1018 The distances of the s tars: historical review

and systematic errors which still exist in the fundamental catalogues have to be determined by new observations of the highest possible accuracy.

X~EFE RENCES

BECQ, (~. a n d DECLEP, CK, | . . . . . . . 1948

CLEMENCE, G. M . . . . . . . . . 1948 DNEPROVSKY, N . . . . . . . . . 1930 DOMINIO~ OBSERVATORY . . . . . 1952 HEINEMANI~', K . . . . . . . . . 1939 HI~S, C. H. and VAN HEaK, G . . . . . 1938 KOPFF, A . . . . . . . . . . . 1939 RABE, W . . . . . . . . . . . 1933 SCHMEIDLER, F . . . . . . . . . 1948

1953 U.S. NAVAL OBSERVATORY . . . . . 1948

1950

Ann. de l'Obs. Royal dc Belgiquc, H I e S~rie. Tome 3, fasc. 3.

Astron. J., 51t, 10. Astron. Nachr., 241, 219. Publ. Dominion Obs. Ot tawa, 15, No. 2. Astron. Nachr., 241, 145. Ann. Sterrewacht Leiden, Deel 18, Eerste Stuk. Astron. Nachr., 269, 160. Astron. Nachr., 248, 369. Astron. Nachr., 276, 63 : Verbj]. Sternwarte

Mi~nehen, Vol. 3, No. 9. M.N. Occasional Notes. Publ. U.S. Naval Obs., 2nd Series, Vol. 15, pa r t 5. Publ. U.S. Naval Obs., 2nd Series, Vol. 16, pa r t 2.

The Distances oi the Stars: a Historical Review

J. JACKSON Lately H.M. Ast ronomer at the Cape*

SUMMARY

A short historical account is given of the determinat ion of stellar parallaxes in the nineteenth century, when in spite of the great am oun t of t ime and skill given to the work the parallaxes of only a few stars were determined, and these wi th relatively large errors. During the present century international co.operat ion by fourteen observatories has resulted in about nine thousand paral lax determinat ions f rom which a new "General Catalogue of Trigonometric Stellar Paral laxes" has been compiled at the Yale Observatory.

FOR those interested in stellar distances the publication of a "General Catalogue of Trigonometric Stellar Parallaxes", by Yale University Observatory is most welcome. The new catalogue (the third from Yale) has been compiled by MISS JENKINS from data available up to May, 1950. I t contains the parallaxes of 5822 stars, nearly all determined at fourteen observatories during the past forty years. The observations have been reduced to a uniform system with adjusted probable errors. Although only about one-third of the stars have been observed at more than one observatory, most of the stars of large parallaxes have been so observed. The average probable error is ~ 0'.'009 but there is a variation from :]: 0':004 to ~: 0'.'014 or even more in a few cases.

1. E A R L Y H I S T O R Y

The history of early attempts to determine stellar parallaxes is well known. The credit of the first determination which carried conviction is given to BESSEL for his observations of 61 Cygni in 1838. With his name we associate that of H E N D E R S O N ,

* Now at Ewell, Surrey, England.

J . JACKSON 1019

whose observations of ~ Centauri at the Cape in 1832-33, not specially made for the determination of parallax, were later reduced to prove that star to be relatively near. But the man who, more than any other, paved the way was W. STRUVE. For more than two decades he had this problem in view. From extensive series of observations he proved that the average parallax of twenty-five bright stars in the northern hemisphere did not exceed 0':l. For detailed attack he selected ~ Lyrae and from his observations of the years 1837-40 he deduced the acceptable parallax of 0'.'262. But, in 1837, before a single parallax had been conclusively established he laid down the only three rules we yet have (apart from indirect methods concerning spectra) for selecting the nearer stars, viz. :

(l) Stars of the first and second magnitude. (2) Stars of large proper motion. (3) Double stars showing rapid orbital motion.

He even indicated the nearest stars with remarkable accuracy. For Arcturus he com- 1

puted the parallax 7r ---- ~ . 0'.'0625, where A ---- d~//, d being the diameter and 1 the

surfacc brightness of the star, expressed in terms of the same quantities for the Sun. We now give the parallax as 0':090 ± 0'-'005. For the double star 61 Cygni--BESSEL'S star--he estimated the semi-major axis as 16" and the period 500 years and deduced ~r~M ~- 0'.'254, where M is the mass of the system. The modern value of the parallax is 0':292 ± 0'.'004.

2. PROGRESS IN THE NINETEENTH CENTURY

Following the success of BESSEL some of the ablest observers carried out observa- tions for parallax during the nineteenth century but although the results were valuable in a general way they did not go far in helping us to a better knowledge of the extent or construction of the stellar system. That had to wait to the present century with extensive data regarding the proper motions, radial velocities and spectra of the stars.

It is interesting to note the actual rate of progress. NEWCOMB in his Popular Astronomy (lst Edition, 1878) gives the parallaxes known to him--s ixty-two deter- minations (not all independent) for seventeen stars. The data for two stars, :¢ Lyrae and 61 Cygni, from NEWCOMB'S Table and from the new catalogue are given below:

Table 1

Lyrae

AIRY, 1836 AIRY, 1836 STRUVE, 1837--40 PETERS, 1842 0 . STRUVE, 185[-53 JOHNSON, 1854--55 BRtiNNOW, 1868--69 BRi3NNOW, 1870 ALLEGHENY McCoRMICK YERKES

I 0':224 -- 0.102

0.262 0.103 ± 0'.'053 0.147 i 0-009 0'154 ~ 0.046 0.212 i 0-010 0.188 ± 0.033 0-120 ~ 0.006 0.131 i 0.010 0.114 ± 0.013

61 Cygni

]~ESSEL, 1838. BESSEL, 1840. PETERS, 1842. JOHNSON, 1852 53 . AUWERS O. STRVVE, lS'52:53 AUWERS ALLEGHENY McCoRMICK YERKES Mt Wilson SPOUL . VAN ~rLECK

0'.'314 0.348 0-349 :~ 0'.'080 0'392 0-42 0.506 ± 0.028 0"564 ~ 0.016 0"285 ± 0'007 0'307 ± 0'009 0'271 ± 0"011 0"322 ± 0"012 0.272 ± 0-009 0"299 ~: 0"009

1020 The distances of the stars: historical review

The absolute parallaxes for these two stars now accepted are 0':123 ± 0':005 and 0'.'292 ± 0'.'004. The two values given by AmY for ~ Lyrae are, of course, earlier t han BESSEL'S results for 61 Cygni. The paral lax of 61 Cygni given b y AUWERS resulted f rom rediscussions of the observat ions of JOgNSON and BESSEL.

In spite of the labour of GILL and others progress was painful ly slow. The position at the end of last cen tu ry m a y be es t imated from the table given by NEWCOMB in his well-known book The Stars, published in 1904. I t gives the parallaxes of seventy- two stars, of which fifteen are noted as subject to more doubt t han usual and one as ent i re ly unreliable. A comparison of these results with the latest da ta for the same stars enables us to es t imate their accuracy, or lack of it.

The average paral lax for these seventy- two stars as given by I~EWCOMB is 0':141, in the new catalogue 0': 116. This shows tha t the early observers did include in their observing lists m a n y of the nearest stars. The systemat ic correction of - - 0':025 can hard ly be considered excessive as there appears to have been a reject ion of all negat ive parallaxes. There are two stars with gross errors of 0:'347 and 0':294, only the first of which was noted as doubtful . Fo r four o ther stars the corrections required are -- 0':157, - - 0'.'130, - - 0':128, and -- 0'.~112. I f we reject the first two stars the mean correction required is reduced to -- 0'.~018 ; while if we reject all those marked as doubtful the correct ion becomes -- 0':014. I f we apply the systemat ic correction and then calculate the probable error f rom the remaining residuals we find it to be ± 0':024 or -V 0':032 according as we include or exclude the two gross errors.

3. ~NTERNATIONAL CO-OPERATION IN THE TWENTIETH CENTURY

Photographic observations by HII~KS and RUSSELL at the turn of the century proved that late type stars may be intrinsically brilliant or faint and the demonstra- tion later that spectra could be used for the estimation of absolute magnitudes led to a demand for trigonometric parallaxes to give a sound basis for the work. Thanks to SCHLESINGER, who devised the occulting shutter as a means of eliminating the magnitude equation, it was possible to embark on an extensive scheme of international co-operation for the determination of parallaxes. As a result of work at a dozen northern observatories SCHLESINGER was able to publish a general catalogue in 1924 giving results for no less than 1870 stars. The work continued and through the co- operation of the Yale station at Johannesburg and the Cape Observatory extended to the south pole. As already stated a new catalogue giving the trigonometric parallaxes of 5822 stars has just been published. Allegheny and McCormick Obser- vatories with the two southern ones have each determined over 1600 parallaxes or nearly three-quarters of the 9000 parallaxes on which the catalogue is based. The fact that two of the four observatories which have contributed most are in the southern hemisphere has resulted in parallax work for the southern stars being not far behind that for the nothern ones. But whereas important stars north of declina- tion -- 30 ° have frequently five or six determinations from different observatories, such stars in the far south have generally two or even one only.

In the new catalogue early observations included in previous editions have been excluded on account of their small weight. That this was reasonable can be deduced at once from the fact that over many years several observatories have each deter- mined annually as many parallaxes as were known from all sources in 1900 and with a weight ten times as great.

J. JACKSON 1021

4. FUTURE WORK

We shall now have a better basis than previously for the determination of absolute magnitudes by indirect methods. I t will be possible to examine anew the relations between apparent magnitude, spectrum, proper motion and parallax. For some types of star it will be found that additional observations are required, e.g. for bright stars of late and early types which are generally excluded from observing programmes on account of the smallness of the parallaxes to be expected. Again it is most desirable to extend observations to very faint stars of very large proper motion so as to extend our knowledge of stars intrinsically very faint. For this a large reflector is necessary but the reward is more certain than for the types just mentioned. Useful work will be the investigation of stars for which VYSSOTSKY has found dwarf characteristics with small proper motion and possibly intermediate between dwarfs and giants. I t will be worth while to get observations of more double stars showing orbital motion, especially faint ones. We can only determine masses of stars from double stars in orbital motion, and this motion is more easily observed the more massive the system. Hence determinations of mass are for the more massive systems.

5. LARGE DISCORDANCES

When you look over the separate determinations of parallax you occasionally find differences which far exceed what would be expected from the probable error. The chance that this can arise from different choice of comparison stars is very small, as with a dependence factor of 0.33 it would require a reference star to have a parallax of 0':150 to produce a difference of 0':050. Not only is this highly improbable but it should be possible to detect such a star from its proper motion. Large differences in parallax observations could arise from orbital motion of the parallax star. I f this orbital motion has a period close to a year the semi-major axis of the orbit would be of the same order of magnitude as that of the earth's orbit, so that the observations reduced in the ordinary way would give a parallax anywhere between zero and twice the true value according as the two orbital motions cancelled or enhanced each other. We really know nothing of orbital motion of a yearly period in stellar systems and there is little hope of finding such a motion except from discordant parallax observa- tions. The two determinations of the parallax of 53 Virginis, 0':012 ± 0"012 and 0':108 ± 0':012, may find an explanation in orbital motion. There are two deter- minations of the spectroscopic parallax for this star, 0':038 and 0':045.

6. REDUCTION TO A UNIFORM SYSTEM

In the new General Catalogue parallaxes determined at the different observatories have been reduced to a uniform system by intercomparison, and to absolute values by comparison with spectroscopic parallaxes. There are still some unexplained differ- ences. I t may be that the group of smallest spectroscopic parallaxes, individually the most reliable, contains some stars of larger parallax which have got into it accidentally to produce a systematic effect. Also the reductions from relative to absolute parallaxes appear to differ for some observatories, especially the southern ones, from those of the second edition of the catalogue. Allegheny and McCormick have the greatest weight in the comparisons, and the differences such as Allegheny minus Yale and Allegheny minus Cape will probably depend on the least reliable parallaxes, trigonometric and spectroscopic. However, as all the relative parallaxes

1022 The distances of the s tars: historical review

are given in the volume (with adjus ted weights) it is possible for anyone to re-examine the da ta from the point of view of systematic corrections. To show the degree of rel iabil i ty of the parallaxes it is interest ing to examine the observat ions for BARNARD'S proper mot ion s t a r - - a p a r t f rom the system of ~ Centauri the nearest to us. The following relat ive parallaxes were (probable errors adjus ted) :

Allegheny McCormick Yale Yerkes Mr. Wilson Sprout . Dearborn Van Vleck Cape

Derived absolute paral lax

de termined at nine different, observatories

~-0~550 ~: 0~007 0.554 0.009 0.555 t).009 0.5(/9 i).012 0-519 0.012 0-552 t).011 t).569 0.018 0.558 0.008 t).526 (}.012

+ 0 ~ 5 4 5 _~ (}~003

The following table gives the number of stars between different ranges of paral lax :

~-0z762 to 0~200 0.199 0.150 0.149 0.100 ti)-099 0.090 I).089 0.080 0.079 t).070 0.069 0.060 0.059 0.050 t).049 0.04t) 0.039 0.030 0.029 0-020 0.019 0-010

+ 0 . 0 0 9 0.000 - -0 .001 - -0 .010 - -0"011 - -0 .020

0~021 to --0~057

3 5 35 95 42 6O

I 98

150 236 417 662 938

1255 1085

485 172

58

751

I t is interest ing to compare these figures with EDDINGTON'S est imate in 1914 of the number of stars within five parsecs, perhaps t h i r t y or fo r ty ; and within t w e n t y parsecs not more than 2000 of which a large propor t ion would be fainter t han the t en th magnitude.