The evolution of white dwarfs is a simple gravothermal process of cooling. Since the shape of their luminosity function is sensitive to the characteristic cooling time, it is possible to use its slope to test the existence of additional sources or sinks of energy, such as those predicted by alternative physical theories. The aim of this paper is to study if the changes in the slope of the white dwarf luminosity function around bolometric magnitudes ranging from 8 to 10 and previously attributed to axion emission are, effectively, a consequence of the existence of axions and not an artifact introduced by the star formatio rate. We compute theoretical luminosity functions of the thin and thick disk, and of the stellar halo including axion emission and we compare them with the existing observed luminosity functions. Since these stellar populations have different star formation histories, the slope change should be present in all of them at the same place if it is due to axions or any other intrinsic cooling mechanism. The signature of an unexpected cooling seems to be present in the luminosity functions of the thin and thick disks, as well as in the halo luminosity function. This additional cooling is compatible with axion emission, thus supporting the idea that DFSZ axions, with a mass in the range of 4 to 10 meV, could exist. If this were the case, these axions could be detected by the future solar axioscope IAXO.
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