CCD UBV and Gaia DR3 Analyses of the Open Clusters King 6 and NGC 1605

A detailed analysis of ground-based CCD UBV photometry and space-based Gaia Data Release 3 (DR3) data for the open clusters King 6 and NGC 1605 was performed. Using the pyUPMASK algorithm on Gaia astrometric data to estimate cluster membership probabilities, we have identified 112 stars in King 6 and 160 stars in NGC 1605 as the statistically most likely members of each cluster. We calculated reddening and metallicity separately using UBV two-color diagrams to estimate parameter values via independent methods. The color excess E(B − V) and photometric metallicity [Fe/H] for King 6 are 0.515 ± 0.030 mag and 0.02 ± 0.20 dex, respectively. For NGC 1605, they are 0.840 ± 0.054 mag and 0.01 ± 0.20 dex, respectively. With reddening and metallicity kept constant, we have estimated the distances and cluster ages by fitting PARSEC isochrones to color–magnitude diagrams based on the Gaia and UBV data. The photometric distances are 723 ± 34 pc for King 6 and 3054 ± 243 pc for NGC 1605. The cluster ages are 200 ± 20 Myr and 400 ± 50 Myr for King 6 and NGC 1605, respectively. The mass function slopes were found to be 1.29 ± 0.18 and 1.63 ± 0.36 for King 6 and NGC 1605, respectively. These values are in good agreement with the value of Salpeter. The relaxation times were estimated as 5.8 Myr for King 6 and 60 Myr for NGC 1605. These indicate that both clusters are dynamically relaxed since these times are less than the estimated cluster ages. A Galactic orbit analysis shows that both clusters formed outside the solar circle and are members of the young thin-disk population.


Introduction
The study of open clusters (OCs) gives insights into both stellar and galactic evolution.The stars making up a cluster are formed at essentially the same time and initially share the same kinematic and positional behavior.While the distances, ages, and chemical compositions of the cluster stars are similar, their masses differ (Maurya & Joshi 2020).In studying a cluster, a number of parameters can be taken as fixed for all of the stars, such as distance and age.This means that differences in the apparent magnitudes of the cluster's stars will primarily be due to mass, making OCs very useful in such work.Beyond investigation of the component stars of a cluster, clusters themselves can act as tracers of the chemical enrichment of the Galaxy with time as generations of stars return their constituent atoms back into the interstellar medium and ultimately into later generations of stars (McKee & Ostriker 2007;Cantat-Gaudin et al. 2020;He et al. 2021;Hou 2021) as they form new clusters.
In this paper, we investigate the OCs King 6 and NGC 1605, which are located in the second Galactic quadrant.Both clusters are very close to the Galactic plane.Moving close to this plane results in increased field contamination.Such contamination makes identification of stars having cluster membership, as distinct from being in the surrounding field and therefore unrelated to the cluster, more difficult.This paper will discuss the statistical, careful removal of such field contamination.This is necessary for the precise determination of cluster parameters.This study is part of a wider project that investigates the detailed properties of OCs in the Galaxy (see Yontan et al. 2015Yontan et al. , 2019Yontan et al. , 2021Yontan et al. , 2022Yontan et al. , 2023;;Yontan 2023).The paper aims to estimate the main parameters of King 6 and NGC 1605 using space-based Gaia Data Release 3 (DR3) data (Gaia Collaboration et al. 2023) and ground-based UBV photometric data.
Turning to the actual clusters themselves: 1. King 6 (α = 03 h 27 m 56 s , d = + ¢  56 26 39 o , l = 143°.3444,b = −0°.0949)was classified by Ruprecht (1966) as Trumpler type IV 2p with a weak central stellar concentration.Ann et al. (2002) presented CCD UBVI photometry, color-magnitude diagrams (CMDs), and main-sequence isochrone fitting for the cluster.They noted strong contamination of the main sequence fainter than V ∼ 18 mag by field stars, and that the color-color diagram could not be fitted by a theoretical zero-age main sequence (ZAMS) with a single reddening value.Stars fainter than V ∼ 16 mag appeared to have a lesser E(B − V ) of 0.4 mag, with stars brighter than V ∼ 13 mag having an extinction of 0.6 mag.A mean value of 0.5 ± 0.1 mag was adopted by Ann et al. (2002), leading to what they noted as a poor isochrone fit.The cluster age was estimated as Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.=  t log 8.4 0.1, [Fe/H] as 0.46 dex, and the apparent distance modulus as 11.25 ± 0.71 mag.They also commented that there could be a binary sequence above the ZAMS.Maciejewski & Niedzielski (2007) collected CCD BV photometry of the cluster.They fit a King (1962) profile with a core radius of 3 6 ± 0 4, densities f 0 = 1.55 ± 0.09 and f bg = 0.62 ± 0.04 stars arcmin -2 , and a limiting radius as 10 9. Here, core radius refers to the radial distance from the cluster center within which the density drops to the half of the central density, f 0 refers to the number density of stars in the center of the cluster, and f bg refers to the number density of field stars.The log-age of King 6 was estimated as 8.4, the distance modulus as -+ 11.17 0.47 0.55 mag, and -= -+ E B V 0.53 0.11 0.12 ( ) mag.The "slope" of the mass function (MF) was estimated as 1.74 ± 0.39 with no statistically different slopes for the core (1.44 ± 0.32) and halo (1.58 ± 0.47), and so not suggesting the presence of mass segregation within the cluster.(1966) as a Trumpler type III 1 m of medium richness.Fang (1970) applied RGU photometry to construct CMDs, and commented on the lack of red giants in the cluster.A distance of 2750 pc was estimated.Sujatha & Babu (2003) presented CCD UBVRI photometric observations, finding an E(B − V ) of 0.14 mag and a distance of 1148 pc.Camargo (2021) noted "an unusual morphology with a sparse stellar distribution and a double core in close angular proximity," i.e., a binary cluster.One of the cores was estimated as being substantially older, at an age of 2 ± 0.2 Gyr compared to the 600 ± 100 Myr of the other core.Camargo (2021) argued for tidal capture being the origin of the binary cluster.The joint distance was estimated as 2.6 ± 0.4 kpc.
Both clusters are also explored in general surveys.See Table 1 for a summary of results from the literature for both clusters.
The astrophysical parameters of OCs are commonly estimated simultaneously from isochrones fitted to the observed CMDs (Angelo et al. 2021;Bisht et al. 2022) and Bayesian statistics (von Hippel et al. 2006;Bossini et al. 2019).Large uncertainties in the derived reddening, metallicity, and hence age are driven by degeneracies between parameters in such simultaneous statistical solutions based on the comparison of stellar isochrones with photometric observations (Janes et al. 2014).To break the reddening-age degeneracy in these simultaneous solutions, several approaches have been proposed.Using the available wavelength range, preferably including a near-infrared band, is the main idea behind most of these advances (Bilir et al. 2006(Bilir et al. , 2010;;de Meulenaer et al. 2013).According to Anders et al. (2004), when near-infrared observations are not available, one of the most suitable photometric band combinations for reliable parameter determination is based on UBVRI photometry.In addition traditional and reliable methods developed for determining reddening and metallicity can be used to constrain these parameters (Ak et al. 2016;Bilir et al. 2016;Banks et al. 2020).In this current study, the reddening and metallicity of the clusters were obtained via independent methods from the UBV photometric data.Hence, the parameter degeneracy between reddening and age values was minimized.
In this paper, we determine the cluster membership probabilities for stars in the general line of sight of the clusters, mean distances, and proper-motion components of King 6 and NGC 1605.We present structural and fundamental parameters, luminosity functions (LFs), and MFs, the dynamical states of mass segregation, and the kinematic and Galactic orbital parameters of both clusters.

CCD UBV Observations
Broadband UBV CCD photometric observations of the two clusters were performed using the f/10 Ritchey-Chrétien focus of the 1 m T100 telescope.The T100 is installed at the TÜBİTAK National Observatory (TUG)6 in Turkey.The CCD is a back-illuminated device with 4k × 4k pixels.Each pixel of the CCD detector is 15 μm across.This corresponds to a 0 31 pixel −1 square on the sky.The CCD therefore has a field of view of ¢ ´¢ 21. 5 21. 5.The gain is 0.55 e − ADU −1 and the readout noise 4.19 e − (100 KHz).
The observations of King 6 and NGC 1605 were carried out on 2019 September 30 and 2014 September 24, respectively.Bias frames and UBV flat-field frames were taken at the beginning of each night.Sets of long and short exposures were collected for the two clusters so as to avoid saturating the brighter stars and also allow for the detection of fainter stars.Identification charts are presented in Figure 1.A log of the observations is given in Table 2. To obtain the equation of extinction and the associated transformation coefficients, 16 Landolt fields were observed.These covered a total of 156 standard stars.The airmass ranges from 1.13 to 1.91 across these standards.The observed Landolt (2009) fields are listed in Table 3.

Reductions and Photometric Calibrations
Bias subtraction and flat-fielding were carried out using standard IRAF7 packages.The instrumental magnitudes of the stars were measured using the IRAF aperture photometry packages (Landolt 2009).The photometric extinction and transformation coefficients were obtained by employing multiple linear regression fits to these calculated instrumental magnitudes.The resulting coefficients are listed in Table 4 for the two observing nights.Applying PyRAF8 and astrometry.net,9astrometric calibrations were performed for all cluster frames.The coordinates of the detected stars in all images of the cluster fields were aligned and combined in each filter for different exposures.This improved the signal-to-noise ratio for fainter stars and made it possible to measure the magnitudes of brighter stars that were saturated in long exposures.Photometry of the detected objects in the cluster regions was performed using the Source Extractor (SExtractor) and PSF Extractor (PSFEx) routines (Bertin & Arnouts 1996).Aperture corrections were then applied to these magnitudes.Finally, the instrumental magnitudes were transformed to standard magnitudes in the UBV filters using expressions from Janes & Hoq (2011), namely: In Equations (1)-(3) U, B, and V are the magnitudes in the standard photometric system.u, b, and v represent the instrumental magnitudes.X is the airmass.k and ¢ k are primary and secondary extinction coefficients, respectively.α and C indicate transformation coefficients to the standard system.

UBV and Complementary Gaia DR3 Data
The final UBV photometric catalogs comprise 884 and 2474 stars with magnitudes brighter than V = 22 mag for King 6 and NGC 1605, respectively.These optical catalogs were crossmatched with Gaia DR3 photometric and astrometric data, which resulted in the final catalogs containing IDs, positions cos , proper-motion components along with ϖ trigonometric parallaxes, and the P membership probabilities as estimated in this study (see Table 5).Both catalogs are available electronically.The internal errors resulting from the point-spread function (PSF) fitting procedure were adopted as the photometric accuracies for the V magnitudes and U − B and B − V color  indices.In Table 6 we list the mean photometric errors in the Johnson and Gaia DR3 filters as a function of V magnitude.It can be seen from the table that stars brighter than V = 22 mag have mean errors lower than 0.04 mag in V magnitude and lower than 0.16 mag in U − B and B − V for King 6, while for NGC 1605, these measurements reach up to 0.05 mag in V magnitude and 0.24 and 0.10 mag in the U − B and B − V colors, respectively.The Gaia DR3-based mean errors are lower than 0.08 mag for the two clusters.
In this study, the photometric completeness limit is needed as part of the information to derive cluster parameters such as LFs and MFs, stellar density distributions, etc. Histograms of stellar counts, as functions by magnitude bin in V and G, were used to determine the photometric completeness limits for the studied clusters.We compared the number of stars found with those counts gathered from Gaia DR3 data with counts of the same regions in the ground-based photometry.The Gaia DR3 data were prepared by considering equatorial coordinates given by Cantat-Gaudin et al. (2020) and stellar magnitudes in the range 8 < G < 22 mag.The stellar counts in V-and Gmagnitude bins are shown in Figure 2: the black solid lines are the observational stellar distributions per V-and G-magnitude bins, while the red dashed lines (see in Figures 2(b) and (d)) indicate the Gaia DR3-based stellar counts.Vertical dashed lines represent the completeness "turnover" magnitudes where the number of stars detected begins to drop (with increasing magnitude), indicating where completeness starts to affect the stellar counts.It can be seen from Figures 2(b) and (d) that the number of stars detected in the study is in good agreement with the stellar distribution from the Gaia DR3 data up to the adopted completeness limits.These limits are V = 20 mag for both King 6 and NGC 1605, which corresponds to G = 19 mag.The number of stars of similar magnitude ranges that will be  Note.The columns denote the observation date (DD-MM-YYYY), star field name from Landolt, the number of standard stars (N st ) observed in a given field, the number of observations for each field (N obs ), and the airmass range the fields were observed over (X).
detected in a given image is related to the properties of CCDtelescope combinations and the exposure times used in the observations.Thus, the number of detected stars in fainter magnitudes will be different between ground-and space-based observations, such as those used in the current study.This could contribute to the dissimilar stellar counts for magnitudes fainter than G = 19 as seen in Figures 2(b) and (d).

Structural Parameters of the Clusters
The structural parameters for King 6 and NGC 1605 were obtained through radial density profile (RDP) analyses.To construct an RDP, we used the Gaia DR3 data set due to its unlimited field of view.For each cluster, we retrieved the sources within a radius of ¢ 40 centered at the coordinates given by Cantat-Gaudin et al. (2020).Considering only stars brighter than the photometric completeness limits (G = 19 mag for both clusters), we counted stars in a series of concentric rings centered on the adopted cluster centers (Cantat-Gaudin et al. 2020) and so derived stellar densities (ρ).These values were calculated by dividing the stellar counts in each ring by the area of the appropriate ring.In order to parameterize the stellar densities, the RDP of King (1962) was fitted to the calculated stellar densities using a χ 2 minimization procedure.The King (1962) profile is expressed by r ) )], where f bg , f 0 , r c , and r indicate the background density, central density, core radius, and the radius from the cluster center, respectively.The best-fitting RDP models of stellar density distribution versus radius from the cluster center are plotted in Figure 3.We calculated the central stellar density and background stellar density of the clusters, together with the core radius, as: 1. f 0 = 2.28 ± 0.24 and f bg = 5.12 ± 0.16 stars arcmin −2 , and = ¢  ¢ r 4.68 1.07 c for King 6, and 2. f 0 = 13.05 ± 0.73 and f bg = 9.81 ± 0.30 stars arcmin −2 , and = ¢  ¢ r 1.90 0.20 c for NGC 1605.
In Figure 3, the best-fitting RDP is shown by a black solid line, while the horizontal gray band is the level of the background density.We obtained the limiting radius (r lim obs ) for each cluster through visual inspection, considering the RDP model fit and background density.The stellar density is above the background level up to 10′ for both clusters (see Figure 3).Hence we adopted the limiting radii as = ¢ r 10 lim obs for King 6 and NGC 1605.We used only the stars inside these limiting radii for further analyses.To compare the accuracy of the observed limiting radii, we also estimated limiting radius (r lim cal ) using the mathematical expression given by Bukowiecki et al. (2011): The calculated limiting radius (r lim cal ) was found to be ¢ 9.1 and ¢ 9.3 for King 6 and NGC 1605, respectively.These values are in good agreement with the observational values.

Member Selection and CMDs
Since OCs are located along the Galactic plane, they are affected by field star contamination.This complicates the confident detection and identification of physical members (of the OC), which in turn influences the determination of reliable astrophysical parameters of the OCs.Therefore the effect of field stars should be identified and eliminated.Cluster member stars have similar vectoral movements as a result of being formed from the same molecular cloud.Using this property offers a path to identify physical cluster members (Yadav et al. 2013;Bisht et al. 2020), as explained in this section.In the study, we used the equatorial coordinates, proper-motion components, and trigonometric parallaxes of the stars to derive cluster members.Such an astrometric approach to determine cluster membership has been successfully applied by various researchers (Vasilevskis et al. 1958;Stetson 1980;Zhao & He 1990;Balaguer-Nunez et al. 1998;Krone-Martins & Moitinho 2014;Sarro et al. 2014;Olivares et al. 2019;Pera et al. 2021).
We used the Unsupervised Photometric Membership Assignment in Stellar Clusters (UPMASK; Krone-Martins & Moitinho 2014) algorithm, as implemented in the PYUPMASK (Pera et al. 2021) package, to identify members of the King 6 and NGC 1605 OCs.PYUPMASK is written in Python and has a general structure that follows the algorithm of UPMASK (Pera et al. 2021).Both algorithms were previously used to calculate the membership probabilities of OCs by various researchers (see Koç et al. 2022;Taşdemir & Yontan 2023;Yontan & Canbay 2023).
We applied PYUPMASK to calculate the membership probabilities (P) of stars detected in the regions of King 6 and NGC 1605.We ran the program in a five-dimensional parametric space which contains equatorial coordinates (α, δ), proper-motion components (m d a cos , μ δ ), and trigonometric parallaxes (ϖ) and the relevant uncertainties of detected stars.By running 1000 iterations we found 148 (for King 6) and 240    (for NGC 1605) likely cluster members.These stars have cluster membership probabilities equal to or greater than 50% (which we considered to be the lower limit for membership probability).
We therefore plotted V × (B − V ) CMDs using the most likely cluster members (P 0.5) and fitted a ZAMS from Sung et al. (2013) to the cluster sequence visually.The ZAMS was shifted by 0.75 mag toward brighter magnitudes to allow equalmass binary stars as members.We considered the V-magnitude limits and the cluster r lim radii, along with the ZAMS fitting, to estimate 112 stars as "most likely" members (P 0.5) of King 6 and 160 for NGC 1605.We subsequently used these stars to determine astrophysical parameters for each cluster, as discussed below.The V × (B − V ) and G × (G BP − G RP ) diagrams are given as Figure 4. Figures 4(a The membership probability distributions (for detected stars in the cluster regions) are shown in Figure 5.We constructed vector-point diagrams (VPDs), as shown in Figure 6.It is clear from that figure that the most likely cluster members for the two clusters are associated with the central points of the clusters.We can interpret that King 6 (Figure 6(a)) is clearly more separated from the scattered field stars than NGC 1605 (Figure 6(b)).Considering only the most likely member stars, we obtained values for the mean proper-motion components.These are shown as the intersections of the blue dashed lines in Figure 6.For King 6 we calculated the mean proper motion as (m d a cos , μ δ ) = (3.833± 0.034, −1.906 ± 0.032) mas yr −1 and for NGC 1605 as (m d a cos , μ δ ) = (0.928 ± 0.104, −1.997 ± 0.082) mas yr −1 .These findings are in good agreement with the values produced with Gaia data for both of the clusters (see Table 1).We also estimated mean trigonometric parallaxes ϖ by fitting Gaussians to the  NGC 1605 histograms of trigonometric parallax (Figure 7).During these analyses, we used the stars having P 0.5 membership probabilities and precise parallaxes (σ ϖ /ϖ < 0.2).This resulted in estimates of the mean ϖ of 1.381 ± 0. Figure 7 shows the distribution of trigonometric parallaxes of member stars with a Gaussian fit (red dashed lines) applied to each data set.

Basic Parameters of the OCs
This section summarizes the procedures used in the astrophysical analyses of King 6 and NGC 1605.We used two-color diagrams (TCDs) to calculate the reddening and photometric metallicities separately.Keeping these two parameters as constants and using CMDs, we next obtained the distance moduli and ages simultaneously (as performed in previous studies; see Bostancı et al. 2015Bostancı et al. , 2018)).

Color Excess through the Cluster Region
The color excesses of the two OCs are estimated by plotting (U − B) × (B − V ) TCDs.We considered the stars located within the limiting radii ( ¢ r 10 lim obs  ) and with membership probabilities greater than 0.5.Stars in the clusters' main sequences were selected for the color excess analyses.With these limitations, we have selected the most likely mainsequence stars within 12 V 17 mag for King 6 and 14.75 V 20 mag for NGC 1605.The selected stars were compared with the dereddened ZAMS of solar metallicity (Sung et al. 2013) in (U − B) × (B − V ) TCDs (Figure 8).The ZAMS was shifted along the slope of the reddening vector α = E(U − B)/E(B − V ) = 0.72 presented by Johnson & Morgan (1953) through the use of χ 2 minimization.Hence, the best-fit solutions indicated that the color excess E(B − V ) is 0.515 ± 0.030 mag for King 6 and 0.840 ± 0.054 mag for NGC 1605. Figure 8 shows the best-fitting ZAMS (red dashed lines) for the two clusters.

Photometric Metallicity
To determine the [Fe/H] photometric metallicities for King 6 and NGC 1605, we adopted the UBV data-based method of Karaali et al. (2011).This method uses the UV excesses of F and G spectral type main-sequence stars, which is consistent with the 0.3 (B − V ) 0 0.6 color range.To apply this method, initially we estimated dereddened (B − V ) 0 and (U − B) 0 values of the most likely cluster main-sequence stars (P 0.5) by using the E(B − V ) and E(U − B) color excesses derived in the study, then we limited the calculated (B − V ) 0 color index within 0.3 (B − V ) 0 0.6 mag (Eker et al. 2018(Eker et al. , 2020) ) to select F-and G-type main-sequence stars.Hence, we obtained 15 and seven stars with membership probabilities greater than 0.5 for King 6 and NGC 1605, respectively.We constructed (U − B) 0 ×(B − V ) 0 diagrams for these stars, along with the Hyades main-sequence stars, to compare their (U − B) 0 values corresponding to the same dereddened (U − B) 0 data.The upper panel of Figure 9 shows (U − B) × (B − V ) TCDs of the selected stars and Hyades main sequence.The comparison is described as UV excess (δ), given by the expression δ = (U − B) 0,H − (U − B) 0,S where the the H and S subscripts indicate Hyades and cluster stars, respectively.The photometric metallicity calibration is defined within the 0.3 (B − V ) 0 0.6 color range and reaches its maximum UV excess at (B − V ) = 0.6 mag.Therefore, the UV excesses calculated for F-and G-type main-sequence stars needs to be normalized by a factor f, which is defined as the guillotine factor (Sandage 1969).In order to employ Karaali et al. (2011)ʼs method we estimated the normalized UV excess of the modeled stars to the UV excess at (B − V ) 0 = 0.6 mag (i.e., δ 0.6 ).After constructing histograms of the normalized UV excesses we fitted Gaussian functions to the distributions and obtained the mean δ 0.6 value for each cluster (Karaali et al. 2003a(Karaali et al. , 2003b)).The Gaussian functions fitted to the normalized UV excesses for each cluster are shown in the lower panels of Figure 9.The result of the fitting procedure provides a mean δ 0.6 value of   In order to select the isochrones that will be used for the determination of a cluster's age reliably, one should transform the estimated [Fe/H] values to the mass fraction z.To do this, we utilized the following equations which are recommended  for the PARSEC isochrones of Bressan et al. (2012) by Bovy. 10  These are given as follows: 10 Fe H log z 1 0.248 2.78 z , 6 x [ ] ( ) and: Here z x and z e represent the intermediate and solar fraction values, respectively.Solar metallicity z e was adopted as 0.0152 (Bressan et al. 2012).We obtained z = 0.016 for King 6 and z = 0.015 for NGC 1605.

Distance Moduli and Ages of the Clusters
In this study, we plotted three CMDs combining the UBV and Gaia photometry to obtain the age and distance of each cluster.These results were also tested in terms of compatibility of the color excesses and metallicity values derived from the TCDs.
The age and distance modulus were estimated together via fitting of PARSEC isochrones by Bressan et al. (2012).For PARSEC isochrones, data from the UBVRIJHK (Bessell 1990;Maíz-Apellániz 2006)  The isochrone fitting procedure made reference to the positions of the most likely main sequence, turnoff point, and giant members (P 0.5) of each cluster.We considered the relation of Carraro et al. (2017) for error estimates of the distance moduli and distances.For the age uncertainties, we used low-and high-age isochrones that well fit the observed scatter about the main sequence and turnoff.We present V × (U − B), V × (B − V ), and G × (G BP − G RP ) diagrams with best-fitting isochrones in Figure 10.It can be seen from Figures 10(a shows that the isochrones well represent the cluster morphology.Therefore, the ∼2 mag gap in the main sequence could be due to a lack of massive stars in the initial mass of the cluster. The following results were estimated from the isochrone fitting to the CMDs:  1. King 6: by superimposing isochrones of = log age ( ) 8.26, 8.30, and 8.34 with z = 0.016 to the UBV-and Gaia-based CMDs, we obtained the apparent distance modulus as μ V = 10.892 ± 0.099 mag.This corresponds to the isochrone-based distance being d iso = 723 ± 34 pc.We applied overweights to the main-sequence and turnoff member stars, determining the cluster age to be t = 200 ± 20 Myr.The estimated distance value matches well with most of the results that were obtained from Gaia data by various researchers (see Table 1 for a detailed comparison).The isochrone distance of King 6 is in good agreement with the Gaia DR3 trigonometric parallax distance value d ϖ = 724 ± 22 pc as estimated in Section 3.3.The derived cluster age is consistent with the findings of Ann et al. (2002) , and 8.65 with z = 0.015.The distance modulus is μ V = 15.028 ± 0.167 mag, matching the isochrone-based distance of d iso = 3054 ± 243 pc.The cluster age is t = 400 ± 50 Myr.Because of its age, during the calculation of the ages and distance moduli, we made reference to the turnoff and giant members.The estimated distance is compatible with the majority of results presented by various researchers listed in Table 1.The distance value is within the errors of the trigonometric parallax distance value d ϖ = 2976 ± 381 pc (Section 3.3).The estimated age of the cluster is in good agreement with the results of Loktin & Popova (2017) and Dias et al. (2021).

Kinematics and Galactic Orbit Integration
The Python-based galactic dynamics library (GALPY; 12Bovy 2015) was used to determine the orbital properties of the two clusters according to the MWPOTENTIAL2014 Galactic potential from Bovy (2015).MWPOTENTIAL2014 includes a module of an axisymmetric potential for the Milky Way galaxy and uses three components, which are bulge, disk, and halo potentials.The adopted bulge potential took the form from Bovy (2015), who presented it based on a spherical power-law density; the disk is in the form of Miyamoto & Nagai (1975), who defined an axisymmetric disk; and the halo is in the form stated by Navarro et al. (1996), who described a spherically symmetric distribution of dark matter in the halo.The explicit parameters of MWPOTENTIAL2014 that were used for the analyses of orbital integration and model fit parameter constraints are given in Bovy (2015) in detail.From that study, we adopted the galactocentric distance and orbital velocity as R GC = 8 kpc and V rot = 220 km s −1 , respectively (Bovy & Tremaine 2012;Bovy 2015).The vertical distance of the Sun from the Galactic plane was adopted to be 27 ± 4 pc as presented by Chen et al. (2000).
For complete orbit integration, the mean radial velocity is needed.In the current study, the radial velocity values for the most likely member stars were taken from Gaia DR3.We considered the stars' existing radial velocity measurements for those stars with membership probabilities of P 0.8.Hence, we obtained 23 stars for King 6 and one star for NGC 1605 to estimate their mean radial velocities.Considering the method of weighted averages (for equations see Soubiran et al. 2018) for the King 6 member stars, we calculated the mean value as V R = −23.40± 3.26 km s −1 , whereas for NGC 1605 we adopted the value of V R = −15.27± 1.35 km s −1 based on the Gaia DR3 measurements.The result for King 6 is in good agreement with the literature studies, being within 1-3 km s −1 of the values listed in Table 1.The radial velocity value adopted in this study for NGC 1605 is compatible with the result of Zhong et al. (2020), who calculated a mean value of V R = −12.033± 17.417 km s −1 from eight stars in their LAMOST DR5 data (Luo et al. 2019).However, the result obtained in this study differs from the V R = −1.15± 0.12 km s −1 value of Soubiran et al. (2018) and Tarricq et al. (2021), who adopted the radial velocity of one cluster member from Gaia DR2 data (Gaia Collaboration et al. 2018).The large errors in the radial velocity measurements given for NGC 1605 in the study of Zhong et al. (2020) may be due to a binary star effect or low spectral resolution.
To estimate the orbital parameters for each cluster, we utilized MWPOTENTIAL2014 with the input parameters of equatorial coordinates (α, δ) taken from Cantat-Gaudin et al. (2020), the mean proper-motion components (m d a cos , μ δ ) derived in Section 3.3, the isochrone distances (d iso ) from Section 4.3, and the radial velocities (V r ) calculated in this study (see also Table 7).Integration of the orbits was carried out backward in time with 1 Myr steps up to an age of 2.5 Gyr in order to achieve a closed orbit and provide reliable estimates of the Galactic orbit parameters for each cluster.The calculated orbital parameters are listed in Table 7, where R a and R p are the apogalactic and perigalactic distances, respectively, while e and    16 The Astronomical Journal, 166:263 (20pp), 2023 December Z max are eccentricity of the orbit and the maximum vertical distance from Galactic plane, respectively.(U, V, W) and P orb represent the spatial velocity components and orbital period, respectively.
The spatial velocity components (U, V, W) were corrected to the velocity components of the local standard of rest (LSR) by using values of Coşkunoǧlu et al. (2011).These values are given as (8.83 ± 0.24, 14.19 ± 0.34, 6.57 ± 0.21) km s −1 .The LSR-corrected spatial velocity components were estimated as (U, V, W) LSR = (18.92± 3.05, −11.44 ± 1.41, 8.58 ± 0.32) km s −1 for King 6 and (U, V, W) LSR = (12.19± 4.72, −19.77 ± 1.48, −2.64 ± 6.47) km s −1 for NGC 1605.From these values, the total spatial velocity is estimated to be S LSR = 23.72 ± 3.38 km s −1 for King 6 and S LSR = 23.38 ± 8.15 km s −1 for NGC 1605 (see also Table 7).The S LSR results show that both of the clusters are formed of young thin-disk stars (Leggett 1992).Moreover, the maximum vertical distance from the Galactic plane and eccentricity of King 6 ).In order to obtain more precise information about the LFs of the clusters and the related MFs, it is important to consider stars with membership probabilities greater than 0 in the calculations (Akbulut et al. 2021).We transformed the apparent V magnitudes to their absolute M V magnitudes using the distance modulus definition ´-E B V 5 3.1 ( ), where V, d, and E(B − V ) indicate the apparent magnitude, isochrone distance, and color excess as previously obtained for the two clusters (Table 7).The absolute magnitude range of the stars is 1.22 < M V < 8.98 mag and −0.90 < M V < 4.98 mag for King 6 and NGC 1605, respectively.Despite both of the clusters being of relatively young age, as King 6 is closer to the Sun than NGC 1605 its absolute magnitude range is wider.LF histograms with intervals of 1 mag are given in Figure 12.It can be interpreted from the figure that the LF of King 6 reaches to approximately M V = 9 mag (Figure 12(a)), and that this limit is M V = 5 mag for NGC 1605 (Figure 12(b)).

MFs
The MF expression that we used is described as follows: Here dN is the number of stars per unit mass range dM, the central mass is designated as M, and Γ is the slope of the MF.
To derive the MFs of the studied clusters, we used PARSEC isochrones from Bressan et al. (2012) that matched the metallicity fractions (z) as estimated in the current study.We generated a high-degree polynomial equation between the theoretical V-band absolute magnitudes and masses from the selected isochrones.Through application of this equation, we transformed the observational absolute magnitudes M V of the stars to masses.The membership probabilities of stars used in the MF analyses are P > 0. There are 213 such stars in King 6 and 462 in NGC 1605.These correspond to stellar masses of 0.58 M/M e 3.59 and 1.03 M/M e 2.94 for the relevant clusters, respectively.The MF slope values were derived as Γ = 1.29 ± 0.18 for King 6 and as Γ = 1.63 ± 0.36 for NGC 1605.These results agrees with Salpeter (1955)ʼs value of 1.35 within the uncertainties.The MF slopes for the two clusters are plotted in Figure 13.Considering the stellar mass ranges used in the MF estimations, we estimated the total cluster masses as 195 M/M e and 623 M/M e for King 6 and NGC 1605, respectively.

The Dynamical State of Mass Segregation
Mass segregation could have a significant association with the dynamical evolution and lifetime of an OC.Several mechanisms such as primordial mass segregation, two-body relaxation, massdependent stellar evolution, stellar dynamics, and mass segregation feedback might contribute to mass segregation in OCs (Fischer et al. 1998;Raboud & Mermilliod 1998;Alcock & Parker 2019;Piecka & Paunzen 2021;Sariya et al. 2021).Primordial mass segregation refers to dynamical interactions and gravitational collapse during the formation of an OC that makes massive stars sink toward the central region (de Grijs et al. 2003;Pavlík 2020).Over time gravitational interactions between cluster members lead to a process of two-body relaxation which causes stars to exchange kinetic energy and momentum, leading to massive stars moving toward the cluster center (Sagar et al. 1988;de La Fuente Marcos 1996;Bisht et al. 2020;Pavlík & Vesperini 2022).Moreover, the mass segregation itself can influence the dynamics of the cluster.A more concentrated distribution of massive stars in the cluster center enhances the interaction rate between them, leading to more frequent gravitational encounters.These encounters might force corecollapse processes, such as core-collapse-induced star formation or binary formation, extending the mass segregation (Pang et al. 2013).
Related to mass segregation, the relaxation time indicates the timescale for two-body relaxation processes to occur within the cluster.The transmission of energy occurs between massive stars to low-mass stars, leading the stellar velocity distribution being Maxwellian (see, e.g., Hillenbrand & Hartmann 1998;Baumgardt & Makino 2003;Dib & Henning 2019).The relaxation time, denoted as T E , can be estimated using the following formula given by Spitzer & Hart (1971) where N is the total number of stars, R h13 is the half-mass radius in parsecs, and 〈m〉 is the average mass of the considered stars in solar units.
To calculate relaxation times for the studied clusters, we used stars with membership probabilities P > 0, located within the clusters' limiting radii ( ¢ r 10 lim obs  ) and brighter than the photometric completeness limit (V 20 mag), which were mentioned in Sections 6.1 and 6.2.The calculated mean stellar mass is 〈m〉 = 1.06 M/M e for King 6 and 〈m〉 = 1.55 M/M e for NGC 1605.The half-mass radii are R h = 0.95 pc for King 6 and R h = 4.01 pc for NGC 1605.The dynamical relaxation time of King 6 was estimated as T E = 5.8 Myr and for NGC 1605 as T E = 60 Myr.We conclude that both clusters are dynamically relaxed due to the derived T E ages being younger than the present ages of the two clusters as estimated in the current study (see Table 7).
To understand the impact of the mass segregation effect in the two clusters, we divided the masses of selected stars into three intervals.These ranges are 0.5 < M/M e 1 (low mass), 1 < M/M e 1.4 (intermediate mass), and 1.4 < M/M e 3.6 (high mass) for King 6 and 1 < M/M e 1.5, 1.5 < M/M e 2, and 2 < M/M e 3 for NGC 1605, respectively.The normalized cumulative radial distributions of the stars in these different mass ranges are shown in Figure 14.Generally, the normalized cumulative radial distributions of the stars in both of the OCs represent a mass segregation effect, as bright stars seem to be more centrally concentrated than the low-mass members.We used a Kolmogorov-Smirnov (K-S) test, finding the confidence level for a mass segregation effect to be 91% for both OCs.

Summary and Conclusion
We investigated two OCs, King 6 and NGC 1605, which are located in the second Galactic quadrant, using newly acquired CCD UBV and Gaia DR3 data.The membership probabilities of stars were calculated in a five-dimensional spatial distribution where Gaia astrometric data and their uncertainties were taken into consideration.In addition, we limited the star selection according to the limiting radius, ZAMS fits, and the completeness limit of each cluster.Thus, we end up with 112 and 160 "most likely" member stars with membership probabilities P 0.5 for King 6 and NGC 1605, respectively.We used these stars during the subsequent estimation of the astrophysical parameters of the two clusters.Ann et al. (2002) indicated that the reddening in the direction of King 6 cannot be obtained as a single value due to the differential reddening affect; they also noted the possible binary sequence above the cluster's ZAMS.In this study, when the UBV-and Gaia-based CMDs and positions of the most probable main-sequence member stars in the TCDs were investigated, differential reddening effects were not found.In addition, the binary star sequence above the ZAMS mentioned by Ann et al. (2002) was not clearly detected for King 6 in our study.We concluded that this may be due to the precision of the photometric data.
Based on the investigation of an RDP of NGC 1605, Camargo (2021) detected an increase in the number density of stars and suggested the possibility of a second cluster (i.e., NGC 1606 is a binary cluster).Camargo (2021) also found a large difference (about 1.4 Gyr) in age between the two clusters and mentioned that this was due to the effects of tidal capture during a close encounter of the two clusters.In this study, the RDP of NGC 1605 shows a small increase in the stellar density between 7′ and 9′ from the cluster center (see Figure 11(b)), but direct evidence for a second cluster was not found.Examination of the radial velocities of faint stars does not support the existence of a second cluster, as shown above.Anders et al. (2022), who recently analyzed the OC NGC 1605 with Gaia EDR3 data (Gaia Collaboration et al. 2021), also found no evidence that the cluster is a pair.
A summary of the main findings of the study is listed as follows: 1. Considering the best solution of the RDP fitting, we estimated limiting radii by visual inspection of the data for the two clusters.These values are = ¢ r 10 lim obs for both King 6 and NGC 1605, which are compatible with the calculated limiting radii for each cluster.within the errors, with the distances derived by taking into account the trigonometric parallaxes (d ϖ ). 5. The radial velocities of member stars with membership probabilities P 0.8 were taken from the Gaia DR3 database to calculate the clusters' mean radial velocity values and to investigate their Galactic orbital parameters.Thus, for King 6 we used 23 stars and derived a mean V R = −23.40± 3.26 km s −1 .For NGC 1605 we used one star with a value of V R = −15.27± 1.35 km s −1 .Orbit integrations showed that both of the clusters belong to the young thin-disk population of the Galaxy and formed outside the solar circle.6.The MF slopes of King 6 and NGC 1605 were calculated as Γ = 1.29 ± 0.18 and Γ = 1.63 ± 0.36, respectively.These findings are compatible with the value of 1.35 given by Salpeter (1955).7. Mass segregation is observed in both of the OCs.The K-S test indicates at the 91% confidence level that this effect is present for both of the clusters.The dynamical relaxation times are less than both of the OC ages, demonstrating that King 6 and NGC 1605 are dynamically relaxed.

Figure 1 .
Figure 1.V-band identification maps for King 6 (left panel) and NGC 1605 (right panel).The field of view of the charts is ¢ ´¢ 21. 5 21. 5. North is up and east is leftward.
) (for King 6) and (c) (for NGC 1605) are UBV-based CMDs.These show the distribution of field stars and the stars considered to be the most probable cluster members, together with the fitted ZAMS.Figures 4(b) (for King 6) and (d) (for NGC 1605) show the distribution of the most likely cluster members on Gaia-based photometry.

Figure 2 .
Figure 2. Stellar counts of King 6 (a), (b) and NGC 1605 (c), (d) for per magnitude bin in the V and G bands.The vertical gray dashed lines show the adopted faint limiting apparent magnitudes in the V and G bands.The black lines represent the star counts in V magnitude, whereas the red dashed lines are counts in Gaia DR3 data for the same cluster regions.

Figure 3 .
Figure 3.The RDPs of the King 6 (a) and NGC 1605 (b) OCs.The fitted black curve in each diagram is the King (1962) profile, whereas the horizontal gray band represents the background stellar density.The red-shaded domain shows the 1σ King fit uncertainty.

Figure 4 .
Figure 4. CMDs of King 6 (a), (b) and NGC 1605 (c), (d) based on UBV (a), (c) and Gaia DR3 (b), (d) data.The blue lines represent the ZAMS (Sung et al. 2013) including main-sequence broadening.The membership probabilities of stars are shown with different colors.These member stars lie within = ¢ r 10 lim obs of the cluster centers obtained for both clusters.The stars with low membership probabilities are plotted as gray dots.
δ 0.6 = 0.023 ± 0.007 mag for King 6 and δ 0.6 = 0.025 ± 0.012 for NGC 1605.The ±1σ standard deviation of the Gaussian fit gives the uncertainty of the mean δ 0.6 .We estimated the photometric metallicity of each cluster by considering the mean δ 0.6 value in the expression ofKaraali et al. (2011):Taking into account the internal errors of the photometric metallicity calibration, as well as the photometric errors of the cluster member stars and the uncertainties in the cluster's color excesses, the external errors in the metallicity have an uncertainty of about 0.19 dex.Internal errors due to calibration (±0.06 dex) and errors due to photometric measurements (±0.19 dex) were evaluated together.Thus, we derived the photometric metallicities as [Fe/H] = 0.02 ± 0.20 dex for King 6 and [Fe/H] = 0.01 ± 0.20 dex for NGC 1605.

Figure 5 .
Figure 5. Distribution of cluster membership probabilities for the stars in the direction of King 6 (a) and NGC 1605 (b).The white shaded bars are the counts of stars which have been detected in the cluster regions.The cyan-colored shaded bars represent the number of stars that lie within the main-sequence band and the cluster limiting radius r lim obs .

Figure 6 .
Figure 6.Gaia DR3 astrometry-based VPDs of King 6 (a) and NGC 1605 (b).The membership probabilities of the stars are represented with the color scale shown on the right side.The zoomed-in boxes in panels (a) and (b) indicate the region of concentration for each cluster in the diagrams.The intersection of the dashed blue lines indicates the mean proper-motion values.

Figure 7 .
Figure 7. Gaia DR3-based trigonometric parallax histograms for King 6 (a) and NGC 1605 (b).The red dashed curve shows the Gaussian fit applied to the distributions.

Figure 8 .
Figure 8.The (U − B) × (B − V ) diagrams of King 6 (a) and NGC 1605 (b).The red dashed lines plot the dereddened ZAMS given by Sung et al. (2013).The green solid lines indicate the ±1σ standard deviation range limits.The reddening vector is represented by the dashed gray line.
and Gaia EDR3 (Riello et al. 2021) photometric systems in CMD 11 are used.The fitting process was done by visual inspection, taking into account the position of the most likely member stars (P 0.5) in the CMDs.We selected isochrones of different ages that scaled to the metal fraction z estimated for each cluster (Section 4.2) and superimposed onto the V × (U − B), V × (B − V ), and G × (G BP − G RP ) diagrams.We fitted the isochrones to the V × (U − B) and V × (B − V ) diagrams according to the E(U − B) and E(B − V ) values calculated in Section 4.1, whereas for the G × (G BP − G RP ) diagram we fitted isochrones using the selective absorption coefficients (A λ /A V ) for the Gaia DR3 G, G BP , and G RP passbands, which were taken from Cardelli et al. (1989) and O'Donnell (1994) as 0.83627, 1.08337, and 0.63439, respectively.
), (b), and (c) that the main sequence of King 6 shows about a 2 mag gap among the brightest stars.The fact that similar age values are given in the literature forKing 6

Figure 9 .
Figure 9.The (U − B) 0 ×(B − V ) 0 TCDs (upper panels) and histograms for the normalized δ 0.6 (lower panels) for 15 (King 6, panel (a)) and seven (NGC 1605, panel (b)) F-and G-type main-sequence stars statistically consider the most probably cluster members.The solid blue lines in the TCDs represent the main sequence of Hyades (in the upper subfigures) and Gaussian fits (in the lower subfigures).

Figure 10 .
Figure 10.UBV-and Gaia-based CMDs for the King 6 (panels (a), (b), and (c)) and NGC 1605 (panels (d), (e), and (f)) OCs.Membership probabilities of the most probable cluster stars are represented with different color scales that are shown by the color bars to the right, whereas field stars are shown as gray-colored dots.The best-fitting PARSEC isochrones and their errors are presented as the blue and green lines, respectively.Superimposed isochrone ages match to 200 Myr for King 6 and 400 Myr for NGC 1605.

Figure 11 .
Figure 11.The Galactic orbit of King 6 (panels (a)-(b)) and NGC 1605 (panels (c)-(d)) in the Z × R GC and R GC × t planes.The filled yellow circles are the presentday positions of the clusters.The triangle symbols indicate the birth positions.The red arrows show the motion vectors of the clusters.The pink and green dotted lines show the orbits when errors in the input parameters are considered.The pink filled triangles represent the birth locations of the clusters based on the upper error estimates, while the green filled triangles represent the birth locations based on the lower error estimates.

Figure 13 .
Figure 13.MFs of King 6 (a) and NGC 1605 (b).Blue lines show the MFs of the OCs, while green lines are the ±1σ standard deviations.The gray dashed lines in the panels represent the slope of Salpeter (1955).

Figure 14 .
Figure 14.The cumulative radial distribution of stars in different mass ranges for King 6 (a) and NGC 1605 (b).
e = 0.076 ± 0.018, respectively) imply that the two clusters are members of the thin-disk component of the Galaxy and move in nearly circular orbits around the Galactic center.Figure11presents the orbits of King 6 and NGC 1605.Figures11(a) (King 6) and (c) (NGC 1605) show the movements of the clusters along Z × R GC as "side-view" orbits, where the red arrows indicate the directions of motion for the clusters.Figures 11(b) (King 6) and (d) (NGC 1605) represent the clusters' changing distances from the Galactic center with time on the R GC × t plane.The results show that the orbits of King 6 and NGC 1605 follow a "boxy" orbital pattern in the Galaxy.The present-day location of the clusters are marked with yellow filled circles, while the birth radii of the two clusters are given by the yellow filled triangles (Figures 11(b) and (d)).The birth radius for King 6 was estimated as 8.64 ± 0.05 kpc and that of NGC 1605 as 10.72 ± 0.44 kpc.These values show that both of the clusters formed outside the solar circle.Considering the R p and R a distances we infer that despite their formation locations, King 6 crosses the solar circle during its orbital movement (see Figure 11(a)), while NGC 1605 completely orbits outside the solar circle (see Figure 11(c)).The birth radii of the two clusters were also calculated by taking into account the uncertainties in proper motion, radial velocity, and distance.The pink and green dotted lines in Figures 11(b) (King 6) and (d) (NGC 1605) illustrate the clusters movement in time, where upper and lower errors of the input parameters are adopted.6.Dynamical Study of the Clusters6.1.LFsWe constructed the LF for each cluster through consideration of main-sequence stars with membership probabilities P > 0 and positions within the limiting radii of the clusters ( 2. The VPD analyses showed that the member stars of King 6 are clearly separated from field stars, whereas the member stars of NGC 1605 nest together with background stars.The mean proper-motion values were estimated as (m for NGC 1605.The mean trigonometric parallaxes were derived as ϖ = 1.381 ± 0.042 mas for King 6 and ϖ = 0.336 ± 0.043 mas for NGC 1605.These equate to distances of d ϖ = 724 ± 22 pc and d ϖ = 2976 ± 381 pc, respectively.3. The color excesses and photometric metallicities of the two clusters were obtained individually from observational (U − B) × (B − V ) TCDs constructed from the "most likely" (as defined above) cluster main-sequence stars.Analyses provided the color excesses to be E(B − V ) = 0.515 ± 0.030 mag for King 6 and E(B − V ) = 0.840 ± 0.054 mag for NGC 1605; the photometric metallicities were found to be [Fe/H] = 0.02 ± 0.20 dex for King 6 and [Fe/H] = 0.01 ± 0.20 dex for NGC 1605.4. We constructed CMDs from the most likely cluster members using the UBV and Gaia DR3 photometric data in order to derive distance moduli and ages.Keeping the color excess and metallicity as constants, we fitted PARSEC isochrones scaled by the estimated z-values to the CMDs.The apparent distance modulus, distance, and age of King 6 were estimated to be μ V = 10.892 ± 0.099 mag, d iso = 723 ± 34 pc, and t = 200 ± 20 Myr, respectively.These values correspond to μ V = 15.028 ± 0.167 mag, d iso = 3054 ± 243 pc, and t = 400 ± 50 Myr for NGC 1605.The CMD-based distances are in agreement,

Table 1
Summary of Results from the Literature for the King 6 and NGC 1605 OCs

Table 4
Transformation and Extinction Coefficients Obtained for the Two Observation Nights and k′ are the primary and secondary extinction coefficients, while α and C are transformation coefficients.

Table 5
The Catalogs forKing 6 and NGC 1605

Table 6
Mean Internal Photometric Errors per Magnitude Bin in V Brightness