Lectures on Stellar Statistics | Page 9

magnitude m' coincide for stars of spectral index 0.0 (A0). The photographic magnitudes are then unequivocally determined. It is found that their values systematically differ from the visual magnitudes, so that for type B (and O) the photographic magnitudes are smaller than the visual, and the contrary for the other types. The difference is greatest for the M-type (still greater for the N-stars, though here for the present only a few determinations are known), for which stars if amounts to nearly two magnitudes. So much fainter is a red star on a photographic plate than when observed with the eye.
The difference between the photographic and the visual magnitudes is called the colour-index (c). The correlation between this index and the spectral-index is found to be rather high (r = +0.96). In L. M. II, 19 I have deduced the following tables giving the spectral-type corresponding to a given colour-index, and inversely.
TABLE 1.
GIVING THE MEAN COLOUR-INDEX CORRESPONDING TO A GIVEN SPECTRAL TYPE OR SPECTRAL INDEX.
+-------------------+----------------+ | Spectral | Colour-index | | type | index | | +-------+-----------+----------------+ | B0 | -1.0 | -0.46 | | B5 | -0.5 | -0.23 | | A0 | 0.0 | 0.00 | | A5 | +0.5 | +0.23 | | F0 | +1.0 | +0.46 | | F5 | +1.5 | +0.69 | | G0 | +2.0 | +0.92 | | G5 | +2.5 | +1.15 | | K0 | +3.0 | +1.38 | | K5 | +3.5 | +1.61 | | M0 | +4.0 | +1.84 | +-------+-----------+----------------+
TABLE 1*.
GIVING THE MEAN SPECTRAL INDEX CORRESPONDING TO A GIVEN COLOUR-INDEX.
+----------------+-------------------+ | Colour-index | Spectral | | | index | type | +----------------+---------+---------+ | | | | | -0.4 | -0.70 | B3 | | -0.2 | -0.80 | B7 | | 0.0 | +0.10 | A1 | | +0.2 | +0.50 | A5 | | +0.4 | +0.90 | A9 | | +0.6 | +1.30 | F3 | | +0.8 | +1.70 | F7 | | +1.0 | +2.10 | G1 | | +1.2 | +2.50 | G5 | | +1.4 | +2.90 | G9 | | +1.6 | +3.30 | K3 | | +1.8 | +3.70 | K7 | | +2.0 | +4.10 | M1 | +----------------+---------+---------+
From each catalogue of visual magnitudes of the stars we may obtain their photographic magnitude through adding the colour-index. This may be considered as known (taking into account the high coefficient of correlation between s and c) as soon as we know the spectral type of the star. We may conclude directly that the number of stars having a photographic magnitude brighter than 6.0 is considerably smaller than the number of stars visually brighter than this magnitude. There are, indeed, 4701 stars for which m < 6.0 and 2874 stars having m' < 6.0.
16. Radial velocity of the stars. From the values of [alpha] and [delta] at different times we obtain the components of the proper motions of the stars perpendicular to the line of sight. The third component (W), in the radial direction, is found by the DOPPLER principle, through measuring the displacement of the lines in the spectrum, this displacement being towards the red or the violet according as the star is receding from or approaching the observer.
The velocity W will be expressed in siriometers per stellar year (sir./st.) and alternately also in km./sec. The rate of conversion of these units is given in §5.
17. Summing up the remarks here given on the apparent attributes of the stars we find them referred to the following principal groups:--
I. The position of the stars is here generally given in galactic longitude (l) and latitude (b). Moreover their equatorial coordinates ([alpha] and [delta]) are given in an abridged notation ([alpha][delta]), where the first four numbers give the right ascension in hours and minutes and the last two numbers give the declination in degrees, the latter being printed in italics if the declination is negative.
Eventually the position is given in galactic squares, as defined in §2.
II. The apparent motion of the stars will be given in radial components (W) expressed in sir./st. and their motion perpendicular to the line of sight. These components will be expressed in one component (u0) parallel to the galactic plane, and one component (v0) perpendicular to it. If the distance (r) is known we are able to convert these components into components of the linear velocity perpendicular to the line of sight (U and V).
III. The intensity of the light of the stars is expressed in magnitudes. We may distinguish between the apparent magnitude (m) and the absolute magnitude (M), the latter being equal to the value of the apparent magnitude supposing the star to be situated at a distance of one siriometer.
The apparent magnitude may be either the photographic magnitude (m'), obtained from a photographic