Parametrizing the local dark matter speed distribution: a detailed analysis

In a recent paper, a new parametrization for the dark matter (DM) speed distribution f(v) was proposed for use in the analysis of data from direct detection experiments. This parametrization involves expressing the logarithm of the speed distribution as a polynomial in the speed v. We present here a more detailed analysis of the properties of this parametrization. We show that the method leads to statistically unbiased mass reconstructions and exact coverage of credible intervals. The method performs well over a wide range of DM masses, even when finite energy resolution and backgrounds are taken into account. We also show how to select the appropriate number of basis functions for the parametrization. Finally, we look at how the speed distribution itself can be reconstructed, and how the method can be used to determine if the data are consistent with some test distribution. In summary, we show that this parametrization performs consistently well over a wide range of input parameters and over large numbers of statistical ensembles and can therefore reliably be used to reconstruct both the DM mass and speed distribution from direct detection data.