Download - OUR UNIVERSE
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OUR UNIVERSEOUR UNIVERSELectures 7 - 9
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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.
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Light is Light is
electromagnetic radiationelectromagnetic radiationOscillating Electric & Magnetic fieldsOscillating Electric & Magnetic fields
E
speed c
Bwavelength
frequency
=c/
c
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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-
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To produceTo produce
electromagnetic radiationelectromagnetic radiationwe must we must accelerate electric chargeaccelerate electric charge
Deflected by a nucleus - bremsstrahlung
+
Radio Gamma raysLow High energy
km 10-14 m
electrone-
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also sometimes called magnetic bremsstrahlung
e-
Bending inmagnetic field:
synchrotronradiation
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+
-
+
-
We can picture adiatomic molecule as a dumbell
C
O
COCarbon
Monoxide=
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To produceTo produce
electromagnetic radiationelectromagnetic radiationwe must we must accelerate electric chargeaccelerate electric charge
Vibrations of a diatomic molecule
Typically
1-100 µmInfrared (IR FIR)
C
O
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To produceTo produce
electromagnetic radiationelectromagnetic radiationwe must we must accelerate electric chargeaccelerate electric charge
Rotation of a diatomic molecule
C
O
Typically
mm cmmm microwaves
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ro-vibrational spectrum of CO
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ro-vibrational spectrum of CO
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ro-vibrational spectrum of CO
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The Electromagnetic The Electromagnetic
SpectrumSpectrum
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The Electromagnetic SpectrumThe Electromagnetic Spectrum
fromfrom
Radio Radio Gamma Rays Gamma Rays
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Radio
mm wavesMicrowaves
Infrared (IR)
VisibleUltraviolet
(UV)
GammaRays
X-rays
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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
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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
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Interference of WavesInterference of WavesDestructive Destructive
InterferenceInterference
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Young’s Experiment:Young’s Experiment:
2-slit interference2-slit interference
Interference of WavesInterference of Waves
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DiffractionDiffraction
peakpeak
D
Interference of Interference of
WavesWavesDiffraction throughDiffraction through
a single slit.a single slit.
D
dth Angular wi
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Diffraction through aDiffraction through a
circularcircular aperture, diameter aperture, diameter D..
D
D
2.1
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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
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Images mergeImages merge
as 2 sources as 2 sources
moved together moved together
to below theto below the
angular resolutionangular resolution
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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
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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”)
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The Rutherford modelThe Rutherford model
of the atom. of the atom. classical classical
e- (electron) (electron)
orbitsorbits
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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
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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
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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
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Absorption & emission of an H photon
by Hydrogen
= 656 nm
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Absorption & emission of an H photon
by Hydrogen
= 656 nm
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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
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L L etc
P P etc
H H etc
Hydrogen atom Spectral Series
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Hydrogen atom Spectral Series
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Emission SpectraEmission Spectra
for for rarefiedrarefied gases gases
& &
vapoursvapours
of the elements.of the elements.
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Emission SpectraEmission Spectra
for rarefied vapoursfor rarefied vapours
of the elements.of the elements.
This example is theThis example is the
Omega nebula, M17Omega nebula, M17
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H =656 nm
M17M17
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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)
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H =656 nm
Hydrogen
NGC NGC
23632363
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H =656 nm
Hydrogen
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NGC 3310: z = 0.0033 v = 1000 km/s
Markarian 609: z = 0.034 v = 10,000 km/s
z = 6.58, 97%c
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Spectra of the 2 galaxies
Wavelength nm
600
650
500
550
Intensity
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Laboratory wavelengths 0
H H
Wavelength nm
500
550
600
650
Intensity
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Emission SpectraEmission Spectra
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..
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What causes the continuous spectrum?
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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..
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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.
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A A low densitylow density hot H gas: hot H gas:
discrete emission lines.discrete emission lines.
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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
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A hot solid A hot solid
emits a emits a
continuous continuous
spectrum.spectrum.
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A boy and his dogare much cooler
than the Sun.They emit radiationin the infrared (IR).
They are NOT inthermodynamic
equilibrium.
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A continuous SpectrumA continuous Spectrum
UV
IR
Incandescentsolid
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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
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A Furnace and its contents emit a
Planck Spectrum
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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 on TSpectrum only depends on TEnergy∝T 4
andpeak ∝T -1
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The The
Black BodyBlack Body
SpectrumSpectrum
Here plotted Here plotted
againstagainstwavelength
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log
log
The Black Body SpectrumThe Black Body Spectrum
Here plotted against Here plotted against log frequencylog frequency,, log
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The The
Black BodyBlack Body
SpectrumSpectrum
Here plotted Here plotted
against against log for for
different different T
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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
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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
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= 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
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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
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APPLICATIONS OFBLACK BODY LAWS
MAX=2 .9×10 -3
Tm
SUN
thereforeMAXn
m
Wien’s Law
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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
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The Star Sirius has a surface
temperature of 10000K MAX=
2 .9×10 -3
Tm
SiriusT = 10000 K
thereforeMAX = 290 nm
Wien’s Law
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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
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THETHE END END OF LECTURE 8OF LECTURE 8
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OUR UNIVERSEOUR UNIVERSELecture No. 9
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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
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• Solar flux at earth’s distance d
F = L⊙/4d2 = 1387 W m-2
Energy reaching Earth: R2 F
•
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• Solar flux at earth’s distance d
F = L⊙/4d2 = 1387 W m-2
Energy reaching Earth: R2 F
• But the Earth reflects back into space a fraction AA = 0.29 is the Earth’s albedo•
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• Solar flux at earth’s distance d
F = L⊙/4d2 = 1387 W m-2
Energy reaching Earth: R2 F
• 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
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• The power retained
by Earth is R2 F (1-A) Watts
• The Earth at temperature Temits into space as a Black Body,losing energy at a rate
Area T4 = 4R2 T4
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• The power retained
by Earth is R2 F (1-A) Watts
• The Earth at temperature Temits into space as a Black Body,losing energy at a rate
Area T4 = 4R2 T4
• In equilibrium, loss = gain,
4 R2 T4 = R2 F (1-A)
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• The power retained
by Earth is R2 F (1-A) Watts
• The Earth at temperature Temits into space as a Black Body,losing energy at a rate
Area T4 = 4R2 T4
• In equilibrium, loss = gain,
4 R2 T4 = R2 F (1-A)
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• The power retained
by Earth is R2 F (1-A) Watts
• The Earth at temperature Temits into space as a Black Body,losing energy at a rate
Area T4 = 4R2 T4
• In equilibrium, loss = gain, 4T4 = F (1-A)
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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
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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
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In equilibrium, loss = gain
Discrepancy T = 32KEarth
Venus
Mars Discrepancy T = 6K
Discrepancy T = 505K
WHY
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In equilibrium, loss = gain
Explanation: Greenhouse effect huge
for Venus mild but significant for
Earth almost none for Mars.
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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
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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.
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Hot youngHot young
O-B starsO-B stars
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OrionVisible
BetelgeuseCool
Red GiantM
RigelB8
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OrionIR
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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
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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)
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Sun, 5800 KSun, 5800 K
Omega Centauri star cluster Omega Centauri star cluster
Hot young stars 60,000 KHot young stars 60,000 K
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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
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The entire UniverseThe entire Universe
glows with a perfectglows with a perfect
Black Body Spectrum Black Body Spectrum
oror
Planck SpectrumPlanck Spectrum
at 2.725 KIsotropic & Homogeneous to 1 part in
105
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COBE COBE
19921992
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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.
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The Sun’s SpectrumThe Sun’s Spectrum
A continuous spectrumA continuous spectrum
with absorption with absorption lineslines
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The Sun’s The Sun’s
continuous continuous
spectrum spectrum
is well is well
approximated approximated
by a by a
Black BodyBlack Body
or or
Planck Planck
SpectrumSpectrum
at 5800 K
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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?
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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..
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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..
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Emission & Absorption of Emission & Absorption of
RadiationRadiationAbsorption & emission of an H photon
by Hydrogen = 656 nm= 656 nm
Absorption
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Absorption SpectraAbsorption Spectra
for cool for cool rarefiedrarefied gases gases emissioemissio
nn
absorptioabsorptio
nn Sodium vapourSodium vapour
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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
gas emits a gas emits a continuous spectrum.continuous spectrum.
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.
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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…...
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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..
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Dense photosphere emitting Planck spectrum
at 5800 K
Cooler rarefied atmosphere
absorbing in spectral linescharacteristic of the
elemental composition
SUN
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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.
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The spectral lines tellThe spectral lines tell
us what elements are presentus what elements are present
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Iron (Fe) in the Iron (Fe) in the
Sun.Sun.
Laboratory spectrum of Fe (incandescent vapour!)
A small part of the Sun’s spectrum
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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
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Stellar spectra for temperatures 3500K to 35,000K
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Element abundances (by number).
Determined from Solar spectra & meteorites. Also found to be typical of most stars.
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HHe
C, N, O
Fe
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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
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Black Body SpectrumBlack Body Spectrum
oror
Planck SpectrumPlanck Spectrum
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?
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The Doppler shift.The Doppler shift.
v
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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
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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
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FWHMh
kTv
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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.
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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..
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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
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Broadening of lines due to stellar rotationenables us to measure
rotation speed.
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An Example:Broadening of lines
due to circumstellar outflow
IRC+10216at 15 km/s
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IRC+10216outflow
Telescope(JCMT)
1000 AU
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THETHE END END OF LECTURE 9OF LECTURE 9