Mixing model for ASCA data. Written for cluster data so uses beta or two power-law surface brightness models. Includes a calculation of the telescope effective area so no arf should be applied to input files. Note that this model is very slow if any of the parameters are free.
The model is used by reading spectra in as separate datagroups. Each input file requires the XFLT0001 keyword set to a different number (eg if concentric annuli are in use then number outwards). The normalizations for each datagroup should be linked since the ascac model takes care of the relative normalizations based on the surface brightness model used. A maximum of five different spatial regions is allowed. The absolute normalization is not reliable so this model should not be used to derive fluxes.
|par4||=||Switch (0 beta model, 1 2-power-law)|
This model performs a 3-D to 2-D projection of prolate ellipsoidal shells onto elliptical annuli. The annuli can have varying ellipticities and position angles but must have the same center. The user should extract spectra in a series of annuli. Each spectrum needs three additional keywords (XFLT0001, XFLT0002, XFLT0003) in the spectrum extension. These keywords contain the semi-major axis, semi-minor axis, and position angle (in degrees) for the outer boundary of the annulus. It is assumed that the inner boundary is specified by the outer boundary of the next annulus in. The lengths can be in any consistent units although for numerical accuracy they should have reasonable values. Optional pairs of extra keywords (eg XFLT0004/5, XFLT0006/7, etc.) can be used to specify start and end angles for a partial annulus. These angles should be given relative to the same zero as the position angle.
The user reads in the spectra as separate datagroups and sets model parameters for each datagroup. The model for datagroup J will be the model in the shell whose outer boundary is a prolate ellipsoid of semi-major and semi-minor axes given by the semi-major and semi-minor axes in the XFLT keywords for dataset J. The projct model sums up the appropriate fractions of each ellipsoid model to make the projected spectrum.
For example, suppose we extract spectrum from three elliptical regions defined by (1,0.5,0), (2,1,0), (3,1.5,0). That is the first region is in an ellipse of semi-major axis 1 and semi-minor axis 0.5. The second region is an elliptical annulus whose inner boundary has semi-major axis 1 and semi-minor axes 0.5 and whose outer boundary has semi-major axis 2 and semi-minor axis 1. The third region is defined similarly. The model fit has a temperature of 2 keV for the first datagroup, 3 keV for the second, and 4 keV for the third. The actual model fit to the first dataset has contributions from all three temperatures, the second only from the 3 and 4 keV components, and the third only from the 4 keV component. The weighting is the fraction of the ellipsoidal volume intersected by the elliptical annular cross-section. Thus the normalizations correspond to the emission measure in each ellipsoidal shell.
The projct model has 3 parameters which can be used to define the inner ellipse of the region being analyzed. For instance, in the example above we could have only read in spectra for the outer two regions but then set the projct parameters to (1.0,0.5,0.0). This would have allowed us to determine the temperatures and emission measures of the outer two annuli without having to worry about fitting a model to the central region.
|par1||=||semi-major axis of inner boundary ellipse|
|par2||=||semi-minor axis of inner boundary ellipse|
|par3||=||position angle of inner boundary ellipse|
Mixing model for XMM data. Mixes the spectra between datagroups based on the PSF overlap between selected regions. A surface brightness model is required to calculate the mixing and this can be supplied in several ways. If XMMPSF-IMAGE has been set to some image file (using xset) then this image will be used for the surface brightness distribution. If XMMPSF-IMAGE has not been set then either a beta or two power-law model is used. In this case the model parameters determine the shape of the surface brightness distribution. If XMMPSF-RA and XMMPSF-DEC are set they are used as the center of the distribution. They should be specified either in decimal degrees or as hh:mm:ss.s and dd:mm:ss.s. If XMMPSF-RA and XMMPSF-DEC are not set then the centroid of the wmap will be used as the center of the surface brightness distribution.
The model works by calculating the mixing factors. It will recalculate these factors if any of the XMMPSF-* or any of the model parameters are changed. Calculating the mixing factors is very slow so should be avoided as much as possible.
Multiple observations can be fit simultaneously. In this case the observations
should be read in each datagroup in the same order eg
1:1 obs1reg1 1:2 obs2reg1 1:3 obs3reg1 2:4 obs1reg2 2:5 obs2reg2...
|par1||=||Alpha (not used if Switch=0|
|par4||=||Switch (0 beta model, 1 2-power-law)|