Download The Doppler Effect in Astronomy and Cosmology

The Doppler Effect in
Astronomy and Cosmology
The Doppler Effect
A passing ambulance
A passing train
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The Doppler Effect for Sound
The radio emits a series of “beeps,”
with period T. If the Flash is
stationary, he will hear the beeps
with a period T’ = T. There is no
Doppler shift.
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The Doppler Effect for Sound
Now the Flash starts running away from the radio.
The Flash is running away, and so the beeps take longer
to reach him, and so he hears a period T’, which is not
equal to T, but is bigger.
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The Doppler Effect for Sound
Now the Flash starts running away from the radio.
Suppose the Flash is running at a constant velocity, v, and
the sound is traveling at a speed vS. They start an initial
distance d apart. Flash hears the first beep at time
d
t1 =
vs " v
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The Doppler Effect for Sound
Now the Flash starts running away from the radio.
The radio waits a time T to send out the next beep, while
the Flash is running the whole time. So, he hears the
next beep at time
d + v sT
t2 =
vs " v
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The Doppler Effect for Sound
Now the Flash starts running away from the radio.
So, the Flash hears a period T’=t2 - t1.
vs
T
T" =
T=
vs # v
1# v v S
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The Doppler Effect for Sound
Now the Flash starts running away from the radio.
Since the frequency is f =1/T’, then we can write
$
v'
f " = &1# ) f
% vS (
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The Doppler Effect for Sound
What if both are moving?
If the speed of the source is v0, the speed of sound is vS,
and the speed of the receiver is vR, then
# vS m vR &
f "=%
(f
$ vS ± v0 '
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The Doppler Effect for Light
Because light behaves
like a wave, it still has a
Doppler effect.
However, the equations
are different!
c±v
f "=
f
c mv
The Special Theory of
Relativity.
!
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The Doppler Effect for Light
Redshift.
Blueshift.
A source of light moving
at v = 0.7c.
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Spectral Lines
When electrons in an atom
make a transition from a
bigger orbit to a lower one,
they emit light.
Every atom has a characteristic spectrum.
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Spectrum of a Star
The Sun emits a continuous
spectrum like a blackbody with
a temperature of 5800 K.
The spectrum of the Sun
shows absorption lines.
By looking at
the spectrum,
we can
determine the
chemical
composition of
a star.
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Spectrum of Stars in a Distant Galaxy
The stars (of a certain type) have
the same spectrum, no matter
where they are.
The spectrum from stars
shows same absorption lines.
Doppler Effect in Cosmology
The lines are
shifted!
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Edwin Hubble
The Universe is
expanding!!!
v = H0d
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Doppler Effect in Cosmology
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The Evolution of the Universe
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The Cosmic Microwave Background
The Universe
started off
extremely hot and
dense, with LOTS of
high-energy photons
around.
As the Universe expands,
the UV photons can start
freestreaming from the
Surface of Last
Scattering at z ~ 1100.
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The Cosmic Microwave Background
The photon wavelength grows with the expansion!
The Universe has expanded by a factor of z ~ 1100
since the LSS, and so the photons are in the
microwave region.
If the Big Bang picture is correct, there should be a
Cosmic Microwave Background!
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Penzias and Wilson
The CMB was discovered
(accidentally) in 1964, and
has a perfect blackbody
spectrum with tiny
deviations!
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Tiny Deviations Lead to Structure in the Universe
COBE
WMAP
This is an area of active
research today, and is based
very much on the Doppler
effect!
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