April, 1905.] 



KNOWLEDGE & SCIENTIFIC NEWS. 



Stellar Brightness Qcr\d 

 Density. 



By J. E. Gore, F.R.A.S. 

 The absolute brightness of a star, or its so-called 

 " magnitude," depends on three factors — (i), its 

 distance from the earth ; (2), its diameter ; and (3), its 

 intrinsic brilliancy, or the actual luminosity of its sur- 

 face per unit of area. The first of these factors — the 

 distance from the earth — has, in a few cases, been 

 determined with considerable approach to accuracy, 

 either by micrometrical observations of comparison 

 stars, or from spectroscopical observations of binary 

 stars. The second factor — the actual diameter of the 

 star — is more difficult to determine, and its measure- 

 ment has not been satisfactorily accomplished, except 

 in some variables of the Algol type. An approximation 

 to its probable value may, however, be arrived at from 

 other considerations. The third factor — the luminosity 

 of the star's surface — may be inferred — to some extent 

 at least — from the character of the star's spectrum. 

 This luminosity of surface, or intrinsic brightness, as it 

 is also called, probably depends on the mass and density 

 of the star. Two stars may have the same mass, but 

 one may have a large diameter and small density, and 

 the other a smaller diameter and greater density. The 

 difference is probably a function of temperature. And 

 then the question arises, which of the two stars will be 

 apparently the brighter? We know that heat causes a 

 mass of gas to expand, and the greater the heat the 

 greater the expansion. And with a gi\en mass, the 

 greater the expansion the smaller the density will be. 

 This is evident. Hence a star with a high temperature 

 will have a large volume and small density. And it 

 seems highly probable that the higher the temperature 

 the greater will be the luminosity of its surface. From 

 this it would follow that a star with a high temperature 

 would have a large volume and light-giving surface, 

 and also a greater luminosity of surface, and both 

 causes would thus combine to increase its apparent 

 brilliancy. This would not, however, apply to the 

 nebulae, but only to bodies, like the stars, which have 

 consolidated to a certain extent. 



It is now usually admitted that stars with the Orion 

 type of spectrum (B, Pickering), such as Bellatrix 

 (7 Orionis), 5, e, and f Orionis,' are — with the possible 

 exception of the " Wolf-Rayet," or bright line, stars — 

 the most luminous among the brighter stars. Next to 

 these come stars with the Sirian type of spectrum (A, 

 Pickering), followed probably in decreasing order of 

 surface luminosity by stars of the second (or solar) 

 type, and then by the third and, perhaps, the fourth 

 type stars. The " Algol variable " U Ophiuchi has a 

 spectrum of the Orion type, and some of the other 

 " Algols," such as Algol itself, X Tauri, and V Puppis, 

 show a spectrum intermediate between the B and A 

 type. These will be considered further on. 



The probably great luminosity of stars with the 

 Orion type of spectrum is shown by the fact that 

 Sir David Gill finds that the parallax of Rigel is almost 

 certainly not more than the hundredth of a second of 

 arc, and yet it is one of the brightest stars in the 

 heavens; se\enth in order of brightness, according to 

 the Harvard photometric measures. At the vast 

 distance indicated by this minute parallax our sun 

 would be reduced to a star of about the tenth magni- 

 tude, and would, therefore, be invisible even with a 

 binocular field glass. Rigel is, therefore, about 7,800 

 times brighter than the sun would be if removed to the 



same distance. It has a small companion of the eighth 

 magnitude, but as the pair have not yet been proved to 

 be a binary (although the companion itself, which is 

 double, probably is), we cannot determine its mass. 

 But it is evident that it must be a body of enormous 

 size and great luminosity of surface to shine as brightly 

 as it does at such a vast distance from the earth — over 

 300 years' journey for light. Comparing it with Sirius, 

 whose mass and parallax have been well determined, I 

 find that the mass of Rigel is probably about 20,000 

 times the sun's mass. 



The great brilliancy of stars with the Sirian type of 

 spectrum is shown by Sirius itself, the distance of which 

 is now well determined. From its apparent brightness 

 and parallax I find that Sirius is about 31.6 times 

 brighter than the sun would be at the same distance. 

 From the orbit of its satellite Dr. See finds the mass of 

 the bright star to be 2.36 times the sun's mass, and 

 from this it follows that its real brightness is about 18 

 times greater than that of the sun in proportion to its 

 mass. Its spectrum shows that it is probably at a 

 higher temperature than our sun. Its volume is, 

 therefore, probably larger, and, as Dr. See says, there 

 " is some reason to suppose that Sirius is very much 

 expanded, more nearly resembling a nebula than the 

 sun." But here the question suggests itself. Is its 

 greater brilliancy due to its larger volume, and, there- 

 fore, smaller density, or to its greater surface 

 luminosity, or to both causes combined? As it is 31.6 

 times brighter than the sun, a diameter equal to the 

 square root of 31.6, or 5.62 times the sun's diameter, 

 would give the necessary brightness, if the surface 

 luminosity of Sirius and the sun were the same. 

 Assuming this for a moment, I find that with a dia- 

 meter of 5.62 times the sun's diameter — or about five 

 millions of miles — its volume would be 177 times the 

 sun's volume, and its density only o.oig (water=i). 

 This seems improbable, judging from the known case 

 of Algol, which has a much higher density than this. 

 We may, therefore, conclude, I think, that the great 

 brilliancy of Sirius is probably due to both causes com- 

 bined — namely, a somewhat larger volume and a 

 greater luminosity of surface than the sun, both 

 probably due to its higher temperature. If we assume 

 its density to be the same as that of Algol, say 0.34, 

 we have the diameter of Sirius about 1,860,000 miles, 

 and its luminosity about seven times that of the sun. 



The well-known double star. Castor (a Geminorum), 

 has a spectrum of the same type as Sirius. The orbit 

 is rather uncertain, but Dr. Dobeeck has recently found 

 a period of 346.82 years, with a semi-axis major of 

 5" 756. A doubtful parallax of o'J.igS was found by 

 Johnson. From these data the mass of the system 

 would be only 0.2042 that of the sun. In 1894 the 

 fainter component of the pair was found by 

 Belopolsky to be a spectroscopic binary with a period 

 of about 2.98 days, and an orbital velocity of 20.7 

 miles a second, the companion being relatively dark. 

 If we assume that the components of the spectro- 

 scopic pair are equal in mass I find that its mass would 

 be o.ogii of the sun's mass. Now as the brighter 

 star of the visual binary is one magnitude brighter than 

 the companion, its mass would be — if of the same sur- 

 face luminosity — four times that of the other, or 0.3644. 

 Hence the total mass of the system would be 0.091 i-f 

 0.3644, or 0.4555 of the sun's mass. We may, there- 

 fore, conclude from the spectroscopic observations that 

 the mass of the system is comparatively small. 

 Assuming the masses found above, namely 0.091 1 and 

 0.3644, the areas of their surfaces would be 0.2024 and 



