A Contribution to the Study of Galactic Dimensions

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ASTRONOMY: H. SHAPLEY

VOL. 19, 1933

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where irregular and bizarre ganglionic masses exist in the complete absence of myotomes. The reduction in the number of ganglia and spinal nerves following somite removal, and especially an increase following the interpolation of an additional somite, constitute strong experimental support of Lehmann's view that the normal segmentation of spinal ganglia and nerves is determined by the mesodermal metamerism. There is no support of the generally held view that nervous metamerism is intrinsic, at least in the spinal cords of the forms which we have studied. 1 Lehmann, F., Jour. Comp. Neur., 49 (1927). 2 Detwiler, S. R., Jour. Exp. Zool., 54 (1932). 3 Detwiler, S. R., op. cit.

Lewis, W., Anat. Rec., 4 (1910). The normal brachial nerves constitute the third, fourth and fifth spinal nerves. 6 Lehmann, F., op. cit. 5

A CONTRIBUTION TO THE STUDY OF GALACTIC DIMENSIONS By HARLOW SHAPLEY HARVARD COLLEGE OBSERVATORY, CAMBRIDGE, MASS.

Read before the Academy, Monday, November 14, 1932

1. In our study of the dimensions of the galactic system, as well as in our exploration of the metagalaxy, we have been gradually driven out of the Milky Way and low galactic latitudes by increasing knowledge of the structural complexities along the Milky Way, and especially by the confusion and uncertainty caused by general and selective absorption of light near the galactic plane. Many years ago three factors had already pointed to the troubles in store for attempted analyses of galactic dimensions along the galactic circle. They were Barnard's and Wolf's work on the distribution and nature of the dark nebulae, the general consideration by many astronomers of the great rift in the Cygnus-toCentaurus part of the Milky Way, and the recognition of the "region of avoidance," the last of special importance in showing that star clusters of any kind in low latitudes can give, when their magnitudes are appropriately corrected for light absorption, an indication of only minimum dimensions of the galaxy and the minimum distance to the center. The region of avoidance is the mid-galactic belt, nearly ten degrees in width, in which practically no globular star clusters are found. There is another well-known region of avoidance, wider and more remote and possibly quite distinct, that affects the apparent distribution of the external galaxies in low galactic latitudes. There can be little doubt that con-

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PROC. N. A. S.

siderable numbers of clusters are behind the nearer obscuring material, mostly in Sagittarius, Scorpio and Ophiuchus. 2. I have pointed out on various occasions that certain globular clusters are partially obscured.' The dark nebulosity is recognizable in the vicinity of some of these affected clusters, and the stars in others seem to be abnormally faint for the angular dimensions of the systems. Presumably the light is scattered as well as obstructed and color excesses should appear, though nothing peculiar is found in the colors in Messier 22 (galactic latitude -9°) from an extended survey of the magnitudes of individual stars.2 Recently Stebbins has found, from colors determined with a photoelectric photometer and standard screens, that globular clusters in low latitude are systematically redder than those away from the galactic circle.3 Probably this reddening is a true color excess and if so is further evidence of the light scattering in low galactic latitudes, already shown by various investigators of distant galactic clusters and Milky Way stars. It is to be noted, however, that Miss 'Cannon's classification of the integrated spectra of globular clusters shows later types in low latitudes. Thus we have data from Appendix A of "Star Clusters" for the following weighted means: GALACTIC LATITUDE

NUMBER OF CLUSTERS

MEAN SPECTRUM

11 13

F9 G3 G8

> =20°014

-200to =111° 10°toO0

The total apparent magnitudes of the low latitude clusters are on the average fainter than those in high latitude. 3. It is clear from what has been said that the globular clusters themselves can afford no conclusive evidence of the total extent of the Milky Way in the direction of the galactic circle. Still less can the galactic clusters serve in giving a value to galactic dimensions either along the Milky Way plane or at right angles to it, for they are almost wholly confined to galactic latitudes less than 100. The examination of the whole system of observable galactic clusters, by Trumpler, Collinder, Shapley and others, accomplishes little more than the rough arrangement of those systems that are not dimmed beyond recognition by general absorption, or blocked out completely by the obscuring matter that produces the great rifts in the Milky Way and the region of avoidance. The galactic system's population of galactic clusters is probably much more incompletely known than the population of globular clusters. Fortunately, a considerable number of globular clusters lie in the higher galactic latitudes that seem to be essentially free of light scattering and direct obscuration. They can thus give a truer picture of the over-all dimensions of the galaxy. This clearness in higher latitudes is indicated

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VOL. 19, 1933

by the essentially normal colors of extragalactic nebulae, by studies of star distribution, and by Stebbins' and my own measures of the colors of and in globular clusters. 4. Ten years ago we began at the Harvard Observatory a special survey of faint variable stars in high latitudes, in the hope of adding to information on the thickness of the Milky Way. Baade and Bailey had found faint cluster type Cepheids in high latitudes, near to, but apparently not members of, globular clusters, and their discoveries suggested that at great distances from the galactic plane there might be large numbers of these important distance-indicators. The Harvard survey was begun with plates of the MC series (16-inch Metcalf doublet). The results with this series of plates were meager, however, and some years later the systematic photometry of high latitude fields was made a part of the study of Milky Way variables. Plates of the MF series, made in Bloemfontein with the 10-inch Metcalf triplet, have proved to be of much value in the investigation. In fourteen fields with galactic latitudes ranging from 200 to 80°, each field covering approximately one hundred square degrees, Miss Hughes has now found a large number of isolated cluster type Cepheids. Detailed data on the individual variables will be published when the study of these fields is complete. The present preliminary report is given because of the significance of the observations in galactic measurement. The results for the fourteen fields are summarized in the following table. VARIABLE STARS IN HIGH GALACTIC LATITUDE GALACTIC

PLATE

LATITUDE

LIMIT

NUMBER OF CLUSTER VARIABLES

+200

16.4 16.6 16.2 16.3 17.0 16.4 16.4 16.4 16.6 16.9 16.5 16.2 16.7 16.7

20 14 6 6 22 13 21 15 7 10 9 7 8 9

MILKY WAY FIELD

16 202 205 204 209 211 212 213 215 216 214 6 217 218

-20 -20 -22 -39 -40 -40 -57 -60 -60 -61 +62 -80 -80

FAINTEST MEDIAN MAGNITUDE

14.9 15.2 14.2 14.3 15.5 15.8 15.6 15.7 15.3 15.6 15.4 15.6 15.5 16.1:

NUMBBR OF NEBULAE PBR SQUARE DEGREE

11 0: 0 0 10:

25 8 15 8: 2: 30: 15 20: 25

All types of variable stars are found in the high latitude fields except the classical Cepheids, but only the cluster type Cepheids are considered in the present discussion because their absolute magnitudes can be taken as a constant, and their apparent magnitudes therefore give a direct measure of distances. The limiting magnitudes given in the third column

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PROC. N. A. S.

are determined from counts of stars on the photographic plates and the van Rhijn and Seares tables relating magnitudes, star numbers and galactic coordinates. The average limit of the plates is 16'.5, and the search for cluster type variables should therefore be effective to magnitude 15.5. Fields 204 and 205 are in the regions of the Pleiades and Orion, and the obscuring nebulosities are immediately revealed for them in the fifth column of the table, where the faintest median magnitudes of newly discovered cluster type Cepheids are 14.3 and 14.2, respectively, about a magnitude above the limit for the other fields. It is seen from this result, and from the data of the last column, that fields in galactic latitudes lower

50CA

B

30 20

-j

_

_

10 14 16 10 14 16 12 12 10 Distribution of cluster type Cepheids in high (A) and in low (B) galactic latitudes. Coordinates are numbers of stars and mean photographic magnitudes.

than 300 are not sufficiently clear of obscuration for a study of galactic dimensions (except, perhaps, at certain favorable longitudes). In higher latitudes the general occurrence of extragalactic nebulae in the fields is definite evidence of a general clarity in those directions, and therefore promises greater security in exploration and measurement within the bounds of our own galaxy. I have previously shown4 that the irregularities in the distribution of external systems in high latitudes down to the eighteenth magnitude are to be attributed to the actual groupings of these systems, and are not to be taken as evidence of the intervention of obscuring nebulosity. 5. The discovery of numerous cluster type Cepheids fainter than the fourteenth magnitude is at once an indication of the great thickness and

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extent of the galactic system, if it can be shown that these remarkable variable stars are actually members of the galactic system, and are not independent bodies in intergalactic space. The proof is both simple and direct. If the increase in number with magnitude should fall below fourfold per magnitude, as with ordinary galactic stars, a concentration to the galactic plane is indicated and we assume that the variables are members of the general galactic organization. In figure A the number of variables for each half magnitude is shown for 121 cluster type Cepheids in the ten fields of latitude greater than 300. The full line indicates the contour for uniform density. The marked deviation from this line shows that the cluster type Cepheids are members of the galaxy. When more fields have been examined and the survey has been taken to fainter magnitudes, it will be possible to determine the degree of concentration to the galaxy, and the actual laws of distribution. 6. As a control on the sufficiency of the MF series of plates for the survey in high latitudes, the comparable data for low latitudes are given in figure B. The material, which comprises observations of 290 variable stars- in seven fields, has'been compiled by Miss Swope from the data obtained for fields in the southern Milky Way, almost wholly in regions that appear essentially clear of obscuring matter. The galactic latitudes of the field centers are i 75'. Because of the great extent of the Milky Way in its plane we should not expect in these latitudes a falling off of number of variables with distance, as in high latitudes. The curve for average uniform density does, indeed, fit the observations satisfactorily. Thus it appears that the dropping off in numbers in high latitude is due to the actual thinning out of cluster type Cepheids with distance from the galactic plane. 7. The faintest median magnitudes (fifth column of the table) show that'in all these high latitude fields we find members of the galactic system as much as 10,000 parsecs away. We may compute the distances in parsecs from the galactic plane and the corresponding median magnitudes from the formulae I = sin# X 10o02t2,+l and mc = 5 log sin + mo where mo is the observed median photographic magnitude. It is readily found that if we take the absolute median magnitude of cluster type Cepheids as 0, as above, or even as +0.5, we have in the present survey many variables 30,000 light years from the galactic plane. A few fainter isolated cluster type Cepheids have been found at Harvard and by Baade at Bergedorf at greater distances. The large number of variables in the present study seems to indicate' that the cluster type Cepheids, as Baade has surmised, are distributed

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ASTRONOMY: P. M. MILLMAN

PROC. N. A. S.

throughout the same region as that occupied by the globular clusters; and these clusters appear more clearly than ever to outline our galaxy, as the globular clusters recently discussed by HubbleW and by Shapley and Mohr,6 outline Messier 31 and the Large Magellanic Cloud, Along the galactic plane our direct measures are troubled by absorption, and we can only surmise, from the distribution of the globular clusters and cluster type Cepheids in galactic latitudes 200 to 400, that the dimensions in this direction are much greater than shown here for the directions perpendicular to the plane. The faintest variables in fields 209, 211 and 212 would project on to the galactic plane at a distance of more than 20,000 light years from the sun. The extension of the search to fainter magnitudes in these fields and in fields of somewhat lower latitudes will be an important step in measuring the extent of the Milky Way in its plane. 1 E.g., in H. Mon., 2, 22 (1930). H. B. 874 (1930). Paper read at Ann Arbor meeting of the National Academy of Sciences, November, 1932. 4 H. B. 890 (1932). 6 Ap. J., 76, 44 (1932). 6 H. B. 889 (1932). 2

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THE THEORETICAL FREQUENCY DISTRIBUTION OF PHOTOGRAPHIC METEORS

By. PETER

M. MILLMAN*

HARvARD COLLEGE OBSERVATORY

Commuiicated December 8, 1932

In considering the frequency distribution of meteors we must first make some simplifying assumptions before the subject can be satisfactorily treated. Let us then assume that: 1. The lutninous part of the paths for all meteors is at an average height of;lb1Jkilometers above the surface of the earth. 2. All meteors are moving with the same constant linear velocity with respect to the earth. 3. If we regard a meteor as a moving point of light, then it radiates a constant quantity of light per second. 4. If the absolute magnitude of a meteor is determined by the light radiated per unit of path when viewed perpendicular to the path at some unit distance, then there is a definite absolute magnitude distribution for meteors entering the atmosphere at the same angle.