62 



KNOWLEDGE 



[March 1, 1898. 



THE MASSES AND DISTANCES OF BINARY 

 STARS. 



By J. E. Gore, f.r.a.s. 



IN a valuable and interesting volume recently published 

 by Doctor See, of the Lowell Observatory, Mexico, 

 he gives a recomputation of the orbits of forty ol 

 the best known binary systems. Some of his results 

 — all of which are based on a careful consideration 

 of the best recorded measures — do not differ widely from 

 those of other computors. In other cases, however, his 

 orbits diiler considerably from those previously published ; 

 and as he has included very recent measures in his dis- 

 cussions, his results are probably more accurate than any 

 hitherto published. In the following table I give the period 

 (P) and the semi-axis major (a) of the orbits found by 

 Dr. See. From these I have computed the hypothetical 

 parallax, /i= "i, or the parallax of the star on the assump- 

 tion that the mass of the system is equal to the sun's mass. 

 To these I have added the magnitudes of the stars which 

 have been photometrically determined at Harvard, and the 

 character of the star's spectrum, 1. being the Sirian and 

 II. the solar type. 



Now, if we take the sun's stellar magnitude as —27: 

 that is, twenty-seven magnitudes below the zero magnitude 

 (see my paper in KNo-nxEixiE for June, 1895) : and compute 

 what its magnitude would be if removed to the distance 

 indicated by the " hypothetical parallax," we find that in 

 most cases the binary star is brighter than the sun would 



be if placed at this distance. It follows that to make the 

 sun of equal brightness with the star it should be placed 

 at a less distance than that indicated by the " hypothetical 

 parallax " — that is, tho parallax of the binary star should 

 be increased. This would have the effect of diminishing 

 the mass of the system, as I showed in a former paper. 

 (Knowledge, December, 1894.) Now if B represents the 

 number of times which the star exceeds the sun in bright- 

 ness when both are placed at the distance indicated by 

 the "hypothetical parallax," and s represents the increased 

 parallax, we have .s =;)^^B = -"^ f Again, if w and »», 



represent the masses of the components of the binary 

 system, and //' + /», -«M, where M is the mass of 

 the sun, we have, taking M=:l, )(=^„ and for the 

 parallax, s, ?i ^^jt;., or, substituting the value of i found 

 above, and reducing, we have ?^ ^= ~. To find B we have 

 (sun's mag. — star's mag.) xO'4 log. B. 



Let us now consider some of the most remarkable cases 

 in the above list which have spectra of the solar type. 

 I omit those in which the difference of magnitude between 

 the sun and star does not exceed one and a half magnitude, 

 or about four times. 



t liootis. In this case the sun would be reduced to a 

 star of 2 88 magnitude, which gives a difference of 1'72 

 magnitude in favour of the sim. This would make the 

 sun 4-H7.J times brighter than the star at equal distances. 

 The parallax must therefore be diminished, and hence the 

 mass of the system would be B|=10-77 times the mass of 

 the sun. 



Scorpii. Here the sun would be reduced to magnitude 

 .5-64, giving a difference of 1'54 magnitude in favour 

 of the star. Hence the mass of the .system would be 

 ^. I.i5 of the sun's mass. The spectrum is a doubtful one 

 of the second type (F '?). 



T Ophiuchi. In this case the sun would be reduced to 

 magnitude 6-98, if placed at the distance indicated by the 

 " hypothetical parallax," and, the star's photometrical 

 magnitude being 4-93, there is a difference of 2 OH 

 magnitudes in favour of the star. Hence B = 6-607, and 

 n = iV> °^ '■^^ mass of the system would be one-seventeenth 

 of the sun's mass, and the star's parallax about 0-085". 

 The spectrum is of the solar type. 



In the case of 99 Herculis the sun would be reduced to 

 magnitude ."cSI, or almost exactly equal to the star in 

 brightness, and, the spectrum being of the solar type, the 

 mass of the system is probably equal to the mass of the 

 sun. The companion is very faint and of a purple colour, 

 and may possibly be approaching the planetary stage of 

 its history. 



a Centauri is a very interesting case. Here the sun 

 would be reduced to a star of magnitude -0-31, or 0-31 

 magnitude brighter than a star of zero magnitude ; and as 

 the star's photometric magnitude is 0-20, we have a 

 difference of 0'.51 magnitude in favour of the sun, or 

 B = ]-:^;. Hence the parallax would be reduced to J 

 =0-746", and the mass of the system would be 2-023 

 times the sun's mass. As Dr. GiU found a parallax of 

 0-75", and Dr. See computes from his orbit a mass of 2 00, 

 the mass of the sun, it would seem that the orbit, parallax, 

 and photometric magnitude of this remarkable star have 

 been correctly determined. 



With reference to the binary stars having the Sirian 

 type of spectrum, let us consider the case of Sirius itself. 

 If the spectrum of Sirius were of the solar type and strictly 

 comparable with the sun, I find that its parallax would be 

 about 1-58", and its mass about one twenty-first part of 



