George Paddock – early work on cosmological redshift

In addition to the work on extragalactic objects, George Paddock did some work on planets, stars, and galactic nebulae. He also worked on the radial velocity equations of binary stars. Here, I will concentrate on his extragalactic work (which contains only couple of papers).

Paddock (1916) discussed spiral galaxies in their relation to the galactic stellar system (this was well before it was established that spiral galaxies are not part of our own galaxy). He made an observation from the radial velocities of different objects:

The average radial velocities except the spirals range in increasing magnitude from zero to fifty kilometers per second. But a considerable jump is noticed from the fifty kilometers to 400 kilometers for the average of the spirals.

Based on this he presented a question:

Are the spirals dissociated from the star system?

Paddock then mentioned some Slipher’s arguments of the radial velocities of spiral galaxies. Paddock also discussed solar motion and its possible effect to the radial velocities of spiral galaxies. He noted that the spirals having measured radial velocities by that time were distributed in two groups and the Magellanic clouds were a third group, but he also said:

These objects, however, can hardly be considered to form a unitary system of associated objects, for it must be noticed that the average velocity of each of the three groups of objects is decisively positive, which means that they are receding not only from the observer or star system but from another.

What he describes here is an expanding motion. He continued:

Accordingly a solution for the motion of the observer thru space should doubtless contain a constant term to represent the expanding or systematic component whether there be actual expansion or a term in the spectroscopic line displacements not due to velocities. This brings up the question whether these large displacements are to be interpreted as due entirely to velocities.

13 years before Hubble’s redshift-luminosity relation, Paddock was already pondering similar questions. He brought up NGC 1068 with its fuzzy and broad spectroscopic lines as a possible example showing that all of the redshift might not be due to velocity (note that later there has been lot of discussion on the possible discordant redshifts in NGC 1068 system). He suggested that there might be a constant term resembling the K-term of stellar radial velocities and went on to quantify the term from the solar motion derived from the radial velocities of galaxies. He got a rather large value for the K-term (about 250-350 km/s) but he concluded that it is likely be due to small sample size and that he expected it to diminish with larger sample.

Campbell & Paddock (1918) discussed their spectroscopy on NGC 4151. They first mentioned that according to a photograph by Curtis, they thought that NGC 4151 was a planetary nebula. They then descibed their spectroscopy. They mentioned not finding the expected spectrum of a planetary nebula, and determined the radial velocity of 940 +/- 40 km/s for NGC 4151. They also noted that a new photograph by Curtis clearly showed a spiral structure, and that the character of the spectrum resembled the spectrum of NGC 1068.

References

Paddock, 1916, PASP, 28, 109, “The Relation of the System of Stars to the Spiral Nebulæ”

Campbell & Paddock, 1918, PASP, 30, 68, “The Spectrum and Radial Velocity of the Spiral Nebula N. G. C. 4151”

Links

(University of California: in memoriam) George Frederic Paddock: Lick Observatory

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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.

Links

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

References

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”

Updates

– 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.

NGC 0010 – some pair alignments

To my knowledge, NGC 0010 has not been discussed as a discordant redshift system before. Of nearby objects, there is one, object 3 in Figure 1, that has similar redshift as NGC 0010. Object 3 is therefore a probable companion to NGC 0010, and it has about 20 km/s higher radial velocity than NGC 0010, according to nominal values in NED. Only other object that can be considered as a companion is object 2, but it has about 1900 km/s lower radial velocity than NGC 0010, which is generally considered too high velocity difference, so it is not likely to be physically associated to NGC 0010 in traditional view. Small apparent size of object 2 suggests that it is some kind of dwarf galaxy. Only object within 20 arcmin from object 2 with similar redshift is 2dFGRS S495Z200 with cz = 4317 km/s and about 15 arcmin angular distance from object 2. 2dFGRS S495Z200 also seems to be quite a small galaxy.

Object 5 is a star, but there’s a galaxy-like object right next to it. One wonders if 2dF galaxy redshift survey’s target selection made a little mistake there and measured the star instead of the galaxy in almost the same position (the galaxy’s redshift would have been interesting to find out, as it seems to be almost exactly aligned across NGC 0010 with object 3).

There’s a rough pair alignment across NGC 0010 with objects 4 and 8. Redshifts of the two are not particularly close to each other but not radically different, either. Alignment is roughly along the minor axis of NGC 0010. The two objects are quite similar in appearance and their magnitudes are quite similar.

Objects 6 and 9 are roughly aligned across NGC 0010. Redshifts of the two are quite close to each other. The two objects are quite similar in appearance and their magnitudes are not that far from each other. Alignment is roughly along the major axis of NGC 0010, and quite accurately perpendicular to alignment line of objects 4 and 8. Other option for pair alignment is objects 7 and 9, but that alignment is worse than in the pair of 6 and 9, and redshifts are not so close to each other as in 6 – 9 pair, but still quite close.

Objects 8 and 9 have the same redshift, so they are a probable galaxy pair or members of same galaxy group. Looking further out from NGC 0010, there are few objects with almost the same redshift so there might be a loose galaxy group present at that redshift.

ngc0010
Figure 1. Objects with available redshift near NGC 0010 (all objects except one within 10 arcmin are presented). Size of the image is 15 x 15 arcmin. Image is from Digitized Sky Survey (POSS2/UKSTU Blue) and it has been adjusted for brightness and contrast to bring out fainter objects more clearly.

Objects and their data

NBR NAME TYPE REDSHIFT (cz) MAG SEPARATION
1 NGC 0010 SAB(rs)bc HII 0.022719 (6811 km/s) 13.3 0
2 2dFGRS S495Z164 galaxy 0.016400 (4917 km/s) 18.84 3.761
3 2dFGRS S495Z331 galaxy 0.022800 (6835 km/s) 18.02 5.068
4 2dFGRS S495Z152 galaxy 0.072000 (21585 km/s) 18.71 5.528
5 2dFGRS S495Z158 star 0.000200 (60 km/s) 19.30 6.738
6 2dFGRS S495Z146 galaxy 0.092600 (27761 km/s) 18.62 6.947
7 2dFGRS S495Z150 galaxy 0.149400 19.13 8.144
8 2dFGRS S495Z182 galaxy 0.114500 19.24 8.252
9 2dFGRS S495Z335 galaxy 0.114400 19.28 9.062

NED objects within 10′ from NGC 0010.

NGC 0423 – pair alignments

To my knowledge, NGC 0423 has not been discussed as a discordant redshift system before. Figure 1 presents nearby objects that have redshift available. Almost all such objects within 10 arcmin are shown there (only three are little bit outside of the pictured field).

Higher redshift objects 2 and 4 are aligned across NGC 0423. The objects have almost same redshift (object 2 z = 0.106 and object 4 z = 0.105). Their distance from NGC 0423 is somewhat similar (d4/d2 = 1.3). Their magnitude is also similar. Alignment is almost exactly across the nucleus of NGC 0423. Field has lot of high redshift objects because it belongs to 2dF coverage area so some alignments are expected. Here we have two of three closest objects aligned almost exactly, and their redshift is the same. However, Object 6 (z = 0.105) also has the same redshift so we are looking at a possible galaxy group in traditional interpretation, and that would increase the odds of having same redshift objects aligned across the main galaxy.

Objects 14 and 17 are aligned across NGC 0423. They have almost same redshift (object 14 z = 0.224 and object 17 z = 0.202) and their angular distance from NGC 0423 is similar (d17/d14 = 1.04). So is their magnitude. There are couple of objects with similar redshift; object 16 has redshift of z = 0.224 and object 21 has redshift of z = 0.219. If we consider these four objects as a galaxy group, there is a problem with large velocity dispersion. When converted to velocity, the redshifts of objects 14 and 17 result in 5200 km/s difference. That seems too large considering that the group doesn’t seem to be very dense (high velocity differences between galaxies are traditionally thought to occur only in dense galaxy clusters). Of course, there is always the possibility that the group is very dense but we only have few redshifts of its members measured, but current knowledge would indicate that objects 14 and 17 don’t belong to same galaxy group. Objects 16 and 21 are situated quite close to each other, as seen in Figure 1, but they too have quite large velocity difference, about 1300 km/s. That is starting to be quite close to what can be traditionally accepted as a velocity difference of physically associated galaxies, but the difference still is suspiciously large.

Objects 11 and 5 are roughly aligned across NGC 0423 but they have very different redshifts and are different kind of objects also (object 5 is a high redshift QSO while object 11 is a galaxy). Object 8 is roughly aligned across NGC 0423 with objects 9 and 10. Redshifts of all objects are quite different, but at least objects 8 and 10 are both QSO’s and their angular distance from NGC 0423 is similar.

ngc0423_1
Figure 1. Objects with available redshift near NGC 0423. Size of the image is 15 x 15 arcmin. Image is from Digitized Sky Survey (POSS2/UKSTU Blue).

There is a strange situation with object 12 (ESO 412-012); it seems to be quite large object as its apparent size almost matches that of NGC 0423 but it has redshift of z = 0.136 in NED! I checked NED’s redshift data for it, and it seems to have three very different redshift values. The highest one, the 0.136 is from Stromlo-APM Redshift Survey (it is named as “412-003-029” in the galaxy.dat file), and it has been measured from absorption features. Lowest redshift is from The 2dF Galaxy Redshift Survey, and is also measured from absorption lines. Third redshift is said to be from Arp 1981, but I didn’t find the object in question there. HyperLeda gives the lowest value and doesn’t even list the high value. I assume that the lower redshift is the correct one, as the highest value doesn’t make any sense and the third redshift might not exist at all.

Objects 3 and 16 are aligned across object 12. Their redshifts are of same order and their magnitudes are similar. Objects 6 and 21 are also aligned across object 12 with similar situation on the redshifts and magnitudes. The whole situation with object 12 is that it has two objects on one side with redshift slightly above z = 0.1 and on other side the objects have roughly the z = 0.22. At the same side of z = 0.22 objects there’s also object 20 with z = 0.15.

Objects 9 and 10 are very close to each other but their redshifts are different. Object 9 is a z = 0.17 galaxy and object 10 is a z = 1.8 quasar. There’s no clear signs of interaction between them. See figure 2 for magnified image of them. Objects 13 and 14 both have apparent companion galaxies, but their redshift is not known. They are also shown in figure 2. Object 18 has two objects aligned across it, objects are directly to north (up) and south (down) from object 18, they also don’t have measured redshifts available.

ngc0423_2
Figure 2. Two sections of zoomed in image of NGC 0423 field. Objects discussed in the text are marked. Image is from Digitized Sky Survey (POSS2/UKSTU Blue) and it has been magnified 4x.

Objects and their data

NBR NAME TYPE REDSHIFT MAG SEPARATION
1 NGC 0423 S0/a? pec 0.005344 14.20 0
2 2dFGRS S294Z221 galaxy 0.105538 18.83 2.409
3 2dFGRS S293Z160 galaxy 0.122800 19.36 2.968
4 2dFGRS S294Z229 galaxy 0.104500 18.22 3.142
5 [VCV2001] J011136.5-291318 QSO 2.397000 20.59 3.215
6 2dFGRS S293Z159 galaxy 0.105200 19.09 3.309
7 [VCV2001] J011140.9-291415 QSO 0.960000 20.41 4.081
8 2QZ J011108.6-291654 NELG 0.606400 20.2 (B) 4.101
9 2dFGRS S294Z216 galaxy 0.169287 19.15 4.821
10 2QZ J011140.4-291056 QSO 1.818600 19.9 (B) 5.066
11 2dFGRS S293Z165 galaxy 0.091300 19.02 5.158
12 ESO 412-012 dwarf spiral 0.018000 16.42 6.004
13 2dFGRS S294Z225 galaxy 0.098000 19.14 6.555
14 2dFGRS S294Z230 galaxy 0.223900 19.32 7.279
15 2dFGRS S293Z154 galaxy 0.115653 19.37 7.403
16 2dFGRS S293Z149 galaxy 0.224205 19.13 7.568
17 2dFGRS S293Z157 galaxy 0.202069 19.43 7.593
18 2dFGRS S293Z148 galaxy 0.154600 18.68 7.612
19 2dFGRS S293Z158 galaxy 0.061100 16.95 7.880
20 2dFGRS S293Z150 galaxy 0.154700 19.20 8.110
21 2dFGRS S294Z213 galaxy 0.218600 19.44 9.508

NED objects within 10′ from NGC 0423.

Intrinsic redshift component

Some time ago, I wrote about anomalous redshifts ending that to a mention of intrinsic redshift component. I followed that post by explaining how redshift components are generally calculated. There I gave the basic equation used for that:

1 + zM = (1 + zC) * (1 + zK) [eq. 1]

where zM is the measured redshift of the object in question, zC is the cosmological redshift component, and zK is kinematical redshift component, which is my own term, it is generally called as redshift caused by peculiar velocity of the object.

In discordant redshift systems, the kinematical redshift component tends to be too large to be explained by peculiar velocity in traditional thinking. Too large is rather subjective concept but there is no generally accepted limit for that. 1000 km/s is largely used but in tight galaxy cluster conditions even few thousand km/s might be accepted. When the kinematical redshift component is too large, we need another redshift component, the intrinsic redshift component. The “intrinsic” comes from the assumption that the additional redshift comes from within the object in question. I’m not particularly keen on this term because it assumes a rather specific cause for the additional redshift, but as it is commonly used, I’ll do so too. Here I will deal only with the mechanics of the addition of intrinsic redshift component to the equations described in above mentioned posts, I will not discuss the possible causes of the component.

This additional redshift component is added to the equation 1 like this:

1 + zM = (1 + zC) * (1 + zK)* (1 + zi) [eq. 2]

where zi is the intrinsic redshift component. Problem we usually are facing is that we don’t know how large the kinematical redshift component is, so we cannot use this equation as such. As a solution, common method is to assume that there is no kinematical redshift component, so the equation 2 reduces to:

1 + zM = (1 + zC) * (1 + zi) [eq. 3]

Basically it is the same equation as equation 1 but we just call the second redshift component by different name. It is important to remember that the assumption of no kinematical redshift is not necessarily a good assumption. When we are dealing with large redshift differences between objects, then the assumption does not distort our results much, but when the redshift differences are small, the unknown kinematical redshift component introduces a large uncertainty to our calculations, as we shall see later.

Let us now calculate the redshift components of an example system. We’ll use the famous NGC 7603 system. There are four relevant objects in this system; NGC 7603, NGC 7603B, and the two high redshift galaxies ([LG2002] 3 and [LG2002] 2) within the bridge area. Redshift of NGC 7603 (according to NED) is z = 0.029524, redshift of NGC 7603B is z = 0.055742, redshift of [LG2002] 3 is z = 0.391000, and redshift of [LG2002] 2 is z = 0.243000.

Let us now use equation 3 to calculate the intrinsic redshift of NGC 7603B. To calculate that we need to know the cosmological redshift of NGC 7603B. For that, we assume that it is at same physical distance from us than NGC 7603, and we also assume that NGC 7603 itself doesn’t have intrinsic redshift or peculiar velocity (lot of assumptions here). With these assumptions, we can use the redshift of NGC 7603 as cosmological redshift. Before we can calculate the values, we need to solve the equation 3 for intrinsic redshift like this:

1 + zM = (1 + zC) * (1 + zi) | /(1 + zC)
=> 1 + zi = (1 + zM)/(1 + zC) | -1
=> zi = (1 + zM)/(1 + zC) – 1

Now we can insert the values and calculate:

zi = (1 + 0.055742)/(1 + 0.029524) – 1 = 0.025466138

Using relativistic Doppler redshift equation to convert that to velocity yields 7537 km/s. We can use exactly the same equation for the other two objects, and we find out that intrinsic redshift of [LG2002] 3 is zi = 0.35111 (87600 km/s) and intrinsic redshift of [LG2002] 2 is zi = 0.207354 (55800 km/s).

What if NGC 7603B would have peculiar velocity? Let us assume that it does have a peculiar velocity of 1000 km/s. That corresponds to zK = 0.00334. Now we have to use equation 2. Solving it for intrinsic redshift gives:

zi = (1 + zM)/{(1 + zC) * (1 + zK)} – 1

Then we’ll put the numbers in:

zi = (1 + 0.055742)/{(1 + 0.029524) * (1 + 0.00334)} – 1 = 0.022052

When large peculiar velocity was involved, the intrinsic redshift changed from 0.025466138 to 0.022052, a change of 13 %. From this we can see that high precision studies relating to this are very difficult, remembering also the many assumptions that were needed to come this far. However, because of the large redshift difference between NGC 7603 and [LG2002] 3, a similar peculiar velocity in [LG2002] 3 would change the intrinsic redshift only by 1 %, so this approach can be used to cases that have high redshift difference between the object in question and the main galaxy.