Astronomical Society of the Pacific 295 Notes From

ASTRONOMICAL SOCIETY OF THE PACIFIC 295

NOTES FROM PACIFIC COAST OBSERVATORIES1

Note on the Diameter of By Frank K. Edmondson

The value of the diameter of Antares which is commonly given in textbooks and other places as being equal to 450 solar diameters is based on a parallax of (//0095. This seems to have been obtained by assigning to Antares the mean parallax of the Scorpio-Centaurus Cluster.2 Since both components of the proper motion of Antares agree both in magnitude and direction with nearby cluster stars, and since the radial velocity is also in agreement with cluster stars, such a procedure seems to be quite legitimate. Furthermore, Antares has a seventh magnitude companion of spectral type Β3 which has the same proper motion as Antares. If Antares did not exist, no one would doubt that the companion is a member of the cluster. The probability that a foreground star would show such agreement of motion by accident is extremely small, and one is thus led to the conclusion that the probability that Antares belongs to the cluster is very high. The direct determinations of parallax, however, are seri- ously out of agreement with the evidence which has been given. Professor Schlesinger has very kindly sent me the trigonometric and spectroscópic determinations. They are as follows :

Observatory Parallax McCormick + 0''025 ± 0'/009 Trigonometric Yale 030 .008 Cape of Good Hope .028 .012 Mount Wilson .014 Spectroscopic Victoria .012 Lockyer .010

The values obtained by the trigonometric method are more ac- cordant among themselves than they have any business to be.

1 A few notes from other observatories are included. 2Piibl. A.S.P., 33, 204, 1921.

The accordance of the spectroscopic values is a matter of cali- bration. It seems quite improbable that good modern determinations of parallax should be systematically large by more than twice their probable error. Yet if we accept the hypothesis that Ant ares is a member of the Scorpio-Centaurus Cluster we are led to the conclusion that the trigonometric parallaxes are too large. In view of the interest in this star, it would be quite worth while for parallax observers to keep it on their observing lists. I have computed the diameter, mass, and density correspond- ing to the average of the trigonometric parallaxes, the average of the spectroscopic determinations, and the cluster parallax. They are as follows :

Diameter Mass Density Parallax (Sun = 1) (Sun = 1) (Air = 1)

(Γ028 150 13 %4o .012 360 35 M225 .0095 450 46 1/1820

The masses were computed from the bolometric magnitudes obtained by subtracting 1^6 from the visual absolute magnitudes. This corresponds to a temperature of 3100°. The trigonometric absolute magnitude is —1^6, whereas the spectroscopic absolute magnitude is —3^4. Taking the spectroscopic value as it stands, Antares is about five times fainter than the average star showing the same spectral peculiarities, and is, therefore, about .2 as massive.1 The mass would therefore be equal to seven solar masses, or about half the mass of an average star of the same brightness. The opposite has been found true in the case of Arcturus. This reasoning is, of course, meaningless if the cluster parallax has been used to calibrate the spectroscopic reduction curves. To sum up what has been said, as far as our present knowl- edge goes there is a very high degree of probability in favor of either 0^/0095 or 0'Ό28 as the parallax of Antares. If the former is true, Antares is the largest known star. If the latter is true, it is surpassed by'ct Herculis ( ?), 0 Ceti, and Betelgeuse. Paral-

1 Russell, Dugan, and Stewart, Astronomy, page 875.

lax observers are strongly urged to keep Ant are s on their observing lists until sufficient evidence is accumulated to settle this question.

Lowell Observatory Flagstaff, Arizona October 19,1933

On the Advance of Periastron in Binaries By W. J. Luyten

In a recent investigation1 of the system 13 Ceti, where the observations seemed to indicate a rapid rotation o£ the line of apsides in the short-period spectroscopic system, I tentatively explained this as caused by the ellipticity of the stars owing to rotation and mutual tidal action. Comparison of the observed rotation with that to be expected—using the formula applicable to an oblate planet and a satellite, which formula, of course, gives too slow a rotation when applied to tidally deformed stars—indicated that the result is of the right order of magnitude. Several years ago Russell2 derived a formula for the advance of periastron in eclipsing binaries which did take into account the tidal deformation and applied it to the case of Y Cygni. Furthermore, while my article was in press, a series of papers appeared by Chandrasekhar3 on the equilibrium of distorted polytropes, in which the question of the tidal deformation of such close binary systems was investigated from a theoretical point of view ; in the subsequent discussion4 it was brought out that only in Y Cygni and in U Monocerotis did the advance of periastron resulting from such ellipticities appear to be definitely established, and in the latter case the period of rotation was 1,000 years. As it is clear from both Russell's and Chandrasekhar's work that the crucial unknown in these cases is the internal density

1 Ap. J., October, 1933 (in press). 2 M.N., 88, 641, 1928. 3 Ibid., 93, 390, 449, 462, and 539, 1933. 4 The Observatory, June 1933.