A deep study of an intermediate age open cluster SAI 35 (Juchert 20) using ground based imaging and Gaia EDR3 astrometry
D. Bisht, Qingfeng Zhu, R. K. S. Yadav, Geeta Rangwal, Alok Durgapal, Devesh P.Sariya, Ing-Guey Jiang
aa r X i v : . [ a s t r o - ph . GA ] F e b A deep study of an intermediate age open cluster SAI 35 (Juchert20) using ground based imaging and Gaia EDR3 astrometry.
D. Bisht , Qingfeng Zhu , R. K. S. Yadav , Geeta Rangwal , Alok Durgapal , Devesh P.Sariya and Ing-Guey Jiang Key Laboratory for Researches in Galaxies and Cosmology, University of Science andTechnology of China, Chinese Academy of Sciences, Hefei, Anhui, 230026, Chinaemail: [email protected] Aryabhatta Research Institute of Observational Sciences,Manora Peak, Nainital 263 002,India Center of Advanced Study, Department of Physics, D. S. B. Campus, Kumaun UniversityNainital 263002, India Department of Physics and Institute of Astronomy, National Tsing-Hua University,Hsin-Chu, Taiwan
ABSTRACT
We present CCD
U BV I photometric study of poorly studied intermediate ageopen cluster SAI 35 (Juchert 20) for the first time. To accomplish this study, wealso used LAMOST DR5, 2MASS, and Gaia EDR3 databases. We identified 214most probable cluster members with membership probability higher than 50%.The mean proper motion of the cluster is found as µ α cosδ = 1 . ± .
01 and µ δ = − . ± .
01 mas yr − . We find the normal interstellar extinction law usingthe various two-color diagrams. The age, distance, reddening, and radial velocityof the cluster are estimated to be 360 ±
40 Myr, 2 . ± .
15 kpc, 0 . ± .
05 mag and − . ± .
39 km/sec. The overall mass function slope for main-sequence stars isfound to be 1 . ± .
16 within the mass range 1.1 − M ⊙ , which is in agreementwith Salpeter’s value within uncertainty. The present study demonstrates thatSAI 35 is a dynamically relaxed. Galactic orbital parameters are determinedusing Galactic potential models. We found that this object follows a circularpath around the Galactic center. Subject headings:
Star:-Color-Magnitude diagrams - open cluster and associa-tions: individual: SAI 35-astrometry-Membership Probability-Dynamics-Kinematics 2 –Fig. 1.— Finding chart of the stars in the field of SAI 35. Filled circles of different sizesrepresent brightness of the stars. Smallest size denotes stars of V ∼
20 mag. Open outercircle represent the cluster size and inner circle represent core region. 3 –
1. Introduction
Open clusters (OCs) have long been used for the understanding of stellar physics, tostudy the star formation scenario and the overall structure of the Milky Way (MW). Theopen cluster SAI 35 (Juchert 20) ( α = 04 h m . s , δ = 46 ◦ ′ ′′ ; l =154 ◦ .494, b =-3 ◦ .422) is located in the second Galactic quadrant. This object is listed in the cataloghttp://ocl.sai.msu.ru/catalog/.This open cluster is listed in the catalog given by Kronberger et al. (2006). Kharchenkoet al. (2012, 2013) cataloged the proper motions, distance, reddening, and log(age) value ofSAI 35 as (-2.36, -6.11) mas/yr, 2812 pc, 0.791 mag, and 8.22, respectively based on 2MASSand PPMXL catalog. Dias et al. (2014) derived proper motion values of this object as-0.11 and -0.90 mas/yr based on UCAC4 catalog. The integrated J HK s magnitudes andluminosity function has been estimated by Kharchenko et al. (2016). A catalog of clustermembership has been given by Sampedro et al. (2017) based on UCAC4 data. Cantat-Gaudin et al. (2018) has made a catalog for cluster members and obtained fundamentalparameters of SAI 35 based on Gaia DR2 data.OCs generally suffer from the field star contamination towards the fainter ends in themain sequence. Hence, knowledge about the cluster membership status of stars is neces-sary. The Gaia DR2 catalog was made public on 25 th April 2018 (Gaia Collaboration etal. 2018a,b). The (early) Third Gaia Data Release (hereafter EDR3; Gaia Collaboration etal. 2020) was made public on 3 rd December 2020. EDR3 consists the central coordinates,proper motions in right ascension and declination and parallax angles ( α, δ, µ α cosδ, µ δ , π ) foraround 1.46 billion sources with a limiting magnitude of 3 to 21 mag in G band. The GaiaEDR3 data is much precise and accurate in comparison to the second data release. TheGaia data can be used for the precise estimation of membership of cluster members to havea better understanding of the fundamental parameters of OCs. Cantat-Gaudin et al. (2018)obtained membership probabilities for 1229 OCs using Gaia DR2 but it is limited to sourcebrighter than 18 mag in G band. Recently they added many clusters to get a catalog of1481 OCs (Cantat-Gaudin & Anders 2020). In this paper, we have estimated membershipprobabilities of stars towards the region of SAI 35 down to ∼
20 mag in V band.Spectroscopic data in Gaia EDR3 is the same as of Gaia DR2. Soubiran et al. (2018)reported 6D phase space information of 861 stars clusters using weighted mean radial velocitybased on Gaia DR2. More than 50% of the above cataloged clusters have radial velocityinformation using less than 3 stars. The cluster studied here (SAI 35) is not listed in theabove spectroscopic catalog given by Soubiran et al. (2018). We have taken radial velocitydata from the fifth release (DR5) of the Large sky Area Multi-Object fiber SpectroscopicTelescope (LAMOST, Cui et al. 2012; Zhao et al. 2012; Luo et al. 2012). 4 –In recent years, many authors have estimated the present day mass function for a sampleof clusters (e.g., Hur et al. 2012, Khalaj & Baumgardt 2013, Dib et al. 2017, Joshi et al.2020). It is still a debatable question to all researchers whether the initial mass function(IMF) of OCs is universal in time and space or it depends on the star forming conditions(Elmegreen 2000, Kroupa 2002, Bastian et al. 2010; Dib & Basu 2018). OCs are consideredas crucial objects to investigate the dynamical evolution of the stellar system (Bisht et al.2019). The study of mass-segregation in OCs give a clue about the distribution of low andhigh mass stars towards the cluster region.The paper is organized as follows. Section 2 describes the observations, data reductionprocedure and other used data sets. The completeness of CCD data is described in Section3. Section 4 deals with the study of proper motion and determination of the membershipprobability of stars. The structural properties and derivation of fundamental parametersusing the most probable cluster members have been carried out in Sections 5 and 6. Thedynamical study of the cluster is discussed in Section 7. The cluster’s orbit is studied inSection 8. Finally, the conclusions are presented in Section 9.
2. Observations and data analysis
We carried out CCD
U BV I observations of stars in the region of open cluster SAI 35on 21 st January 2010. We used a 104-cm Sampurnanand reflector telescope (f/13) locatedat Aryabhatta Research Institute of Observational Sciences, Manora Peak, Nainital, India.Images were acquired using a 2K ×
2K CCD which has 24 µ m square pixel size, resulting in ascale of 0 ′′ .36 pixel − and a square field of view of 12. ′ − /ADUwhile the readout noise was 5.3 e − . In order to improve the S/N ratio, the observationswere taken in the 2 × binned mode. Table 1 lists the date of observations togetherwith the filters used and the corresponding range of exposure time. The identification mapTable 1: Log of observations, with dates and exposure times for each passband.Band Exposure Time Date(in seconds) U ×
2, 300 × st January 2010 B ×
2, 240 × V ×
3, 180 × I ×
2, 60 × V magnitude.Fig. 3.— Plot of proper motions and their errors versus V magnitude. Blue circles are GaiaEDR3 sources while the black filled circles show the Gaia DR2 sources towards the area ofSAI 35. 6 –observed by us is shown in Fig 1.Several biases and twilight flat-field images were taken in U BV I filters, during the ob-serving night. IRAF data reduction package has been used for the initial processing of rawphotometric data which consists of bias subtraction, flat fielding and cosmic ray removal.We used DAOPHOT software to estimate the stellar magnitudes. The instrumental magni-tudes were derived through point spread function (PSF) fitting using DAOPHOT/ALLSTAR(Stetson 1987, 1992) package. To estimate the PSF, we used several well isolated stars forthe entire frame. The Gaussian function was used as an analytical model PSF. The shapeof the PSF was made to vary quadratically with the position on the image. Appropriateaperture corrections were determined by using isolated and unsaturated bright stars in theimage.We have cross-identify the stars of different frames and filters using the DAOMATCH/DAOMASTERprogramme available in DAOPHOT II. To determine the transformation coefficients frominstrumental to standard magnitudes, CCDLIB, CCDSTD routines have been used. Finally,standard magnitudes and colors of all the stars have been obtained using the routine FINAL. We have observed the standard field SA 98 (Landolt 1992) for SAI 35 during the ob-serving night for photometric calibration of CCD system. The 19 standard stars (SA98-650, 670, 653, 666, 671, 675, 676, 682, 685, 688, 1082, 1087, 1102, 1112, 724, 733, 1124,1119, 1122) used in the calibrations have brightness and color range 9.54 ≤ V ≤ IRAF is distributed by the National Optical Astronomical Observatory which are operated by the As-sociation of Universities for Research in Astronomy, under contract with the National Science Foundation
Table 2: Derived Standardization coefficients and its errors.Filter Colour Coeff. ( C ) Zeropoint ( Z )SAI 35 U − . ± . ± B − . ± . ± V − . ± . ± I − . ± . ± V magnitude.Table 3: The rms global photometric errors as a function of V magnitude. V σ V σ B σ I σ U −
11 0 .
04 0 .
05 0 .
04 0 . −
12 0 .
04 0 .
05 0 .
03 0 . −
13 0 .
05 0 .
05 0 .
05 0 . −
14 0 .
05 0 .
05 0 .
04 0 . −
15 0 .
05 0 .
06 0 .
05 0 . −
16 0 .
05 0 .
05 0 .
05 0 . −
17 0 .
06 0 .
05 0 .
06 0 . −
18 0 .
06 0 .
07 0 .
07 0 . −
19 0 .
07 0 .
07 0 .
07 0 . −
20 0 .
08 0 .
08 0 .
09 0 .
25 8 – − . < ( B − V ) < .
909 respectively. For the extinction coefficients, we assumed thetypical values for the ARIES observational site (Kumar et al. 2000). For translating theinstrumental magnitude to the standard magnitude, the calibration equations derived usingthe least square linear regression are as follows: u = U + Z U + C U ( U − B ) + k U Xb = B + Z B + C B ( B − V ) + k B Xv = V + Z V + C V ( B − V ) + k V Xi = I + Z I + C I ( V − I ) + k I X where u, b, v and i denote the aperture instrumental magnitudes and U, B, V and I arethe standard magnitudes whereas airmass is denoted by X . The color coefficients (C) andzeropoints (Z) for different filters are listed in Table 2. The errors in zero points and colorcoefficients are ∼ V magnitude in Fig. 2. This figure shows that the average photometric error is ≤ B , V and I filter at V ∼ th mag, while it is ≤ U filter at V ∼ th mag. Photometric global (DAOPHOT+Calibrations) errors are also calculated, which arelisted in Table 3. For V filter, the error are 0.06 at V ∼
17 mag and 0.08 at V ∼
20 mag.To transform the CCD pixel coordinates to celestial coordinates, we used the onlinedigitized European Southern Observatory catalog included in the
SKY CAT software as anabsolute astrometric reference frame. The
CCM AP and
CCT RAN routine in
IRAF wasused to find a transformation equation which gives the celestial coordinates as a function ofthe pixel coordinates. The resulting celestial coordinates have standard deviations of ∼ To compare the photometry, We cross-matched the present catalog with APASS catalog.For this matching the maximum difference in the positions of stars is 1 arcsec. In this manner,we have found 68 common stars between these two catalogs. A comparison of V magnitudesand ( B − V ) color between the two catalogs is plotted against V magnitude and shown inFig 5. The mean difference and standard deviation in per magnitude bin are listed in Table4. The difference indicates that present V and ( B − V ) measurements are in fair agreementwith those given in APASS catalog. 9 –Fig. 5.— Differences between measurements presented in APASS catalog and in this studyfor V magnitude and (B-V) colors. Zero difference is indicated by the dashed line.Table 4: The difference in V and ( B − V ) between APASS catalog and present study. Thestandard deviation in the difference for each magnitude bin is also given in the parentheses V ∆ V ∆ B − V −
12 0 .
03 (0 .
03) 0 .
02 (0 . −
13 0 .
02 (0 .
05) 0 .
02 (0 . −
14 0 .
06 (0 .
08) 0 .
03 (0 . −
15 0 .
07 (0 .
08) 0 .
05 (0 . −
16 0 .
08 (0 .
10) 0 .
04 (0 . −
17 0 .
09 (0 .
14) 0 .
07 (0 .
21) 10 –
Gaia EDR3 (Gaia Collaboration et al. 2020) the database is used for the astrometricstudy of SAI 35. This data consist of positions on the sky ( α, δ ), parallaxes and propermotions ( µ α cosδ, µ δ ) with a limiting magnitude of G = 21 mag. The uncertainties in parallaxvalues are ∼ G ≤
15 mag and ∼ G ∼
17 mag. The proper motions with their respective errors are plottedagainst G magnitude in the right panel of Fig. 3. The uncertainties in the correspondingproper motion components are ∼ yr − (for G ≤
15 mag), ∼ yr − (for G ∼
17 mag), ∼ yr − (for G ∼
20 mag) and ∼ yr − (for G ∼
21 mag). Wehave compared Gaia EDR3 proper motion and their errors with Gaia DR2 data. We canclearly see in Fig 3 that Gaia EDR3 data base is more precise than Gaia DR2.
The near-Infrared
J HK photometric data for SAI 35 was taken from the Two MicronAll-sky Survey (2MASS). 2MASS consistently scanned the whole sky in three near-IR bands J (1 . µ m), H (1 . µ m) and K (2 . µ m). The 2MASS (Skrutskie et al. 2006) used two highlyautomated 1.3m aperture, open tube, equatorial fork-mount telescopes (one at Mt. Hopkins,Arizona (AZ), USA and other at CTIO, Chile) with a 3-channel camera (256 × M ASS database contains photometry in thenear infrared J , H and K bands to a limiting magnitude of 15.8, 15.1 and 14.3 respectively,with a signal to noise ratio (S/N) greater than 10. The American Association of Variable Star Observers (AAVSO) Photometric All-SkySurvey (APASS) is cataloged in five filters: B, V (Landolt) and g ′ , r ′ , i ′ , with V bandmagnitude range from 7 to 17 mag (Heden & Munari 2014). The DR9 catalog covers about99% of the sky (Heden et al. 2016). To compare the photometry, we have used data in B and V bands for SAI 35. 11 –Fig. 6.— (Bottom panels) Proper-motion vector point diagrams (VPDs) for SAI 35. (Toppanels) V versus ( B − V ) color magnitude diagrams. (Left panel) The entire sample. (Center)Stars within the circle of 0.6 mas yr − radius centered around the mean proper motion of thecluster. (Right) Probable background/foreground field stars in the direction of this object. 12 –Table 5: Variation of completeness factor (CF) in the V , ( V − I ) diagram with the MSbrightness. V mag range CF10- 11 1.0011- 12 1.0012- 13 0.9913 - 14 0.9914 - 15 0.9915 - 16 0.9816 - 17 0.9717 - 18 0.9618 - 19 0.9319 - 20 0.7920 - 21 0.50 Fig. 7.— Proper motion histograms of 0.1 mas yr − bins in right ascension and declinationof the cluster SAI 35. The Gaussian function fit to the central bins provides the mean valuesin both directions as shown in each panel. 13 – LAMOST provided 9 million spectra with radial velocities in its fifth data release (DR5).This data also contains 5.3 million spectra with stellar atmospheric parameters (effectivetemperature, surface gravity and metallicity). We used this data to obtain the value ofmean radial velocity and metallicity towards the region of SAI 35. The mean value of radialvelocity has been used to obtain the orbital parameters of the cluster.
3. Completeness of the CCD data
The observational data may be incomplete because of the stellar crowding, saturation ofbright stars, poor observing conditions, the inefficiency of CCD data reduction programmesetc. The completeness correction is mandatory to compute luminosity function of the stars inthe cluster. To calculate the completeness level in our photometry for SAI 35, we performedthe artificial star (AS) test. We have randomly added only 10 to 15% of actually detectedstars into the original images so that the crowding characteristics of the original imagesremain unchanged. The ADDSTAR routine in DAOPHOT II was used to determine thecompleteness factor (CF). Detailed information about this experiment is given by Yadav& Sagar (2002) and Sagar & Griffiths (1998). In the present analysis, we have adoptedthe method given by Sagar & Griffiths (1998). Artificial stars with known magnitude andposition were added in the original V frames. These images are re-reduced using a similarmethod that was adopted for the original images. The ratio of recovered to added stars indifferent magnitude bins gives the CF. The CF derived in this way are listed in Table 5 forSAI 35. Fig 4 shows the variation of completeness factor versus V magnitude. The value ofCF is found as ∼
93% at V=19 mag.
4. Proper motions and Field star separation
Proper motion is a key parameter to separate field stars from the cluster region to trulyunderstand the main sequence of clusters. PM components ( µ α cosδ , µδ ) are plotted as VPDin the bottom panels of Fig. 6 after matching our observed U BV I data with Gaia EDR3.The panels of top rows show the corresponding V versus ( B − V ) color-magnitude diagrams(CMDs). The left panel shows all the detected stars towards the region of SAI 35, whilethe middle and right panels show the probable cluster members and field region stars. Acircle of 0.6 mas yr − around the distribution of cluster stars in the VPD characterize ourmembership criteria. The chosen radius is a compromise between losing member stars with 14 –Fig. 8.— (Left panel) Membership probability as a function of V magnitude. (Right panel)Parallax as a function of V magnitude. The filled circles show the cluster members withmembership probability higher than 50% in both the panels.Fig. 9.— ( V, B − V ) CMD, identification chart and proper motion distribution of memberstars with membership probability higher than 50%. The plus sign indicates the clustercenter in position and proper motions. 15 –poor PMs and contamination of field region stars (Sariya et al. 2015, Bisht et al. 2020). Wehave also used mean parallax for the cluster member selection. We estimated the weightedmean of parallax for stars inside the circle of VPD having V mag brighter than 20 th mag.We obtained the mean value of parallax as 0 . ± .
02 mas. We considered a star as the mostprobable members if it lies within 0.6 mas yr − radius in VPD and has a parallax within3 σ from the mean parallax of SAI 35. The CMD of the most probable cluster members isshown in the upper-middle panel in Fig. 6. In this figure, the main sequence of the clusteris identified.To estimate the mean proper motion, we considered probable cluster members selectedfrom VPD and CMD as shown in Fig. 6. By fitting the Gaussian function into the con-structed histograms, provides mean proper motion in both the directions of right ascensionand declination as shown in Fig. 7. In this way, we found the mean-proper motion of SAI 35as 1 . ± .
01 and − . ± .
01 mas yr − in µ α cosδ and µ δ respectively. The estimated valueof mean PM for this object is in very good agreement with Cantat-Gaudin et al. (2018).Our derived values of mean proper motion is much reliable than Kharchenko et al. (2012,2013) and Dias et al. (2014) because present estimated is based on accurate Gaia EDR3proper motion data. To estimate the membership probabilities of stars towards the region of SAI 35, weadopted the approach given by Balaguer-N´u˜nez et al. (1998) by using proper motion andparallax data from Gaia EDR3. This membership probability method has been used anddescribed by various authors for a number of clusters (Kaur et al. 2020; Yadav et al. 2013;Sariya et al. 2017; 2018; Bisht et al. 2020b).To describe the distribution functions for cluster and field stars in the adopted method,we used only good stars which have PM errors better than ∼ − . A clear crowdingof stars can be seen at µ xc =1.10 mas yr − , µ yc = − − and in the circular regionhaving radii of 0.6 mas yr − . We estimated dispersion ( σ c ) in PMs as 0.09 mas yr − byfixing cluster distance as 2.9 kpc and the radial velocity dispersion of 1 km s − for open starclusters (Girard et al. 1989). For non members, we have estimated ( µ xf , µ yf ) = ( − − and ( σ xf , σ yf ) = (2.9, 3.3) mas yr − .We obtained 214 stars as cluster members after applying completeness to the obser-vational CCD data along with with membership probability higher than 50% and V ≤
20 16 –Fig. 10.— The (V, B − V ) CMD of our observed data and (G, G BP − G RP ) CMD of Cantat-Gaudin et al. 2018 (CG18) catalog. All stars are plotted with membership probability higherthan 50%.Fig. 11.— Profiles of stellar counts across SAI 35 region. The Gaussian fits have beenapplied. The center of symmetry about the peaks of Right Ascension and Declination istaken to be the position of the cluster’s center. 17 –mag. In the left panel of Fig. 8, we plotted membership probability versus V magnitude.In this figure, cluster members and field stars are separated. In the right panel of this fig-ure, we plotted V magnitude versus parallax of stars. In Fig. 9, we plotted identificationchart, proper motion distribution and V versus B − V color-magnitude diagram using themost probable cluster members. The most probable cluster members with high membershipprobability ( ≥ ∼
5. Structural analysis: radial density profile
To estimate the center coordinates towards the area of SAI 35, we used the star-count method. The resulting histograms in both the RA and DEC directions are shownin Fig. 11. The Gaussian curve-fitting provides the central coordinates as α = 62 . ± . h m s ) and δ = 46 . ± .
004 deg (46 ◦ ′ ′′ ). Our obtained values are very closeto the values given by Sampedro et al. (2017) and Cantat-Gaudin et al. (2018).To obtain the structural parameters of SAI 35, we plotted the radial density profile asshown in Fig. 12. We divided the cluster’s region into many concentric rings and numberdensity ( R i ) calculated in each ring by using the formula R i = N i A i , where N i is the numberof stars and A i is the area of the i th zone. This RDP flattens at r ∼ f ( r ) = f bg + f r/r c ) where r c , f , and f bg are the core radius, central density, and the background densitylevel, respectively. By fitting the King model to the RDP of SAI 35, we obtained the valuesof central density, background density, and core radius as 25 . ± . ,9 . ± . and 1 . ± . r lim , iscalculated by using the formula given by Bukowiecki et al. (2011). The estimated valueof the limiting radius is found to be 7.6 arcmin. The concentration parameter is found as0.8 using the formula given by Peterson & King (1975). Maciejewski & Niedzielski (2007)reported that R lim may vary for individual clusters from 2 R c to 7 R c . We found that thevalue of R lim ( ∼ R c ) for SAI 35 is within the given limit by Maciejewski & Niedzielski(2007).
6. Colour-Colour Diagrams6.1. Reddening law
To understand the nature of extinction law and to find the value of interstellar reddening,we used various color-color diagrams (CCDs) for SAI 35.
Total-to-selective extinction can be different for cluster members and foreground starsif the size of dust is not the same in the cluster’s area and the interstellar medium along thesame line of sight (Mathis 1990). The emitted photons from cluster members are scatteredand absorbed in the interstellar medium by dust particles. The normal reddening law is notapplicable in the line-of-sight that passes through dust, gas and molecular clouds (Snedenet al. (1978)).Chini & Wargue (1990) suggested ( V − λ ) / ( B − V ) CCDs to understand the nature ofreddening law in which λ is any filter, other than V . We plotted various two-color diagramsfor SAI 35 as shown in Fig 13 to understand the reddening law. Our obtained values ofcolor-excesses with normal values have been listed in Table 6. The estimated values of color- 19 –excesses are in good agreement with the normal values. Since, the stellar color values arefound to be linearly dependent on each other, then a linear equation is applied to calculatethe slope ( m cluster ) of each CCD. Total to selective extinction has been estimated using therelation provided by Neckel & Chini (1981): R cluster = m cluster m normal × R normal where m cluster is the normal slope value in each CCD and R normal (3.1) is the normalvalue of total-to-selective extinction ratio. We have estimated R cluster in different passbandsas ∼ ( U − B ) versus ( B − V ) diagram The knowledge of interstellar reddening is important to obtain main fundamental pa-rameters (age, distance, etc.) of clusters. In the absence of spectroscopic observations, wecan use ( B − V ) , ( U − B ) color-color diagram for the reddening estimation of clusters (cf.Becker & Stock 1954). The resultant ( U − B ) versus ( B − V ) plot for SAI 35 is shown in Fig14 using cluster members with membership probability higher than 50%. Blue dots are thematched stars with the catalog provided by Cantat-Gaudin et al. (2018). We have taken theintrinsic zero-age main-sequence (ZAMS) from Schmid-kaler (1982). The ZAMS is fitted bythe continuous curve considering the slope of reddening E ( U − B ) /E ( B − V ) as 0.72. Byfitting ZAMS to the MS, we have calculated mean value of E ( B − V ) = 0 . ± .
05 magfor SAI 35. Present estimate of reddening is close to the value derived by Kharchenko et al.(2012, 2013) and Sampedro et al. (2017).Table 6: A comparison of the extinction law in the direction of the cluster SAI 35 with anormal extinction law given by Cardelli et al. (1989).SAI 35 ( V − I ) / ( B − V ) ( V − J ) / ( B − V ) ( V − H ) / ( B − V ) ( V − K ) / ( B − V )Our derived ratios 1 . ± . . ± .
23 2 . ± .
09 2 . ± . V band. Errors are determinedfrom sampling statistics (= √ N where N is the number of cluster members used in the densityestimation at that point). The smooth line represent the fitted profile of King (1962) whereasdotted line shows the background density level. Long and short dash lines represent the errorsin background density.Fig. 13.— The ( λ − V ) / ( B − V ) CCD for the stars within cluster extent of SAI 35. Thecontinuous lines represent the slope determined through the least-squares linear fit. 21 –Fig. 14.— The ( U − B ) versus ( B − V ) color-color diagram. The continuous curve representslocus of Schmidt-Kaler’s (1982) ZAMS for solar metallicity. Arrow indicates the reddeningvector.Fig. 15.— The plot of ( J − K ) versus ( V − K ) color-color diagram. Solid and dotted linesare the ZAMS taken from Caldwell et al. (1993). 22 – The near-IR photometry is very helpful to understand interstellar extinction (Tapia etal. 1988). Here we have used
J HK photometry from the 2MASS database to study theinterstellar extinction law. The ( J − K ) versus ( V − K ) diagram for SAI 35 is shown in Fig.15. The ZAMS of solar metallicity is taken from Caldwell et al. (1993) as shown by the solidline. The fit of ZAMS provides E ( J − K ) = 0 . ± .
04 mag and E ( V − K ) = 1 . ± . E ( J − K ) E ( V − K ) ∼ . ± .
05 is in good agreement with the normal interstellarextinction value of 0.19 is given by Cardelli (1989).
Age and distance of OCs are important parameters to trace the galactic structure andto understand the chemical evolution of Galaxy (Friel & janes 1993). The main funda-mental parameters (reddening, metallicity, distance modulus, age, etc.) of a cluster can beobtained by fitting the theoretical isochrones to our observed CMDs. We used the theoret-ical isochrones given by Marigo et al. (2017) for Z = 0 . V / ( U − B ) , V / ( B − V ), V / ( V − I ), G/ ( G BP − G ), G/ ( G BP − G RP ) and G/ ( G − G RP ) CMDs along with visuallyfitted isochrones are shown in Fig. 16 and Fig. 17.We superimpose theoretical isochrones of different ages (log(age)=8.50, 8.55 and 8.60)in all the plotted CMDs. Based on this, we have found an age of 360 ±
40 Myr. Our estimatedvalue of age is same as Sampedro et al. (2017). We obtained distance modulus ( m − M )= 14 . ± . . ± . X ⊙ = − .
61 kpc, Y ⊙ = 1 .
25 kpc and Z ⊙ = − . . ± .
02 maswhich corresponds to a distance of 2 . ± .
17 kpc. The calculated value of parallax is ingood agreement with the value obtained by Cantat-Gaudin et al. (2018). We also estimateddistance using the method described by Bailer-Jones et al. (2018). Thus, we obtained adistance of SAI 35 as 2 . ± .
15 kpc. We find a similar value of distance using the meanparallax and distance modulus of the cluster. 23 –
Using optical and near-IR data we have re-determined distance and age of SAI 35. Wehave plotted V versus ( V − K ), K versus ( J − K ) and J versus ( J − H ) CMDs, which isshown in Fig 19. The theoretical isochrones given by Marigo et al. (2017) for Z = 0.019 oflog(age)=8.50, 8.55 and 8.60 have been over plotted in the CMDs. The apparent distancemoduli ( m − M ) V, ( V − K ) and ( m − M ) K, ( J − K ) turn out to be 14.60 ± ± ±
7. Dynamical study7.1. Luminosity and mass function
Luminosity function (LF) is the distribution of members of a cluster in different magni-tude bins. We considered probable cluster members in
V / ( V − I ) CMD to construct the LFfor SAI 35. For the construction of LF, first, we converted the apparent V magnitudes intothe absolute magnitudes by using the distance modulus. Then, we plotted the histogram ofLF as shown in Fig 20. The interval of 1.0 mag was picked so that there would be the suffi-cient number of stars in each bin for statistical usefulness. The LF of SAI 35 rises steadilyup to M V =4.5 mag.Mass function (MF) is defined as the distribution of masses of cluster stars per unitvolume during the time of star formation. LF can be converted into the mass function (MF)using a mass-luminosity relation. Since we could not obtain an observational transformation,so we must depend on theoretical models. To perform the conversion of LF into MF, weused cluster parameters derived in this paper and theoretical models given by Marigo et al.(2017). The resulting MF is shown in Fig. 21. The mass function slope can be derived fromthe linear relationlog dNdM = − (1 + x ) × log( M )+constant 24 –Table 7: Comparison of our obtained fundamental parameters for SAI 35 with the literaturevalues . Parameters Numerical values Reference(Right ascension, Declination) (deg) (62.70, 46.86) Present study(62.70, 46.87) Cantat-Gaudin et al. (2018)(62.69, 46.86) Sampedro et al. (2017)Cluster radius (arcmin) 3.9 Present study3.5 Dias et al. (2014)( µ α cos ( δ ) , µ δ ) (mas/yr) (1 . ± . − . ± .
01) Present study(1.10, -1.64) Cantat-Gaudin et al. (2018)(-0.11, -0.90) Dias et al. (2014)(-2.36, -6.11) Kharchenko et al. (2012, 2013)Age (log) 8.55 Present study8.55 Sampedro et al. (2017)8.22 Kharchenko et al. (2012, 2013)Distance (Kpc) 2 . ± .
15 Present study2.7 Cantat-Gaudin et al. (2018)2.8 Kharchenko et al. (2012, 2013) E ( B − V ) (mag) 0 . ± .
05 Present study0.70 Sampedro et al. (2017)0.79 Kharchenko et al. (2012, 2013)
25 –In the above relation, dN represents the number of stars in a mass bin dM with thecentral mass M and x is the mass function slope. The Salpeter (1955) value for the massfunction slope is x = 1 .
35. This form of Salpeter shows that the number of stars in each massrange decreases rapidly with the increasing mass. Our derived MF slope value, x = 1 . ± . M ⊙ , total mass was obtained as ∼ M ⊙ . As a result of the mass-segregation, massive stars get concentrated towards the centerthan the fainter stars. Many authors have reported mass-segregation phenomenon in clusters(Piatti 2016; Zeidler et al. 2017; Dib, Schmeja & Parker 2018; Bisht et al. 2020a). Tostudy the effect of mass segregation for the clusters, we plot the cumulative radial stellardistribution of stars for different masses in Fig 22. This figure exhibits mass-segregationeffect in the clusters under the present study, which means that the massive stars havegradually sunk towards the cluster center as compared to the distribution of the fainterstars. We have divided the main sequence stars in these three mass ranges, 3.1 ≤ MM ⊙ ≤ ≤ MM ⊙ ≤ ≤ MM ⊙ ≤ K − S ) test.This test indicates that the confidence level of mass-segregation effect is 90 %.Further, it is important to know that the effect of mass-segregation is due to dynamicalevolution or imprint of star formation or both. In the lifetime of star clusters, encoun-ters between its member stars gradually lead to an increased degree of energy equipartitionthroughout the clusters. In this process, the higher mass cluster members accumulate to-wards the cluster center and transfer their kinetic energy to the more numerous lower-massstellar component, thus leading to mass segregation. The time scale in which a cluster will lose all traces of its initial conditions is well rep-resented by its relaxation time T E . The relaxation time is the characteristic time-scale for acluster to reach some level of energy equipartition. The relaxation time given by Spitzer &Hart (1971) stated that: T E = . × N / R / h
26 –Fig. 16.— The color-magnitude diagram of the clusters under study. The curves are theisochrones of (log(age) = 8.50 ,8.55 and 8.60). These ishochrones are taken from Marigo etal. (2017). Black circles are the probable cluster members while the blue circles representthe matched stars with Cantat-Gaudin et al. (2018).Fig. 17.— Same as Fig 16 using Gaia EDR3 photometric magnitudes. 27 –Fig. 18.— Histogram of parallax for SAI 35. Black lines represents all stars in the clusterfield whereas the red lines represents the most probable cluster members. The Gaussianfunction is fitted to the central bins provides mean value of parallax.Fig. 19.— Same as Fig 16 of optical and near-IR color-magnitude diagrams. 28 –Fig. 20.— Luminosity function of stars in the region of SAI 35.Fig. 21.— Mass function histogram derived using the most probable members, where solidline indicates the power law given by Salpeter (1955). The error bars represent √ N . 29 –where N is the number of cluster members, R h is the half-mass radius of the clusterand < m > is mean mass of the cluster stars. The value of R h was taken as 1.64 pc, whichhas been assumed as half of the cluster radius derived by us. Finally, we have estimated thedynamical relaxation time T E as ∼
11 Myr. A comparison of cluster age with its relaxationtime indicates that relaxation time is smaller than the age. Therefore, we conclude that SAI35 is a dynamically relaxed cluster.
Tidal radius is the distance from cluster center where gravitational acceleration causedby the cluster becomes equal to the tidal acceleration due to parent Galaxy (von Hoerner1957). Tidal interactions play important role to understand the initial structure and dynam-ical evolution of clusters (Chumak et al. 2010; Dalessandro et al. 2015). The Galactic mass M G inside a Galactocentric radius R G is given by (Genzel & Townes, 1987), M G = 2 × M ⊙ ( R G pc ) . Estimated value of Galactic mass inside the Galactocentric radius (see Sec. 4.5) is foundas 2 . × M ⊙ . Kim et al. (2000) has introduced the formula for the tidal radius R t ofclusters as R t = ( M c M G ) / × R G where R t and M c indicate the cluster’s tidal radius and total mass (see Sect. 8), respec-tively. The estimated value of the tidal radius is 10 . ± .
82 pc.
8. The orbit of the cluster
We obtained the Galactic orbit of SAI 35 using the Galactic potential models. Weadopted the technique described by Allen & Santillan (1991) for Galactic potentials. Lately,Bajkova & Bobylev (2016) and Bobylev et. al (2017) refined Galactic potential model pa-rameters with the use of new observational data for the galacto-centric distance R ∼ α and δ ), mean proper motions ( µ α cosδ , µ δ ), parallax angles, age and heliocentric distance( d ⊙ )) to obtain orbital parameters of SAI 35. Radial velocity is estimated as − . ± . U, V, W ). The Galactic center is taken at (17 h m s . , − ◦ ′ ′′ ) and North-Galactic pole is at (12 h m s . , ◦ ′ ′′ .
01) (Reid & Brunthaler, 2004). To apply acorrection for Standard Solar Motion and Motion of the Local Standard of Rest (LSR), weused position coordinates of Sun as (8 . , , .
02) kpc and its space-velocity components as(11 . , . , .
25) km/s (Schonrich et al. 2010). Transformed parameters in Galacto-centriccoordinate system are listed in Table 8.Fig. 23 shows the orbits of the cluster SAI 35. In the top left panel of this figure,the motion of cluster is represented in terms of distance from Galactic center and Galacticplane, which show a 2-D side view of the orbits. In the top right panel, the cluster motionis described in terms of x and y components of Galactocentric distance, which shows a topview of orbits. The bottom panel of this figure indicates that motion of SAI 35 in Galacticdisc with time. According to our analysis, SAI 35 follows a boxy pattern. The value ofeccentricity is nearly 0, which demonstrates that the open cluster SAI 35 traces a circularpath around the Galactic center. The birth and present day position of this cluster in theGalaxy are represented by filled circle and triangle in Fig. 23. The orbit is within theSolar circle. We also calculated various orbital parameters, which are listed in Table 9.Here e is eccentricity, R a is the apogalactic distance, R p is perigalactic distance, Z max is themaximum distance traveled by cluster from Galactic disc, E is average energy of orbits, J z is z component of angular momentum and T is time period of the cluster in the orbits. Orbitalparameters determined in the present analysis are similar to the parameters determined byWu et al. (2009).Table 8: Position and velocity components in the Galactocentric coordinate system. Here R is the galactocentric distance, Z is the vertical distance from the Galactic disc, U V W are the radial tangential and the vertical components of velocity respectively and φ is theposition angle relative to the sun’s direction.Cluster R Z U V W φ (kpc) (kpc) (km/s) (km/s) (km/s) (radian)SAI 35 10.98 -0.15 60 . ± . − . ± . − . ± .
99 0.11 31 –Fig. 22.— The cumulative radial distribution of stars in various mass range.Table 9: Orbital parameters obtained using the Galactic potential model.Cluster e R a R p Z max E J z T (kpc) (kpc) (kpc) (100 km/s ) (100 kpc km/s) (Myr)SAI 35 0.01 11.56 11.81 0.18 -10.12 -22.06 341 32 –
9. Conclusions
We have performed a detailed analysis of the newly discovered open cluster SAI 35based on Johnson-Cousins UBVI photometry carried out using 1.04-m Telescope (ARIES,Nainital, India), the 2MASS survey, LAMOST DR5 catalog and Gaia EDR3 photometric andastrometric database. We have identified 214 member stars with membership probabilitieshigher than 50%. We investigated the cluster structure, derived the main fundamentalparameters, explained the dynamical study, and determined the galactic orbit of SAI 35.The main outcomes of this study can be summarized as follows: • The new cluster center is estimated as: α = 62 . ± .
01 deg (4 h m s ) and δ =46 . ± .
004 deg (46 ◦ ′ ′′ ) using cluster members based on VPD. • Using the radial density profile, the cluster radius is obtained as 3.9 arcmin (3.3 pc)using the radial density profile. • Based on the completeness of CCD data, vector point diagram and membership prob-ability estimation, we identified 214 most probable cluster members for SAI 35. Themean PM is estimated as 1 . ± .
01 and − . ± .
01 mas yr − in both the RA andDEC directions respectively. • We detected one BSS towards the region of SAI 35 and it was found a confirmedmember of the cluster. • From the two color diagram, we have estimated E ( B − V ) = 0 . ± .
05 mag. We haveplotted various CCDs and obtain total-to-selective extinction ( R V ) in the range of 2.9to 3.3. Our Analysis indicates that interstellar extinction law is normal towards thedirection of SAI 35. From the combined optical and near-infrared data, we obtained E ( J − K ) = 0 . ± E ( V − K ) = 1 . ± • The distance of SAI 35 is determined as 2 . ± .
15 kpc. This value is well supportedby the distance estimated using mean parallax of the cluster. Age is determined as360 ±
40 Myr by comparing the cluster CMD with the solar metallicity theoreticalisochrones given by Marigo et al. (2017). • The mass function slope is estimated as 1 . ± .
16 in the mass range 1.1-3.1 M ⊙ , whichis in good agreement within uncertainty with the value (1.35) given by Salpeter (1955)for field stars in Solar neighborhood. By using this MF slope, we have estimated totalmass and mean mass as 364 and 1.70 M ⊙ , respectively. 33 – • On the basis of the dynamical evolution study of SAI 35, we found a deficiency of lowmass stars in the core. Our study shows a clear mass-segregation phenomenon in thiscluster. The K-S test indicates 90% confidence level of mass-segregation effect. Thedynamical relaxation time is estimated as 10 Myr, which is less than the age of thecluster. Our study indicates that SAI 35 is a dynamically relaxed open cluster. • The Galactic orbits and orbital parameters were estimated using Galactic potentialmodels. We found the value of eccentricity ∼
0, which concludes that SAI 35 tracecircular path around the center of the Galaxy.
ACKNOWLEDGMENTS e s Stellaires-Strasbourg,France) and of the WEBDA open cluster database. REFERENCES
Ahumada J., Lapasset E., 1995, A&AS, 109, 375Allen, C. & Santillan, A. 1991, Rev. Mexicana Astron. Astrofis., 22, 255 34 – -0.2-0.1 0 0.1 0.2 7 7.7 8.4 9.1 9.8 10.5 11.2 11.9 Z ( k p c ) R (kpc) -10-5 0 5 10 -10 -5 0 5 10 R s i n ( φ ) R cos( φ )-0.2-0.1 0 0.1 0.2 0 5 10 15 20 25 30 35 40 Z ( k p c ) Time (10 yr) Fig. 23.— Galactic orbits of the cluster SAI 35 estimated with the Galactic potential modeldescribed in text in the time interval of age of cluster. The top left panel shows side viewand top right panel shows top view of the orbit. Bottom panel show motion of SAI 35 inGalactic disc with time. The filled triangle and circle denote birth and present day positionof cluster in the Galaxy. 35 –Bailer-Jones C. A. L., Rybizki J., Fouesneau M., Mantelet G., Andrae R., 2018, AJ, 156, 58Bailyn, C. D., 1995, ARA&A, 33, 133Bajkova, A. T. & Bobylev, V. V. 2016, Astronomy Letters, 42, 9Balaguer-N´u˜nez L., Tian, K. P., Zhao, J. L., 1998, A&AS, 133, 387Bastian, Nate; Covey, Kevin R., Meyer, Michael R., 2010, ARA&A, 48, 339BBecker W. and Stock J., 1954, Ze. f. Astrophys. 34, 1.Binney J., Tremaine S., 2008, Galactic Dynamics. Princeton Univ. press, Princeton, NJBisht, D., Yadav, R. K. S., Ganesh, S., Durgapal, A. K., Rangwal, G. & Fynbo, J. P. U.2019, MNRAS, 482, 1471BBisht, D., Zhu, Q., Yadav, R. K. S. et al., 2020a, MNRAS, 482, 607Bisht, D., Elsanhoury W., Zhu, Q., Sariya, D. P. et al., 2020b, AJ, 160, 119 36 –Bobylev, V. V., Bajkova, A. T. & Gromov, A. O. 2017, Astronomy Letters, 43, 4Bukowiecki, L. et al. 2011, AcA, 61, 231Cantat-Gaudin, T., Jordi, C., Vallenari, A., et al. 2018, A&A, 618A, 93CCantat-Gaudin, T., Anders F., 2020, A&A, 633, A99Caldwell, J. A. R., Cousins, A. W. J., Ahlers, C. C., van Wamelen, P., Maritz, E. J., 1993.South African Astron. Observatory (Circ. No. 15).Cardelli J. A., Clayton G. C., Mathis J. S., 1989, ApJ, 345, 245Chini R., Wargue W. F., 1990, A&A, 227, 5Chumak Y. O., Platais I., McLaughlin D. E., Rastorguev A. S., Chumak O. V. E., 2010,MNRAS, 402, 1841Converse J. M., Stahler S. W., 2011, MNRAS, 410, 2787Cui, X. Q., Zhao, Y. H., Chu, Y. Q., et al. 2012, 12, 1197 37 –Dib S., Scmeja S., Hony S., 2017, MNRAS, 464, 1738Dib, Sami., Basu, Shantanu., 2018, A&A, 614A, 43DDias, W. S., Monteiro H., Caetano T. C. et al. 2014, A&A, 564A, 79DDalessandro E., et al. 2015, MNRAS, 449, 1811Elmegreen, B. G. 2000, ApJ, 539, 342Friel E. D., Janes K. A., 1993, A&A, 267, 75Gaia Collaboration et al. 2018a, A&A, 616, A1Gaia Collaboration et al. 2018b, A&A, 616, A11Gaia Collaboration. et al. 2020, A&A, in Prep.Genzel R., Townes C. H., 1987, ARA&A, 25, 377Girard, T. M., Grundy, W. M., Lopez, C. E., & van Altena, W. F. 1989, AJ, 98, 227 38 –Henden, A., Munari, U. 2014, Contrib. Astron. Obs. Skalnate Pleso, 43, 518Heden, A., Templeton, M., Terrell, D., et al. 2016, VizieR Online Data Catalog, II/336Hur H., Sung, H., Bessel M. S., 2012, AJ, 143, 41Johnson H. L., Sandage A. R., 1955, ApJ, 121, 616Joshi Y. C., Maurya J., John A. A., Panchal A., Joshi, S., Kumar B., 2020, MNRAS, 492,3602Kaur, Harmeen., Sharma, Saurabh., Dewangan, Lokesh K. et al., 2020, ApJ, 896, 29KKhalaj, P., Baumgardt, H., 2013, MNRAS, 434, 3236King, I., 1962, AJ 67, 471Kim S. S., Figer D. F., Lee, H. M., MOrris M., 2000, ApJ, 545, 301Kumar B., Sagar R., Rautela B. S., Srivastava J. B., Srivastava R. K., 2000, Bull. Astron.Soc. India, 28, 675Kharchenko N. V., Piskunov A. E., Schilbach, S., Roeser, S. and Scholz R. D. 2012, A&A,543A, 156K 39 –Kharchenko N. V., Piskunov A. E., Schilbach, S., Roeser, S. and Scholz R. D. 2013, A&A,558A, 53KKharchenko N. V., Piskunov A. E., Schilbach, S., Roeser, S. and Scholz R. D. 2016, A&A,585A, 101KKronberger, M., Teutsch, P., Alessi, B. et al. 2006, A&A, 447, 921KKroupa P., 2002, Science, 295, 82Landolt A. U., 1992, AJ, 104, 340Luo, A. L., Zhang, H. T., Zhao, Y. H., et al. 2012, RAA, 12, 1243Maciejewski, G. & Niedzielski, A., 2007, A&A, 467, 1065Marigo, P. et al. 2017, ApJ, 835, 77Mathis, J. S., 1990, ARA&A, 28, 37 40 –Neckel T., Chini R., 1981, A&A, 45, 451Peterson, C. J. & King, I. R., 1975, AJ, 80, 427Piatti A. E., 2016, MNRAS, 463, 3476Reid M J., Brunthaler A., 2004, ApJ, 616, 872Rangwal, G., Yadav, R. K. S., Durgapal, A., Bisht, D. & Nardiello, D. 2019, MNRAS, 490,1383Sagar R. & Griffiths W.K., 1998, MNRAS 299, 777Sampedro, L., Dias, W. S., Alfaro, E. J., Monteiro, H. and Molino, A. 2017, MNRAS, 470,3937SSandage A. R., 1953, AJ, 58, 61Sandage A. R., 1962, ApJ, 135, 333Sariya, D. P., & Yadav, R. K. S. 2015, A&A, 584, A59 41 –Sariya, D. P., Jiang, I.-G., & Yadav R. K. S., 2017, AJ, 153, 134Sariya ,D. P., Jiang, I.-G., & Yadav, R. K. S., 2018, RAA, 18, 126Schonrich, Ralph., Binney, James., Dehnen, Walter. 2010, MNRAS, 403, 1829SSneden C., Gehrz R. D., Hackwell J. A., York D. G., Snow T. P., 1978, ApJ, 223, 168Salpeter, E. E., 1955, ApJ, 121, 161Schmid - Kaler Th., 1982, in Scaitersk., Voigt H. H., eds, Landolt / Bornstein, NumericalData and Functional Relationship in Science and Technology, New series, Group VI,vol. 2b. springer - verlag, Berlin, p. 14Skrutskie, M. F., Cutri, R. M., Stiening, R., et al., 2006, AJ, 131, 1163Spitzer, L., & Hart, M. H., 1971, ApJ, 164,399Stetson P. B., 1987, PASP, 99, 191Stetson P. B., 1992, in Warrall D. M., BiemesderferC., Barnes J., eds, ASp Conf. Ser.Vol. 25, Astronomical Data Analysis Software and System I. Astron. Soc. Pac., SanFrancisco, p. 297 42 –Soubiran ,C., Cantat-Gaudin, T., et al. 2018, A&A, 619Tapia M., Roth M., Marraco H., Ruiz M. T., 1988, MNRAS, 232, 661von Hoerner S., 1957, ApJ, 125, 451Wilkinson M. I., Evans N. W., 1999, MNRAS, 310, 645Wu, Z. Y., Zhou, X., Ma, J. & Du, C. H. 2009, MNRAS, 399, 2146Yadav, R. K. S. & Sagar, R. 2002, MNRAS, 337, 133Yadav R. K. S., Sariya D. P., Sagar R., 2013, MNRAS, 430, 3350Zeidler P., Nota A., Grebel E. K., Sabbi E., Pasquali A., Tosi M., Christian, C. K., 2017,AJ, 153, 122Zhao, G., Zhao Y. H., Chu, Y. Q., et al. 2012, RAA, 12, 723F