The interpretation of microlensing results towards the Large Magellanic Cloud (LMC) still remains controversial. White dwarfs have been proposed to explain these results and, hence, to contribute significantly to the mass budget of our Galaxy. However, several constraints on the role played by regular carbon-oxygen white dwarfs exist. Massivewhite dwarfs are thought to be made of a mixture of oxygen and neon. Correspondingly, their cooling rate is larger than those of typical carbon-oxygen white dwarfs and they fade to invisibility in short timescales. Consequently, they constitute a good candidate for explaining the microlensing results. Here, we examine in detail this hypothesis by using the most recent and up-to-date cooling tracks for massive white dwarfs and a Monte Carlo simulator which takes into account the most relevant Galactic inputs. We find that oxygen-neon white dwarfs cannot account for a substantial fraction of the microlensing depth towards the LMC, independently of the adopted initial mass function, although some microlensing events could be due to oxygen--neon white dwarfs. The white dwarf population contributes at most a 5% to the mass of the Galactic halo.
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