Atoms and StarlightChapter 7

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

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.

Guidepost (continued)

I. AtomsA. A Model AtomB. Different Kinds of AtomsC. Electron Shells

II. The Interaction of Light and MatterA. The Excitation of AtomsB. Radiation from a Heated ObjectC. Two Radiation Laws

Outline

III. Stellar SpectraA. The Formation of a SpectrumB. The Balmer ThermometerC. Spectral ClassificationD. The Composition of the StarsE. The Doppler EffectF. Calculating the Doppler VelocityG. The Shapes of Spectral Lines

Outline (continued)

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. 如果將原子核放大到葡萄籽的大小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電子雲將有好幾個足球場大

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!!

Different Kinds of Atoms• The kind of atom

depends on the number of protons in the nucleus.

Helium 4

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.)

Electron Orbits• Electron orbits in the electron cloud are

restricted to very specific radii and energies.

r1, E1

r2, E2

r3, E3

• 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.

• All other photons pass by the atom unabsorbed.

Eph = E4 – E1

Eph = E3 – E1

(Remember that Eph = h*f)

Wrong energy

• The photon is absorbed, and

the electron is in an excited state.

Color and Temperature

Orion

Betelgeuse

Rigel

Stars appear in different colors,

from blue (like Rigel)

via yellow (like our sun)

to red (like Betelgeuse).

These colors tell us about the star’s

temperature.

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 energy it emits:

F = *T4

where

= Stefan-Boltzmann constant

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 )

Energy Flux

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:

max ≈ 3,000,000 nm / TK

(where TK is the temperature in Kelvin)

Stellar SpectraThe 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.

Kirchhoff’s Laws of Radiation (1)

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 StarsThe 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.

Analyzing Absorption Spectra• Each element produces a specific set of absorption

(and emission) lines.

By far the most abundant elements in the Universe

• Comparing the relative strengths of these sets of lines, we can study the composition of gases.

Metal !!Metal !!

Lines of HydrogenBalmer lines of hydrogen can be seen at optical wavelengths

The Balmer Linesn = 1

n = 2

n = 4

n = 5n = 3

H H H

The only hydrogen lines in the visible wavelength range

Transitions from 2nd to higher levels of hydrogen

2nd to 3rd level = H (Balmer alpha line)2nd to 4th level = H (Balmer beta line)

…

Observations of the H-Alpha LineEmission nebula, dominated by the red H line

Absorption Spectrum Dominated by Balmer Lines

Modern spectra are usually recorded digitally and

represented as plots of intensity vs. wavelength

The Balmer ThermometerBalmer line strength is sensitive to temperature:

Almost all hydrogen atoms in the ground state (electrons in

the n = 1 orbit) => few transitions from n = 2 => weak

Balmer lines

Most hydrogen atoms are ionized => weak Balmer

lines

注意注意 :: 溫度向左增溫度向左增加 加 !!!!

Measuring the Temperatures of Stars

Comparing line strengths, we can measure a star’s surface temperature!

Spectral Classification of Stars (1)

Tem

pera

ture

Different types of stars show different characteristic sets of absorption lines.

Spectral Classification of Stars (2)

Mnemonics (幫助記憶的方法 ) to remember the spectral sequence:

Oh Oh Only

Be Boy, Bad

A An Astronomers

Fine F Forget

Girl/Guy Grade Generally

Kiss Kills Known

Me Me Mnemonics

Stellar Spectra

OB

A

F

GKM

Surface tem

perature

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

The Doppler Effect (1)

The light of a moving source is blue/red shifted by

/0 = vr/c

0 = actual wavelength

emitted by the source

Wavelength change due to

Doppler effect

vr = radial velocity

Blue Shift (to higher frequencies)

Red Shift (to lower frequencies)

vr

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 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.

The Doppler Effect (2)

Example:

The Doppler Effect (4)Take of the H (Balmer alpha) line:

0 = 656 nmAssume, we observe a star’s spectrum with the H line at = 658 nm. Then,

= 2 nm.

We find = 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 BroadeningIn principle, line absorption should only affect a very unique wavelength.

Observer

Atoms in random thermal motion

vr

vr

Red shifted abs.

Blue shifted abs.

In reality, also slightly different wavelengths are absorbed.

↔ Lines have a finite width; we say:

they are broadened

One reason for broadening: The Doppler effect!

Line BroadeningHigher Temperatures

Higher thermal velocities broader lines

Doppler Broadening is usually the most important broadening mechanism.