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On the robustness of the microlensing optical depth as a measure of MACHO density

By E. J. Kerins


The optical depth is widely used in Galactic microlensing studies as a means to determine the density of MACHOs, since in theory it depends only upon their spatial distribution and is therefore less model-dependent than other microlensing observables. We show that determinations of the MACHO density derived from the observed optical depth are much less robust than generally acknowledged. We illustrate this by analysing the 2-year LMC results of the MACHO collaboration for a simple isothermal MACHO halo. We draw the following conclusions: (1) The MACHO density inferred from optical depth measurements is a function of the assumed MACHO mass function for a given Galactic distribution function; (2) without a priori knowledge of the MACHO mass function, optical depth measurements alone cannot usefully constrain the MACHO density for a given Galactic distribution function; (3) in the case of multi-component Galactic models, the relative contribution of each component to the observed optical depth can only be established by assuming prior knowledge of the distribution function and MACHO mass function for each component; (4) comparisons between theoretical and observed optical depths which do not take account of the distribution of timescales are making implicit assumptions about the Galactic distribution function and MACHO mass function, and may therefore be misleading; (5) because of its sensitivity to both the MACHO mass and spatial density, an analysis of the observed rate-timescale distribution is always able to place stronger limits on the MACHO density than an analysis of the measured optical depth. Given these findings we caution that optical depth measures be used only as a consistency check on the results from rate-timescale distribution analyses. We briefly discuss implications for microlensing searches towards the Galactic – 3 – bulge, which are perhaps more reliant on optical depth determinations than LMC searches

Topics: Subject headings, Dark matter — gravitational lensing — Galaxy, halo — Galaxy, stellar content — Galaxy, structure – 4 –
Year: 1997
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