ASTRO 101

1. ASTRO 101 Principles of Astronomy

2. Instructor: Jerome A. Orosz (rhymes with “boris”)Contact: • Telephone: 594-7118 • E-mail: orosz@sciences.sdsu.edu • WWW: http://mintaka.sdsu.edu/faculty/orosz/web/ • Office: Physics 241, hours T TH 3:30-5:00

4. Homework/Announcements • Homework due Tuesday, April 16: Question 4, Chapter 8 (Describe the three main layers of the Sun’s interior.) • Chapter 9 homework due April 23: Question 13 (Draw an H-R Diagram …)

5. Next:How Does the Sun Work?

6. How Does the Sun Work? • Some useful numbers: • The mass of the Sun is 2x1030 kg. • The luminosity of the Sun is 4x1026 Watts. • The first question to ask is: What is the energy source inside the Sun?

7. Energy Sources • A definition: Efficiency = energy released/(fuel mass x [speed of light]2) • Chemical energy (e.g. burning wood, combining hydrogen and oxygen to make water, etc.). • Efficiency = 1.5 x 10-10 • Solar lifetime = 30 to 30,000 years, depending on the reaction. Too short!

8. Energy Sources • A definition: Efficiency = energy released/(fuel mass x [speed of light]2) • Gravitational settling (falling material compresses stuff below, releasing heat). • Efficiency = 1 x 10-6 • Solar lifetime = 30 million years. Too short, although this point was not obvious in the late 1800s.

9. Energy Sources • A definition: Efficiency = energy released/(fuel mass x [speed of light]2) • Nuclear reactions: fusion of light elements (as in a hydrogen bomb). • Efficiency = 0.007 • Solar lifetime = billions of years.

10. How to get energy from atoms • Fission: break apart the nucleus of a heavy element like uranium. • Fusion: combine the nuclei of a light element like hydrogen.

11. More Nuclear Fusion • Fusion of elements lighter than iron can release energy (leads to higher BE’s). • Fission of elements heaver than iron can release energy (leads to higher BE’s).

12. Nuclear Fusion • Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). • Why does this produce energy? • Before: the mass of 4 protons is 4 proton masses. • After: the mass of 2 protons and 2 neutrons is 3.97 proton masses. • Einstein: E = mc2. The missing mass went into energy! 4H ---> 1He + energy

13. Nuclear Fusion • The CNO cycle (left) and pp chain (right) are outlined.

14. Models of the Solar Interior • The interior of the Sun is relatively simple because it is an ideal gas, described by three quantities: • Temperature • Pressure • Mass density • The relationship between these three quantities is called the equation of state.

15. Ideal Gas • For a fixed volume, a hotter gas exerts a higher pressure: Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

16. Hydrostatic Equilibrium • The Sun does not collapse on itself, nor does it expand rapidly. Gravity and internal pressure balance: Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

17. Hydrostatic Equilibrium • The Sun does not collapse on itself, nor does it expand rapidly. Gravity and internal pressure balance. This is true at all layers of the Sun. Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

18. Hydrostatic Equilibrium • The Sun (and other stars) does not collapse on itself, nor does it expand rapidly. Gravity and internal pressure balance. This is true at all layers of the Sun. • The temperature increases as you go deeper and deeper into the Sun!

19. Models of the Solar Interior • The pieces so far: • Energy generation (nuclear fusion). • Ideal gas law (relation between temperature, pressure, and volume. • Hydrostatic equilibrium (gravity balances pressure). • Continuity of mass (smooth distribution throughout the star). • Continuity of energy (amount entering the bottom of a layer is equal to the amount leaving the top). • Energy transport (how energy is moved from the core to the surface).

20. Models of the Solar Interior • Solve these equations on a computer: • Compute the temperature and density at any layer, at any time. • Compute the size and luminosity of the star as a function of the initial mass. • Etc…….

21. Solar Structure Models

22. Solar Structure Models • Here is the model of the structure of the Sun.

23. Next: Characterizing Stars

24. The Sun and the Stars • The Sun is the nearest example of a star. • Basic questions to ask: • What do stars look like on their surfaces? Look at the Sun since it is so close. • How do stars work on their insides? Look at both the Sun and the stars to get many examples. • What will happen to the Sun? Look at other stars that are in other stages of development.

25. Stellar Properties • The Sun and the stars are similar objects. • In order to understand them, we want to try and measure as many properties about them as we can: • Power output (luminosity) • Temperature at the “surface” • Radius • Mass • Chemical composition

26. Observing Other Stars • Recall there is basically no hope of spatially resolving the disk of any star (apart from the Sun). The stars are very far away, so their angular size as seen from Earth is extremely small. • The light we receive from a star comes from the entire hemisphere that is facing us. That is, we see the “disk-integrated” light.

27. Observing Other Stars • To get an understanding of how a star works, the most useful thing to do is to measure the spectral energy distribution, which is a plot of the intensity of the photons vs. their wavelengths (or frequencies or energies). • There are two ways to do this: • “Broad band”, by taking images with a camera and a colored filter. • “High resolution”, by using special optics to disperse the light and record it.

28. Broad Band Photometry • There are several standard filters in use in astronomy. • The filter lets only light within a certain wavelength region through (that is why they have those particular colors).

29. Color Photography • The separate images are digitally processed to obtain the final color image.

30. Color Photography

31. Color Photography

32. Broad Band Photometry • Broad band photometry has the advantage in that it is easy (just need a camera and some filters on the back of your telescope), and it is efficient (relatively few photons are lost in the optics). • The disadvantage is that the spectral resolution is poor, so subtle differences in photon energies are impossible to detect.

33. High Resolution Spectroscopy • To obtain a high resolution spectrum, light from a star is passed through a prism (or reflected off a grating), and focused and detected using some complicated optics.

34. High Resolution Spectroscopy • Using a good high resolution spectrum, you can get a much better measurement of the spectral energy distribution. • The disadvantage is that the efficiency is lower (more photons are lost in the complex optics). Also, it is difficult to measure more than one star at a time (in contrast to the direct imaging where several stars can be on the same image).

35. Stellar Properties • The Sun and the stars are similar objects. • In order to understand them, we want to try and measure as many properties about them as we can: • Power output (luminosity) • Temperature at the “surface” • Radius • Mass • Chemical composition

36. The Luminosity • Luminosity (or power) is a measure of the energy emitted at the surface of the star per second. • We are not at the surface of the star, so we need to extrapolate from measurements we can do. • We can measure the energy received from the star at the Earth. • If we can measure the distance to the star, then we can figure out the energy that the star emitted.

37. The Distance • How can you measure the distance to something? • Direct methods, e.g. a tape measure. Not good for things in the sky. • Sonar or radar: send out a signal with a known velocity and measure the time it takes for the reflected signal. Works for only relatively nearby objects (e.g. the Moon, certain asteroids).

38. The Distance • How can you measure the distance to something? • Direct methods, e.g. a tape measure. Not good for things in the sky. • Sonar or radar: send out a signal with a know velocity and measure the time it takes for the reflected signal. Works for only relatively nearby objects (e.g. the Moon, certain asteroids). • Triangulation: the use of parallax.

39. The Parallax • Parallax is basically the apparent shifting of nearby objects with respect to far away objects when the viewing angle is changes. • Example: hold out your finger and view it with one eye closed, then the other eye closed. Your finger shifts with respect to the background.

40. The Parallax • Example: hold out your finger and view it with one eye closed, then the other eye closed. Your finger shifts with respect to the background.

41. The Parallax • A better example: place an object on the table in front of the room and look at its position against the back wall as you walk by. In most practical applications you will have to change your position to make use of parallax.

42. Triangulation • Triangulation is based on trigonometry, and is often used by surveyors. Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

43. Triangulation • Triangulation is based on trigonometry, and is often used by surveyors. • The length B and the angle p can be measured, so the distance can be computed: d=B/tan(p) Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

44. Triangulation • Triangulation is based on trigonometry, and is often used by surveyors. • This technique can be applied to nearby stars. Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

45. Triangulation • Triangulation is based on trigonometry, and is often used by surveyors. • Here is another diagram showing the technique. This technique can be applied to other stars! Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

46. Triangulating the Stars • The largest baseline one can obtain is the orbit of the Earth! • When viewed at 6 month intervals, a relatively nearby star will appear to shift with respect to distant stars.

47. Triangulating the Stars • The largest baseline one can obtain is the orbit of the Earth! • When viewed at 6 month intervals, a relatively nearby star will appear to shift with respect to distant stars. Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

48. Triangulating the Stars • The largest baseline one can obtain is the orbit of the Earth! • When viewed at 6 month intervals, a relatively nearby star will appear to shift with respect to distant stars. Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

49. Triangulating the Stars http://www.astro.ubc.ca/~scharein/a310/Sim.html#Oneover • Here are two neat Java tools demonstrating parallax: http://spiff.rit.edu/classes/phys240/lectures/parallax/para1_jan.html

50. Triangulating the Stars • When viewed at 6 month intervals, a relatively nearby star will appear to shift with respect to distant stars. • The angle p for the nearest star is 0.77 arcseconds. One can currently measure angles as small as a few thousands of an arcsecond. Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)