Feasibility of incorporating distance-dependent extinction into DF-based likelihoods

Determine the computational feasibility and accuracy of incorporating line-of-sight distance–dependent selection weighting S(Z; X, Y) arising from three-dimensional extinction into the conditional projected likelihood f_proj(V | X, Y) used to fit action-based distribution-function models of the Milky Way nuclear star cluster, by applying S(Z; X, Y) consistently to both the numerator (projected distribution function) and denominator (projected surface density) and by constructing sufficiently dense two-dimensional (X, Y) grids for interpolating the surface density and one-dimensional velocity distribution functions without prohibitive computational cost.

Background

The modelling framework fits action-based distribution functions to discrete kinematic data using the conditional projected velocity distribution at each star’s sky position. In the nuclear star cluster, strong and spatially variable dust extinction along the line of sight implies that the selection function depends on distance Z, which should, in principle, be included as a weight S(Z; X, Y) in both the projected DF and the surface-density normalisation.

The authors outline how such Z-dependent weights could be introduced within their Quasi–Monte Carlo integration for the numerator and via denser (X, Y) grids for the denominator and for one-dimensional velocity distribution interpolators. However, they did not implement this in the present work and note that whether these strategies can be executed with sufficient accuracy at acceptable computational cost is unresolved.