ISBN 963 8361 32 8 HU ISSN 0238 - 2091
CONTENTS page List of participants ...................................................................232 Preface ................................................................................233 K. WLODARCZYK: The accretion disc in OY Car during rise to outburst ....................235 R. HUDEC, B. VALNICEK, J. TREMKO, S. ROSSIGER, W. GOTZ, W. WENZEL, L. PATKOS and Z. KRAICHEVA: Dip features in the light curve of TT Arietis ................239 Z. KRAICHEVA, A. ANTOV, V. GENKOV: Photometric behavior of the X-ray source TT Ari during 1985-1986. .......................................................243 G.A. RICHTER: New statistics on dwarf novae ............................................249 K. WLODARCZYK: On the eclipses of white dwarfs in dwarf novae ..........................253 E.A. KARITSKAYA, N.G. BOCHKAREV: Starlight re-emission and scattering by a precessing accretion disc relevant to the parameters of the Cyg X-1=V1357 Cyg X-ray binary .................................................255 I.L. ANDRONOV: Observational evidence on the asymmetry of the accretion columns in a close binary system .......................................................261 A.M. CHEREPASHCHUK: Close binary systems in late evolutionary state ....................265 M.I. KUMSIASHVILI, V.O. KAKHIANI: Results of photometric observations of V 533 Herculis .................................................................267 L. PATKOS: Previous optical flare in the short period RS CVn system SV Cam .............271 J.M. KREINER, J. TREMKO: Period changes in the close binary system QQ Cassiopeiae ......275 W. GOTZ: Optical behaviour of the polar AM Herculis ....................................279 V.G. KARETNIKOV and E.V. MENCHENKOVA: Spectral peculiarities of V 367 Cygni - a close binary system at the stage of rapid mass exchange ......................285 T. HEGEDUS: Some remarks on eclipsing binaries seeming to be inconsistent with general relativity ........................................................289
LIST OF PARTICIPANTS BULGARIA - Z. Kraicheva CZECHOSLOVAKIA - R. Hudec, - J. Tremko G. D. R. - W. Gotz - G. Richter HUNGARY - T. Hegedus - J. Nuspl - L. Patkos - L. Szabados POLAND - J.M. Kreiner - K. Wlodarczyk - J. Ziolkowski U.S.S.R. - A. Cherepashchuk - E. Karitskaya
P R E F A C E The Symposium "Variable Phenomena in Close Binary Stars" was held in Budapest, Hungary, between 7 and 10 March 1988 at Konkoly Observatory, as part of the biennial conference series of the multilateral cooperation "Stellar Physics and Evolution" subproject "Binary Stars". Binary systems represent one of the most interesting, exciting and puzzling objects in modern astrophysics. In particular, interacting binaries have become very important in recent years. Very many phenomena to be explained in connection with dwarf novae, novae, Wolf-Rayet stars, symbiotic stars, etc. need the assumption of interactions between binary star components. Over the past decades the concept of mass exchange and mass loss has become one of the most fruitful ideas in astronomy. Besides these very fruitful theoretical developments we can recognize enormous progress in observational methods too. Unfortunately not all of these new techniques are available to us. Nevertheless, especially in X-ray astronomy, in the extension of classical photometry to longer wavelengths and in high time-resolution photometry our development is significant. In recent years we have also seen some progress in computer technique both with regard to observations and to the reduction of data. We now present the proceedings of the conference. I should like to thank all those who assisted in organizing the conference and in producing this volume. Finally our thanks go to the Hungarian Academy of Sciences for their financial support of the conference.
Var. Phenomena in Close Bin. Stars
Com. Konkoly Obs. Hung. Akad. Sci.
10, Part 7,(No.93), Budapest 1989.
THE ACCRETION DISC IN OY Car DURING RISE TO OUTBURST
K. Wlodarczyk
Pedagogical University Cracow, POLAND
The eclipsing binary OY Carinae with the orbital period of 91 minutes belongs to
the class of ultra-short period dwarf novae of SU UMa type. The eclipses of the accretion
disc permit one to determine its dimensions and surface brightness distribution. The
observations of OY Car obtained by Vogt (1983) were used. These unique observations contain
two highly symmetric eclipses recorded during rise to a normal outburst (E=2) and shortly
after maximum light was reached (E=15). These two eclipses differ strongly in their shapes.
This is connected with the changes of disc brightness distribution at the beginning of an
outburst. The highly symmetric eclipses indicate that the surface brightness distribution
of the disc is axisymmetric, so we can describe it by a simple function f(r). Other unknown
parameters are the disc's outer radius r_d and the fractional luminosity of the white dwarf
l_1. The principal geometric parameters, namely the mass ratio q, the inclination angle i
and the radius of the white dwarf r_1 are also unknown. To perform the solution of the two
eclipses a new numerical code, described in detail in a previous paper (Wlodarczyk 1986),
was used.
This code - applicable to the case of symmetric eclipses - is based on the
conventional model of dwarf novae, containing a Roche lobe filling cool star and a
mass-gaining white dwarf, surrounded by an accretion disc. The disc is stretched in the
orbital plane from r_1 to r_d. In the simplest model (d_1) the disc is assumed to be flat
with the thickness h=0. We first estimate the geometric parameters q and i. To do this the
second eclipse (E=15) was analysed and the distribution of sigma(q,i) was found, where sigma
is the mean square deviation from observations. The function sigma(q,i) presented in Fig. 1
has two minima but only one of them lies on the line i(q) established for OY Car by Cook
(1985). We adopt the values of q and i -
Figure 1.
corresponding to this minimum (q = 0.30, i = 76.9°). Such parameters are very close to those
inferred by Bailey and Ward (1981).
For our value of q the relation r_1(q) (Cook 1985) gives r_1 = 0.013. The further
calculations were made in two steps. The final solution of the two eclipses is presented in
Fig. 2. It is clearly seen that during rise to a normal outburst (E=2) the outer parts of
the accretion disc became the dominant source of light in the system. Such photometric
behaviour is consistent with the model of dwarf nova eruption presented by Smak (1984) in
case A. Shortly after maximum the distribution f(r) roughly resembles that known from the
stationary accretion disc model but could not be interpreted as a model with a constant
accretion rate m. A more detailed analysis of OY Car is due to be published in Acta
Astronomica. This work was supported in part by the Polish Academy of Sciences (grant
CPBP - 01.11).
Figure 2.
References:
Bailey, J., Ward, M., 1981, M.N.R.A.S., 194, 17P.
Cook, M.C., 1985, M.N.R.A.S., 215, 211.
Smak, J., 1984, P.A.S.P., 96, 5.
Vogt, N., 1983, Astron. Astroph., 128, 29.
Wlodarczyk, K. 1986, Acta Astron., 36, 395.
Var. Phenomena in Close Bin. Stars Com. Konkoly Obs. Hung. Akad. Sci. 10, Part 7, (No.93), Budapest 1989. DIP FEATURES IN THE LIGHT CURVE OF TT ARIETIS R. Hudec^1, B. Valnicek^1, J. Tremko^2, S. Roessiger^3, W. Goetz^3, W.Wenzel^3, L. Patkos^4 and Z. Kraicheva^5 1 Astronomical Institute of the Czechoslovak Academy of Sciences, Ondrejov Czechoslovakia 2 Astronomical institute of the Slovak Academy of Sciences, Tatranska Lomnica, Czechoslovakia 3 Central Astrophysical Institute of the Academy of Sciences of the G.D.R. Sonneberg Observatory, G.D.R. 4 Konkoly Observatory, Budapest, Hungary 5 Department of Astronomy with National Astronomical Observatory of the Bulgarian Academy of Sciences, Sofia, Bulgaria Information on dip features in the optical light curve of TT Arietis, observed both in optical and X-ray wavelengths, is presented. These features are probably related to mass exchange in the system. A coordinated program for detailed observations and analysis of light drops is proposed to better understand the nature of the source. TT Ari is thought to be an accreting (magnetic?) white dwarf in a close low-mass "nova-like" binary, the orbital period of. which amounts to about 3.3 hours. In 1985, a complex coordinated observation program was run in the Intercosmos cooperation involving ground-based instruments as well as the EXOSAT X-ray satellite (Wenzel et al., 1986, Hudec et al., 1987). TT Ari AS DIPPING SOURCE The existence of narrow X-ray and related optical drops in the orbital light-curve of TT Arietis was first mentioned by Jensen et al. (1983) as a result of coordinated X-ray (Einstein) and optical observations. The observed wavelength-dependence of the decrease in X-rays has indicated that photoelectric absorption was probably responsible for the observed decrease. However, only one such event was detected. More details were obtained during the coordinated program of EXOSAT X-ray and optical observations in 1985 (Wenzel et al. 1986 and Hudec et al. 1987). Two well pronounced X-ray drops were revealed within the 11h monitoring interval. For one of the dips simultaneous optical data were obtained showing an analogous feature. Similar dips were also revealed in some parts of the additional optical data (e.g. Rossiger, 1987, Kraicheva et at. 1987). Until now, more than 10 well pronounced dips have been revealed at optical wavelengths with typical durations between 1 and 10 minutes and amplitudes between > 0.3 and ~2 mag. In X-rays, 3 well pronounced dips have been observed lasting ~15 min. and representing more than 90% decrease of the total X-ray flux of the source. Thus the central X-ray source in the system was almost fully obscured during these intervals. The reality of the presence of these narrow absorption features seen both in X-rays and optical light is now supported by the detection of more than 10 such events and also by the simultaneous detecting of dips in both spectral ranges. The duration of X-ray dips is longer than that of those simultaneously observed in the optical region (Einstein satellite X-ray/optical: 17/7 min EXOSAT: 15/8 min.). Analysis of the X-ray light curve based on EXOSAT observations has revealed a possible dip recurrence period of 3h 33m, however, the third dip is less pronounced. No dip recurrence could be found in the Einstein X-ray data because of many gaps in the data set. In the optical region, the dips seem to occur randomly with no clear relation to the phase of photometric or spectroscopic period. Some of the decreases exhibit double, triple or even more complex nature. The dips are probably caused by photoelectric light absorption of the main light source in the TT Ari system (disc component) by structures related to mass exchange in the system. The second light source in the system (the secondary star component) is relatively faint, below 16.5 mag. in B. This upper limit was derived from faintness of the whole system during the very low state (superminimum) observed before 1985 when accretion probably stopped. Thus the strong drops exceeding 1 mag. may also be caused by this. Need of more data Although the reality of dips in the curve of TT Ari seems to be proved, more observational data are needed for a better understanding of this phenomenon. We thus suggest that another stage of coordinated ground-based optical observations of TT Ari be carried out in the near future, e.g. during the observing seasons Summer/Autumn 1988 or 1989. The second main aim of this program should be a more detailed monitoring of changes between the different shapes of orbital light curves of TT Ari as mentioned by Wenzel et al. (1986). References: Hudec, R., et al.: 1987, Astrophys. Space Science 130, 255. Jensen, K.A., Cordova, F.A., Middledith, J., Mason, K.O., Grauer, A.D., Horne, K., Gomer, R.: 1983, Ap. J. 270, 211. Kraicheva, Z., Antov, A. and Genkov, V.: 1987, Inf. Bull. Var. Stars No. 3093. IBVS 3093 Roessiger, S.: 1987, Inf. Bull. Var. Stars No. 3007 IBVS 3007 Wenzel et al.: 1986, Astr. Inst. of the Czechosl. Acad. Sci. Preprint 38 p:1-44.
Var. Phenomena in Close Bin. Stars
Com. Konkoly Obs. Hung. Akad. Sct.
10, Part 7, (No.93), Budapest 1989.
PHOTOMETRIC BEHAVIOR OF THE X-RAY SOURCE TT ARIETIS
DURING 1985 - 1986,
Z. Kraicheva, A. Antov, V. Genkov
Department of Astronomy with National Astronomical Observatory of the
Bulgarian Academy of Sciences, Sofia, Bulgaria
The belonging of TT Arietis to VY Scl objects included in our investigation
programme, prompted us to initiate observations of this system in August 1985 when the
extended programme of coordinated X-ray and optical observations of TT Arietis began.
During the past three seasons, besides estimates of the brightness of the star in the
standard UBV system, the behavior of the object for 3 hours during the night of August
22/23 1985 was followed and seven observational runs were carried out in the "u" region for
the period 1986-1987. The observations were performed using a photoelectric photometer
attached to the 60 cm Cassegrain telescope of the National Astronomical Observatory
employing a photon counting technique. Star "c" (see Wenzel et al. 1986) served as the
comparison star. For transformation of the instrumental u,b,v stellar magnitudes to the
standard UBV magnitudes during 1987 the relations
Delta V - Delta v + 0.1 Delta (B-V)
_
Delta (B-V) - 0.89 Delta (b-v) + 0.034 Delta (b-v) X
_
Delta (U-B) - 0.89 Delta (u-b) + 0.062 Delta (u-b) X
were used. The integration time was 10 sec. The results of these observations are the
following:
1. During all the nights of the observations TT Ari was near maximum
Figure 1.
light: this may be seen from Fig. 1. where all our estimates of the brightness of the star
are plotted. From this figure it is seen too, that the brightness of the star fluctuates
around an increased maximum mean value from 1985 to 1987. The mean of the resulting points
yields the following magnitudes for TT Ari in 1985: V = 10.85, B = 10.75, U = 9.86. For
1987 the mean magnitudes are V = 10.69, B = 10.57, U = 9.58. An increase of average
brightness in 1987 by 0.16 mag in V, 0.18 mag in B and 0.28 mag in U in comparison to 1985
can be suspected. The difference from average UBV magnitudes for 1985 given in a previous
paper (Kraicheva et al. 1987) and this present paper is due to the inclusion of an
additional 24 estimates of brightness from 22/23. 08. 1985. In our opinion this gives a
clearer idea for the interval of variations of the brightness.
Table 1.
Magnitude estimates of TT Arietis during 1987
J.D. 244... V B-V U-B
7032.4803 10.70 ±0.01 -0.14 ±0.02 -0.99 ±0.01
.4908 10.68 ±0.01 -0.09 ±0.01 -0.96 ±0.01
.5024 10.60 ±0.02 -0.04 ±0.02 -0.95 ±0.01
.5181 10.62 ±0.01 -0.09 ±0.02 -1.00 ±0.02
7033.4502 10.66 ±0.02 -0.12 ±0.03 -0.99 ±0.01
.5786 10.70 ±0.01 -0.11 ±0.01 -0.99 ±0.02
.5852 10.72 ±0.01 -0.15 ±0.02 -1.05 ±0.01
.5887 10.65 ±0.01 -0.09 ±0.01 -0.99 ±0.01
7039.4425 10.58 ±0.01 -0.13 ±0.01 -1.02 ±0.01
.5610 10.61 ±0.01 -0.12 ±0.02 -0.98 ±0.03
.5664 10.69 ±0.02 -0.14 ±0.03 -0.99 ±0.02
7040.3920 10.65 ±0.01 -0.11 ±0.02 -1.10 ±0.05
.5470 10.79 ±0.01 -0.11 ±0.01 -1.00 ±0.01
.5549 10.69 ±0.01 -0.08 ±0.02 -0.99 ±0.01
.5608 10.69 ±0.01 -0.09 ±0.02 -1.03 ±0.01
7085.4282 10.71 ±0.02 -0.12 ±0.02 -0.96 ±0.02
.4339 10.73 ±0.02 -0.11 ±0.02 -1.00 ±0.02
.4394 10.71 ±0.01 -0.12 ±0.02 -0.98 ±0.02
7123.3657 10.74 ±0.02 -0.12 ±0.02 -0.99 ±0.03
.3706 10.70 ±0.01 -0.14 ±0.01 -0.89 ±0.03
7137.2016 10.78 ±0.01 -0.16 ±0.02 -0.94 ±0.01
.2071 10.82 ±0.01 -0.12 ±0.01 -0.94 ±0.01
.2123 10.79 ±0.01 -0.16 ±0.01 -0.95 ±0.01
7142.3450 10.59 ±0.01 -0.17 ±0.02 -0.95 ±0.02
.3497 10.63 ±0.01 -0.20 ±0.02 -0.94 ±0.04
7177.2586 10.68 ±0.01 -0.13 ±0.01 -0.96 ±0.02
.2662 10.64 ±0.02 -0.19 ±0.03 -1.06 ±0.01
.2726 10.69 ±0.02 -0.11 ±0.02 -0.95 ±0.01
7179.2072 10.64 ±0.01 -0.09 ±0.02 -1.01 ±0.02
.2131 10.73 ±0.01 -0.11 ±0.01 -0.95 ±0.02
Figure 2.
2. The colour indexes on the individual nights during these 3 observing seasons
were in the intervals -0.04 to -0.2 for (B-V) and -0.84 to -1.0 for (U-B), but in 1987 a
few (U-B) values exceeding -1.0 were observed (Table 1 in Kraicheva et al. 1987 and Table 1
in this paper).
3. The three-colour measurements from August 22/23 1985 show a well-expressed
maximum. The start and the end of the observations are in the neighborhood of brightness
minima (Figure 1 in Kraicheva et al. 1987). The wave shaped variations are 0.25 mag in V
and 0.32 mag in B and U. This is in agreement with the results of coordinated observations
(see Hudec et al. 1987).
4. The observing run during the night of November 2/3 1986, besides rapid variations
with an amplitude up to 0.25 mag, showed an unusually deep dip in the brightness (Delta u
~2.3 mag) of about 10 minutes long. Seven minutes later a new dip of the of the brightness
with an amplitude up to 0.8 mag and a duration of about 10 minutes occurred (see Kraicheva
et al. 1987). One of the purposes of our observations during 1987 was to test the reality
of these "anti flares". Details concerning the observations can be found in Table 2.
TABLE 2 Observing runs of TT Arietis during 1986 - 1987
Date Start time Length Integration A max t
(UT) time (mag) (min)
(s)
1986 Nov 2 21h 31m 1h 06m 10 0.28 3
1987 Aug 25 23 30 2 05 10 0.25 5
1987 Aug 31 23 10 1 50 10 0.30 5
1987 Sep 1 21 55 2 50 10 0.28 7
1987 Dec 7 21 15 1 20 10 0.25 3
1987 Dec 12 20 35 1 15 10 0.45 6
1988 Jan 18 17 35 2 25 10 0.32 5
Figure 3.
Figure 4.
Generally for the six 1987 nights the star was observed for 11h 40m. For this time
only twice did we observe a decrease of brightness larger than 0.4 mag. The observations
during the night of Sep 1/2 1987 began with a dip in the brightness up to 0.8 mag, that can
be seen in Fig. 2 where a portion of the light curve of TT Ari on this night is shown. The
star reached the maximum light for 3 - 4 minutes. The second dip of the brightness, with an
amplitude 0.6 mag, was observed during the night of December 7/8 1987 (Fig. 3). For the
first 6 - 7 minutes the star decreased in brightness by 0.2 mag and in the following 2
minutes it decreased further by 0.4 mag. For the next 3 minutes the star reached the
maximum light again. Rossiger (1987) also observed a deep dip in brightness up to 0.9 mag
in the "b" region.
5. All our observing runs during 1987 show rapid variations of the brightness with
maximum amplitude for separate runs from 0.25 to 0.45 mag. Figure 4 shows the run on
December 12. During this night the maximum amplitude reached 0.45 mag. The maximum
amplitudes for the other runs are given in column 5 of Table 2. In column 6 of the same
table the time scales of those changes are presented. It can be seen that the brightness
of the star varies by several tenths of the magnitude for time scales of 3 - 7 minutes.
References:
Hudec, R., et al. 1987, Astrophys. Sp. Sci., 130, 255.
Kraicheva, Z., Antov, A., Genkov, V., 1987, I.B.V.S. No. 3093. IBVS 3093
Rossiger, S., 1987, I.B.V.S. No. 3007. IBVS 3007
Wenzel, W., et al. 1986, Astron. Inst. of the Czechosl. Acad. of Sci.
Preprint 38, p.:1 - 44.
Var. Phenomena in Close Bin. Stars
Com. Konkoly Obs. Hung. Akad. Sci.
10, Part 7,(No.93), Budapest 1989.
NEW STATISTICS ON DWARF NOVAE
G. A. Richter
Zentralinstitut fur Astrophysik der Akademie der
Wissenschaften der DDR, Sternwarte Sonneberg
By processing the data of the 4th edition of Ritter's (1987) Catalogue of
Cataclysmic Binaries... (and a few additional items of information) I rederived some
statistical relations. Let P be the orbital period: M_2 and R_2, secondary mass and radius:
and C, the cycle length.
Owing the Roche conditions, P is closely connected with R_2, and the rather well
defined log P - M_2 curve (Fig. 1) shows that the secondary component
Figure 1.
comes very near to the mass-radius relation of the main sequence stars. The white dwarf's
masses affect this relation only slightly. The deviations occurring with GK Per (and
perhaps AE Aqr and BV Cen) indicate that their secondaries are in a process of evolution.
Much less pronounced however is the Kukarkin-Parenago relation, which using only
the Ritter data, turns out to have the form of
A = 0.5 + 1.85 log C
(see Fig. 2 top). The large dispersion of the dots cannot simply be put down to the
inaccuracy of A and C. In point of fact, it is interesting to observe that the dots lying
below the regression line mainly correspond to either large or small values of P, while
those lying above the line correspond to values of P that are near the much discussed
period gap between about 2h and 3h. In a word, we are being confronted with an
Figure 2.
A - log P - log C relation. Thorough analysis led, by means of linear regression and
neglecting EX Hya, to these results (Fig. 2 bottom):
A = -1.4 + 5.5 log P + 2.25 log C (P <= 2h)
A = 2.4 - 3.5 log P + 2.25 log C (P >= 3h)
By plotting log P against log C and taking the brightness amplitude A as the
parameter the correlations become even more obvious (Fig. 3). It
Figure 3.
is remarkable that for each A interval, C has a minimum near the period gap. (The dotted
lines through the period gap are drawn only for clarity's sake). The results can be
represented in the following form (Fig. 4.):
Figure 4.
log P - 0.28 - 0.10 (log C - 0.30 A) (P <= 2h)
log P - 0.35 + 0.64 (log C - 0.30 A) (P >= 3h)
EX Hya largely deviates from this relation. It is an extreme intermediate polar, surely
having a disturbed accretion disk. Figure 3 shows that for fixed P, there are objects of
very different values of A and C. They differ in their mass transfer rates, m, a factor of
more than 100. This effect was already discussed in detail by Patterson (1984). The point
is: What is the reason for objects of similar physical and geometrical properties differing
so largely in m? Perhaps this phenomenon is due to the varied efficiency of magnetic braking
- or the objects are living in different states of the "hibernation cycle" of novae (if
the hibernation theory is taken to be correct, see for example Shara et at. (1986). Another
question is: Why do objects of the same amplitude show a minimum of the cycle length near
the period gap? The answer depends on the position you argue from. According to the disk
instability hypothesis of dwarf nova eruptions, near the accretion disc must have a minimum
in its capability for storing matter. According to the fluctuating mass transfer hypothesis,
however, the secondary in systems near the period gap must become dynamically unstable in
shorter intervals, but smaller in quantity. One day, perhaps, a theoretical interpretation
of our findings will help to decide which of the two hypotheses is in accordance with fact,
and which is the real cause for the existence of the period gap.
References:
Patterson, J., 1984, Astrophys. J. Suppl. Ser. 54, 443.
Ritter, H., (1987) Astron. Astrophys. Suppl. Ser. 70, No. 3, 335.
Shara, M.M., Livio, M., Moffat, A.F.J., Orio, M., 1986, Astrophys J. 311, 163.
Var. Phenomena in Close Bin. Stars
Com. Konkoly Obs. Hung. Akad. Sci.
10, Part 7, (No.93), Budapest 1989.
ON THE ECLIPSES OF WHITE DWARFS IN DWARF NOVAE
K. Wlodarczyk
Pedagogical University, Cracow, Poland
There are three ultra-short period dwarf novae - HT Cas, OY Car and Z Cha - in which
the white dwarf is totally eclipsed. This effect is clearly seen only during quiescence
when the fractional luminosity of the white dwarf is biggest. Unfortunately, the total
occultation of the white dwarf is superimposed on the eclipses of an accretion disc with a
bright spot. Consequently, it is very difficult to reconstruct and to select the detailed
shape of the eclipse of the primary star. The eclipse of the white dwarf contains
information on the nature of the central object at the accretion disc. Due to disc
accretion we might expect that the central star has a bright equatorial zone. Such a white
dwarf was found in Z Cha by Smak in 1986. In general, the central object could be the
typical white dwarf or a white dwarf with its lower hemisphere occulted by an optically
thick disc. It could also be a white dwarf surrounded by a boundary layer or it could be a
star with bright polar caps due to a strong magnetic field. A combination of these cases
could also be considered.
In this paper theoretical eclipse profiles and their derivatives are calculated for
the following different configurations of the central object (Fig. 1):
a1) a white dwarf with the limb darkening coefficient x = 0
a2) a white dwarf as above but its lower hemisphere is occulted by a dark disc
Figure 1.
a3) a white dwarf with a bright equatorial boundary layer: in this case the
surface brightness distribution was adopted in the form I ~ cos^n Theta where Theta is the
latitude measured from the equator of the white dwarf, and the width of the bright belt is
then defined by the exponent n
a4) a white dwarf with bright polar caps: in this case I ~ sin^n Theta
Var. Phenomena in Close Bin. Stars Com. Konkoly Obs. Hung. Akad. Sci. 10. Part 7, (No.93), Budapest 1989. STARLIGHT RE-EMISSION AND SCATTERING BY A PRECESSING ACCRETION DISC RELEVANT TO THE PARAMETERS OF THE Cyg X-1 = V1357 Cyg X-RAY BINARY E.A. Karitskaya Astronomical Council of the Academy of Sciences, Moscow, U.S.S.R. N.G. Bochkarev Sternberg State Astronomical Institute, Moscow, U.S.S.R. Photometric and polarimetric variations resulting from re-emission and scattering starlight by an oblique precessing accretion disc are considered. From analysis of observational data of Cyg X-1 it follows that the disc is optically thick and precesses towards orbital motion. The scattering is not important (<= 10% in B band) for intensity variations but it produces some polarimetric effects. The disc radius is r_d = 0.12-0.15 a (where a is the distance between the component centres-of-mass), i.e. the disc fills as little as 40-50% of the entire Roche lobe. The precession angle is j = 15°-20°, the system inclination angle i = 55°-65°. The direct disc precession is probably due to the moment of the forces transferred to the disc by the gas stream outflowing from the star. The optical components of high-mass X-ray binaries are high-luminosity hot stars. In the case of moderate or low X-ray luminosity of such a system, the re-emission and scattering of the optical-component light by the accretion disc form the main mechanism of disc radiation. According to the present-day concepts, the disc may either lie in the binary-system plane or be oblique and precessing. In many cases, the long-term variability found or suspected in numerous X-ray binaries (Priedhorsky, 1987) is probably due to disc precession. In particular, the long-term photometric and polarimetric variability of Cyg X-1 may well be explained in terms of such a model (Karitskaya, 1979, Kemp et at., 1983, 1987). In the case of precessing discs tilted out of the orbital plane, reemitting and scattering the light of the second component, the character of the variations in the radiation field parameters (the intensity I, the Stokes parameters Q and U describing the linear polarization) is defined first of all by the variations of the disc illumination by the star (Karitskaya 1981a,b) which varies with both the orbital phase Phi and with precession phase delta , more accurately, with phi = Phi + delta. The "-" sign means that the precession is in the direction of the orbital motion, the "+" sign corresponding to the reverse direction. Moreover, the conditions vary for the disc visibility which is a function of delta. Thus, the Stokes parameters I(Phi) Q(Phi) and U(Phi) are strong functions of the angle j of disc inclination to the binary-system plane and of the precession phase delta. The intensity and the linear polarization of star radiation scattered by a precessing accretion disc have been calculated by Karitskaya (1981a, b) and Bochkarev and Karitskaya (1988a). In the case of pure electron scattering the linear polarization variation amplitude may reach 3% and the intensity and the polarization vary both with the precession phase delta and with the orbital phase Phi of a binary system due to changes in the mutual position of the scattering disc, the star and the observer's line of sight. Contrary to the case of discs in the orbital plane, at j nonequal 0, the third and higher harmonics appear in the Fourier spectra of I, Q and U. The accretion discs atmospheres are not pure electron scattering. The true absorption is of great importance in them. Therefore, the field parameters of the emission scattered by the disc and their dependence on phase Phi are determined by the single-scattering albedo Omega = chi_s / (chi_s + chi_a) (1) where chi_s and chi_a are respectively the coefficients of scattering and true absorption. The single-scattering albedo Q is generally a function of depth in the disc atmosphere and of coordinates on the disc surface. Any detailed models for accretion disc atmospheres have not been constructed yet, so the dependences are unknown. Therefore, we limited ourselves to calculating the field of disc-scattered radiation in terms of the approximation Omega = const. (Bochkarev and Karitskaya 1988a). In the case of starlight scattering by disc the intensity I is a strong function of Phi at 0.7 <= Phi and varies at Phi <= 0.7 a bit more rapidly than according to the Phi^1 law. The dependence of the Stokes parameters Q and U on Omega is slightly stronger than in accordance with the linear law. The dependences of I, Q, U on the phases Phi and band on the angle j remain, generally, the same as for Omega = 1. The first candidate for black holes, the high-mass X-ray binary Cyg X-1, has been studied in great detail both photometrically (Kemp et at. 1987) and polarimetrically (Kemp 1980a, 1984). The linear polarization of the emission from Cyg X-1 varies by 0.25%. The second harmonic of orbital period P_0 = 5.6d is fundamental with full variation 2A_2 = 0.18% (A is amplitude). Furthermore, the first (A_1 = 0.02%) and higher (up to fifth) harmonics of P_0 are observed to be much weaker (Kemp 1980a). In addition, there are variations with period P_p = 294d (Kemp et al. 1983). The optical component is the main source of accretion disc heating in Cyg X-1 (Karitskaya, 1981a) In this case the disc surface temperature is 12000 K. The contribution of the intrinsic emission of such a disc to the system brightness does not exceed 3% (Bruevich et al., 1978, Karitskaya 1981a). According to Bochkarev and Karitskaya (1983), the variable polarization component of the intrinsic emission from a precessing disc inclined at J~10° does not exceed 1% of the emission from the disc. Therefore, the contribution of this mechanism to the Cyg X-1 polarization variability is < 0.03%. The intrinsic polarization of the emission from the Cyg X-1 optical component due to its tidal distortion is expected to be <0.025% (Bochkarev et at. 1985). Now consider the polarization variability due to starlight scattering by the disc of Cyg X-1. The surface-normal component of gravitational acceleration g corresponds to log g = 1.5 - 2. Thus, according to Bochkarev et at. (1985), we get Omega = 0.4 at T = 12000 K. In this case at the angle i = 45° +/- 20° expected for Cyg X-1 (Bochkarev et al. 1975), even a disc in the orbital plane which fills the Roche lobe (r_d = 0.3a) may give rise to 0.25% polarization variability (Bochkarev, Karitskaya, 1988a). The disc inclination to the orbital plane will lead to a larger amplitude of polarization variability. However the observed ratio between the first and the second harmonics of polarization variability contradicts the considered mechanism. As shown by Karitskaya (1981a), amplitude A_2 of the second harmonic P_0 of the oblique disc polarization is in practice independent of the angle j up to j = 20-30°. At Omega = 0.4 and r_d = 0.3a, we get A_2 = 0.11% which is close to the observed value of 0.09%. However, the polarization of radiation from the disc comprises a strong first harmonic A_1 which rises with j, namely, 0.8 A_2 <= A_1 at 0 <= j. The observed A_1/A_2 ratio is 0.2 (Kemp 1980a, 1984). In the absence of an additional polarization source compensating for the variations with A_1, the scattering of the emission from the star by the accretion disc accounts for not more than 25% of the polarization observed in Cyg X-1. Besides, the dependence of A_2 on the delta phase found by Kemp (1984) (the A_2 value reaches its maxima at delta = 0.25 and 0.75) does not fit the oblique precessing disc for which the A_2 value is peaking at delta = 0. It may be concluded from the dependence A_2 (delta) that, probably, less than half of the A_2 value is due to the precessing accretion disc. The high A_2/A_1 value most probably means that the main contribution to the variable polarization of the emission from Cyg X-1 is from the optically thin gas located asymmetrically with respect to the optical star. In confirmity with the assumptions made by Kemp (1980b) the variable polarization may be related to the hot spot at the accretion disc rim. Thus, the above analysis shows that the starlight scattering by the disc is not the main mechanism of polarimetric variability of Cyg X-1. The contribution of the mechanism to the observed polarization variability does not seem to exceed 25-50%. From this, concerning the Omega value of ~0.4 expected for the disc, it follows that the accretion disc dimension does not exceed 0.2a, that is 60% of the X-ray source Roche lobe dimension. Now let us examine the radiation intensity of an oblique precessing disc re-emitting the optical-component light as applied to Cyg X-1. As in the case of starlight scattering, the oblique processing accretion disc gives rise to photometric variability with precession period P_p (the delta phase) ( due to the variation of disc visibility conditions) and with a period defined by the sum of, or the difference between, the frequencies of the precessional and orbital rotations (the phase phi) (due to the variations of the disc heating conditions). The intensity of radiation can be expanded to a Fourier series with these frequencies (the corresponding and delta) (Bochkarev, Karitskaya, 1988b). The harmonic amplitudes of the expansion are functions of the angles of precessing j and of system inclination i, the relative radii of the disc r_d and the star r*, the angular distribution of disc radiation intensity (generalization of the limb darkening coefficient U), the dependence of the radiation flux spectral density on the temperature (beta = d ln F/d ln T ) and the disc to star brightness ratio (gamma). So one can determine these parameters by comparing the harmonic amplitudes with the observational ones, the coefficients u, beta, gamma, being derived from the model atmosphere. For Cyg X-1 in the B band: beta = 2.0, gamma = 0.13, u = 0.06. In the case of the Cyg X-1 disc the star radiation is absorbed in the outer layer of the atmosphere. This leads to a weak outward gradient of temperature and the limb darkening coefficient turns out to be slightly negative. The reflection albedo is A ~ 0.2 . The light scattering contribution to the photometric variability (B band) is <= 10%. The data of the detailed analysis (Kemp et al., 1987) of the V 1357 Cyg photometric variability in B band have been used to find the amplitudes A_delta, A_phi, A_delta,phi, A_2phi and A_2delta at a (1.2-2.5) sigma significance level for each of the amplitudes. In the fractions of 10^-4 of the system brightness, we get 2A_delta = 70 ± 35, 2A_2delta = -43 ± 35, assuming that the precession is towards orbital motion we get 2A_phi = 71 ± 27, 2A_deltaphi = 39 ± 35, 2A = 39 ± 17.5, assuming that the precession is opposite, which corresponds to the case of slaved disc we get 2A_phi = -5 ± 29, 2Adeltaphi = 42 ± 37, 2Aphi = 84 ± 19. Qualitative analysis has shown that the amplitudes found cannot be fitted to the slaved-disc model with precession opposite to orbital motion The assumption of precession opposite to orbital motion is in better agreement with the optically-thin disc model: in the latter case, however, the amplitudes A_phi and A_delta cannot be fitted to each other at a level better than x^2 = 3. At the same time, all the amplitudes (except A_2delta) and the first harmonic of the orbital period of linear polarization of optical emission from Cyg X-1 are in agreement, at the level of a 5-value total x^2 < 1 (up to x^2 = 0.5), with the model of an optically-thick disc precessing towards the orbital motion of the system with the parameters r* = 0.4-0.45, r_d = 0.12-0.15, i = 55-65°, j = 15-20° (in agreement with Kemp et al. (1987)). The second (main) harmonic of linear polarization was not examined because, on the basis of what has already been said, it is irrelevant to the accretion disc. The direct precession of the disc may be due to the moment of the forces transferred to the oblique disc by gas stream out-flowing from the optical star (Bochkarev, Karitskaya, 1988b). In this case the precession period is P_p = 2*pi*(v_Kepl /v)*(t/tau_d)*cos j where v_Kepl and v are respectively the Kepler velocity of motion at the disc rim and the velocity of gas stream impact against the disc, t is the time within which the matter "leaks" from the rim to the interior of the disc. The observed P_p value of 294d at j = 15-20° arises if t = 10d, which agrees with the absence of delay of the X-ray variations with P_p relative to the optical emission variations with P_p. To the direct precession lead also the forces exerted on the disc by stellar wind and radiation pressure (Kemp, 1988). The small value of t is probably due to the disturbance produced in the outer regions of the disc by the gas stream. References: Bochkarev, N.,G., Karitskaya E.,A., Shakura, N.,I., 1975. Sov. Astron. Lett. 1, 118. Bochkarev, N.,G., Karitskaya, E.,A., 1983, Sov. Astron. Lett., 9, 6. Bochkarev, N.,G., Karitskaya, E.,A., Sakhibullin, N.,A., 1985, Ap. Sp. Sci., 108, 15. Bochkarev, N.,G., Karitskaya, E.,A., 1988a, "The true absorption effect on the field of radiation of starlight-scattering accretion discs" - in: Symp. COSPAR/IAU, Sofia. Adv. Space Res. Bochkarev, N.,G., Karitskaya, E.,A., 1988b, "Starlight re-emission by a precessing accretion disc relevant to the parameters of the Cyg X-1 V1357 Cyg X-Ray binary. In: Symp. Cospar/IAU. Sofia. Adv. Space Res. Bochkarev, N.,G., Karitskaya, E., A., et al. 1986, Sov. Astron., 30, 43. Bruevich, V.,V., Kilyachkov N.,N., et al., 1978, Sov. Astron. Lett. 4, 292. Karitskaya, E.,A., 1979, Sov. Astron. Circ., 1088, 1. Karitskaya, E.,A., 1981a, Thesis for Candidate Degree, Moscow. Karitskaya, E.,A., 1981b, Sov. Astron., 25, 80. Kemp, J.,C., 1980a, Astron. Astropys., 91, 108. Kemp, J.,C., 1980b, Ap. J., 235, 595. Kemp, J.,C., Barbour, M.,S., Henson, G.,D., et al. 1983, Ap.J. Lett. 271, L65 Kemp, J.,C., 1984, Preprint. Kemp, J.,C., Barbour, M.,S., Henson, G.,D., et al. 1983, Ap.J.Lett., 271, L 65. Kemp, J.,C., Karitskaya, E.,A., Kumsiashvili M.,I., et al 1987, Sov. Astron., 31, N2. Kemp, J.,C., 1988. private communication Priedhorsky, W.,C., 1987, Preprint LA-UR-86. 39000.
Var. Phenomena in Close Bin. Stars Con. Konkoly Obs. Hung. Akad. Sci. 10, Part 7, (No.93), Budapest 1989. OBSERVATIONAL EVIDENCE ON THE ASYMMETRY OF THE ACCRETION COLUMNS IN CLOSE BINARY SYSTEMS I. L. Andronov Department of Astronomy, Odessa State University, U. S. S. R. The magnetic field in AM Herculis-type binary stars is sufficiently large to cause the accretion flow to be channelled along field lines, and above the magnetic pole of the white dwarf an accretion column forms, which is the main source of the X-ray, UV, optical and near-IR emission (Chanmugam and Wagner 1977, Stockman et at. 1977, see also the recent reviews of Lamb (1985) and Liebert and Stockman (1985)). However, the angle Theta between the magnetic axis and the column's axis deviates from zero, thus the column's axis is inclined with respect to the surface of the white dwarf (see Andronov 1986a,b, for details). In this case, the orbital changes of flux, radial velocities and polarization may be sufficiently asymmetric. The statistical dependence of the photovisual light curve of AM Her on its luminosity in the "active" state was derived by Andronov (1985). It is highly asymmetric and, with increasing luminosity, the main maximum (hump) tends to be more prominent. The second maximum was not a constant feature of the light curve, contrary to the earlier observations of Szkody and Brownlee (1977) and Gilmozzi et al. (1978). Thus the position and structure of the accretion column may have undergone long-term changes, as was originally pointed out by Bailey and Axon (1981) on the basis of photometric and polarimetric data. Such changes may occur due to the cyclic variations of the orientation of the magnetic axis of the white dwarf in relation to the rotating binary stellar system, which are excited thereby making the accretion possible (Andronov 1983, 1987a). This model of "swinging dipole" may be able to interpret the following phenomena observed in AM Herculis itself and in some other object of the same class: a) cyclic variations of luminosity, which may be caused by the dependence of the "magnetic valve" conductivity on angle Theta. b) cyclic variations of the phases of minima detected in AM Her (Andronov et al. 1982) and QQ Vul (Andronov and Fuhrmann 1987). c) correlation between the above mentioned phenomena (Smykov and Shakun 1985). Another source of the column's asymmetry is connected with the heterogenity of the accretion flow (see Andronov 1987b for a review). The initial plasma "blobs", while moving along field lines are transferred to long plasma "strips", so called "spaghettis", which bombard the shock at the top of the accretion column. In each "spaghetti" the cyclic variations of the structure existing during the penetration of such a "strip" through the shock may appear. Such a quasi-periodic oscillations usually interfer, and one may observe the sum of practically independent variations. The possible "global" oscillations of the column predicted by Langer et al. (1982) may be strongly affected by such "spaghetti". However one may provide an observational test for choosing the more realistic model. In the "active" state, the number of "spaghetti" is larger than in the case of the "intermediate state". At smaller luminosity one may study the single flares ("spaghetti") or, at least, the smaller number of them, and thus may estimate their physical parameters. Because the structure of the column (and thus the characteristic "Noisar" frequency) depends on the value m/A (accretion rate per unit surface of the column's base), one may predict the increase of the "Noisar" cycle duration with decreasing luminosity in the "global" model. In the case of the "spaghetti" model the "coherence duration" is considered to increase as well, because of the increasing length of a single strip. Thus, observations of the ultrashort-time variability of AM Her-type stars are very much needed to obtain the statistical dependence of the "Noisar" characteristics (intensity, frequency and coherence duration") on luminosity and orbital phase (presumably in the "active" state, to study the asymmetry of the column). This observational task needs time, but the results may be really important for investigating the exotic objects known as "AM Her-type stars". References: Andronov, I.L., 1983, Astron. Tsirk. No. 1267, 4. Andronov, I.L., 1985, Pis'ma Astron Zhurn., 11, p.207. Andronov, I.L., 1986a, Astron. Zhurn., 63, 274. Andronov, I.L., 1986b, Commun. Konkoly Obs. Hung. Akad. Sci., 86, p.369. CoKon 86 Andronov, I.L., 1987a, Astrophys and Space Sci., 131, 557. Andronov, I.L., 1987b, Astron. Nachr., 308, 229. Andronov. I.L., Banny, M., Korotin, S.A., Yavorsky, Y.B., 1982, Astron. Tsirk., No. 1225, 4. Andronov, I.L., Fuhrmann, B., 1987, Inform. Bull. Var. Stars. No. 2976. IBVS 2976 Bailey, J., Axon, .I., 1981, Mon. Not. R. Astr. Soc., 194, 187. Chanmugam, G., Wagner, R.L., 1977, Astrophys. J., 213, L13. Gilmozzi, R., Messi, R., Natali, G., 1978, Astron. Astrophys., 68, L1. Lamb, D.Q., 1985, in: "Cataclysmic Variables and Low-Mass X-Ray Binaries", eds. D.Q. Lamb, J. Patterson. (Reidel, Dordrecht) p.179.. Langer, S.H., Chanmugam, G., Shaviv, G., 1982, Astrophys J., 258, 289. Liebert, J., Stockman, H.S. 1985, in: "Cataclysmic Variables and Low-Mass X-ray Binaries", eds. D.Q. Lamb, J. Patterson, (Reidel, Dordrecht), p. 151. Smykov, V.P., Hakun, L.I., 1985, Astron. Tsirk., No. 1384, 3. Stockman, H.S., Schmidt, G.D., Angel, J.R.P., Liebert, J., Tapia, S., Beaver, E.A., 1977, Astrophys. J., 217, 815. Szkody, P., Brownlee, D.E., 1977, Astrophys. J., 212, L113.
Var. Phenomena in Close Bin. Stars Com. Konkoly Obs. Hung. Akad. Sct. 10, part 7, (No.93), Budapest 1989. CLOSE BINARY SYSTEMS IN LATE EVOLUTIONARY STATE A. M. Cherepashchuk Sternberg State Astronomical Institute, Moscow, U.S.S.R. A lot of new observational and theoretical data have been published during the last decade concerning the close binary systems at a late stage of evolution. In this connection the Catalogue of Close Binary Systems at Late Stage of Evolution (editor: A.M. Cherepashchuk) has recently been prepared at Sternberg State Astronomical Institute Moscow. The authors of this catalogue are: A.A. Aslanov, D.E. Kolosov, N.A. Lipunova, T.S. Khrusina and A.M. Cherepashchuk. The catalogue is due to be published at the end of 1988 by Moscow University Press. The catalogue contains about 300 objects of different kinds: beta Lyr and W Ser type systems, WR+OB binaries, run-away OB stars, X-ray binaries of different types (massive and low-mass Xray binaries, X-ray transients, bursters, QPO, etc.), the SS 433 object, single line WR stars with probable relativistic companions, pre-cataclysmic variables, cataclysmic variables, symbiotic stars, intermediate polars, polars and binary radio-pulsars. For the majority of the systems, the finding charts and reference stars are presented in the catalogue. The catalogue is likely to be of use both for theoreticians and for observers because it contains basic parameters of close binary systems: masses, radii, luminosities of the stars, magnitudes, spectral types, periods, etc. Many properties of close binary systems at the late evolutionary state are well explained by the modern theory of evolution of close binaries with mass exchange. Our investigations of WR stars in eclipsing binary systems allow us to estimate the correct values of radii and temperatures of these stars. Based on our results the WR stars are helium-rich remnants formed as a result of the first mass exchange in massive close binaries. The discovery of optical eclipses in the unique object SS 433 allows us to estimate the basic parameters of this massive X-ray binary. Judging from our interpretation of optical eclipses in the SS 433 system, this object is a massive X-ray binary system (similar to Cyg X-1 or Cen X-3) in an advanced stage of evolution: at this stage the star is overfilling its Roche lobe. Due to very high mass transfer in this system an optically bright accretion disk is formed around the relativistic companion. Thus, SS 433 is a massive X-ray binary system at the supercritical accretion regime. A number of single-line WR stars have recently been discovered as close binary systems containing low-mass companions which may be neutron stars accreting in a strong stellar wind of WR star. Mass determinations of X-ray pulsars in X-ray binary systems have been made as well as of black hole candidates. The masses of X-ray pulsars do not exceed 3 M_sun - this being the theoretical upper limit for neutron stars predicted by Einstein's theory of general relativity. The mean value of the mass of X-ray pulsars (neutron stars) obtained from analysis of 7 X-ray binary systems is 1.4 M_sun. All black hole candidates have a mass that exceeds 3 M_sun and none of the 4 black hole candidates shows periodic pulsations of the X-ray radiation characteristic for the magnetic rapidly rotating neutron stars. The search for relativistic companions for OB run-away stars by spectroscopic and photometric methods is now in progress at Moscow's Sternberg State Astronomical Institute.
Var. Phenomena in Close Bin. Stars
Com. Konkoly Obs. Hung. Akad. Sci.
10, Part 7, (No.93), Budapest 1989.
RESULTS OF PHOTOELECTRIC OBSERVATIONS OF V 533 HERCULIS
M.I. Kumsiashvili, V.O. Kakhiani
Abastumani Astrophysical Observatory Georgia, U.S.S.R.
At the Workshop of the head of Project I "Complex Investigations of Stars and
Stellar Systems" of the Problem Commission "Physics and Evolution of Stars" of the
multilateral cooperation of the Academies of the Socialist Countries, held in Suzdal in
1985, the star V 533 Herculis was included in the program of cooperative investigations for
the coming two years within a new structure of the Commission. Additionally, it had earlier
been suggested that we observe this star photoelectrically at Abastumani Astrophysical
Observatory of the Georgian Academy of Sciences using the AZT-11 telescope.
The nova V 533 Her is of significance in the sense that light variations were
observed with the period 63.6 sec, though no such variations were observed later (Robinson
and Nather 1983). Moreover, the orbital period of the star is believed to be equal to 0.28
day (Ritter 1984). However this value needs to be confirmed. The fact that some long-period
light variations with an amplitude of more than 1.0 mag. as well as the light variations
during the night with the amplitude of about 0.2 mag. were observed at Peking Observatory,
attracts one's attention.
The star V 533 Her was observed at Abastumani Astrophysical Observatory from April
- June, 1986 with a two channel electrophotometer attached to the AZT-11 telescope. The
electrophotometer was designed and manufactured at the observatory. The primary mirror of
the telescope is 1.25 m, the equivalent focal length being 16 m. The photometer offers the
possibility of simultaneously measuring the stars removed from each other at an angular
distance of up to 22'.
Within 7 nights the light of the star was measured in B filter during
Figure 1. Figure 2.
a few hours at night. The longest observation lasted 3.5 hours. The star "E" from Lochel's
paper (1966) served as the comparison. The integration time was 10 sec. Due to the fact
that at a distance of 12" from V 533 Her there is a star fainter than that under
investigation by 2 magnitudes, we used a 16" diaphragm in our observations. The results are
given in Figs. 1-4. The time is plotted along the X-axis and the magnitude difference
between the comparison star and the variable along the Y-axis. Each point is obtained by
averaging two observations. On average, the error of a measurement is 0.016 mag. The
slipping mean values are plotted as well. Their measurement error is, on average, 0.005
mag. It is seen that within a
Figure 3. Figure 4.
night there are some irregular variations with an amplitude of 0.3 - 0.4 mag. confirming
Hao Xiang-Liang's and Mei Bao's results (1984). Comparison of observations performed on
different nights shows certain differences in the character of the light variation. Single
observations were averaged merging every 30 points into one. Then using the elements:
Min_Theta = 2446565.4579 + 0.28d*E
we reduced them to the same period.
Figure 5 shows a corresponding curve. As can be seen not all the
Figure 5.
phases overlap equally well. But judging by our results it can be concluded that the light
curve does not show any pronounced light variations with the period of 0.28 day suggested
earlier. It might be that apart from the 6 hours period in this case we are dealing with
some more harmonics with
Figure 6.
shorter periods superimposed on this particular period. In order to solve the problem once
and for all further observations are needed - and it is just that is envisaged by our
program.
In addition, it should be noted that in Hutching's paper (1987), the author gives a
new spectroscopic period of the star : 0.209774d. Using this new period and selecting the
epoch according to our observations a mean curve is plotted in B by averaging the
observational data with 30 points into one.
Figure 6 shows that our photoelectric observations confirm Hutching's spectroscopic
data through in our observations there occur certain irregular light variations during the
night.
Consequently, to finally establish the nature of the light variations for the star
under study, more detailed analysis of the data obtained must be carried out.
The results obtained for two pairs of parameters q,i (q = 0.320, i = 77.5° and
q = 0.146, i = 82°) are presented in Figure 1. Only the egress branches of the eclipses are
reproduced here.
The phase Phi_1/2 at which half the flux is eclipsed occurs nearest phase zero for
case a1 and furthest for case a_3. Such large differences in the half width of the eclipse,
especially for q = 0.320, produce only slight differences in the relation i(q). A detailed
analysis is due to published in Acta Astronomica.
This paper was partly supported by the Polish Academy of Sciences (grant CPBP - 01.11).
References:
Hao, X-L., Mei, B., 1984, Inf. Bull. Var. Stars, No. 2611. IBVS 2611
Hutchings, J.B., 1987, P.A.S.P., 99, 57.
Lochel, K., 1966, Mitt. Ver. St. 3, Heft 7, 213.
Ritter, H., 1984, Astr. Asrophys. Suppl. Ser., 57, 385.
Robinson, E.L. and Nather R.E., 1983, Ap. J. 273, 255.
Var. Phenomena in Close Bin. Stars
Com. Konkoly Obs. Hung. Akad. Sct.
10, Part 7, (No.93), Budapest 1989.
PREVIOUS OPTICAL FLARE IN THE SHORT PERIOD RS CVn SYSTEM SV Cam
L. Patkos
Konkoly Observatory of the Hungarian Academy of Sciences
Short period RS CVn stars are active stars showing "solar-like" activities. They
display all the surface phenomena of our Sun, viz. spots flares, chromospheric activity,
etc. In the case of the RS CVn systems however, all these activities are much more
pronounced, sometimes even by orders of magnitude. This situation is somewhat different in
the case of observed optical flares. There have been only two reported unquestionable
optical flare events in RS CVn systems. Both of them occurred in a short period RS CVn
system: in SV Cam (Patkos 1981) and in XY UMa (Zeilik et al. 1983). Although Srivastava
(1983) reported some "flare-like activity" in AR Lacertae, no other observed optical flare
is known in RS CVn systems.
Therefore the question remains: Why do we not observe optical flares in long period
or regular RS CVn systems? These systems are very well observed and show flare activities
in other wavelengths. In view of this, it is very important to study RS CVn systems showing
optical flares. Table 1 contains the main characteristics of SV Cam and XY UMa.
Table 1.
SV Cam XY UMa
(eclipse) period 0.59 0.48
brightness 8.40 - 9.11 9.50 - 10.17
distortion wave ampl. 0.1 0.11
mass ratio (hotter/cooler) 1.0/0.7 0.95/0.70
(solar units)
radius (hotter/cooler) 1.2/0.7 0.98/0.73
(solar units)
spectra G2-3 V / K4 V G2-5 V / K5 V
The two systems are very alike. In both cases it is questionable which component is
the active one. According to Geyer (1976) in the case of XY UMa the primary component is: -
in the case of SV Cam the migrating distortion wave goes through both the primary and the
secondary minima. Therefore, we have to assume that the spot activity of the system
originates from both the hotter and cooler component. The flare activity itself originates
with greater probability from the secondary component because two of the reported flares
occurred at the bottom of the primary minimum when the hotter component is eclipsed.
Table 2 contains the main characteristics of the observed flares:
Table 2
SV Cam XY UMa
orb. phase 0.61 0.97 0.99 0.57
duration (min) 43 18 9 30
Delta U (mag) 0.12 0.15 0.05 0.33
Delta B (mag) 0.05 0.06 0.03 0.13
Delta V (mag) 0.03 0.03 - 0.09
Because optical flares are so limited in these systems, it might be important to
mention, that I have observed a previous optical flare in SV Cam at J.D. 2441960.4585. The
observation material was published (Patkos 1982, page 86.) without mentioning the three point
flare event observed only in the U light curve. The main characteristics of this previous
optical flare were the following:
orbital phase 0.71
duration (min) 38
Delta U (mag) 0.8
Figure 1.
As the observed light curve (Fig. 1.) shows, in the time interval following the
flare there were also some flare-like spikes in the observed U light curve of SV Camelopardalis.
References:
Geyer, E.H., 1976, in: "Structure and Evolution of Close Binary Systems"
p.:313, eds.: P. Eggleton et al.
Patkos, L.: 1981, Astrophys. Lett. 22, p.1.
Patkos, L.: 1982, Comm. Konkoly Obs. No 80. CoKon 80
Srivastava, R., K.: 1983, Inf. Bull. Var. Stars. No. 2450. IBVS 2450
Zeilik, M., Elston, R., Henson, G., Smith, P.: 1983
in: Activity in Red-Dwarf Stars, IAU Colloquium No. 71. p.411.
eds: P.B. Byrne, M., Rodono: Reidel Dordrecht
Var. Phenomena in Close Bin. Stars
Com. Konkoly Obs. Hung. Akad. Sci.
10, Part 7, (No.93), Budapest 1989.
PERIOD CHANGES IN THE CLOSE BINARY SYSTEM QQ CASSIOPEIAE
J. M. Kreiner
Pedagogical University, Cracow, Poland
J. Tremko
Astronomical Institute, Slovak Academy of Sciences Tatranska
Lomnica, Czechoslovakia
New photoelectric observations of QQ Cas were obtained and the epochs of minima
were derived. The secular variations of the period have been found and an explanation for
their causes is suggested.
The variable star QQ Cas (BD +59°2765 = BV 73) was discovered by Kippenhahn (1955).
The complete list of the photographic epochs of minima was published by Busch (1975). Three
new epochs of minima are included in the paper of Braune and Lichtenknecker (1986).
The light curve given by Busch (1975) is clearly of beta Lyrae-type. The spectral
type of one component is B2, the spectrum of the second component is not known.
As the star has very rarely been observed in the last two decades, we put it into
the observational program at Skalnate Pleso Observatory. The observations were obtained
with the photoelectric photometer installed in the 0.6/7.5 m reflecting telescope in the
years 1985-1987. During seven nights, over 1400 observations (in B region) were obtained.
The observations are due to be published elsewhere. The derived epochs of minima are in
Tab. 1.
Table 1.
J.D. hel. m. e. type of min.
2446743.3985: +0.0025 pri
6756.2465 +0.0025 pri
7060.4305 +0.0015 pri
7061.5030 +0.0010 sec
The spread of the individual epochs of minima in the O-C diagram published by Busch
(1975) is very wide. Many published epochs are actually the epochs when the star has been
found to be fainter. Therefore we decided to divide the whole observational period into 18
intervals. The limits of the intervals as a rule coincide with the season in which no
observation was obtained. As the shift of the secondary minimum was not observed we grouped
together the primary and the secondary minima. The number of observed minima in one
interval varies from 9 to 23. Thus we obtained 18 mean epochs of minima. Due to their large
deviation, one mean epoch of minimum and the visual epoch of minimum from the table
published by Braune and Lichtenknecker (1986) were omitted. Two epochs of minima obtained
by Zonn and Semeniuk (1959) included in the list of Busch (1975) were not used for the
calculation of mean epochs of minima but were used directly for the ephemerides calculation.
The recent calculation of elements published by Braune and Lichtenknecker (1986)
has shown that the period is longer when the observations obtained only in recent years are
used. The ephemeris with the secular term derived by us is as follows:
Min. I. = J.D. 2434330.1918 + 2.14204474E + 1.71*10^-9*E^2
±38 ±43 ±11
The mean error of the secular term is relatively low and thus the increase of the
period is a real effect. The observational period was divided into two parts for which
linear ephemerides were computed. The linear ephemeris before J.D. 2435000 is:
Figure 1.
Min. I. = J.D. 2434330.1749 + 2.14203027E
±47 ±96
The linear ephemeris for the time interval after that date is:
Min. I. = J.D. 2434330.1726 + 2.14203027E
±47 ±14
The sum of (0 - C)^2 values is very close being by 3.5 percent lower for linear
ephemerides.
The secular increase of the period can be explained within the scope of the mass
transfer theory or by the light-time effect. For the mass loss we obtain the value of
Delta m/m = 5.8*10^-7 per year. After removing the quadratic term the rest of the deviations
could be explained by a non-uniform mass transfer if these deviations are real.
This work was supported in part by the Polish Ministry of Education (Grant No. RR I-11).
References:
Braune, W., Lichtenknecker, D., 1986, BAV Rundbrief 38, 1.
Busch, H., 1975, Mitt. der B.H. Burgel-Sternwarte Hartha 8, 15.
Kippenhahn, R., 1955, Kl. Veroff. Remeis Sternw. Bamberg 9, 4.
Zonn, W., Semeniuk, I., 1959, Acta Astron. 9, 159.
Var. Phenomena in Close Bin. Stars
Com. Konkoly Obs. Hung. Akad. Sci.
10, Part 7, (No.93), Budapest 1989.
OPTICAL BEHAVIOUR OF THE POLAR AM HERCULIS
W. Götz
Zentralinstitut fur Astrophysik der Akademie der Wissenschaften
der DDR Sternwarte Sonneberg
AM Herculis is the prototype star of a subgroup of cataclysmic binaries consisting
of a white dwarf as primary, and a low-mass main sequence star as the secondary component.
This type of close binary is characterized, on the one side, by a strong magnetic field of
the white dwarf of about B ~= 10^7 - 10^8 Gauss and, on the other side, by a gas stream
originating from the main sequence star. This gas stream spills over to the primary and is
conducted by the magnetic field. This process causes an accretion column on the magnetic
pole of the white dwarf which is facing the secondary. The existence of an accretion disc
around the primary can also be expected.
The orbital periods of this group of stars are very short. The period of AM Herculis
amounts to p = 0.12892737d, and the corresponding occultation-light-changes of about 0.5
magnitudes are superimposed upon the overall light curve.
This report deals with the long-term behavior of AM Herculis as it appears from
observations given by Hudec and Meinunger (1977) and by myself (1982, 1984a, 1984b, 1986a,
1986b, 1987). My observations were obtained between 1982 and 1987 on 643 blue-sensitive and
40 photovisual plates of the Schmidt camera (50/70/172 cm) of Sonneberg Observatory from
more than 230 nights. Visual observations given by the French Association of Variable Star
Observers published in the AFOEV Bulletin (1982 - 1987) are included.
The optical, the polarimetric and the X-ray behavior of AM Herculis type stars are
mainly determined by the characteristics of their accretion columns. Generally we distinguish
two photometric states in this group of stars: The low state, which is given by inactivities
in the minimum brightness and the high state, which is caused by X-ray heating.
Figure 1.
In the case of AM Herculis the mean levels of the two states can be shown by the
brightness distribution of the observations in B and V. In Fig. 1 the brightness
distribution in B is given. The hatched areas represent observations obtained from Schmidt
plates. The other ones belong to series of observations given by Meinunger and Hudec
obtained on sky patrol and astrograph plates of Sonneberg Observatory.
From the brightness distribution in B it can be seen that the low state is characterized
by observations between m_B = 14.8m and m_B = 15.8m with a mean level of m_B = 15.3m. On the
other hand all observations between m_B = 12.3m and m_B = 14.8m belong to the high state. The
mean level
Figure 2.
in this latter state varies with time as can be seen in the following. But this fact is
also illustrated in Fig. 1 if one compares the mean level of the observations given by
Meinunger and Hudec at m_B = 13.0m with that obtained from my observations at m_B = 14.0m.
The brightness distribution obtained from the visual range, shown in Fig. 2,
confirms the results obtained from the blue range. Observations of the low State are
situated between m_V = 14.5m and m_V = 15.4m. The mean level there amounts to m_V = 14.83m
taking into account the observations given by Verdenet (AFOEV). In the high state we find
observations between m_V = 12.2m and m_V = 14.5m. The mean levels in the high state vary
with time in a similar way to those in the blue range.
Figure 3.
In Fig. 3 the mean values of the brightness of AM Herculis obtained from all
observations of the high state of each season, which represent the seasonal mean levels,
are plotted against time, beginning with the year 1957. In this diagram dots characterize
the behavior of the mean high state brightness in the blue range: circles characterize the
behavior in the visual range.
Figure 3 illustrates the continuous increase in mean brightness between 1957 and
1970 from m_B = 13.4m to m_B = 13.0m. After a period of 10 years of nearly constant mean
brightness, in 1980 the star started a decrease from m_B = 13.0m to m_B = 14.4m within the
following 6 years. The lowest mean brightness was observed in 1986, that is, just in that
year in which the low state had its longest duration - as we can see below. The decrease in
mean brightness of the high state between 1980 and 1986 is confirmed by the visual
observations.
The long-term behavior of AM Herculis between 1982 and 1987 can be seen from the
light curves given in Fig. 4. There, my observations in B are drawn in the upper light
curve: the visual ones obtained and published by the AFOEV are grouped in the lower one.
As we can see from the two light curves, there are phases of the low and the high
state which vary in an irregular manner. From the curves shown the following general
conclusions can be drawn:
1). The durations of the minimum phases, or better of the low state phases, are
very different. One of the shortest minima was observed in
Figure 4.
1982 between April 15 and September 24. The longest one, on the other hand, amounts to
about 290d crossing the observation seasons 1985/86 if we assume that the long-lasting
minimum of 104d at the beginning of the series of 1986 is the continuation of the 120d low
state at the end of the year 1985.
2). In the high state a flare was observed on July 12, 1983. During this flare the
brightness of AM Herculis increased from m_B = 13.74m to m_B = 12.33m, which is an increase
of 1.41 magnitudes within 0.024d This flare proved to be unique: in the series of nights of
the following years nothing of this kind was ever observed again.
3). In each case the high state of AM Herculis starts from the and is caused by X-ray
heating. Therefore it seems to be especially necessary to investigate the low state,
including the influences of the orbital light changes. At Sonneberg Observatory
investigations on this subject have started.
References:
AFOEV, 1982-1987, AFOEV Bulletin
Götz, W., 1982, I.B.V.S. No. 2226. IBVS 2226
Götz, W., 1984a, I.B.V.S. No. 2459. IBVS 2459
Götz, W., 1984b, I.B.V.S. No. 2649. IBVS 2649
Götz, W., 1986a, I.B.V.S. No. 2851. IBVS 2851
Götz, W., 1986b, I.B.V.S. No. 2967. IBVS 2967
Götz, W., 1987, I.B.V.S. No. 3126. IBVS 3126
Hudec, R., Meinunger, L., 1977, MVS 7, 194.
Var. Phenomena in Close Bin. Stars Com. Konkoly Obs. Hung. Akad. Sci. 10, Part 7, (No.93), Budapest 1989. SPECTRAL PECULIARITIES OF V 367 CYGNI - A CLOSE BINARY SYSTEM AT THE STAGE OF RAPID MASS EXCHANGE V. G. Karetnikov and E.V. Menchenkova Astronomical Observatory of Odessa University, U.S.S.R. Of greater actual importance has become the investigation of close binary systems with nonstationary phenomena as objects at the critical stage of their evolution. The system of V 367 Cygni is one of the most interesting objects of this type. This system is at the short-term stage of fast mass exchange as is manifested by the numerous effects observed: light curve deformation, variation in period, emission in lines of Balmer series. The spectrum of V 367 Cygni is a bright example of a "shell"-spectrum and our investigations (Karetnikov and Menchenkova 1987) have shown, in the atmosphere of the primary star there are formed only wings of hydrogen lines and lines of Mg II (lambda = 448.1 nm). A complete bibliography of papers devoted to the investigation of V 367 Cygni is given in Karetnikov and Menchenkova (1985). Our research work is based upon spectrograms obtained with the 6 m telescope at SAO of the Soviet Academy of Sciences, the dispersion being 9 and 14 A/mm as well as with the 122 cm telescope of CrAO of the Soviet Academy of Sciences, the dispersion being 37 A/mm. The spectral region investigated ranges from lambda = 360 to 490 nm. The presence of emission in the first terms of Balmer series including the H_gamma line is a characteristic peculiarity of V 367 Cyg spectrum throughout the whole period. The emission intensity in line H_alpha varies with the phase - amounting to 2.4 at the primary minimum and to 1.1 at the maximum- (Karetnikov and Prekrestnyi 1973), in units of a continuous spectrum. Line H_beta has a complex structure, the Be profile is of particular interest. Whereas in 1981 the blue and red emission component lines of H_beta had different intensity, in 1982 the intensity of the components became similar. This resulted in a central absorption shift as shown by radial velocity measurements: in 1981 the velocity of the latter was -41 km/sec whereas in 1982 it increased to -4 km/sec. Another characteristic peculiarity of V 367 Cygni is the presence of numerous lines of neutral and ionized metals in the spectrum which lines show a practically constant radial velocity and a marked asymmetry. The asymmetry observed seems to be caused by a velocity gradient in the aggregate envelope of the system wherein the line spectrum observed is formed. The most intensive lines of FeII have emission companions. From metal lines using the criteria of spectral classification by Kopylov, we determined the envelope temperature which proved to be equal to 9500° (Karetnikov and Menchenkova, 1985). From the number of the last line observed of the Balmer series of hydrogen we estimated the concentration of free electrons in the envelope lg n_e = 11.96 (m = 30). The physical conditions in the envelope of V 367 Cygni were determined by the curve-of-growth method. The curves of growth have been constructed from lines FeI, FeII, TiII, CrII separately for the most interesting phases of the light curve 0.0, 0.2, 0.5, 0.7 when one can expect a change of conditions in the envelope. A mean curve of growth has been constructed as well using mean values of equivalent widths of lines. The results of the determination are given in Table I. Table I. FeI Theta_ex=0.82 FeII Theta_ex=0.65 TiII Theta_ex=0.56 CrII Theta_ex=0.61 v_t lg N_tau v_t lg N_tau v_t lg N_tau v_t lg N_tau 0.0d - - 33±9 6.11 18±4 6.41 19±9 - 0.2d - - 31±3 5.97 22±7 6.88 18±6 5.36 0.5d 15±1 5.88 26±6 5.85 30±7 6.92 22±7 5.44 0.7d 13±1 5.61 26±5 5.93 23±7 6.68 18±5 5.40 12±2 5.80 27±5 5.85 25±8 6.65 20±5 5.39 The complete absence of stellar origin details in the spectrum is a characteristic peculiarity of the V 367 spectrum, and this markedly impedes investigations into the nature of stellar components. Due to careful position measurements we could detect a single stellar line MgII at lambda = 448.1 nm whereas investigation of the contours of hydrogen lines H_gamma and H_delta has shown that they are of complicated structure, a narrow envelope core being superimposed upon the wide line of atmospheric origin. The radial velocities of the cores of these lines are constant in time and space being equal to -4 km/sec whereas the wings show great shifts with the amplitude up to 160 km/sec and coincidence with the phase of orbital motion of the primary star's system. The wings of these lines appear to be described equally well by three models: T_eff = 12000°, lg g = 2.5, - T_eff = 16000°, lg g = 3.0, - T_eff = 20000°, lg g - 3.5. The consideration of higher terms of Balmer series H_8 - H_14 with the use of synthetic hydrogen spectra calculated by Pavlenko (Main Astronomical Observatory of the Ukrainian Academy of Sciences) made it possible to limit the temperature range to T_eff - 12000° - 16000°, lg g = 2.5 - 3.0. The line MgII (lambda = 448.1 nm) is not sensitive to the magnitude of lg g but the equivalent width of the line decrease with the temperature increase. It enabled us to obtain additional information on the physical parameters of the primary star atmosphere of the V 367 Cyg system. It appeared that T_eff = 12000° - 14000°, lg g = 2.5 - 3.0 (assuming that lg N (Mg) = lg N_0 (Mg). We failed to elicit any detail which could be identified with the spectrum of the second component. There came as no surprise as the difference of stellar magnitudes of the bright star and a companion according to Fresa (1966) is not less than 1.5 mag. The absence of helium lines is a characteristic peculiarity of V 367 Cyg spectrum though the lines of helium should be observed at the temperature of 12000° which we determined for the primary star. It should be noted that these lines are confidently observed in the spectrum of the primary star of the beta Lyr system having close values of T_eff and lg g. The difference between the spectra of these two systems testifies to the fact that V 367 Cygni is at an earlier stage of evolution than beta Lyr in which the stage of a fast mass exchange is completed resulting in an enhanced helium abundance: N(He)/N(H) = 1.55 (Leushin et al. 1979). Possibly in the case of V367 Cyg the helium lines are blended to a greater extent by spectral lines of other elements which formation proceeds in a more powerful and more extended envelope. References: Fresa, A., 1966, Mem. Soc. Astr. Ital., 37, No.3, 607. Karetnikov, V.G., Menchenkova, E.V., 1985, Astron. Zh., 62, 542. Karetnikov, V.G., Menchenkova, E.V., 1987, Problemi astronomii. Part 2. Kiev. Dep in UkrNIINTI N430-Uk87, 2. Karetnikov, V.G., Prekrestnyi, S.M., 1973, Problemi kosmicheskoi fiziki, v.8, 159. Leushin, V.V., Nevsky, M.Yu., Snezhko L.I., 1979, Astrofiz. isledowanija Izv. SAO), II, 40.
Var. Phenomena in Close Bin. Stars
Com. Konkoly Obs. Hung. Akad. Sci.
10, Part 7, (No.93), Budapest 1989.
SOME REMARKS ON ECLIPSING BINARIES
SEEMING TO BE INCONSISTENT WITH GENERAL RELATIVITY
T. Hegedus
Baja Observatory of the Hungarian Academy of Sciences, Hungary
At the present time the eclipsing binary systems are very important objects of
quite different parts of astrophysics due to their numerous advantageous observational and
theoretical features. Two of these properties are the possibility of checking different
models of the internal structure of stars and the testing of General Relativity (GR) by
studying apsidal motion.
There exist a lot of eclipsing systems having well-observable periastron motion.
Many of them have reasonable theoretical representation based on several model computations
of polytropic stars. The theoretical rates of apsidal motion obtained by predicted internal
structure constants are in fair agreement with the observed ones in most cases of the given
binary systems. Besides them, we know some binaries showing considerable periastron advance
in consequence of GR, due to their special physical parameters. Koch turned attention to
such systems in which the relativistic contribution to the net rotation of the line of
apsid is comparable with the classical (CL) effect (Koch, 1973). These binaries are EK Cep,
alpha CrB, V1143 Cyg, DI Her and RR Lyn. This list has, since, been supplemented: Gimenez
proposed 23 candidates and 13 additional eclipsing variables for the study of relativistic
apsidal advance (Gimenez, 1985). In the last decade some of these systems have gained great
importance because these binaries seem to show much slower apsidal rotation than expected
from the combined classical and relativistic (CL+GR) effects. We would like to make some
additional remarks on this problem.
The above mentioned discrepancies have been discussed by several authors. Except
for the attempts to remove the observed differences within
TABLE 1.
ACCEPTED PHYSICAL PARAMETERS OF THE PROBLEMATICAL BINARIES
SYSTEM: REFERENCES: M_1 M_2 P_SID e l(x10^9 cm)
(M_Theta) (M_Theta) (days) M.w. P.w.
Y Cyg Gimenez et a1.,1987 16.7 16.7 2.9963310 0.1456 6.5 6.76
±4 ±4 ±37 ±16
a)Popper,1982 5.15 4.52 10.5501585* 0.4883 2.0 2.014
DI Her b)Guinan & Maloney,1985 ±10 ±6 ±25 ±10 ±32
c)Martynov & Lavrov,1987 (a) (a) (b) (c)
a)Popper,1974 4.53 4.12 2.0287298 0.068 1.8 1.810
AG Per b)Gimenez et al.,1987 ±7 ±6 ±91 ±1 ±26
c)Gudur,1978 (a) (a) (b) (c)
AS Cam Khaliullin&Kozyreva,1983 3.3 2.5 3.4309475* 0.1695 1.3 1.24
±1 ±1 ±16 ±14 ±4
a)taken from Moffat,1984 2.5 2.5 11.1208715* 0.35 1.0 1.08
V889 Aqlb) Gimenez & Scaltriti,1982±5 ±5 ±111 ±3 ±20
(a) (a) (b) (b)
a)Popper,1987 2.02 1.12 4.4277938 0.120 0.66 0.708
EK Cep b)Gimenez & Margrave,1985 ±1 ±1 ±74 ±3 ±4
c)Khaliullin,1983 (a) (a) (b) (c)
V1143 CygGimenez & Margrave,1985 1.33 1.29 7.6407418 0.540 - 0.604
±3 ±3 ±15 ±5 ±12
M_1 and M_2: masses of the components
e : orbital eccentricity,
M.w.: values of "l", taken from Moffat's work (Moffat, 1984),
P.w.: values of "l", resulted from present work.
the range of Newtonian Mechanics, Moffat proposed to interchange GR with a Nonsymmetric
Gravitational Theory (NGT) elaborated by himself. From this new theory another formula
follows for the yearly rate of apsidal motion, instead of the standard Einsteinian one
(Moffat, 1984). This new expression involves a factor, "lambda". This "lambda" not only
reduces the rate but it may also yield a negative sign for it, depending on the value of a
constant of integration "l" appearing in the formula of "lambda" (Moffat, 1984). With his
new theory Moffat could explain the observed behaviour of these peculiar systems. In his
article he presented the results of his calculations for mu^1 Sco, Y Cyg, DI Her, AG Per,
AS Cam, V889 Aql, EK Cep and PSR 1913+16 (Moffat, 1984). He compared the CL+GR and the
CL+NGT combined effects with the observed values of the apsidal motion rates and concluded
that NGT can provide a satisfactory explanation for these binary systems.
COMPARISON OF THEORY WITH OBSERVATIONS
As a first step, we repeated the computation of omega-dot_GR and omega-dot_NGT (contributions
of GR and NGT to the total effects) together with the calculation of their mean errors, using
the recently published or/and the best known physical parameters of the above mentioned systems
(with the exception of mu^1 Sco and PSR 1913+16, but with an additional binary V 1143 Cyg).
The accepted parameters and their mean errors are shown in Table 1, with the source
references. In the fifth column of this table the sidereal orbital periods can be found
with their approximate errors. P_SID values are sometimes calculated (indicated with "*"),
and in the other cases they are taken from the authors directly (if they were calculated by
the author himself). In the last two columns we show the values of the parameter "l" given
by Moffat (1984) and those resulting from our calculations, using the expression which is
valid only for non-degenerated stars (taken from Guinan and Maloney, 1985).
In Table 2 we present the theoretical values of omega-dot_GR and omega-dot_NGT resulting from
our calculations (with their errors), and Moffat's omega-dot_NGT (Moffat has not published errors).
In the third column, one can see the least erroneous (or in some cases the recently published)
observed rates of apsidal motion (omega-dot_OBS). The results of computations of the Newtonian
contributions are taken from several authors, and presented in the last column of Table 2.
Their sources with the references are also shown.
Taking into account the data in Table 2, one can establish:
i) The errors of the observed physical parameters of binary systems cause
TABLE 2.
COMPARISON OF THE THEORETICAL AND OBSERVATIONAL APSIDAL MOTION RATES
THEOR THEOR THEOR THEOR THEOR THEOR
SYSTEM : omega-dot omega-dot omega-dot omega-dot omega-dot omega-dot omega-dot
OBS CL±NGT CL±GR GR NGT NGT CL
(Delta_1) (Delta_2) (this work) M. W.
Y Cyg 7.569 5.588 13.538 0.338 -7.612 -6.55 13.2
±24 ±5 ±28.623
(a) (±1.981) (-5.969) (b)
DI Her 0.00770 0.0043 0.0426 0.0233 -0.0150 -0.0141 0.0193
±7 ±55 ±29 ±3 ±29 ±26
(c) (±0.0034) (-0.0349) (d)
AG Per 4.735 5.330 7.189 0.259 -1.600 -1.57 6.93
±36 ±3 ±1.141
(a) (-0.595) (-2.454) (b)
AS Cam 0.136 0.238 0.442 0.085 -0.119 -0.185 0.357
±15 ±98 ±33 ±2 ±67 ±31
(e) (-0.102) (-0.306) (f)
V889 Aql 0.0151 0.0141 0.0205 0.0119 +0.0055 +0.0072 0.0086
±49 ±19 ±48
(g) (±0.0010) (-0.0054) (b)
EK Cep 0.0823 0.0324 0.0652 0.0362 +0.0034 +0.0117 0.029
±75 ±102 ±102 ±2 ±2 ±10
(h) (±0.0499) (±0.0171) (i)
V1143 Cyg 0.0337 0.0279 0.0419 0.0180 +0.0040 - 0.0239
±20 ±141 ±139 ±4 ±6 ±135
(j) (±0.0058) (-0.0082) (j)
References: a: Gimenez et al., 1987 f: Khaliullin and Kozyreva, 1983
b: Moffat, 1984 g: Gimenez and Scaltriti, 1982
c: Martynov and Lavrov, 1987 h: Hill and Ebbinghausen, 1984
d: Guinan and Valoney, 1985 i: Khaliullin, 1983
e: Maloney et al., 1986 j: Gimenez and Margrave, 1985
M.W.: Data are taken from Moffat (1984). All rates are in (deg/years). THEOR THEOR
THEOR THEOR
Delta_1 = -omega-dot - omega-dot ; Delta_2 = omega-dot - omega-dot .
OBS CL+NGT OBS CL+GR
very large uncertainties in the output omega-dot_NGT.
ii) The above mentioned input errors give a possibility to determine the general
relativistic part with much better accuracy.
iii) The classical effect generally has a large error due to two very uncertain
factors, viz. the internal structure constants and the ratio of rotational and orbital
velocities (omega_r/omega_K).
iv) With the up-dated physical parameters of these systems the CL+NGT combined
effects cannot approximate the observations so well as in Moffat's paper (Moffat, 1984),
but it can be done better than by CL+GR.
v) The traditional CL+GR rates are in agreement with the observed ones within the
limits of error for V 889 Aql, EK Cep and V 1143 Cyg. They are considered as nonproblematic
systems. Thus, only Y Cyg, DI Her, AG Per and AS Cam show some discrepancies from General
Relativity.
vi) The NGT (with classical mechanics) gives an apsidal motion rate (for EK Cep)
which deviates from the observed value by almost 5sigma^1. Although the relative error of
omega-dot_CL is about 34% in this case.
It seems that neither General Relativity nor the Nonsymmetric Gravitational Theory
can be retained or rejected without further detailed study of this problem.
NODAL REGRESSION
As a second step, let us consider what follows if we want to keep the GR at any
cost.
In this case, obviously, we have to dissect the Newtonian contribution. We have two
very uncertain quantities in it, viz. the k_2, k_3, etc. parameters of the internal
structure of stars and the omega_r/omega_K ratio. For the former, one can make only rough
estimates based upon stellar model calculations: for the latter there is a confusion in the
literature. Some authors take for the above mentioned binaries the preliminary (but not
confirmed) assumption of omega_r/omega_K = 1, while some others take the well-known formula
of the synchronized rotational velocity of the components of an eccentric binary system:
omega_r/omega_K = 1 + ((12e^2)^(3/8))/2
to the lowest order in eccentricity (Zahn, 1977 and Giuricin et al., 1984). The theoretical
values of this ratio are 1.30, 1.74, 1.17, 1.34, 1.50, 1.26, 1.80 for Y Cyg, DI Her, AG Per,
AS Cam, V889 Aql, EK Cep and V 1143 Cyg, respectively.
For DI Her, Guinan and Maloney (1985) accepted 3.50 and 3.78 (for the primary and
secondary components, respectively). Other authors took equal values for the two components:
3.6 (Moffat, 1984), 3 (Martynov and Khaliul-lin, 1980), 7 (Koch, 1973). In the cases of EK
Cep and AG Per one can find values from 0.8 to 1.4, and from 1 to 2.5, respectively. The
ratio is usually taken as 1 for AS Cam and V 1143 Cyg, or V 889 Aql and Y Cyg. Moffat took
4.7 and 2.4 for the latters, respectively (Moffat, 1984).
Shakura has shown (Shakura, 1985), that if we omit the generally supposed
circumstances, namely that the rotational axes of both components are perpendicular to the
orbital plane, then we shall be able to rectify the observed discrepancies even under
reasonable conditions. He presented two examples supporting this conception. If one takes
the rotational axes into the orbital plane (alpha_1 = alpha_2 = 90°), one will recover the
observed omega-dot_OBS rates by taking about 3, and 9-10 for the values omega_r/omega_K in the
case of AS Cam and DI Her, respectively (Shakura, 1985). This latter fact demands somewhat
faster axial rotations but, as Shakuira mentioned, it can be compensated by a suitable choice
of beta_1, beta_2 (angles between the rotational axes and the line from the observer to the
center of the system). With appearance of the new part with negative sign in the generalized
expression of omega-dot_CL, the nodal line and the orbital inclination must be affected by secular
variations (Barker and O'Connel, 1978). Nodal regression may also be caused by the perturbations of a third body. This
assumption has also been taken into consideration in the case of DI Her (Martynov and
Khaliullin, 1980), but at present there exists no observational evidence of its existence.
In the case of AS Cam, Al-Naimiy called attention to the existence of an L_3=0.047 (at 525
nm) intensity, which can be cancelled out from the solution of the light curve. This may be
observational evidence of an about 12 mag faint third member of the system (Al-Naimiy,
1978). V 889 Aql also has a possible third body, corresponding to the existence of an
L_3 = 0.185 (in V band, Khaliullin and Khaliullina, 1987).
There are some other likely items of observational evidence for the existence of
nodal regression in the case of OO Aql (Demircan and Gudur, 1981), IU Aur, AY Mus (Schaefer,
1981) and AH Cep (Mayer, 1987). Another possible candidate is alpha CrB (Alexander, 1976). But
for any other eclipsing binaries exact evidence has not been found yet.
The fact that we suppose inclined rotational axes gives rise to some questions
about the origin of binary stars and their evolution. Discussion of this problem is not
our aim. However, one has to keep in mind that all of the problematical systems are young,
with massive components being before or in the main-sequence evolutionary status. The
logarithms of their approximate ages are 7.396 for AG Per (Shibata arid Mimura, 1976) and
7.699 for DI Her (Popper, 1982). The primary of EK Cep is a zero-age main sequence star
while its secondary is a pre-main-sequence one (Popper,1987). V 1143 Cyg, which was concluded
as a non-problematical system, has a log(t) = 9.2 (Gimdnea and Margrave, 1985). With respect
to the other problematical binaries we had no available data for their age.
For such young systems the characteristic time scale of vanishing of the
inclination of the components' rotational axes can easily be much longer than the present
age of the systems itself. This question needs further detailed study.
If the rotational axes are not perpendicular to the orbital plane (or owing to any
other reason) a nodal regression occurs, then it must be reflected on the light curve as
complicated variations of the depth of minima (Shakura, 1985, Hegedus and Nuspl, 1986).
The general view of such kind of variations has shown (under some simplified conditions)
for the concrete example of DI Her (Hegedus and Nuspl, 1986).
DEPTHS OF LIGHT MINIMA
Our third purpose was to search for the existence of such behaviour of depth of
light minima among the above listed stars.
Unfortunately, photometric data in the standard UBV system available to us at the
present time, were limited. Numerous visual or/and photographic estimates are not of use
because of their inaccuracy and incompatibility with the recently used photometric systems.
Some otherwise very good and numerous measurements were also not adopted here since they
were given in an instrumental, or in another standard photometric system. We have accepted
the measurements published transformed into the Johnsonian standard UBV system. The time
variations of minima depth are expected to have about some hundredths of stellar magnitude
as their amplitudes, and are expected to have from 60 to 1000 years as their periods.
This work is in progress: published or unpublished UBV data from individual authors
and from databases are continuously collected. In view of this, the following remarks
represent only a short preliminary report.
All the values of minima depths currently available are shown in Table 3, with the
time intervals covered by the individual data series and
TABLE 3: DEPTHS OF MINIMA OF THE PROBLEMATIC BINARIES
SYSTEM: J.D. R Depth of primary minima Depth of second. minima
(-2400000) (V) (B) (U) (V) (B) (U)
Y Cyg 39712-42577 a 0.601 0.602 0.587
39712-40528 a (0.593) (0.596) (0.573)
±7 ±5 ±21
41127-41229 b (0.574) (0.569) (0.585)
±7 ±15 ±16
44081-44083 s (0.585)
±6
DI Her 38245-38308 c (0.716)?(0.719)? (0.547)?
±16 ? ±21 ? ±18 ?
(1950-1978) d 0.715 0.727 0.785 0.577 0.563 0.530
40016-43718 e (0.707) (0.723) (0.773) (0.549) (0.548) (0.516)
±5 ±6 ±6 ±6 ±6 ±7
AG Per 37963-38020 t (0.273) (0.276) (0.286) (0.253) (0.261) (0.241)
±9 ±13 ±17 ±14 ±17 ±20
38351-38363 c (0.289)? (0.296)?
±10 ? ±12 ?
42330 u (0.266) (0.267) (0.284) (0.263) (0.267) (0.275)
±9 ±9 ±11 ±12 ±10 ±10
42384-42757 f 0.282 0.285 0.281 0.277
(0.277) (0.284) (0.281) (0.277)
±3 ±4 ±3 ±3
44897-44915 v (0.272) (O.274) (0.278) (0.278)
±10 ±11 ±9 ±11
47118.4458 g 0.285 0.295
±13 ±18
AS Cam (1968-1969) h 0.61 ? 0.34 ?
40556-41011 1 0.620 0.655 0.735 0.395 0.395 0.335
±11 ±9 ±19 ±11 ±9 ±19
41547-42580 j 0.595 0.625 0.390 0.385
44937-44971 k 0.593 0.630 0.363 0.355
±3 ±3 ±4 ±5
TABLE 3: (continuation)
SYSTEM: J.D. R Depth of primary minima Depth of second. minima
(-2400000) (V) (B) (U) (V) (B) (U)
AS Cam 44937-44971 k (0.601) (0.365)
±3 ±4
46771 l 0.590
V889 Aql38932-39655 c (0.552)? (0.443)?
±19 ? ±21 ?
41812-43399 m (0.546)? (0.419)
±20 ? ±4
EK Cep 38971-39023 n 1.246 1.326 0.130 O.070
(1.327) (0.070)
±6 ±2
40882-40891 o (0.106) (0.074)
±4 ±6
43144-43874 p (1.20) ? (0.10) ?
43902-44630 q 1.204 1.326 0.115 0.075
±3 ±3 ±4 ±6
(1.217) (O.117)
±5 ±3
V1143 Cyg38932-39655 r 0.525 0.533 0.535 0.214 0.213 0.215
(0.520) (0.527) (0.527) (O.211) (0.210) (0.214)
±4 ±4 ±4 ±2 ±2 ±3
40835-41173 o (0.525) (0.536)
±7 ±6
Remarks: a: O'Connell, 1977 l: Guinan et al., 1987
b: Zaitseva et al., 1971 m: Bernardi and Scaltriti, 1978
c: Semeniuk, 1968 n: Ebbinghausen, 1966
d: Martynov and Khaliullin, 1978 o: Guarnieri et al., 1975
e: Martynov and Khaliullin, 1980 p: Hill and Ebbinghausen, 1984
f: Gudur, 1978 q: Khaliullin, 1983
g: this paper r: Snowden and Koch, 1969
h: Hilditch, 1969 s: Gimenez and Costa, 1980
i: Pndnlia and Srivastava, 1975 t: Jones, 1969
j: Gulmen et al., 1976 u: Woodward and Koch, 1987
k: Khaliullin and Kozyreva, 1983 V: Gimenez et al., 1987
Figure 1. Figure 2.
Depth of pri. min. of AS Cam Depth of sec. min. of AS Cam
Figure 3. Figure 4.
Depth of pri. min. of EK Cep Depth of sec. min. of EK Cep
closed unpublished
(Error bars are opened if they were published in the source literatures).
with their sources. The data in parentheses are resulted from our least-squares parabolic
fitting to the measured points (very near the center of minima). This was done for lack of
published values of the depth of minima, but for some other cases also, in order to check
our method and the methods of other authors. The mean value of brightness measurements
outside of eclipses was taken as the maximum light level. In some cases, due to the lack of
these kinds of measurements we took data from other authors. Establishing the maximum light
of the system was sometimes quite difficult because of slight proximity effects or intrinsic
variations.
At the moment we cannot say anything about the existence or absence of secular
variations of the depth of minima among the problematic systems, and of the constancy among
non-problematic ones. The data at our disposal are very few, and are extended to only a
short time interval in relation to the time scale of the expected variations.
Two interesting cases having many data are shown in Figs. 1-4. AS Cam is a
problematic system. In Figs. 1 and 2 we present the changes of depths of minima, observed
in V and B light. The, measurements in these two bands can be considered as the check of
each other. The error bars of stellar magnitudes are closed in the case of known values,
and are open in the case of suspected ones. The first value is very uncertain. Probably it
was not made in the standard B band, rather in an instrumental one. AS Cam seems to show a
predicted kind of variation.
EK Cep was concluded as a non-problematic system, so it was not expected to show
secular variations of minima depths referring to a nodal regression. As one can see from
Figs. 3 and 4, the B measurements demonstrate the constancy well, while in the V measurements
one can find much deeper minima at the earlier epoch. This latter fact makes it questionable
whether those values are really correct.
FINAL REMARKS
It would be advisable to measure the depth of minima from time to time with greater
accuracy, with the same (UBV) measuring system and using the same procedure in the
standardization and data reduction (making the available data set homogeneous). For the
sake of safe verification of the existence (in the cases of Y Cyg, DI Her, AG Per and AS
Cam) or absence (in the cases of V 889 Aql, EK Cep and V1143 Cyg) of nodal regression we
should have high-quality, homogeneous UBV photometric data on the depth of minima,
distributed over wide time intervals.
Finally, we would like to call attention to the possibility of independent
determination of spatial orientation of the orbit (by polarimetric measurements, see Rudy,
1979), and of the true position of rotational axes of the components of a close binary
system (by spectroscopic method, see Rossitter, 1924). It would be very important to apply
these techniques to the problematic eclipsing binaries.
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