha Centauri system (4.4 LY). RARE CATS

42. Density of Matter in the Solar Neighborhood • Density of matter is expressed in g/cm3. • Water has a density of 1 g/cm3, rocks 2.5-3.5 g/cm3, and gold 19.3 g/cm3. • If a typical star has a mass of 0.4 Msun, the average density in the solar neighborhood is 3x10-24 g/cm3. • This is about 1-2 hydrogen atoms per cubic centimeter (compare that to the 2.4x1019 molecules per cm3 in the air in this room). RARE CATS

43. Binary Stars • Roughly half of all stars are in binary systems (some triple and quadruple). • Visual binaries are binary star systems where each star can be seen with a telescope. • Spectroscopic binaries are those in which the stars are too close to see individually, but the spectral lines show the Doppler shift due to the orbital motion of the stars. RARE CATS

44. Orbit of Kruger 60 RARE CATS

45. Orbit of a Binary Star RARE CATS

46. Spectroscopic Binary RARE CATS

47. Ursa Major, The Big Bear (Big Dipper) RARE CATS

48. Mizar • Mizar is an example of a complicated system. • If you have good eyesight, you can see a faint companion to Mizar called Alcor. These stars are an optical double, that is, they appear close together but do not orbit one another. • In a telescope, Mizar does have a close companion. Thus, Mizar is a visual binary. The two visible components are Mizar A and Mizar B. RARE CATS

49. Mizar • In fact, Mizar was the first binary star, noticed in 1650 by Riccioli. • With a spectroscope, it can be seen that both Mizar A and Mizar B are spectroscopic binaries. RARE CATS

50. Mass of Sirius • When we are dealing with binary stars, the masses of the two stars are often similar, and we cannot simply ignore the mass of the lighter object like we can with planets, moons or satellites. • For example, consider the star Sirius and its companion (a white dwarf). The period of the orbit is 50 years and the distance between the stars is 20 AU. RARE CATS