XMM-Newton Science Analysis System


region (region-7.15.3) [xmmsas_20230412_1735-21.0.0]

The contour method of calculating source region shape

When radiusstyle=`contour', the task calculates the source region shape as an elliptical locus which approximates the contour of the PSF at a given flux value. The procedure uses an analytical model of the PSF which has the following form:

$$PSF(x,y) = A \, exp\Big(-\frac{x^2 + [y/s]^2}{2\sigma^2}\Big) + \frac{(1-A)}{(x^2 + [y/s]^2)^\alpha}$$

where $A$, $\sigma$, $s$ and $\alpha$ depend on the source position in the FOV. The $(x,y)$ coordinate system employed here is transformed into DETXY by addition of $(r_0=\sqrt{x_0^2 + y_0^2},0)$ followed by rotation through an angle $arctan(y_0/x_0)$ where $(x_0,y_0)$ is the centre of the source in DETXY.

Flux contours of the model given above have elliptical shapes. Clearly, in order to calculate the shape of such a flux contour, it is necessary firstly to normalize the PSF to the source brightness and secondly to determine the flux level (in `brightness' units per pixel) at which to find the contour. Note that the units must be compatible: if the source brightness is specified as total counts, for example, then the flux level must be in counts per pixel.

Ideally the source brightness would be specified by allowing the user to supply (via a command-line parameter) the name of the column of the source list which contains such information. However this facility is not yet in place: at present the task is `hard-wired' to look for source brightness in a column of the source list named SCTS. If there is no column of this name in the source list then the radiusstyle=`contour' style cannot be used.

Matters are more flexible as far as specifying the flux level is concerned. The flux level is given in terms of a local background flux level and a multiplying constant. There are several ways in which the user can specify the first of these, the selection being governed by parameter bkgratestyle. The multiplying constant is specified via parameter bkgfraction.

bkgratestyle will eventually provide four choices (`col', `kwdset', `image' and `user') but at present this functionality is only partially realized and the only choices the task will accept are `col' or `user'. These are described as follows:

• bkgratestyle=`col'. In this choice, the task looks for a column in the source list named BG_MAP. In future the user will be able to specify a different name via the parameter bkgratecol, but at present this parameter is not read by the task.

• bkgratestyle=`user'. In tbis choice, the user must supply the background flux (at present the units must be counts per pixel so as to match the source brightness which is tied to column SCTS) via the parameter bkgrateuser.

Notes:

• The background flux $\times$ bkgfraction must evaluate to greater than zero. If not, a warning will be issued and no regions constructed for that source.

• It is of course possible for the specified flux level to exceed the maximum value of the normalized PSF (for instance if the source is faint and background bright). In this case the region is of zero size.

• If it is desired to set the region size in this way, but retain the circular shape, then the user should select nosrcellipse=`yes'. This gives circular source regions with radii equal to the long semi-axes of the respective ellipses.

• Advantages of the choice radiusstyle=`contour' are:
  1. The size of the source region follows the brightness of the source - ie, brighter sources have larger extraction regions.
  2. The shape of the source region follows (approximately) the distortion of the off-axis PSF. NOTE however that this mapping of the PSF shape distortion IS at present only approximate. In future it is hoped to be able to determine it in a more systematic way.

• This choice of radiusstyle cannot as yet be used unless outunit=`xy'.