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Astron. Astrophys. 362, 105-112 (2000)

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2. The X-ray observations

PKS 2155-304 was observed with the ROSAT HRI in 1996 from May 12, UT 21:11 to May 22, UT 21:52. A total of 80 pointings yielded an overall accepted time of [FORMULA] 33.4 ksec. The aim of the observations was to have as dense temporal spacing of observation intervals as possible, i.e., one pointing in every orbit. However, due to scheduling constraints larger gaps could not be avoided. The second observation run took place from November 23, UT 01:55 to November 25, UT 08:44 for a total of [FORMULA] 53 ksec in nine orbits. Correspondingly, the spacing of these data is much closer.

No other known object was seen in the field of view of the HRI. The quasar 2155-302 is not detected and the second brightest source, at a position of RA=[FORMULA]; Dec = [FORMULA] 00´ 16", about 15 arcmin away from PKS 2155-304, has a count rate of [FORMULA] cts s-1 and is optically unidentified.

The Rossi XTE observations overlap with the HRI pointings reasonably well, both in May and in November. In May, a simultaneous stretch of EUVE observations was obtained, as well as 14 pointings with ISO, covering the time May 13 to June 8 (Bertone et al. 2000). Unfortunately, the IUE satellite failed about two weeks prior to the observations.

2.1. Light-curves

Light curves were produced by using standard procedures from the EXSAS environment (Zimmermann et al. 1996). Source photons were extracted from a circle with 250" radius around the source center; the background was taken from the outer source-free region of the detector and amounted to typically less than 5% of the source counts.

In Fig. 1 we show a histogram of the background subtracted source counts radially integrated outwards from the center of the source. As there is clearly a residual rest - wobble visible in the slightly non-circular HRI image we used the above large extraction radius which then contains more than 99% of the photons from the source. The photons were corrected for vignetting and dead time and binned in 1 sec intervals. This turned out to be necessary as the accepted time intervals are frequently disrupted by short gaps. Finally, the binned data were summed up and used only if continuous stretches of more than 30 secs of data were obtained.

[FIGURE] Fig. 1. Background subtracted, normalized fraction of HRI counts as function of the radius from the source center. The total data of the May 1996 observation were used.

The WFC observations yielded 32.9 and 41.0 ksec of good observation time for the May and November 1996 pointings, respectively, with an average count rate of [FORMULA] s-1, similar to that of the November 1991 observation. The WFC light curves were extracted as follows: to improve the statistics, the individual short observation slots were first re-binned into sufficiently long (2-3 ksec), contiguous observation intervals. Then the number of photons within a circle with radius 10´ centered on PKS 2155-304 were counted for each of the individual observation intervals. The number of background photons was determined from an annulus with inner radius 15´ and outer radius 30´. The source count rate in each time interval was then calculated by subtracting the vignetting corrected number of background photons (normalized to the source extraction area) from the source photons and finally dividing it by the length of the individual observation interval.

In Fig. 2 we show the HRI light curves of the May 96 (top panel) and November (bottom panel) observation as full dots. As the individual data intervals are of different length, between 30 sec and about 2000 sec, the statistical errors of the count rates vary, and in some cases they are smaller than the symbol sizes. The open squares in both panels represent the WFC count rates, multiplied by a factor of 200. Although the WFC light curves generally follow the intensity variations of the HRI their statistical significance is too low to allow any more quantitative conclusion about the behavior of the very soft X-rays.

[FIGURE] Fig. 2. HRI light curves of PKS 2155-304 in May 1996 (top) and November, 1996 (bottom). The full dots are the HRI data, open squares the WFC data, multiplied by a factor of 200.

The light curve of May 1996 shows variations as large as a factor of two in two days and a longer stretch of less variability ([FORMULA] 20% amplitude). In November, the flux level was comparable but the variations are modest, about [FORMULA] 20%, as in the PSPC observation of November '91 (see Sect. 2.2). However, note that these data are taken over only about 2.5 days and that there is a general decline in the average intensity.

Apart from some short time scale intensity fluctuations, which partly show large statistical uncertainties of the count rate determination, the long term light curves are rather smooth and do not show sharp, isolated flares, such as seen in May 1994 with ASCA. Despite several gaps due to the satellite scheduling constraints the two observations represent the most extended and complete light curves ever taken of the object.

2.2. Comparison with previous ROSAT observations

In the ROSAT soft X-ray band PKS 2155-304 is the by far best studied BL Lac object. Several observation campaigns have been conducted between 1991 to 1996. Table 1 gives a summary of these observations. In total nearly 175 ksec have been spent on the source, first with the PSPC detector and since 1994 with the HRI.


Table 1. ROSAT observations of PKS 2155-304

We re-analyzed all data and present in Fig. 3 the long term light curve of PKS 2155-304 as seen by ROSAT. Every data point represents a 400 s (one wobble period) average. For a comparison of the source intensities we converted the measured PSPC count rates into `equivalent` HRI count rates. The conversion factor was determined by comparing the count rates obtained by folding the typical, soft X-ray spectrum with the PSPC and the HRI detectors. As reference spectrum we used an average power law obtained in the November, 1991 observation (Brinkmann et al. 1994, Table 2, OBI 3: photon index [FORMULA], [FORMULA] cm-2). With these values the count rates can be related via [FORMULA].

[FIGURE] Fig. 3. Light curve of PKS 2155-304 between 1990 and 1996 as observed by ROSAT. Plotted are the HRI count rates as a function of time; every data point corresponds to a 400 s observation interval.

Long-term spectral variations should not change the conversion factor significantly as they seem to occur predominantly at higher X-ray energies (Sembay et al. 1993). Further, in both detectors the soft source has its maximal count rate at similar energies, below [FORMULA] 1 keV. We tested the range of variations of the conversion factor by changing the spectral power law index by [FORMULA] 0.3 from the above value which results in changes of the conversion factor by [FORMULA] 0.022 (the numerical factor gets smaller for a steeper power law). This uncertainty in the count rate conversion of less than [FORMULA] 10% is thus only a minor effect which can be neglected in the following discussion.

During the All-Sky Survey the source was found at an average intensity of about 39 cts s-1 in the PSPC. The power law slope was [FORMULA] and the object varied by about [FORMULA] 20% during the [FORMULA] 1.5 day Survey coverage; in Fig. 3 we plot the maximum and minimum rates with the errors during the corresponding individual orbits.

Overall, PKS 2155-304 showed a total variability by factors of [FORMULA] 3 - 4 with an average HRI count rate of [FORMULA] 10 cts s-1, corresponding to a soft X-ray luminosity of [FORMULA] erg s-1, assuming the above spectral parameters. The largest flux was observed in the May 1993 observation with a maximal PSPC count rate of more than 99 cts s-1, the lowest in November 1992 with [FORMULA] 22 cts s-1. In both cases the spectrum could not be fit with a single power law but with broken power laws with break energy around 0.7 keV. The high intensity spectrum is flatter at low energies and steeper at high energies. The photon indices are ([FORMULA]; [FORMULA]) and ([FORMULA]; [FORMULA]), respectively. The largest variability seen in a single observation campaign occured in November 1994 when the count rate varied by a factor of 2.7 between two HRI pointings [FORMULA] 21 days apart.

While over several years the historical amplitudes of variability have spanned a range of a factor of [FORMULA] 4.5, PKS 2155-304 varies nearly as much over much shorter periods (factors of 2 in hours - days), thus showing that the dominant time scales in this blazar are truly quite short. Apart from the large variability visible in individual observations the average source flux seems to have remained constant over the years. The large variability of the source on short time scales, the relatively low duty cycle of the observations and the short durations of the individual observations of typically one day prevent further investigation of possible systematic long-term variations.

2.3. Short-term variability: time scale of days

Three ROSAT observations were long enough to study in detail variability on time scales of days, i.e., the observation no.3 in Table 1 which has been discussed already in Brinkmann et al. (1994) and the current HRI observations (nos. 10 and 11 in Table 1).

The most striking impression of the light curves is that on top of a long-term general flux variation there is a short-term variability occuring in form of relatively smooth single shots which appear to be approximately of triangular shape. We therefore subtracted such triangular shots from the prominent peaks in the light curves of May 1996 and November 1996, all with the same amplitude of 4 cts s-1, and with a growth time scale of 10 cts s-1 per day and a slower decay time scale of [FORMULA] 6.1 cts s-1 per day. These values were obtained by eye-fitting the residuals and not by a rigorous mathematical minimization of the variance of the data, thus the time scales as well as the exact shape of the shots must be regarded as first approximations. The residual light curves obtained with this procedure are shown in Fig. 4. Although some residuals, especially in the November 1996 observation indicate that not all the shots are identical (in particular, the amplitudes might vary) the resulting light curves are much smoother over most of the observation periods. The excess variance, a quantity to characterize the variability of a light curve (Nandra et al. 1997) is [FORMULA] for the May '96 observation, and [FORMULA] for the November '96 observation. After subtraction of the short duration triangular shots the variances have decreased to [FORMULA] and [FORMULA], respectively. This indicates that the variability of PKS 2155-304 consists of mainly two components: a long term smooth intensity variation with time scales of more than a week (see Fig. 4) and, superimposed, a component consisting of individual, relatively well defined smooth shots of flux occurring on a typical time scale of slightly less than a day. Their occurrence does not seem to be periodic. The shots taken above would correspond to an absolute growth time scale of [FORMULA]erg s-2, and a slightly smaller decay time scale of [FORMULA] erg s-2. It is worth noting that similar flares were also observed from PKS 2155-304 by SAX on November 20, 1996 (Giommi et al. 1998). In fact after converting the MECS count rate into the HRI count rate with PIMMS the amplitude turned out to correspond to [FORMULA] cts s-1 and the shape was similarly triangular.

[FIGURE] Fig. 4. Residual HRI light curves (as open squares) of PKS 2155-304 in May 1996 (top) and November, 1996 (bottom) obtained by subtracting individual `shots' from the light curves of Fig. 2, plotted as filled dots.

2.4. Short-term variability: time scale of minutes

The very dense light curve of November 1996 and the virtual independence of the HRI count rate from the wobbling motion of the satellite allows an analysis of the temporal variations on time scales of minutes. Accumulating the data in 100 sec time bins we have typically 1000 counts per bin, i.e., the statistical error is of the order of [FORMULA] 3%.

In Fig. 5 we plot the light curve from the November 1996 observation. The light curve clearly shows the well defined long term intensity variations and the large scatter of the data taken over the individual satellite orbits. This scatter is so strong that, in general, the long term trend of the intensity variation cannot be seen in a particular orbit when a linear least square fit for the long term variations is applied to the data. Further, about a third of the individual orbits yield unacceptable fits ([FORMULA]), often with indications for substructures in the data with time scales of 600-700 secs. The time scales involved are similar to those found in the optical ([FORMULA] 15 min, Paltani et al. 1997).

[FIGURE] Fig. 5. HRI light curve of PKS 2155-304 in November 1996. Data are binned in 100 sec intervals. Time runs from start of the observation.

A periodogram analysis of the data yielded a strong signal at the satellite's orbital period of [FORMULA] 5730 sec. From the window function we found that the remaining peaks are related to the irregular scheduling of the actual observation interval (typically [FORMULA] s long) during the different satellite orbits. Therefore, the rapid variability of the HRI flux must be attributed to variations of the instrumental conditions over the satellite's orbit. On shorter time scales (100 s to 1000 s) there are no statistically significant indications for persistent periodic source flux variations.

2.5. Structure function analysis

A structure function analysis is a method to quantifying time variability without the problems encountered in the traditional Fourier analysis technique in case of unevenly sampled data. The general definition of structure functions and their basic properties are given by Simonetti et al. (1985). The first-order structure function measures the mean deviation for data points separated by a time lag [FORMULA], [FORMULA]. It is commonly characterized in terms of its slope: [FORMULA]. One of the most useful features of the structure function is its ability to discern the range of time scales that contribute to the variations in the data set. For lags shorter than the smallest correlation time scale and for lags longer than the longest correlation time scale, the structure function displays two plateau states ([FORMULA]) at different levels. These regions are linked by a curve whose slope depends on the nature of the intrinsic variation of the source (e.g. flicker noise, shot noise, etc.).

The large scatter of the structure function shown in Fig. 6 must be attributed to the sparse, highly irregularly spaced data, taken over long time scales of years. PKS 2155-304 shows little variation at time scales lower than [FORMULA]. For longer time scales the slope of the structure function is [FORMULA]. This indicates typical correlation time scales for PKS 2155-304 of the order of days and the nature of the variation of the source can be ascribed to shot noise. This result is fully consistent with the findings of Hughes et al. (1992), who found for a sample of 20 BL Lac objects an average slope of [FORMULA].

[FIGURE] Fig. 6. Structure function of PKS 2155-304 . Time lags are in secs.

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© European Southern Observatory (ESO) 2000

Online publication: October 30, 19100