Term Paper

Introduction to Spectroscopy

Matthias Kobelt

21.11.2014

Table of contents

Introduction

Historical background

Spectroscopy

Physics of atoms and molecules

Stellar surfaces and atmospheres

Radiative transfer

List of figures

List of references

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Introduction - Rainbow

I One of the most famous phenomena ofthe light spectrum is the rainbow.

I The first correct explanation of therainbow was from Dietrich von Freiberg in1304.

I Rene Descartes and Isaac Newtonexplained it completely in terms ofgeometrical optics.

[1]

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Historical background

I The first telescopes had too much chromatic aberration.

I Newton separated in 1666 sun light with prisms in its colors and recombined it.

I Thomas Melville discovered the emission spectra of flames in the early eighteenthcentury.

I William Wollaston found in 1802 the dark lines, but he thought that they are thenatural boundaries between the different colors.

I Joseph von Fraunhofer saw 1814 almost 600 lines in the spectrum of the sun.This was possible not only because he used a slit but also because of his betterprisms.

I In 1823 Fraunhofer was able to measure wavelengths and so he did. He labelledthe nine most prominent lines, still known today as Fraunhofer lines.

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Historical background

I Alexandre Becquerel took the first picture of the solar spectrum in 1842.

[3]

I A decade later Jean Foucault discovered, that the spectrum of a sodium flamecontains partly the lines from the solar spectrum.

I In 1859 Kirchhoff and Bunsen formulated Kirchhoff’s law:

ελ(T )

kλ(T )= constant

I With this knowledge the discovery of elements became really fast.

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Historical background

I In 1862 Andres Angstrom found hydrogen in the Sun.

I In 1863 Norman Lockyer found Helium lines in the solar spectrum. The next 30years it was not found on earth.

I In 1864 William Huggins identified hydrogen, iron, sodium and calcium in stars.

I Huggins developed the procedure of comparing a spectrum with the spectrum ofan artificial light source.

I Angelo Secchi classified in 1863 stars according to the appearance of their spectrain four simple classes.

I The star classification was soon extended. They were classified by the complexityof their spectra. A, B, C...

I The system used today categorise by temperature but with the same categories,so it becomes complex: Oh Be A Fine Girl/Guy Kiss Me

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Historical background

I In 1885 Johann Balmer found a law, to predict the wavelengths of the hydrogenlines:

ν = R

(1

n21

−1

n22

)I Joseph Thomson discovered the electron in 1897.

I Albert Einstein explained the photo effect in 1905.

I In 1913 Niels Bohr presented a model of the Atoms. So energy differencebetween electron orbits correspond to lines in the spectrum.

I Karl Jansky discovered radio waves from space in 1933.

I Microwaves, ultraviolet x- and gamma ray only can be measured withoutatmosphere, so is done since 1960.

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Spectroscopy - Different types

There are several types of spectroscopy, however only three of them are usable inastrophysics currently.

I Atomic and molecular absorption and emission spectroscopy (mostly)

I Fluorescence spectroscopy

I Spectroscopy of solids

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Spectroscopy - A spectrograph

[4]

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Spectroscopy - Example for spectral atlas

[5]

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Physics of atoms and molecules - Motivation

I The structure of atoms and molecules determines their spectra.

I This can be calculated with quantum mechanics.

I But the Bohr-Sommerfeld model is enough for many purposes in astrospectroscopy.

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Physics of atoms and molecules - Bohr model

I In QM electrons have the de Brogliewavelength λ = h/p

I In a quantum-mechanical view only theorbits are allowed whose length are integermultiples of the de Broglie wavelength,due to the momentum of the orbit.

I Since the electron is captured by thenucleus due to the coulomb force thepossible radii are given by:

r =ε0n2h2

πZe2m

I The energy for an electron in orbit “n” isgiven by:

E = −Z2e4m

8ε20n2h2

I Energy differences only depends onn−21 − n−2

2 , so we got Balmers law.

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Physics of atoms and molecules - Bohr Sommerfeld model

I Sommerfeld introduced three optimisations:1 Use of the reduced mass instead of the electron mass.2 Elliptical orbits are allowed → second degree of freedom: l3 Allows relativistic effects, so the electron can precess. So energy dependence of l.

E = −Z2e4µ

8ε20n2h2

[1 +

α2Z2

n

(1

l + 1−

3

4n

)]

n=1, l=0n=2, l=0n=2, l=1n=3, l=0n=3, l=1n=3, l=2

5 Å

4 Å

3 Å

2 Å

1 Å

1 Å

2 Å

3 Å

4 Å

5 Å

6 Å 4 Å 2 Å 2 Å 4 Å 6 Å 8 Å 10 Å

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Stellar surfaces and atmospheres - The sun

Spectroscopy useful to study Stars → need to know their structure

1 Core

2 Radiative zone

3 Convective zone

4 Photosphere

5 Chromosphere

6 Corona

7 Sunspot

8 Granulation

9 Solar prominence

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Stellar surfaces and atmospheres - Optical depth

The optical depth describes the opacity of a medium

τν =

∫ r2

r1

κνρdr with r2 > r1

I τν big → optical thick

I τν small → optical thin

I τν = 1 defines the radius of the sun, for every wavelength

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Radiative transfer - Intensity loss and gain

Knowledge about physical model for the radiation transport in the atmosphere⇒ get information out of measured spectra

How does the radiation intensitychange while passing a layer ofmaterial?

I Absorption

I Scattering

I Emission

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Radiative transfer - Intensity loss and gain

Absorption depends on

I Incoming intensity

I Radiation frequency

I Material density

I Material temperature

I Present elements

dIν cos(θ) = −Iνκνρdr

κ contains also the scatteringcoefficient.

The emission can be characterisedby the coefficient εν , so the totalintensity change is:

dIν cos(θ) = (−Iνκνρ+ εν) dr[10]

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Radiative transfer - Intensity loss and gain

With dτ = −κνρdr and dIν cos(θ) = (−Iνκνρ+ εν) dr we get:

dIν cos(θ) =

(Iν −

εν

κνρ

)dτ = (Iν − Sν) dτ

Here the quotient of emission and absorption is Sν , the source function, which is ingeneral an arbitrary complicated function.

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Radiative transfer - Local thermodynamic equilibrium

Need to know source function ⇒ find easy model

I Temperature gradient → no thermodynamic equilibrium!

I Consider small volume with not too low ρ → LTE

I So the source function can be described by the Kirchhoff-Planck function:

Sν = Bν(T ) =2hν3

c21

ehνkT − 1

This means that the sun can be seen as a black body with a temperature around6000K. So the continuum spectrum is explained

With other formulas in LTE the wings of most of the spectral lines and the entireprofile of weak lines can be explained.

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Radiative transfer - Formation of spectral lines

Question: Why are there only absorption and no emission lines?

I A continuous spectrum comes from the inner sun

I Most of the lines form in the photosphere, rarely also inchromosphere and corona

I If a photon with a certain wavelength is absorbed by anatom/ion → two possibilities:

1 Emission of several photons with other wavelength2 Re-emission with same wavelength

I These photons are emitted equally in all directions

I If 1 → intensity of the original wavelength reducedI If 2 → two possibilities:

a Absorbed again, so start from beginningb Photo-effect → wavelength disappears

I Just some photons with this certain wavelength canleave the sun → absorption line at this wavelength

I No emission lines because the photons emitted atpossibility 1 can be absorbed in the same way

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Radiative transfer - Line shapes

In reality the absorption lines are not perfectly sharp.They are broadened by several effects, the main ones are:

I Natural broadening

I Doppler broadening

I Collision broadening

Additionally there are some other effects, which are less powerful.

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The end

UV IRsichtbarer

Bereich

idealer Schwarzer Körper (Temperatur 5900 K)

extraterrestrische Sonnenstrahlung(Luftmasse AM0)

terrestrische Sonnenstrahlung(Luftmasse AM1,5)

500

1000

1500

2000

2500

250 500 750 1000 1250 1500 1750 2000 2250

Wellenlänge / nm[11]

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List of figures

[1] A rainbow9.11.14: https://en.wikipedia.org/wiki/Rainbow#mediaviewer/File:WhereRainbowRises.jpg

[2] Rainbow model9.11.14: https://de.wikipedia.org/wiki/Regenbogen#mediaviewer/File:Rainbow1.svg

[3] Solar spectrum20.11.14: http://www.bu.edu/astronomy/files/2009/09/spectrum_merged.jpg

[4] A simple spectrograph20.11.14: http://www.ipf.uni-stuttgart.de/lehre/online-skript/optik/spektrograph.gif

[5] Solar spectral atlas20.11.14: http://bass2000.obspm.fr/solar_spect.php?WL=6530&DW=70&sel_resol=0.01&Find.x=15&Find.y=21

[6] Bohr model15.11.14: https://de.wikipedia.org/wiki/Bohrsches_Atommodell#mediaviewer/File:Bohr-atom-PAR.svg

[7] Standing electron wave on orbitKitchin - Optical Astronomical Spectroscopy from 1995

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List of figures

[8] Bohr-sommerfeld model14.11.14: https://de.wikipedia.org/wiki/Bohr-sommerfeldsches_Atommodell#mediaviewer/File:Bohr-sommerfeld_Atommodell_%28Elektronenbahnen%29.svg

[9] The sun18.11.14: https://de.wikipedia.org/wiki/Sternaufbau#mediaviewer/File:Sun_diagram.svg

[10] Radiative transferPrialnik - An Introduction to the Theory of Stellar Structure and Evolution - Secondedition from 2010

[11] The spectrum of the sun20.11.14: https://de.wikipedia.org/wiki/Sonnenstrahlung#mediaviewer/File:Sonne_Strahlungsintensitaet.svg

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List of references

I Kitchin - Optical Astronomical Spectroscopy from 1995

I Prialnik - An Introduction to the Theory of Stellar Structure and Evolution -Second edition from 2010

I Stix - The Sun - Second edition - Corrected second printing from 2004

I Novotny - Introduction to stellar atmospheres and interiors from 1973

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