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XMM-Newton Science Analysis System


emldetect (emldetect-4.32.1) [xmmsas_20040318_1831-6.0.0]

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Description

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 (alpha, delta), 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 three hardness ratios.

All detection likelihoods are transformed to equivalent likelihoods $L_2$ (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):

$$L_2 = -\ln (1-P(\frac{\nu}{2},L')) \;\;\; {\rm with} \;\;\; L' = \sum_{i=1}^n L_i$$

where $P$ is the incomplete Gamma function, $n$ is the number of energy bands involved, $\nu$ is the number of degrees of freedom of the fit ($\nu = 3+n$ if task parameter fitextent=yes and $\nu = 2+n$ otherwise), and $L_i = C_i/2$ with $C$ as defined by Cash (1979). Note, that $n$=1 in the case of the individual energy band detection likelihoods listed in source table rows with ID_BAND $>$ 0 and $n$ is equal to the total number of energy bands in the ID_BAND=0 summary rows. The transformed detection likelihoods obey the simple relationship $L_2 = - \ln(p)$ where $p$ is the probability for a random Poissonian fluctuation to have caused the observed source counts. This is in agreement with the detection likelihoods as defined in task eboxdetect (column SIGMA of eboxdetect source lists). Note that for very small numbers of source counts (less than $\approx$ 9 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.

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 $\beta$-model profile via the parameter extentmodel. In the case of extentmodel=beta the surface brightness is calculated as

$$f(x,y)=\left(1+\frac{(x-x_0)^2+(y-y_0)^2}{r_c^2}\right)^{-3/2}$$

The value of the core radius $r_c$ is written to the column EXT of the output source list. I the case of a Gaussian extent model $\sigma$ is written to column EXT.

From version 4.27 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 three hardness ratios are calculated from the source counts rates in the individual bands. The hardness ratios are defined as follows:

$$HR_i = \frac{B_m - B_n}{B_m + B_n}$$

where B denotes the count rates in energy bands n and m, respectively. The energy bands n and m 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:

$i$	$n$	$m$
1	1	2
2	2	3
3	3	4

All EPIC PN source count rates and fluxes written to the emldetect source list are corrected for photons arriving 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.

Output source table columns

ML_ID_SRC	EMLDETECT source number
BOX_ID_SRC	corresponding EBOXDETECT input source number
ID_INST	instrument ID; 1: PN, 2: MOS1, 3: MOS2
ID_BAND	energy band number (band number 0: summary band)
ID_CLUSTER	cluster id; sources fit simultaneously have same number
SCTS	source counts
SCTS_ERR	source counts error
X_IMA	source image pixel X coordinate
X_IMA_ERR	error of image pixel X coordinate
Y_IMA	source image pixel Y coordinate
Y_IMA_ERR	error of image pixel Y coordinate
EXT	source extent, gaussian sigma or beta model core radius (arcsec)
EXT_ERR	extent error error
DET_ML	Likelihood of detection
EXT_ML	Likelihood of extent
BG_MAP	background at source location (counts/pixel)
EXP_MAP	exposure at source location (seconds)
FLUX	source flux (cgs units)
FLUX_ERR	source flux error error
RATE	source count rate (counts/sec)
RATE_ERR	count rate error
RA	source right ascension (degrees)
DEC	source declination (degrees)
RADEC_ERR	error (arcsec)
LII	source galactic longitude (degrees)
BII	source galactic latitude (degrees)
RAWX	raw X source coordinate
RAWY	raw Y source coordinate
CCDNR	chip number
HRn (n=1..3)	hardness ratios 1..3
HRn_ERR (n=1..3)	hardness ratio error
CUTRAD	source cut out radius
EFF	encircled energy fraction
VIGNETTING	vignetting
DIST_NN	distance to nearest neighbour (arcsec)
VAL_FLAG	V&V flags
VER_FLAG	V&V flags
VER_COMM	V&V comment

The band numbers n, and m 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 a threshold, 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 instruments (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 where ID_INST refers to the EPIC instrument (1: PN, 2: MOS1, 3: MOS2, 0: summary row) and 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 0 again refers to the summary information. An ID_BAND value of 9 stands for the XID energy band (0.5 - 4.5 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 aa_n_ELO and aa_n_EHI where aa stands for the EPIC camera (PN, M1, or M2) and n stands for the energy band number as given in table column ID_BAND. Additional keywords N_INST, aa_BNDS, and XID_BND specify the number of EPIC cameras, 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 2 and 3, as defined in ID_BAND column) are not appropriate.

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 sources with overlapping PSFs are fitted simultaneously. Up to six neighbouring sources may be fitted simultaneously. Selection of sources for simultaneous fitting is controlled by a distance parameter (scut) and the maximum number of sources to be fit simultaneously (parameter nmaxfit. Sources fit simultaneous are identified in the the output table through the ID_CLUSTER table column. It is also possible to fit several PSFs (up to three) for each input source position by setting parameter nmulsou to the appropriate value.

If parameter usecalpsf is set to true (this is the default) PSF fitting is performed using a tabulated energy and position dependent PSF as provided in the calibration database (accuracy level = medium). Alternatively, an internal, hardcoded PSF as specified in section ``Algorithm'' is used. The hardcoded PSF consists of a superposition of four Gaussian profiles with an off-axis dependent width. It is axially symmetric and currently has no energy dependence. Right ascension and declination of the optical axis positions used for the calculation of the off-axis angles are stored in keywords with the names OARAaann and OADEaann where ``aa'' designates the EPIC camera (PN, M1, or M2) and ``nn'' is a running number. Note that the $\beta$-model source extent function (extentmodel=beta) can only be used with the CAL PSF (usecalpsf=true).

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 parameter nmulsou is $>1$. Both ecut and scut are given as encircled energy fraction of the calibration PSF. The actual radii in pixel units therefore change slightly with energy band and source position. The actual value for the cutout radius for each sources is listed in the column CUTRAD of the output source list.

From version 4.32 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.