Colour Transformations between BVRc and g'r'i' Photometric Systems for Giant Stars

The transformation equations from $BVR_c$ to $g'r'i'$ magnitudes and vice versa for the giants were established from a sample of 80 stars collected from Soubiran et al. (2010) with confirmed surface gravity ($2\leq \log g$ (cms$^{-2}$)$\leq3$) at effective temperatures $4000<T_{eff} (K)<16000$. The photometric observations, all sample stars at $g'r'i'$ and 65 of them at $BVR_c$, were obtained at T\"UB\.ITAK National Observatory (TUG) 1m (T100) telescope, on the Taurus Mountains in Turkey. The $M_V$ absolute magnitudes of the giant stars were estimated from the absolute magnitude-temperature data for the giant stars by Sung et al. (2013) using the $T_{eff}$ from the intrinsic colours considered in this study. The transformation equations could be considered to be valid through the ranges of the following magnitudes and colours involved: $7.10<V_0<14.50$, $7.30<g'_0<14.85$, $-0.20<(B-V)_0<1.41$, $-0.11<(V-R_c)_0<0.73$, $-0.42<(g'-r')_0<1.15$, and $-0.37<(r'-i')_0<0.47$ mag. The transformations were successfully applied to the synthetic $BVR_c$ data of 427 field giants in order to obtain the $g'r'i'$ magnitudes and colours. Comparisons of these data with the $g'r'i'$ observations of giants in this study show that the mean residuals and standard deviations lie within [-0.010, 0.042] and [0.028, 0.068] mag, respectively.