Multivariate Monte Carlo Methods for the Reflection Grating Spectrometers on XMM-Newton

We propose a novel multivariate Monte Carlo method as an efficient and flexible approach to analyzing extended X-ray sources with the reflection grating spectrometers (RGS) on XMM-Newton. A multidimensional interpolation method is used to efficiently calculate the response function for the RGS in conjunction with an arbitrary spatially varying spectral model. Several methods of event comparison that effectively compare the multivariate RGS data are discussed. The use of a multidimensional instrument Monte Carlo method also creates many opportunities for the use of complex astrophysical Monte Carlo calculations in diffuse X-ray spectroscopy. The methods presented here could be generalized to other X-ray instruments as well.