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Effect of OH depletion on measurements of the mass-to-flux ratio in molecular cloud cores

The ratio of mass and magnetic flux determines the relative importance of magnetic and gravitational forces in the evolution of molecular clouds and their cores. Its measurement is thus central in discriminating between different theories of core formation and evolution. Here we discuss the effect of chemical depletion on measurements of the mass-to-flux ratio using the same molecule (OH) both for Zeeman measurements of the magnetic field and the determination of the mass of the region. The uncertainties entering through the OH abundance in determining separately the magnetic field and the mass of a region have been recognized in the literature. It has been proposed however that, when comparing two regions of the same cloud, the abundance will in both cases be the same. We show that this assumption is invalid. We demonstrate that when comparing regions with different densities, the effect of OH depletion in measuring changes of the mass-to-flux ratio between different parts of the same cloud can even reverse the direction of the underlying trends (for example, the mass-to-flux ratio may appear to decrease as we move to higher density regions). The systematic errors enter primarily through the inadequate estimation of the mass of the region.