Absolute Magnitude Calibration for Giants based on the Colour-Magnitude Diagrams of Galactic Clusters. II-Calibration with SDSS

We present an absolute magnitude calibration for red giants with the colour magnitude diagrams of six Galactic clusters with different metallicities i.e. M92, M13, M3, M71, NGC 6791 and NGC 2158. The combination of the absolute magnitudes of the red giant sequences with the corresponding metallicities provides calibration for absolute magnitude estimation for red giants for a given $(g-r)_{0}$ colour. The calibration is defined in the colour interval 0.45 $\leq(g-r)_{0}\leq$ 1.30 mag and it covers the metallicity interval $-2.15\leq \lbrack Fe/H \rbrack \leq$ +0.37 dex. The absolute magnitude residuals obtained by the application of the procedure to another set of Galactic clusters lie in the interval $-0.28< \Delta M \leq +0.43$ mag. However, the range of 94% of the residuals is shorter, $-0.1<\Delta M \leq+0.4$ mag. The mean and the standard deviation of (all) residuals are 0.169 and 0.140 mag, respectively. The derived relations are applicable to stars older than 2 Gyr, the age of the youngest calibrating cluster.Comment: 12 pages, including 5 figures and 10 tables, accepted for publication in PASA. arXiv admin note: substantial text overlap with arXiv:1204.429

Galactic longitude dependent Galactic model parameters

We present the Galactic model parameters for thin disc estimated by Sloan Digital Sky Survey (SDSS) data of 14 940 stars with apparent magnitudes $16<g_{o}\leq21$ in six intermediate latitude fields in the first Galactic quadrant. Star/galaxy separation was performed by using the $SDSS$ photometric pipeline and the isodensity contours in the $(g-r)_{0}-(r-i)_{0}$ two colour diagram. The separation of thin disc stars is carried out by the bimodal distribution of stars in the $(g-r)_{o}$ histogram, and the absolute magnitudes were evaluated by a procedure presented in the literature Bilir et al. (2005). Exponential density law fits better to the derived density functions for the absolute magnitude intervals $8<M(g)\leq9$ and $11<M(g)\leq12$, whereas sech/sech$^{2}$ laws are more appropriate for absolute magnitude intervals $9<M(g)\leq10$ and $10<M(g)\leq11$. We showed that the scaleheight and scalelength are Galactic longitude dependent. The average values and ranges of the scaleheight and the scalelength are $=220$ pc ($196\leq H \leq 234$ pc) and $=1900$ pc ($1561\leq h \leq 2280$ pc) respectively. This result would be useful to explain different numerical values claimed for those parameters obtained by different authors for the fields in different directions of the Galaxy.Comment: 28 pages, including 12 figures and 7 tables, accepted for publication in New Astronom

SDSS Absolute Magnitudes for Thin Disc Stars based on Trigonometric Parallaxes

We present a new luminosity-colour relation based on trigonometric parallaxes for thin disc main-sequence stars in SDSS photometry. We matched stars from the newly reduced Hipparcos catalogue with the ones taken from 2MASS All-Sky Catalogue of Point Sources, and applied a series of constraints, i.e. relative parallax errors ($\sigma_{\pi}/\pi\leq0.05$), metallicity ($-0.30\leq[M/H]\leq0.20$ dex), age ($0\leq t \leq 10$ Gyr) and surface gravity ($\log g>4$), and obtained a sample of thin disc main-sequence stars. Then, we used our previous transformation equations (Bilir et al. 2008a) between SDSS and 2MASS photometries and calibrated the $M_{g}$ absolute magnitudes to the $(g-r)_{0}$ and $(r-i)_0$ colours. The transformation formulae between 2MASS and SDSS photometries along with the absolute magnitude calibration provide space densities for bright stars which saturate the SDSS magnitudes.Comment: 7 pages, including 7 figures and 2 tables, accepted for publication in MNRA

Luminosity-Colours relations for thin disc main-sequence stars

In this study we present the absolute magnitude calibrations of thin disc main-sequence stars in the optical ($M_{V}$), and in the near-infrared ($M_{J}$). Thin disc stars are identified by means of Padova isochrones, and absolute magnitudes for the sample are evaluated via the newly reduced Hipparcos data. The obtained calibrations cover a large range of spectral types: from A0 to M4 in the optical and from A0 to M0 in the near-infrared. Also, we discuss the of effects binary stars and evolved stars on the absolute magnitude calibrations. The usage of these calibrations can be extended to the estimation of galactic model parameters for the thin disc individually, in order to compare these parameters with the corresponding ones estimated by $\chi{^2}_{min}$ statistics (which provides galactic model parameters for thin and thick discs, and halo simultaneously) to test any degeneracy between them. The calibrations can also be used in other astrophysical researches where distance plays an important role in that study.Comment: 8 pages, including 12 figures and 4 tables, accepted for publication in MNRA

Absolute Magnitude Calibration for Red Giants based on the Colour-Magnitude Diagrams of Galactic Clusters. III-Calibration with 2MASS

We present two absolute magnitude calibrations, $M_{J}$ and $M_{K_s}$, for red giants with the colour magnitude diagrams of five Galactic clusters with different metallicities i.e. M92, M13, M71, M67, and NGC 6791. The combination of the absolute magnitudes of the red giant sequences with the corresponding metallicities provides calibration for absolute magnitude estimation for red giants for a given colour. The calibrations for $M_{J}$ and $M_{K_s}$ are defined in the colour intervals $1.3\leq(V-J)_{0}\leq2.8$ and $1.75 \leq (V-K_{s})_{0}\leq 3.80$ mag, respectively, and they cover the metallicity interval $-2.15 \leq \lbrack Fe/H \rbrack \leq +0.37$ dex. The absolute magnitude residuals obtained by the application of the procedure to another set of Galactic clusters lie in the intervals $-0.08<\Delta M_{J}\leq +0.34$ and $-0.10< \Delta M_{K_s}\leq +0.27$ mag for $M_{J}$ and $M_{K_s}$, respectively. The means and standard deviations of the residuals are $= 0.137$ and $\sigma_{M_J}=0.080$, and $=0.109$ and $\sigma_{M_{K_{s}}}=0.123$ mag. The derived relations are applicable to stars older than 4 Gyr, the age of the youngest calibrating cluster.Comment: 20 pages, including 8 figures and 22 tables, accepted for publication in PASA. arXiv admin note: substantial text overlap with arXiv:1206.275

Volume limited dependent Galactic model parameters

We estimated 34 sets of Galactic model parameters for three intermediate latitude fields with Galactic longitudes l=60, l=90, and l=180, and we discussed their dependence on the volume. Also, we confirmed the variation of these parameters with absolute magnitude and Galactic longitude. The star samples in two fields are restricted with bright and unit absolute magnitude intervals, (4,5], and (5,6], whereas for the third field a larger absolute magnitude interval is adopted, (4,10]. The limiting apparent magnitudes of star samples are g=15 and g=22.5 mag which provide space densities within distances in the line of sight 0.9 and 25 kpc. The Galactic model parameters for the thin disc are not volume dependent. However, the ones for thick disc and halo do show spectacular trends in their variations with volume, except for the scalelength of the thick disc. The local space density of the thick disc increases, whereas the scaleheight of the same Galactic component decreases monotonically. However, both model parameters approach asymptotic values at large distances. The axial ratio of the halo increases abruptly for the volumes where thick disc is dominant, whereas it approaches an asymptotic value gradually for larger volumes, indicating a continuous transition from disclike structure to a spherical one at the outermost region of the Galaxy. The variation of the Galactic model parameters with absolute magnitude can be explained by their dependence on the stellar luminosity, whereas the variation with volume and Galactic longitude at short distances is a bias in analysis.Comment: 12 pages, including 8 figures and 5 tables, accepted for publication in PAS