The inverse problem in microlensing: from the optical depth to the galaxy models parameters

Abstract

We present in this paper a simple method to obtain informations on galaxy models parameters using the measured value of the microlensing optical depth. Assuming a 100 percent MACHO's dark halo, we ask the predicted optical depth for a given model to be the same as the observed one, in a given direction. Writing the optical depth in terms of the given halo model parameters and inverting this relation with respect to one of them, it is possible to get information on it, fixing under reasonable hypothesis the other parameters. This is what we call the "inverse problem in microlensing. We apply this technique to the class of power-law models with flat rotation curves, determining the range for the core radius R_c compatible with the constraints on the halo flattening q and the measures of the optical depth towards LMC. Next, we apply the same method to a simple triaxial model, evaluating the axial ratios.Comment: 23 LaTex Pages, including 5 Postscript Figures, uses astron.sty, submitted to A&