Atoms and Starlight

1. 0 Atoms and Starlight Chapter 7

2. 0 Guidepost • In the last chapter you read how telescopes gather light from the stars and how spectrographs spread the light out into spectra. Now you are ready to see what all the fuss is about. Spectra contain the secrets of the stars. Here you will find answers to four essential questions: • What is an atom? • How do atoms interact with light? • What kinds of spectra do you see when you look at celestial objects? • What can you learn from a star’s spectrum?

3. 0 Guidepost (continued) • This chapter marks a change in the way you will look at nature. Up to this point, you have been thinking about what you can see with your eyes alone or aided by telescopes. In this chapter, you begin using modern astrophysics to search out secrets of the stars that lie beyond what you can see, and that leads to an important question about science: • How can we understand the world around us if it depends on the atomic world we cannot see? • The analysis of spectra is a powerful tool, and in the chapters that follow you will use that tool to study the sun and stars.

4. 0 Outline I. Atoms A. A Model Atom B. Different Kinds of Atoms C. Electron Shells II. The Interaction of Light and Matter A. The Excitation of Atoms B. Radiation from a Heated Object C. Two Radiation Laws

5. 0 Outline (continued) III. Stellar Spectra A. The Formation of a Spectrum B. The Balmer Thermometer C. Spectral Classification D. The Composition of the Stars E. The Doppler Effect F. Calculating the Doppler Velocity G. The Shapes of Spectral Lines

6. 0 The Amazing Power of Starlight Just by analyzing the light received from a star, astronomers can retrieve information about a star’s • Total energy output • Surface temperature • Radius • Chemical composition • Velocity relative to Earth • Rotation period

7. 0 Atomic Structure • An atom consists of an atomic nucleus (protons and neutrons) and a cloud of electrons surrounding it. • Almost all of the mass is contained in the nucleus, while almost all of the space is occupied by the electron cloud. 如果將原子核放大到葡萄籽的大小 電子雲將有好幾個足球場大

8. 0 Nuclear Density If you could fill a teaspoon just with material as dense as the matter in an atomic nucleus, it would weigh ~ 2 billion tons!!

9. 0 Different Kinds of Atoms • The kind of atom depends on the number of protons in the nucleus. Different numbers of neutrons↔ different isotopes(同位素) • Most abundant: Hydrogen (H), with one proton (+ 1 electron) • Next: Helium (He), with 2 protons (and 2 neutrons + 2 el.) Helium 4

10. 0 Electron Orbits • Electron orbits in the electron cloud are restricted to very specific radii and energies. r3, E3 r2, E2 r1, E1 • These characteristic electron energies are different for each individual element.

11. 0 Atomic Transitions • An electron can be kicked into a higher orbit when it absorbs a photon with exactly the right energy. Eph = E3 – E1 Eph = E4 – E1 Wrong energy • The photon is absorbed, and • the electron is in an excited state. (Remember that Eph = h*f) • All other photons pass by the atom unabsorbed.

12. 0 Color and Temperature Stars appear in different colors, Orion Betelgeuse from blue (like Rigel) via yellow (like our sun) to red (like Betelgeuse). These colors tell us about the star’s temperature. Rigel

13. 0 Black Body Radiation (1) The light from a star is usually concentrated in a rather narrow range of wavelengths. The spectrum of a star’s light is approximately a thermal spectrum called a black body spectrum. A perfect black body emitter would not reflect any radiation. Thus the name “black body”.

14. 0 Two Laws of Black Body Radiation 1. The hotter an object is, the more energy it emits: Energy Flux F = s*T4 where F = Energy Flux = = Energy given off in the form of radiation, per unit time and per unit surface area [J/s/m2](J:焦耳) s = Stefan-Boltzmann constant

15. 0 Two Laws of Black Body Radiation • 2. The peak of the black body spectrum shifts towards shorter wavelengths when the temperature increases. • Wien’s displacement law: • lmax≈ 3,000,000 nm / TK • (where TK is the temperature in Kelvin)

16. 0 Stellar Spectra The spectra of stars are more complicated than pure blackbody spectra. They containcharacteristic lines, called absorption lines. With what we have learned about atomic structure, we can now understand how those lines are formed.

17. 0 Kirchhoff’s Laws of Radiation (1) • A solid, liquid, or dense gas excited to emit light will radiate at all wavelengths and thus produce a continuous spectrum.

18. 0 Kirchhoff’s Laws of Radiation (2) 2. A low-density gas excited to emit light will do so at specific wavelengths and thus produce an emission spectrum. Light excites electrons in atoms to higher energy states Transition back to lower states emits light at specific frequencies

19. 0 Kirchhoff’s Laws of Radiation (3) 3. If light comprising a continuous spectrum passes through a cool, low-density gas, the result will be an absorption spectrum. Light excites electrons in atoms to higher energy states Frequencies corresponding to thetransition energies are absorbed from the continuous spectrum.

20. 0 The Spectra of Stars The inner, dense layers of a star produce a continuous (blackbody) spectrum. Cooler surface layers absorb light at specific frequencies. => Spectra of stars are absorption spectra.

21. 0 Analyzing Absorption Spectra • Each element produces a specific set of absorption (and emission) lines. • Comparing the relative strengths of these sets of lines, we can study the composition of gases. By far the most abundant elements in the Universe Metal !!

22. 0 Lines of Hydrogen Balmer lines of hydrogen can be seen at optical wavelengths

23. 0 The Balmer Lines n = 1 n = 4 Transitions from 2nd to higher levels of hydrogen n = 5 n = 3 n = 2 Ha Hb Hg The only hydrogen lines in the visible wavelength range 2nd to 3rd level = Ha (Balmer alpha line) 2nd to 4th level = Hb (Balmer beta line) …

24. 0 Observations of the H-Alpha Line Emission nebula, dominated by the red Ha line

25. 0 Absorption Spectrum Dominated by Balmer Lines Modern spectra are usually recorded digitally and represented as plots of intensity vs. wavelength

26. 0 The Balmer Thermometer Balmer line strength is sensitive to temperature: Most hydrogen atoms are ionized => weak Balmer lines Almost all hydrogen atoms in the ground state (electrons in the n = 1 orbit) => few transitions from n = 2 => weak Balmer lines 注意: 溫度向左增加 !!

27. 0 Measuring the Temperatures of Stars Comparing line strengths, we can measure a star’s surface temperature!

28. 0 Spectral Classification of Stars (1) Different types of stars show different characteristic sets of absorption lines. Temperature

29. 0 Spectral Classification of Stars (2) Mnemonics (幫助記憶的方法)to remember the spectral sequence:

30. 0 Stellar Spectra O B A F Surface temperature G K M

31. 0 The Composition of Stars From the relative strength of absorption lines (carefully accounting for their temperature dependence), one can infer the composition of stars.

32. 0 The Doppler Effect (1) Sound waves always travel at the speed of sound – just like light always travels at the speed of light, independent of the speed of the source of sound or light. The light of a moving source is blue/red shifted by Dl/l0 = vr/c l0 = actual wavelength emitted by the source Dl = Wavelength change due to Doppler effect vr = radial velocity Blue Shift (to higher frequencies) Red Shift (to lower frequencies) vr

33. 0 The Doppler Effect (2) The Doppler effect allows us to measure the component of the source’s velocity along our line of sight. This component is called radial velocity, vr.

34. 0 The Doppler Effect (2) Example:

35. 0 The Doppler Effect (4) Take l0 of the Ha (Balmer alpha) line: l0 = 656 nm Assume, we observe a star’s spectrum with the Ha line at l = 658 nm. Then, Dl = 2 nm. We findDl/l0 = 0.003 = 3*10-3 Thus, vr/c = 0.003, or vr = 0.003*300,000 km/s = 900 km/s. The line is red shifted, so the star is receding from us with a radial velocity of 900 km/s.

36. 0 Doppler Broadening In principle, line absorption should only affect a very unique wavelength. In reality, also slightly different wavelengths are absorbed. ↔Lines have a finite width; we say: they are broadened Blue shifted abs. Red shifted abs. One reason for broadening: The Doppler effect! vr Observer vr Atoms in random thermal motion

37. 0 Line Broadening • Higher Temperatures • Higher thermal velocities  broader lines Doppler Broadening is usually the most important broadening mechanism.