2.2. The 1936 observational campaign

In a most important paper two years later, Hubble (1936b) made an attempt to reduce the count data to a reliable system of magnitudes and to push the counts to a fainter limit.

It is important to point out that none of the photometry was done on individual galaxies as is done today. Rather, the "limiting" magnitude of plates taken with a particular exposure time, "reduced to standard conditions" ("full" photometric development, particular seeing conditions, particular emulsion batch, particular telescope, and standard photometric conditions) was estimated, based on comparisons using standard stars. The next step was to estimate the difference in the limiting magnitude between stars and the in-focus galaxy images. This was accomplished by a series of experiments (Hubble 1932, 1936b), among which were out-of-focus images of stars made to resemble galaxy images of particular sizes. In this way, the "limiting magnitude" of galaxies was estimated on the "standard condition plates." These are the magnitudes listed for each of the log N values in Table IV of Hubble (1936b).

There are two major problems with this procedure. (1) The apparent magnitudes of the stars used as standards had large systematic errors starting as bright as m_pg = 16, conclusively demonstrated only as late as 1950 (cf. Stebbins, Whitford, and Johnson 1950, see later). (2) Stars in the Mount Wilson Catalog used as standards reached magnitudes only as faint as m_pg ~ 18.5 in most of the Selected Areas, considerably brighter than what was needed by Hubble for his deepest counts. Hubble (1936b) writes "the estimation of the limiting magnitude for 2-hour exposures necessarily involved considerable extrapolation." The limit for his faintest counts was eventually listed as m_pg = 21.03.

Furthermore, even as Hubble's survey work was proceeding in 1934, Baade, whose main Mount Wilson duties were to determine scale errors in the Mount Wilson Catalog, was discovering substantial errors in Selected Area 68 which was the principal Area used by Hubble in his 1929 study of M31. The deviations from a Pogson scale began as bright as m_pg ~ 17. Baade's methods were still photographic, but now, using platinum neutral half filter methods (e.g., Weaver 1946; Stock and Williams 1962), his results were a substantial advance over the multiple exposure plus graded diaphragm methods used by Seares for the Mount Wilson Catalog ⁽¹⁾ between 1910 and 1925.

Hubble's (1936b) final table of log N(m) values at faint magnitudes shows five data points for the counts at m_pg magnitudes of 18.47, 19.0, 19.4, 20.4, and 21.03, plotted as Fig. 1 here from Fig. 1 of Hubble. The analysis for the curvature of space and Hubble's answer whether the redshift is a true Friedmann-Lemaitre expansion depended on these five points.

Plotted are the integral counts as the log of the number of galaxies per square degree that are brighter than apparent magnitude m. The line labeled "Uniform Distribution" has a slope of dlog N(m)/dm = 0.6. The five points show a shallower slope. The departures of the five points from the "Uniform Distribution" line is shown as the lower curve. It is this "departure" curve that comprise the entire data set discussed by Hubble concerning the curvature of space and the reality of the expansion.

Figure 1. Hubble's final formulation of the log N(m) integral count-magnitude relation upon which his subsequent analysis of spatial curvature and the question of the reality of the expansion was based. N(m) is the number of galaxies per square degree brighter than apparent magnitude m. Diagram from Fig. 1 of Hubble (1936b).

¹ Baade never published his new photometry in any complete detail, although he did summarize his corrections to Hubble's M31 magnitude scale in the paper announcing the resolution of the disk of M31 into stars (Baade 1944). Baade needed the faint magnitudes, transferred from his new scale in SA 68, to estimate that the resolved stars in the M31 disk had absolute magnitudes of M_pg ~ -1.5 and therefore that they are similar to globular cluster stars at the top of the giant branch. This connection played a central role in Baade's development of the population concept (Sandage 1986). Back.