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Photometric and spectroscopic analysis of YY CrB
The eclipsing binary YY Coronae Borealis is a short-period contactsystem of the W UMa type (sub-type A) and one of the systems with agreat potential for providing a combined photometric and spectroscopicsolution. Using WD and FOTEL codes we reanalyzed the system, and applieda spotted model to treat the asymmetry of the light curve. The resultsshow that the more massive component is cooler than the less massivewith ΔT˜100K. The system is an overcontact one with fill-outfactor approximately equal to 64% and distance to the system 88±7pc.
| The Minimum Mass Ratio for Contact Close Binary Systems of W Ursae Majoris-type
Extreme mass ratio close binaries of W UMa-type represent an interestingclass of objects in which ˜1M main-sequence star is in contactwith a significantly less massive companion (M˜0.1M). Earliertheoretical investigations of these systems found that there is aminimum mass ratio q=M/M≈0.085-0.095 (obtained for n=3polytrope-fully radiative primary) above which these systems are stable.If the mass ratio is lower than minimum, a tidal instability develops(Darwin's instability). This instability, which is secular, growing on aviscous dissipation timescale, eventually forces the stars to merge intoa single, rapidly rotating object (such as FK Com-type stars or bluestragglers), implying that such systems would not be observed. Thereappear to be, however, some W UMa-type binaries with empiricallyobtained q values below the theoretical limit for stability. The aim ofthis dissertation was to try to resolve the discrepancy between theoryand observations by considering rotating polytropes. Other candidatesystems for stellar mergers such as AM CVn-type stars have also beendiscussed in the dissertation.
| Possible solution to the problem of the extreme mass ratio W UMa-type binaries
When the total angular momentum of a binary system is at a critical(minimum) value, a tidal instability occurs (Darwin's instability),eventually forcing the stars to merge into a single, rapidly rotatingobject. The instability sets in at some critical separation which in thecase of contact binaries corresponds to a minimum mass ratio dependingon dimensionless gyration radius k1. If one considers n = 3polytrope (fully radiative primary with Γ1 = 4/3),k21 = 0.075 and qmin ~ 0.085-0.095.There appears to be, however, some W UMa-type binaries with q valuesvery close, if not below these theoretical limits, implying that primaryin these systems is probably more centrally condensed. We try to solvethe discrepancy between theory and observations by considering rotatingpolytropes. We show by deriving and solving a modified Lane-Emdenequation for n = 3 polytrope that including the effects of rotation doesincrease the central concentration and could reduce qmin toas low as 0.070-0.074, more consistent with the observed population.
| New absolute magnitude calibrations for W Ursa Majoris type binaries
Parallaxes of W UMa stars in the Hipparcos catalogue have been analyzed.31 W UMa stars, which have the most accurate parallaxes(σπ/π<0.15) which are neither associated with aphotometric tertiary nor with evidence of a visual companion, wereselected for re-calibrating the Period-Luminosity-Color (PLC) relationof W UMa stars. Using the Lutz-Kelker (LK) bias corrected (mostprobable) parallaxes, periods ({0.26< P< 0.87}, P in days), andcolors ({0.04<(B-V)0<1.28}) of the 31 selected W UMa,the PLC relation have been revised and re-calibrated. The differencebetween the old (revised but not bias corrected) and the new (LK biascorrected) relations are almost negligible in predicting the distancesof W UMa stars up to about 100 pc. But, it increases and may becomeintolerable as distances of stars increase. Additionally, using(J-H)0 and (H-K_s)0 colors from 2MASS (Two MicronAll Sky Survey) data, a PLC relation working with infrared data wasderived. It can be used with infrared colors in the range-0.01<(J-H)0<0.58, and{-0.10<(H-K_s)0<0.18}. Despite of the fact that the2MASS data refer to single epoch observations which are not guaranteedto be taken at maximum brightness of the W UMa stars, the establishedrelation has been found surprisingly consistent and reliable inpredicting LK corrected distances of W UMa stars.
| Angular momentum and mass evolution of contact binaries
Various scenarios of contact binary evolution have been proposed in thepast, giving hints of (sometimes contradictory) evolutionary sequencesconnecting A- and W-type systems. As the components of close detachedbinaries approach each other and contact binaries are formed, followingevolutionary paths transforms them into systems of two categories:A-type and W-type. The systems evolve in a similar way but underslightly different circumstances. The mass/energy transfer rate isdifferent, leading to quite different evolutionary results. Analternative scenario of evolution in contact is presented and discussed,based on the observational data of over one hundred low-temperaturecontact binaries. It results from the observed correlations amongcontact binary physical and orbital parameters. Theoretical tracks arecomputed assuming angular momentum loss from a system via stellar wind,accompanied by mass transfer from an advanced evolutionary secondary tothe main-sequence primary. A good agreement is seen between the tracksand the observed graphs. Independently of details of the evolution incontact and a relation between A- and W-type systems, the ultimate fateof contact binaries involves the coalescence of both components into asingle fast rotating star.
| DN Bootis: A low mass-ratio W UMa-type contact binary
New photoelectric BVR light curves and radial velocity curves wereobtained for the HIPPARCOS discovery DN Boo at theTÜBİTAKTÜBİTAK: The Scientific and TechnicalResearch Council of Turkey.1 National Observatory of Turkey(TUG) and Dominion Astrophysical Observatory (DAO), respectively, todetermine physical nature of the variable. The character of the obtainedlight curves and double-lined spectroscopic structures in the obtainedspectra are revealed that DN Boo is a genuine EW type eclipsing binary.During the analysis of our new observations a simultaneous solution werederived for the photometric and spectroscopic data by using the WilsonDevinney code and orbital parameters with absolute dimensions of thesystem were determined for the first time. Finally, the importance ofvery low mass-ratio contact binaries in the late stages of close binaryevolution was discussed.
| The evolutionary status of W Ursae Majoris-type systems
Well-determined physical parameters of 130 W Ursae Majoris (W UMa)systems were collected from the literature. Based on these data, theevolutionary status and dynamical evolution of W UMa systems areinvestigated. It is found that there is no evolutionary differencebetween W- and A-type systems in the M-J diagram, which is consistentwith the results derived from the analysis of observed spectral type andof M-R and M-L diagrams of W UMa systems. M-R and M-L diagrams of W- andA-type systems indicate that a large amount of energy should betransferred from the more massive to the less massive component, so thatthey are not in thermal equilibrium and undergo thermal relaxationoscillation. Moreover, the distribution of angular momentum, togetherwith the distribution of the mass ratio, suggests that the mass ratio ofthe observed W UMa systems decreases with decreasing total mass. Thiscould be the result of the dynamical evolution of W UMa systems, whichsuffer angular momentum loss and mass loss as a result of the magneticstellar wind. Consequently, the tidal instability forces these systemstowards lower q values and finally to rapidly rotating single stars.
| Contact Binaries with Additional Components. III. A Search Using Adaptive Optics
We present results of the Canada-France-Hawaii Telescope adaptive optics(AO) search for companions of a homogeneous group of contact binarystars, as a contribution to our attempts to prove the hypothesis thatthese binaries require a third star to become as close as observed. Inaddition to directly discovering companions at separations of>=1″, we introduced a new method of AO image analysis utilizingdistortions of the AO diffraction ring pattern at separations of0.07″-1″. Very close companions, with separations in thelatter range, were discovered in the systems HV Aqr, OO Aql, CK Boo, XYLeo, BE Scl, and RZ Tau. More distant companions were detected in V402Aur, AO Cam, and V2082 Cyg. Our results provide a contribution to themounting evidence that the presence of close companions is a very commonphenomenon for very close binaries with orbital periods <1 day.Based on observations obtained at the Canada-France-Hawaii Telescope,which is operated by the National Research Council of Canada, theInstitut National des Sciences de l'Univers of the Centre National de laRecherche Scientifique of France, and the University of Hawaii.
| The minimum mass ratio of W UMa-type binary systems
When the total angular momentum of a binary system Jtot =Jorb + Jspin is at a certain critical (minimum)value, a tidal instability occurs which eventually forces the stars tomerge into a single, rapidly rotating object. The instability occurswhen Jorb = 3Jspin, which in the case of contactbinaries corresponds to a minimum mass ratio qmin ~0.071-0.078. The minimum mass ratio is obtained under the assumptionthat stellar radii are fixed and independent. This is not the case withcontact binaries where, according to the Roche model, we haveR2 = R2(R1, a, q). By finding a newcriterion for contact binaries, which arises from dJtot = 0,and assuming k21 ≠ k22for the component's dimensionless gyration radii, a theoretical lowerlimit qmin = 0.094-0.109 for overcontact degree f = 0-1 isobtained.
| Formation and Evolution of W Ursae Majoris Contact Binaries
The origin and evolution of W UMa systems are discussed based on All SkyAutomated Survey (ASAS) data and the mean kinematic ages of foursubgroups of 97 field contact binaries (FCBs). The period distributionof eclipsing binaries discovered by ASAS suggests that a period limit totidal locking for the close binaries is about 2.24 days, so that most WUMa systems might be formed from detached binaries with periodsP<~2.24 days, and a maximum advanced time from a detached system to aW UMa is about 3.23 Gyr. Moreover, the secular evolution of the angularmomentum (AM), the system mass, and the orbital period of 97 FCBs wereinvestigated according to the mean kinematic ages, which were setaccording to AM bins. AMs, systemic masses, and orbital periods wereshown to be decreasing with kinematic age. Their first-order decreasingrates have been determined as J˙/J=1.86×10-10yr-1, M˙/M=0.95×10-10 yr-1,and P˙/P=1.24×10-10 yr-1, and theaverage amplification (A¯=dlnJ/dlnM) is derived to be 1.96. Theseare lower than those derived from detached chromospherically activebinaries (CABs). This suggests that the magnetic activity level of FCBsis indeed weaker than that of CABs. Meanwhile, the decreasing rate of AMof FCBs is found to be equal to an average value in a cycle of a cyclicmodel of contact binaries. This might suggest that the evolution of FCBsundergoes thermal relaxation oscillation (TRO) and that the coalescenceof W UMa systems is a very long process, which is also indicated by thedynamical evolution of FCBs.
| Physical parameters and multiplicity of five southern close eclipsing binaries
Aims.We detected tertiary components of close binaries from spectroscopyand light curve modelling, investigated the light-travel time effect andthe possibility of magnetic activity cycles, measured mass ratios forunstudied systems, and derived absolute parameters. Methods: We carriedout new photometric and spectroscopic observations of five bright (< 10.5 mag) close eclipsing binaries, predominantly in thesouthern skies. We obtained full Johnson BV light curves, which weremodelled with the Wilson-Devinney code. Radial velocities were measuredwith the cross-correlation method using IAU radial velocity standards asspectral templates. Period changes were studied with the O-C method,utilising published epochs of minimum light (XY Leo) and ASAS photometry(VZ Lib). Results: For three objects (DX Tuc, QY Hya, V870 Ara),absolute parameters have been determined for the first time. Wespectroscopically detected the tertiary components in XY Leo and VZ Liband discovered one in QY Hya. For XY Leo we updated the light-timeeffect parameters and detected a secondary periodicity of about 5100 din the O-C diagram that may hint at the existence of short-periodmagnetic cycles. A combination of recent photometric data shows that theorbital period of the tertiary star in VZ Lib is likely to be over 1500d. QY Hya is a semi-detached X-ray active binary in a triple system withK and M-type components, while V870 Ara is a contact binary with thethird smallest spectroscopic mass ratio for a W UMa star to date (q =0.082 ± 0.030). Being close to the theoretical minimum forcontact binaries, this small mass ratio suggests that V870 Ara has thepotential of constraining evolutionary scenarios of binary mergers. Theinferred distances to these systems are compatible with the Hipparcosparallaxes.Based on observations made at the Siding Spring Observatory, Australia.Light curves and radial velocity data are only available in electronicform at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5)or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/465/943
| Pulkovo compilation of radial velocities for 35495 stars in a common system.
Not Available
| 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. II. A Spectroscopic Search for Faint Tertiaries
It is unclear how very close binary stars form, given that during thepre-main-sequence phase the component stars would have been inside eachother. One hypothesis is that they formed farther apart but were broughtin closer after formation by gravitational interaction with a thirdmember of the system. If so, all close binaries should be members oftriple (or higher order) systems. As a test of this prediction, wepresent a search for the signature of third components in archivalspectra of close binaries. In our sample of 75 objects, 23 show evidencefor the presence of a third component, down to a detection limit oftertiary flux contributions of about 0.8% at 5200 Å (consideringonly contact and semidetached binaries, we find 20 out of 66). In ahomogeneous subset of 59 contact binaries, we are fairly confident thatthe 15 tertiaries we have detected are all tertiaries present with massratios 0.28<~M3/M12<~0.75 and implied outerperiods P<~106 days. We find that if the frequency oftertiaries were the same as that of binary companions to solar-typestars, one would expect to detect about 12 tertiaries. In contrast, ifall contact binaries were in triple systems, one would expect about 20.Thus, our results are not conclusive but are sufficiently suggestive towarrant further studies.
| Masses and angular momenta of contact binary stars
Results are presented on component masses and system angular momenta forover 100 low-temperature contact binaries. It is found that thesecondary components in close binary systems are very similar in mass.Our observational evidence strongly supports the argument that theevolutionary process goes from near-contact binaries to A-type contactbinaries, without any need of mass loss from the system. Furthermore,the evolutionary direction of A-type into W-type systems with asimultaneous mass and angular momentum loss is also discussed. Theopposite direction of evolution seems to be unlikely, since it requiresan increase of the total mass and the angular momentum of the system.
| The dynamical stability of W Ursae Majoris-type systems
Theoretical study indicates that a contact binary system would mergeinto a rapidly rotating single star due to tidal instability when thespin angular momentum of the system is more than a third of its orbitalangular momentum. Assuming that W Ursae Majoris (W UMa) contact binarysystems rigorously comply with the Roche geometry and the dynamicalstability limit is at a contact degree of about 70 per cent, we obtainthat W UMa systems might suffer Darwin's instability when their massratios are in a region of about 0.076-0.078 and merge into thefast-rotating stars. This suggests that the W UMa systems with massratio q <= 0.076 cannot be observed. Meanwhile, we find that theobserved W UMa systems with a mass ratio of about 0.077, correspondingto a contact degree of about 86 per cent would suffer tidal instabilityand merge into the single fast-rotating stars. This suggests that thedynamical stability limit for the observed W UMa systems is higher thanthe theoretical value, implying that the observed systems have probablysuffered the loss of angular momentum due to gravitational waveradiation (GR) or magnetic stellar wind (MSW).
| 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.
| Evolutionary Status of Late-Type Contact Binaries
The old model of an unevolved, cool contact binary, in which thesecondary component is strongly oversized due to energy transfer fromthe primary, and the whole system is out of thermal equilibrium,encounters serious problems.I present a new scenario for evolution of contact binaries, which solvesthe problem of thermal nonequilibrium by assuming that contact binariesare past mass exchange with a mass ratio reversal. The scenario isdivided into three phases. In PhaseI loss of angular momentum (AM) dueto magnetized wind of a detached binary is followed until the primarycomponent fills its critical Roche lobe. In Phase II mass transfer takesplace until mass ratio reversal. Arguments are given in favor of such aprocess in pre-contact binaries. In PhaseIII an approximate evolutionarypath of the contact binary is followed until a possible coalescence. AMloss, evolutionary effects of the components and mass transfer to theprimary are taken into account.It is concluded that WUMa type binaries are old objects with secondariesin an advanced evolutionary stage, possibly with small helium cores.Both components fulfill the mass-radius relation for contact binarieswhile being in thermal equilibrium.
| Luminosity function of contact binaries based on the All Sky Automated Survey (ASAS)
The luminosity function for contact binary stars of the W UMa type isevaluated on the basis of the All Sky Automated Survey (ASAS)photometric project covering all stars south of δ=+ 28° withina magnitude range 8 < V < 13. Lack of colour indices enforced alimitation to 3374 systems with P < 0.562 d (i.e. 73 per cent of allsystems with P < 1 d) where a simplified MV(logP)calibration could be used. The spatial density relative to themain-sequence FGK stars of 0.2 per cent, as established previously fromthe Hipparcos sample to V= 7.5, is confirmed. While the numbers ofcontact binaries in the ASAS are large and thus the statisticaluncertainties small, derivation of the luminosity function required acorrection for missed systems with small amplitudes and with orbitalperiods longer than 0.562 d; the correction, by a factor of 3, carriesan uncertainty of about 30 per cent.
| 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. V. The Lowest Mass Ratio Binary V857 Herculis
Charge-coupled device (CCD) photometric light curves in the B, V, and Rbands of the complete eclipsing binary star V857 Her are presented. Itis shown that the light curves of the W UMa-type binary are symmetricand of A type according to Binnendijk's classification. Our four epochsof light minimum along with others compiled from the literature wereused to revise the period and study the period change. Weak evidenceindicates that the orbital period of V857 Her may show a continuousincrease at a rate of dP/dt=+2.90×10-7 daysyr-1. The photometric parameters of the system weredetermined with the 2003 version of the Wilson-Devinney code. It isshown that V857 Her is a deep overcontact binary system withf=83.8%+/-5.1%. The derived mass ratio of q=0.06532+/-0.0002 suggeststhat it has the lowest mass ratio among overcontact binary systems. Asthe orbital period increases, the decrease of the mass ratio will causeit to evolve into a single rapidly rotating star when it meets the morefamiliar criterion that the orbital angular momentum be less than 3times the total spin angular momentum. To understand the evolutionarystate of the system, long-term photometric monitoring and spectroscopicobservations will be required.
| Physical Parameters of Components in Close Binary Systems: IV
The paper presents new geometric, photometric and absolute parameters,derived from combined spectroscopic and photometric solutions, for tencontact binary systems. The analysis shows that three systems (EF Boo,GM Dra and SW Lac) are of W-type with shallow to moderate contact. Sevensystems (V417 Aql, AH Aur, YY CrB, UX Eri, DZ Psc, GR Vir and NN Vir)are of A-type in a deep contact configuration. For six systems (V417Aql, YY CrB, GM Dra, UX Eri, SW Lac and GR Vir) a spot model isintroduced to explain the O'Connell effect in their light curves. Thephotometric and geometric elements of the systems are combined with thespectroscopic data taken at David Dunlap Observatory to yield theabsolute parameters of the components.
| Kinematics of W Ursae Majoris type binaries and evidence of the two types of formation
We study the kinematics of 129 W UMa binaries and we discuss itsimplications on the contact binary evolution. The sample is found to beheterogeneous in the velocity space. That is, kinematically younger andolder contact binaries exist in the sample. A kinematically young (0.5Gyr) subsample (moving group) is formed by selecting the systems thatsatisfy the kinematical criteria of moving groups. After removing thepossible moving group members and the systems that are known to bemembers of open clusters, the rest of the sample is called the fieldcontact binary (FCB) group. The FCB group is further divided into fourgroups according to the orbital period ranges. Then, a correlation isfound in the sense that shorter-period less-massive systems have largervelocity dispersions than the longer-period more-massive systems.Dispersions in the velocity space indicate a 5.47-Gyr kinematical agefor the FCB group. Compared with the field chromospherically activebinaries (CABs), presumably detached binary progenitors of the contactsystems, the FCB group appears to be 1.61 Gyr older. Assuming anequilibrium in the formation and destruction of CAB and W UMa systems inthe Galaxy, this age difference is treated as an empirically deducedlifetime of the contact stage. Because the kinematical ages (3.21, 3.51,7.14 and 8.89 Gyr) of the four subgroups of the FCB group are muchlonger than the 1.61-Gyr lifetime of the contact stage, the pre-contactstages of the FCB group must dominantly be producing the largedispersions. The kinematically young (0.5 Gyr) moving group covers thesame total mass, period and spectral ranges as the FCB group. However,the very young age of this group does not leave enough room forpre-contact stages, and thus it is most likely that these systems wereformed in the beginning of the main sequence or during thepre-main-sequence contraction phase, either by a fission process or mostprobably by fast spiralling in of two components in a common envelope.
| Times of Minima for Neglected Eclipsing Binaries in 2004
Times of minima obtained during 2004 for a number of neglected eclipsingbinaries are presented.
| Physical Parameters of Components in Close Binary Systems: III
The paper presents combined spectroscopic and photometric orbitalsolutions for five close binary systems: V 402Aur, SX Crv, V829 Her, VZLib and V753 Mon. The photometric data consist of new complete,multicolor light curves, while the spectroscopy has been recentlyobtained within the radial velocity program at the David DunlapObservatory. For one target, SX Crv, new spectroscopic data wereobtained using the 6.5 m Magellan telescope. A contact configuration wasfound through light curve modeling for all targets except V753 Mon. Oursolution for V753 Mon resulted in a semidetached configuration with theslightly less massive component filling its Roche lobe.
| SB9: The ninth catalogue of spectroscopic binary orbits
The Ninth Catalogue of Spectroscopic Binary Orbits(http://sb9.astro.ulb.ac.be) continues the series of compilations ofspectroscopic orbits carried out over the past 35 years by Batten andcollaborators. As of 2004 May 1st, the new Catalogue holds orbits for2386 systems. Some essential differences between this catalogue and itspredecessors are outlined and three straightforward applications arepresented: (1) completeness assessment: period distribution of SB1s andSB2s; (2) shortest periods across the H-R diagram; (3)period-eccentricity relation.
| Contact binary stars of the W UMa-type as distance tracers
Contact binaries can be used for distance determinations of stellarsystems. They are easy to discover and identify and are very abundantamong solar-type stars, particularly for MV>+3. Theperiod-luminosity-colour (PLC) relations have similar properties tothose for pulsating stars and can currently predict individual values ofMV to about +/-0.25 mag.
| Up-to-Date Linear Elements of Eclipsing Binaries
About 1800 O-C diagrams of eclipsing binaries were analyzed and up-todate linear elements were computed. The regularly updated ephemerides(as a continuation of SAC) are available only in electronic form at theInternet address: http://www.as.ap.krakow.pl/ephem/.
| 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.
| The 7.5 Magnitude Limit Sample of Bright Short-Period Binary Stars. I. How Many Contact Binaries Are There?
A sample of bright contact binary stars (W UMa type or EW, and related:with β Lyr light curves, EB, and ellipsoidal, ELL-in effect, allbut the detached, EA) to the limit of Vmax=7.5 mag is deemedto include all discoverable short-period (P<1 day) binaries withphotometric variation larger than about 0.05 mag. Of the 32 systems inthe final sample, 11 systems have been discovered by the Hipparcossatellite. The combined spatial density is evaluated at(1.02+/-0.24)×10-5 pc-3. The relativefrequency of occurrence (RFO), defined in relation to the main-sequencestars, depends on the luminosity. An assumption of RFO~=1/500 forMV>+1.5 is consistent with the data, although the numberstatistics is poor with the resulting uncertainty in the spatial densityand the RFO by a factor of about 2. The RFO rapidly decreases forbrighter binaries to a level of 1/5000 for MV<+1.5 and to1/30,000 for MV<+0.5. The high RFO of 1/130, previouslydetermined from the deep OGLE-I sample of disk population W UMa typesystems toward Baade's window, is inconsistent with and unconfirmed bythe new results. Possible reasons for the large discrepancy arediscussed. They include several observational effects but also apossibility of a genuine increase in the contact-binary density in thecentral parts of the Galaxy. Based on data from the Hipparcos satellitemission and from the David Dunlap Observatory, University of Toronto.
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