Physics IAL Unit 5 - Evidence for the Big Bang Theory

1. Lesson Objective:
To explain the evidence for the ‘Big
Bang’ Theory and apply red-shift
equations.
Lesson Outcomes:
Describe the evidence for the Big
Bang Theory.
Explain how red-shift provides
evidence for the Big Bang Theory
Apply red-shift equations to solving
problems in various contexts
Keywords:
Big Bang Theory, Doppler
Effect, Red-shift,
Atomic Line Spectra,
speed of recession
Starter:
Write down what do you
remember about the ‘Big
Bang’ Theory from GCSE?
EVIDENCE FOR THE BIG BANG THEORY

2. Evidence for the ‘Big Bang’ Theory
• Galaxies receding
• Chemical composition of early galaxies
(mostly hydrogen with ~25% helium and
traces of lithium and beryllium)
• Cosmic microwave background radiation,
which corresponds to a temperature of
the universe of about 2.7K

3. ▶ What is the Doppler Effect (you studied this last year) – Write an
explanation.
▶ What is an absorption spectrum (you studied this last year) –
Write an explanation
How do we know galaxies are receeding?

4. The Doppler Effect
A B C D E
A B C D
As the ambulance travels
forwards:
The sound wave in front is
compressed
- decreasing its wavelength
- increasing its frequency
The sound wave behind is
stretched out:
- increasing its wavelength
- decreasing its frequency
ambulance
sound demo

5. The Doppler Effect also occurs with light and radio waves.
With light waves:
In front of the moving object
decreasing wavelength and increasing frequency
makes the light BLUER
Behind the moving object
increasing wavelength and decreasing frequency
makes the light REDER

6. Also:
change of wavelength = object radial speed
source wavelength speed of light
Δλ = v
λ c

7. How do we know galaxies are receding?

8. Doppler effect equations
When the speed of the object, v is
MUCH LESS than the speed of light, c.
change of frequency = object speed
source frequency speed of light
Δf = v
f c

9. Question 1
Light of frequency
4.000 x 1014 Hz is emitted from
a galaxy that is moving away
from us at 600 kms-1. Calculate:
(a) the frequency shift caused
and,
(b) the observed frequency.
c = 300 000 kms-1
(a) v is << c
and so: Δf / f = v / c can be used
Δf = (v / c) x f
= (600 kms-1 / 300 000 kms-1)
x 4.000 x 1014 Hz
= 0.002 x 4.0 x 1014
frequency shift = 8.0 x 1011 Hz
(b) The galaxy is receding and so the observed
frequency is lower than the source frequency.
source frequency = (4000 - 8) x 1011 Hz
= 3992 x 1011 Hz
observed frequency = 3.992 x 1014 Hz

10. Question 2
The Andromeda Galaxy has a Doppler
Shift of 0.000 5.
The observed wavelengths are also
smaller than the source wavelengths.
(a) Calculate velocity of the Andromeda
Galaxy relative to the Earth.
(b) What will be the observed
wavelength of red light if the source
was 700.00 nm?
c = 300 000 kms-1
(a) A Doppler Shift of 0.000 5 will mean
that v is << c
and so: Δλ / λ = v / c = z can be used.
v = z x c
= 0.000 5 x 300 000 kms-1
speed = 150 kms-1
The wavelengths are decreased therefore the Andromeda
Galaxy is moving towards the Earth.
radial velocity = 150 kms-1 towards the Earth
(b) Δλ / λ = z
Δλ = z x λ
= 0.000 5 x 700.00 nm
= 0.35 nm
less than the source
observed wavelength = 699.65 nm

11. Question 3
A hydrogen radio source emits
waves of frequency 1420 MHz.
A radio telescope observes
these waves to have a
frequency of 1430 MHz.
Calculate velocity of the source
relative to the Earth.
c = 300 000 kms-1
Δf = (1430 – 1420) MHz
= 10 MHz
Δf / f = z
z = 10 MHz / 1420 MHz
= 0.00704
A Doppler Shift of 0.00704 will mean
that v is << c
and so: z = v / c can be used
v = z x c
= 0.00704 x 300 000 kms-1
radial speed = 2 112 kms-1
The frequency is increased therefore the radio source
is moving towards the Earth.
radial velocity
= 2 112 kms-1 towards the Earth

12. Doppler shift summary
Doppler
shift, z
in frequency
Δf
f
in wavelength
Δλ
λ
Colour shift
with light
Source
moves
towards
observer
Source
moves away
from
observer
+ v
c
+ v
c
- v
c
- v
c
RED
SHIFT
BLUE
SHIFT

13. 400 500 600 700
wavelength / nm
Doppler shift in spectra
Stationary source
Hα
Receding source
RED SHIFT
Hα
Approaching source
BLUE SHIFT
Hα

14. Question
The hydrogen-alpha
spectra line of a distant
galaxy occurs at a
wavelength of 680 nm. In
the Sun this wavelength is
656 nm.
Calculate the recessional
velocity of the galaxy.
c = 300 000 kms-1
Δλ = (680 – 656) nm
= 24 nm
Δλ/ λ = z
z = 24 nm / 656 nm
= 0.0366
A Doppler Shift of 0.0366 will mean
that v is << c
and so: z = v / c can be used
v = z x c
= 0.0366 x 300 000 kms-1
= 10 980 kms-1
recessional speed = 11 000 kms-1

15. The Doppler effect with binary stars
A binary star system consists of two stars in mutual orbit about
each other.
The two stars are often too close together to be resolved by a
telescope as separate stars.
However, as they orbit each other they will be moving away and
towards the Earth.
The stars will produce both red and blue shifts which can be
measured.
This type of system is called a spectroscopic binary.
From the Doppler shift measurements the orbital speeds of the
stars can be found.

16. In the example above, star A is more massive than star B.
This results in the orbital radius and speed of star A being less than star B.
star A star B
line of sight
SPECTRA
From star A
From star B
Combined
H-alpha line position
from a stationary source
Red shift
Blue shift
Blue shift
Red shift
No shift

17. Question
A spectral line of a certain spectroscopic
binary merges once every 4 years and
splits to a maximum displacement of
0.036 nm and 0.015 nm from its
laboratory wavelength of 656 nm.
Calculate:
(a) the orbital speed of each star and
(b) the radius of the larger orbit.
c = 300 000 kms-1
The slower star has the smaller Δλ
= 0.015 nm
Δλ/ λ = v / c
becomes: v = c x (Δλ/ λ)
= 300 000 x (0.015 / 656)
slower star = 6.86 kms-1
With the faster star:
v = 300 000 x (0.036 / 656)
faster star = 16.5 kms-1
The merging of the line occurs every half-period.
Therefore: T = 8 years
The faster star will have the greater orbital radius, R
The orbital speed of the faster star, v = 2πR / T
and so: R = Tv / 2π
= [(8 x 365 x 24 x 60 x 60s) x (16.5 kms-1)] / 2π
= [(252 288 000s) x (16 500 ms-1)] / 2π
= (4.162 x 1012 m) / 2π
= 6.63 x 1011 m
larger radius = 662 million km

18. As the universe expands, the space between galaxies is
expanding. The more distance between us and a galaxy,
the more quickly the galaxy will appear to be moving
away from us. It is important to remember that although
such distant galaxies can appear to be moving away
from us at near the speed of light, the galaxy itself is not
traveling so fast. Its motion away from us is due to the
expansion of the space between us.

19. Hubble’s Law
In 1929 after plotting the redshift calculated speeds of about
thirty galaxies against their distances Hubble noticed that a
‘rough’ straight line through the origin was obtained.

20. Hubble’s law states that the speed of recession of a galaxy is
proportional to the distance to the galaxy.
v α d
inserting a constant of proportionality:
v = Hd
H = the Hubble constant = 70 km s-1 Mpc-1
Notes:
(a) Mpc = megaparsec (= 3.26 million light years)
(b) Hubble’s law does not work with some nearby galaxies
(which are approaching us!)

21. Question 1
Calculate or state the speeds expected for galaxies at distances:
(a) 1 Mpc; (b) 10 Mpc & (c) 1 billion light years.
1 Mpc = 3.26 million light years
(a) From the definition of the Hubble constant, H:
A galaxy at distance 1 Mpc will have a speed of 70 km s-1
(b) At 10 Mpc the speed will be 700 km s-1
(c) 1 billion light years = (1000 / 3.26) Mpc
= 306.7 Mpc
therefore speed = 306.7 x 70
speed = 21469 km s-1

22. Question 2
Calculate the distance, in light years, to a galaxy if its recessional
velocity is 10% of the speed of light.
c = 300 000 kms-1 & 1 pc = 3.26 lyr
v = Hd
therefore:
d = v / H
= (0.1 x 300 000 kms-1) / (70 km s-1 Mpc-1)
= 30 000 / 70
= 428.6 Mpc
= (428.6 x 3.26) Mlyr
= 1 397 Mlyr
= 1.4 billion light years

23. The expansion of the Universe
Hubble’s law tells us that distant galaxies are receding
from us and that the further they are away the faster
they are moving away from us.
Hence the Universe is expanding.
Balloon model of the
expanding Universe
The space between the
galaxies expands and so the
galaxies grow further apart

24. Estimating the age of the Universe
Hubble’s constant tells us that the speed of a galaxy increases by 70
kms-1 for every Mpc or 3.26 million light years.
For a galaxy to be receding at the speed of light its distance would be:
(300 000 kms-1) / (70 kms-1 Mpc-1)
= 4 285 Mpc
= 4 285 x 3.26 million light years
= 14 billion light years
Galaxies cannot travel this fast.
Therefore light cannot have been travelling for this length of time.
Therefore the Universe must be less than 15 billion years old.
The current greatest length of time observed is about 13.5 billion years.

25. As can be seen in the above calculation, the maximum size of the Universe,
D is given by:
D = c / H
But distance = speed x time
For a galaxy travelling at speed c for the age of the Universe T.
D = c T
Therefore: c / H = c T
1 / H = T
Hence the maximum age of the Universe is given by:
T = 1
H
Note: All of the above assumes that the Hubble constant has not changed
during the lifetime of the Universe.

26. Question 1
The unit of 1 / H must be one of time. Calculate the
value of 1 / H in seconds. 1 Mpc = 3.1 x 1022 m
H = 70 kms-1 Mpc-1
Therefore 1 / H = 0.0143 Mpc s km-1
But 1 Mpc = 3.1 x 1022 m = 3.1 x 1019 km
Hence:
1 / H = 0.0143 x 3.1 x 1019 km s km-1
= 4.43 x 1017 s (14 000 million years)

27. Question 2
In 2009 measurements from the Hubble Space Telescope yielded a Hubble
constant of 74.2 ± 3.6 km s-1 Mpc-1. What is the maximum age of the Universe, in
years, based on this measurement?
1 Mpc = 3.1 x 1019 km
T = 1 / H
Maximum T will come from a minimum value of H.
that is: 74.2 - 3.6
= 70.6 km s-1 Mpc-1
Therefore: T = 1 / 70.6
= 0.0142 Mpc s km-1
But 1 Mpc = 3.1 x 1019 km
Hence: 1 / H = 0.0142 x 3.1 x 1019 km s km-1
= 4.40 x 1017 s
= (4.40 x 1017 s) / (365 x 24 x 60 x 60) years
Maximum age = 14 000 million years

28. The Big Bang theory
• Hubble’s law supports the idea that the Universe
started in some form of massive explosion.
• This idea is called the ‘Big Bang theory’.
• This theory was not generally accepted until 1965
before which an alternative explanation for the
expansion of the Universe called the ‘Steady State
theory’ was dominant.

29. Evidence for the Big Bang theory
1. Cosmic Microwave Background (CMB) radiation
All of space emits thermal radiation with a maximum intensity wavelength
corresponding to a temperature of 2.7K.
It is radiation created in the Big Bang that has been travelling ever since the
Universe became transparent (about 377 000 years after the Big Bang).
The expansion of the Universe has gradually increased the wavelengths of
this radiation so that it now occurs in the microwave region of the
electromagnetic spectrum.
This radiation was first detected by Penzias and Wilson in 1965.
Expanding Universe

30. The microwave detector used
by Penzias and Wilson
Cosmic Microwave Background radiation.
CMB map of the whole Universe obtained
by the COBE satellite in 1989

31. 2. Relative abundance of hydrogen to helium
Using the Big Bang model it is possible to calculate the ratio of
concentration of hydrogen to helium-4 by mass.
This depends on the ratio of photons to baryons, which itself can be
calculated independently from the detailed structure of Cosmic
Microwave Background fluctuations.
The ratio by mass predicted is about 4:1.
The measured ratio of abundance is 3:1 which is roughly in agreement.
Other ratios such as hydrogen to Lithium-7 or Helium-3 also give
roughly similar results.

32. Dark energy
• In 1998 astronomers discovered that very distant type 1a supernovae
were much further away than expected. Their red-shifts (and therefore
recessional speeds) are not as great as would be expected for their
distances.
• These and further measurements have led astronomers to conclude that
the expansion of the Universe has been accelerating for about the past
5000 million years.
• Before this discovery, the expansion of the Universe was expected to be
decelerating due to the attractive gravitational forces of galaxies on each
other.
• Therefore there appears to be some unknown repulsive force acting which
is releasing some hidden ‘potential’ energy which is currently known as
dark energy.

33. • The nature of dark energy is unclear. It is thought to be a form of
background energy present throughout space and time.
• It is more prominent than gravity at large distances as gravity becomes
weaker with distance (inverse square law) whereas the force associated
with dark energy is thought to remain constant.
• Current theories suggest that it makes up 70% of the total energy of the
Universe.
• The idea of dark energy leads to the speculation that in the future the
force associated with dark energy will ultimately tear apart all
gravitationally bound structures, including galaxies and solar systems, and
eventually overcome the electrical and nuclear forces to tear apart atoms
themselves, ending the universe in a "Big Rip".

34. Dark energy controversy
It has been noted that if Newton’s law of gravitation:
F = GMm/r2
became: F = GMm/r
at large, intergalactic distances,
then the acceleration of the expansion of the universe
no longer requires the existence of Dark Energy.
Other alternative ideas for dark energy have come from
string theory, brane cosmology and the holographic
principle.

35. Quasars
‘Quasar’ stand for ‘quasi-stellar radio source’.
A quasar is a compact region in the centre of a
massive galaxy surrounding a central supermassive
black hole.
Its size is 10-10,000 times the Schwarzschild radius
of the black hole.
The quasar is powered by an accretion disc around
the black hole.
Quasars were first identified as being high redshift
sources of electromagnetic energy, including radio
waves and visible light, that were point-like, similar
to stars, rather than extended sources similar to
galaxies.
Infra-red image
of a quasar.
Artist’s impression of a quasar

36. Quasars are among the oldest and most distant objects
in the Universe.
A quasar is characterised by:
• its very powerful light output, much greater than the
most massive of stars
• its relatively small size, not much larger than a star
• a large red shift indicating its distance is between 5
and 10 billion light years away.
The first quasar discovered, 3C 273 produced strong
radio emissions. However, not all quasars produce such
emissions.

37. Question
Light from a certain quasar was
found to contain a spectral line
that had been red-shifted by 80
nm from its normal wavelength
of 486 nm.
Calculate the recessional speed
of this quasar.
c = 300 000 kms-1
z = Δλ / λ
= 80 nm / 486 nm
= 0.164
A Doppler Shift of 0.164 will mean
that v reasonably smaller than c
and so: z = v / c can be used to a
reasonable accuracy
v = z x c
= 0.164 x 300 000 kms-1
recessional speed
= 49 300 kms-1