For the spectral fitting, the astrophysical background components are determined from a simultaneous fit to data from the RASS4 (Snowden etal. 1997). The extraction region for the RASS data is an annulus from 0.7 to 1 around the cluster centre (for NGC4636, NGC1399 and A3526 r500 is larger than 0.7, so the RASS data were extracted from 1.5 to 2). The particle background was directly subtracted from the Chandra spectra using the stow events files from an epoch close to the observation date. The stow events files are created when the ACIS detector is in a position where it is not exposed to the sky and the HRC-I camera is in the field of view. This configuration is also called event histogram mode. As shown by comparisons to dark moon observations only particle events are recorded in the stow position (Markevitch etal. 2003; Wargelin etal. 2004). For each annulus, the same detector region was used to extract the particle background spectra. These background spectra are normalized by the ratio of the (9.512)keV band count rate of the observation and the stow events file to account for variations of the quiescent particle background component. The cluster emission is modelled by an absorbed thermal model (phabs*apec), where all parameters apart from the redshift and the NH are left free to vary. Following Willingale etal. (2013), the hydrogen columns density used as a tracer for the X-ray absorption,

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\begin{eqnarray}
N_\mathrm{H\, tot} = N_\mathrm{H\,\small {I}} + 2\cdot N_{\mathrm{H}_2\mathrm{m}} \cdot \left[ 1-\exp \left(-N_\mathrm{{\rm H\,\small {I}}}\cdot \frac{ E\left(B-V\right) }{ N_\mathrm{c}} \right) \right]^\alpha , \nonumber\\
\end{eqnarray}

where the parameters NH2m  7.2  0.3  1020cm 2, Nc3.0  0.31020cm2 and 1.1  0.1 were calibrated using X-ray afterglows of Gamma-ray bursts in the aforementioned reference. Both, the absorption E(BV) from the IRAS and COBE/DIRBE infrared dust maps (Schlegel, Finkbeiner  Davis 1998) and the $N_\mathrm{H\,\small {I}}$ from Kalberla etal. (2005) are computed at each cluster position. The combined effect of the uncertainties of these parameters, the scatter of this scaling relation (0.087) plus accounting for a 10percent uncertainty on $N_\mathrm{H\,\small {I}}$ and E(BV) has only an 11percent effect on NHtot, which typically affects best-fitting temperatures by 1percent. Since this is much smaller than the typical statistical uncertainties, any statistical uncertainty of NHtot is neglected. For the relative abundance of heavy elements the Asplund etal. (2009) abundance table was used. For each observation, all spectra from the different regions and chips5 are fit simultaneously. The temperature and metallicity of spectra from the same region but different chips are linked together, while the normalizations are not because of spatial variations of the density distribution. For all observations, the steppar command was run on the temperatures. This task calculates the 2 for the parameter within a given range of values in order not to get best-fitting parameters of a local minimum of the likelihood distribution. The reduced 2 of all spectral fits was on average 1.03, while in 95percent of the cases it was below 1.17. This gives a hint that the spectral modelling is appropriate.
Citation: Wargelin etal. 2004
Citation function: Background