ASTRONOMISCHE NACHRI-CHTEN.

2 : 12

3 116

Band 236. Nt. 5641. 1.

6.0 I +2.2 6.56 5.9' +2.2 7.41

Photographic magnitudes of globula The knowledge of the integral brightness of stellar

clusters is very important for recent investigations on the structure of our universe. Still the investigations are based on the integral magnitudes given by Ho/etschd, which are rather incomplete and sometimes somewhat rough. It should be noted that the simple visual observations of such kind ere very erroneous due to various imperfections of the eye as has been generally brought about. Many systematical errors exist in the comparison of the extrafocal image of a star cluster with the extrafocal images of stars. The magnitudes given in this way refer to something lying between the integral brightness of a cluster and its surface brightness, specially for the clusters of great angular diameters. The lack of homo- geneity refers even to methods like that used by C. Wirta1). Probably the most perfect is the method proposed by M. N d o & d ) , but its application to all clusters would take a long time, whereas it is desirable to have the approximate data as soon as possible. Therefore besides the visual obser- vgtions made at Goursouf (Crimea) with Mr. N o h & o v ~ , we tried to find another method. It occurred to us to derive the photographic magnitudes of star clusters by using a camera of short focus. The images of clusters must have been starlike thus making easy their comparison with those of stars. This gave an independent method of observation which for some reasons could be thought to be even more homogeneous and more precious.

The method. Two cameras with Zeiss Tessar lenses (F/D=4.5) of focal length 7 and 21 cm were attached to a 3i-inch telescope. (These cameras were kindly lent by Mr. N&&w and Mr. Micrhilou.) The guiding was done by the hand, the exposure time being 3-40m. This time was long enough to bring out the star clusters down to I I' (on the large sole plates). . Ilford Monarch plates were used. During two sommer months of 1925 and of 1926 we got 30 plates which several times covered the sky in the constellations Scorpius, Sagittarius, Serpens, Scutum and Ophiuchus. 2 plates were kindly guided by Mr. Fedidy . The revision of the platesdone at Moscow was rather long and minute. Nearly all clusters were more or less starlike. They were compared with the neigh- bouring stars by putting a magnifying glass so, that all images on the plate seemed to be diffus~ However the estimutions are somewhat. uncertain and conditional, but the individuality of the investigator has no great influence as it will be shown further. The comparison stars were chosen from the D.C. in order to exclude the influence of differential atmospheric absorption. The brightness of a cluster was estimated in fractions of the interval between the two comparison stars. The number of comparison' stars and of their combinations was taken as great as possible in order to exclude the accidental

3 14 7.0, I +LO I I ' , 1 1 .10.0 I +0.2

3 17 6 .8 ' +o.g

clusters. By B. Yhvntso~- Vehamim. errors of the magnitudes of the D.C. and of the estimates. In particular this was done for the faint clusters, where the magnitudes of the D.C. are obtained from those of the B. D. In order to render this easier we traced a map containing the stars of the H. R. P. down to 8% and the maps containing the stars of the D.C. Every plate gave from 3 to 14 estimations of the cluster. In forming the mean, different weights were given to the plates according to their quality, to the distance of the cluster from the centre etc. On the large scale plates clusters the brightness of which is lower than am, and on the small scale plates clusters which arc fainter than 6+7m could be estimated. Any systematical ditrerence between the two series of mean magnitudes could not be established. Therefore all platcs entered in forming the final magnitude. In the table are listed 27 globular clusters the brightness of which was determined at brst. The abbreviations are: D = diameter of a cluster according to Sapfey and Soaryn'); W-our final photographic magnitude; #=number of plates used; N- number of estimates; S= photographic magnitude uamrding to ShuprcY and Sotuyrt5); vis. =mean visual magnitude according to the catalogue compiled by M. Nubo&m6). NGC 6656 is put in parenthesis its diameter being too large for exact estimations. Its'brightness from different plates varies from 6% (or even 5?2) to 6%. The probable errors are sufficiently small, for instance: *om03 (6171); &om02 (6287);

6.87 7 . 1 1 -

*-9 (6723). N C C I M i D 1 W

6144 3.3 10.24 6171 I 2.2 [1o.o3 6218 1 2 I 9.3 ' 8.22 6254 10 8.2 8.05 6266 I " 62 I 4.3 I 8.01 6273 I 19 4.3 ! 7.67 6284 1.5 10.2

10.7 I 9.28: I 9.52 I I

10.06: 2

, 1.4 '10.2 I

6 * 7.4 i + 1.4 13 ,IO.O +O.I 4 10.2 ! 0.0

2 0 , 8.6 + 1.0

28 ' I 6.8 + 1.3

' i

1 4 . I 7.5 I + 1 .2

9.61

9.76

7.50 8.57 7.96

I 8.57

-

- - 9.22

7.45 9-13

- W-ViS

t 1m1o

+ 0.53 + 0.58 + 0.82 + 1.66 + 0.64 + 1.15

+ 0.56

+ 1.09

-

-

- S - V h .

-0?62 - 1.72 + 0.64 - 0.31 - 0.56 - 1.5'

+0.13 - 0.31

+ 0.79

-

.-

+o.71 +0.23 -0.24/-0.56 - + 1.14 I-0.10

+ 0.48 + 0.03 + 0.87 * - 0.56

I

-

- . - t 0.33 - 0.62

-0.42 I - 1.63 t 0.61 ! -0.65

- - 1) Luad M d . (2) 39.

'1 AN&.325,425. 4) H. B. 852. 6) H. B. 848. 4) Not publirbed.

3 5641 4

Com p a r is on with o ther inve s t i g a t i on s. We did not expect that the comparison of our data with the visually obs served magnitudes could give the value of the Color Index for any individual star cluster. The differences W-vis. are large and diverse. Although the average difference is + om70 (NGC 6638 and 6715 are omitted) and corresponds to the mean spectrum of globular clusters, it is evident that the individual W-vis. are mainly caused by the difference of the two methods and by the different accidental errors. The average deviation of individual magnitudes from C. 1. = + om7 is koO'p5, while they range from - I ~ Z to -t 1910. For the bright clusters W-vis. seems to be smaller than for the faint ones, but the number of differences is too small to make this reliable. No correlation was found between the values of W-vis. (or their dispersion) and the diameters of the clusters, the last result being somewhat unexpected. Generally the, comparison shows that on the average the systematical errors of our photographic and of the visual observations are nearly the same, for the mean value of W - vis. is of the same order as would .be the case if the data of both series were absolutely correct.

The same method of short focus camera was used by H . ShapZey and H. Sawyer (loc. cit.] in 1927. They used plates taken with Ross Zeiss Tessar and Zeiss Tessar cameras (F/D =4.0). Their scale was I mm = 10'. It is to be regretted that in their article, like in many other american papers, the way of measurements and the reductions involved are too briefly described OT fail altogether. We do not admit that the com- parison could be made with the stars of standard regions, for they are too rarely distributed. The comparison of bright clusters is much impeded by the considerable extent of bright stars. Still greater it must be in the case of faint clusters. After our experience the comparison becomes imaginary or rather impossible if the comparison stars do not occur simul- taneously in the field of the magnifying glass (in the field of eye sight). The manner of estimating adopted by the authors is unknown. From H.B. 852 it .can be supposed that the exposure times of the plates used vary from I to 2 hours. The authors remark : ',the integrated photographic magnitude of a globular cluster depends on the lenses, plates and the photographic development involved. . . But in the present case it seems that the conditions of their investigation were nearly the same as in our work and therefore the resulting data could be expected to be near, nearer than if compared with the visual ones. Still the comparison of the two systems is remar- kable. It shows a systematical difference which increases with the increasing brightness of the clusters and surpasses '2 mgn.

The deviations from the formula are within om5 and their mean is equal to *om17 (25 clusters were used).

W- S can be represented by the formula W-S=4mC)O-om48 (s) .

Such a difference is too great, from any point of vie1 it might be considered. Although the concordance of ou magnitudes derived frdm different plates is slightly better tha that of the Harvard magnitudes, it can tell nothing, as the botb refer to the constmy of the plates and to the cOnstanc of the investigator's impression. The comparison of th Harvard magnitudes with the visual ones is striking alsc Except the fact that the S-vis. range from -3% to + 1% i suggests that the S-vis. increase for the bright clusters beini negative. In average (if it can be spoken of here) the magni tudes of Harvard Observatory being corrected for the C.1 are 1% higher than the visual ones. I t means that if th Harvard magnitudes are true, the visual integrated magnitud of M z a (well known cluster in Sagittarius) is z'P9. This i quite impossible. The comparison shows that we have t deal not with the effective wave length which operates in th dieerent methods, but with something other. H. Shapie- and H. Sawyer say ,An attempt has been made to make th whole series of measures homogeneous, whatever the syste matic deviations of these magnitudes may be with. respec to other visual or photographic seriescc. So did we do, but th result is quite different. The absolute accuracy of such mea sures is required as well as their homogeneity. Such systeinatira differences lead to quite a different correlation of facts.

There are few othe photographic observations. For M3 the visual observation of Holetschek give 6F56, Wirtd) from an extrafocal plat' found 6m94, PanneRoek*) from the distribution of brightnes in the centre and from the counting of stars a t the edge calculated 6m69. The last value relied on the magnitudi of Harvard Observatory Catalogue is 4115.

Let us take now the formula for computing the distanci from the apparent visual integral magnitude given by Shapiey3)

logr=o.z (m + 13.8) . Let us take for instance the mean visual magnitude and thi photographic one of the Harvard Catalogue (corrected for thi C.I.) for NGC 6624, to which according to its brightnes ( ( 7 9 the formula can be well applied as is said in H.B. 848 The corresponding distances are 39800 and 21900 parsec respectively. Determined from its diameter this distance i 28600 parsecs.

Further it can be shown that the influence of sucl differences in the integral magnitudes on the total number o the stars, and accordingly on the density of their distributioi is still more considerable. Mr. PariisRy') in his attempt tc evaluate the total number of the stars in M13 comes to t b expression :

log N = 0 . 4 (m0-o.~3o/ha-M) if we admit Kapieyn's luminosity function. In the case o integral visual magnitude M = 5.7 the calculation give N = 525000. For M = 3.5 we have N=407oooo. This diffe rence is higher than in the case when we take the curves obtainet by Seares and by Kapteyn-wan Rhvn, the value of M being adopted the same in both cases.

Further, A . Pannekoek (loc. cit.) showed the relatior which exists between the integral brightness H of the cluste and the luminosity function. If we admit that the numbe

Impor t ance of deviations.

1) Publ. Sternw. Kiel XV. ') Bull. Astr. Inst. Netherlands 1.5 . I) Mt. Wilson Contrib. I ~ O ( ~ g z o ) . ') Russian A. J . 3.14

5 564 I 6

N ( m ) of stars of any given magnitude m is expressediby the

we have

- equation logN(m)= C-7(m-nro)~

+oo H = cJIo-r(sn-nto)'--od m dm =

-00

= c V(n/~.Ioge) I O - ~ . ' ~ ~ I O - ~ . O ~ I ~ = N 1 i 1 F 1 (1)

If m, be the ,most contributing magnitudecc, /r 1 - - 10-0.4'nr; N 1- - c IO-O.W/*; ~ l = l / ( n / ~ - l O g e )

this shows how many times the total luminosity of the cluster surpasses the luminosity of stars of the most contributing niagnitudecc. In the case of Kapfeyn's luminosity curve we have F1=6.3; r=o.o345; M l = + 1.9. For M3 Pannekoek has found 2.5 logH=6.7; ml=17?6. This order of m1 was confirmed by somewhat another method. From another hand, if we take.N(nr) = f l i / v n - e-Ap(m-d', where N i s the total number of stars in the cluster, we have H=N 10-~~4"'1 I O - ~ . ~ ~ " .

Hence N=cV(n/r.loge). Determined with the data n= 0 ~ 0 0 0 0 7 2 ; M = -9 .0 ; M, = + 1.9; 7 -0.0345 we have logc= 4.721; 10gN1=3.560; logN-5.518. The equation (I) can be represented in the form

7 { 2 ( 0 . 4 ( m 1 - ~ - ~ o g [ c ~ ( z ~ 0 g e ) ] ) + ~ o g r } = - 0 . 0 8 . (2)

For M = -11.2 ( m p . of Harvard Cat.) we have computed:

We see that taking c to be const., the value of the integral magnitude according to Harvard Observatory cannot be satisfied by any combination of admissible values of m, and Y .

PanneRoek has found, that generally the stars of Mr3 follow Ka'pfeyn's curve, and that m, must be lower than 17'?0. For ml = I 7?o and fainter the equation (2) cannot be satisfied by any positive value of 7 .

Discussion. I . The method of short focus camera concerns the study of all diffuse objects in general and there- fore the disaccordances, which were noted, are worth to be dis- cussed. We studied several effects which could influence the values of integral magnitudes. The first thought was that the systematical differences of W-vis. could be caused by the ind iv idua l i ty of t h e observers. Therefore on our request MM. Nabokov, Parenago, Iuanov and KosZov made several estimations for clusters of different brightness. The disaccordance between the observers showed to be small. We give an extract:

2. The effect of the linear diameter of the image could be found from the plot, where the deviations W-S were associated with the diameters. It is strange that this graphic shows a very rapid increase of W- S when D increases from I I O to 3', while for diameters much larger they remain nearly the same. Still stranger it seems when we remember that in the scale of all plates used, all these diameters (1'-3') prac- tically are negligible' and cannot much influence the esti- mations.

3. The effect of exposure time, of atmospheric absorp- tion and of aperture would work in a similiar way. If the exposure time were longer, or the extinction smaller, the photographic impression of the edges of a faint cluster would add to the brightness of the photographic image of a faint cluster relatively more than to that of a bright one (The limiting magnitude able to give an impression on the plate is the same in both cases). This would afford an increase of the differences for the faint clusters, but as we see it is quite the contrary. I t seems that the development was full in both cases, but even if it were not its effect would be as above. We have compared the measures of M13 made on the plates taken with Tessar lenses of 7 cm, 21 cm focal length and with a Steinheil Aplanat of 64 cm (for the last one F / B = 6.7 and the exposure time is 2"). They give no systematical differences (5m35, 5m06, 5m26 respectively), and are very demonstrative. The measure of these plates gives for the diameter of the cluster which forms the image practically to be estimated (to derive its brightness) g!o, 3!7, 4Io respectively'), while the photo- graphic images of q Herculis (4?61 ph) are 4I1, 318, 6I6. The measurement done at Harvard Observatory (H. B. 852) gives the diameters of the cluster as follows: 10!6 (Franklin Adams cart), 810 (AX Series), I I I O (24" telescope, Exp. = ~h), 120 (8" telescope, Exp. = 15m). We think that the diameters of the photographic image of a cluster on the short focus photographs are quite effective and are composed from their real angular dia- meter and from the general law of spreading of photographic images with increasing exposure time. In the usual compari- sons of brightness from a photograph enters the diameter of the image as well as its intensity, but the spreading of the image of a star cluster together with its blackening goes in quite a different way than it does for a star. In this sence the influence of exposure time and of the focal length could be expected to be very great. I t seems that in particular there can be an ,upper limit of exposure timecc for every cluster of given dia- meter (brightness). When this limit is surpassed the photo- graphic brightness of a cluster becomes greater and greater and attains quite fantastic values. This can be well illustrated by the fact that a, Centaun on the reproduction in oAstro- nomycc (Rusm'Z, Dugan, Stewart, p. 618) must be estimated 1?3 phot.! This fact and our measures of M13 mentioned above, are they in contradiction?

Summary. By the method of short focus camera the integral magnitudes of 2 7 globular clusters were determined. On the average they give the color index foF7, if compared with the mean visual magnitudes. The comparison with the results obtained at Harvard Observatory by the same method nearly simultaneously with ours, shows very great systematical difference [ W - S = 4m90 - 0?48 (S)], the Harvard magnitudes

I *

7

being much higher. Although there are indications that the latters far the bright clusters are incorrect, it seems that gene- rally the method of short focus camera in the photometry of diffuse objects must be applied very carefully. There are

5 641

some unknown conditions on which the method cannot be applied. For the considerable disaccordance between the two systems of magnitudes (obtained at Goursouf and at Harvard Observatory) we cannot find any reasonable explanation.

The observations were made with my colorimeter supplied with the blue wedge before the photometer lamp. The colour of the surface of comparison may be made almost the same as the colour of the lunar sea. Therefore the obser- vations are as exact as it is possible with the instrument of this type.

In the paper #Determination of stellar temperaturesa (Russ. Astr. J. Vol. VI, Nr. 2) I have given the reduction for- mulae connecting the reading s of the wedge with the tem- perature T of the object under observation, which are obtained in the system of Wilsing's catalogue of 199 stars. By these formulae we have the values of T-l for different seas observed 1928 Aug. o and I. The analogous values for 1 9 2 8 Aug. 29,

when Jupiter was only taken as the object of comparison, were obtained supposing, that the colour temperature of this

'

planet is 5oooo, as it follows nearly exactly from the mean reduction formula for all days of observations.

Taking into consideration the correction for selective absorption in the atmosphere we obtained, as it was explained in the above mentioned paper, that

p1 = 0.4 54 - 0.00869s where the quantity 0.00869 coincides almost exactly with that obtained by the direct investigation of the transmission property of the blue wedge, On 1 9 2 8 Aug. 2 9 I also made a series of comparisons of dxerent seas arranged in symmetrical order with Mare Tranquillitatis. Using the same formula the values T-l were deduced for this series separately. Thr individual values of T-1 for different seas are given in thr following table.

1928

0.211 - -

0 . 2 1 3 0 . 2 1 2 - I

- - -

0.217 0.217

0 . 2 1 8 0 .220

-

-

Aug. o

Aug. I

Aug. 2 9

__.

0.214 0 . 2 1 0 0 .212 - 0.212

- - 0 . 2 2 8 0 .215 0 . 2 1 5 0 . 2 1 4

0 .211 0 .212 - - - -

- I

0 . 2 1 9

l - - . ' - 0 . 2 1 4 0 . 2 1 5

- 0.219 0 .219

- -

- -

Aug. 2 9

symmetrica series

In these observations each lunar sea was compared with Mare Tranquillitatis and the latter in its turn was compared with

for M. Tranquillitatis. different stars and with Jupiter. For different days we have

M. Tranq.

I 2 " ' l n I & I 80 I T _ oC. ~~~~~l~~~~~ M. Serenitatis M. Tranquillitatis

0.202 0 .202

0 .202 0 .201

0 .198

0 . 2 1 2 0 . 2 0 9

0 . 2 1 0 0 . 2 1 4

0 . 2 0 3 0 . 2 0 j

0 .210 0 .205

0.200

0 . 2 1 0

M. Foecunditatis M. Crisium M. Nubium

- -

M. Tranq. -

0.217 j 1 .002 . O O ~ 4610

.oo5 4500

~~

Oc. Procell.

0 .213 0 . 2 0 2 - -

0.211 0 . 2 1 9

0 . 2 1 4 - - - -

0 . 2 1 3 0 . 2 1 4

0 .230 0 . 2 2 4

- -

-- M. Seren.

0 . 2 1 2 0 . 2 1 3 - -

0 . 2 2 2 0 . 2 1 6

0 . 2 1 5 0 . 2 2 0

0 . 2 1 8

0 . 2 2 5 0 . 2 2 4

0 . 2 2 8

-

0.210 0 . 2 1 7

0 . 2 1 1 0.208 0 . 2 2 5 0 . 2 2 3

0 .225 0 . 2 2 4

- ~~

M. Hum.

0 .217 0 . 2 1 3 - -

0 . 2 2 1 0 . 2 2 3

0 . 2 2 4 0 . 2 2 3 - - - -

0 . 2 1 1 0 .208

0 . 2 3 0 0.223

-

-

~~

M. Imbr.

0 .211 0 .207

0 .207

0 . 2 2 3 0 . 2 2 0

0 . 2 1 5 0 .213

-

- -

0 . 2 2 3 -

0 . 2 1 4 0 .211

0 .225 0 . 2 2 5

-

-

T-l Obs. Aug. o 0 . 2 0 1 5

I 0 .208 7 2 9 0 .212 1 9

The last value as was stated previously was obtained with 7'-1 = 0 . 2 0 0 for Jupiter. Adopting for M. Tranquillitatis T - l = 0 . 2 1 2 we have the corrections for the two previous days which are + 0.01 I and + 0.004 respectively and which are added to every value of T-l of other lunar seas.

The mean of all these corrected values for each sea is represented in the following table.

Moscow, 1 9 2 9 March.