Lectures on Stellar Statistics | Page 5

from the observer, the intensity increasing indirectly as the square of the distance of the star. In order to make the magnitudes of the stars comparable with each other it is convenient to reduce them to their value at a certain unit of distance. As such we choose one siriometer. The corresponding magnitude will be called the absolute magnitude and is denoted by M.[4] We easily find from the table given in the preceding paragraph that the absolute magnitude of the sun, according to Z?LLNER's value of m, amounts to +3.4, of the moon to +31.2. For Jupiter we find M = +24.6, for Venus M = +25.3. The other planets have approximately M = +30.
For the absolute magnitudes of those stars for which it has hitherto been possible to carry out a determination, we find a value of M between -8 and +13. We shall give in the third chapter short tables of the absolutely brightest and faintest stars now known.
8. Photographic magnitudes. The magnitudes which have been mentioned in the preceding paragraphs all refer to observations taken with the eye, and are called visual magnitudes. The total intensity of a star is, however, essentially dependent on the instrument used in measuring the intensity. Besides the eye, the astronomers use a photographic plate, bolometer, a photo-electric cell, and other instruments. The difference in the results obtained with these instruments is due to the circumstance that different parts of the radiation are taken into account.
The usual photographic plates, which have their principal sensibility in the violet parts of the spectrum, give us the photographic magnitudes of the stars. It is, however, to be remarked that these magnitudes may vary from one plate to another, according to the distributive function of the plate (compare L. M. 67). This variation, which has not yet been sufficiently studied, seems however to be rather inconsiderable, and must be neglected in the following.
The photographic magnitude of a star will in these lectures be denoted by m', corresponding to a visual magnitude m.
In practical astronomy use is also made of plates which, as the result of a certain preparation (in colour baths or in other ways), have acquired a distributive function nearly corresponding to that of the eye, and especially have a maximum point at the same wave-lengths. Such magnitudes are called photo-visual (compare the memoir of PARKHURST in A. J. 36 [1912]).
The photographic magnitude of a star is generally determined from measurements of the diameter of the star on the plate. A simple mathematical relation then permits us to determine m'. The diameter of a star image increases with the time of exposure. This increase is due in part to the diffraction of the telescope, to imperfect achromatism or spherical aberration of the objective, to irregular grinding of the glass, and especially to variations in the refraction of the air, which produce an oscillation of the image around a mean position.
The zero-point of the photographic magnitudes is so determined that this magnitude coincides with the visual magnitude for such stars as belong to the spectral type A0 and have m = 6.0, according to the proposal of the international solar conference at Bonn, 1911.
Determinations of the photographic or photo-visual magnitudes may now be carried out with great accuracy. The methods for this are many and are well summarised in the Report of the Council of the R. A. S. of the year 1913. The most effective and far-reaching method seems to be that proposed by SCHWARZSCHILD, called the half-grating method, by which two exposures are taken of the same part of the sky, while at one of the exposures a certain grating is used that reduces the magnitudes by a constant degree.
9. Colour of the stars. The radiation of a star is different for different wave-lengths ([lambda]). As regarding other mass phenomena we may therefore mention:--(1) the total radiation or intensity (I), (2) the mean wave-length ([lambda]0), (3) the dispersion of the wave-length ([sigma]). In the preceding paragraphs we have treated of the total radiation of the stars as this is expressed through their magnitudes. The mean wave-length is pretty closely defined by the colour, whereas the dispersion of the wave-length is found from the spectrum of the stars.
There are blue (B), white (W), yellow (Y) and red (R) stars, and intermediate colours. The exact method is to define the colour through the mean wave-length (and not conversely) or the effective wave-length as it is most usually called, or from the colour-index. We shall revert later to this question. There are, however, a great many direct eye-estimates of the colour of the stars.
Colour corresponding to a given spectrum.
Sp. Colour Number B3 YW- 161 A0 YW- 788 A5 YW 115 F5 YW, WY- 295 G5 WY 216 K5 WY+, Y- 552 M Y, Y+ 95 -----------------------------