Astronomy 4230

Astronomy 4230

天文学概论A Brief Course of Astronomy

Lecture 3 Stellar Spectrum

Chapter 3 Stellar Spectrum A Brief Course of Astronomy

Lecture 3, Astronomy 4230 J. 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



Spectrum

Prism

WhiteLight

Prisms disperse light into its component colors



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



The wave picture gets a boost

• 1801 Thomas Young– Double-slit experiment – Include graphic– Demonstrates wave nature of light, rejects particle

picture



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



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)



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”.



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.



Electromagnetic Wave



Visible Light Waves

• Wavelengths: 400 – 700 nanometers (nm)– 1 nm = 10-9 meters

• Frequencies: 7.51014–4.31014 waves/second

• Visible Spectrum:

• RRed ed OOrange range YYellow ellow GGreen reen BBlue lue IIndigo ndigo VVioletiolet

• 700 nm 700 nm ------------- ------------- 550 nm550 nm ------------ ------------ 400 nm400 nm

• R O Y G. B I V

• Wavelengths: 400 – 700 nanometers (nm)– 1 nm = 10-9 meters

• Frequencies: 7.51014–4.31014 waves/second

• Visible Spectrum:

• RRed ed OOrange range YYellow ellow GGreen reen BBlue lue IIndigo ndigo VVioletiolet

• 700 nm 700 nm ------------- ------------- 550 nm550 nm ------------ ------------ 400 nm400 nm

• R O Y G. B I V



• 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 m1 Ångstrom 1010 m( 波长 λ)×( 频率 ν) 光速 c 3×1010 cms-1



• 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。



The Electromagnetic Spectrum



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.



太阳光谱

M17 中恒星形成区的热气体辐射谱



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.



ContinuumSource

Continuous Spectrum

Absorption-lineSpectrum

Emission-line Spectrum

Cloud of Hydrogen Gas



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.



• 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

)1(

12)(

/2

3

kThec

hTB

不同温度黑体的辐射谱



• Wien 定律黑体辐射最强处的波长 peak 与温度之间的关系为 peakT 0.29 (cm K)

高温黑体主要辐射短波，低温黑体主要辐射长波。



In Words:“Hotter objects are BLUER”

“Cooler objects are REDDER”

• Relates peak wavelength and Temperature:

Wien’s Law

2,900,000 nmTpeak



Example:Radiation from various objects with different temperature

Cluster

Sun

Young star

Gas cloud



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。



Example 1: The Sun

光学紫外

X 射线射电



Example 2: The Spiral Galaxy M81

光学中红外远红外

X 射线紫外射电



• Energy emitted per second per area by a blackbody with Temperature (T):

Stefan-Boltzmann Law

4TE is Boltzmann's constant (a number).

In Words:“Hotter objects are Brighter at All Wavelengths”



Examples I

• Heat a piece of iron from 300K to 600K– Temperature increases by 2×– Brightness increases by 24 = 16×– Peak wavelength shifts towards the blue by 2×

from ~10m in the mid-Infrared to ~5m in the near-Infrared.

• Hotter objects get brighter at all wavelengths and get bluer in color.



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 3.81026 Watts of mostly visible

light, infrared and ultraviolet.



Infrared Camera ImageWavelength ~2200nm (2.2 microns)



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.



• 19th 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.



Hydrogen

Helium

Oxygen

Neon

Iron



• 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

ContinuumSource Cloud of

Hydrogen Gas

LampLight

Absorbedby

HydrogenAtomsin theCloud

Lamp emits light at all energies

The Solar Spectrum



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.



Simple Atoms (Schematic)

protonelectronneutron

1H 4He



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.



Hydrogen: The Simplest Atom

• An atom of Hydrogen (1H) 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 (2nd excited state)

n=2 (1st excited state)

n=4n=5

Energy Level Diagram of 1H

Continuum

n=



n=1

n=3n=6



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 (2nd excited state)

n=2 (1st excited state)

n=4n=5

n=3262 52 42

Larger Jump = More Energy = Bluer Wavelength

n=6



氢原子光谱



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.



– 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 ＝ En2 - En1

吸收线的产生过程



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.



恒星的光谱

典型的恒星光谱由连续谱和吸收线构成



• 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。



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



• 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。



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。



太阳的化学组成

元素质量丰度Hydrogen 73.5%

Helium 24.8%

Oxygen 0.788%

Carbon 0.326%

Nitrogen 0.118%

Iron 0.162%

Silicon 0.09%

Magnesium 0.06%

Neon 0.16%



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）。

c

Vr

0



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



• 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。



Stellar Colors and Temperatures

COLOR INDEX SURFACE TEMPERATURE (K)FB/FV B – V

1.3 – 0.28 30,000

1.0 0.0 10,000

0.55 0.65 6,000

0.21 1.7 3,000



光谱分类

• Harvard 大学天文台的天文学家在 1890-1910 年首先提出的恒星光谱分类法。

Annie Jump Cannon



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 09 十个次型。太阳的光谱型为 G2.



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

B 20,000 蓝白中性 He 线，重元素一次电离线， H 线

A 10,000 白 H 线，重元素一次电离线F 7,000 黄白重元素一次电离线， H 线

和中性金属线G 6,000 黄重元素一次电离线，中性金

属线K 4,000 红橙中性金属线，重元素一次电

离线M 3,000 红中性金属线，分子带



恒星的颜色与光谱型

不同光谱型恒星的辐射能量比较



Example: Digital Stellar Spectra

K5-F7 main sequence starsA9-O5 main sequence stars



The Spectral Sequence

Bluest Reddest

Spectral Sequence is a Temperature Sequence

Hottest Coolest50,000K 1300K

O B A F G K M L



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？

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Astronomy 4230

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