Knut Lundmark – extragalactic distance scale

Lundmark & Lindblad (1917) studied the spectral types of spiral galaxies. For NGC 3031 (Messier 81) they noted that Edward Fath had earlier determined that the spectrum resembles that of a K star, and their analysis also showed that if the spectral types of stars were applied to NGC 3031 spectrum, it would belong to spectral class K. They proceeded to analyse some other galaxies in the same manner. They ended their analysis by studying the differences in calculated and observed spectral types:

Hence it follows that the spectral type calculated by us should on an average differ from those determined in the usual way, where the spectral lines have been observed, by an interval at least twice as large as A-K. This not being the case, it seems to us that our investigation can be considered as a confirmation of the result found by Shapley, Hertzsprung and others, that no sensible absorption exists in space.

In a follow-up paper Lundmark & Lindblad (1919) continued these studies.

Lundmark (1921) discussed Messier 33 and wondered about possible distance indicators:

Another question is: As the only difference between the rifts in Messier 33 and those in Milky Way seems to be that the former have dimensions about 1/100 of the latter’s, will that mean that the objects in the spiral are 100 times as far away as the corresponding objects in the Milky Way?

Lundmark then noted that M33 seemed to have nearby background galaxies:

A long exposure Crossley photograph by Sanford shows that some of the nebulae apparently belonging to Messier 33 must have spiral structure. It is too early to speculate about spirals of different order, primary and secondary systems. The most natural explanation is perhaps that in this region we must expect to see several far away small spirals mixed up with nebular objects belonging to the great spiral.

Then follows what I think is quite remarkable thought from the point of view of the subject here in this blog. Lundmark had earlier noted that there has been some nebulous objects found near M33 that seemingly are extensions of M33’s spiral arms, then he said:

If the spaces between the spiral arms are filled with absorbing dark matter we get the impression of an arrangement in the extension of the spiral arms also of these background objects.

(Note that dark matter here doesn’t refer to the modern concept of dark matter, instead it refers just to regular matter that is not bright and therefore not visible to us, and absorbs the background light.) Remarkable thing here is that it is an example of how alignments between unassociated objects can occur sometimes with quite natural explanations. At the end of the paper, Lundmark gave some arguments of the large distance of M33; size of star clusters compared to Milky Way and the presence of apparent foreground stars.

Lundmark (1922) addressed some of the questions raised by parallax measurements made by van Maanen that differed from Lundmark’s measurements. Lundmark argued that the measured proper motions in that time only represented an upper limit. He also presented a calculation of parallax based on assumed systematic motions of spiral galaxies based on their measured radial velocities. He then mentioned a method to determine distance:

Parallaxes obtained by assigning to the brightest resolved stars in spirals an absolute magnitude equal to that of the brightest stars of our stellar system give still larger distances.

He didn’t specify any distances but he did give a range:

To sum up: different methods give for spiral nebulae distances ranging from about 10,000 light-years to 1,500,000 light-years.

He also suggested that diameters of galaxies could be distance indicators:

We have very likely to deal with millions of spirals, and it would be strange if we should have the largest of the spirals in our neighborhood. It is more natural to assume the spirals to have roughly the same linear dimensions, and that the smaller angular diameters in the mean indicate the more distant object.

He then estimated that visible universe extends out to 2,000,000 lightyears. He returned to van Maanen’s measurements, first discussing the extent of the Milky Way briefly and then using van Maanen’s measurements to derive masses for a few spiral galaxies. He got enormous masses as result, larger than the estimates of our own galaxy by that time. He then proceeded to discuss the motions in galaxies and made an interesting remark, showing how spiral galaxies was thought to work back then:

The matter we see in the measured spirals, if moving with a rather constant velocity, as indicated by the measures, must have been ejected during an interval of time of about 100,000 to 300,000 years.

He then made some arguments, based on this, about development stage of spiral galaxies and about the stellar ages. He also noted that amount of stars and supposed young ages of the galaxies meant that star production must be very rapid. But he ended the discussion with a note of doubt of the correctness of it.

Lundmark (1924) discussed the problem of redshifts and specifically the high redshifts of galaxies. He stated the problem:

Another question is, whether such a large Doppler shift represents motion in the line of sight alone or is caused in other ways? The validity of the Doppler principle has been proved by laboratory experiments only for velocities smaller than 1 km./sec. or so. The measures of stellar spectrograms giving such velocities as can be computed from the laws of gravitational astronomy… …have proved the correctness of the Doppler formula for velocities as high as 100 km./sec., and thus it seems allowable to assume that the displacements found for globular clusters and spiral nebulae are due to motions of the objects in the non-relativistic sense or to motions and the above mentioned effect of the curvature of the space-time.

He then proceeded to discuss the apex of the solar motion derived from the redshifts of globular clusters and spiral galaxies. He noted that they gave a different motion than nearby stars and hypothesized that our local system has a motion as a whole relative to the globular clusters and sipral galaxies. He also noted that our own motion seemed to suggesting that we are revolving around galactic centre, but he calculated the orbital period to be 3 billion years (3 x 109 years).

He then turned to de Sitter’s suggestions of the curvature of the space. He studied if there’s relation between the radial velocity of objects and their distance. He first compared the radial velocities of globular clusters to their distance estimations, and found no correlation. He did the same with different type of stellar objects (cepheids, novae, O stars, eclipsing variables, R stars, N stars). He then started analysing spiral galaxies in same manner. He started with a discussion of the situation on their distance estimates. As a sidenote, he argued that nearest spiral galaxies cannot be at distances of many millions of lightyears because some of them had shown to be resolved into stars and that novae and variable stars had been observed in them.

He used a distance scale based on the angular dimensions and magnitudes of the spiral galaxies assuming that they only depend on their distance. He plotted the resulting distance estimates against the radial velocities of spiral galaxies and concluded:

Plotting the radial velocities against these relative distances (fig. 5), we find that there may be a relation between the two quantities, although not a very definite one.

Lundmark was very close here to establish the redshift-distance relation five years before Hubble, probably only restricted by his distance indicators which were not very good ones. He also derived the value for the curvature radius of space-time, and got R = 2.4 x 1012 km as result.

Lundmark (1924b) studied the distance to Large Magellanic Cloud (LMC). He first argued that LMC was in many ways similar as spiral galaxies but decided to call objects like LMC as “nebulae of the Magellanic Cloud type”. He then determined the parallax of LMC with different methods. From the mean of these parallaxes, he determined the distance to the LMC to be 100,000 lightyears.

Lundmark (1924c) derived solar motion based on spiral galaxy measurements and the mean parallax of the spiral galaxies, and finally derived the mean distance to spiral galaxies. He got two values, 76,000 and 61,000 lightyears. Lundmark (1925) reviewed the distance determination methods to spiral galaxies. He noted that spiral galaxies seem to be out of reach of parallax measurements. Proper motion measurements seemed to be too noisy at the time. He then started discussing radial velocities. He first briefly noted that redshift doesn’t seem to correlate with the inclination of the spiral galaxy, indicating that they don’t “move like a discus thrown through space”. There were no correlation with redshift and galactic position either, but there was a correlation between the redshift and the dimensions of the spiral galaxies.

Lundmark then noted a kind of redshift-type relation. He assumed an evolutionary sequence where redshift got smaller when objects get older. “Globular” nebulae were youngest and had highest mean redshift, sequence then continued: “early spirals”, “late” spirals, Magellanic cloud nebulae, Magellanic clouds. This is of course interesting in the context of this blog because here we have the first suggestion of age dependent redshift. Lundmark interpreted this as a sort of K-effect (calling it “Campbell shift”):

The most characteristic feature of the radial velocities of spirals is the presence of a very large Campbell shift of the same nature as is found in most classes of giant stars.

Lundmark then proceeded to derive a value for the Campbell shift of spiral galaxies. Very interesting thing here is that his result included distance. His result is:

VCs = 513 + 10.365r – 0.047r2 km/s

Here r has unit of Andromeda distance multiples. He interpreted the result:

According to the above expression the shift reaches its maximum value, 2250 km./sec. at some 110 Andromeda units, which, according to results given later on, corresponds to a distance of 108 light-years. As the peculiar velocities of spirals seems to be smaller than 800 km./sec. one would scarcely expect to find any radial velocity larger than 3000 km./sec. among the spirals.

The last comment is of course wrong, but it is worth emphasizing that Lundmark gave a redshift-distance relation here. Whether it was the first one ever made, I don’t know, but this was four years before Hubble published his redshift-distance relation.

Lundmark then discussed some details on our own motion in space and the efforts to determine parallax of spiral galaxies. Then he discussed novae as standard candles for measuring distance to spiral galaxies. He reviewed the evidence that novae really occur in spiral galaxies, and then he described the research of Curtis on the subject and how he had arrived to a conclusion that closest spiral galaxies are millions of lightyears away from us based on the magnitude difference of novae in our galaxy and novae in spiral galaxies.

Lundmark then gave results of his studies of distances to the novae in our own galaxies, determined by their parallax. He determined the absolute magnitude of novae in our own galaxy, and did the same with the novae in Andromeda galaxy (M31). He also presented arguments for the similarity of the novae in Andromeda galaxy to the novae in our own galaxy, and for the Andromeda galaxy being a galaxy of its own instead of a stellar system in our own galaxy. Finally, he used the absolute magnitudes he had derived to calculate the distance to the Andromeda galaxy, and got 1.4 million lightyears, a very good estimate by that time (Hubble published his famous result when Lundmark was writing this paper, Hubble’s result was 930,000 lightyears, current value is about 2.7 million lightyears). Lundmark repeated this to NGC 4486 and got a distance of 8 million lightyears (current value is about 53 million lightyears).

Following Hubble’s lead, Lundmark determined the distance to Andromeda galaxy also by using Cepheids. He got few distance estimates; 620,000, 880,000, and 1,500,000 lightyears. Lundmark also used “Oepik’s method” to derive the distance to NGC 4594. The method uses rotation velocity of the spiral galaxy, so it seems to have some similarity to Tully-Fisher relation. The resulting distance to NGC 4594 was 56 million lightyears (current value is about 35 million lightyears). Lundmark mentioned having determined the distance to Messier 33 in 1920 as 1.5 million light years (current value is about 3 million lightyears) using the absolute magnitudes of regular stars. Lundmark closes this remarkable paper by presenting rather mathematically heavy discussion of the extent of the universe.

Lundmark (1930) studied the question if globular clusters and elliptical galaxies are related. Based on some similar features, he suggested that elliptical galaxies are made of stars just like spiral galaxies. He then mentioned the difference of the mean radial velocity between spiral and elliptical galaxies. He also argued that the two elliptical galaxies near Andromeda galaxy were associated with it because they were practically in same direction and had almost the same radial velocity. He then compared the absolute magnitudes of elliptical galaxies and globular clusters and found:

[The absolute magnitude of brightest globular cluster] is a considerably lower value for M than the value of the Andromeda companion, but, on the other hand, there seems to be no real cleft between the absolute magnitudes of several elliptical anagalactic nebulae and those of the brightest globular clusters.

Overall, he built a case where globular clusters are slightly outside of our own galaxy. Elliptical galaxies seemed generally to be companions to spiral galaxies, and as their appearance was also quite similar, it was natural to suggest that globular clusters and elliptical galaxies are related objects. This goes against current thinking, though. He closed the paper by saying:

If the sequence of globular clusters here suggested exists and if the smaller ones have a rapid motion, it might very well be that the globular clusters keep up the relations between the stellar systems and travel from Galaxy to Galaxy. These clusters are then something like what the comets were thought to be in the cosmogonies of Laplace and Schiaparelli – they are “the wandering boys of the Universe”.

In addition to the works mentioned here, Lundmark worked on different properties of stars and nebulae, and made a galaxy catalog. He also published in German and in Swedish, which papers were not considered here due to my poor skills in those languages. Lundmark (1956) would be very interesting paper with apparently a thorough historical overview on extragalactic research and distance indicators, but not freely available. I’ll just finish with the abstract of that paper:

First, an historical outline is given of the “Island-Universe” conception (Galilei, 1609), and of the development of our knowledge of the nebulae. The cosmological views of the eighteenth century are surveyed, and in particular the developments in England during the Restoration Period (1660-1700), the Augustan Age (1700-1745), and the era of Rationalism and Neo-Romanticism (1750-1820), due to Newton, Halley, Hooke, Bradley, Thomas Wright, and John mitchell. The latter’s work founded on stellar-statistical principles resulted in 1767 in the derivation of an average distance of nebulae. Herschel’s work, and Herbert Spencer’s dictum of 1858 are discussed. Bolin’s attempt of 1907 referring to the parallax of the Andromeda nebula, and other work by Curtis in 1917 and Lundmark in 1919 are described. The various distance-indicators are introduced ( e.g. the use of novae since 1919, of supergiants since 1920, of Cepheids since 1924, and of globular clusters since 1931), and absorption effects are considered. On the basis of these indicators a distance of the Andromeda nebula of 1.23 × 106 light-years is derived. The importance of supernovae in this connection is indicated, and also the facts pointing towards a necessary increase in the metagalactic distance-scale.


1959, MNRAS, 119, 342, “Obituary Notices : Knut Emil Lundmark”.

Hetherington, 1976, JHA, 7, 73, “New Source Material on Shapley, Van Maanen and Lundmark”

There seems to have been a dispute between Lundmark and Hubble about their galaxy classification systems published in 1926:
Hart & Berendzen, 1971, JHA, 2, 200, “Hubble, Lundmark and the Classification of Non-Galactic Nebulae”. A brief note on the subject.
Teerikorpi, 1989, JHA, 20, 165, “Lundmark’s Unpublished 1922 Nebula Classification”. See this article for the new piece of information about Lundmark’s unpublished work on galaxy classifications in 1922.

Wikipedia: Knut Lundmark


Lundmark & Lindblad, 1917, ApJ, 46, 206, “Photographic effective wavelengths of some spiral nebulae and globular clusters”

Lundmark & Lindblad, 1919, ApJ, 50, 376, “Photographic effective wavelengths of nebulae and clusters”

Lundmark, 1921, ApJ, 50, 376, “The Spiral Nebula Messier 33”

Lundmark, 1922, PASP, 34, 108, “On the Motions of Spirals”

Lundmark, 1924, MNRAS, 84, 747, “The determination of the curvature of space-time in de Sitter’s world”

Lundmark, 1924b, Obs, 47, 276, “The distance of the Large Magellanic Cloud”

Lundmark, 1924c, Obs, 47, 279, “Determination of the apices and the mean parallax of the spirals”

Lundmark, 1925, MNRAS, 85, 865, “Nebulæ, The motions and the distances of spiral”

Lundmark, 1930, PASP, 42, 23, “Are the Globular Clusters and the Anagalactic Nebulae Related?”

Lundmark, 1956, VA, 2, 1607, “On metagalactic distance-indicators”


– November 22: Changed the “radius of the curvature of the universe” to “curvature radius of space-time”. Added the missing names and characters of the abstract of Lundmark (1956), the abstract has parts missing in ADS too (probably due to careless copy-pasting), so it wasn’t exactly my mistake.


2 Responses

  1. So the universe was smaller than the current measured distance to the Andromeda galaxy? 🙂

    10,000 – 1.5 MLyr is quite a spread! No wonder Cepheids as standard candles were so awe-inspiring 🙂

    So what have we learned in the intervening 92 years? 🙂

  2. Ritchie said:
    So the universe was smaller than the current measured distance to the Andromeda galaxy?

    You know, I first had trouble finding the place you are talking about here. It seems to be this one:

    “He then estimated that visible universe extends out to 2,000,000 lightyears.”

    Before noticing that, I looked also this one:

    “He also derived the value for the radius of the curvature of the universe, and got R = 2.4 x 1012 km as result.”

    I changed that because that would have caused misunderstandings, Lundmark talks about curvature radius of space-time, not universe. The calculated number for R is less than one lightyear, so that would have eventually raised the eyebrows for anyone looking more deeply into the matter. 🙂

    Anyway, yes, the value given early in the text is smaller than the distance to the closest large galaxy today, but later on in the text it is mentioned that Lundmark calculated how redshift-distance relation peaks at 108 lightyears. So, you are working with outdated numbers here. 😛

    Ritchie said:
    10,000 – 1.5 MLyr is quite a spread! No wonder Cepheids as standard candles were so awe-inspiring

    True, but I think later Lundmark got quite a good results even without them.

    Ritchie said:
    So what have we learned in the intervening 92 years?

    Stay tuned for subsequent posts here to find out. 😉

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