Lectures on Stellar Statistics

by C. V. L. Charlier

The nearest stars. The star α in Centaurus was long considered as the nearest of all stars. It has a parallax of 0″.75, corresponding to a distance of 0.27 siriometers (= 4.26 light years). This distance is obtained from the annual parallax with great accuracy, and the result is moreover confirmed in another way (from the study of the orbit of the companion of α Centauri). In the year 1916 Innes discovered at the observatory of Johannesburg in the Transvaal a star of the 10^th magnitude, which seems to follow α Centauri in its path in the heavens, and which, in any case, lies at the same distance from the earth, or somewhat nearer. It is not possible at present to decide with accuracy whether Proxima Centauri—as the star is called by Innes—or α Centauri is our nearest neighbour. Then comes Barnard's star (175204), whose large proper motion we have already mentioned. As No. 5 we find Sirius, as No. 8 Procyon, as No. 21 Altair. The others are of the third magnitude or fainter. No. 10—61 Cygni—is especially interesting, being the first star for which the astronomers, after long and painful endeavours in vain, have succeeded in determining the distance with the help of the annual parallax (Bessel 1841).

From column 4 we find that the distribution of these stars on the sky is tolerably uniform, as might have been predicted. All these stars have a large proper motion, this being in the mean 3″.42 per year. This was a priori to be expected from their great proximity. The radial velocity is, numerically, greater than could have been supposed. This fact is probably associated with the generally small mass of these stars.

Their apparent magnitude is upon an average 6.3. The brightest of the near stars is Sirius (m = -1.6), the faintest Proxima Centauri (m = 11). Through the systematic researches of the astronomers we may be sure that no bright stars exist at a distance smaller than one siriometer, for which the distance is not already known and well determined. The following table contains without doubt—we may call them briefly all near stars—all stars within one siriometer from us with an apparent magnitude brighter than 6^m (the table has 8 such stars), and probably also all near stars brighter than 7^m (10 stars), or even all brighter than the eighth magnitude (the table has 13 such stars and two near the limit). Regarding the stars of the eighth magnitude or fainter no systematic investigations of the annual parallax have been made and among these stars we may get from time to time a new star belonging to the siriometer sphere in the neighbourhood of the sun. To determine the total number of stars within this sphere is one of the fundamental problems in stellar statistics, and to this question I shall return immediately.

TABLE 5.
THE NEAREST 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	α Centauri	(143260)	GD10	284	- 2	0.759	0.27	3.68	- 5	0.33	+ 3.2	G	1.25
3	Barnards p. m. star	(175204)	GC12	358	+12	0.515	0.40	10.29	-19	9.7	+11.7	Mb	11.5
4	Lal. 21185	(105736)	GB5	153	+66	0.403	0.51	4.77	-18	7.6	+ 9.1	Mb	8.9
5	Sirius	(064016)	GD7	195	- 8	0.376	0.55	1.32	- 2	-1.58	- 0.3	A	-1.58
6	..	(111357)	GC6	158	+ 3	0.337	0.60	2.72	..	..	..	..	12.5
7	τ Ceti	(013916)	GF1	144	-74	0.334	0.62	1.92	- 3	3.6	+ 4.6	K0	4.6
8	Procyon	(073405)	GC7	182	+14	0.324	0.64	1.24	- 1	0.48	+ 1.5	F5	0.90
9	C. Z. 5h.243	(050744)	GE7	218	-35	0.319	0.65	8.75	+51	9.2	+10.1	K2	10.6
10	61 Cygni	(210238)	GD2	50	- 7	0.311	0.66	5.27	-13	5.6	+ 6.5	K5	7.2
11	Lal. 26481	(142515)	GB9	124	-40	0.311	0.66	0.47	..	7.8	+ 8.7	G5	8.9
12	ε Eridani	(032809)	GE5	153	-42	0.295	0.70	0.97	+ 3	3.8	+ 4.6	K0	4.8
13	Lac. 9352	(225936)	GE10	333	-66	0.292	0.71	6.90	+ 2	7.5	+ 8.2	K	8.9
14	Pos. Med. 2164	(184159)	GC2	56	+24	0.292	0.71	2.28	..	8.9	+ 9.6	K	10.3
15	ε Indi	(215557)	GE9	304	-47	0.284	0.73	4.70	- 8	4.7	+ 5.4	K5	6.3
16	Groom. 34	(001243)	GD3	84	-20	0.281	0.73	2.89	+ 1	8.1	+ 8.8	Ma	9.5
17	Oe. A. 17415	(173768)	GC8	65	+32	0.268	0.77	1.30	..	9.1	+ 9.7	K	10.5
18	Krüger 60	(222457)	GC3	72	0	0.256	0.81	0.94	..	9.2	+ 9.6	K5	10.8
19	Lac. 8760	(211139)	GE10	332	-44	0.248	0.88	3.53	+ 3	6.6	+ 7.0	G	7.5
20	van Maanens p. m. star	(004304)	GE3	92	-58	0.246	0.84	3.01	..	12.3	+12.7	F0	12.9
21	Altair	(194508)	GD1	15	-10	0.238	0.87	0.66	- 7	0.9	+ 1.2	A5	1.12
22	C. G. A. 32416	(235937)	GF2	308	-75	0.230	0.89	6.11	+ 5	8.2	+ 8.5	G	9.1
23	Bradley 1584	(112932)	GC6	252	+28	0.216	0.95	1.06	- 5	6.1	+ 6.2	G	6.9
							sir.		sir./st.				m′
	Mean	..	..	..	30°.8	0″.344	0.67	3″.42	9.1	6m.3	+7m.3	G6	7.5

The mean absolute magnitude of the near stars is distributed in the following way:—

M	0	1	3	4	5	6	7	8	9	10	11	12	13
Number	1	2	1	2	1	2	1	4	4	1	1	1	1.

What is the absolute magnitude of the near stars that are not contained in table? Evidently they must principally be faint stars. We may go further and answer that all stars with an absolute magnitude brighter than 6^m must be contained in this list. For if M is equal to 6 or brighter, m must be brighter than 6^m, if the star is nearer than one siriometer. But we have assumed that all stars apparently brighter than 6^m are known and are contained in the list. Hence also all stars absolutely brighter than 6^m must be found in [table 5]. We conclude that the number of stars having an absolute magnitude brighter than 6^m amounts to 8.

If, finally, the spectral type of the near stars is considered, we find from the last column of the table that these stars are distributed in the following way:—

Spectral type	B	A	F	G	K	M
Number	0	2	2	5	9	3.