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Guidepost Chapter 7 Atoms and Starlight 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? Guidepost (continued) Outline 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: I. Atoms A. A Model Atom B. Different Kinds of Atoms C. Electron Shells • How can we understand the world around us if it depends on the atomic world we cannot see? II. The Interaction of Light and Matter A. The Excitation of Atoms B. Radiation from a Heated Object C. Two Radiation Laws 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. 1 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 The Amazing Power of Starlight Just by analyzing the light received from a star, astronomers can retrieve information about a star’s 1. Total energy output 2. Surface temperature 3. Radius 4. Chemical composition 5. Velocity relative to Earth 6. Rotation period 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. 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!! 2 Different Kinds of Atoms Electron Orbits • The kind of atom depends on the number of protons in the nucleus. • Electron orbits in the electron cloud are restricted to very specific radii and energies. 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.) • These characteristic electron energies are different for each individual element. Atomic Transitions Color and Temperature Stars appear in different colors, Eph = E3 – E1 Eph = E4 – E1 from blue (like Rigel) Orion Betelgeuse via green / yellow (like our sun) Wrong energy • The photon is absorbed, and the electron is in an excited state. r2, E2 r1, E1 Helium 4 • An electron can be kicked into a higher orbit when it absorbs a photon with exactly the right energy. r3, E3 (Remember that Eph = h*f) to red (like Betelgeuse). These colors tell us about the star’s temperature. Rigel • All other photons pass by the atom unabsorbed. 3 Black Body Radiation (1) The light from a star is usually concentrated in a rather narrow range of wavelengths. Two Laws of Black Body Radiation 1. The hotter an object is, the more energy it emits: Energy Flux F = σ*T4 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”. where F = Energy Flux = = Energy given off in the form of radiation, per unit time and per unit surface area [J/s/m2]; σ = Stefan-Boltzmann constant 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: λmax ≈ 3,000,000 nm / TK (where TK is the temperature in Kelvin) Stellar Spectra The spectra of stars are more complicated than pure blackbody spectra. They contain characteristic lines, called absorption lines. With what we have learned about atomic structure, we can now understand how those lines are formed. 4 Kirchhoff’s Laws of Radiation (1) Kirchhoff’s Laws of Radiation (2) 1. A solid, liquid, or dense gas excited to emit light will radiate at all wavelengths and thus produce a continuous spectrum. 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. The Spectra of Stars The inner, dense layers of a star produce a continuous (blackbody) spectrum. Light excites electrons in atoms to higher energy states Cooler surface layers absorb light at specific frequencies. Frequencies corresponding to the transition energies are absorbed from the continuous spectrum. => Spectra of stars are absorption spectra. 5 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. Lines of Hydrogen Most prominent lines in many astronomical objects: Balmer lines of hydrogen By far the most abundant elements in the Universe The Balmer Lines 4 n = 3 n= 2 Hα n=5 n= n=1 Observations of the H-Alpha Line Transitions from 2nd to higher levels of hydrogen Hβ Emission nebula, dominated by the red Hα line Hγ The only hydrogen lines in the visible wavelength range 2nd to 3rd level = Hα (Balmer alpha line) 2nd to 4th level = Hβ (Balmer beta line) … 6 Absorption Spectrum Dominated by Balmer Lines The Balmer Thermometer Balmer line strength is sensitive to temperature: Most hydrogen atoms are ionized => weak Balmer lines Modern spectra are usually recorded digitally and represented as plots of intensity vs. wavelength Measuring the Temperatures of Stars Almost all hydrogen atoms in the ground state (electrons in the n = 1 orbit) => few transitions from n = 2 => weak Balmer lines Spectral Classification of Stars (1) Temperature Different types of stars show different characteristic sets of absorption lines. Comparing line strengths, we can measure a star’s surface temperature! 7 Spectral Classification of Stars (2) Stellar Spectra Mnemonics to remember the spectral sequence: Oh Oh Be Boy, Bad A An Astronomers Fine F Forget Girl/Guy Grade Generally Kiss Kills Known Me Me Mnemonics F G K M Only The Composition of Stars From the relative strength of absorption lines (carefully accounting for their temperature dependence), one can infer the composition of stars. Surface temperature O B A 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 ∆λ/λ0 = vr/c λ0 = actual wavelength emitted by the source Blue Shift (to higher frequencies) vr Red Shift (to lower frequencies) ∆λ = Wavelength change due to Doppler effect vr = radial velocity 8 The Doppler Effect (2) The Doppler Effect (2) The Doppler effect allows us to measure the component of the source’s velocity along our line of sight. Example: This component is called radial velocity, vr. The Doppler Effect (4) Doppler Broadening In principle, line absorption should only affect a very unique wavelength. Take λ0 of the Hα (Balmer alpha) line: λ0 = 656 nm In reality, also slightly different wavelengths are absorbed. Assume, we observe a star’s spectrum with the Hα line at λ = 658 nm. Then, ∆λ = 2 nm. ↔ Lines have a finite width; we say: 3*10-3 We find ∆λ/λ0 = 0.003 = 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. Blue shifted abs. Red shifted abs. vr vr they are broadened One reason for broadening: The Doppler effect! Observer Atoms in random thermal motion 9