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The Geneva-Copenhagen survey of the solar neighbourhood. III. Improved distances, ages, and kinematics
Context: Ages, chemical compositions, velocity vectors, and Galacticorbits for stars in the solar neighbourhood are fundamental test datafor models of Galactic evolution. The Geneva-Copenhagen Survey of theSolar Neighbourhood (Nordström et al. 2004; GCS), amagnitude-complete, kinematically unbiased sample of 16 682 nearby F andG dwarfs, is the largest available sample with complete data for starswith ages spanning that of the disk. Aims: We aim to improve theaccuracy of the GCS data by implementing the recent revision of theHipparcos parallaxes. Methods: The new parallaxes yield improvedastrometric distances for 12 506 stars in the GCS. We also use theparallaxes to verify the distance calibration for uvby? photometryby Holmberg et al. (2007, A&A, 475, 519; GCS II). We add newselection criteria to exclude evolved cool stars giving unreliableresults and derive distances for 3580 stars with large parallax errorsor not observed by Hipparcos. We also check the GCS II scales of T_effand [Fe/H] and find no need for change. Results: Introducing thenew distances, we recompute MV for 16 086 stars, and U, V, W,and Galactic orbital parameters for the 13 520 stars that also haveradial-velocity measurements. We also recompute stellar ages from thePadova stellar evolution models used in GCS I-II, using the new valuesof M_V, and compare them with ages from the Yale-Yonsei andVictoria-Regina models. Finally, we compare the observed age-velocityrelation in W with three simulated disk heating scenarios to show thepotential of the data. Conclusions: With these revisions, thebasic data for the GCS stars should now be as reliable as is possiblewith existing techniques. Further improvement must await consolidationof the T_eff scale from angular diameters and fluxes, and the Gaiatrigonometric parallaxes. We discuss the conditions for improvingcomputed stellar ages from new input data, and for distinguishingdifferent disk heating scenarios from data sets of the size andprecision of the GCS.Full Table 1 is only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/501/941
| 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.
| Hα and the Ca II H and K lines as activity proxies for late-type stars
Context: The main chromospheric activity indicator is the S index, whichis the ratio of the flux in the core of the Ca II H and K lines to thecontinuum nearby, and is well studied for stars from F to K. Anotherchromospheric proxy is the Hα line, which is believed to betightly correlated with the Ca II index. Aims: In this work wecharacterize both chromospheric activity indicators, the one associatedwith the H and K Ca II lines and the other with Hα, for the wholerange of late type stars, from F to M. Methods: We present periodicmedium-resolution echelle observations covering the complete visualrange, taken at the CASLEO Argentinean Observatory over 7 years. We usea total of 917 flux-calibrated spectra for 109 stars that range from F6to M5. We statistically study these two indicators for stars ofdifferent activity levels and spectral types. Results: We directlyderive the conversion factor that translates the known S index to fluxin the Ca II cores, and extend its calibration to a wider spectralrange. We investigate the relation between the activity measurements inthe calcium and hydrogen lines, and found that the usual correlationobserved is the product of the dependence of each flux on stellarcolour, and not the product of similar activity phenomena.Tables 1 and 2 and full Figs. 1 and 6 are only available in electronicform at http://www.aanda.org
| 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.
| 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.
| 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.
| 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/.
| The Geneva-Copenhagen survey of the Solar neighbourhood. Ages, metallicities, and kinematic properties of 14 000 F and G dwarfs
We present and discuss new determinations of metallicity, rotation, age,kinematics, and Galactic orbits for a complete, magnitude-limited, andkinematically unbiased sample of 16 682 nearby F and G dwarf stars. Our63 000 new, accurate radial-velocity observations for nearly 13 500stars allow identification of most of the binary stars in the sampleand, together with published uvbyβ photometry, Hipparcosparallaxes, Tycho-2 proper motions, and a few earlier radial velocities,complete the kinematic information for 14 139 stars. These high-qualityvelocity data are supplemented by effective temperatures andmetallicities newly derived from recent and/or revised calibrations. Theremaining stars either lack Hipparcos data or have fast rotation. Amajor effort has been devoted to the determination of new isochrone agesfor all stars for which this is possible. Particular attention has beengiven to a realistic treatment of statistical biases and errorestimates, as standard techniques tend to underestimate these effectsand introduce spurious features in the age distributions. Our ages agreewell with those by Edvardsson et al. (\cite{edv93}), despite severalastrophysical and computational improvements since then. We demonstrate,however, how strong observational and theoretical biases cause thedistribution of the observed ages to be very different from that of thetrue age distribution of the sample. Among the many basic relations ofthe Galactic disk that can be reinvestigated from the data presentedhere, we revisit the metallicity distribution of the G dwarfs and theage-metallicity, age-velocity, and metallicity-velocity relations of theSolar neighbourhood. Our first results confirm the lack of metal-poor Gdwarfs relative to closed-box model predictions (the ``G dwarfproblem''), the existence of radial metallicity gradients in the disk,the small change in mean metallicity of the thin disk since itsformation and the substantial scatter in metallicity at all ages, andthe continuing kinematic heating of the thin disk with an efficiencyconsistent with that expected for a combination of spiral arms and giantmolecular clouds. Distinct features in the distribution of the Vcomponent of the space motion are extended in age and metallicity,corresponding to the effects of stochastic spiral waves rather thanclassical moving groups, and may complicate the identification ofthick-disk stars from kinematic criteria. More advanced analyses of thisrich material will require careful simulations of the selection criteriafor the sample and the distribution of observational errors.Based on observations made with the Danish 1.5-m telescope at ESO, LaSilla, Chile, and with the Swiss 1-m telescope at Observatoire deHaute-Provence, France.Complete Tables 1 and 2 are only available in electronic form at the CDSvia anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/418/989
| 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 W UMa-type variable star V759 Cen.
Not Available
| 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.
| 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.
| Multiperiodicities from the Hipparcos epoch photometry and possible pulsation in early A-type stars
A selection criterion based on the relative strength of the largestpeaks in the amplitude spectra, and an information criterion are used incombination to search for multiperiodicities in Hipparcos epochphotometry. The method is applied to all stars which have beenclassified as variable in the Hipparcos catalogue: periodic, unsolvedand microvariables. Results are assessed critically: although there aremany problems arising from aliasing, there are also a number ofinteresting frequency combinations which deserve further investigation.One such result is the possible occurrence of multiple periods of theorder of a day in a few early A-type stars. The Hipparcos catalogue alsocontains a number of these stars with single periodicities: such starswith no obvious variability classifications are listed, and informationabout their properties (e.g., radial velocity variations) discussed.These stars may constitute a new class of pulsators.
| Chemical enrichment and star formation in the Milky Way disk. I. Sample description and chromospheric age-metallicity relation
The age-metallicity relation of the solar neighbourhood is studied usinga sample of 552 late-type dwarfs. This sample was built from theintersection of photometric catalogues with chromospheric activitysurveys of the Mount Wilson group. For these stars, metallicities wereestimated from uvby data, and ages were calculated from theirchromospheric emission levels using a new metallicity-dependentchromospheric activity-age relation developed by Rocha-Pinto &Maciel (\cite{RPM98}). A careful estimate of the errors in thechromospheric age is made. The errors in the chromospheric indices areshown to include partially the effects of the stellar magnetic cycles,although a detailed treatment of this error is still beyond ourknowledge. It is shown that the results are not affected by the presenceof unresolved binaries in the sample. We derive an age-metallicityrelation which confirms the mean trend found by previous workers. Themean metallicity shows a slow, steady increase with time, amounting atleast 0.56 dex in 15 Gyr. The initial metallicity of the disk is around-0.70 dex, in agreement with the G dwarf metallicity distribution(Rocha-Pinto & Maciel \cite{RPM96}). According to our data, theintrinsic cosmic dispersion in metal abundances is around 0.13 dex, afactor of two smaller than that found by Edvardsson et al. (\cite{Edv}).We show that chromospheric ages are compatible with isochrone ages,within the expected errors, so that the difference in the scatter cannotbe caused by the accuracy of our ages and metallicities. This reinforcessome suggestions that the Edvarsson et al.'s sample is not suitable tothe determination of the age-metallicity relation.
| A Multiplicity Survey of Chromospherically Active and Inactive Stars
Surveys of three samples of solar-type stars, segregated bychromospheric emission level, were made to determine their multiplicityfractions and to investigate the evolution of multiplicity with age. Intotal, 245 stars were searched for companions with DeltaV <= 3.0 andseparations of 0.035" to 1.08" using optical speckle interferometry. Byincorporating the visual micrometer survey for duplicity of theLamontHussey Observatory, the angular coverage was extended to 5.0" withno change in the DeltaV limit. This magnitude difference allows massratios of 0.63 and larger to be detected throughout a search region of2-127 AU for the stars observed. The 84 primaries observed in thechromospherically active sample are presumably part of a youngpopulation and are found to have a multiplicity fraction of 17.9% +/-4.6%. The sample of 118 inactive, presumably older, primaries wereselected and observed using identical methods and are found to have amultiplicity fraction of only 8.5% +/- 2.7%. Given the known linkbetween chromospheric activity and age, these results tentatively implya decreasing stellar multiplicity fraction from 1 to 4 Gyr, theapproximate ages of the two samples. Finally, only two of the 14 veryactive primaries observed were found to have a companion meeting thesurvey detection parameters. In this case, many of the systems areeither very young, or close, RS CVn type multiples that are unresolvableusing the techniques employed here.
| Metallicity effects on the chromospheric activity-age relation for late-type dwarfs
We show that there is a relationship between the age excess, defined asthe difference between the stellar isochrone and chromospheric ages, andthe metallicity as measured by the index [Fe/H] for late-type dwarfs.The chromospheric age tends to be lower than the isochrone age formetal-poor stars, and the opposite occurs for metal-rich objects. Wesuggest that this could be an effect of neglecting the metallicitydependence of the calibrated chromospheric emission-age relation. Wepropose a correction to account for this dependence. We also investigatethe metallicity distributions of these stars, and show that there aredistinct trends according to the chromospheric activity level. Inactivestars have a metallicity distribution which resembles the metallicitydistribution of solar neighbourhood stars, while active stars appear tobe concentrated in an activity strip on the logR'_HKx[Fe/H] diagram. Weprovide some explanations for these trends, and show that thechromospheric emission-age relation probably has different slopes on thetwo sides of the Vaughan-Preston gap.
| High-Resolution Spectroscopy of Some Very Active Southern Stars
We have obtained high-resolution echelle spectra of 18 solar-type starsthat an earlier survey showed to have very high levels of Ca ii H and Kemission. Most of these stars belong to close binary systems, but fiveremain as probable single stars or well-separated binaries that areyounger than the Pleiades on the basis of their lithium abundances andHα emission. Three of these probable single stars also lie morethan 1 mag above the main sequence in a color-magnitude diagram, andappear to have ages of 10 to 15 Myr. Two of them, HD 202917 and HD222259, also appear to have a kinematic association with thepre-main-sequence multiple system HD 98800.
| 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)
| A Survey of Ca II H and K Chromospheric Emission in Southern Solar-Type Stars
More than 800 southern stars within 50 pc have been observed forchromospheric emission in the cores of the Ca II H and K lines. Most ofthe sample targets were chosen to be G dwarfs on the basis of colors andspectral types. The bimodal distribution in stellar activity first notedin a sample of northern stars by Vaughan and Preston in 1980 isconfirmed, and the percentage of active stars, about 30%, is remarkablyconsistent between the northern and southern surveys. This is especiallycompelling given that we have used an entirely different instrumentalsetup and stellar sample than used in the previous study. Comparisons tothe Sun, a relatively inactive star, show that most nearby solar-typestars have a similar activity level, and presumably a similar age. Weidentify two additional subsamples of stars -- a very active group, anda very inactive group. The very active group may be made up of youngstars near the Sun, accounting for only a few percent of the sample, andappears to be less than ~0.1 Gyr old. Included in this high-activitytail of the distribution, however, is a subset of very close binaries ofthe RS CVn or W UMa types. The remaining members of this population maybe undetected close binaries or very young single stars. The veryinactive group of stars, contributting ~5%--10% to the total sample, maybe those caught in a Maunder Minimum type phase. If the observations ofthe survey stars are considered to be a sequence of snapshots of the Sunduring its life, we might expect that the Sun will spend about 10% ofthe remainder of its main sequence life in a Maunder Minimum phase.
| Walraven photometry of nearby southern OB associations
Homogeneous Walraven (VBLUW) photometry is presented for 5260 stars inthe regions of five nearby southern OB associations: Scorpio Centaurus(Sco OB2), Orion OB1, Canis Major OB1, Monoceros OB1, and Scutum OB2.Derived V and (B - V) in the Johnson system are included.
| V759 Centauri: New Times of Minima and Revised Period
Not Available
| Eclipsing binaries in open clusters. I - Preliminary study
A preliminary list of suspected eclipsing binaries in open clusters ispresented. The period, the mass ratio, the correlation between the massratio and cluster age, and the periodicity diagram are investigated.
| The rate of the angular-momentum loss due to magnetic breaking, as derived from binary statistics
Not Available
| 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.
| Spectral Classification and DDO Photometry of a Southern Group of Stars with Common Motions - Part One
Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1982PASP...94..304L&db_key=AST
| Light Elements of HD 123732
Not Available
| 58th Name-List of Variable Stars
Not Available
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Observation and Astrometry data
| Constellation: | Centaure |
| Right ascension: | 14h10m41.26s |
| Declination: | -47°46'08.4" |
| Apparent magnitude: | 7.549 |
| Distance: | 62.972 parsecs |
| Proper motion RA: | -89.1 |
| Proper motion Dec: | -11.1 |
| B-T magnitude: | 8.234 |
| V-T magnitude: | 7.606 |
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