Adriaan van Maanen's monumental work on of spiral nebulae, as it stood in 1921, offers a long overlooked (read "rejected") solution to the flat rotational velocity curves for "galaxies." In the author's opinion, van Maanen's investigations have been wrongfully relegated to oblivion. Evidence will be presented below to hopefully help rectify the situation, and to commend van Maanen's findings as an already-accomplished solution to one half of the missing mass problem.

From 1916 through 1927 van Maanen, who was a recognized authority on precision astronomical position measurements, produced twelve papers dealing with astrometrically determined internal motions of spiral nebulae. Shapley used his findings as ammunition in the great debate, but later on lost the faith in a groundswell of criticism directed at van Maanen's findings.

In his 1921 paper on the spiral nebula M 81, van Maanen summarized his findings on the internal motions of four spirals, M33, M51, M81 and M101. He states,

    "As in the case of M101, 33, and 51, there is a question as to whether the [nearly circular]
    displacements [of M 81] are best represented by a rotation or by a motion along the arms
    of the spiral. (MA21)

See the tabular summary: Internal Proper Motions for M101, M33, M51 and M81.
[Added 27 July 2003.]

This motion of matter along the arms was river-like, i.e., gaseous and/or unresolved-stars spiraling outward in stream-like fashion.

See: Messier 81 Internal Motions. (Added 19 July 2003.)
       Messier 33 Internal Motions. (Added 9 June 2005.)

For each of the spirals he subtracted the average proper motion (in milliarcseconds per year) of the spiral from the measurements for individual data points to arrive at his rotational versus stream angular displacements.

He divided his measured displacements by the number of years between photographs to obtain the annual rates for angular displacements.

There is no direct information in van Maanen's 1921 paper (MA21) that identifies his estimated sizes of or the distances to the spirals, but if we assume, with Curtis, that the spirals should have similar tangential linear rotation speeds to our own, i.e., 320 km/sec at our location in the Milky Way disk, and use that speed to convert van Maanen's rotational periods to spiral diameters, we get the following results.

Table 1

These "starting point" spiral diameters are quite contrary to Curtis' idea for other island universes, where diameters on the order of 30,000 light-years were desired. That kind of information had to be available to his colleagues, and van Maanen's train was headed down the wrong track!

The average of recent spectroscopic determinations of rotational velocities for the four objects in Table 1 is 178 km/sec. That's within a factor of two of the 320 km/sec starting point velocity used above. See Table 2.

Table 2

A Cornell University astronomy course webpage shows an edge-on rotation curve for the spiral "galaxy" UGC 9242. The Doppler shift rotation velocities, in the "flat" part of the curve, vary from 195 to 235 Km/sec, and average approximately 220 Km/sec. Please see: Example: Galaxy Rotation Curve [Added 8 Aug 2003.]

Table 3 shows how van Maanen's linear proper motions for a very limited sample of spirals and globular clusters compared to other astronomical objects.

Table 3

In their paper Internal Motions in Globular Clusters (KA00), King and Anderson report astrometric measurements of internal proper motions in globular cluster 47 Tucanae, using HST's WFPC2 camera with photographic epochs separated by two years. In 47 Tuc, the dispersion of internal proper motions has been found to be about 0.6 milli-arcsec/year in each coordinate.

Referring back to a radial velocity study of 47 Tuc (Meylan & Mayor 1986, get ref.) which showed evidence of rotation of the cluster, King and Anderson report "We can in fact see rotation clearly in the proper motions too..." [No quantitaive value given yet.]

Based on asymmetry [a slight flattening] found in several globular clusters (Pease and Shapley), Van Maanen (MA27) stated "...it follows that the motions resulting from a possible rotation of the clusters are small. Tangential components of the motions are derived therefore only because evidence of such motions had been found in the measures of spiral nebulae." [Emphasis added.]

Van Maanen's findings included the following. For the plates taken at the 25-foot focus of the Mt. Wilson 60-inch reflector, the mean [internal proper motion] tangential component for globular clusters M 13 and M2 was 3 milli-arcsecs/year, compared to the average for seven spirals of 18.4 milli-arcsecs/year.

Comparing findings from 47 Tuc to those of M13 and M2 is not quite the same as comparing apples and oranges, but it does leave much to be desired. Even so, King and Anderson's 0.6 milli-arcsecond/year dispersion for 47 Tuc and van Maanen's 3 milli-arcsecond/year average tangential component for M13 and M2 are within a factor of ten-to-one of another. It might be worthwhile to bring HST's astrometric capabilities to bear on one or both of these latter objects.

[Added 10 August 2003.]

The proper motions of Quasi-Stellar Objects (QSOs) that the author has found so far, have mostly been attributed to gravitational lensing by intervening objects. It will be of interest to see if the gravitational lenses (which have to be moving in order to induce apparent QSO proper motions) move on, and let the QSOs return to their stationary outposts.

The following comments are from van Maanen's 1921 paper. (MA21) Certain words or phases have been italicized or bolded for emphasis.

    For M 101 there is no appreciable change in the measured rotational component
    with distance from the center, but for M 33, 51, and 81 there appears to be some
    increase of [rotational] motion with distance."

Was 1970 a year for echoes - a' la flat galactic-rotation curves?

    "In all cases, however, the measured displacements agree better with the hypothesis of
    outward motion along the arms of the spiral than they do with an assumed rotation
    of the nebulae as a whole."

Those colleagues of van Maanen who were pushing for an expanding universe, were "unable" to repeat his findings. They dismissed his work as it being a case of his finding what he wanted to find. One of the primary, and often repeated, (and to this writer, fallacious) criticisms levied against van Maanen was that the precision of his measurements was smaller than normally encountered measurement errors. He was said to be reading positional variations much smaller than the sizes of the atmospherically blurred photographic images. References (BA02), (GK02), (IU), and (TV95) provide evidence of how his work was demeaned.

Here's a quote from the first of the four references above. It is typical of the precision arguments made against van Maanen. The quote is taken from Andrew Bell's section on Suggested Discussion Topics (Part II) under the second sub heading of Achievable precision. The other three references are left to the reader.

* Strictly speaking, van Maanen reported on internal motions in spiral nebulae.
These motions were not synonymous with rotations. See: Messier 81 Internal Motions.

**Baade was one of van Maanen's detractors.