The Influence of the Metal Mass Fraction Z, Age, and Mixing-length Parameter on the RGB Bump Magnitude for the M4 Cluster

We identify the location of the RGB bump of M4 (NGC 6121) using the available photometric data, and measure VRGBB (similar to 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 delta V-bump between the predicted and the observed bump magnitude. Based on the best fit of the MESA model with [Fe/H] = -1.05, [alpha/Fe] =0, alpha(MLT) = 2.0, and t = 13.3 Gyr, the bump magnitude difference delta V-bump is about 0.46 mag. Based on the best fit of the BaSTI model with alpha(MLT) = 2.2 similar to 2.4, [Fe/H] = -1.05, [alpha/Fe] = 0.4, and t = 12.5 Gyr, the bump magnitude difference delta V-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, delta V-RGBB vertical bar(t=12.0,alpha MLT =2.2, [alpha/Fe] = 0,Z=0.0076), delta V-RGBB vertical bar(t=12.0,alpha MLT) (=2.2, [alpha/Fe]=0, Z=0.0085), and delta V-RGBB vertical bar(t=11.0,alpha MLT=2.4,[alpha/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 similar to 0.60 dex for the MESA models, is ruled out by the spectroscopic data.