Astronomy 4230 天 文 学 概 论 A Brief Course of Astronomy

Lecture 3 Stellar Spectrum

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Measuring Star Colours Stars have different colours ! Colours depend on surface temperature –Hot stars appear to be blue –Cooler stars appear to be red ‘Measure’ colours by filters

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Spectrum Prism White Light Prisms disperse light into its component colors

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Two opposing views Light consists of particles –Newton (c.1670) Light as waves –Christiaan Huygens (1678) Seemingly a ‘either – or’ situation –Particles cannot behave like waves –Waves cannot behave like particles

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 The wave picture gets a boost 1801 Thomas Young –Double-slit experiment –Include graphic –Demonstrates wave nature of light, rejects particle picture

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 A slight problem In what medium do light waves travel ? –Concept of ether (check spelling !!) –Concept of fields An unexpected solution : –Complete theory of electricity and magnetism by James Clerk Maxwell (c.1860) allows for electro- magnetic waves to travel in vacuum with speed of light

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Measuring Waves Waves are described by two numbers: Wavelength ( ): –Distance between wave crests. Frequency (f): –Number of wave crests passing per second. The wave speed, c, is the product of these: c = f

Wavelength ( ) Speed (c) Frequency (f) (# waves/second)

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Examples of Waves Ocean waves: – = 100 m, f = 0.1/second; –wave speed: c = 10 m/second (36 km/hr) –Speed depends on water depth, salinity, etc. Sound waves (A 440): – = 0.73 m, f = 440/second; –wave speed: c = 320 m/second (1150 km/hr) –For sound, “frequency” = “pitch”.

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Light as electromagnetic waves Can treat light as an Electromagnetic Wave –Fluctuation in the intensity of electric and magnetic fields. –Travels through a vacuum at the speed of light. –Doesn’t need a medium to “wave” in. Speed of light is a constant for all light waves: c = 300,000 km/sec Independent of wavelength or frequency.

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Electromagnetic Wave

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Visible Light Waves Wavelengths: 400 – 700 nanometers (nm) –1 nm = meters Frequencies: 7.5  –4.3  waves/second Visible Spectrum: Red Orange Yellow Green Blue Indigo VioletRed Orange Yellow Green Blue Indigo Violet 700 nm nm nm700 nm nm nm R O Y G. B I V

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 电磁辐射是以变化的电磁场传递能量、具有特 定波长和强度的波（波动性）。 波长范围：＜ 0.01Å – 30 m 1 Ångstrom  10  10 m ( 波长 λ)×( 频率 ν)  光速 c  3×10 10 cms -1

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 根据波长由长到短，电磁辐射可以分为射电、 红外、光学、紫外、 X 射线和 g 射线等波段，可 见光又可分解为七色光。

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 The Electromagnetic Spectrum

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 光谱 ( 电磁波谱 ) A spectrum is the distribution of photon energies coming from a light source: –How many photons of each energy are emitted by the light source? Spectra are observed by passing light through a spectrograph: –Breaks the light into its component wavelengths and spreads them apart (dispersion). –Uses either prisms or diffraction gratings.

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 太阳光谱 M17 中恒星形成区的热 气体辐射谱

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Kirchoff’s Laws 1) A hot solid or hot, dense gas produces a continuous spectrum. 2) A hot, low-density gas produces an emission-line spectrum. 3) A continuous spectrum source viewed through a cool, low-density gas produces an absorption-line spectrum.

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Continuum Source Continuous Spectrum Absorption-line Spectrum Emission-line Spectrum Cloud of Hydrogen Gas

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 黑体辐射 (blackbody radiation) 黑体 (blackbody) 能吸收所有的外来辐射（无反射）并全部再辐射的理想 天体。 –Absorbs at all wavelengths. –As it absorbs light, it heats up. –Characterized by its Temperature. 黑体辐射 (blackbody radiation) 具有特定温度的黑体的热辐射。 大部分正常恒星的辐射可以近似地用黑体辐射来表示。 –Emits at all wavelengths (continuous spectrum) –Energy emitted depends on the Temperature. –Peak wavelength also depends on Temperature.

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Planck 定律 温度为 T 的黑体在单位面积、单位时间、单位 频率内、向单位立体角发射的能量为 不同温度黑体的辐射谱

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Wien 定律 黑体辐射最强处的波长 peak 与温度之间的 关系为 peak T ＝ 0.29 (cm K) 高温黑体主要辐射短波，低温黑体主要 辐射长波。

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 In Words: “Hotter objects are BLUER” “Cooler objects are REDDER” Relates peak wavelength and Temperature: Wien’s Law

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Example: Radiation from various objects with different temperature Cluster Sun Young star Gas cloud

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 同一天体的不同波段的辐射来自不同 （温度）的区域和物理过程。

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Example 1 : The Sun 光学紫外 X 射线 射电

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Example 2: The Spiral Galaxy M81 光学 中红外 远红外 X 射线 紫外 射电

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Energy emitted per second per area by a blackbody with Temperature (T): Stefan-Boltzmann Law  is Boltzmann's constant (a number). In Words: “Hotter objects are Brighter at All Wavelengths”

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Examples I Heat a piece of iron from 300K to 600K –Temperature increases by 2× –Brightness increases by 2 4 = 16× –Peak wavelength shifts towards the blue by 2× from ~10  m in the mid-Infrared to ~5  m in the near-Infrared. Hotter objects get brighter at all wavelengths and get bluer in color.

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Examples II Person: Body Temperature = 310 K –Peak wavelength = 9400 nm (infrared) –Typical adult emits about 100 Watts of infrared light. Sun: surface temperature = 5770 K –Peak wavelength = 503 nm (visible light) –Emits about 3.8  Watts of mostly visible light, infrared and ultraviolet.

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Infrared Camera Image Wavelength ~2200nm (2.2 microns)

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Emission-Line Spectra A hot, low-density gas emits a non-continuous emission-line spectrum. –Emits only at particular wavelengths, giving the appearance of bright, discrete “emission lines”. –Darkness in between the emission lines.

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, th chemists century noticed that each element, heated into an incandescent gas in a flame, emitted unique emission lines. –Mapped out the emission-line spectra of known atoms and molecules. –Used this as a tool to identify the composition of unknown compounds. They did not, however, understand how it worked.

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Hydrogen Helium Oxygen Neon Iron

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Light from a continuous spectrum through a vessel containing a cooler gas shows: –A continuous spectrum from the lamp crossed by of dark “absorption lines” at particular wavelengths. –The wavelengths of the absorption lines exactly correspond to the wavelengths of emission lines seen when the gas is hot! Light is being absorbed by atoms in the gas. Absorption-Line Spectrum

Continuum Source Cloud of Hydrogen Gas Lamp Light Absorbed by Hydrogen Atoms in the Cloud Lamp emits light at all energies

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006

The Solar Spectrum

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Why does it work? Why does each element have a characteristic line spectrum? Answer: –It reflects the detailed structure of the atom. –Depends on the number and arrangement of electrons in orbit around the nucleus. Discovering why unlocked the secrets of the atom.

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Simple Atoms (Schematic) proton electron neutron 1H1H 4 He

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Looking inside the Atom Electrons cannot orbit just anywhere around a nucleus: –Can only orbit in discrete orbitals. Each orbital corresponds to a particular energy of the orbiting electron. –If an electron does not have exactly the right energy, it cannot be in an orbital (all or nothing). Details are dictated by quantum mechanics.

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Hydrogen: The Simplest Atom An atom of Hydrogen ( 1 H) consists of: –A single proton in the nucleus. –A single electron orbiting the nucleus. First orbital: Ground State (n=1) –Lowest energy orbital the electron can reside in. Higher orbitals: Excited States (n=2,3,...) –Higher orbits around the nucleus. –Come at specific, exact energies.

n=1 (Ground State) n=3 (2 nd excited state) n=2 (1 st excited state) n=4 n=5 Energy Level Diagram of 1 H Continuum n= 

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 n=1 n=3 n=6

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Emission & Absorption Lines Emission Lines: –When an electron jumps from a higher to a lower energy orbital, a single photon is emitted with exactly the energy difference between orbitals. No more, no less.

n=1 (Ground State) n=3 (2 nd excited state) n=2 (1 st excited state) n=4 n=5 n=3  2626252524242 Larger Jump = More Energy = Bluer Wavelength n=6

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 氢原子光谱

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Emission & Absorption Lines Emission Lines: –When an electron jumps from a higher to a lower energy orbital, a single photon is emitted with exactly the energy difference between orbitals. No more, no less. Absorption Lines: –When an electron absorbs a photon with exactly the energy needed to jump from a lower to a higher orbital. No more, no less.

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 – 当电子从高能态跃迁到低能态时，原子释放光 子，产生发射线；反之产生吸收线。 – 吸收或发射的光子能量为 hv ＝ E n2 - E n1

吸收线的产生过程

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 The Importance of Spectroscopy From the emission or absorption lines in an object's spectrum, we can learn: –Which elements are present, and in what proportions. –Which elements are ionized, in whole or in part. –Which elements are seen as molecules. These data give us a nearly complete picture of the physical conditions in the object.

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 恒星的光谱 典型的恒星光谱由连续谱和吸收线构成

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 恒星的连续谱来自相对较热、致密的恒星内部。 吸收线来自较冷、稀薄的恒星大气。

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 恒星的特征谱线强度提供了恒星的表面温 度的信息。 例如， A 型星的 H 线最 强，温度比 A 型星低或 高的恒星， H 线都相 对较弱。 不同温度恒星的特征谱线强度

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 谱线与恒星的化学成分不同元素的原子具有不同的结 构，因而有不同的特征谱线。

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 通过比较太阳光谱和实 验室中各种元素的谱线， 可以确定太阳大气的化 学成分。 按质量计， 约 70%H, 28% He 和 2% 重元素。 按数目计， 90.8%H, 9.1%He 和 0.1% 重元素。

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 太阳的化学组成 元素质量丰度 Hydrogen73.5% Helium24.8% Oxygen0.788% Carbon0.326% Nitrogen0.118% Iron0.162% Silicon0.09% Magnesium0.06% Neon0.16%

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Doppler 谱线位移 Doppler 谱线位移 ( Doppler shift ) 由于辐射源在观测者视 线方向上的运动而造成 接收到的电磁辐射波长 或频率的变化。 远离（接近）观测者辐 射源发出的电磁辐射波 长变长（短），称为谱 线红移（蓝移）。

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 恒星的温度和颜色 恒星的颜色反映了恒星的表面温度 的高低 温度越高（低），颜色越蓝（红） Rigel Betelgeuse

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 色指数 ( color index ) — 在不同波段测量得到的星等之 差，如 U-B, B-V 等。 由于天体的颜色和辐射谱的形状取决于表面温度的高 低，色指数的大小反映了天体的温度。

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Stellar Colors and Temperatures COLOR INDEXSURFACE TEMPERATURE (K) FB/FVFB/FV B – V 1.3– , , , ,000

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 光谱分类 Harvard 大学天文台的天文学家在 年首先提 出的恒星光谱分类法。 Annie Jump Cannon

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Oh, Be A Fine Guy (Girl), Kiss Me! 根据恒星光谱中 Balmer 线的强弱，恒星的光谱 首先被分成从 A 到 P 共 16 类。 后来经过调整和合并， 按照温度由高到低的次 序，将恒星光谱分成 O, B. A, F, G, K, M 七种光 谱型 (spectral type) 。 每一种光谱型可以继续 分为 0  9 十个次型。 太阳的光谱型为 G2.

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 光谱型 表面温度 (K) 颜色特征谱线 O 30,000 蓝强电离 He 线，重元素多次 电离线 B20,000 蓝白中性 He 线，重元素一次电 离线， H 线 A10,000 白 H 线，重元素一次电离线 F7,000 黄白重元素一次电离线， H 线和 中性金属线 G6,000 黄重元素一次电离线，中性金 属线 K4,000 红橙中性金属线，重元素一次电 离线 M3,000 红中性金属线，分子带

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 恒星的颜色与光谱型 不同光谱型恒星的 辐射能量比较

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 Example: Digital Stellar Spectra K5-F7 main sequence starsA9-O5 main sequence stars

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 The Spectral Sequence BluestReddest Spectral Sequence is a Temperature Sequence HottestCoolest 50,000K1300K O B A F G K M L

Chapter 3 Stellar SpectrumA Brief Course of Astronomy Lecture 3, Astronomy 4230J. B. ZhangMar 19, 2006 两颗大小相等的恒星各自的温 度是 4,000K 和 12,000K 。请问 (1) 哪一颗恒星每秒钟辐射较 多的能量？多多少？ (2) 两颗恒星各是什么颜色？ (3) 哪颗恒星在光谱的红区 辐射较多的能量？ Homework 3