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OUR UNIVERSE
Lectures 7 - 9
The Physics of
Radiation & Spectroscopy
The windows to Our Universe
&
the keys to our
knowledge & understanding.
The Physics in Astrophysics.
Light is
electromagnetic radiation
Oscillating Electric & Magnetic fields
E
c
speed

B
wavelength
frequency
c
=c/
To produce
electromagnetic radiation
we must accelerate electric charge
e
-
Oscillation
back-and-forth
Oscillating currents (e-)
• in antennae (radio, TV,
radar, microwaves, etc)
• in atoms
(IR, visible light, X-rays, etc)
To produce
electromagnetic
radiation
Radio  Gamma
rays
we must accelerate electric charge
Low  High energy
-14
  km  10 m
+
e
-
electron
Deflected by a nucleus -
Bending in
magnetic field:
synchrotron
radiation
e
also sometimes called magnetic
We can picture a
diatomic molecule as a dumbell
+
+
-
C
=
O
CO
Carbon
Monoxide
To produce
electromagnetic radiation
we must accelerate electric charge
C
O
Typically
  1-100 µm
Infrared (IR FIR)
Vibrations of
a diatomic molecule
To produce
electromagnetic radiation
we must accelerate electric charge
C
O
Typically
  mm  cm
mm  microwaves
Rotation of
a diatomic molecule
ro-vibrational spectrum of CO
ro-vibrational spectrum of CO
ro-vibrational spectrum of CO
The Electromagnetic
Spectrum
The Electromagnetic Spectrum

from
Radio  Gamma Rays
Gamma
Rays
X-rays
Ultraviolet (UV)
Visible
Infrared (IR)
mm waves
Microwaves
Radio
Atmospheric Windows
Transmission
Radio
Window
Optical
Window
Atmosphere
is
transparent
100 nm
10 µm
1 µm
1mm
1cm
1 m 10 m
100 µm
Visible: 400-700 nm
Wavelength

Interference of Waves
A consequence of the
wave-like nature of radiation
is
interference
&
Constructive Interference
diffraction.
Interference
of
Waves
Destructive Interference
Interference of Waves
Young’s Experiment:
2-slit interference
Interference of Waves
Diffraction through
a single slit.
D
Diffraction
peak
Angular wi dth 

D
  1.2

D
D
Diffraction through a
circular aperture, diameter D.
Diffraction through a telescope
of Diameter D:
the diffraction-limited angular
resolution is:
  1.2

D
 in radians
  0.25 10
6

D
 in arcsec
Images merge
as 2 sources
moved together
to below the
angular resolution
What is the diffraction limit for a
2.4m telescope for light with =600 nm?
  0.25 10
6

 in arcsec
D
600 10
 = 0.25 10 
2.4
9
6
= 0.063 arcsec
Electromagnetic Radiation
behaves in 2 complementary ways:
• waves - frequency  = c/
• particles (photons) - energy E = h
Atoms & molecules emit and absorb
radiation in discrete quanta of energy h
• The frequencies are characteristic
of atomic & molecular structure.
(The photons are their “fingerprints” or “DNA”)
The Rutherford model
of the atom.
classical
e- (electron)
orbits
Quantum Mechanics gives
discrete “orbits” for the e
in a Hydrogen atom.
In each orbit the
discrete energy:
1
En = 13.6 eV  2
n
e
has a
n = 1, 2, 3, 4,. ..
H atom: Allowed orbits for the e-
Ground
state n=1
1st Excited state
n=2
3rd
2nd Excited state
n=3
Excited state n = 4
Emission & Absorption of Radiation
• In each orbit the e- has a
1
En ∝- 2
n
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.
Absorption & emission of an H photon
by Hydrogen
 = 656 nm
Absorption & emission of an H photon
by Hydrogen
 = 656 nm
Emission & 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 Spectral lines provide
powerful methods for:
(a) identifying different elements
(b) discovery physical conditions in space
Hydrogen atom
Spectral Series
L L
etc
H H
etc
P P
Hydrogen atom
Spectral Series
Emission Spectra
for rarefied gases
&
vapours
of the elements.
Emission Spectra
for rarefied vapours
of the elements.
This example is the
Omega nebula, M17
M17
H =656 nm
The typical reddish pink
glow of
Hydrogen excited
by young stars
in the galaxy
NGC 2363
(in the constellation Camelopardis)
NGC 2363
H =656 nm
Hydrogen
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
500
550
600
650
Wavelength
Intensity
 nm
500
550
600
650
Wavelength
Intensity
H
H
Laboratory wavelengths 0
 nm
Emission Spectra
for rarefied gases & vapours
are line spectra,
unique for each element;
but we also often see
an underlying
continuum.
What causes the continuous spectrum?
Kirchoff’s Laws of spectroscopy.
1) A low density hot gas emits
discrete lines - emission lines.
2) A hot solid, liquid or dense enough
gas emits a continuous spectrum.
3) A cool gas absorbs radiation at the
same frequencies as it emits
when hot - this produces dark
absorption lines.
Kirchoff’s Laws of spectroscopy.
1) A low density hot gas emits
discrete lines - emission lines.
These lines are a unique signature
of the atoms in the gas.
A low density hot H gas:
discrete emission lines.
Kirchoff’s Laws of spectroscopy.
2) A hot solid, liquid or dense
enough gas emits a continuous
spectrum.
The spectrum is independent of
the constitution of the solid, but
depends only on its Temperature, T
This is the Black Body Spectrum
or Planck Spectrum
A hot solid
emits a
continuous
spectrum.
A boy and his dog
are much cooler
than the Sun.
They emit radiation
in the infrared (IR).
They are NOT in
thermodynamic
equilibrium.
A continuous Spectrum
Incandescent
solid
IR
UV
The Black Body Spectrum
or
the Planck Spectrum
is produced by a body
in thermodynamic
equilibrium.
Spectrum only depends on T
A Furnace and its contents emit a
Planck Spectrum
The Black Body Spectrum
or
the Planck Spectrum
is produced by a body
in thermodynamic
4
equilibrium.
Ene rgy ∝T
Spectrum only depends
and on T
pe ak ∝T
-1
The
Black Body
Spectrum
Here plotted
against
wavelength 
log
The Black Body Spectrum
Here plotted against log frequency, log 
log
The
Black Body
Spectrum
Here plotted
against log 
for
different T
The Sun’s
continuous spectrum
can be well approximated by
a Black Body Spectrum
or Planck Spectrum
at 5800 K
RADIATION
Specific
Intensity
-1
-2
-1
I = Js m ste r Hz
solid
angle
integrate over
frequency
Intensity
-1
-2
I= Js m ste r
integrate over
solid angle
Flux
-1
-1
F= Js m
-2
-1
BLACK BODY RADIATION
Emitted by a body, at temperature T
in thermodynamic equilibrium
3
Planck’s
Law
2h
I = 2 h /kT
c e
-1
-1
-2
-1
-1
= Js m ste r Hz
Stefan-Boltzmann
Law
F=
T
4
-1
Js m
-2
 = 5.6710-8 W m-2 K-4
Stefan-Boltzmann constant
BLACK BODY RADIATION
Planck’s I = 2 h
2 h
c e
Law
3
/ kT
-2
-1
-1
W m ste r Hz
-1
At the peak:
h
M AX = 2
M AX =
.82 k T J
5. 88× 10
2. 9 × 10
M AX =
T
Wien’s Law
10
M AX ∝T
T Hz
-3
m
1
M AX ∝
T
APPLICATIONS OF
BLACK BODY LAWS
Wien’s Law
2 . 9 × 10
M AX =
T
SUN
T = 5800 K
therefore
MAX = 500 nm
-3
m
APPLICATIONS OF
BLACK BODY LAWS
F=
For a Star:
T
4
Wm
-2
• radius R*
• Temperature T
• Total energy output/sec
Luminosity L* Watts
L st ar = 4 π R st ar
2
T
4
The Star Sirius has a
surface
temperature
2 .of
9 × 10
Wien’s Law
=
M
AX
10000K
T
Sirius
T = 10000 K
therefore
MAX = 290 nm
-3
m
What is the relative Flux of Sirius
compared with the Sun?
F=
F sirius
=
F S un
T
4
T sirius
=
4
T S un
4
Wm
-2
4
10000
= 8.8
4
5800
THE END
OF LECTURE 8
OUR UNIVERSE
Lecture 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
R
radiation
reaching Earth
covers a
circular
area
R2
• Solar flux at earth’s distance d
F = L⊙/4d2 = 1387 W m-2
Energy reaching Earth: R2 F
•
• Solar flux at earth’s distance d
F = L⊙/4d2 = 1387 W m-2
Energy reaching Earth: R2 F
• But the Earth reflects back into space
a fraction A
A = 0.29 is the Earth’s albedo
•
• Solar flux at earth’s distance d
F = L⊙/4d2 = 1387 W m-2
Energy reaching Earth: R2 F
• But the Earth reflects back into space
a fraction A
A = 0.29 is the Earth’s albedo
• Therefore the power retained
by Earth is R2 F (1-A) Watts
• The power retained
by Earth is R2 F (1-A) Watts
• The Earth at temperature T
emits into space as a Black Body,
losing energy at a rate
Area  T4 = 4R2 T4
• The power retained
by Earth is R2 F (1-A) Watts
• The Earth at temperature T
emits into space as a Black Body,
losing energy at a rate
Area  T4 = 4R2 T4
• In equilibrium, loss = gain,
4 R2 T4 = R2 F (1-A)
• The power retained
by Earth is R2 F (1-A) Watts
• The Earth at temperature T
emits into space as a Black Body,
losing energy at a rate
Area  T4 = 4R2 T4
• In equilibrium, loss = gain,
4 R2 T4 = R2 F (1-A)
• The power retained
by Earth is R2 F (1-A) Watts
• The Earth at temperature T
emits into space as a Black Body,
losing energy at a rate
Area  T4 = 4R2 T4
• In equilibrium, loss = gain,
4T4 = F (1-A)
In equilibrium, loss = gain
4T = F (1  A)
4
F (1  A _)
T =
4
4
For the Earth:
 1387  0.71 
T =
8 
 4  5.7  10 
T = 256 K
i.e. T = -16.6oC
1
4
F (1  A _)
T =
4
4
In equilibrium
loss = gain
Earth
Actual surface T = 288K
T = 256 K
+15 C
Mars
Actual surface T = 223K
T = 217 K
-50 C
Venus
Actual
surface
T
=
732K
T = 227 K
459 C
In equilibrium, loss = gain
Earth
Discrepancy T = 32K
Mars
Discrepancy T = 6K
Venus
Discrepancy T = 505K
WHY
In equilibrium, loss = gain
Explanation: Greenhouse effect
huge
for Venus mild but significant
for
Earth almost none for Mars.
Planck spectrum:
& therefore
the colours of stars
only depend on T
Peak   T
1
Peak   T
1
The colours of stars
tell us their temperatures.
Note the different colours
of stars in the following picture.
The interaction between
galaxies has triggered star
formation: the hot
young stars are blue.
Hot young
O-B stars
Betelgeuse
Cool
Red Giant
M
Orion
Visible

Rigel
B8
Orion
IR

Examples
for a variety of cosmic objects
showing their
Black Body Spectrum / Planck Spectrum
• Rho Ophiuchi at 60 K (mm waves)
• Young IR star in Orion 600 K (IR)
• Sun, 5800 K
• Omega Centauri star cluster
very hot young stars around 60,000 K
Black Body Spectra
Rho Ophiuchi at 60 K (mm)
Young IR star in Orion 600 K (IR)
Sun, 5800 K
Omega Centauri star cluster
Hot young stars 60,000 K
The entire Universe
glows with a perfect
Black Body Spectrum
or
Planck Spectrum
Isotropic & Homogeneous to 1 part in 105
The entire Universe
glows with a perfect
Black Body Spectrum
or
Planck Spectrum
at 2.725 K
Isotropic & Homogeneous to 1 part in 105
COBE 1992
What produced the Universe’s
Planck spectrum?
The hot dense early universe.
The radiation has been cooling
down ever since
as the universe expands.
The Sun’s Spectrum
A continuous spectrum
The Sun’s
continuous
spectrum
is well
approximated
by a
Black Body
or
Planck
Spectrum
at 5800 K
Our success in fitting the Sun’s
continuous spectrum with a
Black Body (Planck) Spectrum
tells us that it is a dense sphere
at 5800 K.
But what about the
absorption lines?
Kirchoff’s Laws of spectroscopy.
1) A low density hot gas emits
discrete lines - emission lines.
2) A hot solid, liquid or dense enough
gas emits a continuous spectrum.
3) A cool gas absorbs radiation at the
same frequencies as it emits
when hot - this produces dark
absorption lines.
Kirchoff’s Laws of spectroscopy.
3.) A cool gas absorbs radiation at the
same frequencies as it emits when hot:
this produces dark absorption lines.
Dense Hot
Black Body
Cooler gas
cloud
Absorption line
spectrum
Emission & Absorption of Radiation
Absorption & emission of an H
photon
by Hydrogen
 = 656 nm
Absorption
Absorption Spectra
for cool rarefied gases
emission
absorption
Sodium vapour
All Kirchoff’s Laws I n
action.
1.) A low density hot gas emits discrete
lines - emission lines.
2.) A hot solid, liquid or dense enough
gas emits a continuous spectrum.
3.) A cool gas absorbs radiation at
the same frequencies as it emits
when hot - this produces
dark absorption lines.
Interpreting the Sun’s spectrum:
(2) The line spectrum is an
absorption spectrum
We know this is produced by
a rarefied gas
cooler than the Sun’s photosphere.
(Kirchoff’s 3rd law)
Therefore we infer…...
The Sun is a dense sphere
emitting a
Black Body (Planck)
Spectrum at 5800 K
with a cool rarefied
gas atmosphere.
Dense photosphere
emitting Planck spectrum
at 5800 K
SUN
Cooler rarefied atmosphere
absorbing in spectral lines
characteristic of the
elemental composition
The spectral lines tell
us what elements
are present in the Sun’s
atmosphere
(and for other stars too).
Their strength tells us
how much there is.
The spectral lines tell
us what elements are present
Iron (Fe) in the Sun.
A small part of the Sun’s spectrum
Laboratory spectrum of Fe
(incandescent vapour!)
Hydrogen Balmer lines
in spectrum of the star
HD 193182
around 20 Balmer lines from
H13 to H40 are seen here.
(H to H12 are present,
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.
H
He
C, N, O
Fe
A Reminder:
The Black Body
Spectrum
is a
continuous
spectrum
Spectrum only
depends on T
Black Body Spectrum
or
Planck Spectrum
How is a continuous spectrum
produced by a dense collection of
atoms if each atom only produces
a line spectrum?
The Doppler shift.
v
The Red shift.
• Speed of source is v, the red shift is z
• the rest wavelength is
0
• the observed wavelength is 
  0
1 vc
z=
=
1

1 vc
v
z≈
c
For v/c << 1
A spectral line from a hot
gas has a width which
increases with the
temperature of the gas.
kT
v 
h
kT
v 
h
FWHM
Light-emitting atoms moving
randomly in the hot gas
produce broadened
spectral lines.
A spectral line is the sum
of the Doppler shifts
of billions of light-emitting
atoms.
Black Body Radiation
In a solid the interactions
and collisions between the
atoms increase the
range of velocities so much,
that the broadened lines overlap and
merge into a continuum.
Spectral information from starlight
• Peak  or :
• Presence of Line:
• Line intensity:
• Line width :
• Doppler shift:
T = Temperature
Composition & T
Composition & T
T, density, rotation,
outflows, jets,…..
Line-of-sight
velocity
Broadening of lines
due to stellar rotation
enables us to measure
rotation speed.
An Example:
Broadening of lines
due to
circumstellar outflow
IRC+10216
at 15 km/s
IRC+10216
outflow
Telescope
(JCMT)
1000 AU
THE END
OF LECTURE 9