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Activity: Expanding universe

The universe has existed and will exist far beyond the time during which humans have lived on the earth. In this activity you will be introduced to the Doppler effect (if you're not already studying AHL Waves) and come to investigate the relationship between recession velocity and distance of galaxies from the earth. We'll develop a statement for Hubble's law and understand it's significance as well as the idea of expanding space-time and. Let's estimate the age of the universe and consider the relevance of the CMB.

Cosmology

Cosmology is the study of the Universe which up to now (in this course) has been modeled by Newton's universal law of gravitation but this had some problems for scientists 100 years ago.

100 years ago it was accepted that the Universe was static but how can it be static if gravity is acting on everything.

  • Explain why Newton might have thought the Universe should be contracting.
  • Given that the Universe was static, why might Newton conclude that it was infinite?
  • if the universe was infinite and static, why does this imply that time is also infinite?
  • Why would the night sky be completely filled with stars if both space and time were infinite in a static universe?

Doppler effect

The Universe was thought to be static because it doesn't move in the time frame of any observations but in the 1920's more accurate measurements were done using the Doppler effect.

The Doppler effect is the change in frequency due to relative motion between source and observer. This is often observed when a car drives past sounding it's horn (not such a regular occurrence where I live).

The frequency is increased when the car approaches because the car catches up with the waves causing them to be squashed and reduced when the car recedes as the waves are spread out. The result is a change in wavelength leading to a change in frequency (f = c/λ). This can be seen on the simulation below.

  • Observe the change in wavelength in front of an behind the source.
  • Try varying the velocity of the source.

HL students will do more about this in the waves topic (HL) Doppler activity

Here sound has been used to illustrate the effect but it also happens with light causing a change of colour. An approaching galaxy would have shorter wavelength light so would be shifted to the blue end of the spectrum, a receding galaxy would be red shifted.

The fractional shift in wavelength (z parameter) is related to the velocity by the equation

z equals fraction numerator capital delta lambda over denominator lambda end fraction equals v over c

To see the change in wavelength we need to know the original wavelength so the absorption lines are used. There are many lines that could be used, in this example we will use the Calcium H line. Seen here on an intensity vs wavelength plot. Measured for a Calcium source on Earth this line is at 397 nm.

Determining galaxy distance

Certain types of galaxy are approximately the same size but they don't look like it, the close one's look big and the far one small.

The distance to a galaxy can therefore be determined by its angular size when viewed with a telescope.
Measure the size of the two galaxies below by moving the scale from one to the other.

  • Which galaxy is the furthest?
  • What is the ratio of their distance from the Earth?

We can now analyse the spectra from each galaxy.
Use the slider to move the red line to the Calcium H line. Zoom in if it helps.

  • Which galaxy has the biggest Doppler shift?
  • Are the galaxies approaching or receding?
  • Which galaxy has the biggest velocity?

Hubble plotted data from many galaxies and found that galaxies are receding from the Earth with a velocity that is proportional to their distance. His data had large uncertainties but in the 1950's Abell made these measurements that were published by Kelsey.

data source

Distance/Mpcvelocity/km s-1
383810
463860
535430
804960
586657
1207200
10510400
14512800
30023400
36822400
30719200
45740400
55240000
  • Using this data plot a graph of velocity(y) vs distance (x).
  • The Hubble constant (Ho) is the gradient. Find this from your graph

The reason that all galaxies are moving away from us and from one another is because space is expanding like spots on a balloon as it is blown up.

  • Explain why the furthest galaxies are travelling faster than the closer ones.

Cosmic red shift

According to Einstein's General Theory of Relativity the galaxies aren't travelling through space but the space they are in is expanding this means that the wavelength of light travelling in space will get greater as it expands.

Scale factor (R)

The scale factor gives an indication of how big the universe is relative to now.

Rnow = 1

If Rt = 4 then the universe will be 4 times bigger at time t

  • What does a value of R = 1/4 imply?

The amount of expansion between 2 moments in time is proportional to the change in wavelength of light that has been in space for that time. So the ratio of scale factors now and at time t is equal to the ratio of the wavelength at time t and now


R subscript t over R subscript n o w end subscript equals lambda subscript t over lambda subscript n o w end subscript

b u t space z space equals fraction numerator space lambda subscript n o w end subscript minus lambda subscript t over denominator lambda subscript t end fraction

  • Show that

R subscript t space end subscript equals fraction numerator 1 over denominator z plus 1 end fraction

The age of the universe

If the universe is expanding then in the past it must have been smaller, this led to the idea that the universe started with a big bang. At the beginning there was no distance between the galaxies so the age of the universe can be found from separation now /velocity. This is the same as 1/Ho.

  • Calculate the age of the universe from the gradient of your graph. (you will have to convert the units to SI)

History of the universe

First there was a mix of fundamental particles that joined to form protons, neutrons and their antiparticles. These continually annihilated producing photons that the turned into particle - antiparticle pairs. As space expanded the photons wavelength got longer so they had less energy and could no longer produce pairs. Further cooling allowed nuclei to form. At this stage the universe is opaque since as photons are always ionizing any atoms that are formed. At this stage the radiation would have the same as that from a black body. Once the universe cools to 3000 K ionisation no longer takes place and the photons are released. These photons should still be around today but will have a much longer wavelength

  • Why does the radiation in the opaque universe have the characteristics of black body radiation?
  • Why doesn't ionisation take place when cooler than 3000 K?

Cosmic Microwave Background radiation (CMB)

In 1964 a source of microwaves was discovered that seemed to be the same in all directions and had a characteristic black body spectrum with a peak at around 1mm. This is the red shifted radiation left over from when the Universe was 3000 K.

  • What is the temperature of the black body radiation shown.

Summary

Something to take with you to your TOK discussions

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