The Eclipsing Binary V 836 Cygni: Photometric Evidence for an Early Evolutionary Status

J. Astrophys. Astr. (1982) 3, 219 231 The Eclipsing Binary V 836 Cygni: Photometric Evidence for an Early Evolutionary Status R. A. Breinhorst* Sternwarte der Universität Bonn, 5300 Bonn, F R Germany H. W. Duerbeck Observatorium Hoher List der Universitäts-Sternwarte Bonn, 5568 Daun, F R Germany Received 1982 March 24; accepted 1982 May 20 Abstract. Three UBV light curves of the short-period EB-type eclipsing binary V 836 Cyg, observed in 1971, 1976 and 1980, are presented. The instability of the light curve found by previous authors is confirmed. However, the activity was not very strong between 1971 and 1980. From the observed period variation, previous light-curve analysis data and spectroscopic data it is concluded that V 836 Cyg consists of two mainsequence stars, and will undergo rapid mass exchange before terminating the main sequence (case A evolution). Key words: eclipsing binaries period variations mass exchange 1. Introduction V 836 Cyg is an eclipsing binary of EB-type light-curve variability with a relatively short orbital period of 0 653 d. Since its discovery on Bamberg plates (Strohmeier, Kippenhahn and Geyer 1956), and a subsequent photometric investigation by Deinzer and Geyer (1959) in 1957 58, pronounced variations of the light curve have drawn attention to this system which in turn led to an almost regular observational control. In contrast to the earlier results of Deinzer and Geyer depicting a strongly disturbed secondary maximum, the observations of Cester (1963) fit to a more regular light curve with only a modest asymmetry. Cester s orbital solution, based on the classical Russell-Merrill method, yields a contact system. Harris (1968) collected his observations over a relatively long period (1963 1965) which obviously coincided with a phase of irregular brightness variations, and therefore resulted in a strong obser- *Visiting astronomer, Kitt Peak National Observatory, operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation

220 R. A. Breinhorst and Η. W. Duerbeck vational scatter. The more recent observations of Wester (1977) again led to a light curve contaminated by short-term variations. By applying synthetic light-curve techniques, he determined from his orbital solution a state of marginal undercontact. No spectroscopic data have been published hitherto, except for a spectral classification by Hill et al. (1975). Thus the solutions for the essential parameters of the system are vague. It may be surmised, however, that the binary consists of two main-sequence components proceeding in an early evolutionary stage prior to the rapid mass exchange. The present observations were aimed therefore at obtaining complete BV light curves over short time intervals ( t 10 2 P) in order to minimize the influence of superimposed secular brightness variations (see e.g. Bergeat et al. 1981), and to improve the precision of photometric element determination. 2. Observations A first set of two observing runs was obtained in 1971 and 1976 at the Hoher List Observatory with a single-channel UBV photometer (unrefrigerated 1P21 photomultiplier) attached to the 35-cm Cassegrain telescope. Each of these series covers an almost complete, almost instantaneous light curve, the data of both samples being confined to an interval of roughly 100 cycles (or two months). It should be mentioned that while the mechanical photometer construction has been replaced by an improved design in between the identical photomultiplier and filter combination has been retained throughout. A third observing run was performed at Kitt Peak National Observatory in 1980 July, using the No. 3 0 4-m telescope, equipped with a singlechannel standard UBV photometer. Here, an essentially complete light curve was sampled over a period of only 10 cycles. The Hoher List observations were measured against BD + 35 4461 and BD + 35 4460 as comparison and check star, respectively. For the KPNO data set, BD + 35 4497 was chosen as comparison star, occasionally checked against BD + 35 4461. Its small angular distance from the variable improved the measuring speed fairly well, however, at the expense of introducing secondorder extinction coefficients because of its widely differing spectral type. All necessary data on variable, comparison and check stars are given in Table 1. Figs 1 3 show Table 1. Catalogue data of variable and comparison stars. *photometric classification by Harris (1968)

Eclipsing binary V 836 Cygni 221 Figure 1. UBV light curves of V 836 Cyg in 1971, relative to BD + 35 446L. the light curves observed in 1971, 1976 and 1980. The individual observations will be published separately (Breinhorst and Duerbeck 1983). 3. The light curves Some of the previously reported light-curve anomalies (in particular those mentioned by Deinzer and Geyer) are confirmed by the present observations. In the Hoher List observations of 1976 as well as in the Kitt Peak data of 1980, there is a clearly-visible brightness deficiency over a short phase interval on the ascending branch of minimum II, around phase 0 55. The effect is strongly pronounced in the U curves, and is

222 R. A. Breinhorst and Η. W. Duerbeck Figure 2. UBV ligit curves of V 836 Cyg in 1976, relative to BD + 35 4461. almost invisible in the V observations. We further note a light curve asymmetry in the sense m (maximum I maximum II) < 0. Only the Hoher List data of 1971 show an almost regular, nearly symmetric EB-type light curve. However, a pronounced disturbance of maximum II, as observed by Deinzer and Geyer in 1957 58, was never observed in the time interval 1960 1980. Fourier coefficients up to the second harmonics have been calculated for all Β light curves to specify the out-of-eclipse variations. They are normalized by division by (A 0 A 2 ), and are listed in Table 2. They outline possible light curve changes from secular variations of reflection (A 1, A 2 ), ellipticity (A 2 ), and asymmetry (B 1, B 2 ). No dramatic changes are obvious. Mean differences between different light curves are always below 0.01 mag.

Eclipsing binary V 836 Cygni 223 Figure 3. UBV light curves of V 836 Cyg in 1980, relative to BD + 35 4497. From the Β and. V observations of all new data sets, there are clear indications for a flat-bottomed minimum II, i.e. for a short phase of totality during the secondary eclipse. As judged from these observations, the interval of constant light extends over almost 0 05 in phase. Cester (1963), Harris (1968) and Wester (1977) have attempted to solve the light curve. Cester s and Harris solutions are based on the Russell-Merrill method, while Wester tried the Wood and the Hutchings-Hill synthetic light-curve techniques. A summary of the solutions is given in Table 3. While the solutions of Cester, Harris and Wester (Wood model) result in partial eclipses, Wester s Hutchings-Hill solution yields total eclipses, resulting in an occultation during secondary and a transit during

224 R. A. Breinhorst and Η. W. Duerbeck Table 2. Fourier coefficients of the Β light curves of V 836 Cyg. Table 3. Geometric and photometric elements of V 836 Cyg. *RM: Russell-Merrill; HH: Hutchings-Hill. primary minimum. However, the primary minimum of V 836 Cyg does not exhibit a gently curved transit-like shape, as, for example, the similar system TX Cet (Duerbeck and Ammann 1978), but appears to be very acute, indicating a partial eclipse.

Eclipsing binary V 836 Cygni 225 4. Period study A large amount of fairly precise photoelectrically-observed minimum times has been published in the last two decades. All hitherto published minimum-time determinations are compiled in Table 4. This table also includes five primary and two secondary minima, derived from the present observations, which were averaged from individual determinations independently evaluated in each colour. Some of the minima of Deinzer and Geyer, and of Harris differ from the results given in this compilation. Here, the original observations (kindly put at our disposal by Professor Geyer) have been used to re-determine uniformly (by an iterated Kweevan Woerden method), and to possibly confirm the earlier results. With these modifications, all photoelectric minimum times (except for a few results of lower precision, labelled 0 in the table and shown with smaller circles in Fig. 4) were used to determine the improved linear light elements JD (minimum I) = 2441 239 4687 + 0 65341146 E. ± 0005 ± 00000012 The resulting values of (O C) are plotted in Fig. 4. The normal points in this diagram, averaged from adequately grouped individual (O C) data, depict a strictly parabolic distribution of all photoelectrically determined values. A quadratic fit yields JD (minimum I) = 2441 239 4671 + 0 65341169 E+ 1 00 10 10 E 2. ± 0003 ± 00000008 ± 17 The period increase P/P is about 4 7 10 10, with an uncertainty ΔP/P of ± 8 0 10 11. Evidently the earlier photographic minimum determinations do not fit the accurate parabolic (O C) curve. Gross errors, resulting from misidentifications of the epochs of early minimum times can almost safely be excluded. This obvious complication in the (O C) structure prevents any definite conclusion to be drawn on the nature of period variations from the data available at present. A considerable increase in the precision and number of future observations of minimum times is needed to test the following hypotheses. 1. The (O C) pattern is sinusoidal (i.e. periodic) and results from the light-time effect due to the motion of the binary in the orbit of a triple system(apsidal motion in the binary system is excluded because of the constant phase lag of 0 5 Ρ between primary and secondary minimum). Since no complete cycle has yet been covered, the period of the light-time orbit is very uncertain. A rough estimate yields P 1 = 40000 P= 71 5 yr, K 1 = 0 0050 ± 0 0008 d (corresponding to a 1 = 0 86 ± 0 14 AU). If this orbit is coplanar to that of the eclipsing system whose mass is assumed to be 4 M, a third body with m 3 = 0 12 M, a 2 = 26 6 AU is derived, which would be unnoticeable in the spectrum and in the photometric solution. Thus, a third body in an orbit which is not strongly inclined to that of the eclipsing binary is compatible with the (O C) diagram. However, more

226 R. A. Breinhorst and Η. W. Duerbeck Table 4. Minimum times of V 836 Cyg.

Eclipsing binary V 836 Cygni 227 Table 4. Concluded. *See correction in Popovici (1971). Abbreviations: pg = photographic observations pe = photoelectric observations vis = visual observations 0 = zero weight nr = new reduction BBSAG = Bedeckungsveränderlichen-Beobachter der Schweizerischen Astronomischen Gesellschaft-Bulletin (edited by K. Locher)

228 R. A. Breinhorst and Η. W. Duerbeck Figure 4. The (O C) diagram of V 836 Cyg. Crosses, means form two or three photographic minima; large dots, photoelectric minima; small dots, visual minima or photoelectric minima having zero weight. The quadratic (parabolic) ephemeris curve shown in the diagram is a fit to the normal points which were omitted for reasons of clarity. minimum times over a much longer time interval are necessary to prove or to disprove the reality of the light-time orbit. 2. The (O C) data are uniformly represented as a sequence of parabolic segments, as proposed in the theory of Biermann and Hall (1973); see also Hall (1975). This theory has primarily been developed to explain the (O C) pattern of Algol systems which proceed in an evolutionary state posterior to the phase of rapid mass exchange; it requires, via short-term processes of sudden mass transfer from the cooler to the hotter component, the temporary storage of (orbital) angular momentum as rotation of the mass-accreting layers around the primary star, and its subsequent feedback to the orbit. Since the matter is released from the evolved (i.e. less massive) component, the secular period increases, i.e. the series of upwardcurved parabolic sections (each resulting from a short-time period increase due to the feedback of angular momentum to the orbit) is also enveloped by an upwardcurving parabola. Application of this model to an unevolved system requires a downward curvature for the parabolic envelope common to all single parabolic sections, since in the pre-mass-exchange phase the mass-losing component has the larger mass. 5. The evolutionary status of V 836 Cyg The determination of suitable combinations of parameters (luminosity temperature; radius mass) which are subject to sensible changes on the evolutionary track of the star off the main sequence is limited to systems with reliable observational results (see, e.g. Kreiner and Ziolkowski 1978). For binaries actually being in contact, Leung and Schneider (1978) compare the observed orbital period with the corresponding critical period adjusting such a distance A through Kepler s 3rd law that the

Eclipsing binary V 836 Cygni 229 Primary component with its actual (ZAMS, main-sequence or TAMS) radius just fills its critical Roche volume. The corresponding relations, tabulations and references are given in detail by Plavec (1968). Because of the Roche geometry involved, the dependence on the mass ratio q is weak: R 1 /R 2 =(M 1 /M 2 ) 0.46. Therefore a rough estimate of the primary mass, based on spectral classification, may suffice to decide at which evolutionary state the system (actually in contact) is. Since V 836 Cyg is an out-of-contact system with poorly determined elements, none of these methods is applicable. However, from a number of single-lined spectra, the mass function could be derived (Duerbeck and Schumann 1982). The result, f (m) =0 050 ± 0 005, agrees well with the Hutchings-Hill model solution of Wester, where main-sequence stars are assumed. Then, by adopting i=80 o (weighted mean of photometric results),both the individual masses and the separation of the components can immediately be evaluated as a function of the (unknown) mass ratio q (cf. Plavec 1970). A plot of these relationships is given in Fig. 5. It also contains, as a function of q, the fractional radius Y 1 of component 1, constituting an upper limit to the radial extent of the primary, and in addition the radii R 1 of normal ZAMS, main sequence and TAMS stars with corresponding masses. The TAMS and Y 1 lines intersect at q 0 39, or m 1 1 7 m, i.e. for primary masses exceeding this limit (corresponding to spectral types earlier than A9) the radius of component 1 expands beyond the Roche limit and initiates the rapid mass exchange before terminating the mainsequence stage A few conclusions can be drawn. The mass ratio q 0 =0 3l, being at variance with the photometric result (Table 3), uniquely determines m 1 =3 3 m (which is compatible with the ΜΚ classification A0 by Hill et al. (1975), and with Wester s value T eff = 10800 K), and m 2 =1 02m (in agreement with Wester s value T eff 6000 Κ, i.e. G1 V; Koch (1973) also derives, from the surface intensity ratio J 2 /J 1 =0 006(B), a spectral type G1 for the secondary component). We note that the combination of spectroscopic and photometric results yields a secondary radius R 2 =a s A=0 87 10 6 km =1 25 R, which is only modestly in excess of the corresponding G1 V radius. Thus we are safe to state that the system consists of two unevolved main-sequence stars prior to the phase of rapid mass exchange, and is likely to proceed through case A evolution. Since component 1 is almost filling the corresponding Roche lobe, light curve and period variations may be considered as the result of small-scale transient mass flow from the primary component. It is obvious that either case conservative mass transfer onto component 2 and/or mass loss from the system leads to a secular decrease of the systemic angular momentum, and therefore to a shortening of the period. The period increase, as deduced from the parabolic section of the (O C) diagram (Fig. 4), is under due consideration of the earlier photographic minima only a transient phenolmenon and (when interpreted in terms of the Biermann-Hall model as resulting from the restoration of angular momentum on a short dynamical time scale) not in contradiction to an overall secular decrease of the period. Since the available minimum-time observations are too scanty to test any secular period changes, the interpretation of the (O C) diagram by a modified Biermann- Hall theory (involving mass loss from the primary component of an unevolved binary system) remains hypothetical. Future photometric and minimum-time observations supplying more accurate data for an extended (O C) diagram should, however, be supported by spectroscopic observations with advanced detectors to prove the

230 R. A. Breinhorst and Η. W. Duerbeck Figure 5. The individual masses m 1 and m 2 of V 836 Cyg versus mass ratio q for the mass function f (m) = 0 050 and i = 80 in units of solar mass (left side, logarithmic scale). The log m 1 curve is labelled in units of m. Note that the definition of m 1 or a corresponding effective temperature (or spectral type) determines q and m 2. The separation A of the components and the distances X 1 and Y 1 of L 1 from the centre of m 1 as functions of q are given in absolute units of 10 6 km (right ordinate, linear scale). Drawn to scale are the corresponding radii R 1 of normal stars on the ZAMS, TAMS, and standard main sequence (MS). The intersection of the TAMS and the Y 1 curves at q 0 39, m 1 1 7 m defines a lower limit for primary masses undergoing rapid mass loss before terminating the main sequence (case A evolution). As derived from spectroscopic and photometric results, V836 Cyg is found in the interval marked by dashed lines. presence of circumstellar matter and to determine the physical and kinematical properties of mass flow. Acknowledgement It is a pleasure to thank the director and community of Kitt Peak National Observatory for their generous assistance and hospitality, and the referee for his helpful

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