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Astron. Astrophys. 359, 960-966 (2000)

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2. X-ray observations

The X-ray observations were obtained with the ROSAT X-Ray Telescope (Trümper et al. 1991) in combination with the High-Resolution Imager (HRI, David et al. 1995). The log of the observations is given in Table 1 ; the last entry in that table is the one obtained near the BeppoSAX observations, the other entries refer to earlier observations in the ROSAT data archive. The standard data reduction was done with the Extended Scientific Analysis System (Zimmermann et al. 1996). To take into account the re-calibration of the pixel size (Hasinger et al. 1998), we multiply the [FORMULA] pixel coordinates of each photon with respect to the HRI center with 0.9972. Then a search for sources is made by comparing counts in a box with the counts in a ring surrounding it, and by moving this detection box across the image. The sources thus detected are excised from the image and a background map is made for the remaining photons. A search for sources is made by comparing the number of photons in a moving box with respect to the number expected on the basis of the background map. Finally, at each position in which a source was found, a maximum-likelihood technique is used to compare the observed photon distribution with the point spread function of the HRI (Cruddace et al. 1988). The resulting countrates for significant detections near the centre of each image are given in Table 1.


[TABLE]

Table 1. Log of the ROSAT HRI observations of NGC 6440. For each observation we give the JD at start and end of the exposures and the effective exposure time, and the number of counts and the countrate for the central source, according to the standard reduction. Errors for detections are 1-[FORMULA]; the upper limits are 2-[FORMULA].


2.1. The 1998 observation

No source is detected in the 1998 Sep 8 observation. For a point source at the center of the image, 90% of the photons arrive within a circle with a 5" radius, in stable HRI pointings (David et al. 1995). At the time of observation the ROSAT satellite pointing was experiencing difficulties, effectively extending the radius of the point spread function by a few arcseconds. We therefore search a circle with a 10" radius around the center of NGC 6440 (according to Picard & Johnston 1995; see Table 3), only five photons are detected. The maximum of five photons detected remains if we move the center of the circle to any location within 30" of the nominal cluster centre, thus allowing for possible inaccurate reconstruction of the satellite pointing.

For an expected number of 10 photons, the Poisson probability of detecting 5 or fewer photons is 7%. We thus take 10 photons as the 2-[FORMULA] upper limit, which for the exposure of 1940 s gives an upper limit for the count rate of 0.005 [FORMULA]. To convert this countrate into a luminosity we use one of the fits made to the BeppoSAX data by in 't Zand et al. (1999), viz. a sum of a black body with temperature [FORMULA] keV and a bremsstrahlung spectrum with temperature 46.6 keV, absorbed by a column [FORMULA]. In the ROSAT bandpass of 0.5-2.5 keV the bremsstrahlung and blackbody components contribute 83 and 17%, respectively, to the total flux. For this spectrum, the upper limit of 0.005 [FORMULA] in the HRI corresponds to an X-ray luminosity of [FORMULA] between 0.5 and 2.5 keV, or [FORMULA] between 2 and 10 keV. Note that the ROSAT range from 0.1-2.5 keV is effectively limited to above 0.5 keV because of the high reddening. Since SAX measures the flux down to 2 keV, the estimates of the ROSAT flux are quite accurate.

This implies that the flux of the transient in NGC 6440 dropped by a factor 250 or more between the BeppoSAX observation on Aug 26 and the ROSAT HRI observation on Sep 8.

2.2. Earlier ROSAT observations: standard analysis

The ROSAT data archive contains several hitherto unpublished observations of NGC 6440 made with the ROSAT HRI after the 1991 observation reported by Johnston et al. (1995). A list of all ROSAT observations is given in Table 1. We have analyzed each observation separately with the standard procedure, and detect the source in NGC 6440 in the 1993 observation and in the Sep 1994 observation, i.e. in the observations with the longer exposure times. In the shorter observations, we only obtain upper limits. From the observed number of 3 counts in a circle with 5" radius near the cluster center we derive an upper limit to the countrate of 8 counts for the central source for both the 1992 and the March 1994 observation. The three detections are compatible with a constant countrate, at a level below the derived upper limits. We therefore have no indication of variability between the ROSAT observations. On the other hand, a variation by a factor 2 in the countrate between the 1991 and the 1993 detections is well within the range allowed by the limited statistics.

The only source, other than the central source, detected significantly in any of the ROSAT HRI pointings, is a point source in the 1993 observation, listed as X3 in Table 3. There is no bright ([FORMULA]) optical counterpart to this source in the digitized sky survey; and no object in SIMBAD within 1´ of its position. We therefore cannot determine an accurate bore sight correction, and the uncertainty in the position of the central X-ray source is dominated by the inaccuracy of the bore sight determination, which is about 5" (1-[FORMULA]; see David et al. 1995). With this uncertainty, the three positions found for the central source in 1991, 1993 and 1994 Sep are all compatible.

For each of the two longest observations, the standard analysis indicates that the central source is extended, i.e. the distributions of the photons is not compatible with that of a single point source. No such indication is present in the 1991 observation, which has a very small number of detected counts.

2.3. Closer investigation of the central source

To establish the nature of the extension of the central source we first study the longest observation, obtained in 1993. A smoothed X-ray image of the central region of NGC 6440, shown in Fig. 1, suggests that two sources are present. They are too close to be separated by the standard analysis. We therefore implement a further analysis, based on the maximum-likelihood method (see e.g. Cash 1979, Mattox et al. 1996), as follows.

[FIGURE] Fig. 1. The central area of NGC 6440 as observed with the ROSAT HRI in 1993 March. The top frame shows the locations on the detector of the detected photons. 176 photons fall within the frame, of which about 70 are from the sources. The lower frame shows the X-ray contours obtained after smoothing with a 2-d Gaussian of width [FORMULA]. The positions of the sources in a fit with two central sources are indicated with [FORMULA]; the positions for a fit with three sources are indicated [FORMULA].

The probability at detector pixel i to obtain [FORMULA] photons when a model predicts [FORMULA] photons is described by Poisson statistics

[EQUATION]

The probability that the model describes the observations is given by the product of the probabilities for all i in the region considered: [FORMULA]. For computational ease we maximize the logarithm of this quantity:

[EQUATION]

The last term in this equation doesn't depend on the assumed model, and - in terms of selecting the best model - may be considered as a constant. Thus maximizing [FORMULA] is equivalent to minimizing L, where

[EQUATION]

Our further analysis of the 1993 ROSAT HRI observation is limited to the central [FORMULA] area, and consists of four steps, in which we fit a constant background, or a constant background plus one, two, or three sources. The values of [FORMULA] for the best models of these fits are denoted as [FORMULA], [FORMULA], [FORMULA], and [FORMULA] respectively. The significance of the nth source is found by comparing [FORMULA] with a [FORMULA] distribution for three degrees of freedom (for the flux and position of the source).

In performing the fits, we use the analytical result that the best fit has a number of model photons equal to the number of detected photons. Thus, in the model of a constant background, i.e. a constant value of [FORMULA], the optimum value of [FORMULA] is found directly by dividing the observed number of photons by the number of pixels under consideration.

In fitting a constant plus one source, we distribute the source counts around the source position according to the ROSAT HRI point spread function at the center of the detector (David et al. 1995). We then vary the background and source counts, and the source position, to minimize [FORMULA]. In doing so we keep the sum of the source and background counts fixed at the observed number.

Next, we fit a constant background plus two or three point sources. In this fit, the parameters of the first source are allowed to vary; we use a Downhill Simplex method as implemented by Press et al. (1992) to minimize [FORMULA] with respect to the 7 or 10 variables. Here again, the sum of the model counts for the background and the two/three sources is kept constant, at the observed number.

The results of this fitting procedure are summarized in Table 2 ; the resulting source positions are shown in Fig. 1 and listed in Table 3. A third source in the center is nominally significant at the 3-[FORMULA] level; however, our analysis doesn't take into account any remaining jitter in the Point Spread Function, and we consider the existence of this source not proven. Therefore, we do not list the source in Table 3 ; its position is shown in Fig. 1.


[TABLE]

Table 2. Results of further maximum likelihood analysis of the ROSAT HRI observations of two central sources in NGC 6440. For each observation we give the number of counts and the countrate for both sources X1 and X2, the significance of detection (in terms of [FORMULA] for X1, [FORMULA] for X2) and the difference in position between the two sources [FORMULA] and [FORMULA].



[TABLE]

Table 3. Positions of the SAX transient, of the three X-ray sources detected in the 1993 March ROSAT observation, of the center of NGC 6440 (Picard & Johnston 1995), and of optical variables discussed in the text. X1 and X2 are in the center of NGC 6440; X3 is not related to the cluster. The errors [FORMULA] in the X-ray positions refer only to the statistical error; the overall positional error is dominated by the uncertainty of 5" in the projection of the HRI on the sky. We also give the countrates, and for the sources in the cluster the luminosity in the 0.5-2.5 keV band.


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Online publication: July 13, 2000
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