Lectures on Stellar Statistics Part 6

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 bipart.i.tion of the stars. Arguing from these statistics some astronomers have put forward the theory that the stars in s.p.a.ce are divided into two cla.s.ses, which are not in reality closely related. The one cla.s.s consists of intensely luminous stars and the other of feeble stars, with little or no transition between the two cla.s.ses. If the parallax stars are arranged according to their apparent proper motion, or even according to their absolute proper motion, a similar bipart.i.tion is revealed in their frequency distribution.

Nevertheless the bipart.i.tion of the stars into two such distinct cla.s.ses must be considered as vague and doubtful. Such an _apparent_ bipart.i.tion 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 s.p.a.ce. 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 . But _m_ and are both positively correlated to _M_. By the selection of stars with small _m_ and great we get a series of stars which regarding the attribute _M_ seem to be divided into two distinct cla.s.ses.

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 cla.s.ses. There is on the whole no reason to suppose the existence at all of cla.s.ses of giant and dwarf stars, not any more than a cla.s.sification 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 | +--+---------------------+----------+--------+-----+-------+-------+-------+ | | | Position | Distance | | | _Name_ |----------+--------+-----+-------+-------+-------+ | | | (ad) | Square | _l_ | _b_ | p | _r_ | +--+---------------------+----------+--------+-----+-------+-------+-------+ | | | | | | | | sir. | | 1|Proxima Centauri |(1422{62})| GD_10 | 281| - 2 |0?.780 | 0.26 | | 2|van Maanens star |(004304) | GE_8 | 92 | -58 | 0.246 | 0.84 | | 3|Barnards star |(175204) | GC_12 | 358 | +12 | 0.515 | 0.40 | | 4|17 Lyrae C |(190332) | GC_2 | 31 | +10 | 0.128 | 1.60 | | 5|C. Z. 5h.243 |(0507{44})| GE_7 | 218 | -35 | 0.319 | 0.65 | | 6|Gron. 19 VIII 234 |(161839) | GB_1 | 29 | +44 | 0.162 | 1.27 | | 7|Oe. A. 17415 |(173768) | GB_8 | 65 | +32 | 0.268 | 0.77 | | 8|Gron. 19 VII 20 |(162148) | GB_2 | 41 | +43 | 0.133 | 1.55 | | 9|Pos. Med. 2164 |(184159) | GC_2 | 56 | +24 | 0.292 | 0.71 | |10|Kruger 60 |(222457) | GC_8 | 72 | 0 | 0.256 | 0.81 | |11|B. D. +56532 |(021256) | GD_8 | 103 | - 4 | 0.195 | 1.06 | |12|B. D. +55581 |(021356) | GD_8 | 103 | - 4 | 0.185 | 1.12 | |13|Gron. 19 VIII 48 |(160438) | GB_1 | 27 | +46 | 0.091 | 2.27 | |14|Lal. 21185 |(105736) | GB_5 | 153 | +66 | 0.403 | 0.51 | |15|Oe. A. 11677 |(111466) | GB_3 | 103 | +50 | 0.198 | 1.04 | |16|Walkey 653 |(155359) | GB_2 | 57 | +45 | 0.175 | 1.18 | |17|Yerkes parallax star |(021243) | GD_8 | 107 | -16 | 0.045 | 4.58 | |18|B. D. +56537 |(021256) | GD_8 | 103 | - 4 | 0.175 | 1.18 | |19|Gron. 19 VI 266 |(062084) | GC_3 | 97 | +27 | 0.071 | 2.80 | +--+---------------------+----------+--------+-----+-------+-------+-------+ | | | | | | | | sir. | | | Mean | .. | .. | .. | 27.5|0?.244 | 0.99 | +--+---------------------+----------+--------+-----+-------+-------+-------+

+--+---------------------+------+--------+---------+---------+----+------+ | 1| 2 | 9 | 10 | 11 | 12 | 13 | 14 | +--+---------------------+------+--------+---------+---------+----+------+ | | | Motion | Magnitude | Spectrum | | | _Name_ +------+--------+---------+---------+----+------+ | | | | _W_ | _m_ | _M_ |_Sp_| _m'_ | +--+---------------------+------+--------+---------+---------+----+------+ | | | |sir./st.| | | | _m'_ | | 1|Proxima Centauri | 3?.85| .. | 11m.0 |+13m.9 |.. |13.5 | | 2|van Maanens star | 3.01| .. | 12.3 | +12.7 |F0 |12.95 | | 3|Barnards star | 10.29| -19 | 9.7 | +11.7 |Mb | 8.9 | | 4|17 Lyrae C | 1.75| .. | 11.3 | +10.3 |.. |12.5 | | 5|C. Z. 5h.243 | 8.75| +51 | 9.2 | +10.1 |K2 |10.68 | | 6|Gron. 19 VIII 234 | 0.12| .. | 10.3 | + 9.8 |.. | .. | | 7|Oe. A. 17415 | 1.30| .. | 9.1 | + 9.7 |K |10.5 | | 8|Gron. 19 VII 20 | 1.22| .. | 10.5 | + 9.6 |.. | ..0 | | 9|Pos. Med. 2164 | 2.28| .. | 8.9 | + 9.6 |K |10.3 | |10|Kruger 60 | 0.94| .. | 9.2 | + 9.6 |K5 |10.8 | |11|B. D. +56532 | .. | .. | 9.5 | + 9.4 |.. | .. | |12|B. D. +55581 | .. | .. | 9.4 | + 9.2 |G5 |10.2 | |13|Gron. 19 VIII 48 | 0.12| .. | 11.1 | + 9.3 |.. | .. | |14|Lal. 21185 | 4.77| -18 | 7.6 | + 9.1 |Mb | 8.9 | |15|Oe. A. 11677 | 3.03| .. | 9.2 | + 9.1 |Ma |11.0 | |16|Walkey 653 | .. | .. | 9.5 | + 9.1 |.. | .. | |17|Yerkes parallax star | .. | .. | 12.4 | + 9.1 |.. | .. | |18|B. D. +56537 | .. | .. | 9.4 | + 9.0 |.. | .. | |19|Gron. 19 VI 266 | 0.09| .. | 11.3 | + 9.0 |.. | .. | +--+---------------------+------+--------+---------+---------+----+------+ | | | |sir./st.| | | | _m'_ | | | Mean | 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 a 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 s.p.a.ce 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.

FOOTNOTES:

[Footnote 15: Compare ADAMS' memoirs in the Contributions from Mount Wilson.]

[Footnote 16: The first line gives the stars of an absolute magnitude between -4.9 and -4.0, the second those between -3.9 and -3.0, &c. The stars of type B and A are from WALKEY's catalogue.]