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Section 2: The Great Debate and the Great Mistake: Shapley, Hubble, Baade

2.1 A new Cepheid calibration by Shapley

Shapley’s calibration (1918) followed Hertsprung's early attempt and was widely regarded as a significant improvement upon it. Shapley discarded two of the Cepheids Hertzsprung had used for his statistical parallax, on the basis of their light-curves being "atypical", and thereby produced a revised zero point. He also applied a more sophisticated colour correction method to the conversion of Leavitt’s photographic magnitudes to visual ones. However, it was eventually realised that, due mainly to systematic errors and a failure to take into account extinction, his zero point was approximately 1.5 magnitudes too dim. Nevertheless, an extraordinary coincidence led to this not being realised for over 30 years.

Shapley’s particular interest at that time lay in the globular clusters. Leavitt herself had remarked upon the similarity of the bright globular cluster variables to those in the SMC. Shapley examined the PL curve for the "longer - period" variables in the globular clusters and found that its slope was very similar to that for the SMC, accordingly he incorporated these stars in his PL relation as "Cepheids". In his 1918 paper, variables from no fewer than 7 stellar systems were combined into the single relation shown below:

Fig. 5

Inspection of Fig. 5 illustrates that Shapley had gone even further than this: the linear relationship breaks down at bottom right due to his inclusion of faint, short period variables. He called these stars "cluster-type Cepheids"; now termed RR Lyrae variables.

Although Shapley had made the distinction between these "cluster Cepheids" and the bright, "longer - period" Cepheids, he had no idea that he had unwittingly included a third group in his relation – a group hidden in the straight line section. Shapley had not realised that his longer-period variables consisted of two distinct populations. Those he had incorporated from the globular clusters are now termed population II Cepheids, or W Virginis stars, and are of a different type to Leavitt’s population I Cepheids, now termed Classical Cepheids, or simply "Cepheids". Whilst their light and PL curves are similar, population II Cepheids are approximately 1.5 magnitudes fainter than their population I counterparts. A fuller discussion of this, and of the implications of Shapley’s mistake, will be given later.

With regard to the RR Lyraes, Shapley observed that:

The flattening of the luminosity – period curve for magnitudes fainter than -0.5 indicates that for the typical cluster-type variable the median brightness is essentially invariable and is independent of the length of period.

After some analysis, he concluded that their median magnitude could be taken to be –0.23. As such, he had discovered a new standard candle, albeit a faint one, with which to determine cluster distances. It will be shown later that, by an improbable combination of errors, which had somehow conspired to cancel each other out, Shapley’s value of M » 0 for RR Lyraes had come out about right.

Using both his Cepheid and RR Lyrae distance scale Shapley determined the distance to 7 globular clusters. This enabled the calibration of the next step on his distance ladder – the mean magnitude of the 25 brightest stars in a typical cluster, which was reasonably consistent for his 7 clusters. With the distances to 28 clusters so determined, he extended his ladder yet further by using cluster angular diameters, as he was now reasonably confident they were all of similar size. Webb (1999) wrote, "Shapley knew his distance ladder was a rickety structure, and it was built on the quicksand of his Cepheid period-luminosity relation". Nevertheless, Shapley successfully used his scale to investigate the structure of our Galaxy, and by 1920 had come up with a model consisting of a halo of globular clusters, a central bulge and a broad disc several tens of kpc in diameter. In the process he also moved the Sun from a previously assumed position near the centre, to an outlying location in the disc. Shapley’s model remains, in all its essential features, the same one we use today.

2.2 Extragalactic Distances obtained with Cepheid Variables

Whilst we can never have absolute confidence in a distance scale based upon the properties of Cepheids, they played a central role in the early appreciation of the vast scale of the Universe, and the existence of other galaxies.

The ‘Great Debate’ regarding the nature of the spiral nebulae had been raging for years. The thrust of the debate was concerned with whether these nebulae were part of our Galaxy, or remote "island universes" in their own right. Shapley was convinced that his Galaxy was essentially the Universe, and of sufficient size to contain these mysterious objects. His principle antagonist, Curtis, asserted that the Galaxy was both smaller than Shapley believed, and that these objects lay outside it. Evidence from novae already suggested that the spirals might lie at a great distance, but nobody could be certain that the novae were associated with the spiral nebulae, or indeed whether the nebulae were stellar systems at all. Whilst there were some persuasive arguments on both sides of the argument, none could claim to be conclusive and it became something of an impasse. The debate was finally settled by Edwin Hubble using Cepheid distance measurements.

Hubble is justifiably famous for his discovery that the spiral nebulae are galaxies in their own right. But his first published paper on the subject of galactic distance concerned an irregular, NGC 6822. In this paper, modestly entitled, "A remote stellar system", Hubble estimated a distance of 214 kpc for NGC 6822, a staggering distance at that time which far exceeded even Shapley’s overestimated Galactic disc diameter of 90 kpc. Hubble wrote:

"The present investigation identifies NGC 6822 as an isolated system of stars and nebulae of the same type as the Magellanic Clouds, although somewhat smaller and much more distant" (Hubble 1925).

This paper appeared to receive little attention at the time, but this was because Hubble had already released preliminary data regarding the distance to the spirals - as far as the astronomical community was concerned the Great Debate was already over.

Fig. 6: NGC 6822 (Barnard’s Galaxy) an irregular now estimated to be at a distance of 520 kpc.

Working with the 100-inch Mount Wilson Telescope, then the most powerful in the world, Hubble had managed to locate Cepheids in the arms of M31 (Andromeda) and M33 (Triangulum). He was unable to resolve these galaxy's central regions, or indeed any stars from population II. Hubble’s observational restriction to population I Cepheids would have important ramifications when Shapley’s error was later discovered. Nevertheless, when, "A spiral nebula as a stellar system, Messier 33" was finally published, Hubble estimated it to be at a distance of 263 kpc (Hubble 1926). He also showed that M31 (Andromeda) lay at a similar huge distance, and was more than twice the diameter of M33.


Fig 7: M31 & M33. Hubble demonstrated that they were ‘Island-Universes’ in their own right.

2.3 The Great Mistake: Two Cepheid Populations

During World War II Walter Baade, working at the Mount Wilson Observatory, undertook a detailed study of M31 and its accompanying "early-type" nebulae M32 and NGC 205. He was able to take advantage of almost unlimited telescope time and excellent seeing conditions due to wartime blackouts. Baade found that if he used red-sensitive photographic plates it was possible, for the first time, to resolve stars in these companion galaxies and in the central region of M31 itself. When he analysed the Hertzsprung-Russell (H-R) diagram for these three regions he found it to be almost identical to that for the globular clusters. He wrote:

Although the evidence presented in the preceding discussion is still very fragmentary, there can be no doubt that, in dealing with galaxies, we have to distinguish two types of stellar populations, one which is represented by the ordinary H-R diagram (type I), the other by the H-R diagram for the globular clusters (type II). Characteristic of the first type are highly luminous O- and B- type stars and open clusters; of the second globular clusters and short-period Cepheids. Early-type nebulae (E-Sa) seem to have populations of pure type II. Both types coexist, although differentiated by their spatial arrangement, in the intermediate spirals like the Andromeda nebula and our own Galaxy. (Baade 1944)

Baade and Hubble had already discussed at some length an apparent discrepancy in the distance calibration; they could not understand why the globular clusters associated with Andromeda appeared to be 1.5 magnitudes fainter than those in the Galaxy. "Hubble took the more cautious line that one should not overwork the principle of uniformity and that there may be a real difference..", but Baade was less certain (Baade 1956). His discovery of the two populations suggested a solution. Baade later wrote:

Miss Leavitt’s cepheids in the Magellanic Clouds and the classical cepheids in our galaxy are clearly members of population I, while the cluster-type variables and the long-period cepheids of the globular clusters are members of population II. Since the color-magnitude diagrams of the two populations leave no doubt that .. we are dealing with stars in different physical states, there was no a priori reason to expect that two cepheids of the same period, the one a member of population I, the other of population II, should have the same luminosity. (Baade 1956)

To remove the discrepancy in the Andromeda globular clusters, Baade realised that it would be necessary to brighten the PL relation for population I Cepheids by 1.5 magnitudes. He awaited completion of the 200-inch Hale telescope at Palomar to verify this. His first few observations with the new telescope immediately supported his theory: the cluster-type variables (RR Lyraes) should have been visible at the limiting magnitude of his plates, but they were not. However, other population II stars known to be intrinsically 1.5 magnitudes brighter than the RR Lyraes were just visible. The whole of population II appeared to be about 1.5 magnitudes dimmer than predicted. Using this, and other magnitude-comparison arguments, he eventually satisfied himself that:

instead of one period-luminosity relation there are actually two, one for type I cepheids, the other for type II. On the average a type one cepheid is 1.5 magnitudes brighter than a type II cepheid of the same period (Baade 1956).

This 1.5 magnitude discrepancy would correspond to a four-fold underestimate of luminosity for classical Cepheids, and a corresponding two-fold increase in their distances. The cosmos was re-scaled when Baade presented his findings to the International Astronomical Union in 1952. The Universe, and indeed Hubble’s constant for galactic recession, both doubled in size. The Andromeda globular clusters were brought into line with the Galaxy’s, and the Galaxy itself lost its status as giant of the local group – M31, now at twice its previously assumed distance, was easily the largest member.

Surprisingly, the revision had no effect on the size of the Galaxy itself. This had been based principally upon studies of the globular clusters and the RR Lyraes. The zero point of Shapley’s distance calibration had been based on Population I Cepheids and had always been 1.5 magnitudes in error, but when unwittingly applied to the Population II Cepheids, which were 1.5 magnitudes dimmer than realised, the mistake largely cancelled out. His RR Lyrae calibrations were similarly correct, because they too had been determined using the Population II Cepheids. This, in particular, was why it took so long to discover the mistake; independent calibrations of RR Lyrae distances had been in good agreement with Shapley’s. Regarding this matter, Fernie (1969) was amused enough to write:

The definitive study of the herd instincts of astronomers has yet to be written, but there are times when we resemble nothing so much as a herd of antelope, heads down in tight formation, thundering with firm determination in a particular direction across the plain. At a given signal from the leader we whirl about, and, with equally firm determination, thunder off in a quite different direction, still in tight parallel formation.

Shapley’s calibration had nevertheless obtained a number of important results, and had proved to be remarkably accurate – as long as you did not stray outside the Galaxy!

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