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1.1 A brief history

The last century saw an expansion in our view of the world from a static, Galaxy-sized Universe, whose constituents were stars and “nebulae” of unknown but possibly stellar origin, to the view that the observable Universe is in a state of expansion from an initial singularity over ten billion years ago, and contains approximately 100 billion galaxies. This paradigm shift was summarised in a famous debate between Shapley and Curtis in 1920; summaries of the views of each protagonist can be found in [27] and [140].

The historical background to this change in world view has been extensively discussed and whole books have been devoted to the subject of distance measurement in astronomy [125Jump To The Next Citation Point]. At the heart of the change was the conclusive proof that what we now know as external galaxies lay at huge distances, much greater than those between objects in our own Galaxy. The earliest such distance determinations included those of the galaxies NGC 6822 [61], M33 [62] and M31 [64].

As well as determining distances, Hubble also considered redshifts of spectral lines in galaxy spectra which had previously been measured by Slipher in a series of papers [142143]. If a spectral line of emitted wavelength λ0 is observed at a wavelength λ, the redshift z is defined as

z = λ∕λ0 − 1. (1 )
For nearby objects, the redshift corresponds to a recession velocity v which for nearby objects is given by a simple Doppler formula, v = cz. Hubble showed that a relation existed between distance and redshift (see Figure 1View Image); more distant galaxies recede faster, an observation which can naturally be explained if the Universe as a whole is expanding. The relation between the recession velocity and distance is linear, as it must be if the same dependence is to be observed from any other galaxy as it is from our own Galaxy (see Figure 2View Image). The proportionality constant is the Hubble constant H0, where the subscript indicates a value as measured now. Unless the Universe’s expansion does not accelerate or decelerate, the slope of the velocity-distance relation is different for observers at different epochs of the Universe.
View Image

Figure 1: Hubble’s original diagram of distance to nearby galaxies, derived from measurements using Cepheid variables, against velocity, derived from redshift [63Jump To The Next Citation Point]. The Hubble constant is the slope of this relation, and in this diagram is a factor of nearly 10 steeper than currently accepted values.
View Image

Figure 2: Illustration of the Hubble law. Galaxies at all points of the square grid are receding from the black galaxy at the centre, with velocities proportional to their distance away from it. From the point of view of the second, green, galaxy two grid points to the left, all velocities are modified by vector addition of its velocity relative to the black galaxy (red arrows). When this is done, velocities of galaxies as seen by the second galaxy are indicated by green arrows; they all appear to recede from this galaxy, again with a Hubble-law linear dependence of velocity on distance.

Recession velocities are very easy to measure; all we need is an object with an emission line and a spectrograph. Distances are very difficult. This is because in order to measure a distance, we need a standard candle (an object whose luminosity is known) or a standard ruler (an object whose length is known), and we then use apparent brightness or angular size to work out the distance. Good standard candles and standard rulers are in short supply because most such objects require that we understand their astrophysics well enough to work out what their luminosity or size actually is. Neither stars nor galaxies by themselves remotely approach the uniformity needed; even when selected by other, easily measurable properties such as colour, they range over orders of magnitude in luminosity and size for reasons that are astrophysically interesting but frustrating for distance measurement. The ideal H0 object, in fact, is one which involves as little astrophysics as possible.

Hubble originally used a class of stars known as Cepheid variables for his distance determinations. These are giant blue stars, the best known of which is αUMa, or Polaris. In most normal stars, a self-regulating mechanism exists in which any tendency for the star to expand or contract is quickly damped out. In a small range of temperature on the Hertzsprung–Russell (H-R) diagram, around 7000 – 8000 K, particularly at high luminosity1, this does not happen and pulsations occur. These pulsations, the defining property of Cepheids, have a characteristic form, a steep rise followed by a gradual fall, and a period which is directly proportional to luminosity. The period-luminosity relationship was discovered by Leavitt [86] by studying a sample of Cepheid variables in the Large Magellanic Cloud (LMC). Because these stars were known to be all at the same distance, their correlation of apparent magnitude with period therefore implied the P-L relationship.

The Hubble constant was originally measured as 500 km s–1 Mpc–1 [63] and its subsequent history was a more-or-less uniform revision downwards. In the early days this was caused by bias2 in the original samples [8], confusion between bright stars and Hii regions in the original samples [65131] and differences between type I and II Cepheids3 [4]. In the second half of the last century, the subject was dominated by a lengthy dispute between investigators favouring values around 50 km s–1 Mpc–1 and those preferring higher values of 100 km s–1 Mpc–1. Most astronomers would now bet large amounts of money on the true value lying between these extremes, and this review is an attempt to explain why and also to try and evaluate the evidence for the best-guess (2007) current value. It is not an attempt to review the global history of H0 determinations, as this has been done many times, often by the original protagonists or their close collaborators. For an overall review of this process see, for example, [161] and [149]; see also data compilations and reviews by Huchra (External Linkhttp://cfa-www.harvard.edu/~huchra/hubble) and Allen (External Linkhttp://www.institute-of-brilliant-failures.com/).


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