XMM-Newton large program on SN1006 - I. Methods and initial results of spatially resolved spectroscopy

Based on our newly developed methods and the XMM-Newton large program ofSN1006, we extract and analyse the spectra from 3596 tessellated regionsof this supernova remnant (SNR) each with 0.3-8 keV counts>10^4. For the first time, we map out multiple physicalparameters, such as the temperature (kT), electron density(n_e), ionization parameter (n_et), ionization age(t$_ion), metal abundances, as well as the radio-to-X-ray slope($\alpha$) and cutoff frequency ($\nu$$_cutoff$) of thesynchrotron emission. We construct probability distribution functions ofkT and n$_e$t, and model them with several Gaussians, in orderto characterize the average thermal and ionization states of such anextended source. We construct equivalent width (EW) maps based oncontinuum interpolation with the spectral model of each region. We thencompare the EW maps of O VII, O VIII, O VII K$\delta$ - $\zeta$, Ne, Mg,Si XIII, Si XIV, and S lines constructed with this method to thoseconstructed with linear interpolation. We further extract spectra fromlarger regions to confirm the features revealed by parameter and EWmaps, which are often not directly detectable on X-ray intensity images.For example, O abundance is consistent with solar across the SNR, exceptfor a low-abundance hole in the centre. This `O hole' has enhanced O VIIK$\delta$ - $\zeta$ and Fe emissions, indicating recently reverse shockedejecta, but also has the highest n$_e$t, indicating forwardshocked interstellar medium (ISM). Therefore, a multitemperature modelis needed to decompose these components. The asymmetric metaldistributions suggest there is either an asymmetric explosion of thesupernova or an asymmetric distribution of the ISM.