2018ApJ...869..109S

We identify the location of the RGB bump of M4 (NGC 6121) using the available photometric data, and measure V_RGBB (∼13.57 ± 0.04 mag). According to the observed [Fe/H], we compute theoretical isochrones with the scaled-solar composition in the MESA model and alpha-enhanced composition in the BaSTI model, respectively. Using a color-magnitude diagram, we compare these isochrones with the observed data to obtain the magnitude difference δV_bump between the predicted and the observed bump magnitude. Based on the best fit of the MESA model with [Fe/H] = -1.05, [α/Fe] = 0, α_MLT = 2.0, and t = 13.3 Gyr, the bump magnitude difference δV_bump is about 0.46 mag. Based on the best fit of the BaSTI model with α_MLT = 2.2 ∼ 2.4, [Fe/H] = -1.05, [α/Fe] = 0.4, and t = 12.5 Gyr, the bump magnitude difference δV_bump is about 0.2 mag. To try and explain the bump magnitude differences, the metal mass fraction Z is enhanced as 0.0037, 0.00591, 0.0076, and 0.0085. Accordingly, δV_RGBB|_t=12.0,αMLT=2.2,[α/Fe]=0,Z=0.0076_, δV_RGBB|_t=12.0,αMLT=2.2,[α/Fe]=0,Z=0.0085_, and δV_RGBB|_t=11.0,αMLT=2.4,[α/Fe]=0,Z=0.0085_ by the MESA model are 0, -0.01, and 0 mag, respectively. Increasing the assumed metallicity can decrease the discrepancy between the predicted and observed bump magnitudes. However, a metallicity increase large enough to resolve the offset, roughly ∼0.60 dex for the MESA models, is ruled out by the spectroscopic data.