OUR UNIVERSE

OUR UNIVERSEOUR UNIVERSELectures 7 - 9

The Physics ofThe Physics of

Radiation & SpectroscopyRadiation & SpectroscopyThe windows to Our UniverseThe windows to Our Universe

&&

the keys to our the keys to our

knowledge & understanding.knowledge & understanding.

The Physics in Astrophysics.The Physics in Astrophysics.

Light is Light is

electromagnetic radiationelectromagnetic radiationOscillating Electric & Magnetic fieldsOscillating Electric & Magnetic fields

E

speed c

Bwavelength

frequency

=c/

c

To produceTo produce

electromagnetic radiationelectromagnetic radiationwe must we must accelerate electric chargeaccelerate electric charge

Oscillation back-and-forth

Oscillating currents (e-)• in antennae (radio, TV,

radar, microwaves, etc)• in atoms (IR, visible light, X-rays, etc)

e-



Deflected by a nucleus - bremsstrahlung

+

Radio Gamma raysLow High energy

km 10-14 m

electrone-

also sometimes called magnetic bremsstrahlung

e-

Bending inmagnetic field:

synchrotronradiation

+

-

+

-

We can picture adiatomic molecule as a dumbell

C

O

COCarbon

Monoxide=



Vibrations of a diatomic molecule

Typically

1-100 µmInfrared (IR FIR)

C

O



Rotation of a diatomic molecule

C

O

Typically

mm cmmm microwaves

ro-vibrational spectrum of CO



The Electromagnetic The Electromagnetic

SpectrumSpectrum

The Electromagnetic SpectrumThe Electromagnetic Spectrum

fromfrom

Radio Radio Gamma Rays Gamma Rays

Radio

mm wavesMicrowaves

Infrared (IR)

VisibleUltraviolet

(UV)

GammaRays

X-rays

Atmospheric WindowsAtmospheric WindowsTransmission Radio

WindowOpticalWindow

10 m100 nm

10 µm 1cm 1 m

1 µm100 µm

Wavelength

Atmosphere

is

transparent

1mm

Visible: 400-700 nm

Interference of WavesInterference of WavesA consequence of the A consequence of the

wave-like nature of radiationwave-like nature of radiation

isis

interferenceinterference

&&

diffraction.diffraction.Constructive Constructive

InterferenceInterference

Interference of WavesInterference of WavesDestructive Destructive

InterferenceInterference

Young’s Experiment:Young’s Experiment:

2-slit interference2-slit interference

Interference of WavesInterference of Waves

DiffractionDiffraction

peakpeak

D

Interference of Interference of

WavesWavesDiffraction throughDiffraction through

a single slit.a single slit.

D

dth Angular wi

Diffraction through aDiffraction through a

circularcircular aperture, diameter aperture, diameter D..

D

D

2.1

Diffraction through a telescopeDiffraction through a telescope

of Diameter of Diameter DD: :

the diffraction-limited angular the diffraction-limited angular

resolution is:resolution is:

in radians

in arcsec

D

2.1

D

61025.0

Images mergeImages merge

as 2 sources as 2 sources

moved together moved together

to below theto below the

angular resolutionangular resolution

What is the diffraction limit for a What is the diffraction limit for a

2.4m telescope for light with 2.4m telescope for light with =600 nm?=600 nm?

in arcsec

arcsec

D

61025.0

4.2

106001025.0

96

Electromagnetic RadiationElectromagnetic Radiationbehaves in 2 complementary ways:behaves in 2 complementary ways:• waves - waves - frequency = c/• particles (photons) - particles (photons) - energy E = h Atoms & molecules emit and absorb Atoms & molecules emit and absorb

radiation in discrete quanta of energy radiation in discrete quanta of energy h• The frequencies are characteristic The frequencies are characteristic

of atomic & molecular structure.of atomic & molecular structure. (The photons are their “fingerprints” or “DNA”)(The photons are their “fingerprints” or “DNA”)

The Rutherford modelThe Rutherford model

of the atom. of the atom. classical classical

e- (electron) (electron)

orbitsorbits

Quantum Mechanics givesQuantum Mechanics gives

discrete “orbits” for the discrete “orbits” for the e-

in a Hydrogen atom.in a Hydrogen atom.

n= 1, 2 , 3 , 4 , . . .

In each orbit the e- has a discrete energy:

2

eV 1

6.13n

En

H atom: Allowed orbits for theH atom: Allowed orbits for the e-

Ground Ground

state state nn=1=1

11stst Excited state Excited state

nn=2=2

22ndnd Excited state Excited state

n n = 3= 333rdrd Excited state Excited state n n = 4= 4

Emission & Absorption of RadiationEmission & Absorption of Radiation• In each orbit the e- has a unique quantised energy:• In falling down from orbit m n a photon of energy

h = Em - En is emitted.

• In jumping up from orbit n m a photon of energy

h = Em - En is absorbed.

En∝ - 1n2

Absorption & emission of an H photon

by Hydrogen

= 656 nm

Absorption & emission of an H photon

by Hydrogen

= 656 nm

Emission & Absorption of RadiationEmission & Absorption of Radiation• In each orbit the e- has a unique quantised energy:• Transitions down (emission) & up (absorption) from level n give rise to unique, identifiable spectral lines.• Therefore Therefore Spectral lines provide powerful methods for: (a) identifying different elements (b) discovery physical conditions in space

L L etc

P P etc

H H etc

Hydrogen atom Spectral Series

Hydrogen atom Spectral Series

Emission SpectraEmission Spectra

for for rarefiedrarefied gases gases

& &

vapoursvapours

of the elements.of the elements.


for rarefied vapoursfor rarefied vapours

of the elements.of the elements.

This example is theThis example is the

Omega nebula, M17Omega nebula, M17

H =656 nm

M17M17

The typical reddish pinkThe typical reddish pink

glow ofglow of

Hydrogen excitedHydrogen excited

by young starsby young stars

in the galaxyin the galaxy

NGC 2363NGC 2363(in the constellation Camelopardis)(in the constellation Camelopardis)

H =656 nm

Hydrogen

NGC NGC

23632363

H =656 nm

Hydrogen

NGC 3310: z = 0.0033 v = 1000 km/s

Markarian 609: z = 0.034 v = 10,000 km/s

z = 6.58, 97%c

Spectra of the 2 galaxies

Wavelength nm

600

650

500

550

Intensity

Laboratory wavelengths 0

H H

Wavelength nm

500

550

600

650

Intensity


for for rarefiedrarefied gases & vapours gases & vapours

are are line spectraline spectra, ,

unique for each element;unique for each element;

but we also often seebut we also often see

an underlyingan underlying

continuumcontinuum..

What causes the continuous spectrum?

Kirchoff’s Laws of spectroscopy.Kirchoff’s Laws of spectroscopy.1) A 1) A low densitylow density hot gas emits hot gas emits

discretediscrete lines - lines - emission linesemission lines..

2) A hot solid, liquid or dense enough2) A hot solid, liquid or dense enough

gas emits a gas emits a continuous spectrum.continuous spectrum.

3) A cool gas absorbs radiation at the3) A cool gas absorbs radiation at the

same frequencies as it emitssame frequencies as it emits

when hot - this produces dark when hot - this produces dark

absorption linesabsorption lines..

Kirchoff’s Laws of spectroscopyKirchoff’s Laws of spectroscopy..

1) A 1) A low densitylow density hot gas emits hot gas emits

discrete lines - emission lines.discrete lines - emission lines.

These lines are a unique signatureThese lines are a unique signature

of the atoms in the gas.of the atoms in the gas.

A A low densitylow density hot H gas: hot H gas:

discrete emission lines.discrete emission lines.

Kirchoff’s Laws of Kirchoff’s Laws of

spectroscopy.spectroscopy.2) A hot solid, liquid or dense2) A hot solid, liquid or dense

enough gas emits a enough gas emits a continuouscontinuous

spectrum.spectrum.

The spectrum is independent ofThe spectrum is independent of

the constitution of the solid, butthe constitution of the solid, but

depends only on itsdepends only on its Temperature, T

This is theThis is the Black BodyBlack Body SpectrumSpectrum

oror Planck Planck SpectrumSpectrum

A hot solid A hot solid

emits a emits a

continuous continuous

spectrum.spectrum.

A boy and his dogare much cooler

than the Sun.They emit radiationin the infrared (IR).

They are NOT inthermodynamic

equilibrium.

A continuous SpectrumA continuous Spectrum

UV

IR

Incandescentsolid

The Black Body SpectrumThe Black Body Spectrum

oror

the Planck Spectrumthe Planck Spectrum

is produced by a bodyis produced by a body

in thermodynamicin thermodynamic

equilibrium.equilibrium.

Spectrum only depends onSpectrum only depends on T

A Furnace and its contents emit a

Planck Spectrum


oror

the Planck Spectrumthe Planck Spectrum

is produced by a bodyis produced by a body

in thermodynamicin thermodynamic

equilibrium.equilibrium.

Spectrum only depends on TSpectrum only depends on TEnergy∝T 4

andpeak ∝T -1

The The

Black BodyBlack Body

SpectrumSpectrum

Here plotted Here plotted

againstagainstwavelength

log

log


Here plotted against Here plotted against log frequencylog frequency,, log

The The


SpectrumSpectrum

Here plotted Here plotted

against against log for for

different different T

The Sun’s The Sun’s

continuous spectrum continuous spectrum

can be well approximated bycan be well approximated by

a Black Body Spectruma Black Body Spectrum

or Planck Spectrumor Planck Spectrum

at 5800 K

I= Js-1 m -2ster-1

F= Js-1 m -2

I= Js-1 m -2 ster -1 Hz -1

RADIATION

Flux

Intensity

solid angle

integrate over frequency

SpecificIntensity

integrate over solid angle

= 5.6710-8 W m-2 K-4

Stefan-Boltzmann constant

Js-1 m-2F= T 4

I=2hc 2

3

eh /kT -1= Js-1m-2ster-1Hz -1

Stefan-Boltzmann

Law

Planck’s Law

BLACK BODY RADIATIONEmitted by a body, at temperature

Tin thermodynamic equilibrium

h MAX=2 .82 kT J

I=2hc2

3

eh / kT -1Wm-2 ster-1 Hz-1

At the peak:

Planck’s Law

BLACK BODY RADIATION

MAX=5.88×1010 T Hz

MAX=2.9×10 -3

Tm

MAX∝T

MAX∝1T

Wien’s Law

APPLICATIONS OFBLACK BODY LAWS

MAX=2 .9×10 -3

Tm

SUN

thereforeMAXn

m

Wien’s Law

F= T 4

Lstar=4πRstar2 T4

APPLICATIONS OFBLACK BODY LAWS

Wm-2

For a Star:

• radius R*

• Temperature T• Total energy output/sec

Luminosity L* Watts

The Star Sirius has a surface

temperature of 10000K MAX=

2 .9×10 -3

Tm

SiriusT = 10000 K

thereforeMAX = 290 nm

Wien’s Law

F= T 4

F sirius

FSun

=T sirius

4

TSun4

= 100004

58004=8.8

What is the relative Flux of Siriuscompared with the Sun?

Wm -2

THETHE END END OF LECTURE 8OF LECTURE 8

OUR UNIVERSEOUR UNIVERSELecture No. 9

An application of Black Body law: The Earth is heated

by the Sun. What is the equilibrium temperature of

the Earth? Sun’s radiation

reaching Earthcovers acircular

area

R2

R

• Solar flux at earth’s distance d

F = L⊙/4d2 = 1387 W m-2

Energy reaching Earth: R2 F

•


F = L⊙/4d2 = 1387 W m-2


• But the Earth reflects back into space a fraction AA = 0.29 is the Earth’s albedo•


F = L⊙/4d2 = 1387 W m-2


• But the Earth reflects back into space a fraction AA = 0.29 is the Earth’s albedo• Therefore the power retained

by Earth is R2 F (1-A) Watts

• The power retained


• The Earth at temperature Temits into space as a Black Body,losing energy at a rate

Area T4 = 4R2 T4




Area T4 = 4R2 T4

• In equilibrium, loss = gain,

4 R2 T4 = R2 F (1-A)




Area T4 = 4R2 T4

• In equilibrium, loss = gain,

4 R2 T4 = R2 F (1-A)




Area T4 = 4R2 T4

• In equilibrium, loss = gain, 4T4 = F (1-A)

In equilibrium, loss = gain

T = 256 Ki.e. T = -16.6oC

For the Earth:

)1(4 4 AFT

4_)1(4 AF

T

41

8107.54

71.01387

T

In equilibriumloss = gain

Actual surface T = 288K +15 C

Venus

Mars

T = 217 K

T = 227 K

Actual surface T = 223K -50 C

Actual surface T = 732K 459 C

Earth

T = 256 K

4_)1(4 AF

T


Discrepancy T = 32KEarth

Venus

Mars Discrepancy T = 6K

Discrepancy T = 505K

WHY


Explanation: Greenhouse effect huge

for Venus mild but significant for

Earth almost none for Mars.

Planck spectrum:Planck spectrum:

& therefore& therefore

the colours of starsthe colours of stars

only depend on only depend on T

1

1

Peak

Peak

T

T

The The colourscolours of stars of stars

tell us their tell us their temperaturestemperatures..

Note the different coloursNote the different colours

of stars in the following picture.of stars in the following picture.

The interaction between The interaction between

galaxies has triggered star galaxies has triggered star

formation: the hotformation: the hot

young stars are blue.young stars are blue.

Hot youngHot young

O-B starsO-B stars

OrionVisible

BetelgeuseCool

Red GiantM

RigelB8

OrionIR

ExamplesExamples

for a variety of cosmic objectsfor a variety of cosmic objects

showing their showing their

Black Body Spectrum / Planck SpectrumBlack Body Spectrum / Planck Spectrum

• Rho Ophiuchi at 60 K (mm waves)Rho Ophiuchi at 60 K (mm waves)• Young IR star in Orion 600 K (IR)Young IR star in Orion 600 K (IR)• Sun, 5800 KSun, 5800 K• Omega Centauri star cluster Omega Centauri star cluster

very hot young stars around 60,000 Kvery hot young stars around 60,000 K

Black BodyBlack Body SpectraSpectra

Rho Ophiuchi at 60 K Rho Ophiuchi at 60 K

(mm)(mm)

Young IR star in Orion 600 K Young IR star in Orion 600 K

(IR)(IR)

Sun, 5800 KSun, 5800 K

Omega Centauri star cluster Omega Centauri star cluster

Hot young stars 60,000 KHot young stars 60,000 K

The entire UniverseThe entire Universe

glows with a perfectglows with a perfect

Black Body Spectrum Black Body Spectrum

oror

Planck SpectrumPlanck Spectrum

Isotropic & Homogeneous to 1 part in 105

The entire UniverseThe entire Universe

glows with a perfectglows with a perfect

Black Body Spectrum Black Body Spectrum

oror


at 2.725 KIsotropic & Homogeneous to 1 part in

105

COBE COBE

19921992

What produced the Universe’sWhat produced the Universe’s

Planck spectrum?Planck spectrum?

The hot dense The hot dense earlyearly universe. universe.

The radiation has been The radiation has been

coolingcooling

down ever sincedown ever since

as the universe expands.as the universe expands.

The Sun’s SpectrumThe Sun’s Spectrum

A continuous spectrumA continuous spectrum

with absorption with absorption lineslines

The Sun’s The Sun’s

continuous continuous

spectrum spectrum

is well is well

approximated approximated

by a by a


or or

Planck Planck

SpectrumSpectrum

at 5800 K

Our success in fitting the Sun’s Our success in fitting the Sun’s

continuous spectrum with a continuous spectrum with a

Black Body (Planck) Spectrum Black Body (Planck) Spectrum

tells us that it is a dense spheretells us that it is a dense sphere

at 5800 K.at 5800 K.

But what about theBut what about the

absorption lines?absorption lines?

Kirchoff’s Laws of spectroscopy.Kirchoff’s Laws of spectroscopy.

1) A 1) A low densitylow density hot gas emits hot gas emits

discretediscrete lines - lines - emission linesemission lines..

2) A hot solid, liquid or dense enough2) A hot solid, liquid or dense enough


3) A cool gas absorbs radiation at the3) A cool gas absorbs radiation at the

same frequencies as it emitssame frequencies as it emits

when hot - this produces dark when hot - this produces dark

absorption linesabsorption lines..

Kirchoff’sKirchoff’s LawsLaws ofof

spectroscopyspectroscopy..

Dense Hot Black Body

Cooler gascloud

Absorption line spectrum

3.) A cool gas absorbs radiation at the 3.) A cool gas absorbs radiation at the

same frequenciessame frequencies as it emits when hot: as it emits when hot:

this produces dark this produces dark absorption linesabsorption lines..

Emission & Absorption of Emission & Absorption of

RadiationRadiationAbsorption & emission of an H photon

by Hydrogen = 656 nm= 656 nm

Absorption

Absorption SpectraAbsorption Spectra

for cool for cool rarefiedrarefied gases gases emissioemissio

nn

absorptioabsorptio

nn Sodium vapourSodium vapour

1.) A 1.) A low densitylow density hot gas emits discrete hot gas emits discrete

lines - emission lines.lines - emission lines.

2.) A hot solid, liquid or dense enough2.) A hot solid, liquid or dense enough


3.) A cool gas absorbs radiation at 3.) A cool gas absorbs radiation at

the same frequencies as it emitsthe same frequencies as it emits

when hot - this produces when hot - this produces

dark dark absorption linesabsorption lines..

AllAll Kirchoff’s Kirchoff’s LawsLaws I nI n

action.action.

Interpreting the Sun’s spectrum:Interpreting the Sun’s spectrum:

(2) (2) The line spectrumThe line spectrum is an is an

absorption spectrumabsorption spectrumWe know this is produced by We know this is produced by

a rarefied gas a rarefied gas

cooler than the Sun’s photosphere.cooler than the Sun’s photosphere.

(Kirchoff’s 3rd law)(Kirchoff’s 3rd law)

Therefore we infer…...Therefore we infer…...

The Sun is a dense sphereThe Sun is a dense sphere

emitting aemitting a

Black Body (Planck)Black Body (Planck)

SpectrumSpectrum at 5800 Kat 5800 K

with a cool rarefiedwith a cool rarefied

gas atmospheregas atmosphere..

Dense photosphere emitting Planck spectrum

at 5800 K

Cooler rarefied atmosphere

absorbing in spectral linescharacteristic of the

elemental composition

SUN

The spectral lines tellThe spectral lines tell

us what elements us what elements

are present in the Sun’sare present in the Sun’s

atmosphereatmosphere

(and for other stars too).(and for other stars too).

Their strength tells usTheir strength tells us

how much there is.how much there is.

The spectral lines tellThe spectral lines tell

us what elements are presentus what elements are present

Iron (Fe) in the Iron (Fe) in the

Sun.Sun.

Laboratory spectrum of Fe (incandescent vapour!)

A small part of the Sun’s spectrum

Hydrogen Balmer linesHydrogen Balmer lines

in spectrum of the starin spectrum of the star

HD 193182HD 193182

around 20 Balmer lines fromaround 20 Balmer lines from

HH1313 to H to H40 40 are seen here.are seen here.

(H(H to H to H1212 are present, are present,

but not shown here.)but not shown here.)Balmer limit =364.6 nm

Stellar spectra for temperatures 3500K to 35,000K

Element abundances (by number).

Determined from Solar spectra & meteorites. Also found to be typical of most stars.

HHe

C, N, O

Fe

A Reminder:A Reminder:

The Black BodyThe Black Body

SpectrumSpectrum

is a is a

continuouscontinuous

spectrumspectrum

Spectrum only Spectrum only

depends on Tdepends on T

Black Body SpectrumBlack Body Spectrum

oror


How is a continuous spectrumHow is a continuous spectrum

produced by a dense collection of produced by a dense collection of

atomsatoms if each atom only produces if each atom only produces

a line spectrum?a line spectrum?

The Doppler shift.The Doppler shift.

v

TheThe RedRed shift.shift.• Speed of source is v, the red shift is z

• the rest wavelength is 0

• the observed wavelength is

z≈ vc For v/c << 1

11

10

c

v

cv

z

A spectral line from a hot A spectral line from a hot

gas has a width which gas has a width which

increases with the increases with the

temperature of the gas.temperature of the gas.

h

kTv

FWHMh

kTv

Light-emitting atoms moving Light-emitting atoms moving

randomly in the hot gas randomly in the hot gas

produce broadened produce broadened

spectral lines. spectral lines.

A spectral line is the sum A spectral line is the sum

of the Doppler shiftsof the Doppler shifts

of billions of light-emittingof billions of light-emitting

atoms.atoms.

Black Body RadiationBlack Body Radiation

In a solid the In a solid the interactionsinteractions

and and collisionscollisions between the between the

atoms increase the atoms increase the

range of velocities so much, range of velocities so much,

that the broadened lines overlap andthat the broadened lines overlap and

merge into a continuummerge into a continuum..

Spectral information from starlightSpectral information from starlight

• Peak or :• Presence of Line:• Line intensity:• Line width : • Doppler shift:

T = TemperatureComposition & TComposition & TT, density, rotation,outflows, jets,…..Line-of-sightvelocity

Broadening of lines due to stellar rotationenables us to measure

rotation speed.

An Example:Broadening of lines

due to circumstellar outflow

IRC+10216at 15 km/s

IRC+10216outflow

Telescope(JCMT)

1000 AU

THETHE END END OF LECTURE 9OF LECTURE 9

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