Lectures on Stellar Statistics

by C. V. L. Charlier

Stars with the greatest proper motion. In [table 3] I have collected the stars having a proper motion greater than 3″ per year. The designations are the same as in the preceding table, except that the names of the stars are here taken from different catalogues.

In the astronomical literature of the last century we find the star 1830 Groombridge designed as that which possesses the greatest known proper motion. It is now distanced by two other stars C. P. D. 5^h.243 discovered in the year 1897 by Kapteyn and Innes on the plates taken for the Cape Photographic Durchmusterung, and Barnard's star in Ophiuchus, discovered 1916. The last-mentioned star, which possesses the greatest proper motion now known, is very faint, being only of the 10^th magnitude, and lies at a distance of 0.40 sir. from our sun and is hence, as will be found from [table 5] the third nearest star for which we know the distance. Its linear velocity is also very great, as we find from column 10, and amounts to 19 sir./st. (= 90 km./sec.) in the direction towards the sun. The absolute magnitude of this star is 11^m.7 and it is, with the exception of one other, the very faintest star now known. Its spectral type is Mb, a fact worth fixing in our memory, as different reasons favour the belief that it is precisely the M-type that contains the very faintest stars. Its apparent velocity (i.e., the proper motion) is so great that the star in 1000 years moves 3°, or as much as 6 times the diameter of the moon. For this star, as well as for its nearest neighbours in the table, observations differing only by a year are sufficient for an approximate determination of the value of the proper motion, for which in other cases many tens of years are required.

Regarding the distribution of these stars in the sky we find that, unlike the brightest stars, they are not concentrated along the Milky Way. On the contrary we find only 6 in the galactic equator squares and 12 in the other squares. We shall not build up any conclusion on this irregularity in the distribution, but supported by the general thesis of the preceding paragraph we conclude only that these stars must be relatively near us. This follows, indeed, directly from column 8, as not less than eleven of these stars lie within one siriometer from our sun. Their mean distance is 0.87 sir.

TABLE 3.
STARS WITH THE GREATEST PROPER MOTION.

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	Barnards star	(175204)	GC12	358°	+12°	0″.515	0.40	10″.29	-19	9m.7	+11m.7	Mb	11.5
2	C. Z. 5h.243	(050744)	GE7	218	-35	0.319	0.65	8.75	+51	9.2	+10.1	K2	10.6
3	Groom. 1830	(114738)	GA1	135	+75	0.102	2.02	7.06	-20	6.5	+5.0	G5	7.6
4	Lac. 9352	(225936)	GE10	333	-66	0.292	0.71	6.90	+2	7.5	+8.2	K	8.9
5	C. G. A. 32416	(235937)	GF2	308	-75	0.230	0.89	6.11	+5	8.2	+8.5	G	9.1
6	61 Cygni	(210238)	GD2	50	- 7	0.311	0.66	5.27	-13	5.6	+6.5	K5	7.2
7	Lal. 21185	(105736)	GB5	153	+66	0.403	0.51	4.77	-18	7.6	+9.1	Mb	8.9
8	ε Indi	(215557)	GE9	304	-47	0.284	0.73	4.70	-8	4.7	+5.4	K5	6.3
9	Lal. 21258	(110044)	GB4	135	+64	0.203	1.02	4.47	+14	8.5	+8.5	Ma	10.3
10	O2 Eridani	(041007)	GE5	168	-36	0.174	1.19	4.11	-9	4.7	+4.3	G5	5.8
11	Proxima Centauri	(142262)	GD10	281	- 2	0.780	0.26	3.85	..	11.0	+13.9	..	13.5
12	Oe. A. 14320	(150415)	GB9	314	+35	0.035	5.90	3.75	+61	9.0	+5.1	G0	9.9
13	μ Cassiopeiæ	(010154)	GD4	93	- 8	0.112	1.84	3.73	-21	5.7	+4.4	G3	6.8
14	α Centauri	(143260)	GD10	284	- 2	0.759	0.27	3.68	-5	0.3	+3.2	G	1.2
15	Lac. 8760	(211139)	GE10	332	-44	0.248	0.83	3.53	+3	6.6	+7.0	G	7.5
16	Lac. 1060	(031543)	GE7	216	-55	0.162	1.27	3.05	+18	5.6	+5.1	G5	6.7
17	Oe. A. 11677	(111466)	GB8	103	+50	0.198	1.04	3.03	..	9.2	+9.1	Ma	11.0
18	Van Maanens star	(004304)	GD8	92	-58	0.246	0.84	3.01	..	12.3	+12.7	F0	12.9
							sir.		sir./st.				m′
	Mean...	..	..	..	41°	0″.298	0.87	5″.00	17.8	7m.3	+7m.6	G8	8.7

That the great proper motion does not depend alone on the proximity of these stars is seen from column 10, giving the radial velocities. For some of the stars (4) the radial velocity is for the present unknown, but the others have, with few exceptions, a rather great velocity amounting in the mean to 18 sir./st. (= 85 km./sec.), if no regard is taken to the sign, a value nearly five times as great as the absolute velocity of the sun. As this is only the component along the line of sight, the absolute velocity is still greater, approximately equal to the component velocity multiplied by √2. We conclude that the great proper motions depend partly on the proximity, partly on the great linear velocities of the stars. That both these attributes here really cooperate may be seen from the absolute magnitudes (M).

The apparent and the absolute magnitudes are for these stars nearly equal, the means for both been approximately 7^m. This is a consequence of the fact that the mean distance of these stars is equal to one siriometer, at which distance m and M, indeed, do coincide. We find that these stars have a small luminosity and may be considered as dwarf stars. According to the general law of statistical mechanics already mentioned small bodies upon an average have a great absolute velocity, as we have, indeed, already found from the observed radial velocities of these stars.

As to the spectral type, the stars with great proper motions are all yellow or red stars. The mean spectral index is +2.8, corresponding to the type G8. If the stars of different types are put together we get the table

Type	Number	Mean value of M
G	8	5.3
K	4	7.5
M	4	9.6