34.
Parallax stars. In [§22] I have paid attention to the now available catalogues of stars with known annual parallax. The most extensive of these catalogues is that of Walkey, containing measured parallaxes of 625 stars. For a great many of these stars the value of the parallax measured must however be considered as rather uncertain, and I have pointed out that only for such stars as have a parallax greater than 0″.04 (or a distance smaller than 5 siriometers) may the measured parallax be considered as reliable, as least generally speaking. The effective number of parallax stars is therefore essentially reduced. Indirectly it is nevertheless possible to get a relatively large catalogue of parallax stars with the help of the ingenious spectroscopic method of Adams, which permits us to determine the absolute magnitude, and therefore also the distance, of even farther stars through an examination of the relative intensity of certain lines in the stellar spectra. It may be that the method is not yet as firmly based as it should be,[15] but there is every reason to believe that the course taken is the right one and that the catalogue published by Adams of 500 parallax stars in Contrib. from Mount Wilson, 142, already gives a more complete material than the catalogues of directly measured parallaxes. I give here a short resumé of the attributes of the parallax stars in this catalogue.
The catalogue of Adams embraces stars of the spectral types F, G, K and M. In order to complete this material by parallaxes of blue stars I add from the catalogue of Walkey those stars in his catalogue that belong to the spectral types B and A, confining myself to stars for which the parallax may be considered as rather reliable. There are in all 61 such stars, so that a sum of 561 stars with known distance is to be discussed.
For all these stars we know m and M and for the great part of them also the proper motion μ. We can therefore for each spectral type compute the mean values and the dispersion of these attributes. We thus get the following table, in which I confine myself to the mean values of the attributes.
TABLE 6.
MEAN VALUES OF m, M AND THE PROPER MOTIONS (μ) OF PARALLAX STARS OF DIFFERENT SPECTRAL TYPES.
| Sp. | Number | m | M | μ |
| B | 15 | +2.03 | -1.67 | 0″.05 |
| A | 46 | +3.40 | +0.64 | 0.21 |
| F | 125 | +5.60 | +2.10 | 0.40 |
| G | 179 | +5.77 | +1.68 | 0.51 |
| K | 184 | +6.17 | +2.31 | 0.53 |
| M | 42 | +6.02 | +2.30 | 0.82 |
We shall later consider all parallax stars taken together. We find from [table 6] that the apparent magnitude, as well as the absolute magnitude, is approximately the same for all yellow and red stars and even for the stars of type F, the apparent magnitude being approximately equal to +6m and the absolute magnitude equal to +2m. For type B we find the mean value of M to be -1m.7 and for type A we find M = +0m.6. The proper motion also varies in the same way, being for F, G, K, M approximately 0″.5 and for B and A 0″.1. As to the mean values of M and μ we cannot draw distinct conclusions from this material, because the parallax stars are selected in a certain way which essentially influences these mean values, as will be more fully discussed below. The most interesting conclusion to be drawn from the parallax stars is obtained from their distribution over different values of M. In the memoir referred to, Adams has obtained the following table (somewhat differently arranged from the table of Adams),[16] which gives the number of parallax stars for different values of the absolute magnitude for different spectral types.
A glance at this table is sufficient to indicate a singular and well pronounced property in these frequency distributions. We find, indeed, that in the types G, K and M the frequency curves are evidently resolvable into two simple curves of distribution. In all these types we may distinguish between a bright group and a faint group. With a terminology proposed by Hertzsprung the former group is said to consist of giant stars, the latter group of dwarf stars. Even in the stars of type F this division may be suggested. This distinction is still more pronounced in the graphical representation given in figures ([plate IV]).
TABLE 7.
DISTRIBUTION OF THE PARALLAX STARS OF DIFFERENT SPECTRAL TYPES OVER DIFFERENT ABSOLUTE MAGNITUDES.
| M | B | A | F | G | K | M | All | |
| - 4 | .. | .. | .. | .. | .. | 1 | .. | |
| - 3 | .. | .. | .. | .. | .. | .. | .. | |
| - 2 | 1 | 4 | 1 | 7 | .. | 2 | 15 | |
| - 1 | 2 | 7 | 7 | 28 | 15 | 4 | 63 | |
| - 0 | 3 | 10 | 6 | 32 | 40 | 10 | 91 | |
| + 0 | 1 | 11 | 6 | 7 | 14 | 11 | 50 | |
| + 1 | 1 | 3 | 20 | 9 | 4 | 1 | 38 | |
| + 2 | .. | 5 | 48 | 26 | .. | 1 | 80 | |
| + 3 | .. | 1 | 32 | 36 | 2 | .. | 71 | |
| + 4 | .. | 1 | 5 | 25 | 25 | .. | 56 | |
| + 5 | .. | 1 | .. | 6 | 25 | .. | 32 | |
| + 6 | .. | 2 | .. | 3 | 10 | .. | 15 | |
| + 7 | .. | 1 | .. | .. | 14 | .. | 15 | |
| + 8 | .. | .. | .. | .. | 3 | 7 | 10 | |
| + 9 | .. | .. | .. | .. | 2 | 4 | 6 | |
| +10 | .. | .. | .. | .. | .. | .. | .. | |
| +11 | .. | .. | .. | .. | .. | 1 | 1 | |
| Total | 8 | 46 | 125 | 179 | 154 | 42 | 554 |
In the distribution of all the parallax stars we once more find a similar bipartition of the stars. Arguing from these statistics some astronomers have put forward the theory that the stars in space are divided into two classes, which are not in reality closely related. The one class consists of intensely luminous stars and the other of feeble stars, with little or no transition between the two classes. If the parallax stars are arranged according to their apparent proper motion, or even according to their absolute proper motion, a similar bipartition is revealed in their frequency distribution.
Nevertheless the bipartition of the stars into two such distinct classes must be considered as vague and doubtful. Such an apparent bipartition is, indeed, necessary in all statistics as soon as individuals are selected from a given population in such a manner as the parallax stars are selected from the stars in space. Let us consider three attributes, say A, B and C, of the individuals of a population and suppose that the attribute C is positively correlated to the attributes A and B, so that to great or small values of A or B correspond respectively great or small values of C. Now if the individuals in the population are statistically selected in such a way that we choose out individuals having great values of the attributes A and small values of the attribute B, then we get a statistical series regarding the attribute C, which consists of two seemingly distinct normal frequency distributions. It is in like manner, however, that the parallax stars are selected. The reason for this selection is the following. The annual parallax can only be determined for near stars, nearer than, say, 5 siriometers. The direct picking out of these stars is not possible. The astronomers have therefore attacked the problem in the following way. The near stars must, on account of their proximity, be relatively brighter than other stars and secondly possess greater proper motions than those. Therefore parallax observations are essentially limited to (1) bright stars, (2) stars with great proper motions. Hence the selected attributes of the stars are m and μ. But m and μ are both positively correlated to M. By the selection of stars with small m and great μ we get a series of stars which regarding the attribute M seem to be divided into two distinct classes.
The distribution of the parallax stars gives us no reason to believe that the stars of the types K and M are divided into the two supposed classes. There is on the whole no reason to suppose the existence at all of classes of giant and dwarf stars, not any more than a classification of this kind can be made regarding the height of the men in a population. What may be statistically concluded from the distribution of the absolute magnitudes of the parallax stars is only that the dispersion in M is increased at the transition from blue to yellow or red stars. The filling up of the gap between the “dwarfs” and the “giants” will probably be performed according as our knowledge of the distance of the stars is extended, where, however, not the annual parallax but other methods of measuring the distance must be employed.
TABLE 8.
THE ABSOLUTELY FAINTEST STARS.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| Name | Position | Distance | Motion | Magnitude | Spectrum | ||||||||
| (αδ) | Square | l | b | π | r | μ | W | m | M | Sp | m′ | ||
| sir. | sir./st. | m′ | |||||||||||
| 1 | Proxima Centauri | (142262) | GD10 | 281° | - 2° | 0″.780 | 0.26 | 3″.85 | .. | 11m.0 | +13m.9 | .. | 13.5 |
| 2 | van Maanens star | (004304) | GE8 | 92 | -58 | 0.246 | 0.84 | 3.01 | .. | 12.3 | +12.7 | F0 | 12.95 |
| 3 | Barnards star | (175204) | GC12 | 358 | +12 | 0.515 | 0.40 | 10.29 | -19 | 9.7 | +11.7 | Mb | 8.9 |
| 4 | 17 Lyræ C | (190332) | GC2 | 31 | +10 | 0.128 | 1.60 | 1.75 | .. | 11.3 | +10.3 | .. | 12.5 |
| 5 | C. Z. 5h.243 | (050744) | GE7 | 218 | -35 | 0.319 | 0.65 | 8.75 | +51 | 9.2 | +10.1 | K2 | 10.68 |
| 6 | Gron. 19 VIII 234 | (161839) | GB1 | 29 | +44 | 0.162 | 1.27 | 0.12 | .. | 10.3 | + 9.8 | .. | .. |
| 7 | Oe. A. 17415 | (173768) | GB8 | 65 | +32 | 0.268 | 0.77 | 1.30 | .. | 9.1 | + 9.7 | K | 10.5 |
| 8 | Gron. 19 VII 20 | (162148) | GB2 | 41 | +43 | 0.133 | 1.55 | 1.22 | .. | 10.5 | + 9.6 | .. | .. |
| 9 | Pos. Med. 2164 | (184159) | GC2 | 56 | +24 | 0.292 | 0.71 | 2.28 | .. | 8.9 | + 9.6 | K | 10.3 |
| 10 | Krüger 60 | (222457) | GC8 | 72 | 0 | 0.256 | 0.81 | 0.94 | .. | 9.2 | + 9.6 | K5 | 10.8 |
| 11 | B. D. +56°532 | (021256) | GD8 | 103 | - 4 | 0.195 | 1.06 | .. | .. | 9.5 | + 9.4 | .. | .. |
| 12 | B. D. +55°581 | (021356) | GD8 | 103 | - 4 | 0.185 | 1.12 | .. | .. | 9.4 | + 9.2 | G5 | 10.2 |
| 13 | Gron. 19 VIII 48 | (160438) | GB1 | 27 | +46 | 0.091 | 2.27 | 0.12 | .. | 11.1 | + 9.3 | .. | .. |
| 14 | Lal. 21185 | (105736) | GB5 | 153 | +66 | 0.403 | 0.51 | 4.77 | -18 | 7.6 | + 9.1 | Mb | 8.9 |
| 15 | Oe. A. 11677 | (111466) | GB3 | 103 | +50 | 0.198 | 1.04 | 3.03 | .. | 9.2 | + 9.1 | Ma | 11.0 |
| 16 | Walkey 653 | (155359) | GB2 | 57 | +45 | 0.175 | 1.18 | .. | .. | 9.5 | + 9.1 | .. | .. |
| 17 | Yerkes parallax star | (021243) | GD8 | 107 | -16 | 0.045 | 4.58 | .. | .. | 12.4 | + 9.1 | .. | .. |
| 18 | B. D. +56°537 | (021256) | GD8 | 103 | - 4 | 0.175 | 1.18 | .. | .. | 9.4 | + 9.0 | .. | .. |
| 19 | Gron. 19 VI 266 | (062084) | GC3 | 97 | +27 | 0.071 | 2.80 | 0.09 | .. | 11.3 | + 9.0 | .. | .. |
| sir. | sir./st. | m′ | |||||||||||
| Mean | .. | .. | .. | 27°.5 | 0″.244 | 0.99 | 2″.96 | 29.3 | 10m.0 | +9m.9 | K1 | 10.9 | |
Regarding the absolute brightness of the stars we may draw some conclusions of interest. We find from [table 7] that the absolute magnitude of the parallax stars varies between -4 and +11, the extreme stars being of type M. The absolutely brightest stars have a rather great distance from us and their absolute magnitude is badly determined. The brightest star in the table is Antares with M = -4.6, which value is based on the parallax 0″.014 found by Adams. So small a parallax value is of little reliability when it is directly computed from annual parallax observations, but is more trustworthy when derived with the spectroscopic method of Adams. It is probable from a discussion of the B-stars, to which we return in a later chapter, that the absolutely brightest stars have a magnitude of the order -5m or -6m. If the parallaxes smaller than 0″.01 were taken into account we should find that Canopus would represent the absolutely brightest star, having M = -8.17, and next to it we should find Rigel, having M = -6.97, but both these values are based on an annual parallax equal to 0″.007, which is too small to allow of an estimation of the real value of the absolute magnitude.
If on the contrary the absolutely faintest stars be considered, the parallax stars give more trustworthy results. Here we have only to do with near stars for which the annual parallax is well determined. In [table 8] I give a list of those parallax stars that have an absolute magnitude greater than 9m.
There are in all 19 such stars. The faintest of all known stars is Innes' star “Proxima Centauri” with M = 13.9. The third star is Barnard's star with M = 11.7, both being, together with α Centauri, also the nearest of all known stars. The mean distance of all the faint stars is 1.0 sir.
There is no reason to believe that the limit of the absolute magnitude of the faint stars is found from these faint parallax stars:—Certainly there are many stars in space with M > 13m and the mean value of M, for all stars in the Galaxy, is probably not far from the absolute value of the faint parallax stars in this table. This problem will be discussed in a later part of these lectures.
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