Study of open cluster King 13 using CCD VI, 2MASS and Gaia DR2 Astrometry
Alok Durgapal, D Bisht, Geeta Rangwal, Harmeen Kaur, R. K. S. Yadav
aa r X i v : . [ a s t r o - ph . GA ] J a n Study of open cluster King 13 using CCD VI, 2MASSand Gaia DR2 Astrometry.
Alok Durgapal , D Bisht , Geeta Rangwal , Harmeen Kaur , R. K. S. Yadav Department of Physics, DSB Campus, Kumaun University, Nainital-263002, Uttarakhand, India Key Laboratory for Researches in Galaxies and Cosmology, University of Science andTechnology of China, Chinese Academy of Sciences, Hefei, Anhui 230026, China Aryabhatta Research Institute of Observational Sciences, Manora Peak Nainital 263 002, India
Abstract
In this paper, we present astrophysical parameters of the open cluster King13 based on the
V I
CCD and 2MASS
JHK s photometric data. This is a poorlystudied cluster, for which new results have been found in the present work. Toidentify probable members, we use proper motion data from Gaia DR2 catalogue.The mean proper motion of the cluster is determined as − . ± . − . ± . yr − and cluster extent is derived as 3 ′ .
2. Using color-magnitude diagrams,we estimate the age and distance of the cluster as 510 ±
60 Myr and 3 . ± . E ( B − V ) in the direction of the cluster isdetermined as 0 . ± . M ⊙ . The present analysis shows that King 13 is adynamically relaxed cluster. Keywords:
Star cluster - individual: King 13 - star: Astrometry, mass function, dynamicalstate, Galaxy: structure. E-mail: [email protected] (Alok Durgapal); [email protected] (D.Bisht); [email protected] (Geeta Rangwal); [email protected](Harmeen Kaur); [email protected] (R. K. S Yadav) Corresponding author; Tel: + Preprint submitted to Elsevier January 22, 2020 . Introduction
Open clusters (OCs) are very helpful objects to understand the structure andstellar evolution of the Milky Way. Indeed, each cluster includes stars of di ff erentmass, which were formed in the same cloud, i.e. they share the same age andchemical composition. The structure of most OCs can be roughly described bytwo subsystems, the dense core and the sparse halo (Bonatto and Bica, 2009). OCshave become fundamental probes of Galactic disk properties by their location onGalactic disk (Lynga, 1982; Janes and Phelps, 1994; Friel, 1995; Piskunov et al.,2006; Carraro et al., 2010). The fundamental parameters of an open cluster e.g.distance, age and interstellar extinction can be estimated by comparing color-magnitude diagram (CMD) and color-color (CC) diagrams with the modern the-oretical models. It is important to study the unexplored OCs to determine theirproperties with the aim of improving the picture of the Galactic disk.King 13 is positioned at α = h m s and δ = ◦ ′ (J2000.0), correspond-ing to Galactic coordinates l = ◦ .
96 and b = − ◦ .
3. This object is located in thePerseus arm, in the second Galactic quadrant of Milky Way. Marx and Lehmann(1979) obtained UBV photographic photometry for King 13 and calculated itsdistance as 1.73 kpc. Subramaniam and Bhatt (2007) determined its distance as3 . ± .
33 kpc and its age as 300 Myr, while Bukowiecki et al. (2011) estimatedcluster distance as 2 . ± .
19 kpc and age as 794 Myr. Therefore, there is a dif-ference in parameters from one study to another. So there is a need to re-visit thiscluster and determine its parameters in a more accurate way, making use of newtools and data.A new era in dynamical astronomy has begun with the second data release ofthe Gaia mission in 2018 April (Gaia Collaboration et al., 2016). In the presentanalysis, we used CCD photometric data in
V I filters, 2MASS data in
JHK s filtersand Gaia DR2 proper motion data to determine the fundamental and structuralparameters of the cluster King 13.The paper is organized as follows: Data reduction is presented in Section 2.Selection of cluster members is described in Section 3. Fundamental astrophys-ical parameters are estimated in Section 4. Study of luminosity, mass functionand mass-segregation are given in Section 5. Finally, we concluded our study inSection 6.
2. Observational data and data reduction
The CCD broadband
V I images for King 13, were collected using a 2K × /
13 Cassegrain focus of the 104 cm Sampurnanand telescope2ocated at ARIES, Manora peak, Nainital, India. The CCD used for the presentobservations has 24 µ m square pixel size, resulting in a scale of 0 ′′ .36 pixel − anda square field of view of 12 ′ .6 size. The CCD gain was 10 e − / ADU while thereadout noise was 5.3 e − . Log of observations is listed in Table 1. Observationswere taken in 2 × / N ratio. The identificationmap of the observed region for King 13 is shown in Fig. 1. In this figure, the coreand cluster regions are indicated by the inner and outer circle respectively.Bias and twilight flats were also taken along with the target field. We haveused IRAF software for the pre-processing of our observed CCD images. In thisstep, we have done bias subtraction, flat field correction and removal of cosmicrays from science images. The subsequent data reduction and analysis were doneusing the DAOPHOT software (Stetson, 1987). The stellar photometric routineof DAOPHOT was used for the instrumental magnitude determination. Both PSFand aperture photometry was carried out to find the instrumental magnitudes ofthe stars. The details of the processing of the images can be found in our previouspapers (Pandey et al., 1997; Durgapal et al., 1997; Durgapal and Pandey, 2001;Bisht et al., 2016, 2019).
We observed the standard field SA 95 (Landolt, 1992) in V and I filters forcalibrating the observational data of King 13. The 7 standard stars (SA95-41, 42,43, 97, 102, 112, 115) used in the calibrations having brightness and color range12.77 ≤ V ≤ − . < ( V − I ) < .
448 respectively, thus covering thebulk of the cluster stars. For the extinction coe ffi cients, we considered the valuesfor the ARIES site (Kumar et al., 2000). The derived calibration equations usingleast square linear regression for converting the instrumental magnitude into thestandard magnitude, are as follows: v = V + Z V + C V ( B − V ) + k V X (1) i = I + Z I + C I ( V − I ) + k I X (2)where v and i are the instrumental and V and I are the standard magnitudes, X is the airmass. The color coe ffi cients ( C ) and zero points ( Z ) for di ff erent filtersare listed in Table 2. The errors in zero points using standard stars from LandoltSA 95 field and color coe ffi cients are 0.01 mag.The internal errors derived from DAOPHOT are plotted against V magnitudein Fig. 2. Photometric global (DAOPHOT + Calibrations) errors are also estimated,3hich are listed in Table 3. For V filter, the error is 0.05 mag at V ∼
17 mag and0.07 mag at V ∼
20 mag.In Fig. 3, we present a comparison of present photometry with the photo-metric data of Glushkova et al. (2010). In this figure, the di ff erence between thetwo photometries is plotted as a function of the present photometry. The dottedlines represent the zero di ff erence between present photometry and photometryby Glushkova et al. (2010). This shows that most of the data points lie near thezero di ff erence line so our photometric data is in good agreement with that ofGlushkova et al. (2010). The mean di ff erence and standard deviation per magni-tude bin are also given in Table 4. We used Gaia DR2 data (Gaia Collaboration et al., 2016) to select the clustermembers and determine to mean proper motion of cluster King 13. This dataconsist of five parametric astrometric solution, which includes positions on the sky( α, δ ), parallaxes and proper motion (PM) ( µ α cos δ, µδ ) with a limiting magnitudeof G ∼
21 mag. Parallax uncertainties are in the range of up to 0.04 milliarcsecond(mas) for sources at G ≤
15 mag and ∼ G ∼
17 mag.The uncertainties in the respective proper motion components are up to 0.06 mas yr − (for G ≤
15 mag), 0.2 mas yr − (for G ∼
17 mag) and 1.2 mas yr − (for G ∼
20 mag). The proper motion and their corresponding errors plotted against G magnitude are shown in Fig 2. This figure shows that errors in proper motioncomponents are ∼ . G ∼
20 mag.
3. Mean proper motion and cluster membership
The contamination due to field stars always a ff ects the determination of funda-mental parameters of the cluster. Proper motion is one of the tools to remove thosefield stars from the cluster main sequence. We used Gaia DR2 proper motion andparallax data to separate cluster members from non member stars.To see the distribution of member and non member stars, we plotted vectorpoint diagram (VPD) in PMs µ α cos δ and µ δ as shown in Fig 4. Corresponding V versus ( V − I ) CMDs are also shown in top panels. The left panel shows all theobserved stars, while the middle and right panel shows probable cluster membersand field stars respectively.We determined the average value of parallax for stars inside the circle of vectorpoint diagram, by building a histogram of 0.15 mas bin as shown in Fig 6. Theaverage value of parallax is determined as 0 . ± .
006 mas after incorporating4he zero point o ff set (-0.05 mas) as suggested by Riess et al. (2018). The clusterdistance corresponding to the average parallax is obtained as 3 . ± .
15 kpc. Thisvalue is in good agreement with the distance estimated by Cantat-Gaudin et al.(2018).We also used parallax of cluster stars along with the proper motion data to findtrue cluster members. A star is considered as probable member if it lies inside thecircle of 0.7 mas yr − in VPD and has a parallax within 3 σ from the mean clusterparallax. In this way we obtained a total 172 stars as probable cluster membersfor King 13. We have matched our members with Cantat-Gaudin et al. (2018)catalog as well. We have shown these matched stars with red open circles in theobserved colour magnitude and color-color diagrams. In our previous analysis(Rangwal et al. (2019)), we clearly explained this method in detail. The CMD ofthe probable cluster members having PM error ≤ yr − are shown in theupper-middle panels of Fig 4. The main sequence of King 13 is clearly separatedfrom the field stars.To calculate the mean proper motion of King 13, we constructed histogramsof proper motions and fitted their peaks with Gaussian functions ( see Fig 5). Wefound − . ± . − . ± . mas yr − as mean proper motions in RA andDEC directions respectively. These proper motion values are very close to thevalues given by Cantat-Gaudin et al. (2018). By visual inspection, we define acircle of 0.7 mas yr − radius, around the cluster center in the VPD which definesour member selection criteria. The chosen radius is a boundary between losingcluster members with poor PMs and the inclusion of field stars.
4. Cluster structure and its fundamental parameters
In order to investigate the cluster structure, the primary step is to find veryprecise center coordinates. For this, we have plotted the histogram of star countsin Right Ascension (RA) and Declination (DEC) using Gaia database. Our mainaim is to estimate the maximum central density of the cluster. The cluster centeris estimated by fitting Gaussian function of star counts in RA and DEC as shownin Fig 7, finding coordinates as α = . ± .
01 deg and δ = . ± .
01 deg.The cluster center in celestial coordinates is at α = h m s , δ = ◦ ′ ′′ . These coordinates are very close to the values given by Glushkova et al.(2010) and are also in good agreement with the center coordinates reported byCantat-Gaudin et al. (2018). 5o estimate the cluster extent, we established the radial density profile (RDP)of King 13. To construct RDP the observed area of the cluster is divided into manyconcentric circles. The number density, R i , in the i th zone is calculated by usingthe formula R i = N i A i , where N i is the number of stars and A i is the area of the i th zone. RDP of the cluster King 13 is shown in Fig. 8. A smooth continuous linerepresents the fitted King (1962) profile, which can be expressed as: f ( r ) = f b + f + ( r / r c ) (3)where f is the central density, r c is the core radius and f b is the backgrounddensity. The background density level with errors is shown with dotted lines inthis figure. This RDP flattens at r ∼ . ± . stars / arcmin , 16 . ± . stars / arcmin and 0 . ± . δ c = + f f b for the cluster is estimated as 2.8,which is smaller than the values (7 ≤ δ c ≤
23) given for compact star clusters byBonatto and Bica (2009). This shows that King 13 is a sparse cluster.The tidal radius generally depends on the e ff ects of Galactic tidal fields andsubsequent internal relaxation dynamical evolution of clusters (Allen and Martos,1988). To evaluate the clusters tidal radius, we have adopted the following rela-tion as given by Je ff ries et al. (2001) R t = . × ( M c ) / (4)where R t and M c are the tidal radius and the total mass (see Sec. 5) of thecluster respectively. The estimated value of the tidal radius is found as 8.5 pc. The interstellar extinction and the ratio of total-to-selective extinction towardsthe cluster are very important for a proper use of photometric data. The value ofinterstellar extinction E ( B − V ) in the direction of King 13 has been estimated usingnear-IR JHK data from 2MASS catalogue in combination with the optical data.We followed Persson et al. (1998) to convert K s magnitude into K magnitude. Weplotted ( J − K ) versus ( V − K ), ( J − K ) versus ( J − H ) and ( V − I ) versus ( V − K )color-color diagrams which are shown in Fig. 9. The ZAMS by Bressan et al.62012) is fitted over the color-color diagrams as shown by the solid black line.We have also shown the shifted ZAMS also by dotted line in this figure. We haveestimated E ( G BP − G RP ) = . ± .
26 and A G = G , G BP and G RP filters. The error in the calculated value of E ( G BP − G RP ) is the fitting error of ZAMS. With the help of this, errors in colour-excess are calculated in further transformations. We used the absorption ratioin the optical and infrared wavelengths to visual absorption from Cardelli et al.(1989). Using the transformation equations by Hensy (2018), we found the valueof interstellar reddening E ( B − V ) as 0 . ± .
2. The shifted ZAMS provides E ( V − K ) = . E ( J − K ) = . ± . E ( J − H ) = . ± . A k = . × E ( J − K ) (Mathis, 1990); A k = . × A v (Cardelli et al., 1989) and A v = R × E ( B − V ) to estimate the value of A v and R . Using the above relations we found the value of A v as 2.43 and R as ∼ E ( J − K ) E ( V − K ) ∼ .
19 and E ( J − K ) E ( J − H ) ∼ .
84, which arein good agreement with the normal interstellar extinction value as suggested byCardelli et al. (1989).
The metallicity, age and distance of King 13 have been estimated by compar-ing the observed CMDs with theoretical stellar evolutionary isochrones. For thispurpose we adopted the isochrones of Bressan et al. (2012). The main-sequenceof the cluster is well reproduced by isochrones with a nearly solar metallicity,Z = ff erent age isochrones to get the best fit with morphologicalfeatures in V , ( V − I ); V , ( V − K ) and K , ( J − K ) CMDs. To get a clear sequencein the CMDs, we consider only probable cluster members based on the cluster’sVPD. In Fig. 10, we superimpose isochrones of di ff erent age (log(age) = Z = .
012 in V , ( V − I ); V , ( V − K ) and K , ( J − K )CMDs. Assuming the brightest star as an evolved star, we found an age of 510 ± m − M ) = . ± . . ± . JHK s data. The Galactocentric coordinatesfor the cluster are determined as X = .
68 kpc, Y = .
57 kpc and Z = − .
08 kpc.The calculated Z value indicates that the cluster King 13 is in the thin Galacticdisk. The Galactocentric distance of the cluster is determined as 11 .
23 kpc.7 . Mass function and dynamical state of King 13
The distribution of the stars of an OC based on their brightness is termed asluminosity function. To get the luminosity function, it is very important to knowthe completeness factor (CF) of CCD data. We implemented the artificial star testfor the estimation of CF. To perform this test we have used ADDSTAR routinein DAOPHOT II. We randomly added many stars in di ff erent magnitude bins tothe original V and I images having the same geometrical positions. We added ∼
10 % of the number of stars actually detected and inserted more stars into faintermagnitude bins. Then we again performed the same procedure of photometry fornew images as well. The CF is calculated as the ratio between the number ofartificial stars recovered in V and I passbands and the number of added stars permagnitude bin. The values of CF are listed in Table 6 corresponding to each V magbin. From this table, we can conclude that almost every star has been recovered inthe brighter end and as we go towards the fainter end the completeness of the datadecreases.To establish the luminosity function for King 13, we have used V versus ( V − I )CMD. Firstly, we converted the apparent V magnitudes of probable member starsinto the absolute magnitudes using the value of distance modulus. To removefield star contamination completely from the main sequence of King 13, we usedprobable cluster members selected by using vector point diagram and parallax.Then we constructed the true histogram of LF as shown in Fig. 11. The histogramshows that the luminosity function for the cluster King 13 rises steadily up to 4.2mag. For the main sequence stars, the LF is transformed into the mass function(MF) using the theoretical model given by Bressan et al. (2012). The resultingmass function is plotted in Fig 12.The mass function slope has been derived by using the relation log dNdM = − (1 + x ) log( M ) + constant, where dN is the number of stars in a mass bin dM withcentral mass M and x is the slope of MF. The derived MF slope ( x = . ± . V I data along with GAIA DR2 astrometry. Our derived value of MFslope for this cluster in the mass range 1.1-2.6 M ⊙ is in good agreement with thevalue 1.35 given by Salpeter (1955) for field stars in the Solar neighbourhood.8he Total mass of King 13 was estimated as ∼ M ⊙ , considering the derivedmass function slope within the mass range 1.1 M ⊙ - 2.6 M ⊙ and using the followingrelationship as used by Yadav et al. (2008) M = C R M U M L M Γ MdM (5)where C is the constant, M L and M U are the upper and lower mass limits ofthe cluster stars, Γ is the slope of the mass function. To characterize the degree of mass-segregation e ff ect in King 13, we plottedthe cumulative radial distribution (CRD) of stars for various mass ranges in Fig.13. The main sequence stars are subdivided into three mass ranges 2.1 ≤ MM ⊙ < ≤ MM ⊙ < ≤ MM ⊙ ≤ K − S ) test showsthe evidence for statistical significance of this e ff ect with a confidence level of 80%. CRD of the stars having a mass range 2 . < MM ⊙ ≤ . . ≤ MM ⊙ ≤ . ff ect in clusters may be attributed to dynamical evolutionor star formation or both. During the lifetime of a cluster, encounters between itsmembers moderately lead to an increased degree of energy equipartition. At thesame time, bright stars gradually sink towards the cluster center and deliver theirkinetic energy to the low mass stars, thus leading to this e ff ect. The relaxationtime T E , is the time scale in which the cluster will lose the memory of dynam-ical initial conditions. Mathematically, T E is denoted by the following formula(Spitzer and Hart, 1971): T E = . × √ N × R h / √ m × log (0 . N ) (6)where N is the number of cluster members, R h is the half mass radius of thecluster and < m > is the mean mass of the cluster stars (Spitzer and Hart, 1971).The value of R h has been assumed as half of the cluster extent value derived byus. Using the above formula, we have estimated the dynamical relaxation time ofKing 13 as 7.5 Myr.The estimated values of relaxation time for this cluster is less than the clusterage. Therefore we conclude that King 13 is a dynamically relaxed cluster.9 . Conclusion We present a
V I CCD photometric, 2MASS near-IR and Gaia DR2 astrometricstudy of the open cluster King 13, which is not well studied in the literature. Theestimated fundamental parameters are listed in Table 7. The main results of thepresent analysis are summarized as follows:1. To separate cluster members from the field stars, we used Gaia DR2 propermotion and parallax data and obtained a clear main sequence for the cluster.The mean proper motion of the cluster is determined as − . ± . − . ± . yr − in RA and DEC directions respectively.2. We calculated the structural properties of the cluster. The Center of thecluster is determined as α = h m . s , δ = ◦ ′ ′′ . The Radiusand tidal radius of the cluster are determined as 3 . ′ and 8.5 pc respectively.The value of density contrast parameter δ c shows that King 13 is a sparsecluster.3. The values of color-excess ratios E ( J − K ) E ( V − K ) and E ( J − K ) E ( J − H ) are found to be ∼ . = ±
60 Myr,0 . ± . . ± .
15 kpc respectively.5. To study the dynamical properties of cluster, we constructed luminosity andmass function for the cluster. The luminosity function increases towards thefainter end. This indicates that fainter stars are still bound to the cluster.Mass function slope for the cluster is determined as 1 . ± .
31 which is inagreement with Salpeter (1955) value. The cumulative radial stellar distri-bution plot shows presence of mass segregation in the cluster. Dynamicalrelaxation time of the cluster is found to be 7.5 Myr, which shows that King13 is a dynamically relaxed cluster.
7. ACKNOWLEDGEMENTS
We thank the sta ff of ARIES for assistance during observations and data reduc-tion. This work has been partially supported by the Natural Science Foundation ofChina (NSFC-11590782, NSFC-11421303). This work has made use of data fromthe European Space Agency (ESA) mission GAIA processed by Gaia Data pro-cessing and Analysis Consortium (DPAC, htt ps : // . cosmos . esa . int / web / gaia / d pac / consortium ).10his publication has made use of data from the 2MASS, which is a joint projectof the University of Massachusetts and the Infrared Processing and Analysis Cen-ter / California Institute of Technology, funded by the National Science Foundation.
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North is upand East in the right direction. The outer circle represents the extent of the cluster while the innercircle shows the extent of core of the cluster. The smallest size denotes star of V ∼
20 mag. igure 2: Left panel shows photometric errors in V and I magnitudes against V magnitude anderrors in J , H and K magnitudes against J magnitudes. Right panel shows the plot of propermotions in both RA and DEC directions and their errors versus G magnitude. igure 3: A comparison of the present photometry with photometric data of Glushkova et al.(2010) for King 13. The open circles represent di ff erence of both the photometries as a func-tion of present photometry. igure 4: Colour magnitude diagrams (CMDs) based on our VI photometry (top panels) andproper motion vector point diagrams (VPDs) based on Gaia
DR2 data (bottom panels). Leftpanels display the entire sample. Central panels display the candidate members (enclosed in acircle of radius 0 . mas yr − around the cluster center in VPD). Probable background / foregroundfiled stars in the direction of the cluster are displayed in the right panels. igure 5: The histograms for proper motion in right ascension (left) and declination (right). TheGaussian function fit to the central bins provides the mean values in RA and DEC. panels. igure 6: The histograms for the estimation of mean parallax. The Gaussian function fit to thecentral bins. igure 7: The histograms for the estimation of center coordinates. The Gaussian function fit to thecentral bins provides cluster center. igure 8: Surface density distribution of stars in the field of the cluster King 13. Errors aredetermined from sampling statistics( = √ N where N is the number of stars used in the densityestimation at that point). The smooth line represent the fitted profile whereas dotted line shows thebackground density level. Long and short dash lines represent the errors in background density. igure 9: The ( J − K ) , ( V − K ), ( J − K ) , ( J − H ) and ( V − I ) , ( V − K ) colour-colour diagramsfor the cluster King 13. The solid line is the ZAMS taken from Bressan et al. (2012). The dottedline is the ZAMS shifted by the values given in the text. Red open circles are matched stars withCantat-Gaudin et al. (2018) having membership probability higher than 0.5. igure 10: The V , ( B − V ), V , ( V − K ) and K , ( J − K ) colour-magnitude diagram of the clusterKing 13. The curves are the isochrones of (log(age) = igure 11: The luminosity functions of the cluster under consideration. igure 12: Mass function for King 13 derived using Bressan et al. (2012) isochrones. Standarddeviations from the central values are represented by the error bars. igure 13: The cumulative radial distribution of stars in various mass range. able 1: Log of observations for the cluster under study. King 13 was observed on 2 nd December2014.
Pass band Exposure Time(in seconds) V ×
2, 120 × I ×
2, 60 × able 2: Derived Standardization coe ffi cients and its errors. C and Z are color coe ffi cients andzeropoints respectively. Filter
C ZV − . ± . ± I − . ± . ± able 3: The rms global photometric errors as a function of V magnitude. V σ V σ I −
15 0 .
04 0 . −
16 0 .
04 0 . −
17 0 .
05 0 . −
18 0 .
06 0 . −
19 0 .
06 0 . −
20 0 .
07 0 . able 4: Di ff erences in V and ( V − I ) between Glushkova et al. (2010) and our study. The standarddeviation for the di ff erence in each magnitude bin is also given in the parentheses. V ∆ V ∆ ( V − I )13 − − .
01 (0 .
01) 0 .
02 (0 . − − .
02 (0 . − .
02 (0 . − − .
04 (0 . − .
03 (0 . − − .
05 (0 . − .
05 (0 . − − .
07 (0 .
07) 0 .
06 (0 . − − .
08 (0 .
08) 0 .
07 (0 . − − .
10 (0 .
10) 0 .
09 (0 . able 5: Structural parameters of the cluster King 13. Background and central density are in theunit of stars per arcmin . r c is in arcmin while R t is in pc. Name f f b r c R t δ c King 13 36 . .
04 0 . . . able 6: The photometric completeness of the data in each magnitude bin for the cluster King 13. V (mag) Completeness14 - 15 0.9915 - 16 0.9716 - 17 0.9517 - 18 0.9118 - 19 0.75 able 7: Various fundamental parameters of the cluster King 13. Parameter King 13Radius 3 . . ± .
01 degDeclination 61 . ± .
01 deg µ α cos δ − . ± . yr − µ δ − . ± . yr − Age 510 ±
60 Myr[ Fe / H ] − . ± .
01 dexMetal abundance 0 . E ( G BP − G RP ) 0 . ± . . ± . A V R V . ± .
20 magDistance (From Isochrone fitting) 3 . ± .
40 KpcDistance (From mean Parallax) 3 . ± .