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 of SN1006, we extract and analyse the spectra from 3596 tessellated regions of this supernova remnant (SNR) each with 0.3-8 keV counts >10^4. For the first time, we map out multiple physical parameters, 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$) of the synchrotron emission. We construct probability distribution functions of kT and n$_e$t, and model them with several Gaussians, in order to characterize the average thermal and ionization states of such an extended source. We construct equivalent width (EW) maps based on continuum interpolation with the spectral model of each region. We then compare the EW maps of O VII, O VIII, O VII K$\delta$ - $\zeta$, Ne, Mg, Si XIII, Si XIV, and S lines constructed with this method to those constructed with linear interpolation. We further extract spectra from larger regions to confirm the features revealed by parameter and EW maps, which are often not directly detectable on X-ray intensity images. For example, O abundance is consistent with solar across the SNR, except for a low-abundance hole in the centre. This `O hole' has enhanced O VII K$\delta$ - $\zeta$ and Fe emissions, indicating recently reverse shocked ejecta, but also has the highest n$_e$t, indicating forward shocked interstellar medium (ISM). Therefore, a multitemperature model is needed to decompose these components. The asymmetric metal distributions suggest there is either an asymmetric explosion of the supernova or an asymmetric distribution of the ISM.