THE SPECTROGRAPHIC ORBIT OF THE BRIGHTER COMPONENT OF THE VISUAL SYSTEM ZETA HERCULIS. By Louis Berman

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1 22 PUBLICATIONS OF THE THE SPECTROGRAPHIC ORBIT OF THE BRIGHTER COMPONENT OF THE VISUAL SYSTEM ZETA HERCULIS By Louis Berman Certain minute peculiarities in the orbital motion of the wellknown double star, Zeta Herculis (a = 1 h 3 m, ô = 31 4P ; mag. 3.0,.5; sp. GO,?), have in the past led various investigators to raise the question regarding the existence of a third invisible component forming part of the system. Nearly a quarter of a century ago G. C. Comstock, 1 in his excellent analysis of the visual material then available, drew the conclusion that systematic errors of observation could, within the limits of accidental error, account for the small observed deviations from true elliptic motion. So far as this writer is aware, no attempt has been made since then to re-establish the thesis that a third member attends the system. Although enough radial velocities of the brighter component have been secured during the past half-century to make possible a determination of the spectrographic orbit of the system, the character of the data does not readily lend itself to an investigation of the type seeking to prove or disprove the existence of a third member. Undoubtedly, the combination of future radial velocities and photographic measurements of the pair should ultimately settle the problem with some degree of finality. In Table I are summarized the known radial velocities of the brighter component reduced to the Lick system. 2 The lettered footnotes at the bottom of the table refer to the observatory at which the velocities were obtained, the type of spectrograph employed, and the systematic corrections to the Lick system. All measures deviating by more than 3 from the velocity curve, as indicated by a line under the values, were rejected. 1 G. C. Comstock, A.J., 30, 13, Pub. Lick Obs., 1, xxxi, 128.

2 ASTRONOMICAL SOCIETY OF THE PACIFIC 23 The Pulkowa corrections were derived by shifting the 183 and 187 series each vertically with respect to the velocity-curve established from the other velocity data so as to obtain the best fit. It was found that the Lick-Pulkowa corrections as given in Volume XVI of the Publications of the Lick Observatory (+2.4 ) were obtained from only two stars in common with the Lick observers and required a correction. TABLE I Summary of Radial Velocities Date Velocity Date Velocity Date * C C d ' Velocity -.7'.3.0* Date Velocity -.* " a Pulkowa (Belopolsky), A.N., 133, 22, 183; 3-prism; Lick-Pulkowa, 0.0. & Cambridge (Newall), L.O.B., 1, 15, 102; Lick-Cambridge; c Pulkowa (Belopolsky), Mitt. Pulk., Ill, 220, 110; 3 -prism; Lick-Pulkowa, 1.3. d Bonn, Ap. J., 27, 315, 108; 3-prism; Lick-Bonn, 0.2. Columbus (Maag), Ap. J., 21, 318, 105; 3-prism; Lick-Columbus, 2.0. /'Victoria, by private correspondence; 1-prism; Lick; 3-prism; no correction. h Mount Wilson, by private correspondence; coudé spectrograph; no correction.

3 24 PUBLICATIONS OF THE The data of the preceding table were incorporated to form the weighted annual means presented in the second and third columns of Table II below. Since the interval covered by the velocities extends over little more than the period of the binary, TABLE II Normal Places Number Date Radial Velocity Total Weight o c (Final Elemente) it was considered inadvisable to include the period as one of the unknown elements to be determined; hence Silbernagl s value 3 of the period, years, derived from the visual orbit, was used in calculating the yearly averages. The following system of weighting the individual velocities based on a scale was adopted in conformity with (1) the type of spectrograph employed and (2) the reliability of the data : Pulkowa, 2 ; Cambridge, 1 ; Bonn, 3 ; Columbus, 1 ; Victoria, 2 ; Lick, 3 ; Mount Wilson, 3. The fourth column of 8 E. Silbernagl, A.N., 233, 145, 128.

4 ASTRONOMICAL SOCIETY OF THE PACIFIC 25 Table II gives the combined weight of all the observations included in each yearly mean according to the method just described. The entries of Table II were subsequently adopted as the normal places in the final derivation of the spectrographic elements. Following the usual procedure, an ephemeris was computed with the aid of a preliminary set of elements, and differential coefficients were derived preparatory to a least-squares reduction. The solution of the normal equations led to the following final spectrographic elements : Spectrographic Elements T ±0.002 P = years <? = ± ± 2.52 y =.8 K = 3.81 ± 0.41 a sin i 5.14 X 10 s km Visual Elements 4 T= P years e 0.4 œ= 114?5 i = 4 Q = a = 1'.'34 For purposes of comparison, the visual elements are also presented. The probable error of a single observation of radial velocity is ±0.50. The computed velocity together with the observed velocity data (Table II, columns 2 and 3) and the residuals (Table II, column 5) have been plotted in the diagram shown below (Fig. 1). Although the individual velocities exhibit a larger scatter than would ordinarily be tolerated for an object of this spectral type (GO), it is doubtful in view of the heterogeneous and rather limited spectrographic material available, whether any actual significance can be attached to the distribution of even the mean place residuals shown in the diagram. However, there may be noted a bare suggestion of sinuosity, possibly in period of about ten years. Comstock, himself, pointed out that the small deviations occurring in the visual orbit could, without benefit of systematic correction, be represented by the circular motion of an invisible companion with a periodic time of 18 years. 4 E. Silbernagl, A.N., 233, 145, 128.

5 2 PUBLICATIONS OF THE Attention may be directed to the single 12 Lick observa- tion which is noteworthy because of its large residual. This is also true of the Lick observation. While several other velocities from different sources show similar discrepancies, we have mentioned the Lick observations because of the habitual carefulness and accuracy with which they are generally secured * ) ii T 1 T'l I 1 I 1 I 1 III 1 I»"ITT I I ri r I i'i I'I Tin II I I I \ i IT i i I i~i I i I T"i"r T I + L oo V-* * --»! _2.qLi-i i t i I i I I * I i» I I.i-i-.l-i.-i I -I- i I I >» i» * I i» I» i 1» i i i i» 1 i till I I I Year Fig. 1. Velocity-curve and residuals of the brighter component of the visual binary, Zeta Herculis. Nevertheless, so far as the present radial velocities are concerned, we must conclude that the presence of a third body revolving about the brighter component of Ç Herculis is not definitely indicated. This does not, of course, exclude the possible existence of an invisible companion revolving about the fainter visual component.

6 ASTRONOMICAL SOCIETY OF THE PACIFIC 27 From the known mass ratio of the system it is possible to derive the spectrographic parallax. Thus y, _ nib a" X X 10 8 = Q m V M a A înb where = 0.387, the mass ratio 5 of the fainter companion M to that of the total mass, a" = l'/34, the semi-major axis in seconds of arc, and a A 8.05 X 10 8 km, the mean separa- tion of the primary from the center of gravity of the pair in kilometers. For comparison we quote the value of p = O'.TIO (trigonometric) and p = O'.'IOO (spectroscopic) as compiled from eleven different sources according to Schlesinger s Gen- eral Catalog of Stellar Parallaxes. The mean distance between the components is very nearly 14 astronomical units ; the fainter companion is, on the average, 8. astronomical units distant from the center of gravity of the system. It may be of interest to mention that the period of this spectrographic orbit is one of the longest known at the present time. We wish to express our indebtedness to Dr. J. H. Moore of the Lick Observatory for his courtesy in rendering available the necessary material for this investigation ; also to Dr. J. A. Peirce and to Dr. O. C. Wilson for their velocity contributions from the Dominion Astrophysical Observatory and Mount Wilson Observatory, respectively; and finally to Harold Weaver of the Students Observatory at Berkeley for his kindness in measuring the Mount Wilson coudé spectrograms. San Francisco Junior College San Francisco, California November 20,140 5 P. Van de Kamp, Pub. Amer. Astr. Sac., 10 (No. 1), 30, 140.