ARlogo Annu. Rev. Astron. Astrophys. 1999. 37: 445-486
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5.2. The Velocity-Distance Relation

5.2.1. The Mount Wilson Years

Following Hubble's announcement of the primitive form of a velocity-distance relation (Hubble 1929b), anticipated by Robertson (1928), Lemaitre (1927, 1931), Humason began an extended program of redshift measurements with the Mount Wilson 100-inch Hooker reflector. By 1931 these data were combined (Hubble & Humason 1931) with apparent magnitude estimates to define a redshift-apparent magnitude relation for field galaxies and for the few galaxy clusters known at the time.

By 1936 Humason (1936) had carried the redshift data to 40,000 km s-1 using a total of 10 great clusters known at the time (found by serendipitous discoveries in other survey programs). These data permitted Hubble (1936b) to define a velocity-"distance" relation for clusters to what was the enormous redshift of z = 0.13 for the Bootis cluster. It was here that the analysis and further observations from Mount Wilson stopped in 1936, awaiting the completion of the 200-inch.

Hence, at the time of the 1948 Palomar dedication, the cluster redshift-magnitude relation was defined by only ten clusters, and the field galaxy data numbered fewer than 200 objects. Essentially no data existed on (1) the isotropy of the expansion (the same in all directions?), (2) systematic velocity deviations, if any, from a linear velocity-distance relation that is required in all expanding models where large-scale homogeneity is maintained throughout cosmic time, and (3) the coldness of the flow itself as measured by the mean random motion about the systematic linear expansion.

These and other problems are what Hubble either meant, anticipated, or implied in 1951 in his program to study "the law of redshifts." That study was to take 30 years at Palomar.

5.2.2. The Humason-Mayall Redshift Catalog and its Analysis

By 1935 Mayall, having designed and put into operation a fast spectrograph at the Lick Observatory for the 36-inch Crossley reflector, began a redshift program on the brighter Shapley-Ames (1932) galaxies, mostly of spiral type. At the same time, Humason continued his 1931 redshift determinations using spectrographs at the Cassegrain focus of the Mount Wilson 100-inch Hooker telescope. Humason and Mayall continued observations through 1941, and began again in 1945 at the close of World War II (see the dates in Table V of Mayall in HMS 1956).

Humason began his extended redshift program at Palomar immediately upon the commissioning of the 200-inch, using a highly efficient new solid-block Schmidt camera that had been designed by Hendricks (1939), Hendricks & Christie (1939), and whose difficult optics were eventually made by Hendricks in the Mount Wilson optical shop (Bowen 1960).

By 1956, Humason had obtained redshifts of 472 field galaxies at Mount Wilson and at Palomar, and 152 galaxies at Palomar in 26 clusters whose redshifts had reached the remarkable value of z = 0.2 for the Hydra cluster.

Most of the distant clusters were new. As mentioned earlier, many had been found in the systematic visual scanning of the Sky Survey plates as they were brought down to Pasadena as the survey progressed. This special search for clusters by Humason and the writer is described by Bowen (1954). At the time of HMS, the Abell Catalog was yet several years in the future.

Once candidate clusters had been found on the deep Schmidt plates, 200-inch prime focus photographs of the candidates were taken to prepare for Humason's later 200-inch spectroscopic observations. Because even the first-ranked galaxies in most of these clusters were not bright enough to be seen on the spectrograph slit, the plates, taken several months prior to the spectrographic observations, were measured in Pasadena for coordinate offsets relative to bright stars that Humason could see. Using these "offset" coordinates, Humason could move the prime focus spectrograph with precision screws to the invisible galaxy whose redshift was sought. The offset plates also were made with star trails superposed on them, made by stopping the telescope drive so that the brighter stars would show trails, from which the precise cardinal directions at the position could be determined. All of this was necessary during the 20 years before television viewing came to a data room that was remote from the telescope itself.

Mayall had also determined redshifts for 300 field galaxies at Lick. There were 114 overlaps between the lists of Humason and Mayall, which, together with many duplicate measures of a given galaxy at each observatory, permitted a thorough evaluation of the accuracy of the redshifts.

In the meantime, Pettit (1954) had measured photoelectric magnitudes at the Mount Wilson 60-inch of most of the field galaxies in the two lists, with a few also measured by Stebbins and Whitford (1952), also at Mount Wilson. For the extensive list of Virgo cluster members, individual photoelectric magnitudes of large-diameter galaxies had been measured by Whitford (1936). Others had been measured by Bigay (1951).

The entire photometry was combined with the Humason and Mayall redshifts to discuss the velocity-"distance" relation (Humason et al 1956, HMS), but now with a much larger database than was available to Hubble (1936) and Humason (1935) in the decade of the 1930s.

The Hubble diagram (redshift versus apparent magnitude, corrected for aperture effects and for the effects of redshift), now for 18 clusters reaching 60,000 km s-1, showed that the velocity-"distance" relation was indeed linear, as had been suspected from Hubble and Humason's earlier results. Linearity is, of course, the most fundamental requirement of the theory and all models if the expansion is real (Heckmann 1942). Every place in the manifold appears to be the center of the expansion, but only if the velocity-"distance" relation is linear. The importance of this linearity requirement is the reason why such a large effort was put into the observational proof at Palomar of linearity from 1950 to well into the 1970s.

Besides testing for linearity, the new feature of the work was the early attempt to obtain the second-order term (the deceleration) from the cluster data, but the result was clearly premature, requiring a much larger data sample.

Following Humason et al (1956), the work was then expanded to eventually include more than 100 clusters over many directions to test for isotropy and for deviations from a pure Hubble flow (Sandage 1970b, 1975).

5.2.3. The Expanded Palomar Program on the Hubble Diagram

It was clear that a large campaign on clusters was needed to search for any anisotropy in the expansion rate and to attempt to measure the second-order (deceleration) term in the Hubble diagram (Robertson 1955, Hoyle & Sandage 1956). The program was begun before Mattig (1958) had found the exact solution of the Friedmann scale factor valid for arbitrarily large redshifts (see Sandage 1995, 1998b).

The observational campaign to extend the Hubble diagram using a large sample of remote clusters lasted from 1955 into the 1980s. The beginning of the program and the results to 1969 were outlined in a progress report (Sandage 1970b). The principal limitation was again the discovery and subsequent photometry and spectroscopy of suitable remote galaxy clusters beyond the limit of the Abell Catalog and of the 1956 HMS program.

Candidate clusters were found by two methods. The first was to exploit the discoveries of clusters that contained radio sources. The second, described in Section 5.2.4, was again a search with the 48-inch Schmidt. We discuss first the radio sources.

By the mid-1960s a number of identifications of the radio sources in the 3CR Cambridge radio source catalog had been made with relatively bright galaxies. These were generally the first or second ranked E galaxies in clusters. Following the earlier work of Minkowski (1960), Schmidt (1965) had begun a 200-inch observing program in the early 1960s for the redshifts of many of the identified radio galaxies.

Photoelectric photometry was also begun on many of the clusters and radio sources then known. The observations were made with the 200-inch prime focus photometer for the faint sources. The brighter radio galaxies were measured with the two Mount Wilson reflectors.

The results were published from 1972 to 1975 in a series of eight papers. The theme of the program was to continue to test the linearity of the velocity-distance relation and its isotropy (the same in all directions?), and to attempt again a measurement of the second-order deceleration term. The contents of the papers are too detailed to describe adequately here. Table 1 gives an outline of the problems discussed in each paper.

Table 1. Summary of the eight papers of the Redshift Distance series

Paper Subject Reference

I Distinction is made between metric and isophotal diameters. Method to correct aperture photometry to a standard metric diameter is derived as used in the remaining papers of the series. Sandage (1972a)
II Hubble diagram for 84 first-ranked galaxies in clusters is derived, including data from Peterson (1970a), Westerland & Wall (1969). qo = 0.94 ± 0.4 derived. Evolutionary correction is discussed (see Sandage & Tammann 1983). Sandage (1972b)
III Hubble diagram of 128 radio galaxies shows the equality of <M> for 3CR radio galaxies with that of first-ranked cluster E galaxies. A form of the Spaenhauer (1978) diagram is first used to illustrate selection bias. Sandage (1972c)
IV Position in the Hubble diagram of QSO relative to first-ranked cluster galaxies is discussed with a two-component luminosity model with QSO as the central component combined with the distributed luminosity of the host E galaxy. Color decomposition is given of the two components. Model is tested by Kristian (1973). Veron-Cetty & Veron (1985), Hewitt & Burbidge (1987) show the continuum of QSO luminosities relating QSO, N galaxies (Matthews et al 1964) with Seyferts and LINERS. Sandage (1973a)
V V-r colors introduced as a photometric system (Sandage & Smith (1963) that proved to be identical (Sandage 1997) to (V-R)J by Johnson (1964, 1965). Hubble diagram of first-ranked galaxies first given in r magnitudes. Sandage (1973b)
VI Deviations from the mean line of the Hubble diagram studied as functions of cluster richness, and Bautz-Morgan (1970) luminosity contrast. Debate on the meaning of the constancy of the luminosity function for the first few ranked cluster members as a function of cluster richness (Peebles 1969, Peterson 1970a, 1970b). Sandage (1973c)
VII Luminosity functions of first three ranked cluster E galaxies. Comparison of known luminosity functions (Abell 1975 from 1968, Rood 1969, Oemler 1974, Krupp 1974, Sandage 1976). Argument by Geller & Peebles (1976), Schechter & Peebles (1976), Oemler (1976), Dressler (1978) based on cD galaxies (Matthews et al 1964, Morgan & Lesh 1965). qo derived again. Sandage & Hardy (1973)
VIII Redshifts (Sandage 1978) given for part of the remaining galaxies observed from Stromlo necessary to complete the redshift coverage of the Revised Shapley-Ames Catalog (Sandage & Tammann 1981, 1987). Isotropy of the local velocity expansion field studied with the result that the Rubin-Ford effect does not exist (see Rubin et al 1976). Sandage (1975a)

5.2.4. The Extension of the Hubble Diagram to Higher Redshifts

By 1975 the available cluster candidates from the Abell catalog and from southern clusters and groups had been nearly exhausted for the high redshifts necessary to determine qo. The redshift range was limited to less than z = 0.5, the largest being Minkowski's (1960) redshift for 3C 295. The conclusion from Paper VII was that qo = 1 ± 1, hardly a useful result.

Two parallel programs to discover clusters more remote than those in the Abell catalog were then begun at Palomar. One was carried out by the writer and described in Westphal et al (1975), and the other was by Gunn and Oke (1975).

The first search was made with the 48-inch Palomar Schmidt using photographic plates taken on the fine grain IIIaJ and 127-04 red plates that had recently been developed at Eastman Kodak by Millikan. These plates reached 0.5 mag fainter than the Sky Survey plates. Thirty fields were surveyed with a total area of 1500 square degrees. About 200 new clusters were found which, together with the clusters found between 1952 and 1957 by Humason & Sandage (1957), Bowen (1954, 1957) but not observed by Humason, constituted the sample that we began to observe with a new sky-subtracting digital spectrograph invented by Westphal et al (1975). No catalog was published.

The survey by Gunn & Oke (1975) was begun using the 48-inch Schmidt, but they also went to fainter magnitudes by making a blind photographic search with the Hale telescope, eventually covering 11.3 square degrees and finding thereby 76 faint clusters (Gunn, Hoessel, & Oke 1986). The catalog from this program, augmented by the search made by Hoessel with the Kitt Peak four-meter Mayall reflector, was eventually published by Gunn, Hoessel, & Oke (1986). It still contains today the faintest sample of clusters found by optical searches.

The photometry and redshifts from the first survey were published in three papers (Westphal et al 1975, WKS, Sandage et al 1976, SKW, Kristian et al 1978, KSW). In the final paper we could extend the Hubble diagram to z = 0.75. Many of the new clusters had measured redshifts between 0.25 and 0.50. From the measurements of the colors as a function of redshift, no evolutionary effects in B-V or V-R were detected (KSW 1978) at the 0.05 mag level over the entire redshift range. This result heavily constrains theoretical models of E galaxy evolution in the relevant look-back times to those with only passive evolution (Sandage 1961, 1963, Oke 1971, Wilkinson & Oke 1978, Sandage & Tammann 1983).

After 1975 the program was carried entirely by Gunn, Oke, and their students. A series of papers were published on all aspects of the Hubble diagram, confirming the correlations in Papers VI and VII (Table 1) of luminosity of first-ranked cluster galaxies with cluster richness and Bautz-Morgan types, and extending the work to larger redshifts. Not only did they find new distant clusters, but Gunn and Oke individually developed powerful new instruments for the 200-inch that benefited all observers.

Oke (1969) designed and oversaw the construction of a 32-channel spectrum scanner used at the Cassegrain focus of the 200-inch. Gunn designed and oversaw construction of two instruments that also saw major use. They were (a) a combined photometric and spectroscopic instrument named PFUEI for Prime Focus Universal Extragalactic Instrument (Gunn & Westphal 1981), and (b) the prototype instrument for the Hubble Space Telescope WFPC camera, called the "four-shooter," built for Palomar at Jet Propulsion Laboratory under the leadership of Gunn and Westphal (Gunn et al 1984).

In their first paper on the Hubble diagram, Gunn & Oke (1975) initiated a new technique for the reduction of the aperture magnitudes, restricting the final observed raw magnitude to a fixed metric aperture of 16 Kpc (for Ho = 60). They then corrected for aperture effect using a correction that depended on the slope of the growth curve at their standard fixed metric diameter. This method differs from the procedure invented in HMS and adopted in the Redshift-Distance series (Table 1) where a standard growth curve was used to correct aperture magnitudes to essentially "total" magnitudes (Sandage 1972a, Paper I). The procedure of Gunn & Oke has also been used in more modern times by Postman & Lauer (1995) in their study of first-ranked cluster galaxies. The small differences in the conclusions of KSW 78, Gunn & Oke (1975) concerning qo can probably be traced to these different reduction procedures, showing the extreme sensitivity of the conclusions to the minuteness of the qo effect.

New photometry on the intermediate band photometric system of Thuan & Gunn (1976) of first-ranked cluster galaxies in many Abell clusters was set out by Hoessel, Gunn, & Thuan (1980, HGT). They solved for the deceleration parameter giving qo = -0.55 ± 0.45. This, of course, is an accelerating universe, indicating a finite value of the cosmological constant, but the errors are too large to secure the result. As part of the same program Hoessel (1980) presented the surface photometry determined from two-dimensional detectors then available, for the galaxies studied by HGT.

In a major study, Schneider, Gunn, & Hoessel (1983a, SGH) analyzed the Hubble diagram for redshifts between 0.04 and 0.3, using the CCD photometry from the previous data papers. They obtained results similar to those of Sandage & Hardy (1973, SH) which showed that there are systematic variations of the absolute magnitude of first several ranked cluster galaxies with cluster richness and Bautz-Morgan contrast class. The work was extended to the first three ranked cluster members by SGH (1983b) where they also confirmed the result of SH concerning cannibalism.

Hoessel & Schneider (1985) published their surface photometry of the first-ranked cluster galaxies done at Palomar, again confirming the previous correlations with cluster richness (their Figure 4) and Bautz-Morgan contrast class (their Figure 3).

An important advance was made by Gunn, Hoessel, & Oke (1986) with the publication of their extensive catalog of remote clusters, discussed earlier. The catalog lists 418 clusters whose redshifts range from 0.15 to 0.92. It has provided the candidate lists for many of the current programs on distant clusters (Postman et al 1996, Oke et al 1998, Postman et al 1998, Lubin et al 1998).

This long narrative of the Palomar program on the "law of the redshifts" shows the central importance of the Palomar 48-inch and the Hale 200-inch telescopes in the development of practical (observational) cosmology during the last 50 years. The fleshing out of the Hubble diagram by the many varied programs shows how Hubble's proposed program was in fact carried to a level that could not have been foreseen in 1951.

Hubble's penultimate program, (see Section 5), was the recalibration of the extragalactic distance scale, which we discuss next. We have no space to discuss his last proposed program of "Cosmological Theory," which in fact now fills many current textbooks such as Narlikar's (1983) exemplar.

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