arXiv subjects

S. Bilir

Publications and source records attributed to S. Bilir.

At least 37 records · Page 2Linked to original sources

arXiv2023

Galactic Model Parameters and Space Density of Cataclysmic Variables in Gaia Era: New Constraints to Population Models

The spatial distribution, Galactic model parameters and luminosity function of cataclysmic variables (CVs) are established using re-estimated trigonometric parallaxes of {\it Gaia} DR3. The data sample of 1,587 CVs in this study is claimed to be suitable for Galactic model parameter estimation as the distances are based on trigonometric parallaxes and the {\it Gaia} DR3 photometric completeness limits were taken into account when the sample was created. According to the analysis, the scale height of All CVs increases from 248$\pm$2 to 430$\pm$4 pc towards shorter periods near the lower limit of the period gap and suddenly drops to 300$\pm$2 pc for the shortest orbital period CVs. The exponential scale heights of All CVs and magnetic systems are found to be 375$\pm$2 and 281$\pm$3 pc, respectively, considerably larger than those suggested in previous observational studies. The local space density of All CVs and magnetic systems in the sample are $6.8^{+1.3}_{-1.1}\times$10$^{-6}$ and $2.1^{+0.5}_{-0.4}\times10^{-6}$ pc$^{-3}$, respectively. Our measurements strengthen the 1-2 order of magnitude discrepancy between CV space densities predicted by population synthesis models and observations. It is likely that this discrepancy is due to objects undetected by CV surveys, such as the systems with very low $\dot{M}$ and the ones in the period gap. The comparisons of the luminosity function of white dwarfs with the luminosity function of All CVs in this study show that 500 times the luminosity function of CVs fits very well to the luminosity function of white dwarfs. We conclude that the estimations and data sample in this study can be confidently used in further analysis of CVs.

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arXiv2022

A Silent Revolution in Fundamental Astrophysics

Arbitrariness in the zero point of bolometric corrections is a nearly century-old paradigm leading to two more paradigms. "Bolometric corrections must always be negative," and "bolometric magnitude of a star ought to be brighter than its $V$ magnitude". Both were considered valid before IAU 2015 General Assembly Resolution B2, a revolutionary document that supersedes all three aforementioned paradigms. The purpose of this article is to initiate a new insight and a new understanding of the fundamental astrophysics and present new capabilities to obtain standard and more accurate stellar luminosities and gain more from accurate observations in the era after Gaia. The accuracy gained will aid in advancing stellar structure and evolution theories, and also Galactic and extragalactic research, observational cosmology and dark matter and dark energy searches.

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arXiv2022

A study of the NGC 1193 and NGC 1798 open clusters using CCD UBV photometric and Gaia EDR3 data

We present photometric, astrometric, and kinematic studies of the old open star clusters NGC 1193 and NGC 1798. Both of the clusters are investigated by combining data sets from Gaia EDR3 and CCD UBV observational data. Analysis of the radial distribution of stars through the cluster regions indicates that the cluster limit radii are $r_{\rm lim}=8'$ for both of the clusters. We determine the membership probabilities of stars considering Gaia EDR3 proper motion and trigonometric parallax data, resulting in 361 stars in NGC 1193 and 428 in NGC 1798 being identified as most likely cluster members, having membership probabilities greater than P>0.5. Mean proper motion components are estimated as ($μ_α\cos δ$, $μ_δ) = (-0.207(0.009), -0.431(0.008)$) for NGC 1193 and ($μ_α\cos δ$, $μ_δ)=(0.793(0.006), -0.373(0.005)$) mas/yr for NGC 1798. E(B-V) color excesses were derived for NGC 1193 as $0.150(0.037)$ and for NGC 1798 as 0.505(0.100) mag through the use of two-color diagrams. Photometric metallicities are also determined from two-color diagrams with the results of [Fe/H] = -0.30(0.06) dex for NGC 1193 and [Fe/H]=-0.20(0.07) dex for NGC 1798. The isochrone fitting distance and age of NGC 1193 are 5562(381) pc and 4.6(1) Gyr, respectively. For NGC 1798, these parameters are 4451(728) pc and 1.3(0.2) Gyr. These ages indicate that NGC 1193 and NGC 1798 are old open clusters. The overall present-day mass function slopes for main-sequence stars are found as 1.38(2.16) for NGC 1193 and 1.30(0.21) for NGC 1798, which are in fair agreement with the value of Salpeter (1955). Kinematic and dynamic orbital calculations indicate that NGC 1193 and NGC 1798 belong to the thick-disk and thin-disk populations, respectively. In addition, both of the clusters were born outside the solar circle, and both orbit in the metal-poor region of the Galactic disk.

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arXiv2022

A photometric and astrometric study of the open clusters NGC 1664 and NGC 6939

This study calculated astrophysical parameters, as well as kinematic and galactic orbital parameters, of the open clusters NGC 1664 and NGC 6939. The work is based on CCD UBV and Gaia photometric and astrometric data from ground and space-based observations. Considering Gaia Early Data Release 3 (EDR3) astrometric data, we determined membership probabilities of stars located in both of the clusters. We used two-color diagrams to determine $E(B-V)$ color excesses for NGC 1664 and NGC 6939 as $0.190 \pm 0.018$ and $0.380 \pm 0.025$ mag, respectively. Photometric metallicities for the two clusters were estimated as [Fe/H] = $-0.10 \pm 0.02$ dex for NGC 1664 and as [Fe/H] = $-0.06 \pm 0.01$ dex for NGC 6939. Using the reddening and metallicity calculated in the study, we obtained distance moduli and ages of the clusters by fitting PARSEC isochrones to the color-magnitude diagrams based on the most likely member stars. Isochrone fitting distances are $1289 \pm 47$ pc and $1716 \pm 87$ pc, which coincide with ages of $675 \pm 50$ Myr and $1.5 \pm 0.2$ Gyr for NGC 1664 and NGC 6939, respectively. We also derived the distances to the clusters using Gaia trigonometric parallaxes and compared these estimates with the literature. We concluded that the results are in good agreement with those given by the current study. Present day mass function slopes were calculated as $Γ=-1.22\pm0.33$ and $Γ=-1.18\pm0.21$ for NGC 1664 and NGC 6939, respectively, which are compatible with the Salpeter (1955) slope. Analyses showed that both of clusters are dynamically relaxed. The kinematic and dynamic orbital parameters of the clusters were calculated, indicating that the birthplaces of the clusters are outside the solar circle.

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arXiv2022

Spatially Resolved Chandra Spectroscopy of Supernova Remnant DEM L71 in the Large Magellanic Cloud

We present a detailed X-ray spectroscopic study of the supernova remnant DEM L71 in the Large Magellanic Cloud. Based on deep $\sim 103$ ks archival {\it Chandra} data, we perform a detailed spatially resolved spectral analysis of DEM L71. We analyze regional spectra extracted from thin-sliced regions along several different azimuthal directions of the SNR to construct radial profiles of elemental abundances for O, Ne, Mg, Si, and Fe. Our elemental abundance measurements reveal an asymmetrical spatial distribution of metal-rich ejecta gas. Especially the asymmetry on the western part of the central Fe distribution is remarkable. While the location of the contact discontinuity is generally at $\sim 5$ pc from the geometric center of the X-ray emission of DEM L71, it is uncertain in western part of the remnant. Fe is enhanced in the ejecta while O and Ne abundances are generally negligible. This finding confirms the Type Ia origin of DEM L71. We estimate an upper limit on the Sedov age of $\sim 6,660\pm 770$ yr and explosion energy of $\sim 1.74\pm 0.35\times 10^{51}$ erg for the remnant. This explosion energy estimate is consistent with a canonical explosion of a Type Ia supernova remnant.

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arXiv2021

Standard stellar luminosities; what are typical and limiting accuracies in the era after Gaia?

Methods of obtaining stellar luminosities (L) have been revised and a new concept, standard stellar luminosity, has been defined. Among the three methods (direct method from radii and effective temperatures, method using a mass-luminosity relation (MLR), and method requiring a bolometric correction), the third method, which uses the unique bolometric correction (BC) of a star extracted from a flux ratio ($f_{\rm V}/f_{\rm Bol}$) obtained from the observed spectrum with sufficient spectral coverage and resolution, is estimated to provide an uncertainty ($ΔL/L$) typically at a low percentage, which could be as accurate as 1% perhaps more. The typical and limiting uncertainties of the predicted L of the three methods were compared. The secondary methods requiring either a pre-determined non-unique BC or MLR were found to provide less accurate luminosities than the direct method, which could provide stellar luminosities with a typical accuracy of 8.2% - 12.2% while its estimated limiting accuracy is 2.5%.

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arXiv2021

A study of the Czernik 2 and NGC 7654 open clusters using CCD UBV photometric and Gaia EDR3 data

We analysed the open clusters Czernik 2 and NGC 7654 using CCD UBV photometric and Gaia Early Data Release 3 (EDR3) photometric and astrometric data. Structural parameters of the two clusters were derived, including the physical sizes of Czernik 2 being r=5 and NGC 7654 as 8 min. We calculated membership probabilities of stars based on their proper motion components as released in the Gaia EDR3. To identify member stars of the clusters, we used these membership probabilities taking into account location and the impact of binarity on main-sequence stars. We used membership probabilities higher than $P=0.5$ to identify 28 member stars for Czernik 2 and 369 for NGC 7654. We estimated colour-excesses and metallicities separately using two-colour diagrams to derive homogeneously determined parameters. The derived $E(B-V)$ colour excess is 0.46(0.02) mag for Czernik 2 and 0.57(0.04) mag for NGC 7654. Metallicities were obtained for the first time for both clusters, -0.08(0.02) dex for Czernik 2 and -0.05(0.01) dex for NGC 7654. Keeping the reddening and metallicity as constant quantities, we fitted PARSEC models using colour-magnitude diagrams, resulting in estimated distance moduli and ages of the two clusters. We obtained the distance modulus for Czernik 2 as 12.80(0.07) mag and for NGC 7654 as 13.20(0.16) mag, which coincide with ages of 1.2(0.2) Gyr and 120(20) Myr, respectively. The distances to the clusters were calculated using the Gaia EDR3 trigonometric parallaxes and compared with the literature. We found good agreement between the distances obtained in this study and the literature. Present day mass function slopes for both clusters are comparable with the value of Salpeter (1955), being X=-1.37(0.24) for Czernik 2 and X=-1.39(0.19) for NGC 7654.

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arXiv2021

On the Zero Point Constant of the Bolometric Correction Scale

Arbitrariness attributed to the zero point constant of the $V$ band bolometric corrections ($BC_V$) and its relation to "bolometric magnitude of a star ought to be brighter than its visual magnitude" and "bolometric corrections must always be negative" was investigated. The falsehood of the second assertion became noticeable to us after IAU 2015 General Assembly Resolution B2, where the zero point constant of bolometric magnitude scale was decided to have a definite value $C_{Bol}(W)= 71.197~425~...$~. Since the zero point constant of the $BC_V$ scale could be written as $C_2=C_{Bol}-C_V$, where $C_V$ is the zero point constant of the visual magnitudes in the basic definition $BC_V=M_{Bol}-M_V=m_{bol}-m_V$, and $C_{Bol}>C_V$, the zero point constant ($C_2$) of the $BC_V$ scale cannot be arbitrary anymore; rather, it must be a definite positive number obtained from the two definite positive numbers. The two conditions $C_2>0$ and $0<BC_V<C_2$ are also sufficient for $L_V<L$, a similar case to negative $BC_V$ numbers, which means that "bolometric corrections are not always negative". In sum it becomes apparent that the first assertion is misleading causing one to understand bolometric corrections must always be negative, which is not necessarily true.

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arXiv2020

A Study of Open Clusters Frolov 1 and NGC 7510 using CCD UBV Photometry and Gaia DR2 Astrometry

We present reddening, photometric metallicity, age and distance estimates for the Frolov 1 and NGC 7510 open clusters based on CCD UBV photometric and Gaia data. Photometric observations were collected using the 1-m telescope of the TÜBİTAK National Observatory. Gaia DR2 proper motion data in the direction of two groupings were used to identify cluster membership. We determined mean proper motion values ($ μ_α\cosδ, μ_δ$) = ($-3.02\pm 0.10$, $-1.75 \pm 0.08$) and ($-3.66 \pm 0.07$, $-2.17 \pm 0.06$) mas yr$^{-1}$ for Frolov 1 and NGC 7510, respectively. We used two-colour diagrams to obtain $E(B-V)$ colour excesses for Frolov 1 and NGC 7510 as $0.65\pm0.06$ and $1.05\pm0.05$ mag, respectively. We derived the photometric metallicity of Frolov 1 as [Fe/H] = 0.03$\pm$0.03 dex and adopted a solar metallicity for NGC 7510. Based on these reddening and metallicities we determined the distance moduli and ages of the clusters via fitting PARSEC isochrones to the cluster colour-magnitude diagrams. Isochrone fitting distances for Frolov 1 and NGC 7510 are $2864 \pm 254$ and $2818 \pm 247$ pc, respectively, which correspond to the ages $35\pm 10$ Myr and $18\pm 6$ Myr. We also calculated mean Gaia distances and compared them with those given in the literature and in this study, concluding that our results are in good agreement with previous work. Finally, we calculated the mass function slopes as being $X=-1.21\pm0.18$ for Frolov 1 and $X=-1.42\pm0.27$ for NGC 7510.

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arXiv2020

Kepler Binary Stars in NGC 6819 Open Cluster: KIC 5113146 and KIC 5111815

In this study, investigation of two double-lined binary stars KIC 5113146 and KIC 5111815 in NGC 6819 is presented based on both photometric and spectroscopic data. Simultaneous analysis of light and radial velocity curves was made and the absolute parameters of the systems' components were determined for the first time. We find that both systems have F-type main-sequence components. The masses and radii were found to be $M_1=1.29\pm0.02 M_{\odot}$, $R_{1}=1.47\pm0.03 R_{\odot}$ and $M_{2}=1.19\pm0.02 M_{\odot}$, $R_{2}=1.13\pm0.02 R_{\odot}$ for the primary and secondary components of KIC 5113146; $M_{1}=1.51\pm0.08 M_{\odot}$, $R_{1}=2.02\pm0.05 R_{\odot}$ and $M_{2}=1.19\pm0.07 M_{\odot}$, $R_{2}=1.32\pm0.04 R_{\odot}$ for components of KIC 5111815, respectively. Evolutionary status of the components was evaluated based on the MESA evolutionary tracks and isochrones. The ages of the KIC 5111815 and KIC 5113146 were derived to be about $2.50\pm0.35$ Gyr and $1.95\pm0.40$ Gyr, respectively. Photometric distances were calculated to be $2850\pm 185$ pc for KIC 5113146 and $3120\pm 260$ pc for KIC 5111815. The results obtained in this study, astrometric data and researches in the literature reveal that both KIC 5113146 and KIC 5111815 systems are the most likely member of NGC 6819.

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arXiv2020

Empirical Bolometric Correction Coefficients for Nearby Main-Sequence Stars in Gaia Era

Nearby detached double-lined eclipsing binaries with most accurate data were studied and 290 systems were found with at least one main-sequence component having a metallicity $0.008\leq Z\leq 0.040$. Stellar parameters, light ratios, Gaia DR2 trigonometric parallaxes, extinctions and/or reddening were investigated and only 206 systems were selected eligible to calculate empirical bolometric corrections. NASA-IPAC Galactic dust maps were main source of extinctions. Unreliable extinctions at low Galactic latitudes $|b|\leq5^o$ were replaced with individual determinations, if they exist in the literature, else associated systems are discarded. Main-sequence stars of remaining systems were used to calculate bolometric corrections ($BC$) and to calibrate $BC-T_{eff}$ relation, which is valid in the range 3100-36000 K. De-reddened $(B-V)_0$ colours, on the other hand, allowed us to calibrate two intrinsic colour effective temperature relations, where the linear one is valid for $T_{eff}>10000$ K, while the quadratic relation is valid for $T_{eff}<10000$ K, that is, both are valid in the same temperature range $BC-T_{eff}$ relation is valid. New $BC$ computed from $T_{eff}$ and other astrophysical parameters are tabulated, as well.

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arXiv2020

Bridging the Ultraviolet and Optical Regions: Transformation Equations between {\it GALEX} and {\it UBV} Photometric Systems

We derive transformation equations between GALEX and UBV colours by using the reliable data of 556 stars. We present two sets of equations; as a function of (only) luminosity class, and as a function of both luminosity class and metallicity. The metallicities are provided from the literature, while the luminosity classes are determined by using the PARSEC mass tracks in this study. Small colour residuals and high squared correlation coefficients promise accurate derived colours. The application of the transformation equations to 70 stars with reliable data shows that the metallicity plays an important role in estimation of more accurate colours.

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arXiv2019

Metallicity and absolute magnitude calibrations for F-G type main-sequence stars in the Gaia era

In this study, photometric metallicity and absolute magnitude calibrations were derived using F-G spectral type main-sequence stars in the Solar neighbourhood with precise spectroscopic, photometric and Gaia astrometric data for UBV photometry. The sample consists of 504 main-sequence stars covering the temperature, surface gravity and colour index intervals $5300 4$ (cgs) and $0.3<(B-V)_0<0.8$ mag, respectively. Stars with relative trigonometric parallax errors $σ_π/π\leq0.01$ were preferred from Gaia DR2 data for the estimation of their $M_V$ absolute magnitudes. In order to obtain calibrations, $(U-B)_0$ and $(B-V)_0$ colour indices of stars were preferred and a multi-variable second order equation was used. Calibrations are valid for main-sequence stars in the metallicity and absolute magnitude ranges $-2<{\rm [Fe/H]}<0.5$ dex and $2.5<M_V<6$ mag, respectively. The mean value and standard deviation of the differences between original and estimated values for the metal abundance and absolute magnitude are $\langleΔ{\rm[Fe/H]}\rangle=0.00\pm0.11$ dex and $\langleΔM_V \rangle=0.00\pm0.22$ mag, respectively. In this work, it has been shown that more precise iron abundance and absolute magnitude values were obtained with the new calibrations, compared to previous calibrations in the literature.

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arXiv2019

Analysis of the disc components of our Galaxy via kinematic and spectroscopic procedures

We used the spectroscopic and astrometric data provided from the GALAH DR2 and Gaia DR2, respectively, for a large sample of stars to investigate the behaviour of the [$α$/Fe] abundances via two procedures, i.e. kinematically and spectroscopically. With the kinematical procedure, we investigated the distribution of the [$α$/Fe] abundances into the high/low probability thin disc, and high/low probability thick-disc populations in terms of total space velocity, [Fe/H] abundance, and age. The high probability thin-disc stars dominate in all sub-intervals of [$α$/Fe], including the rich ones: [$α$/Fe]$>0.3$ dex, where the high probability thick-disc stars are expected to dominate. This result can be explained by the limiting apparent magnitude of the GALAH DR2 ($V<14$ mag) and intermediate Galactic latitude of the star sample. Stars in the four populations share equivalent [$α$/Fe] and [Fe/H] abundances, total space velocities and ages. Hence, none of these parameters can be used alone for separation of a sample of stars into different populations. High probability thin-disc stars with abundance $-1.3<{\rm[Fe/H]}\leq -0.5$ dex and age $9<τ\leq13$ Gyr are assumed to have different birth places relative to the metal rich and younger ones. With the spectroscopic procedure, we separated the sample stars into $α$-rich and $α$-poor categories by means of their ages as well as their [$α$/Fe] and [Fe/H] abundances. Stars older than 8 Gyr are richer in [$α$/Fe] than the younger ones. We could estimate the abundance [$α$/Fe]=0.14 dex as the boundery separating the $α$-rich and $α$-poor sub-samples in the [$α$/Fe]$\times$[Fe/H] plane.

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arXiv2019

CCD UBV photometric and Gaia astrometric study of eight open clusters- ASCC 115, Collinder 421, NGC 6793, NGC 7031, NGC 7039, NGC 7086, Roslund 1 and Stock 21

In this study, we carried out CCD UBV photometry of eight open clusters, ASCC 115, Collinder 421, NGC 6793, NGC 7031, NGC 7039, NGC 7086, Roslund 1, Stock 21, and determined their reddening, metallicity, distance, age, and mass functions. We used new Gaia Data Release 2 (DR2) astrometric data to separate cluster member stars from the field stars and obtain precise structural and astrophysical parameters. To identify cluster member stars we utilized an unsupervised membership assignment code (UPMASK), which is based on the photometric and astrometric data. The density distributions for the open clusters show good fits with the empirical King model except for Roslund 1 and Stock 21 not having central concentration. The colour excesses and metallicities were derived separately using U-B vs B-V two-colour diagrams. Keeping these parameters as constants, we simultaneously calculated distance moduli and ages of the clusters from V vs B-V and V vs U-B colour-magnitude diagrams using PARSEC theoretical isochrones. Taking into account Gaia DR2 proper motion components and parallaxes of the member stars, we also calculated mean proper motions and distances for the clusters. Distances derived both from isochrone fitting to colour-magnitude diagrams of the clusters and Gaia DR2 trigonometric parallaxes are compatible with each other. Slopes of the mass functions of the eight open clusters are in good agreement with Salpeter (1955) value of 1.35.

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arXiv2019

Study of Eclipsing Binary and Multiple Systems in OB Associations V: MQ Cen in Crux OB1

The early-type massive binary MQ Cen (P$_{orb}$=3.7 d) has been investigated by means of high-resolution ($R\sim48\,000$) spectral analysis and multi-band (Johnson $BVRI$ and Strömgren $vby$) light curve modeling. The physical parameters of the components have been found to be $M_1= 4.26\pm0.10$ M$_{\odot}$, $R_1= 3.72\pm0.05 $R$_{\odot}$, $T_{\rm eff1}=16\,600\pm520$ K, and $M_2= 5.14\pm0.09 $M$_{\odot}$, $R_2= 7.32\pm0.03 $R$_{\odot}$, $T_{\rm eff2}=15\,000\pm500$ K for the primary and secondary, respectively. The orbital inclination is $i=87.0\pm0.2$ deg. The distance to MQ Cen has been derived to be $d=2\,460\pm310$ pc which locates it in the Crux OB1 association. However, the age of MQ~Cen ($\sim70$ Myr) is higher than the one reported for the Crux OB1 association ($\sim$6 Myr). The derived masses are implying a spectral type of B5 for the primary and B4 for the secondary component. Nevertheless, the secondary component, which is more massive, appears to be cooler than the primary component: It has completed its lifetime on the main-sequence and it is now positioned at the turn-off point of the giant branch, meanwhile the less massive primary component is still staying on the main-sequence.

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arXiv2018

A Detailed Archival CHANDRA Study of the Young Core-Collapse Supernova Remnant 1E 0102.2-7219 in the Small Magellanic Cloud

We present an archival Chandra study of the O-rich supernova remnant (SNR) 1E 0102.2-7219 in the Small Magellanic Cloud. Based on the deep $\sim$ 265 ks archival Chandra data we performed a detailed spatially resolved spectral analysis of 1E 0102.2-7219. Our aim is to reveal the spatial and chemical structures of this remnant in unprecedented details. Radial profiles of O, Ne and Mg abundances based on our analysis of regional spectra extracted along nine different azimuthal directions of 1E 0102.2-7219 suggest the contact discontinuity at $\sim$ 5-5.5 pc from the geometric center of the X-ray emission of the SNR. We find that the metal-rich ejecta gas extends further outward in west and southwest than in other directions of the SNR. The average O/Ne, O/Mg and Ne/Mg abundance ratios of the ejecta are in plausible agreement with the nucleosynthesis products from the explosion of a $\sim 40 M_\odot$ progenitor. We estimate an upper limit on the Sedov age of $\sim 3500$ yr and explosion energy of $\sim 1.8\times10^{51}$ erg for 1E 0102.2-7219. We discuss the implications of our results on the geometrical structure of the remnant, its circumstellar medium and the nature of the progenitor star. Our results do not fit with a simple picture of the reverse-shocked emission from a spherical shell-like ejecta gas with a uniformly-distributed metal abundance and a power-law density along the radius of the SNR.

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arXiv2018

Vertical and radial metallicity gradients in high latitude galactic fields with SDSS

We used the ugr magnitudes of 1,437,467 F-G type main-sequence stars with metal abundance -2<[Fe/H]<+0.2 dex and estimated radial and vertical metallicity gradients for high Galactic-latitude fields (b>50) of the Milky Way Galaxy. The radial metallicity gradient d[Fe/H]/dR=-0.042(0.011) dex/kpc estimated for the stars with 1.31 5 kpc) in three R distance intervals, 6<R<=10, 10<R<=15 and 15<R<=20 kpc. The first one corresponding to the interval 6<R<=10 kpc is equal to d[Fe/H]/dz= -0.023(0.006) dex/kpc, while the others at larger R distances are close to zero. We derived synthetic vertical metallicity gradients for 2,230,167 stars and compared them with the observed ones. There is a good agreement between the two sets of vertical metallicity gradients for the thin disc, while they are different for the thick disc. For the halo, the conspicuous difference corresponds to the R distance interval 6<R<=10 kpc, while they are compatible at higher R distance intervals.

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