The validation of made-to-measure method for reconstruction of phase-space distribution functions

Abstract

We investigate how accurately phase space distribution functions (DFs) in galactic models can be reconstructed by a made-to-measure (M2M) method, which constructs $N$-particle models of stellar systems from photometric and various kinematic data. The advantage of the M2M method is that this method can be applied to various galactic models without assumption of the spatial symmetries of gravitational potentials adopted in galactic models, and furthermore, numerical calculations of the orbits of the stars cannot be severely constrained by the capacities of computer memories. The M2M method has been applied to various galactic models. However, the degree of accuracy for the recovery of DFs derived by the M2M method in galactic models has never been investigated carefully. Therefore, we show the degree of accuracy for the recovery of the DFs for the anisotropic Plummer model and the axisymmetric St\"{a}ckel model, which have analytic solutions of the DFs. Furthermore, this study provides the dependence of the degree of accuracy for the recovery of the DFs on various parameters and a procedure adopted in this paper. As a result, we find that the degree of accuracy for the recovery of the DFs derived by the M2M method for the spherical target model is a few percent, and more than ten percent for the axisymmetric target model.