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EXTRA-GALACTIC NEBULAE

Transcriber's Note:

ABSTRACT

This contribution gives the results of a statistical investigation of 400 extra-galactic nebulae for which Holetschek has determined total visual magnitudes. The list is complete for the brighter nebulae in the northern sky and is representative to 12.5 mag. or fainter.

Recent studies have emphasized the fundamental nature of the division between galactic and extra-galactic nebulae. The relationship is not generic; it is rather that of the part to the whole. Galactic nebulae are clouds of dust and gas mingled with the stars of a particular stellar system; extra-galactic nebulae, at least the most conspicuous of them, are now recognized as systems complete in themselves, and often incorporate clouds of galactic nebulosity as component parts of their organization. Definite evidence as to distances and dimensions is restricted to six systems, including the Magellanic Clouds. The similar nature of the countless fainter nebulae has been inferred from the general principle of the uniformity of nature.

The extra-galactic nebulae form a homogeneous group in which numbers increase rapidly with diminishing apparent size and luminosity. Four are visible to the naked eye; 41 are found on the Harvard "Sky Map"; 700 are on the Franklin-Adams plates; 300,000 are estimated to be within the limits of an hour's exposure with the 60-inch reflector. These data indicate a wide range in distance or in absolute dimensions. The present paper, to which is prefaced a general classification of nebulae, discusses such observational material as we now possess in an attempt to determine the relative importance of these two factors, distance and absolute dimensions, in their bearing on the appearance of extra-galactic nebulae.

The classification of these nebulae is based on structure, the individual members of a class differing only in apparent size and luminosity. It is found that for the nebulae in each class these characteristics are related in a manner which closely approximates the operation of the inverse-square law on comparable objects. The presumption is that dispersion in absolute dimensions is relatively unimportant, and hence that in a statistical sense the apparent dimensions represent relative distances. The relative distances can be reduced to absolute values with the aid of the nebulae whose distances are already known.

GENERAL CLASSIFICATION

The classification used in the present investigation is essentially the detailed formulation of a preliminary classification published in a previous paper. It was developed in 1923, from a study of photographs of several thousand nebulae, including practically all the brighter objects and a thoroughly representative collection of the fainter ones. It is based primarily on the structural forms of photographic images, although the forms divide themselves naturally into two groups: those found in or near the Milky Way and those in moderate or high galactic latitudes. In so far as possible, the system is independent of the orientation of the objects in space. With minor changes in the original notation, the complete classification is as follows, although only the extra-galactic division is here discussed in detail:

CLASSIFICATION OF NEBULAE

REGULAR NEBULAE

The characteristic feature of extra-galactic nebulae is rotational symmetry about dominating non-stellar nuclei. About 97 per cent of these nebulae are regular in the sense that they show this feature conspicuously. The regular nebulae fall into a progressive sequence ranging from globular masses of unresolved nebulosity to widely open spirals whose arms are swarming with stars. The sequence comprises two sections, elliptical nebulae and spirals, which merge into each other.

Although deliberate effort was made to find a descriptive classification which should be entirely independent of theoretical considerations, the results are almost identical with the path of development derived by Jeans from purely theoretical investigations. The agreement is very suggestive in view of the wide field covered by the data, and Jeans's theory might have been used both to interpret the observations and to guide research. It should be borne in mind, however, that the basis of the classification is descriptive and entirely independent of any theory.

The only criterion available for further classification appears to be the degree of elongation. Elliptical nebulae have accordingly been designated by the symbol "E," followed by a single figure, numerically equal to the ellipticity /a with the decimal point omitted. The complete series is E0, E1, ..., E7, the last representing a definite limiting figure which marks the junction with the spirals.

The frequency distribution of ellipticities shows more round or nearly round images than can be accounted for by the random orientation of disk-shaped objects alone. It is presumed, therefore, that the images represent nebulae ranging from globular to lenticular, oriented at random. No simple method has yet been established for differentiating the actual from the projected figure of an individual object, although refined investigation furnishes a criterion in the relation between nuclear brightness and maximum diameters. For the present, however, it must be realized that any list of nebulae having a given apparent ellipticity will include a number of tilted objects having greater actual ellipticities. The statistical average will be too low, except for E7, and the error will increase with decreasing ellipticity.

The structural transition is so smooth and continuous that the selection of division points for further classification is rather arbitrary. The ends of the series are unmistakable, however, and, in a general way, it is possible to differentiate a middle group. These three groups are designated by the non-committal letters "a," "b," and "c" attached to the spiral symbols "S," and, with reference to their position in the sequence, are called "early," "intermediate," and "late" types. A more precise subdivision, on a decimal scale for example, is not justified in the present state of our knowledge.

In the early types, the group Sa, most of the nebulosity is in the nuclear region and the arms are closely coiled and unresolved. N.G.C. 3368 and 4274 are among the latest of this group.

The intermediate group, Sb, includes objects having relatively large nuclear regions and thin rather open arms, as in M 81, or a smaller nuclear region with closely coiled arms, as in M 94. These two nebulae represent the lateral extension of the sequence in the intermediate section. The extension along the sequence is approximately represented by N.G.C. 4826, among the earliest of the Sb, and N.G.C. 3556 and 7331, which are among the latest. The resolution in the arms is seldom conspicuous, although in M 31, a typical Sb, it is very pronounced in the outer portions.

The characteristics of the late types, the group Sc, are more definite--an inconspicuous nucleus and highly resolved arms. Individual stars cannot be seen in the smaller nebulae of this group, but knots are conspicuous, which, in larger objects, are known to be groups and clusters of stars. The extent to which the arms are opened varies from M 33 to M 101, both typical Sc nebulae.

H. D. Curtis first called attention to these nebulae when he described several in the intermediate stages of the series and called them ?-type spirals. The bar, however, never extends beyond the inner spiral arms, and the structure, especially in the early portion of the sequence, is more accurately represented by the Greek letter ?. From a dynamical point of view, the distinction has considerable significance. Since Greek letters are inconvenient for cataloguing purposes, the English term, "barred spiral," is proposed, which can be contracted to the symbol "SB."

The SB series, like that of the normal spirals, is divided into three roughly equal sections, distinguished by the appended letters "a," "b," and "c." The criteria on which the division is based are similar in general to those used in the classification of the normal spirals. In the earliest forms, SBa, the arms are not differentiated, and the pattern is that of a circle crossed by a bar, or, as has been mentioned, that of the Greek letter ?. When the bar is oriented nearly in the line of sight, it appears foreshortened as a bright and definite minor axis of the elongated nebular image. Such curious forms as the images of N.G.C. 1023 and 3384 are explained in this manner. The latest group, SBc, is represented by the S-shaped spirals such as N.G.C. 7479.

IRREGULAR NEBULAE

About 3 per cent of the extra-galactic nebulae lack both dominating nuclei and rotational symmetry. These form a distinct class which can be termed "irregular." The Magellanic Clouds are the most conspicuous examples, and, indeed, are the nearest of all the extra-galactic nebulae. N.G.C. 6822, a curiously faithful miniature of the Clouds, serves to bridge the gap between them and the smaller objects, such as N.G.C. 4214 and 4449. In these latter, a few individual stars emerge from an unresolved background, and occasional isolated spots give the emission spectrum characteristic of diffuse nebulosity in the galactic system, in the Clouds, and in N.G.C. 6822 These features are found in other irregular nebulae as well, notably in N.G.C. 1156 and 4656, and are just those to be expected in systems similar to the Clouds but situated at increasingly greater distances.

The system outlined above is primarily for the formal classification of photographic images obtained with large reflectors and portrait lenses. For each instrument, however, there is a limiting size and luminosity below which it is impossible to classify with any confidence. Except in rare instances, these small nebulae are extra-galactic, and their numbers, brightness, dimensions, and distribution are amenable to statistical investigation. For cataloguing purposes, they require a designating symbol, and the letter "Q" is suggested as convenient and not too widely used with other significations.

THE DATA

When known galactic nebulae, clusters, and the objects in the Magellanic Clouds are weeded out, the remaining 700 nebulae may be treated as extra-galactic. Very few can be classified from the Franklin-Adams plates; for this purpose photographs on a much larger scale are required. Until further data on the individual objects are available, Hardcastle's list can be used only for the study of distribution over the sky. This shows the well-known features--the greater density in the northern galactic hemisphere, the concentration in Virgo, and the restriction of the very large nebulae to the southern galactic hemisphere.

Fortunately, numerical data do exist in the form of total visual magnitudes for many of the nebulae in the northern sky. These determinations were made by Holetschek, who attempted to observe all nebulae within reach of his 6-inch refractor. He later restricted his program; but the final list is reasonably complete for the more conspicuous nebulae north of declination -10?, and is representative down to visual magnitude about 12.5. Out of 417 extra-galactic nebulae in Holetschek's list, 408 are north of -10?, as compared with 400 in Hardcastle's. The two lists agree very well for the brighter objects, but diverge more and more with decreasing luminosity. At the twelfth magnitude about half of Holetschek's nebulae are included by Hardcastle. Since the two lists compare favorably in completeness over so large a region of the sky, Holetschek's may be chosen as the basis for a statistical study and advantage taken of the valuable numerical data on total luminosities.

Hopmann has revised the scale of magnitudes by photometric measures of the comparison stars used by Holetschek. New magnitudes were thus obtained for 85 individual nebulae and from these were derived mean correction tables applicable to the entire list. The revised magnitudes are used throughout the following discussion. Hopmann's corrections extend to about 12.0 mag., and have been extrapolated on the assumption that they are constant for the fainter magnitudes. The errors involved are unimportant in view of selective effects which must be present among the observed objects near the limit of visibility.

The nebulae were classified and their diameters measured from photographs of about 300 of them taken with the 60-inch and 100-inch reflectors at Mount Wilson. Most of the others are included in the great collection of nebular photographs at Mount Hamilton, which have been described by Curtis; and, through the courtesy of the Director of the Lick Observatory, it has been possible to confirm the classification inferred from the published description by actual inspection of the original negatives.

Types, diameters, and total visual magnitudes are thus available for some 400 of the nebulae in Holetschek's list. The few unclassified objects are all fainter than 12.5 mag. The data are listed in Tables I-IV, in which the N.G.C. numbers, the total magnitudes, and the logarithms of the maximum diameters in minutes of arc are given for each type separately. A summary is given in Table V, in which the relative frequencies and the mean magnitudes of the various types will be found.

RELATIVE LUMINOSITIES OF THE VARIOUS TYPES

The various types are homogeneously distributed over the sky, their spectra are similar, and the radial velocities are of the same general order. These facts, together with the equality of the mean magnitudes and the uniform frequency distribution of magnitudes, are consistent with the hypothesis that the distances and absolute luminosities as well are of the same order for the different types. This is an assumption of considerable importance, but unfortunately it cannot yet be subjected to positive and definite tests. None of the individual similarities necessarily implies the adopted interpretation, but the totality of them, together with the intimate series relations among the types, which will be discussed later, suggests it as the most reasonable working hypothesis, at least until inconsistencies should appear.

RELATION BETWEEN LUMINOSITIES AND DIAMETERS

Among the nebulae of each separate type are found linear correlations between total magnitudes and logarithms of diameters. These are shown in Figures 2-5 for the beginning, middle, and end of the sequence of types and also for the irregular nebulae. In Figures 2 and 3 adjacent types have been grouped in order to increase the material, and in Figure 5 the Magellanic Clouds have been added to increase the range.

The correlations can be expressed in the form

where K is constant from type to type, but C varies progressively throughout the sequence. The value of K cannot be accurately determined from the scattered data for any particular type, but, within the limits of uncertainty, it approximates the round number 5.0, the value which is represented by the lines in Figures 2-5.

When K is known, the value of C can be computed from the mean magnitude and the logarithm of the diameter for each type. This amounts to reading from the curves the magnitudes corresponding to a diameter of one minute of arc, but avoids the uncertainty of establishing the curves where the data are limited.

NOTES TO TABLES I-IV

+ N.G.C. 524 and 3998 are late elliptical nebulae in which the equatorial planes are perpendicular to the line of sight. They might be included with the E6 or E7 nebulae.

? Absorption very conspicuous.

? N.G.C. 3607, 4459, and 5485 appear to be elliptical nebulae with narrow bands of absorption between the nuclei and the peripheries.

REDUCTION OF NEBULAE TO A STANDARD TYPE

The slope, K, in the formula relating magnitudes with diameters, appears to be closely similar for the various types, but accurate determinations are restricted by the limited and scattered nature of the data for each type separately. With a knowledge of the parameter C, however, it is possible to reduce all the material to a standard type and hence to determine the value of K from the totality of the data. The mean of E7, SBa, and Sa was chosen for the purpose, as representing a hypothetical transition-point between the elliptical nebulae and the spirals, and was designated by the symbol "S0." The corresponding value of C, in round numbers, is 13.0. Corrections were applied to the logarithms of the diameters of the nebulae of each observed class, amounting to

The corrected values of log d were then plotted against the observed magnitudes. This amounts to shifting the approximately parallel correlation curves for the separate types along the axis of log d until they coincide. Since the mean magnitudes of the various types are nearly constant, the relative shifts will very nearly equal the differences in the mean observed log d, and hence the effect of errors in the first approximation to the values of K will be negligible.

The correlation of the data is very closely represented by the formula

This falls between the two regression curves derived from least-square solutions and could be obtained exactly by assigning appropriate weights to the two methods of grouping. The nature of the data is such that a closer agreement can scarcely be expected. No correction to the assumed value of the slope appears to be required. The material extends over a range of 12 mag., and the few cases which have been investigated indicate that the correlation can be extended another 3 mag., to the limit at which nebulae can be classified with certainty on photographs made with the 100-inch reflector. The relation may therefore be considered to hold throughout the entire range of observations.

The following method has been used to determine the relative frequencies with which nebulae of a given actual ellipticity, oriented at random, will be observed as having various apparent ellipticities.

From the equation of the tangent, PP?,

Since

where

The results are given in Table X, where the actual ellipticities, listed in the first column, are followed across the table by the percentages which, on the assumption of random orientation, will be observed as having the various apparent ellipticities. The bottom row will be seen to show the percentages of apparent ellipticities observed in an assembly of nebulae in which the numbers for each actual ellipticity are equal and all are oriented at random.

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