4 Source extraction, simulations

An important part of the present work is the extraction of the sources, the simulation of point source observations and the analyses of noise. After detecting sources on a median-filtered-like map, we measure the fluxes on the final maps with aperture photometry. Our simulation tool validates the flux determination as well as the noise analysis.

4.1 Source extraction

Our original maps are dominated by the fluctuations of the background at 170 $\mu$m, at all spatial scales, mainly due to the cirrus confusion noise and the CIB fluctuations (Lagache & Puget 2000). Because of this, classical extraction algorithms based on thresholding and local background determination mostly fail: it is not easy to use a robust detection algorithm on maps dominated by structures at all scales. On the contrary, flat background maps allow reliable detection with the available processing techniques, like Gaussian fitting methods, e.g. for faint ISOCAM sources by Désert et al. (1999). Because of the undersampling of the PHT Point Spread Function together with a highly fluctuating background, CLEAN-like methods (Hogbom 1974) are difficult to use. Wavelet decomposition, e.g. for ISOCAM by Starck et al. (1999), is not easily implementable because of the poor spatial dynamics of our maps ("big pixels and small maps''). To overcome these difficulties we have developed the following method by combining some well-known techniques for source extraction and flux determination:

Figure 2: Example of a source map for source detection in the FSM field. Background is subtracted using a median filter in the time space (AAP). Data with only high spatial frequencies are then reprojected on a map with the FIRBACK pipeline.

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background is subtracted in the one dimensional time data (AAP level, brightness as a function of time) using a median filter (size: 5 positions) to create source time data;

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source time data are processed to create 2-dimensional source maps (Fig. 2) through the FIRBACK pipeline as decribed in Sect. 3;

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source detection is performed on the source maps using SExtractor (Bertin & Arnouts 1996);

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flux measurements are performed on the unfiltered maps, using aperture photometry at the positions found by the source detection only if there are at least 4 different observations, and make a temporary version of the source catalog;

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by subtracting iteratively the brightest sources from the temporary catalog using a CLEAN-like method on the final maps, we remeasure with better accuracy the flux of the sources which have bright neighbours. This gives the final catalog after two more corrections: short term transient of 10%, and flux offset of about 15% derived from simultation (see Sect. 5).

Source detection is performed using SExtractor version 2.1.0 on the source maps with the parameters given in Table 3. Note that we do not use the background estimator and set it to a constant value because source maps are flat maps containing fluctuations due to resolved sources, since the background has been filtered. Only the positions in the map of the detected sources will be used in the output catalog computed by SExtractor (e.g. not the flux). We discard the edges by considering only parts of the sky that have been observed at least 4 times. This reduces the total area by about 5%.

 

 

Table 3: Parameters used in SExtractor 2.1.0 applied on the Source Maps.

Parameter	Value
DETECT_MINAREA	10
DETECT_THRESH	3.0
BACK_SIZE	10
BACK_FILTERSIZE	1,1
BACK_TYPE	MANUAL
BACK_VALUE	-0.04,0.0

4.2 Simulations

We have developed a simulation tool of point sources in order to validate the flux determinations and study source completeness of our survey. Kawara et al. (1998) did not make such simulations and Juvela et al. (2000) only tested the significance of their source detection because of a lack of redundancy in their observations. The work of Efstathiou et al. (2000) included large simulations at 90 $\mu$m, but the source detection is performed by eye.

Thanks to the quiet behaviour of the C200 camera at 170 $\mu$m, together with redundancy, the detector noise as well as effects induced by glitches can be neglected to first order with respect to the confusion noise. (This is unlike conditions applying to the C100 camera (Linden-Vornle et al. 2000).)

Here, we present a summary of our simulation process, followed by some details concerning the addition of the sources and the validation:

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select a random sky position for a simulated source inside a FIRBACKfield;

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add the source in each raster in AAP level which has observed the source itself or its wings;

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process maps through the FIRBACKpipeline;

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extract sources with SExtractor;

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identify the extracted sources by comparing the coordinates with the input catalog;

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compute a flux with aperture photometry using the effective footprint (defined in Sect. 5.1);

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validate on different flat backgrounds;

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validate on real data: different input fluxes and positions.

Figure 3: Example of the addition of 500 mJy sources in the FSM field. There are 8 sources spread randomly throughout the field. One example is near the center of the eastern survey square (FSM1).

4.2.1 Adding the sources

We use the best footprint available for PHT at 170 $\mu$m (Lagache & Dole 2001) to simulate a source with a known input flux; its spatial extension is taken to be a five pixel square, that is about $7.7' \times 7.7'$ (note that the PIA footprint profile given in the calibration files extends to only 4.2 arcminutes). This simulated source is added in the one dimensional time data (AAP level). To avoid biases due to specific positions in the fields, we select random positions.

Because we have either 2 or 4 different raster observations of the same parts of the sky, the randomly-selected sky position may fall e.g. on the edge of a pixel in one raster, and at the center of another pixel in another raster. We thus make the following approximation: we cut each PHT pixel in 9 square sub-pixels of about $30.7 \times 30.7$ square arcseconds. We compute the pixelized footprint for the nine configurations corresponding to the cases where the source center falls on one of the sub-pixels.

We make separate realizations for 8 input fluxes (100, 150, 200, 300, 500, 650, 800 and 1000 mJy) and create maps using the FIRBACKpipeline. We add only between 6 and 20 sources per square degree at a time depending on their flux, in order to avoid changing the confusion level when sources are added in the data. We compute the needed number of maps to get 1200 realizations for each flux in each field, or 28800 sources in total, in order to have a statistically significant sample. We finally get about $2 \times 1230$ different simulated maps per field (1 final map + 1 source map for each realization) taking about 14 Gbyte, after about one week of computation under IDL on a MIPS R12000 at 300MHz SGI. Figure 3 shows an example of added sources.

4.2.2 Validation

We extract sources on the final maps and compute fluxes as explained below by aperture photometry. The aperture photometry filter parameters have been optimized to obtain the best signal to noise ratio using the simulations.

The validation is performed on flat background maps with different surface brightness values (0.01, 3 and 10 MJy/sr), to check that the recovered flux does not depend on the background. The difference between the input and recovered flux is less than 1% on an individual raster when the source is centered on a pixel. When using random positions of the sources and 2 or 4 rasters co-added, the recovered fluxes have a dispersion explained by the "edge effect'' (due to the dilution of the flux in other pixels when the source falls on the edge of a pixel) and by the poor sampling of the sky, leading to an overall uncertainty of 10%.