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AKARI's infrared view on nearby stars. Using AKARI infrared camera all-sky survey, 2MASS, and Hipparcos catalogs
Context. The AKARI, a Japanese infrared space mission, has performed anAll-Sky Survey in six infrared-bands from 9 to 180 ?m with higherspatial resolutions and better sensitivities than IRAS. Aims: Weinvestigate the mid-infrared (9 and 18 ?m) point source catalog (PSC)obtained with the infrared camera (IRC) onboard AKARI, in order tounderstand the infrared nature of the known objects and to identifypreviously unknown objects. Methods: Color-color diagramsand a color-magnitude diagram were plotted with the AKARI-IRC PSCand other available all-sky survey catalogs. We combined the Hipparcosastrometric catalog and the 2MASS all-sky survey catalog with theAKARI-IRC PSC. We furthermore searched literature and SIMBADastronomical database for object types, spectral types, and luminosityclasses. We identified the locations of representative stars and objectson the color-magnitude and color-color diagram schemes. Theproperties of unclassified sources can be inferred from their locationson these diagrams. Results: We found that the (B-V) vs.(V-S9W) color-color diagram is useful for identifying thestars with infrared excess emerged from circumstellar envelopes ordisks. Be stars with infrared excess are separated well from other typesof stars in this diagram. Whereas (J-L18W) vs. (S9W-L18W)diagram is a powerful tool for classifying several object types.Carbon-rich asymptotic giant branch (AGB) stars and OH/IR stars formdistinct sequences in this color-color diagram. Young stellarobjects (YSOs), pre-main sequence (PMS) stars, post-AGB stars, andplanetary nebulae (PNe) have the largest mid-infrared color excess andcan be identified in the infrared catalog. Finally, we plot the L18W vs.(S9W-L18W) color-magnitude diagram, using the AKARI data togetherwith Hipparcos parallaxes. This diagram can be used to identify low-massYSOs and AGB stars. We found that this diagram is comparable to the [24]vs. ([8.0]-[24]) diagram of Large Magellanic Cloud sources usingthe Spitzer Space Telescope data. Our understanding of Galactic objectswill be used to interpret color-magnitude diagram of stellar populationsin the nearby galaxies that Spitzer Space Telescope observed. Conclusions: Our study of the AKARI color-color andcolor-magnitude diagrams will be used to explore properties ofunknown objects in the future. In addition, our analysis highlights afuture key project to understand stellar evolution with a circumstellarenvelope, once the forthcoming astronometrical data with GAIA areavailable.Catalog (full Tables 3 and 4) are only available in electronic form atthe CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/514/A2
| Pulkovo compilation of radial velocities for 35495 stars in a common system.
Not Available
| Mass-loss from dusty, low outflow-velocity AGB stars. I. Wind structure and mass-loss rates
We present the first results of a CO(2-1), (1-0), and 86 GHz SiO masersurvey of AGB stars, selected by their weak near-infrared excess. Amongthe 65 sources of the present sample we find 10 objects with low COoutflow velocities, vexp <~ 5 km s-1.Typically, these sources show (much) wider SiO maser features.Additionally, we get 5 sources with composite CO line profiles, i.e. anarrow feature is superimposed on a broader one, where both componentsare centered at the same stellar velocity. The gas mass-loss rates,outflow velocities and velocity structures suggested by these lineprofiles are compared with the results of hydrodynamical modelcalculations for dust forming molecular winds of pulsating AGB stars.The observations presented here give support to our recent lowoutflow-velocity models, in which only small amounts of dust are formed.Therefore, the wind generation in these models is dominated by stellarpulsation. We interpret the composite line profiles in terms ofsuccessive winds with different characteristics. Our hydrodynamicalmodels, which show that the wind properties may be extremely sensitiveto the stellar parameters, support such a scenario.Based on observations obtained at the European Southern Observatory, LaSilla, Chile and at the IRAM, Pico Veleta, Spain.
| Infrared Colors and Variability of Evolved Stars from COBE DIRBE Data
For a complete 12 μm flux-limited sample of 207 IRAS sources(F12>=150 Jy, |b|>=5deg), the majority ofwhich are AGB stars (~87%), we have extracted light curves in seveninfrared bands between 1.25 and 60 μm using the database of theDiffuse Infrared Background Experiment (DIRBE) instrument on the CosmicBackground Explorer (COBE) satellite. Using previous infrared surveys,we filtered these light curves to remove data points affected by nearbycompanions and obtained time-averaged flux densities and infraredcolors, as well as estimates of their variability at each wavelength. Inthe time-averaged DIRBE color-color plots, we find clear segregation ofsemiregulars, Mira variables, carbon stars, OH/IR stars, and red giantswithout circumstellar dust (i.e., V-[12]<5) and with little or novisual variation (ΔV<0.1 mag). The DIRBE 1.25-25 μm colorsbecome progressively redder and the variability in the DIRBE databaseincreases along the oxygen-rich sequence nondusty slightly varying redgiants-->SRb/Lb-->SRa-->Mira-->OH/IR and the carbon-richSRb/Lb-->Mira sequence. This supports previous assertions that theseare evolutionary sequences involving the continued production andejection of dust. The carbon stars are redder than their oxygen-richcounterparts for the same variability type, except in theF12/F25 ratio, where they are bluer. Of the 28sources in the sample not previous noted to be variable, 18 are clearlyvariable in the DIRBE data, with amplitudes of variation of ~0.9 mag at4.9 μm and ~0.6 mag at 12 μm, consistent with them being verydusty Mira-like variables. We also present individual DIRBE light curvesof a few selected stars. The DIRBE light curves of the semiregularvariable L2 Pup are particularly remarkable. The maxima at1.25, 2.2, and 3.5 μm occur 10-20 days before those at 4.9 and 12μm, and, at 4.9 and 12 μm, another maximum is seen between the twonear-infrared maxima.
| How many Hipparcos Variability-Induced Movers are genuine binaries?
Hipparcos observations of some variable stars, and especially oflong-period (e.g. Mira) variables, reveal a motion of the photocentercorrelated with the brightness variation (variability-induced mover -VIM), suggesting the presence of a binary companion. A re-analysis ofthe Hipparcos photometric and astrometric data does not confirm the VIMsolution for 62 among the 288 VIM objects (21%) in the Hipparcoscatalogue. Most of these 288 VIMs are long-period (e.g. Mira) variables(LPV). The effect of a revised chromaticity correction, which accountsfor the color variations along the light cycle, was then investigated.It is based on ``instantaneous'' V-I color indices derived fromHipparcos and Tycho-2 epoch photometry. Among the 188 LPVs flagged asVIM in the Hipparcos catalogue, 89 (47%) are not confirmed as VIM afterthis improved chromaticity correction is applied. This dramatic decreasein the number of VIM solutions is not surprising, since the chromaticitycorrection applied by the Hipparcos reduction consortia was based on afixed V-I color. Astrophysical considerations lead us to adopt a morestringent criterion for accepting a VIM solution (first-kind risk of0.27% instead of 10% as in the Hipparcos catalogue). With this moresevere criterion, only 27 LPV stars remain VIM, thus rejecting 161 ofthe 188 (86%) of the LPVs defined as VIMs in the Hipparcos catalogue.Based on observations from the Hipparcos astrometric satellite operatedby the European Space Agency (ESA 1997).Table 1 is also available in electronic form at the CDS, via anonymousftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/399/1167
| Hipparcos red stars in the HpV_T2 and V I_C systems
For Hipparcos M, S, and C spectral type stars, we provide calibratedinstantaneous (epoch) Cousins V - I color indices using newly derivedHpV_T2 photometry. Three new sets of ground-based Cousins V I data havebeen obtained for more than 170 carbon and red M giants. These datasetsin combination with the published sources of V I photometry served toobtain the calibration curves linking Hipparcos/Tycho Hp-V_T2 with theCousins V - I index. In total, 321 carbon stars and 4464 M- and S-typestars have new V - I indices. The standard error of the mean V - I isabout 0.1 mag or better down to Hp~9 although it deteriorates rapidly atfainter magnitudes. These V - I indices can be used to verify thepublished Hipparcos V - I color indices. Thus, we have identified ahandful of new cases where, instead of the real target, a random fieldstar has been observed. A considerable fraction of the DMSA/C and DMSA/Vsolutions for red stars appear not to be warranted. Most likely suchspurious solutions may originate from usage of a heavily biased color inthe astrometric processing.Based on observations from the Hipparcos astrometric satellite operatedby the European Space Agency (ESA 1997).}\fnmsep\thanks{Table 7 is onlyavailable in electronic form at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/397/997
| New periodic variables from the Hipparcos epoch photometry
Two selection statistics are used to extract new candidate periodicvariables from the epoch photometry of the Hipparcos catalogue. Theprimary selection criterion is a signal-to-noise ratio. The dependenceof this statistic on the number of observations is calibrated usingabout 30000 randomly permuted Hipparcos data sets. A significance levelof 0.1 per cent is used to extract a first batch of candidate variables.The second criterion requires that the optimal frequency be unaffectedif the data are de-trended by low-order polynomials. We find 2675 newcandidate periodic variables, of which the majority (2082) are from theHipparcos`unsolved' variables. Potential problems with theinterpretation of the data (e.g. aliasing) are discussed.
| Long period variable stars: galactic populations and infrared luminosity calibrations
In this paper HIPPARCOS astrometric and kinematic data are used tocalibrate both infrared luminosities and kinematical parameters of LongPeriod Variable stars (LPVs). Individual absolute K and IRAS 12 and 25luminosities of 800 LPVs are determined and made available in electronicform. The estimated mean kinematics is analyzed in terms of galacticpopulations. LPVs are found to belong to galactic populations rangingfrom the thin disk to the extended disk. An age range and a lower limitof the initial mass is given for stars of each population. A differenceof 1.3 mag in K for the upper limit of the Asymptotic Giant Branch isfound between the disk and old disk galactic populations, confirming itsdependence on the mass in the main sequence. LPVs with a thin envelopeare distinguished using the estimated mean IRAS luminosities. The levelof attraction (in the classification sense) of each group for the usualclassifying parameters of LPVs (variability and spectral types) isexamined. Table 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/374/968 or via ASTRIDdatabase (http://astrid.graal.univ-montp2.fr).
| 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.
| Period-Luminosity-Colour distribution and classification of Galactic oxygen-rich LPVs. I. Luminosity calibrations
The absolute K magnitudes and kinematic parameters of about 350oxygen-rich Long-Period Variable stars are calibrated, by means of anup-to-date maximum-likelihood method, using Hipparcos parallaxes andproper motions together with radial velocities and, as additional data,periods and V-K colour indices. Four groups, differing by theirkinematics and mean magnitudes, are found. For each of them, we alsoobtain the distributions of magnitude, period and de-reddened colour ofthe base population, as well as de-biased period-luminosity-colourrelations and their two-dimensional projections. The SRa semiregulars donot seem to constitute a separate class of LPVs. The SRb appear tobelong to two populations of different ages. In a PL diagram, theyconstitute two evolutionary sequences towards the Mira stage. The Mirasof the disk appear to pulsate on a lower-order mode. The slopes of theirde-biased PL and PC relations are found to be very different from theones of the Oxygen Miras of the LMC. This suggests that a significantnumber of so-called Miras of the LMC are misclassified. This alsosuggests that the Miras of the LMC do not constitute a homogeneousgroup, but include a significant proportion of metal-deficient stars,suggesting a relatively smooth star formation history. As a consequence,one may not trivially transpose the LMC period-luminosity relation fromone galaxy to the other Based on data from the Hipparcos astrometrysatellite. Appendix B is 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/Abstract.html
| The Infrared Spectral Classification of Oxygen-rich Dust Shells
This paper presents infrared spectral classifications for a flux-limitedsample of 635 optically identified oxygen-rich variables includingsupergiants and sources on the asymptotic giant branch (AGB). Severalclasses of spectra from oxygen-rich dust exist, and these can bearranged in a smoothly varying sequence of spectral shapes known as thesilicate dust sequence. Classification based on this sequence revealsseveral dependencies of the dust emission on the properties of thecentral star. Nearly all S stars show broad emission features fromalumina dust, while most of the supergiants exhibit classic featuresfrom amorphous silicate dust. Mira variables with symmetric light curvesgenerally show broad alumina emission, while those with more asymmetriclight curves show classic silicate emission. These differences may arisefrom differences in the photospheric C/O ratio.
| HIPPARCOS Astrometry of Infrared-Selected Sources and the Connection Between Optical and Infrared Reference Frames
Astrometric data from the Hipparcos satellite are reported for theoptical counterparts of 87 bright infrared sources. These sources may beuseful in defining a reference frame for infrared observations. The dataare also useful in studying the locations of circumstellar SiO masers.(SECTION: Stars)
| Classification and Identification of IRAS Sources with Low-Resolution Spectra
IRAS low-resolution spectra were extracted for 11,224 IRAS sources.These spectra were classified into astrophysical classes, based on thepresence of emission and absorption features and on the shape of thecontinuum. Counterparts of these IRAS sources in existing optical andinfrared catalogs are identified, and their optical spectral types arelisted if they are known. The correlations between thephotospheric/optical and circumstellar/infrared classification arediscussed.
| A Renewed Search for Water Maser Emission from Mira Variables.
Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1997AJ....114.1602L&db_key=AST
| Semiregular variables of types SRa and SRb. New JHKL' M-photometry for 44 stars.
This paper supplements Kerschbaum & Hron (1994, Paper IIa), wherenew JHKL'M observations of 200 Semiregular variables (SRVs) of types SRaand SRb were presented with additional 44 near infrared observations and5 literature data sets. The total sample was defined in Kerschbaum &Hron (1992, Paper I) by means of a certain limit in bolometricmagnitude. From the sample of 350 objects, 303 now have near infrared(NIR) photometry. In total 339 datasets are available because of somemultiple observations. A detailed analysis of the whole dataset will bepresented in a forthcoming paper.
| Mainline OH detection rates from blue circumstellar shells.
We identified 240 accessible circumstellar shells with water and/or SiOmasers, and used the Arecibo and Nancay radio telescopes to search formainline OH emission from them. Our targets are often Mira variableswithout previously known mainline masers. This search results in 89detections, of which 77 are new. The probability of detecting a maser islarger once a water maser is known, and becomes progressively larger thethicker and redder the shell. Nevertheless, almost all of our examplesof solitary 1665MHz masers, rather than the joint occurrence of both1665 and 1667MHz masers, are in the bluest shells. The IRAS lowresolution spectral type is the strongest factor correlating with themainline detection rate. We find that 67% of objects with a silicateemission feature exhibit masers, whereas only 27% of objects with acomparatively featureless 1n type do. These rates are colourinsensitive. We ascribe this clearcut difference to differing UVextinction properties of the two grain types, which is likely to resultfrom differing grain-size distributions. The IR colour sensitivity ofthe overall mainline detection rate is thus almost entirely anincidental artifact of the changing proportion of the two grain typeswith colour. Inferentially, since 90% of the sample exhibit watermasers, and the proportion of blue sources with silicate features issubstantially larger than an unbiased selection from the IRAS PointSource Catalog would give, the incidence of water masers is similarlysensitive to spectral type.
| Circumstellar dust envelopes of oxygen-rich AGB stars.
Using IRAS observational data, the best-fitting models are searched foroxygen-rich AGB stars in various evolutionary stages from opticallyvisible red giant stars to OH/IR stars with heavy mass loss. The modelinfrared spectral energy distributions of the red giant stars withcircumstellar dust envelopes are calculated with the use of a radiativetransfer code. It is found that the oxygen-rich IRAS AGB starssurrounded by circumstellar dust envelopes are divided into threegroups, which can be clearly distinguished by their mass loss rate andthe grain temperature at the inner boundary of the circumstellar dustenvelopes. One group corresponds to Mira type objects with a moderatemass loss rate and a grain formation temperature of about 500 K, thesecond to OH/IR star type objects with a large mass loss rate and a highgrain formation temperature, and the third to M stars with a very coldgrain temperature at the inner boundary, indicating that the moderatemass loss stopped a considerable time ago in these objects. The highergrain formation temperature of the OH/IR star type objects indicates agrain formation point closer to the stellar surface, suggesting aneffective acceleration of dust grains by radiation pressure. Such aneffective acceleration can play an important role in the mass lossphenomena of OH/IR stars with large mass loss rates. From the modelfitting results, it is suggested that an AGB star undergoes severaldozen phases of moderate mass loss of˙(M)~10^-7^-10^-6^Msun_/yr for a period of10^3^-10^4^years with interruptions of 10^3^-10^4^years during theordinary Mira variable phase before becoming an OH/IR star with a massloss rate exceeding 10^-5^Msun_/yr and a lifetime of about10^3^-10^4^years.
| Circumstellar shells resolved in the IRAS survey data. I - Data processing procedure, results, and confidence tests
We have examined the IRAS 60 and 100 micron survey data covering 512evolved stars and young planetary nebulae for evidence of spatiallyresolved structure. A simple model, consisting of a central unresolvedsource surrounded by a resolved isothermal shell, was fitted to the datafor each star. Seventy-six stars were found to be resolved in the 60micron data. Tests have been performed to verify that the extendedstructure seen is not an artifact of the data-processing algorithm.
| SiO maser emission and the intrinsic properties of Mira variables
Observations of SiO maser emission from 161 Mira variables distributedover a wide range of intrinsic parameters like spectral type, bolometricmagnitude, and amplitude of pulsation are reported. The observationswere made at 86.243 GHz, using the 10.4 m millimeter-wave telescope ofthe Raman Research Institute at Bangalore, India. The maser emission isfound to be restricted to Miras having mean spectral types between M6and M10. The IR period-luminosity relation for Mira variables isemployed to calculate their distances and hence estimate their maserluminosities from the observed fluxes. The maser luminosity is found tobe correlated with the bolometric magnitude of the Mira variable. On anH-R diagram, the masing Mira variables are shown to lie in a regiondistinct from that for the nonmasing ones.
| Near-infrared photometry of a sample of IRAS point sources
This paper presents the J, H, K, L, M photometry of 516 sourcespertaining to a sample of 787 sources which has been extracted from theIRAS Point Source Catalog in order to study the late stages of stellarevolution and the concomitant phenomena of mass loss. Three differentclssifications of these sources based on broad-band photometry and IRASlow-resolution spectra are given, and the distributions of the sourcesin terms of these classifications are presented. A subsample of peculiarsources, believed to have recently undergone a helium flash, has beenisolated using the K - L, (12-micron) color diagram. Some objectsmeriting further study are also mentioned.
| A survey of circumstellar CO emission from a sample of IRAS point sources
The first results from a survey of circumstellar CO(1-0) emission arepresented. The sources were selected from the IRAS point source catalogaccording to the IRAS color criteria described in van der Veen andHabing (1988). The sources have good quality fluxes at 12, 25, and 60microns, flux densities larger than 20 Jy at 25 microns, and aresituated more than 5 deg away from the Galactic plane. The survey isundertaken to study the relationship between mass loss rates, dustproperties, and the evolution along the AGB. The sample consists of 787sources and contains both oxygen and carbon-rich stars, including Miravariables, OH/IR objects, protoplanetary nebulae, planetary nebulae, and60-micron excess sources. So far, 519 objects, situated on both thenorthern and the southern sky, have been observed; 163 sources werefound to have circumstellar CO emission, and in 58 of these CO emissionhas not previously been detected.
| A survey for infrared excesses among high galactic latitude SAO stars
This project involves extending the previous analysis of infraredexcesses among a volume-limited sample of 134 nearby A-K main-sequencestars to a magnitude-limited sample of stars, culled from the SAOCatalog, with excesses determined from the IRAS Point Source Catalogflux density ratios. This new sample includes 5706 B-M type stars, 379of which have infrared excesses. The objective involved use of astatistically complete survey of objects in a standard catalog in orderto assess the frequency with which different physical processes canaffect the infrared output of stars. These processes include, but arenot limited to, orbiting cold particle clouds and the onset of rapidmass loss. It is concluded that cold disks are consistent with theinfrared excesses found among A-G dwarfs and G-K giants in the sample.
| M Giant Populations and Galactic Structure
Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1990MNRAS.247..227F&db_key=AST
| Detection of 51 new 86 GHz SiO, V = 1, J = 2-1 masers associated with IRAS point sources
This paper reports the results of a search for southern stellar SiO, v =1, J = 2-1 masers in a survey of IRAS point sources. Out of the 116observed southern sources, 51 identified as new SiO, v = 1, J = 2-1masers, on the basis of their position in IRAS color-color plot. Ofthese, 42 masers have stellar identifications in IPSC, two arepreviously known non-IRAS IR objects, and six have no identification inIPSC.
| New SiO masers associated with bright southern IRAS sources
The discovery of 31 new SiO v = 1, J = 1 - 0 (43.122 GHz) masersassociated with southern IRAS sources is reported. The candidate listfor the search was produced systematically, and the high detectionsuccess rate (about 50 percent) led to the consideration of differencesbetween stars associated with masers and those showing maser emission. Aset of conditions is proposed which virtually guarantee the presence ofdetectable stellar SiO maser. One of the most important requirements islarge optical variability (2.5 mag or greater), a condition associatedwith high mass-loss rate. In addition, it is found that themaser-to-infrared flux ratio is approximately proportional to themass-loss rate. New polarization observations of the SiO maserassociated with R Aqr, one of the two symbiotic stars known to show anytype of maser emission, are also presented.
| IRAS catalogues and atlases - Atlas of low-resolution spectra
Plots of all 5425 spectra in the IRAS catalogue of low-resolutionspectra are presented. The catalogue contains the average spectra ofmost IRAS poiont sources with 12 micron flux densities above 10 Jy.
| The stellar component of the galaxy as seen by the AFGL infrared sky survey
The noise-limited magnitudes for the Air Force Geophysical Laboratory(AFGL) Infrared Sky Survey have been estimated by direct comparison withground-based observations. Using these limiting magnitudes, 'pruned'versions of the AFGL catalog have been generated. Infrared observationsof all the stellar objects seen at 11, 20, or 27 microns and astatistical sample of the stars seen only at 4 microns are reported.Analysis of the observations leads to estimates of the absolute 4 and 10microns magnitudes and space densities for the two clases of objects.The expected results from the Infrared Astronomical Satellite arereexamined.
| Characteristics of the H2O emission from Mira variables
Absolute fluxes at maximum in the 1.35 cm water-vapor line wereestimated for the H2O mira variables by correcting observed fluxes forthe distances of the stars and phase at the epochs of observations. Theaverage photon rate at maximum is 4 x 10 to 43rd power photons/sec, witha small dispersion. This small dispersion is interpreted in terms of themodel of spherically symmetric expanding envelope. Proximity of the staras major criterion for detection of H2O emission in Miras is inferredfrom the small dispersion. Nine new H2O-Miras were discovered, seven ofwhich belong to the list of Miras closer than about 320 pc.
| Classification of 831 two-micron sky survey sources south of +5 degrees.
Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1975AJ.....80.1011H&db_key=AST
| New H20 sources associated with infrared stars.
Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1973ApJ...180..831D&db_key=AST
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Observation and Astrometry data
| Constellation: | Centaurus |
| Right ascension: | 14h30m58.62s |
| Declination: | -30°05'51.8" |
| Apparent magnitude: | 8.521 |
| Distance: | 317.46 parsecs |
| Proper motion RA: | -35.8 |
| Proper motion Dec: | -23.1 |
| B-T magnitude: | 10.027 |
| V-T magnitude: | 8.646 |
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