3 Data reduction

Data reduction took place in two centers: the Paris Data Analysis Center (PDAC) and the Leiden Data Analysis Center (LDAC). PDAC pre-processed the raw data and LDAC extracted and parametrized objects ranging from point sources to small extended sources. The reduction at LDAC by the first author led to the detection of numerous technical problems (astrometry for example), which had escaped the checks of the automatic pipeline. Compared to the first relase of DENIS data (Epchtein et al. [1999]) this catalogue differs in terms of flags, astrometric reference catalogue, association criteria and photometric calibration (use of the overlapping region between adjacent strips). Besides, our catalogue covers a portion of the sky not overlapping with the first DENIS data release. The source list (Table 7) and the photometric information (Table 8) are electronically available at CDS via this catalogue. With further DENIS data releases data on a strip by strip basis, therefore not merged into a single catalogue without treating the overlapping regions in terms of photometry and astrometry, will also be available. This means that all the strips covering the same region of the sky regardless of their quality will be available; multiple entries for a single objects could then be retrieved. We show in Sect. 3.2.3 the consistency of our calibration within each cloud.

The work of Fouqué et al. ([1999]) focuses on the absolute photometric calibration of the DENIS data. This calibration, once completed after the termination of the survey, might induce a systematic shift on the photometry of the present catalogue.

3.1 PDAC: Paris Data Analysis Center

At the PDAC the images were corrected for sensitivity differences and atmospheric and instrumental effects. Their optical quality was judged on the basis of the parameters that describe the point spread function (see Sect. 3.1.2).

3.1.1 Flat and bias

The received intensity from the target image also contains background contribution from the telescope and the atmospheric radiation. Besides, the sensitivity varies across the array of the camera. The true signal (TS) for the pixel i,j is obtained from:

$$TS_{i,j} = I_{i,j}(t)-F_{i,j}\times b(t) - B_{i,j}\, ,$$ (1)

where I_i,j is the measured intensity after subtraction of dark currency, F_i,j is the flat field after dark subtraction, b(t) is the background and B_i,jis the bias level. The background is estimated per image, at time t, with

$$b(t)=\frac{\sum_{ij}^{N}[I_{i,j}(t)/F_{i,j}]}{N}\, ,$$ (2)

where N is the total number of pixels per image. At this stage the flat field and the dark current values estimated from the previous night are used. Points outside the $3\sigma$ level are rejected in the sum. The four I quadrants are treated separately. This is also done for each of the 9 sub-images in the J and $K_{\rm s}$ bands.

As a second step we select low-background images from the sunrise sequence (180 in a normal strip) with a low background value. To identify and avoid crowded fields and fields affected by saturated stars we combine measurements taken during different nights. We then determine the flat F_i,j and the bias B_i,j by minimizing the expression:

$$\sum_{t=1}^{N} [I_{i,j} (t)- F_{i,j} b (t) - B_{i,j} ]^2\, ,$$ (3)

where N is the number of selected images ($\leq 180$). In the third step, we applied the new values of the flat and the bias to the set of selected images to obtain a new estimate of the background value, more appropriate to the particular night. The quality of the determination of the parameters involved is improved by iteration of the above procedure.

The bias so far determined is a mean value for the night. Because it varies during the night, its value for a given strip is estimated to be:

$$B_{i,j} = \frac{\sum_{t=1}^{N}[I_{i,j} (t)- F_{i,j} b (t)]}{N}\, ,$$ (4)

where N is the total number of images per strip (180). After dark subtraction, the bias contains only the contribution of the instrumental and atmospheric emission which does not affect the Iband, but does affect strongly the $K_{\rm s}$ band and a higher number of iterations is sometimes necessary.

The large number of available flat/bias-images (180) gives a quite high degree of statistical confidence to both determinations. This is not true in case of calibration sequences that involve only 8images. In this case, the bias determined for the strip nearest in time is applied.

3.1.2 Point spread function

The pixel size of the J and $K_{\rm s}$ channels is $3\hbox{$^{\prime\prime}$ }$ and the sampling is $1\hbox{$^{\prime\prime}$ }$ in both directions. The real width of any point source is therefore potentially narrower than the pixel ( $3\hbox{$^{\prime\prime}$ }$). In terms of signal processing the sources are not under-sampled, but the width of the filter is broader than the sampling. To estimate the width of the signal the convolution of the signal profile (assumed to be elliptical) and the pixel size has been taken into account. The method of least squares has been applied to the projection of sources onto RA, DEC and diagonal axes (Borsenberger [1997]). In the Iand the J bands there are enough sources to build a model that describes the behaviour of the projected widths in each image. In the $K_{\rm s}$ band several images were stacked together prior to the determination.

We refer to http://www-denis.iap.fr/docs/tenerife.html for more details on the PDAC data reduction.

3.2 LDAC: Leiden Data Analysis Center

LDAC extracts point sources from the images delivered by PDAC. From these sources, it derives and then applies astrometric and photometric calibration to obtain a homogeneous point source catalogue. The astrometric reference catalogue is the USNO-A2.0 (Monet [1998]) that provides on average 100 "stars'' per DENIS image. The photometric DENIS standard stars belong to different photometric systems of which the major ones are: Landolt ([1992]), Graham ([1982]), Stobie et al. ([1985]) and Menzies et al. ([1989]) in I; Casali & Hawarden ([1992]), Carter ([1990]) and Carter & Meadows ([1995]) in J and $K_{\rm s}$. An absolute calibration, together with a definition of DENIS photometric bands is given by Fouqué et al. ([1999]).

3.2.1 Source extraction

The first LDAC task is to reduce the information from each image into an object list. This is done using the SExtractor program (Bertin & Arnouts [1996]) version 2.0.15.

3.2.2 Astrometric calibration

Positions are determined through pairing information among frames, channels and with the reference catalogue. The astrometric solution makes use of the fact that each map has an area of overlap with neighboring maps, and that objects in the overlapping region have been observed many times. The projected position of the multiply observed sources, in terms of their pixel positions, contains information on the telescope pointing and the plate deformations. The plate deformation is derived through a triangulation technique, matching bright extracted objects with astrometric reference objects. The resulting global solution for each strip takes into account possible variations along the strip. The plate offsets are determined using all but the faintest extracted objects, matching among channels (wave bands) and in overlap. A least square fitting technique is then applied to the functional description of the detector deformation and its variation to obtain the full solution on the basis of the pairing information. Thereafter, the celestial position, its error and the geometric parameters of each object are calculated.

The standard position accuracy derived is RMS 0.001 arcsec with maximum excursions of 1.32 arcsec. This error is in addition to the RMS of 0.3 arcsec of the astrometric reference catalogue.

3.2.3 Photometric calibration

Magnitudes are estimated within a circular aperture of $7\hbox{$^{\prime\prime}$ }$ in diameter after a de-blending process, that determines which pixels are within the aperture, and what fraction they contribute to each individual source (Bertin & Arnouts [1996]). This aperture collects $95\%$ of the light when considering a seeing of $1.5\hbox{$^{\prime\prime}$ }$and the pixel size of $3\hbox{$^{\prime\prime}$ }$ for the infrared wave bands. For homogeneity we used the same aperture also for the I band. The source magnitude (m) corresponding to the wavelength $\lambda$ is defined as:

$$m_{\lambda} = -2.5\log(S_{\lambda}) + m_{\lambda0}\, ,$$ (5)

where $S_{\lambda}$ is the observed flux and $m_{\lambda0}$ defines the zero-point of the magnitude scale at the wavelength $\lambda$. The determination of the instrumental quantity $m_{\lambda0}$ to correct the stellar magnitude for atmospheric effects is done on a nightly basis. First, standard star measurements are matched with the information stored in the standard star catalogue. Second the instrumental zero-point ( $m_{\lambda0}$) is derived for each of the eight measurements of the standard star assuming a fixed extinction coefficient, $\epsilon$ (Eq. 6). The adopted values of $\epsilon$ are 0.05 for the I band and 0.1 for both the J and $K_{\rm s}$ bands. These values have been determined from the photometric measurements performed during calibration nights (nights where only standard stars were observed).

$$m_{\lambda0} = 2.5\log(S_{\lambda}) + m_{\lambda \mathrm{ref}} + \epsilon \times z\,$$ (6)

m_ref is the magnitude of the standard star from the standard star catalogue and $S_{\lambda}$ is the flux as measured at a given air mass (z). Standard stars were selected near the airmass limit of the strips and to be roughly of the same spectral type; this simplifies the Taylor expression used to describe the extinction law because colour terms (Guglielmo et al. [1996]) and the non-linear terms are of minor importance; in the infrared the dependence of the extinction on z is almost linear for z<2. In principle, both $m_{\lambda0}$ and $\epsilon$ can be determined simultaneously and the non-linear terms can be incorporated as well if a sufficient number of star measurements are available, but for a single night there are not enough, in fact the use of the approximated law (Eq. 6) gives a systematic offset between the magnitude of the source in the overlap of two strips of comparable, but different, photometric conditions. After a considerable investigation it turned out that this offset could be greatly reduced if a fixed extinction coefficient is used. Some differences are left when the observations have been performed in different photometric conditions or when too few standard star measurements were done. Figure 1 shows the computed differences between the magnitudes of the sources detected in the overlapping region of two strips observed under comparable photometric conditions ((a), (b), (c)) and of two strips observed with different photometric conditions ((d), (e), (f)) in the I, J and $K_{\rm s}$bands, respectively. Faint sources give rise to a larger dispersion. The systematic shift is clearly visible in Figs. 1d-f.

Figure 1: Magnitude differences of overlapping sources, between strip 4944 and strip 4945 observed under good photometric conditions a, b, c) and between strips 6997 and 7004 d, e, f), strip 7004 was observed under poor photometric conditions

The final nightly value of $m_{\lambda0}$, for each wave band, is calculated by averaging the single determinations for each standard star and among all the standard stars observed during that night, after removal of flagged (Sect. 4) measurements (this reduces on average the number of measurements per star from 8 to 6). The flagged measurements have a non-zero value for at least one of the types of flag considered in the pipeline reduction. Only standards fainter than I=10.5, J=8.0 and $K_{\rm s}$ = 6.5 mag are used. The instrumental $m_{\lambda0}$ and its standard deviation are listed for each strip in the quality table (Table 8). Mean values ( $\pm 1\sigma$) are: $23.42\pm 0.07$ (I), $21.11\pm 0.13$ (J) and $19.12\pm 0.16$ ($K_{\rm s}$).

Using the overlapping regions of adjacent strips to correct for remaining differences we performed a general photometric calibration, separately for the LMC and for the SMC. We calculated the magnitude difference of cross-identified sources between two adjacent strips of sources detected in three wave bands. The histogram of these differences in magnitude shows when a systematic shift is present between the two strips (Fig. 1). In only a few cases is the average magnitude affected by more than 0.1 mag. If necessary we applied a systematic shift (Table 8). Experience showed that if a strip is poorly calibrated the magnitude difference in the overlap with the previous strip has a sign opposite to the difference found in the overlap with the next strip. Note that observing a strip in good photometric conditions but having too few standard star measurements to perform the calibration may induce alone this offset; the equal number of detected objects as a function of magnitude per band in both strips indicates, as just mentioned, a minor difference in the photometric conditions under which each strip was observed, increasing the confidence we place in the correction procedure. Only 9 strips out of 108 for LMC observations and 3 strips out of 81 for SMC observations show this behaviour. Sources with corrected magnitude are easily recognized from their strip number associated to each detected band (Table 7). Table 8 reports the amount of the applied shift as a function of strip number. In some cases, the difference shows a dependence on declination, but the effect on the averaged magnitude, in the area of the Magellanic Clouds, is not significant (less than 0.1 mag), and can be ignored. The internal statistical RMS error is between 0.001 and 0.4 mag at the detection limit, faint sources have larger errors. For completeness we included in the catalogue sources detected above and below the reference saturation and detection limits, their photometric errors (larger than 0.4 mag) show the confidence of the detection. The standard deviation on $m_{\lambda0}$ is in most of the strips below 0.05 mag, but spreads from 0.01 to 0.2 mag. Larger values are detected in the strips where a photometric shift was also applied, therefore the resulting accuracy is, for these few cases, not better than 0.1 mag. In all other cases the resulting accuracy has an RMS error better than 0.05 mag.

3.2.4 Association

All extracted objects are matched on the basis of their geometrical information assuming an elliptical shape (RA, DEC, a: semi-major axis, b: semi-minor axis, $\theta$: inclination angle) within one wave band, among the three wave bands within a strip and among different strips. The geometrical parameters of each object are evaluated at the $3\sigma$ level of the row image; a and b are the second order moments of the pixel distribution within the size of the photometric aperture. Typical values are $1.8\hbox{$^{\prime\prime}$ }$, $1.0\hbox{$^{\prime\prime}$ }$and $0.5\hbox{$^{\prime\prime}$ }$ for the I, J and $K_{\rm s}$ band, respectively, differences among the three wave bands mainly depend on the differences in sensitivity; the second order moments characterize the PSF. The effective area used during the association procedure is 1.5 times (tolerance) the area defined by the a and b values of both object, when the association is performed within each band of a strip. Sources previously de-blended are not associated. When the association is done among different bands the tolerance value increases to 2.5.

We associate two objects when the center position of one of them is within the bounds of the ellipse of the other, even if the center of the second is outside the ellipse of the first one, and vice versa. For the coordinates, we always used a weighted average (based on the signal to noise ratio and detection conditions as derived from the source extraction program and the astrometric calibration). For the magnitudes we decided not to average or to combine magnitudes from different epochs (strips) because of the possible variability of a large fraction of the detected objects. Objects associated within the same strip are given with the average of the magnitudes. When the association involves overlapping strips we distinguish the following cases: (1) for objects detected in all three wave bands in both strips we choose the entry from the strip with the lowest value of $\sum_{i=1}^{N}\sqrt{a_ib_i}$, where N is the number of sources detected in the overlap; (2) for objects detected in an unequal number of wave bands, we chose the entry from the strip with the highest number of detected wave bands; (3) for objects detected in two different wave bands we choose the entry from the strip with the lowest $\sum_{i=1}^{N}\sqrt{a_ib_i}$, including the third magnitude from the other strip. When the strip numbers of the detected wave bands differ the observations refer to different epochs. The criteria given conserve the major property of the DENIS data: simultaneousness.

We refer to ftp.strw.leidenuniv.nl/pub/ldac/software/ pipeline.ps for more details on the LDAC data reduction.