Absolute Magnitude Calibration for Red Giants based on the Colour-Magnitude Diagrams of Galactic Clusters. I- Calibration with V and (B-V)

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, M5, 47 Tuc, M67, and NGC 6791. The combination of the absolute magnitude offset from the fiducial of giant sequence of the cluster M5 with the corresponding metallicity offset provides calibration for absolute magnitude estimation for red giants for a given (B-V)o colour. The calibration is defined in the colour interval 0.75<=(B-V)o<=1.50 mag and it covers the metallicity interval -2.15<[Fe/H]<=+0.37 dex. 91% of the absolute magnitude residuals obtained by the application of the procedure to another set of Galactic clusters lie in the interval -0.40<\Delta M<=+0.40 mag. The mean and the standard deviation of the residuals are 0.05 and 0.19 mag, respectively. We fitted the absolute magnitude also to metallicity and age for a limited sub-sample of (B-V)o colour, just to test the effect of age in absolute magnitude calibration. Comparison of the mean and the standard deviation of the residuals evaluated by this procedure with the corresponding ones provided by the procedure where the absolute magnitude fitted to a third degree polynomial of metallicity show that the age parameter may be omitted in absolute magnitude estimation of red giants. The derived relations are applicable to stars older than 4 Gyr, the age of the youngest calibrating cluster.Comment: 15 pages, including 6 figures and 16 tables, accepted for publication in PAS

Strength–dilatancy and critical state behaviours of binary mixtures of graded sands influenced by particle size ratio and fines content

Binary granular soil mixtures, as common heterogeneous soils, are ubiquitous in nature and man-made deposits. Fines content and particle size ratio are two important gradation parameters for a binary mixture, which have potential influences on mechanical behaviours. However, experimental studies on drained shear behaviour considering the whole range of fines content and different particle size ratios are scarce in the literature. For this purpose, a series of drained triaxial compression tests was performed on dense binary silica sand mixtures with four different particle size ratios to investigate systematically the effects of fines content and particle size ratio on the drained shear behaviours. Based on these tests, the strength-dilation behaviour and critical state behaviour were examined. It was observed that both fines content and particle size ratio have significant influence on the stress–strain response, the critical state void ratio, the critical state friction angle, the maximum dilation angle, the peak friction angle and the stress–dilatancy relation. The underlying mechanism for the effects of fines content and particle size ratio was discussed from the perspective of the kinematic movements at particle level