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Chapter 7 Starlight and Atoms

Guidepost Some chapters in textbooks do little more than present facts. The chapters in this book attempt to present astronomy as organized understanding. But this chapter is special. It presents us with a tool. The interaction of light with matter gives astronomers clues about the nature of the heavens, but the clues are meaningless unless astronomers understand how atoms leave their traces on starlight. Thus, we dedicate an entire chapter to understanding how atoms interact with light. This chapter marks a transition in the way we look at nature. Earlier chapters described what we see with our eyes and explained those observations using models and theories. With this chapter, we turn to modern astrophysics, the application of physics to the study of

Guidepost (continued) the sky. Now we can search out secrets of the stars that lie beyond the grasp of our eyes. If this chapter presents us with a tool, then we should use it immediately. The next chapter will apply our new tool to understanding the sun.

Outline I. Starlight A. Temperature and Heat B. The Origin of Starlight C. Two Radiation Laws D. The Color Index II. Atoms A. A Model Atom B. Different Kinds of Atoms C. Electron Shells III. The Interaction of Light and Matter A. The Excitation of Atoms B. The Formation of a Spectrum

Outline (continued) IV. Stellar Spectra A. The Balmer Thermometer B. Spectral Classification C. The Composition of the Stars D. The Doppler Effect E. Calculating the Doppler Velocity F. The Shapes of Spectral Lines

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

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

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”.

Two Laws of Black Body Radiation 1. The hotter an object is, the more luminous it is: L = A*s*T4 where A = surface area; s = Stefan-Boltzmann constant 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).

The Color Index (1) The color of a star is measured by comparing its brightness in two different wavelength bands: The blue (B) band and the visual (V) band. We define B-band and V-band magnitudes just as we did before for total magnitudes (remember: a larger number indicates a fainter star). B band V band

The Color Index (2) B – V We define the Color Index (i.e., B magnitude – V magnitude). The bluer a star appears, the smaller the color index B – V. The hotter a star is, the smaller its color index B – V.

Light and Matter Spectra of stars are more complicated than pure blackbody spectra.  characteristic lines, called absorption lines. To understand those lines, we need to understand atomic structure and the interactions between light and atoms.

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.

Atomic 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!!

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

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.

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.

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.

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

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 the transition energies are absorbed from the continuous spectrum.

The Spectra of Stars 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.

Kirchhoff’s Laws (SLIDESHOW MODE ONLY)

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

Lines of Hydrogen Most prominent lines in many astronomical objects: Balmer lines of hydrogen

The Balmer Lines Ha Hb Hg … 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) …

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

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

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

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

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

Spectral Classification of Stars (2) Mnemonics to remember the spectral sequence: Oh Only Be Boy, Bad A An Astronomers Fine F Forget Girl/Guy Grade Generally Kiss Kills Known Me Mnemonics

Stellar Spectra O B A F Surface temperature G K M

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

The Doppler Effect Dl/l0 = vr/c vr 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

The Doppler effect allows us to measure the source’s radial velocity. vr

The Doppler Effect (3) 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 find Dl/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.

Doppler Broadening Observer 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

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

New Terms temperature Kelvin temperature scale absolute zero thermal energy electron black body radiation wavelength of maximum intensity (λmax) color index nucleus proton neutron isotope ionization ion molecule Coulomb force binding energy quantum mechanics permitted orbit energy level excited atom ground state continuous spectrum absorption spectrum (dark-line spectrum) absorption line emission spectrum (bright-line spectrum) emission line Kirchhoff’s laws transition Lyman series Balmer series Paschen series spectral class or type

New Terms (continued) spectral sequence L dwarf T dwarf Doppler effect blue shift red shift radial velocity (Vr) transverse velocity line profile Doppler broadening collisional broadening density

Discussion Questions 1. In what ways is our model of an atom a scientific model? How can we use it when it is not a completely correct description of an atom? 2. Can you think of classification systems we commonly use to simplify what would otherwise be very complex measurements? Consider foods, movies, cars, grades, clothes, and so on.

Quiz Questions 1. Which of the following statements is true about the Celsius and Kelvin (Absolute) temperature scales? a. Zero is at the same temperature on both scales. b. The size of one degree is the same on both scales. c. Zero degrees Celsius is the same temperature as -273 K. d. The size of one Celsius degree is 5/9 that of a Kelvin. e. The size of one Kelvin is 5/9 that of a Celsius degree.

Quiz Questions 2. The temperature of a gas is a measure of the a. total amount of internal energy in the gas. b. amount of heat that flows out of the gas. c. total number of atoms in the gas. d. density of the gas. e. average motion of its atoms.

Quiz Questions 3. Which subatomic particle has a negative charge? a. The electron. b. The proton. c. The neutron. d. Both a and b above. e. Both a and c above.

Quiz Questions 4. The wavelength of maximum intensity that is emitted by a black body is a. proportional to temperature. b. inversely proportional to temperature. c. proportional to temperature to the fourth power. d. inversely proportional to temperature to the fourth power. e. Both a and c above.

Quiz Questions 5. Of the following, which color represents the lowest surface temperature star? a. Yellow. b. Blue. c. Orange. d. Red. e. White.

Quiz Questions 6. The amount of electromagnetic energy radiated from every square meter of the surface of a blackbody each second is a. proportional to temperature. b. inversely proportional to temperature. c. proportional to temperature to the fourth power. d. inversely proportional to temperature to the fourth power. e. Both a and c above.

Quiz Questions 7. The B - V color index of a star indicates its a. density. b. total mass. c. radius. d. chemical composition. e. surface temperature.

Quiz Questions 8. If a star appears brighter through a B filter than it does through a V filter, its B - V color index is a. negative. b. zero. c. positive. d. greater than or equal to zero. e. less than or equal to zero.

Quiz Questions 9. An atom that is ionized must have a. more neutrons than protons. b. more protons than neutrons. c. more electrons than protons. d. more protons than electrons. e. Either c or d above.

Quiz Questions 10. Which of the following is true of an atomic nucleus? a. It contains more than 99.9% of an atom’s mass. b. It contains all of an atom's positive charge. c. It contains no electrons. d. Both a and b above. e. All of the above.

Quiz Questions 11. At what energy level are the electrons in hydrogen gas at a temperature of 25,000 K? a. Most are in energy level 1 (also known as the ground state). b. Most are in energy level 2. c. Most are in levels higher than energy level 2. d. Half are in energy level 1, and half are in level 2. e. None of the above.

Quiz Questions 12. What conditions produce a dark (absorption line) spectrum? a. A hot solid, liquid, or high-density gas. b. A hot low-density gas. c. Light from a continuous spectrum source passing through a cooler low-density gas. d. Both a and b above. e. All of the above.

Quiz Questions 13. Where is the location of the cooler low-density gas that yields the dark (absorption) line stellar spectra that were studied by Annie Jump Cannon? a. In the interior of the star. b. In the star's lower atmosphere. c. In Earth's atmosphere. d. Both a and b above. e. Both b and c above.

Quiz Questions 14. Which electron energy level transition corresponds to a hydrogen atom absorbing a visible-light photon that has a wavelength of 656 nanometers? a. The electron makes the transition from energy level 1 to energy level 2. b. The electron makes the transition from energy level 2 to energy level 1. c. The electron makes the transition from energy level 2 to energy level 3. d. The electron makes the transition from energy level 3 to energy level 2. e. The electron makes the transition from energy level 3 to energy level 4.

Quiz Questions 15. What does the presence of molecular bands in the spectrum of a star indicate? a. The star has a low surface temperature. b. The star has a high surface temperature. c. The star is about to go supernova. d. The star is spectral type G. e. The star is spectral type TiO.

Quiz Questions 16. Of the following spectral types, which one represents a star with the highest surface temperature? a. A b. B c. F d. K e. G

Quiz Questions 17. All stars are composed of mostly hydrogen and helium, yet many stars have no lines for hydrogen or helium in their spectrum. What causes this apparent contradiction? a. Spectral lines are created in the lower atmospheres of stars, and for many stars hydrogen and helium are hidden below the atmosphere. b. The upper layers of a star contain hot low-density gases that produce bright lines at precisely the same wavelengths as the dark lines, thus making them invisible. c. Hot hydrogen and helium gas in the interstellar medium produces bright lines to fill in the dark lines. d. The resolution of many spectrographs is too poor to show the extremely thin spectral lines for hydrogen and helium. e. The surface temperature is such that the electrons are not at the proper energy levels to produce spectral lines at visible wavelengths.

Quiz Questions 18. You research the star Sirius and find that its spectral lines are blue shifted. What does this tell you about Sirius? a. Its surface temperature is higher than that of the Sun. b. It has a transverse velocity that is away from us. c. It has a transverse velocity that is toward us. d. It has a radial velocity that is away from us. e. It has a radial velocity that is toward us.

Quiz Questions 19. Suppose that you take the spectrum of several stars and identify the 656-nanometer line of hydrogen. You then measure against the reference spectrum on the same image and find that some of the 656-nm lines are shifted due to the Doppler Effect. Of the following shifted locations of this line, which one signals a star that is moving away from us at the highest speed? a. Star A @ 655 nm. b. Star B @ 657 nm. c. Star C @ 658 nm. d. Star E @ 659 nm. e. Star D @ 654 nm.

Quiz Questions 20. What property of a star can broaden the width of its spectral lines? a. Rapid rotation of the star. b. High-density atmosphere. c. High-temperature atmosphere. d. Both b and c above. e. All of the above.

Answers 1. b 2. e 3. a 4. b 5. d 6. c 7. e 8. a 9. e 10. e 11. c 12. c 13. e 14. c 15. a 16. b 17. e 18. e 19. d 20. e