Some corrections to Raine & Thomas

An Introduction to the Science of Cosmology, by D. J. Raine and E. G. Thomas, is probably the text that is closest in level to this course (it covers more ground on the theory side, and less on the observational side). Like most textbooks there are some errors in it. These are the ones that I have found.
Section 1.2
The correct size of the Galaxy is about 30 kpc = 9x1020 m.
Finger of God effect (Sections 1.2 & 9.4)
Not, as claimed here, due to our random motion through the background, and nothing to do with the moving cluster effect as suggested. Clusters of galaxies appear elongated towards the observer in redshift-space maps. At first sight this appears to put Earth in a special position at the centre of the Universe, as in the medieval cosmology (hence the name). In fact it is just due to the random motion of the galaxies in the clusters which adds a moderately large, random, red- or blue-shift to the cosmological redshift.
Section 1.3
Matter and anti-matter are not 'interconvertible' at high temperatures as stated. They mean to say that high-energy collisions produce particle-antiparticle pairs, hence both matter and anti-matter are abundant at high temperature.
Definition of redshift (Section 2.1)
Delta(lambda) should be Lambda(observed) - Lambda(emitted), not the other way round.
Olbers' Paradox (Section 2.8)
At present the darkness of the night sky is not due to the finite lifetimes of the stars, as claimed here, but to the finite age of the Universe, which sets a maximum distance we can see (the particle horizon). Only when the Universe becomes so old that most stars have died out would stellar evolution have anything to do with this.
Microwave sources (Sections 4.1.1 and 4.2)
I take exception to the claim that there are no known sources of microwave emission (apart from the CMB); in fact radio astronomy is largely concerned with observing microwave sources including stars, galaxies and quasars. Similarly, Galactic emission is detectable over much of the sky to wavelengths as short as 2 cm, not 50 cm as quoted in Section 4.2.
Section 4.1.3
Relation between surface brightness and energy density should be: i = u c /(4 pi).
Figure 4.2
The caption should mention that the error bars are only visible because they are plotted at 400 standard deviations!
Baryogenesis (Section 7.7)
Item 5 in this list is of course a speculation and not a known fact, as X particles have not yet been discovered.
Random walks in the Early Universe (Sections 7.10.2 & 7.10.3)
These two sections use related arguments based on random walks to argue that absorption and collision timescales are shorter in the early universe than you might naively think. Don't worry if you can't follow this argument, because it is completely bogus. The time to cover a distance L in a random walk of N steps, when each step is travelled at speed c, is of course not L/c, but Sqrt(N) L/c.

In Section 7.10.2 the free-free timescale quoted in the first paragraph is the correct one and the revision is wrong; random walking makes no change to the answer when the correct Sqrt(N) factor is included. Therefore absorption ceases to be important near the peak of the CMB spectrum when the temperature falls below 104 eV, a few days after the Big Bang (it remains important for much longer in the long-wavelength tail of the spectrum).

In Section 7.10.3 the final answer is correct because the premise is wrong. The expression quoted in the second paragraph is the classic Compton scattering formula, applicable to stationary electrons. In the early Universe the electrons were rapidly moving, and the Compton shift is swamped by the effects of the Doppler shift to and from the rest frame of the electrons, which gives a fractional frequency shift df/f of order v/c. A little algebra shows that this is of order the square root of the expression quoted by Raine & Thomas. This cancels out the mistake about random walks to give the right answer.

Jeans Mass (Section 9.8)
The final formula omits a factor of rho0 on the right-hand side.

Last modified: 2002 May 24
J. P. Leahy

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