The metallicity of M4: Accurate spectroscopic fundamental parameters for four giants

High-quality spectra, covering the wavelength range 5480 to 7080 A, have been obtained for four giant stars in the intermediate-metallicity CN-bimodal globular cluster M4 (NGC 6121). We have employed a model atmosphere analysis that is entirely independent from cluster parameters, such as distance, age, and reddening, in order to derive accurate values for the stellar parameters effective temperature, surface gravity, and microturbulence, and for the abundance of iron relative to the Sun, (Fe/H), and of calcium, Ca/H, for each of the four stars. Detailed radiative transfer and statistical equilibrium calculations carried out for iron and calcium suggest that departures from local thermodynamic equilibrium are not significant for the purposes of our analysis. The spectroscopically derived effective temperatures for our program stars are hotter by about 200 K than existing photometric calibrations suggest. We conclude that this is due partly to the uncertain reddening of M4 and to the existing photometric temperature calibration for red giants being too cool by about 100 K. Comparison of our spectroscopic and existing photometric temperatures supports the prognosis of a significant east-west gradient in the reddening across M4. Our derived iron abundances are slightly higher than previous high-resolution studies suggested; the differences are most probably due to the different temperature scale and choice of microturbulent velocities adopted by earlier workers. The resulting value for the metallicity of M4 is (Fe/H )(sub M4) = -1.05 + or - 0.15. Based on this result, we suggest that metallicities derived in previous high-dispersion globular cluster abundance analyses could be too low by 0.2 to 0.3 dex. Our calcium abundances suggest an enhancement of calcium, an alpha element, over iron, relative to the Sun, in M4 of (Ca/H) = 0.23.