5.3 The redshift of the 3 K radiation

The temperature, T, of the radiation is proportional to the most probable photon energy, E, which as we have said is proportional to f, and hence inversely proportional to the wavelength λ. Thus,

According to Equation 1, we have for the redshift, z


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5.2 The origin of the 3 K radiation

In speaking of the radiation as having a cosmic origin, what do we have in mind? Essentially this:

In the violent conditions of the early evolution of the Universe, a stage was reached where the matter consisted of a plasma of electrons, protons, neutrons, and some light nuclei such as helium. There were no atoms as such for the simple reason that atoms would have been too fragile to withstand the violence of the collisions that were taking place at the temperature that then existed. As
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5.1 A second major discovery

In the introduction to this unit, we said that there were three pillars of evidence for the big bang. We now turn to the second. It rests on a discovery that ranks in importance with that of Hubble's law. It came about when observations in a new region of the electromagnetic spectrum – the microwave region – became possible. This was due to the invention of new detectors, working at frequencies as high as 30 000 MHz. In 1965, two Bell Telephone scientists, A. Penzias and R. Wilson, were i
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4.2 Evidence for a big bang

Having interpreted the redshift as indicating a recessional speed proportional to distance, one may extrapolate into the future to predict how the positions of the galaxies will evolve with time. One can also run the sequence backwards, so to speak, to discuss what their positions were in the past. Clearly, at former times the galaxies were closer to each other.

But not only that. Because of the proportional relationship between speed and distance (Equation 6), at a certain time in the
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4.1 Hubble's discoveries

In this section, we bring together two important features of galaxies – their redshifts and their distances.

This crucial development owes its origins to Edwin Hubble. His pioneering work in 1923 first led to the confirmation that certain of the fuzzy patches in the sky, loosely called ‘nebulae’, were in fact galaxies like our own.

3.3 Extending the distance scale

Having reviewed some of the properties of galaxies, we are now in a position to return to the question of how we are to develop further our methods of measuring distance.

The various steps taken in determining larger distances from known smaller ones are often called ‘rungs in the distance ladder’. The process of constructing a rung has been:

  1. Find a measurable quantity associated with a class of objects.

  2. Observe how the measura
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3.2 Some general properties of galaxies

Firstly, we note that galaxies tend to occur in clusters rather than singly. The mutual gravitational attraction of galaxies naturally tends to hold them on paths that remain close to each other. Typically a cluster contains tens or hundreds of galaxies. There are, however, large clusters with thousands of galaxies, and there are some solitary galaxies. Our own Galaxy is a member of a smallish cluster of about 36 galaxies called the Local Group (see Author(s): The Open University

3.1 First steps towards a distance scale

As you will see from Table 2, when it comes to astronomy and cosmology, one is called on to deal with a wide range of distances. (Note that a light-year (ly) is the distance light travels in one year, i.e. 9.46 × 1015 m. The distances are also quoted in a very commonly used astronomical unit of distance: the megapar
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2 Radiation from the galaxies

Stars occur in great collections called galaxies. The distribution and motion of galaxies provide us with the first important experimental information on which we shall build our understanding of the type of universe we inhabit. So, what do we know about galaxies?

All the stars that can be distinguished by the naked eye – a few thousand in number – belong to one galaxy: our own Milky Way Galaxy. Sometimes it is just written Galaxy, with a capital G, to distinguish it from all
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1 Introducing cosmology

General relativity has a very different conceptual basis from that of Newtonian mechanics. Its success in accounting for the precession of Mercury's orbit, and the bending of light by massive objects like the Sun, gives us confidence that our picture of space and time should be Einstein's rather than Newton's. In this and the following units, we turn our attention to the study of the large-scale structure of spacetime. We see how spacetime as a whole is curved by the gross distribution of mas
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Learning outcomes

By the end of this unit you should be able to:

  • describe the characteristics of light emitted by stars, and hence the information of cosmological interest that can be deduced from it;

  • distinguish between true and false statements relevant to the distribution and motion of stars within galaxies, and of galaxies within clusters and superclusters;

  • outline the methods used for estimating the distances to stars and to galaxies;

  • explain and
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Introduction

In this unit, we present the three main lines of experimental evidence pointing to the big bang origin of the Universe: (i) the recession of the galaxies; (ii) the microwave remnant of the early fireball; and (iii) the comparison between the calculated primordial nuclear abundances and the present-day composition of matter in the Universe.

A data sheet of useful information is provided as a pdf for your use. You may wish to print out a copy to keep handy as you progress through the unit
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Acknowledgements

The material acknowledged below is Proprietary and used under licence (not subject to Creative Commons licence). See Terms and Conditions.

Grateful acknowledgement is made to the following for permission to reproduce:

Figure 1a: Neil Borden/Science Photo Library; Figure: 1b NOAA/Science Photo Library; Figure 1c: Max-Planck-Institute for Radio Astronomy/Science Photo Library; Figure 11: Science Photo Library; Figure 14: Science Museum.


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6 Appendix: a note on displacement current density

This appendix is optional reading. It is included for the sake of comparison with other texts.

The Ampère–Maxwell law,

is sometimes expressed in the form


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5.2 The energy of electromagnetic waves

The energy density of an electric field E is

Although we will not prove it in this unit, a very similar result applies to magnetic fields. The energy density of a magnetic field B is

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5.1.6 Pulling it all together

The electric and magnetic fields given by Equations 7.21 and 7.23 can satisfy all four of Maxwell's equations in empty space. Gauss's law and the no-monopole law are immediately satisfied because the fields are transverse. Faraday's law and the Ampère–Maxwell law will also be satisfied if we can find electric and magnetic fields that obey Equations 7.24 and 7.26.

We are looking for wave-like solutions, so it is sensible to try

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5.1.5 Getting agreement with the Ampère–Maxwell law

Finally, our electric and magnetic fields must satisfy the Ampère–Maxwell law in empty space. Using Equations 7.21 and 7.23, we obtain

which requires that

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5.1.4 Getting agreement with the no-monopole law

Substituting Equation 7.23 into the no-monopole law gives immediate agreement because

The no-monopole law is analogous to Gauss's law in empty space, and it leads to a similar conclusion: the magnetic wave must be transverse. This has already been established using Farada
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5.1.3 Getting agreement with Faraday's law

Substituting Equation 7.21 into Faraday's law gives

This shows that a propagating electric wave is automatically accompanied by a transverse magnetic wave. The magnetic field oscillates in the y-direction, which is perpendicular to the direction of propagation and
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5.1.2 Getting agreement with Gauss's law

Substituting the assumed form of the electric field (Equation 7.20) into the empty-space version of Gauss's law (Equation 7.16) gives

The first two partial derivatives are equal to zero because f does not depend on x or y. So we obtain


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