April 14, 192 1] 



NATURE 



205 



Stellar Magnitudes and their Determination.^ 



By H. Spencer Jones, Chief Assistant, The Royal Observatory, Greenwich. 



III. — Absolute Magnitudes. 



THE absolute magnitude of a star is a measure 

 of its intrinsic luminosity. In order to deter- 

 mine it, the distance of the star must be known. 

 Star distances are so great that it is customary 

 and convenient to express them in angular 

 measure by means of the angle (cr) subtended 

 at the star by the radius of the earth's orbit, sup- 

 posed viewed broadside on from the star. If I is 

 the apparent luminosity of a star at its actual 

 distance, then the apparent luminosity when 

 placed at any definite fixed distance from the sun 

 will give a true relative measure of its intrinsic 

 luminosity : its apparent luminosity being then 

 I/CT^, its absolute magnitude must differ by a con- 

 stant from 



-2-5(logI-2logCT), 



or from »n + 5 log CT. There is not entire uni- 

 formity amongst astronomers as to the constant 

 distance to which stars must be considered as 

 placed in order to obtain a definite measure of 

 their absolute magnitude ; this non-uniformity is 

 not serious, provided the convention adopted is 

 always explicitly stated. The most common prac- 

 tice is to define the absolute magnitude as the 

 value of the apparent magnitude when the star's 

 parallax (w) is one-tenth of a second of arc. If, 

 then, J7 is expressed in seconds, the absolute mag- 

 nitude, M, is given by 



M = m-i-5-t-5log CT. 



If, on the other hand, a distance corresponding 

 to a parallax of i" is adopted as the standard, 

 the absolute magnitude is given by 

 M = m-h5logCT. 



The magnitude m may be either the visual or the 

 photographic apparent magnitude, although it is 

 more general to use the former. There will be a 

 relative difference in the absolute magnitudes of 

 two stars of different colours according to which 

 apparent magnitude is used. To define absolute 

 magnitudes without any ambiguity, it would be 

 necessary to use a bolometric magnitude which 

 would take account of all the energy emitted by 

 the star, whatever its wave-length might be. 



The intrinsic luminosity of a star may also be 

 expressed in terms of the luminosity of the sun 

 as a unit, a means of expression which conveys 

 more meaning to the average person. Various 

 measures have been made of the apparent magni- 

 tude of the sun, on the scale used for the stars, 

 and the most probable value is now accepted as 

 — 26-5m. This corresponds to an absolute mag- 

 nitude for the sun of 51M or of oiM, accord- 

 ing as the distance used in defining absolute mag- 

 nitude corresponds to a parallax of o"-i or 1" 

 respectively. These values are uncertain to the 

 same extent that the value of the apparent magni- 

 tude is uncertain, and are, therefore, liable to 



1 Continued from p. 176. 



NO. 2685, VOL. 107] 



future revision. As it is not advisable that the 

 value of a star's luminosity, in terms of the sun's 

 luminosity as a unit, should be liable to frequent 

 change, it would be preferable to adopt a value 

 — 26-6in as the apparent magnitude of a hypo- 

 thetical sun, nearly equal in brightness to our sun, 

 and having the same position in space, and then 

 the absolute magnitude of this hypothetical sun 

 becomes 50M or ooM, according to the unit 

 of distance adopted. If a distance corresponding 

 to 1" (called by general acceptance a parsec) is 

 adopted as the unit, then the absolute magnitude 

 will give a direct measure of luminosity in terms 

 of the sun's luminosity as unit, the luminosity 

 being then simply the antilogarithm of — o-4M. 

 The convenience of having the zero of absolute 

 magnitude to agree with the brightness of the sun 

 is so great that, in spite of the much more general 

 acceptance hitherto of the scale of absolute mag- 

 nitudes based on a distance of 10 parsecs 

 (rrr = o"i), the time does not seem too late to 

 change the convention. The matter is one which 

 deserves the attention of the International Astro- 

 nomical Union. 



Since the determination of absolute magnitudes 

 necessarily involved, until recently, the determina- 

 tion of the distance of a star and also of its ap- 

 parent magnitude, and since the former of these 

 quantities is small and liable to a relatively large 

 error in its determination, it follows that absolute 

 magnitudes could be determined only with a much 

 greater uncertainty than attached to determina- 

 tions of apparent magnitude. Fortunately, we are 

 not dependent for our knowledge of absolute mag- 

 nitudes simply and solely upon direct trigono- 

 metrical determinations of stellar distances ; 

 methods have been devised of recent years by 

 which the problem may be attacked by somewhat 

 indirect means. 



One particularly interesting method has been 

 worked out at the Mount Wilson Observatory, 

 mainly by Adams, who succeeded in detecting dif- 

 ferences in the relative intensities of certain lines 

 in the spectra of various stars of a given spectral 

 type. These spectral differences within the same 

 spectral type are due to differences in density or 

 in surface brightness or both, and indicate differ- 

 ences in absolute magnitude. By using the best 

 determined trigonometrical parallaxes, Adams 

 was able to standardise these relative intensity 

 differences in terms of absolute magnitudes ; and 

 using the standardised basis so found, it becomes 

 possible to determine the absolute magnitudes of 

 stars simply from an examination of their spectra. 

 Since the basis of these determinations is the col- 

 lective results of direct parallax measures, the 

 result for any given star is liable to a much smaller 

 uncertainty than would be the result derived from 

 a direct determination of the parallax of that star, 

 provided the .«tar is at such a distance that the 



