Optimal binning of X-ray spectra and response matrix design

A theoretical framework is developed to estimate the optimal binning of X-ray spectra. We derived expressions for the optimal bin size for model spectra as well as for observed data using different levels of sophistication. It is shown that by taking into account both the number of photons in a given spectral model bin and their average energy over the bin size, the number of model energy bins and the size of the response matrix can be reduced by a factor of $10-100$. The response matrix should then contain the response at the bin centre as well as its derivative with respect to the incoming photon energy. We provide practical guidelines for how to construct optimal energy grids as well as how to structure the response matrix. A few examples are presented to illustrate the present methods.Comment: 16 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

The mass and energy budget of Cassiopeia A

Further analysis of X-ray spectroscopy results recently obtained from the MOS CCD cameras on-board XMM-Newton provides a detailed description of the hot and cool X-ray emitting plasma in Cas A. Measurement of the Doppler broadening of the X-ray lines is consistent with the expected ion velocities, ~1500 km/s along the line of sight, in the post shock plasma. Assuming a constant total pressure throughout the remnant we estimate the total remnant mass as 10 Msun and the total thermal energy as 7E43 J. We derive the differential mass distribution as a function of ionisation age for both X-ray emitting components. This distribution is consistent with a hot component dominated by swept up mass heated by the primary shock and a cool component which are ablated clumpy ejecta material which were and are still being heated by interaction with the preheated swept up material. We calculate a balanced mass and energy budget for the supernova explosion giving 1E44 J in ejected mass; approximately 0.4 Msun of the ejecta were diffuse with an initial rms velocity of 15000 km/s while the remaining ~1.8 Msun were clumpy with an initial rms velocity of ~2400 km/s. Using the Doppler velocity measurements of the X-ray spectral lines we can project the mass into spherical coordinates about the remnant. This provides quantitative evidence for mass and energy beaming in the supernova explosion. The mass and energy occupy less than 4.5 sr (<40 % of the available solid angle) around the remnant and 64 % of the mass occurs in two jets within 45 degrees of a jet axis. We calculate a swept up mass of 7.9 Msun in the emitting plasma and estimate that the total mass lost from the progenitor prior to the explosion could be as high as ~20 Msun.Comment: 8 pages, 7 figures, submitted to Astronomy & Astrophysic

Proper Motions of H-alpha filaments in the Supernova Remnant RCW 86

We present a proper motion study of the eastern shock-region of the supernova remnant RCW 86 (MSH 14-63, G315.4-2.3), based on optical observations carried out with VLT/FORS2 in 2007 and 2010. For both the northeastern and southeastern regions, we measure an average proper motion of H-alpha filaments of 0.10 +/- 0.02 arcsec/yr, corresponding to 1200 +/- 200 km/s at 2.5kpc. There is substantial variation in the derived proper motions, indicating shock velocities ranging from just below 700 km/s to above 2200 km/s. The optical proper motion is lower than the previously measured X-ray proper motion of northeastern region. The new measurements are consistent with the previously measured proton temperature of 2.3 +/- 0.3 keV, assuming no cosmic-ray acceleration. However, within the uncertainties, moderately efficient (< 27 per cent) shock acceleration is still possible. The combination of optical proper motion and proton temperature rule out the possibility that RCW 86 has a distance less than 1.5kpc. The similarity of the proper motions in the northeast and southeast is peculiar, given the different densities and X-ray emission properties of the regions. The northeastern region has lower densities and the X-ray emission is synchrotron dominated, suggesting that the shock velocities should be higher than in the southeastern, thermal X-ray dominated, region. A possible solution is that the H-alpha emitting filaments are biased toward denser regions, with lower shock velocities. Alternatively, in the northeast the shock velocity may have decreased rapidly during the past 200yr, and the X-ray synchrotron emission is an afterglow from a period when the shock velocity was higher.Comment: Accepted for publication in MNRA