SOME GROUPS OF KNOWN STARS.
29. The number of cases in which all the eight attributes of the stars
discussed in the first chapter are well known for one star is very
small, and certainly does not exceed one hundred. These cases refer
principally to such stars as are characterized either by great
brilliancy or by a great proper motion. The principal reason why these
stars are better known than others is that they lie rather near our
solar system. Before passing on to consider the stars from more general
statistical points of view, it may therefore be of interest first to
make ourselves familiar with these well-known stars, strongly
emphasizing, however, the exceptional character of these stars, and
carefully avoiding any generalization from the attributes we shall here
find.
30. _The apparently brightest stars._ We begin with these objects so
well known to every lover of the stellar sky. The following table
contains all stars the apparent visual magnitude of which is brighter
than 1m.5.
The first column gives the current number, the second the name, the
third the equatorial designation ([alpha][delta]). It should be
remembered that the first four figures give the hour and minutes in
right ascension, the last two the declination, italics showing negative
declination. The fourth column gives the galactic square, the fifth and
sixth columns the galactic longitude and latitude. The seventh and
eighth columns give the annual parallax and the corresponding distance
expressed in siriometers. The ninth column gives the proper motion
([mu]), the tenth the radial velocity _W_ expressed in sir./st. (To get
km./sec. we may multiply by 4.7375). The eleventh column gives the
apparent visual magnitude, the twelfth column the absolute magnitude
(_M_), computed from _m_ with the help of _r_. The 13th column gives the
type of spectrum (_Sp_), and the last column the photographic magnitude
(_m'_). The difference between _m'_ and _m_ gives the colour-index
(_c_).
TABLE 2.
_THE APPARENTLY BRIGHTEST STARS._
[Transcriber's Note: To conserve space (ad) is used in place of
([alpha][delta]).]
+--+---------------------+----------+--------+-----+-------+-------+-------+
| 1| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+--+---------------------+----------+--------+-----+-------+-------+-------+
| | | Position | Distance |
| | _Name_ |----------+--------+-----+-------+-------+-------+
| | | (ad) | Square | _l_ | _b_ | [pi] | _r_ |
+--+---------------------+----------+--------+-----+-------+-------+-------+
| | | | | | | | sir. |
| 1|Sirius |(0640{16})| GD_7 | 195°| - 8° |0".876 | 0.5 |
| 2|Canopus |(0621{52})| GD_8 | 229 | -24 | 0.007 | 29.5 |
| 3|Vega |(183338) | GC_2 | 30 | +17 | 0.094 | 2.2 |
| 4|Capella |(050945) | GC_5 | 131 | + 5 | 0.066 | 3.1 |
| 5|Arcturus |(141119) | GA_2 | 344 | +68 | 0.075 | 2.7 |
| 6|[alpha] Centauri |(1432{60})| GD_10 | 284 | - 2 | 0.759 | 0.3 |
| 7|Rigel |(0509{08})| GD_6 | 176 | -24 | 0.007 | 29.5 |
| 8|Procyon |(073405) | GC_7 | 182 | +14 | 0.324 | 0.6 |
| 9|Achernar |(0134{57})| GE_8 | 256 | -59 | 0.051 | 4.0 |
|10|[beta] Centauri |(1356{59})| GC_10 | 280 | + 2 | 0.037 | 5.6 |
|11|Altair |(194508) | GD_1 | 15 | -10 | 0.238 | 0.9 |
|12|Betelgeuze |(054907) | GD_6 | 168 | - 8 | 0.030 | 6.9 |
|13|Aldebaran |(043016) | GD_5 | 149 | -19 | 0.078 | 2.8 |
|14|Pollux |(073928) | GC_6 | 160 | +25 | 0.064 | 3.2 |
|15|Spica |(1319{10})| GB_8 | 286 | +51 | .. | .. |
|16|Antares |(1623{26})| GC_11 | 320 | +14 | 0.029 | 7.1 |
|17|Fomalhaut |(2252{30})| GE_10 | 348 | -66 | 0.138 | 1.5 |
|18|Deneb |(203844) | GC_2 | 51 | + 1 | .. | .. |
|19|Regulus |(100312) | GB_6 | 196 | +50 | 0.033 | 6.3 |
|20|[beta] Crucis |(1241{59})| GC_10 | 270 | + 3 | 0.008 | 25.8 |
+--+---------------------+----------+--------+-----+-------+-------+-------+
| | | | | | | | sir. |
| | Mean | .. | .. | .. | 23°.5|0".134 | 7.3 |
+--+---------------------+----------+--------+-----+-------+-------+-------+
+--+---------------------+------+--------+---------+---------+----+------+
| 1| 2 | 9 | 10 | 11 | 12 | 13 | 14 |
+--+---------------------+------+--------+---------+---------+----+------+
| | | Motion | Magnitude | Spectrum |
| | _Name_ +------+--------+---------+---------+----+------+
| | | [mu] | _W_ | _m_ | _M_ |_Sp_| _m'_ |
+--+---------------------+------+--------+---------+---------+----+------+
| | | |sir./st.| | | | _m'_ |
| 1|Sirius | 1".32| - 1.56| -1m.58 | -0m.3 |A |-1.58 |
| 2|Canopus | 0.02| + 4.39| -0.86 | -8.2 |F |-0.40 |
| 3|Vega | 0.35| - 2.91| 0.14 | -1.6 |A | 0.14 |
| 4|Capella | 0.44| + 6.38| 0.21 | -2.8 |G | 1.13 |
| 5|Arcturus | 2.28| - 0.82| 0.24 | -1.9 |K | 1.62 |
| 6|[alpha] Centauri | 3.68| - 4.69| 0.33 | +3.2 |G | 1.25 |
| 7|Rigel | 0.00| + 4.77| 0.34 | -7.0 |B8p | 0.25 |
| 8|Procyon | 1.24| - 0.74| 0.48 | +1.5 |F5 | 1.17 |
| 9|Achernar | 0.09| .. | 0.60 | -2.4 |B5 | 0.87 |
|10|[beta] Centauri | 0.04| + 2.53| 0.86 | -2.9 |B1 | 0.45 |
|11|Altair | 0.66| - 6.97| 0.89 | +1.2 |A5 | 1.12 |
|12|Betelgeuze | 0.03| + 4.43| 0.92 | -3.3 |Ma | 2.76 |
|13|Aldebaran | 0.20| +11.63| 1.06 | -1.2 |K5 | 2.67 |
|14|Pollux | 0.07| + 0.82| 1.21 | -1.3 |K | 2.59 |
|15|Spica | 0.06| + 0.34| 1.21 | .. |B2 | 0.84 |
|16|Antares | 0.03| - 0.63| 1.22 | -3.0 |Map | 3.06 |
|17|Fomalhaut | 0.37| + 1.41| 1.29 | +0.4 |A3 | 1.43 |
|18|Deneb | 0.00| - 0.84| 1.33 | .. |A2 | 1.42 |
|19|Regulus | 0.25| .. | 1.34 | -2.7 |B8 | 1.25 |
|20|[beta] Crucis | 0.06| + 2.74| 1.50 | -5.6 |B1 | 1.09 |
+--+---------------------+------+--------+---------+---------+----+------+
| | | | | | | | _m'_ |
| | Mean | 0".56| 3.26| +0m.64 | -2m.1 |F1 |+1.13 |
+--+---------------------+------+--------+---------+---------+----+------+
The values of ([alpha][delta]), _m_, _Sp_ are taken from H. 50. The
values of _l_, _b_ are computed from ([alpha][delta]) with the help of
tables in preparation at the Lund Observatory, or from the original to
plate I at the end, allowing the conversion of the equatorial
coordinates into galactic ones. The values of [pi] are generally taken
from the table of KAPTEYN and WEERSMA mentioned in the previous chapter.
The values of [mu] are obtained from B. P. C., those of the radial
velocity (_W_) from the card catalogue in Lund already described.
There are in all, in the sky, 20 stars having an apparent magnitude
brighter than 1m.5. The brightest of them is _Sirius_, which, owing to
its brilliancy and position, is visible to the whole civilized world. It
has a spectrum of the type A0 and hence a colour-index nearly equal to
0.0 (observations in Harvard give _c_ = +0.06). Its apparent magnitude
is -1m.6, nearly the same as that of Mars in his opposition. Its
absolute magnitude is -0m.3, _i.e._, fainter than the apparent
magnitude, from which we may conclude that it has a distance from us
smaller than one siriometer. We find, indeed, from the eighth column
that _r_ = 0.5 sir. The proper motion of Sirius is 1".32 per year, which
is rather large but still not among the largest proper motions as will
be seen below. From the 11th column we find that Sirius is moving
towards us with a velocity of 1.6 sir./st. (= 7.6 km./sec.), a rather
small velocity. The third column shows that its right ascension is 6h
40m and its declination -16°. It lies in the square GD_7 and its
galactic coordinates are seen in the 5th and 6th columns.
The next brightest star is _Canopus_ or [alpha] Carinæ at the south sky.
If we might place absolute confidence in the value of _M_ (= -8.2) in
the 12th column this star would be, in reality, a much more imposing
apparition than Sirius itself. Remembering that the apparent magnitude
of the moon, according to §6, amounts to -11.6, we should find that
Canopus, if placed at a distance from us equal to that of Sirius (_r_ =
0.5 sir.), would shine with a lustre equal to no less than a quarter of
that of the moon. It is not altogether astonishing that a fanciful
astronomer should have thought Canopus to be actually the central star
in the whole stellar system. We find, however, from column 8 that its
supposed distance is not less that 30 sir. We have already pointed out
that distances greater than 4 sir., when computed from annual
parallaxes, must generally be considered as rather uncertain. As the
value of _M_ is intimately dependent on that of _r_ we must consider
speculations based on this value to be very vague. Another reason for a
doubt about a great value for the real luminosity of this star is found
from its type of spectrum which, according to the last column, is F0, a
type which, as will be seen, is seldom found among giant stars. A better
support for a large distance could on the other hand be found from the
small proper motion of this star. Sirius and Canopus are the only stars
in the sky having a negative value of the apparent visual magnitude.
Space will not permit us to go through this list star for star. We may
be satisfied with some general remarks.
In the fourth column is the galactic square. We call to mind that all
these squares have the same area, and that there is therefore the same
probability _a priori_ of finding a star in one of the squares as in
another. The squares GC and GD lie along the galactic equator (the Milky
Way). We find now from column 4 that of the 20 stars here considered
there are no less than 15 in the galactic equator squares and only 5
outside, instead of 10 in the galactic squares and 10 outside, as would
have been expected. The number of objects is, indeed, too small to allow
us to draw any cosmological conclusions from this distribution, but we
shall find in the following many similar instances regarding objects
that are principally accumulated along the Milky Way and are scanty at
the galactic poles. We shall find that in these cases we may _generally_
conclude from such a partition that we then have to do with objects
_situated far from the sun_, while objects that are uniformly
distributed on the sky lie relatively near us. It is easy to understand
that this conclusion is a consequence of the supposition, confirmed by
all star counts, that the stellar system extends much farther into space
along the Milky Way than in the direction of its poles.
If we could permit ourselves to draw conclusions from the small material
here under consideration, we should hence have reason to believe that
the bright stars lie relatively far from us. In other words we should
conclude that the bright stars seem to be bright to us not because of
their proximity but because of their large intrinsic luminosity. Column
8 really tends in this direction. Certainly the distances are not in
this case colossal, but they are nevertheless sufficient to show, in
some degree, this uneven partition of the bright stars on the sky. The
mean distance of these stars is as large as 7.5 sir. Only [alpha]
Centauri, Sirius, Procyon and Altair lie at a distance smaller than one
siriometer. Of the other stars there are two that lie as far as 30
siriometers from our system. These are the two giants Canopus and Rigel.
Even if, as has already been said, the distances of these stars may be
considered as rather uncertain, we must regard them as being rather
large.
As column 8 shows that these stars are rather far from us, so we find
from column 12, that their absolute luminosity is rather large. The mean
absolute magnitude is, indeed, -2m.1. We shall find that only the
greatest and most luminous stars in the stellar system have a negative
value of the absolute magnitude.
The mean value of the proper motions of the bright stars amounts to
0".56 per year and may be considered as rather great. We shall, indeed,
find that the mean proper motion of the stars down to the 6th magnitude
scarcely amounts to a tenth part of this value. On the other hand we
find from the table that the high value of this mean is chiefly due to
the influence of four of the stars which have a large proper motion,
namely Sirius, Arcturus, [alpha] Centauri and Procyon. The other stars
have a proper motion smaller than 1" per year and for half the number of
stars the proper motion amounts to approximately 0".05, indicating their
relatively great distance.
That the absolute velocity of these stars is, indeed, rather small may
be found from column 10, giving their radial velocity, which in the mean
amounts to only three siriometers per stellar year. From the discussion
below of the radial velocities of the stars we shall find that this is a
rather small figure. This fact is intimately bound up with the general
law in statistical mechanics, to which we return later, that stars with
large masses generally have a small velocity. We thus find in the radial
velocities fresh evidence, independent of the distance, that these
bright stars are giants among the stars in our stellar system.
We find all the principal spectral types represented among the bright
stars. To the helium stars (B) belong Rigel, Achernar, [beta] Centauri,
Spica, Regulus and [beta] Crucis. To the Sirius type (A) belong Sirius,
Vega, Altair, Fomalhaut and Deneb. To the Calcium type (F) Canopus and
Procyon. To the sun type (G) Capella and [alpha] Centauri. To the K-type
belong Arcturus, Aldebaran and Pollux and to the M-type the two red
stars Betelgeuze and Antares. Using the spectral indices as an
expression for the spectral types we find that the mean spectral index
of these stars is +1.1 corresponding to the spectral type F1.
31. _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. 5h.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 10th
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 11m.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._
[Transcriber's Note: To conserve space (ad) is used in place of
([alpha][delta]).]
+--+---------------------+----------+--------+-----+-------+-------+-------+
| 1| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+--+---------------------+----------+--------+-----+-------+-------+-------+
| | | Position | Distance |
| | _Name_ |----------+--------+-----+-------+-------+-------+
| | | (ad) | Square | _l_ | _b_ | [pi] | _r_ |
+--+---------------------+----------+--------+-----+-------+-------+-------+
| | | | | | | | sir. |
| 1|Barnards star |(175204) | GC_12 | 358°| +12° |0".515 | 0.40 |
| 2|C. Z. 5h.243 |(0507{44})| GE_7 | 218 | -35 | 0.319 | 0.65 |
| 3|Groom. 1830 |(114738) | GA_1 | 135 | +75 | 0.102 | 2.02 |
| 4|Lac. 9352 |(2259{36})| GE_10 | 333 | -66 | 0.292 | 0.71 |
| 5|C. G. A. 32416 |(2359{37})| GF_2 | 308 | -75 | 0.230 | 0.89 |
| 6|61 Cygni |(210238) | GD_2 | 50 | - 7 | 0.311 | 0.66 |
| 7|Lal. 21185 |(105736) | GB_5 | 153 | +66 | 0.403 | 0.51 |
| 8|[epsilon] Indi |(2155{57})| GE_9 | 304 | -47 | 0.284 | 0.73 |
| 9|Lal. 21258 |(110044) | GB_4 | 135 | +64 | 0.203 | 1.02 |
|10|O^2 Eridani |(0410{07})| GE_5 | 168 | -36 | 0.174 | 1.19 |
|11|Proxima Centauri |(1422{62})| GD_10 | 281 | - 2 | 0.780 | 0.26 |
|12|Oe. A. 14320 |(1504{15})| GB_9 | 314 | +35 | 0.035 | 5.90 |
|13|[mu] Cassiopeiæ |(010154) | GD_4 | 93 | - 8 | 0.112 | 1.84 |
|14|[alpha] Centauri |(1432{60})| GD_10 | 284 | - 2 | 0.759 | 0.27 |
|15|Lac. 8760 |(2111{39})| GE_10 | 332 | -44 | 0.248 | 0.83 |
|16|Lac. 1060 |(0315{43})| GE_7 | 216 | -55 | 0.162 | 1.27 |
|17|Oe. A. 11677 |(111466) | GB_8 | 103 | +50 | 0.198 | 1.04 |
|18|Van Maanens star |(004304) | GD_8 | 92 | -58 | 0.246 | 0.84 |
+--+---------------------+----------+--------+-----+-------+-------+-------+
| | | | | | | | sir. |
| | Mean | .. | .. | | 41° |0".298 | 0.87 |
+--+---------------------+----------+--------+-----+-------+-------+-------+
+--+---------------------+------+--------+---------+---------+----+------+
| 1| 2 | 9 | 10 | 11 | 12 | 13 | 14 |
+--+---------------------+------+--------+---------+---------+----+------+
| | | Motion | Magnitude | Spectrum |
| | _Name_ +------+--------+---------+---------+----+------+
| | | [mu] | _W_ | _m_ | _M_ |_Sp_| _m'_ |
+--+---------------------+------+--------+---------+---------+----+------+
| | | |sir./st.| | | | _m'_ |
| 1|Barnards star |10".29| -19 | 9m.7 | +11m.7|Mb |11.5 |
| 2|C. Z. 5h.243 | 8.75| +51 | 9.2 | +10.1 |K2 |10.6 |
| 3|Groom. 1830 | 7.06| -20 | 6.5 | +5.0 |G5 | 7.6 |
| 4|Lac. 9352 | 6.90| +2 | 7.5 | +8.2 |K | 8.9 |
| 5|C. G. A. 32416 | 6.11| +5 | 8.2 | +8.5 |G | 9.1 |
| 6|61 Cygni | 5.27| -13 | 5.6 | +6.5 |K5 | 7.2 |
| 7|Lal. 21185 | 4.77| -18 | 7.6 | +9.1 |Mb | 8.9 |
| 8|[epsilon] Indi | 4.70| -8 | 4.7 | +5.4 |K5 | 6.3 |
| 9|Lal. 21258 | 4.47| +14 | 8.5 | +8.5 |Ma |10.3 |
|10|O^2 Eridani | 4.11| -9 | 4.7 | +4.3 |G5 | 5.8 |
|11|Proxima Centauri | 3.85| .. | 11.0 | +13.9 |.. |13.5 |
|12|Oe. A. 14320 | 3.75| +61 | 9.0 | +5.1 |G0 | 9.9 |
|13|[mu] Cassiopeiæ | 3.73| -21 | 5.7 | +4.4 |G3 | 6.8 |
|14|[alpha] Centauri | 3.68| -5 | 0.3 | +3.2 |G | 1.2 |
|15|Lac. 8760 | 3.53| +3 | 6.6 | +7.0 |G | 7.5 |
|16|Lac. 1060 | 3.05| +18 | 5.6 | +5.1 |G5 | 6.7 |
|17|Oe. A. 11677 | 3.03| .. | 9.2 | +9.1 |Ma |11.0 |
|18|Van Maanens star | 3.01| .. | 12.3 | +12.7 |F0 |12.9 |
+--+---------------------+------+--------+---------+---------+----+------+
| | | |sir./st.| | | | _m'_ |
| | Mean | 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 [square root]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 7m. 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
We conclude that, at least for these stars, the mean value of the
absolute magnitude increases with the spectral index. This conclusion,
however, is not generally valid.
32. _Stars with the greatest radial velocities._ There are some kinds of
nebulae for which very large values of the radial velocities have been
found. With these we shall not for the present deal, but shall confine
ourselves to the stars. The greatest radial velocity hitherto found is
possessed by the star (040822) of the eighth magnitude in the
constellation Perseus, which retires from us with a velocity of 72
sir./st. or 341 km./sec. The nearest velocity is that of the star
(010361) which approaches us with approximately the same velocity. The
following table contains all stars with a radial velocity greater than
20 sir./st. (= 94.8 km./sec.). It is based on the catalogue of VOUTE
mentioned above.
Regarding their distribution in the sky we find 11 in the galactic
equator squares and 7 outside. A large radial velocity seems therefore
to be a galactic phenomenon and to be correlated to a great distance
from us. Of the 18 stars in consideration there is only one at a
distance smaller than one siriometer and 2 at a distance smaller than 4
siriometers. Among the nearer ones we find the star (050744), identical
with C. P. D. 5h.243, which was the "second" star with great proper
motion. These stars have simultaneously the greatest proper motion and
very great linear velocity. Generally we find from column 9 that these
stars with large radial velocity possess also a large proper motion. The
mean value of the proper motions amounts to 1".34, a very high value.
In the table we find no star with great apparent luminosity. The
brightest is the 10th star in the table which has the magnitude 5.1. The
mean apparent magnitude is 7.7. As to the absolute magnitude (_M_) we
see that most of these speedy stars, as well as the stars with great
proper motions in table 3, have a rather great _positive_ magnitude and
thus are absolutely faint stars, though they perhaps may not be directly
considered as dwarf stars. Their mean absolute magnitude is +3.0.
Regarding the spectrum we find that these stars generally belong to the
yellow or red types (G, K, M), but there are 6 F-stars and, curiously
enough, two A-stars. After the designation of their type (A2 and A3) is
the letter _p_ (= peculiar), indicating that the spectrum in some
respect differs from the usual appearance of the spectrum of this type.
In the present case the peculiarity consists in the fact that a line of
the wave-length 448.1, which emanates from magnesium and which we may
find on plate III in the spectrum of Sirius, does not occur in the
spectrum of these stars, though the spectrum has otherwise the same
appearance as in the case of the Sirius stars. There is reason to
suppose that the absence of this line indicates a low power of radiation
(low temperature) in these stars (compare ADAMS).
TABLE 4.
_STARS WITH THE GREATEST RADIAL VELOCITY._
[Transcriber's Note: To conserve space (ad) is used in place of
([alpha][delta]).]
+--+---------------------+----------+--------+-----+-------+-------+-------+
| 1| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+--+---------------------+----------+--------+-----+-------+-------+-------+
| | | Position | Distance |
| | _Name_ |----------+--------+-----+-------+-------+-------+
| | | (ad) | Square | _l_ | _b_ | [pi] | _r_ |
+--+---------------------+----------+--------+-----+-------+-------+-------+
| | | | | | | | sir. |
| 1|A. G. Berlin 1366 |(040822) | GD_5 | 141°| -20° |0".007 | 30.8 |
| 2|Lal. 1966 |(010361) | GD_4 | 93 | - 2 | 0.016 | 12.9 |
| 3|A. Oe. 14320 |(1504{15})| GB_9 | 314 | +35 | 0.035 | 5.9 |
| 4|C. Z. 5h.243 |(0507{44})| GE_7 | 218 | -35 | 0.319 | 0.6 |
| 5|Lal. 15290 |(074730) | GC_6 | 158 | +26 | 0.023 | 9.0 |
| 6|53 Cassiop. |(015563) | GC_4 | 98 | + 2 | .. | .. |
| 7|A. G. Berlin 1866 |(055719) | GD_6 | 159 | - 2 | 0.021 | 9.8 |
| 8|W Lyræ |(181136) | GC_2 | 31 | +21 | .. | .. |
| 9|Boss 1511 |(0559{26})| GD_7 | 200 | -20 | 0.012 | 17.0 |
|10|[omega] Pavonis |(1849{60})| GD_11 | 304 | -24 | .. | .. |
|11|A. Oe. 20452 |(2017{21})| GE_10 | 351 | -31 | 0.015 | 13.5 |
|12|Lal. 28607 |(1537{10})| GB_10 | 325 | +34 | 0.033 | 6.2 |
|13|A. G. Leiden 5734 |(161132) | GB_1 | 21 | +45 | 0.002 | 89.2 |
|14|Lal. 37120 |(192932) | GC_2 | 33 | + 6 | 0.050 | 4.1 |
|15|Lal. 27274 |(1454{21})| GB_9 | 308 | +34 | 0.013 | 16.2 |
|16|Lal. 5761 |(030225) | GD_5 | 126 | -28 | 0.039 | 5.1 |
|17|W. B. 17h.517 |(172906) | GC_12 | 358 | +20 | 0.014 | 14.1 |
|18|Lal. 23995 |(1247{17})| GB_8 | 271 | +46 | 0.012 | 17.0 |
+--+---------------------+----------+--------+-----+-------+-------+-------+
| | | | | | | | sir. |
| | Mean | .. | .. | | 23°.9|0".041 | 16.7 |
+--+---------------------+----------+--------+-----+-------+-------+-------+
+--+---------------------+------+--------+---------+---------+----+------+
| 1| 2 | 9 | 10 | 11 | 12 | 13 | 14 |
+--+---------------------+------+--------+---------+---------+----+------+
| | | Motion | Magnitude | Spectrum |
| | _Name_ +------+--------+---------+---------+----+------+
| | | [mu] | _W_ | _m_ | _M_ |_Sp_| _m'_ |
+--+---------------------+------+--------+---------+---------+----+------+
| | | |sir./st.| | | | _m'_ |
| 1|A. G. Berlin 1366 | 0".54| +72 | 8m.9 | +1m.4 |F0 | 9.4 |
| 2|Lal. 1966 | 0.64| -69 | 7.9 | +2.3 |F3 | 8.5 |
| 3|A. Oe. 14320 | 3.75| +61 | 9.0 | +5.1 |G0 | 9.9 |
| 4|C. Z. 5h.243 | 8.75| +51 | 9.2 | +10.1 |K2 |10.6 |
| 5|Lal. 15290 | 1.96| -51 | 8.2 | +3.4 |G0 | 9.1 |
| 6|53 Cassiop. | 0.01| -44 | 5.6 | .. |B8 | 5.5 |
| 7|A. G. Berlin 1866 | 0.76| -40 | 9.0 | +4.0 |F0 | 9.9 |
| 8|W Lyræ | .. | -39 | var. | .. |Md | var. |
| 9|Boss 1511 | 0.10| +39 | 5.2 | -1.0 |G5 | 6.4 |
|10|[omega] Pavonis | 0.14| +38 | 5.1 | .. |K | 6.5 |
|11|A. Oe. 20452 | 1.18| -38 | 8.1 | +2.4 |G8p | 9.4 |
|12|Lal. 28607 | 1.18| -36 | 7.3 | +3.3 |A2p | 7.4 |
|13|A. G. Leiden 5734 | 0.04| -35 | 8.3 | -1.5 |K4 | 9.9 |
|14|Lal. 37120 | 0.52| -34 | 6.6 | +3.5 |G2 | 7.6 |
|15|Lal. 27274 | 0.79| +34 | 8.3 | +2.2 |F4 | 8.9 |
|16|Lal. 5761 | 0.86| -32 | 8.0 | +4.4 |A3p | 8.1 |
|17|W. B. 17h.517 | 0.63| -31 | 8.6 | +2.8 |F1 | 9.1 |
|18|Lal. 23995 | 0.88| +30 | 8.2 | +2.0 |F3 | 8.8 |
+--+---------------------+------+--------+---------+---------+----+------+
| | | |sir./st.| | | | _m'_ |
| | Mean | 1".34| 16.7 | 7m.7 | +3m.0 |F9 | 8.5 |
+--+---------------------+------+--------+---------+---------+----+------+
33. _The nearest stars._ The star [alpha] 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 [alpha] Centauri). In the year 1916 INNES
discovered at the observatory of Johannesburg in the Transvaal a star of
the 10th magnitude, which seems to follow [alpha] 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 [alpha] 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 6m (the table has 8 such stars), and probably
also all near stars brighter than 7m (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._
[Transcriber's Note: To conserve space (ad) is used in place of
([alpha][delta]).]
+--+----------------------+----------+--------+-----+-------+-------+-------+
| 1| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+--+----------------------+----------+--------+-----+-------+-------+-------+
| | | Position | Distance |
| | _Name_ |----------+--------+-----+-------+-------+-------+
| | | (ad) | Square | _l_ | _b_ | [pi] | _r_ |
+--+----------------------+----------+--------+-----+-------+-------+-------+
| | | | | | | | sir. |
| 1|Proxima Centauri |(1422{62})| GD_10 | 281°| - 2° |0".780 | 0.26 |
| 2|[alpha] Centauri |(1432{60})| GD_10 | 284 | - 2 | 0.759 | 0.27 |
| 3|Barnards p. m. star |(175204) | GC_12 | 358 | +12 | 0.515 | 0.40 |
| 4|Lal. 21185 |(105736) | GB_5 | 153 | +66 | 0.403 | 0.51 |
| 5|Sirius |(0640{16})| GD_7 | 195 | - 8 | 0.376 | 0.55 |
| 6| .. |(1113{57})| GC_6 | 158 | + 3 | 0.337 | 0.60 |
| 7|[tau] Ceti |(0139{16})| GF_1 | 144 | -74 | 0.334 | 0.62 |
| 8|Procyon |(073405) | GC_7 | 182 | +14 | 0.324 | 0.64 |
| 9|C. Z. 5h.243 |(0507{44})| GE_7 | 218 | -35 | 0.319 | 0.65 |
|10|61 Cygni |(210238) | GD_2 | 50 | - 7 | 0.311 | 0.66 |
|11|Lal. 26481 |(1425{15})| GB_9 | 124 | -40 | 0.311 | 0.66 |
|12|[epsilon] Eridani |(0328{09})| GE_5 | 153 | -42 | 0.295 | 0.70 |
|13|Lac. 9352 |(2259{36})| GE_10 | 333 | -66 | 0.292 | 0.71 |
|14|Pos. Med. 2164 |(184159) | GC_2 | 56 | +24 | 0.292 | 0.71 |
|15|[epsilon] Indi |(215557) | GE_9 | 304 | -47 | 0.284 | 0.73 |
|16|Groom. 34 |(001243) | GD_3 | 84 | -20 | 0.281 | 0.73 |
|17|Oe. A. 17415 |(173768) | GC_8 | 65 | +32 | 0.268 | 0.77 |
|18|Krüger 60 |(222457) | GC_3 | 72 | 0 | 0.256 | 0.81 |
|19|Lac. 8760 |(2111{39})| GE_10 | 332 | -44 | 0.248 | 0.88 |
|20|van Maanens p. m. star|(004304) | GE_3 | 92 | -58 | 0.246 | 0.84 |
|21|Altair |(194508) | GD_1 | 15 | -10 | 0.238 | 0.87 |
|22|C. G. A. 32416 |(2359{37})| GF_2 | 308 | -75 | 0.230 | 0.89 |
|23|Bradley 1584 |(1129{32})| GC_6 | 252 | +28 | 0.216 | 0.95 |
+--+----------------------+----------+--------+-----+-------+-------+-------+
| | | | | | | | sir. |
| | Mean | .. | .. | .. | 30°.8|0".344 | 0.67 |
+--+----------------------+----------+--------+-----+-------+-------+-------+
+--+-----------------------+------+--------+---------+---------+----+------+
| 1| 2 | 9 | 10 | 11 | 12 | 13 | 14 |
+--+-----------------------+------+--------+---------+---------+----+------+
| | | Motion | Magnitude | Spectrum |
| | _Name_ +------+--------+---------+---------+----+------+
| | | [mu] | _W_ | _m_ | _M_ |_Sp_| _m'_ |
+--+-----------------------+------+--------+---------+---------+----+------+
| | | |sir./st.| | | | _m'_ |
| 1|Proxima Centauri | 3".85| .. | 11m.0 | +13m.9 |.. |13.5 |
| 2|[alpha] Centauri | 3.68| - 5 | 0.33 | + 3.2 |G | 1.25 |
| 3|Barnards p. m. star | 10.29| -19 | 9.7 | +11.7 |Mb |11.5 |
| 4|Lal. 21185 | 4.77| -18 | 7.6 | + 9.1 |Mb | 8.9 |
| 5|Sirius | 1.32| - 2 | -1.58 | - 0.3 |A |-1.58 |
| 6| .. | 2.72| .. | .. | .. |.. |12.5 |
| 7|[tau] Ceti | 1.92| - 3 | 3.6 | + 4.6 |K0 | 4.6 |
| 8|Procyon | 1.24| - 1 | 0.48 | + 1.5 |F5 | 0.90 |
| 9|C. Z. 5h.243 | 8.75| +51 | 9.2 | +10.1 |K2 |10.6 |
|10|61 Cygni | 5.27| -13 | 5.6 | + 6.5 |K5 | 7.2 |
|11|Lal. 26481 | 0.47| .. | 7.8 | + 8.7 |G5 | 8.9 |
|12|[epsilon] Eridani | 0.97| + 3 | 3.8 | + 4.6 |K0 | 4.8 |
|13|Lac. 9352 | 6.90| + 2 | 7.5 | + 8.2 |K | 8.9 |
|14|Pos. Med. 2164 | 2.28| .. | 8.9 | + 9.6 |K |10.3 |
|15|[epsilon] Indi | 4.70| - 8 | 4.7 | + 5.4 |K5 | 6.3 |
|16|Groom. 34 | 2.89| + 1 | 8.1 | + 8.8 |Ma | 9.5 |
|17|Oe. A. 17415 | 1.30| .. | 9.1 | + 9.7 |K |10.5 |
|18|Krüger 60 | 0.94| .. | 9.2 | + 9.6 |K5 |10.8 |
|19|Lac. 8760 | 3.53| + 3 | 6.6 | + 7.0 |G | 7.5 |
|20|van Maanens p. m. star | 3.01| .. | 12.3 | +12.7 |F0 |12.9 |
|21|Altair | 0.66| - 7 | 0.9 | + 1.2 |A5 | 1.12 |
|22|C. G. A. 32416 | 6.11| + 5 | 8.2 | + 8.5 |G | 9.1 |
|23|Bradley 1584 | 1.06| - 5 | 6.1 | + 6.2 |G | 6.9 |
+--+-----------------------+------+--------+---------+---------+----+------+
| | | |sir./st.| | | | _m'_ |
| | Mean | 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 6m_ must be contained in this list. For if _M_ is equal to 6 or
brighter, _m_ must be brighter than 6m, if the star is nearer than one
siriometer. But we have assumed that all stars apparently brighter than
6m are known and are contained in the list. Hence also all stars
_absolutely_ brighter than 6m must be found in table 5. We conclude that
the number of stars having an absolute magnitude brighter than 6m
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.
For two of the stars the spectrum is for the present unknown.
We find that the number of stars increases with the spectral index. The
unknown stars in the siriometer sphere belong probably, in the main, to
the red types.
If we now seek to form a conception of the _total_ number in this sphere
we may proceed in different ways. EDDINGTON, in his "Stellar movements",
to which I refer the reader, has used the proper motions as a scale of
calculation, and has found that we may expect to find in all 32 stars in
this sphere, confining ourselves to stars apparently brighter than the
magnitude 9m.5. This makes 8 stars per cub. sir.
We may attack the problem in other ways. A very rough method which,
however, is not without importance, is the following. Let us suppose
that the Galaxy in the direction of the Milky Way has an extension of
1000 siriometers and in the direction of the poles of the Milky Way an
extension of 50 sir. We have later to return to the fuller discussion of
this extension. For the present it is sufficient to assume these values.
The whole system of the Galaxy then has a volume of 200 million cubic
siriometers. Suppose further that the total number of stars in the
Galaxy would amount to 1000 millions, a value to which we shall also
return in a following chapter. Then we conclude that the average number
of stars per cubic siriometer would amount to 5. This supposes that the
density of the stars in each part of the Galaxy is the same. But the sun
lies rather near the centre of the system, where the density is
(considerably) greater than the average density. A calculation, which
will be found in the mathematical part of these lectures, shows that the
density in the centre amounts to approximately 16 times the average
density, giving 80 stars per cubic siriometer in the neighbourhood of
the sun (and of the centre). A sphere having a radius of one siriometer
has a volume of 4 cubic siriometers, so that we obtain in this way 320
stars in all, within a sphere with a radius of one siriometer. For
different reasons it is probable that this number is rather too great
than too small, and we may perhaps estimate the total number to be
something like 200 stars, of which more than a tenth is now known to the
astronomers.
We may also arrive at an evaluation of this number by proceeding from
the number of stars of different apparent or absolute magnitudes. This
latter way is the most simple. We shall find in a later paragraph that
the absolute magnitudes which are now known differ between -8 and +13.
But from mathematical statistics it is proved that the total range of a
statistical series amounts upon an average to approximately 6 times the
dispersion of the series. Hence we conclude that the dispersion
([sigma]) of the absolute magnitudes of the stars has approximately the
value 3 (we should obtain [sigma] = [13 + 8] : 6 = 3.5, but for large
numbers of individuals the total range may amount to more than 6
[sigma]).
As, further, the number of stars per cubic siriometer with an absolute
magnitude brighter than 6 is known (we have obtained 8 : 4 = 2 stars per
cubic siriometer brighter than 6m), we get a relation between the total
number of stars per cubic siriometer (_D_0_) and the mean absolute
magnitude (_M_0_) of the stars, so that _D_0_ can be obtained, as soon
as _M_0_ is known. The computation of _M_0_ is rather difficult, and is
discussed in a following chapter. Supposing, for the moment, _M_0_ = 10
we get for _D_0_ the value 22, corresponding to a number of 90 stars
within a distance of one siriometer from the sun. We should then know a
fifth part of these stars.
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 [mu]. 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 ([mu]) OF PARALLAX STARS
OF DIFFERENT SPECTRAL TYPES._
+---+-------+-------+-------+-------+
|Sp.|Number | _m_ | _M_ | [mu] |
+---+-------+-------+-------+-------+
| 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 [mu] 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 [mu].
But _m_ and [mu] are both positively correlated to _M_. By the selection
of stars with small _m_ and great [mu] 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._
[Transcriber's Note: To conserve space (ad) is used in place of
([alpha][delta]).]
+--+---------------------+----------+--------+-----+-------+-------+-------+
| 1| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+--+---------------------+----------+--------+-----+-------+-------+-------+
| | | Position | Distance |
| | _Name_ |----------+--------+-----+-------+-------+-------+
| | | (ad) | Square | _l_ | _b_ | [pi] | _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 Lyræ 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|Krüger 60 |(222457) | GC_8 | 72 | 0 | 0.256 | 0.81 |
|11|B. D. +56°532 |(021256) | GD_8 | 103 | - 4 | 0.195 | 1.06 |
|12|B. D. +55°581 |(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. +56°537 |(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_ +------+--------+---------+---------+----+------+
| | | [mu] | _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 Lyræ 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|Krüger 60 | 0.94| .. | 9.2 | + 9.6 |K5 |10.8 |
|11|B. D. +56°532 | .. | .. | 9.5 | + 9.4 |.. | .. |
|12|B. D. +55°581 | .. | .. | 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. +56°537 | .. | .. | 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 [alpha]
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.
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.]
[Illustration: PLATE I.
_CONVERSION OF EQUATORIAL COORDINATES INTO GALACTIC COORDINATES._]
[Illustration: PLATE II.
_Squares and Constellations._]
[Illustration: PLATE III.
_The Harvard Classification of Stellar Spectra._]
[Illustration: Plate IV.
_Distribution of the parallax stars over different absolute
magnitudes._]
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[Transcriber's Note: The following corrections have been made to the
original text.
Page 4: "Terrestial distances" changed to "Terrestrial distances"
Page 9: "we must chose," changed to "we must choose,"
Page 12: "acromasie" changed to "achromatism"
Page 15: "inparticular" changed to "in particular"
"supposing, that" changed to "supposing that"
Page 16: "393.4 mm" changed to "393.4 [mu][mu]"
Page 20: "for which stars if" changed to "for which stars it"
Page 22: "sphaerical" changed to "spherical"
Page 23: "principal scource" changed to "principal source"
Page 25: "lense with 15 cm" changed to "lens with 15 cm"
Page 27: "Through the spectroscopie method" changed to "Through the
spectroscopic method"
"made to its principal" changed to "made its principal"
"american manner" changed to "American manner"
Page 35: "many tenths of a year" changed to "many tens of years"
Page 38: "same appearence" changed to "same appearance"
Page 47: "red stears" changed to "red stars"
"_dispersion_ in M" changed to "_dispersion_ in _M_"
Page 49: "smaller the" changed to "smaller than"]