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Radial Velocity Studies of Southern Close Binary Stars. I. Winter Systems
Radial velocity measurements and sine-curve fits to the orbital velocityvariations are presented for nine contact binaries: V1464 Aql, V759 Cen,DE Oct, MW Pav, BQ Phe, EL Aqr, SX Crv, VZ Lib, and GR Vir. For thefirst five of these, our observations are the first available radialvelocity data. For the three remaining radial velocity variables, CE Hyiis a known visual binary, while CL Cet and V1084 Sco are suspected to bemultiple systems in which the contact binary is spectrally dominated byits companion (which itself is a binary in V1084 Sco). Five additionalvariable stars, V872 Ara, BD Cap, HIP 69300, BX Ind, and V388 Pav, areof unknown type, but most are pulsating stars; we give their mean radialvelocities and Vsini.Based on data obtained at the European Southern Observatory.
| Contact Binaries with Additional Components. I. The Extant Data
We have attempted to establish observational evidence for the presenceof distant companions that may have acquired and/or absorbed angularmomentum during the evolution of multiple systems, thus facilitating orenabling the formation of contact binaries. In this preliminaryinvestigation we use several techniques (some of themdistance-independent) and mostly disregard the detection biases ofindividual techniques in an attempt to establish a lower limit to thefrequency of triple systems. While the whole sample of 151 contactbinary stars brighter than Vmax=10 mag gives a firm lowerlimit of 42%+/-5%, the corresponding number for the much better observednorthern-sky subsample is 59%+/-8%. These estimates indicate that mostcontact binary stars exist in multiple systems.
| V781 Tauri: a W Ursae Majoris binary with decreasing period
We analyze light curves of the W UMa type eclipsing binary V781 Taurifrom three epochs and radial velocity curves from two epochssimultaneously, including previously unpublished B and V data. Theoverall time span is from 1983 to 2000 and the solution is donecoherently in time (not phase) with five light curves and two sets ofprimary and secondary velocity curves. Minor systematic differencesamong the individual light curves are not large enough to undermine thevalue of a coherent solution that represents 18 years of observations.Times of minima confirm a period of 0.34491d and the general solutionfinds a small period change, dP/P, of(5.08±{04})×10-11 that represents recentbehavior. The eclipse timings cover the last half-century and find dP/Pabout four times smaller, corresponding to a period change time scale,P/(dP/dt) of about 6 million years. The system is over-contact with afilling factor of 0.205. The solution produces a temperature differenceof about 260 K between the components, an inclination of 65.9dg, and amass ratio M_2/M_1=2.47. Separate solutions of the several light curvesthat incorporate dark spots find parameters that differ little fromcurve to curve. Absolute masses, luminosities, radii and the distanceare derived, with luminosities and distance based on star 1 being oftype G0V. The orbital angular momentum is compared with those of other WUMa type binaries and is normal. The star to star mass flow that one caninfer from dP/dt is opposite to that expected from TRO (ThermalRelaxation Oscillator) theory, but pertains to a time span that is veryshort compared to the time scale of TRO oscillations.
| A catalogue of eclipsing variables
A new catalogue of 6330 eclipsing variable stars is presented. Thecatalogue was developed from the General Catalogue of Variable Stars(GCVS) and its textual remarks by including recently publishedinformation about classification of 843 systems and making correspondingcorrections of GCVS data. The catalogue1 represents thelargest list of eclipsing binaries classified from observations.
| Deep, Low Mass Ratio Overcontact Binary Systems. III. CU Tauri and TV Muscae
New CCD photometric light curves in the B and V bands of the neglected WUMa-type eclipsing variable star CU Tauri are presented. The O'Connelleffect in the V light curve obtained in 2001 by Yang and Liu was aboutΔV=+0.015, but it vanished in our 2004 observations. Thevariations in the levels of both minima were seen. Our two epochs oflight minimum and others compiled from the literature were used for theperiod study. It is shown that the types of some eclipse times wereincorrect and the values of the period obtained by previousinvestigators were aliases that prevented formation of a plausible O-Ccurve. A new linear ephemeris was derived, and it is discovered that theorbital period of CU Tau shows a continuous decrease at a rate ofdP/dt=-1.81×10-6 days yr-1. The presentsymmetric light curves were solved with the 2003 version of theWilson-Devinney (W-D) code. Both our solutions and those derived by Yangand Liu reveal that CU Tau is a deep (f=50.1%+/-3.2%), low mass ratio(q=0.1770+/-0.0017) overcontact binary system.Meanwhile, the photoelectric light curves in the B, V, R, and I bands ofTV Muscae published by Hilditch and coworkers were reanalyzed with the2003 version of the W-D code. It is shown that the low mass ratio binaryturns out to be a deep overcontact system with f=74.3%+/-11.3%. A periodanalysis with all collected times of light minimum revealed acombination of a long-term period decrease(dP/dt=-2.16×10-7 days yr-1) and a possiblecyclic change with a period of 29.1 yr. The rapid long-term perioddecreases of both systems can be explained as a combination of the masstransfer from the more massive component to the less massive one and theangular momentum loss due to mass outflow from the L2 point. In thatway, the overcontact degrees of the two systems will become deeper astheir periods decrease, and finally they will evolve into a singlerapid-rotation star. However, for CU Tau, the rate of the secular perioddecrease is very large when compared with the other systems of the sametype. This suggests that the long-term period decrease may be part of along-period periodic change, which we need more data to check.
| On the properties of contact binary stars
We have compiled a catalogue of light curve solutions of contact binarystars. It contains the results of 159 light curve solutions. Theproperties of contact binary stars were studied using the cataloguedata. As is well known since Lucy's (\cite{Lucy68a},b) and Mochnacki's(\cite{Mochnacki81}) studies, primary components transfer their ownenergy to the secondary star via the common envelope around the twostars. This transfer was parameterized by a transfer parameter (ratio ofthe observed and intrinsic luminosities of the primary star). We provethat this transfer parameter is a simple function of the mass andluminosity ratios. We introduced a new type of contact binary stars: Hsubtype systems which have a large mass ratio (q>0.72). These systemsshow behaviour in the luminosity ratio- transfer parameter diagram thatis very different from that of other systems and according to ourresults the energy transfer rate is less efficient in them than in othertypes of contact binary stars. We also show that different types ofcontact binaries have well defined locations on the mass ratio -luminosity ratio diagram. Several contact binary systems do not followLucy's relation (L2/L1 =(M2/M1)0.92). No strict mass ratio -luminosity ratio relation of contact binary stars exists.Tables 2 and 3 are available in electronic form athttp://www.edpsciences.org
| A CCD photometric study of the W UMa contact binary Y Sextantis
A V light curve of the W UMa contact binary Y Sex is presented inthis paper. From the observations, two times of minimum light wasdetermined and from the present times of minimum light and thosecollected from the references, the change in the orbital period of thesystem was analyzed with the method of Kalimeris et al. [A&A 282(1994) 775]. The result reveals that the orbital period of the systemoscillates with a cycle of about 50 years and an amplitude of1.1×10-6 days. The light curve was analyzed by means ofthe latest version of the Wilson-Devinney code, which was also used tocorrect photometric effects on the radial-velocity curve obtained byMcLean and Hilditch [MNRAS 203 (1983) 1]. The results suggest that Y Sex is an A-subtypecontact binary with a mass ratio of q=0.180(2). In the new photometricsolution, a positive value of the third light of the system suggeststhat the sinusoidal variation of the period could be caused by a thirdcomponent in the system. The absolute dimensions of Y Sex are found tobe: M1=1.21(18) Msolar, M2=0.22(3)Msolar, R1=1.50(2) Rsolar,R2=0.75(1) Rsolar, L1=3.00(44)Lsolar, L2=0.69(10) Lsolar, A=2.66(11)Rsolar.
| Are overcontact binaries undergoing thermal relaxation oscillation with variable angular momentum loss?
Orbital period variations of five W-type overcontact binaries, GW Cep,VY Cet, V700 Cyg, EM Lac and AW Vir, are presented based on the analysisof all available times of light minimum. It is discovered that theperiod of GW Cep is decreasing at a rate of dP/dt=-6.62×10-8 d yr-1. For VY Cet and V700 Cyg, acyclic oscillation is found superimposed on a secular period increase,which can be explained either by the light-time effect of an assumedthird body or by magnetic activity cycles. For the other two, EM Lac andAW Vir, the periods show a secular increase. GW Cep is a low mass ratiosystem with q= 0.37, while the others are high mass ratio systems (q=0.67, 0.65, 0.63 and 0.76, respectively). The period changes of the fivesample stars are in good agreement with Qian's conclusion that low massratio overcontact binaries usually show a decreasing period, while theperiods of high mass ratio systems are increasing.Based on the period variations of 59 overcontact binaries, a statisticalinvestigation of period change is given. It is confirmed that the periodchange of a W UMa-type binary star is correlated with the mass ratio (q)and with the mass of the primary component (M1). Meanwhile,some statistical relations (M1-P,Js-M1, Js-M2 andJs-P) for overcontact binaries are presented using theabsolute parameters of 78 systems. From these relations, the followingresults may be drawn: (i) free mass transfer in both directions existsbetween the components, which is assumed by thermal relaxationoscillation (TRO) theory; (ii) angular momentum loss (AML) can make a WUMa-type star maintain shallow overcontact and not evolve fromovercontact to semidetached configurations as proposed by Rahunen; (iii)the evolution of the W UMa-type systems may be oscillation around acritical mass ratio, while the critical mass ratio varies with the massof the primary component. These results can be plausibly explained bythe combination of the TRO and the variable AML via a change of depth ofthe overcontact, which is consistent with the X-ray and IUEobservations.
| Catalogue of the field contact binary stars
A catalogue of 361 galactic contact binaries is presented. Listedcontact binaries are divided into five groups according to the type andquality of the available observations and parameters. For all systemsthe ephemeris for the primary minimum, minimum and maximum visualbrightness and equatorial coordinates are given. If available,photometric elements, (m1+m2)sin3i,spectral type, parallax and magnitude of the O'Connell effect are alsogiven. Photometric data for several systems are augmented by newobservations. The quality of the available data is assessed and systemsrequiring modern light-curve solutions are selected. Selectedstatistical properties of the collected data are discussed.
| Orbital period changes of contact binary systems: direct evidence for thermal relaxation oscillation theory
Orbital period changes of ten contact binary systems (S Ant, ɛCrA, EF Dra, UZ Leo, XZ Leo, TY Men, V566 Oph, TY Pup, RZ Tau and AGVir) are studied based on the analysis of their O-C curves. It isdiscovered that the periods of the six systems, S Ant, ɛ CrA, EFDra, XZ Leo, TY Men and TY Pup, show secular increases. For UZ Leo, itssecular period increase rate is revised. For the three systems, V566Oph, RZ Tau and AG Vir, weak evidence is presented that a periodicoscillation (with periods of 20.4, 28.5 and 40.9yr respectively) issuperimposed on a secular period increase. The cyclic period changes canbe explained by the presence of an unseen third body in the threesystems. All the sample stars studied are contact binaries withM1>=1.35Msolar. Furthermore, orbital periodchanges of 27 hot contact binaries have been checked. It is found that,apart from AW UMa with the lowest mass ratio (q=0.072), none shows anorbital period decrease. The relatively weak magnetic activity in thehotter contact binaries means little angular momentum loss (AML) fromthe systems via magnetic stellar winds. The period increases of these WUMa binaries can be explained by mass transfer from the secondary to theprimary components, which is in agreement with the prediction of thethermal relaxation oscillation (TRO) models. This suggests that theevolution of a hotter W UMa star is mainly controlled by TRO. On theother hand, for a cooler W UMa star(M1<=1.35Msolar), its evolution may be TRO plusAML, which coincides with the recent results of Qian.
| A CCD Photometric Study of the Contact Binary V396 Monocerotis
Complete BV light curves of the W Ursae Majoris binary V396 Mon arepresented. The present CCD photometric observations reveal that thelight curves of the system are obviously asymmetric, with the primarymaximum brighter than the secondary maximum (the ``O'Connell effect'').The light curves are analyzed by means of the latest version of theWilson-Devinney code. The results show that V396 Mon is a W-subtype WUMa contact binary with a mass ratio of 0.402. The asymmetry of thelight curves is explained by a cool spot on the secondary component. Thenature of the overluminosity of the secondary of a W UMa-type system isanalyzed. It is shown that the overluminosity of the secondary isclearly related to the mass of the primary and that, for a W UMa system,the higher the mass of the primary, the greater the overluminosity ofthe secondary. In addition, the overluminosity of the secondary is alsorelated to its own density: the lower the density of the secondary, thegreater its overluminosity.
| UY Ursae Majoris: A W-subtype W UMa system with a small mass ratio
We present light curves and photometric solutions of the contact binaryUY UMa in this paper. The light curves appear to exhibit a typicalO'Connell effect, with Maximum I being 0.034 mag(V) and 0.030 mag(B)brighter than Maximum II, respectively, and Maximum I shifting to phase0.26. The light curves are analyzed by means of the latest version ofthe WD program. The results show that UY UMa is a W-subtype contactbinary with a small mass ratio q=0.134. The asymmetry of the lightcurves is explained by star spot models. From the collected data of 9UMa contact systems with a smaller mass ratio than 0.20, the nature ofthe secondaries is analyzed. The results show that the luminosities anddensities of the secondaries could be controlled by the primaries andthat the smaller the mass ratio, the stronger the control.
| ROSAT all-sky survey of W Ursae Majoris stars and the problem of supersaturation
From ROSAT all-sky survey (RASS) data we obtained X-ray fluxes for 57 WUMa type contact systems. In our sample we detected three stars whichare the shortest period main sequence binaries ever found as X-raysources. For stars with (B-V)_0 < 0.6 the normalized X-ray fluxdecreases with a decreasing color index but for (B-V)_0 > 0.6 aplateau is reached, similar to the saturation level observed for single,rapidly rotating stars. The X-ray flux of W UMa stars is about 4-5 timesweaker than that of the fastest rotating single stars. Because earlytype, low activity variables have longer periods, an apparentperiod-activity relation is seen among our stars, while cool stars with(B-V)_0 > 0.6 and rotation periods between 0.23 and 0.45 days do notshow any such relation. The lower X-ray emission of the single, ultrafast rotators (UFRs) and W UMa stars is interpreted as the result of adecreased coronal filling factor. The physical mechanisms responsiblefor the decreased surface coverage differs for UFRs and W UMa systems.For UFRs we propose strong polar updrafts within a convection zone,driven by nonuniform heating from below. The updrafts should beaccompanied by large scale poleward flows near the bottom of theconvective layer and equatorward flows in the surface layers. The flowsdrag dynamo generated fields toward the poles and create a field-freeequatorial region with a width depending on the stellar rotation rate.For W UMa stars we propose that a large scale horizontal flow embracingboth stars will prevent the magnetic field from producing long-livedstructures filled with hot X-ray emitting plasma. The decreased activityof the fastest rotating UFRs increases the angular momentum loss timescale of stars in a supersaturated state. Thus the existence of a periodcutoff and a limiting mass of W UMa stars can be naturally explained.
| Photometric Study of An A-Type Contact Binary: AP Aurigae
We present here a new photometric light curve analysis of the eclipsingbinary AP Aur. The CCD photometry, performed at the Yunnan Observatoryusing the 1.06 m telescope, has given 179 individual data points in Band V bandpass filters. From these data we have obtained two minimumtimes. Based on these two minima, together with some other photoelectricminima collected from the literature, we have determined a new epoch andthe rate of the period variation (p=1.268×10-9 dayscycle-1) of the system. The Wilson-Devinney model (firstdescribed in 1971) was used to derive the photometric solutions. AP Auris a W UMa-type contact binary system. The mass ratio(q=m2/m1=0.246) suggests that the system has anA-type W UMa binary configuration. We find that the asymmetry of thelight curve is most likely caused by mass transfer from the secondary tothe primary or a circulation effect in the common envelope. Theevolutionary status is considered, and we find that AP Aur has justevolved away from the main sequence. Finally the evolutionary future ofthe system is discussed.
| Stars with the Largest Hipparcos Photometric Amplitudes
A list of the 2027 stars that have the largest photometric amplitudes inHipparcos Photometry shows that most variable stars are all Miras. Thepercentage of variable types change as a function of amplitude. Thiscompilation should also be of value to photometrists looking forrelatively unstudied, but large amplitude stars.
| CCD photometric study of the contact binary FG Hydrae
A new light curve of the contact binary FG Hya is presented in thispaper. The new light curve and those obtained by other authors from 1955to 1985 show the change in the shape of the light curves of the system.The difference in the depths between the primary and secondary eclipsesincreased yearly from 1955 to 1985, but the present light curve seems toexhibit the same shape as the light curve of Smith in 1955. Thelong-term decrease of the orbital period of the system may be clear ifMahdy et al.'s (1985) timings in question were counted out. The presentlight curve and those obtained by Binnendijk in 1962 and Yang et al. in1982 are all analyzed by means of the latest version of the WD program.The results show that FG Hya is an over-contact binary with a small massratio. Although the light curves of the system changed considerably, thesolutions of the light curves obtained in 1955, 1982 and 1999 are inagreement. Table 4 is only available in electronic form athttp://www.edpsciences.org
| An observational approach for the determination of gravity darkening in contact binaries of W UMa type
A new method for the determination of the gravity darkening exponents inclose binaries of W UMa type is presented. The method is based onKopal's method of Fourier analysis of the light changes of eclipsingvariables in the Frequency Domain. In the analysis, the exponents forboth components of a W UMa system are assumed to be the same. First, themethod was successfully applied to two theoretical (test) light curves,belonging to two systems with radiative and convective envelopes,respectively. Then the method was applied to 36 W UMa systems for whichgeometric and photometric elements have been derived by the mostpowerful techniques. Systems showing large light curve anomalies wereexcluded from the analysis, since the effectiveness of the methoddepends strongly on the quality of the observations. Our results confirmthe previous results with the assumed, same geometrical parameters.Thederived values of the gravity darkening exponents are very close to thepredicted ones by the existing theory of radiative transfer orconvective equilibrium.
| Absolute Magnitude Calibration for the W UMa-Type Systems Based on HIPPARCOS Data
Hipparcos parallax data for 40 contact binary stars of the W UMa-type(with epsilon M_V < 0.5) are used to derive a new, (B-V)-basedabsolute-magnitude calibration of the form M_V = M_V(log P,B-V). Thecalibration covers the ranges 0.26 < (B-V)_0 < 1.14, 0.24 < P< 1.15 day, and 1.4 < M_V < 6.1; it is based on a solutionweighted by relative errors in the parallaxes (2.7% to 24%). Previouscalibrations have not been based on such a wide period and color space,and while they have been able to predict M_V with sufficient accuracyfor systems closely following the well-known period-color relation, thenew calibration should be able to give also good predictions for moreexotic ``outlying'' contact binary systems. The main limitations of thiscalibration are the inadequate quality of the ground-based photometricdata, and the restriction to the (B-V) index, which is more sensitive tometallicity effects than the (V-I) index; metallicities are, however,basically unknown for the local W UMa-type systems. (SECTION: Stars)
| The properties of W Ursae Majoris contact binaries: new results and old problems.
The physical properties of W UMa binary systems are revisited on thebasis of the observational data published in the last decade and of therecent theoretical studies on angular-momentum-loss-driven secularevolution. The absolute elements (masses, radii, luminosities) arederived by an inference method and a calibration based on the availablehigh quality spectroscopic orbits. The derived age (8Gy) agrees with theestimate of Guinan and Bradstreet from space motions. The analysis ofthe resulting physical parameters shows little correlation between thestandard classification in A and W subtype (first proposed by Binnendijk(1970) and only related to the light curve morphology) and theevolutionary status and origin of the systems. Most A-subtype systemsseem to have no evolutionary link with W-subtype ones. The relationbetween total mass and mass ratio for the "bona fide" sample alsosuggests that mass loss from the system may play an important role.
| The structure of late-type contact binaries
A unified treatment of late-type and early-type contact binaries basedon the assumption of hydrostatic equilibrium is extended here andapplied to late-type systems assuming systems in a steady state withminimized mass motions. A survey of configurations with M/M(solar) = 2or greater is presented, and the observational facts are shown to agreewith the theory.
| General properties of W Ursae Majoris systems
The light curves of a sample of 42 W Ursae Majoris binary systems (21W-type, 21 A-type) have been synthesized using the computer code ofWilson and Devinney (1971). The masses, radii and luminosities of thestars have been derived assuming the global properties of a contactbinary system are the same as those of an analogous detached system. Atable listing the main photometric data is given. Substantial continuitywas observed in the physical properties of the A-type and the W-typesystems, suggesting a scenario in which almost all of the A-type systemsare the evolved counterparts of the W-types. The existence of aninhomogeneous group, probably evolved into contact from a detachedconfiguration, is confirmed. An upper limit for the primary mass of theunevolved objects is derived.
| Statistics of categorized eclipsing binary systems Lightcurve shapes, periods, and spectral types
The statistics of the light curve morphologies, eclipse depths, orbitalperiods, and spectral types of about 1000 eclipsing binary systems areexamined, after attempting to subdivide these binaries into variousbasic evolutionary categories. The applicability of statisticalcriteria, based on light curve morphologies and eclipse depths, for thecategorization of eclipsing binaries has been found more limited thanpreviously believed. In particular, EW-type light curves turn out to begood indicators of contact systems (though not conversely), while EA-and EB-type light curves have little physical significance. Moreover,the study reveals a strong deficit of short-period noncontact systems inthe whole spectral range, together with an underabundance of early-typecontact binaries (compared with the number of late-type contact pairs).Interestingly, the distribution of evolved Algol-type systems isshifted, on average, to periods longer than those of unevolved detachedsystems in the OB and early A spectral range (and to shorter periods inthe F spectral range).
| Violet and ultraviolet continua of W UMa systems on the basis of UVBY photometry observations
New observations of 17 southern WUMa systems are discussed together withprevious uvby data for 44 systems to determine properties of violet andultraviolet spectral distributions and to relate them to theperiod-color relation. The interstellar-reddening-corrected delta(m1)values extend from -0.02 to +0.10, which could be interpreted by aplausible range of metallicities; the most positive values of delta(m1)and largest ultraviolet excesses are observed for systems having theshortest periods at a given spectral type. The reddening-correcteddelta(c1) values are close to zero and are only slightly positive forearlier spectral types - mean delta (cl) = +0.04 for (b-y)O less than0.31 - indicating only very slight evolutionary advancement. Traces of adelta(cl) = -delta(ml) correlation for least evolved systems - smallestdelta(cl) - leave the possibility of intrinsic excesses still open.
| A uvby, beta photometric survey of southern hemisphere
A uvby, beta photometric study of southern hemisphere eclipsing binarystars has been undertaken at Cerro Tololo Inter-American Observatory.The standardized colors and V magnitudes for 288 binaries at quadratureand/or at minimum are presented, along with an indication of theaccuracy of the standardization and photometry. Discussions of theresolving time of the pulse-counting photometers and of the atmosphericextinction at CTIO are included.
| Estimated absolute dimensions and the inferred lifetime and angular momentum of W Ursae Majoris contact binaries
The masses, radii, spectral types, and total specific angular momenta ofthe primary components of 47 W UMa contact binaries are estimated fromthe observed system spectral types and from an empirical spectraltype-mass relation. The binaries examined include 25 W-type and 22A-type systems. The absolute lifetimes of the primaries and theirfractional lifetimes with respect to the time required for crossing themain-sequence band are determined by finding the positions of theprimaries in theoretical evolutionary sequences for single stars. Afurther subdivision of the classical A- and W-type groups is discoveredin which each subclass corresponds to a characteristic origin andevolutionary state.
| On the evolutionary state of the W Ursae Majoris contact binaries
The observed spectral type of 17 A-type and 14 W-type W Uma binaries arecompared with the expected type when their primary components are normalmain sequence objects. For both groups the observed spectral typeappears on average to be shifted towards the later spectral types. Thisshift corresponds to an excess of the mass and radius of the primarycomponents with respect to the main sequence mass and radius inconformity with their observed spectral type. It is argued that neitherfor the W- nor all the A-type systems this excess should be explained asthe result of a normal nuclear evolution of the system.
| Fundamental photometric data for two contact binaries - MW Pavonis and TY Mensae
Abstract image available at:http://adsabs.harvard.edu/abs/1980AJ.....85.1098L
| A catalogue of parameters for eclipsing binaries
Not Available
| Contact binaries . III. Early-type systems.
Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1978AJ.....83..288E&db_key=AST
| UBV light variation and orbital elements of MW Pavonis
Photoelectric UBV observations of the W UMa-system MW Pavonis arepresented; they were made at Bosque Alegre Station ofCórdoba Observatory in 1972 and 1974. The period and linearephemeris were obtained from nine times of minimum observed in eachcolor. Satisfactory orbital elements were determined for the three lightcurves on the basis of the Russell model
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