For an input list of eboxdetect source locations, simultaneous maximum likelihood PSF fits to the source count distribution are performed in all energy bands of each EPIC telescope. A description of the main properties of the detection algorithm may be found in Cruddace, Hasinger, Schmitt (1988).
Free fit parameters are: Source location (image coordinates X_IMA, Y_IMA), source extent (Gaussian sigma or beta model core radius), and source count rates in each energy band of each telescope. The source location and source extent are constrained to the same best-fit value in all energy bands of each EPIC instrument whereas the source count rates are adjusted to their individual best-fit value in each energy band of each EPIC instrument. Derived parameters are: Total source count rate, likelihood of detection (total and in each energy band), likelihood of source extent, and up to four hardness ratios (default: three).
All detection likelihoods are transformed to equivalent likelihoods (column DET_ML of the output source table), corresponding to the case of two free parameters to allow comparison between detection runs with different numbers of free parameters (i.e., when different numbers of input images are used):
where is the incomplete Gamma function, is the number of energy bands involved, is the number of degrees of freedom of the fit ( if task parameter fitextent=yes and otherwise), and with as defined by Cash (1979). Note that is 1 for the individual energy-band detection likelihoods that are listed in source table rows with ID_BAND 0, and is equal to the total number of energy bands in the ID_BAND=0 summary rows. The equivalent detection likelihoods obey the simple relationship , where is the probability for a random Poissonian fluctuation to have caused the observed source counts. This is in agreement with the equivalent detection likelihoods as defined in task eboxdetect (column SIGMA of eboxdetect source lists). Note that for very small numbers of source counts (less than counts, Cash 1979) this relation has to be treated with caution. Therefore, it will only give a rough estimate of the number of expected spurious sources.
A summary of all the columns in the output source list can be found in Table 2 in the Section 8 on the output files.
If the parameter fitextent is set to ``yes'', the point spread function will be convolved with a source extent model, that can be set to either a Gaussian profile or a -model profile via the parameter extentmodel. In the case of extentmodel=beta, the surface brightness is calculated as
The value of the core radius is written to the column EXT of the output source list. In the case of a Gaussian extent model, is written to column EXT.
From version 4.27 on, also the extent likelihood values (EXT_ML) are corrected for the number of input images with the formalism described above.
If detection over several energy bands is performed, up to four hardness ratios are calculated from the source count rates in the individual bands (default: three). The hardness ratios are defined as follows:
where denotes the count rates in energy bands and , respectively. The energy bands and used to calculate the hardness ratios can be specified for each instrument via the parameters hrpndef, hrm1def, and hrm2def. The default band assignments (identical for all instruments) are given in the following table.
All EPIC PN source count rates and fluxes written to the emldetect source list are corrected for photons that arrive during readout of the PN CCDs and therefore are not detected on the nominal source position (out-of-time events). The correction factor is 1.0626 for PrimeFullWindow mode and 1.0223 for the PrimeFullWindowExtended mode. No correction is applied to data in other observing modes. From eexpmap v3.31 on, the OOT events correction is applied to the exposure maps in all observing modes. emldetect (v4.28 or higher) reads the keyword OOTCORR from the FITS header of the exposure maps. If OOTCORR is existing and set to ``true'', no further correction is applied by emldetect.
The band numbers , and are assigned to the individual bands by numbering the corresponding input images in the order in which they are given on the command line. It is therefore important that the ordering of the input images is consistent with the contents of hrdef to obtain meaningful hardness ratios.
Note that the source extent can only be determined reliably for relatively bright objects. If the likelihood of the source extent falls below the threshold given via dmlextmin (default: ), point source parameters are derived.
For each detected source, the output source table contains one row for each energy band of each instrument. In addition, summary rows list combined results per instrument and total. The summary rows over the energy bands for each instrument (ID_BAND = 0) contain sums of the entries in the individual energy bands, where appropriate (counts, count rates, fluxes, and detection likelihoods). Spatial parameters (positions and extent values) are identical for all energy bands and repeated in the summary row. The individual source rows are identified through the column entries ID_INST and ID_BAND in the output table (see Table 2 in Section 8). ID_INST refers to the EPIC instrument (: PN, : MOS1, : MOS2, : summary row). ID_BAND is the energy band number as defined by the ordering in which the energy bands are given on the command line. An ID_BAND value of again refers to the summary information. An ID_BAND value of stands for the XID energy band ( keV) which will only be present if the input parameter withxidband has been set to true. The upper and lower bounds of each energy band are available in the header keywords __ELO and __EHI where stands for the EPIC camera (PN, M1, or M2) and stands for the energy band number as given in table column ID_BAND. Additional keywords N_INST, _BNDS, and XID_BND specify the number of EPIC cameras, the number of energy bands for each EPIC camera, and whether XID band information is present in the source table. Note that the energy bands which constitute the XID band have to be specified for each instrument separately using the parameters xidpndef, xidm1def, xidm2def if the default values (bands and , as defined in ID_BAND column) are not appropriate.
From v4.42.5 on, a new method to treat the XID band has been introduced: With the parameter xidfixed set, emldetect can be run on one XID band image per instrument using an emldetect output list as input source list. Positions and source extent values will be kept fixed and only fluxes and detection likelihoods are determined. In this case, the input images (science images, exposure maps, background images) for the desired band (e.g. keV) have to be prepared beforehand. The parameters xidpndef, xidm1def, xidm2def are used to determine which energy bands from the input source list are used to provide the start values for the fit. Note that when using this method, the parameter withxidband should be set to ``no'', and the parameter ecf is used to set the energy conversion factors.
Simultaneous fitting of data from different instruments (i.e., all EPIC pn and MOS data) or different exposures is supported. The PSF fitting may either be performed in single-source or in multi-source mode. In multi-source mode, neighbouring sources with overlapping PSFs are fitted simultaneously. Selection of sources for simultaneous fitting is controlled by the distance parameter scut and by the parameter nmaxfit that gives the maximum number of sources to be fit simultaneously ( nmaxfit ). Sources fit simultaneously are identified in the output table through the ID_CLUSTER table column. It is also possible to fit several PSFs for each input source position by setting the parameter nmulsou to the corresponding value ( nmulsou , nmaxfitnmulsou ).
Since both multi-PSF fitting and extent fitting are CPU intensive, two methods exist to reduce the CPU requirements of an emldetect run using multi-PSF fitting. With the option withthreshold, the user can limit the application of multi-PSF fitting (as specified by nmulsou) to sources exceeding a certain threshold. The threshold is set by the parameter threshold in the input column that can be defined by the parameter threshcolumn. The column may be LIKE, SCTS, or RATE.
The second method to save CPU time for combined extent and multi-PSF fitting is provided by the option withtwostage, which is used in combination with fitextent=''true'' and nmulsou . If withtwostage is set to ``true'', emldetect will perform the fit for each source in two stages: In the first stage, one extended source is fitted to the source. Only if the extent is significant, the second stage will be performed, and a multi-PSF fit with one extended source and nmulsou point sources is applied. This withtwostage option avoids misidentification of close pairs of point sources as extended sources in most cases and significantly reduces CPU time.
Two parameters determine the image region on which a source fit is performed: The parameter ecut determines the size of the subimage used for fitting a source. The parameter scut determines the radius around each source, in which other input sources are considered for multi-PSF fitting, if the parameter nmulsou is . Both ecut and scut are given as encircled energy fractions of the calibration PSF. The actual radii in pixel units therefore change slightly with energy band and source position. Alternatively, ecut can be given as a fixed value in units of image pixels (if ecut is ). The actual value for the cutout radius for each source is listed in the column CUTRAD of the output source list.
From version 4.32 on, the maximum value of the extent fit parameter can be given via the task parameter maxextent. The unit is image pixels. Large values of maxextent can in some cases lead to spurious detection of extended sources. With the parameter minextent, the minimum extent can be specified, which is still considered to be significant. If the best fit extent is less than minextent, a point source model will be adopted for the source.
From version 5.0 onward, the parameter imagebuffersize is implemented. The main purpose of this parameter is to make the processing of mosaic-pointings more efficient, where the mosaicked sky image will contain large areas without photon data. The value of imagebuffersize characterizes the memory that is allocated for each individual image and is given in image pixels: imagebuffersize is (at least) the size of the sub-image per pointing that contains non-zero pixels (Fig. 1). Its default is , which is the side length of a typical pipeline-produced EPIC image with a bin size of arcsec.
Starting with SAS 10.0 and emldetect version 5.1, a full 2d parametrization of the EPIC PSF as a function of instrument, energy, and off-axis angle is introduced (Release Notes). The PSF model can be chosen via the parameter psfmodel. Up to version 5.17.1, the medium-accuracy PSF (psfmodel=medium) is used by default. The analytical 2d PSF (psfmodel=ellbeta) is the default value from version 5.17.2 on.