| Hubble's original value for "his" constant was 500-550 km s-1 Mpc-1, as opposed to our current estimate of 71 ± 4 km s-1 Mpc-1. | |
| Explain why Hubble's value, taken in combination with other information available in the 1940s, favours the Steady State cosmological model. | [2] |
| This value of H0 gives an age for the universe of <2 Gyr (1.3 Gyr for matter dominated flat case). But the age of the Earth was known from radiochemical dating to be probably greater than this (~3 Gyr from old crust). Having the Earth older than the universe is not satisfactory! | [1] |
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In the Steady State, the value of 1/H gives a typical age for a galaxy,
but individual galaxies can be older than this, so no problem.
(Note that you have to explain why the Steady State is OK, not just why the Big Bang isn't. An observational datum that agreed with neither model would not "favour the Steady State", any more than one that agrees with both does!) |
[1] |
| Briefly describe the two main errors in Hubble's distance determinations which led to this erroneous result. | [3] |
| The initial point to make is that if you use m - M = 5 log(d/10) to get distance, an error in your assumed M translates directly into an error on the gradient of a line v = Hd: wrongly taking M' = M + ΔM gives d' = d × 10-ΔM/5, so if v = Hd it follows that v = H'd' where H' = H × 10ΔM/5. | [1] |
| The first error made by Hubble concerned the zero-point of the Cepheid variable period-luminosity relation. This was not well calibrated at the time, because there are no Cepheids close enough for ground-based parallax, and was additionally confused because in the 1920s and 1930s it was not realised that the "Cepheid variables" in globular clusters were a different and fainter class of star (W Virginis variables) than the Cepheid variables in galactic discs. Therefore, comparing a globular cluster "Cepheid" (about 4× fainter) with an extragalactic Cepheid of the same period, you will believe that the extragalactic Cepheid is only half as far away as it really is. | [1] |
| For galaxies in which Cepheids could not be resolved, but the very brightest stars could be, Hubble assumed that there exists a well defined maximum luminosity for a star, i.e. that all these "brightest stars" were likely to be about equally bright. This is not a bad idea – the Eddington limit sets an upper limit for stellar masses – but Hubble was making a fundamental error in assuming that the small bright blobs on his photographic plates were single stars. In fact they turned out to be H II regions, which are typically excited by several OB class massive stars, and are therefore considerably brighter than individual OB stars. H II regions are red, whereas OB stars are blue, but Hubble could not use this to distinguish the two because in the 1920s photographic plates were not sensitive to red light. The later development of red-sensitive plates allowed Allan Sandage to discover this error in the 1950s. | [1] |
(2006 Q3.)