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Astron. Astrophys. 361, 121-138 (2000)

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3. Results

3.1. Light curves, color-color and hardness-intensity diagrams

Fig. 2 shows the global evolution of the persistent emission during our observations. Each point gives the 2-20 keV background subtracted count rate integrated over a single observation. Each plotting symbol is associated with an observation (see the right corner of Fig. 2). As could have been anticipated from Fig. 1, our observations sampled various intensity states of the source: the PCA count rate changes by a factor of [FORMULA] 5 from roughly 20 to 100 cts s-1 PCU-1. We also generated light curves in different energy bands between 2 and 30 keV for each observation. No substantial variation is noticeable in the persistent emission over timescales of a few hours.

[FIGURE] Fig. 2. Evolution of the persistent emission during the observations. The 2-20 keV background subtracted count rates are averaged over each observation. The corresponding exposure time is given in Table 2. The symbols labeled with the date of the observation will be used throughout the remainder of this paper.

Fig. 3 shows the color-color diagram. The points seem to form a "Banana" shape than can be approximated by a spline.

[FIGURE] Fig. 3. Color-Color diagram. The binning time is 512 seconds and a typical error bar is shown. The thick line is the spline used to approximate the position on the color-color diagram. This position is quantified by the curvilinear coordinate Sa chosen arbitrary. The positions Sa=1 and Sa=2 are indicated by arrows.

Fig. 4 shows the soft (top panel) and hard (bottom panel) colors as a function of the count rate. In the main panels, the binning time is 512 seconds while in the inset panels, each point is the average over an observation. Looking at the behaviour of the source within an observation, we see, from the vertical tracks drawn by the points with a same symbol (main panels), that the colors can vary a lot while the intensity remains nearly constant, especially the hard color at low count rates.

[FIGURE] Fig. 4. Hardness-intensity diagrams for the soft color (top panel) and the hard color (bottom panel). In the main panels, the binning time is 512 seconds and a typical error bar is shown. In the inset panels, each point is the average over an observation. The asterisks and the large crosses indicate observations of the LS and HS respectively.

Looking at the global behaviour of the source along the observations (inset panels), two groups corresponding to two different spectral states may be distingished: we refer to the observations with the 5-30 keV intensity below and above [FORMULA] 30 cts s-1 PCU-1 as being in the low and high states (LS, HS) respectively. In the LS, we see a trend for the mean hard color to decrease as the intensity increases (Fig. 4 bottom), while the soft color remains nearly constant (Fig. 4 top), so that, on average, the emission softens with the intensity. On the contrary, in the HS, the hard color is nearly constant (Fig. 4 bottom), while the soft color increases with the intensity (Fig. 4 top), so that, on average, the emission hardens. 4U1915-05 is in a low intensity/hard spectrum regime in the LS and in a high intensity/soft spectrum regime in the HS. The spectral modeling of the persistent emission confirms this picture (Bloser et al. 2000). Assuming a source distance of 9.3 kpc, we derived a 2-20 keV luminosity of [FORMULA] ergs s-1 on March 13th (when 4U1915-05 is the brighest and in the HS) and of [FORMULA] ergs s-1 on May 18th (when 4U1915-05 is the faintest and in the LS).

3.2. Variability in the [FORMULA] Hz frequency range

3.2.1. Average power density spectra

In order to better characterize the source, we looked for possible correlations between the aperiodic variability and the spectral behaviour. We thus averaged together low frequency PDS of the LS on one hand (Fig. 5 left), and PDS of the HS on the other hand (Fig. 5 right), provided that they were obtained from the same timing mode data.

[FIGURE] Fig. 5. Average PDS in the LS (left panel) and HS (right panel). The first one is obtained by averaging the PDS of the LS observations available in the 122 µs resolution mode: all the LS observations except a segment of the June 1st observation and the May 17th observation. The second PDS is obtained by averaging the PDS of the HS observations: February 10th, March 13th, May 5th and 6th (all obtained in 1 µs resolution mode). The total exposure time of the first PDS is more than 15 hours whereas it is only [FORMULA] 3 hours for the second one. The inset panel is a zoom of the PDS above 1 Hz. The solid lines are the best fits to the data.

The average PDS of Fig. 5 (left) has an integrated RMS over the entire [FORMULA] Hz frequency range of [FORMULA]%. The PDS shows VLFN up to roughly 1 Hz and HFN around 20 Hz. The model C+PL+CPL provides a better fit than a simple PL ([FORMULA] [FORMULA] 166/146 and 324/149 respectively). Looking at Fig. 5 (right), we note an excess power around 0.2 Hz. We have fitted that excess with a Gaussian and assessed its significance through the standard F-test. We define P as the probability of rejecting the hypothesis that the fit is better with the additional Gaussian component. In the present case, we have P = 0.09, which means that the QPO is significant at a level of [FORMULA] 91%. With the 0.2 Hz Gaussian added, the results of the best fit are given in Table 3.


[TABLE]

Table 3. Best fit parameters obtained for the state averaged PDS shown in Fig. 5. The RMS is given in the frequency range [FORMULA] Hz for the VLFN, 1-128 Hz for the HFN and 0.1-0.3 Hz for the QPO.


We have searched for the same signal in different energy ranges. As an example, in the 2-30 keV band, the significance of the 0.2 Hz signal reaches 93%. The best fit parameters are given in Table 3. In addition to the state averaged PDS, we computed PDS for each observing day. In some of these PDS, power excesses are visible around 0.2 Hz. However, they are statisticaly marginal with significance levels less than 90%.

In the HS, the source displays very low variability. The total RMS in the 5-30 keV energy range is [FORMULA]%. At low frequencies, the PDS is still dominated by VLFN up to roughly 0.1 Hz. But above this frequency, the PDS is consistent with having no power. No QPO nor HFN component are present in the PDS. The best fit parameters are given in Table 3.

Looking at each individual PDS, we found that what we called previously the HFN component in the state averaged PDS could be in fact resolved into broad QPO-like features of varying centroid frequencies. In the following, we call these features LFQPOs. Fig. 6 shows two examples of daily-averaged PDS where such a LFQPO is clearly detected. Detailed properties of the LFQPOs are given in the next section. To conclude, 4U1915-05 displays aperiodic variability below [FORMULA] 1 Hz (the VLFN) and quasi-periodic variability or no variability above 1 Hz.

[FIGURE] Fig. 6. PDS showing LFQPOs in the persistent emission of two segments of observations on October 29th (top panel) and June 1st (bottom panel). The mean count rate is 35 cts s-1 PCU-1 for the first PDS and 41 cts s-1 PCU-1 for the second (no background subtraction). The exposure time of both PDS is 1800 seconds. The inset panel is a zoom of the PDS above 1 Hz. The solid lines are the best fits to the data.

Fig. 7 displays the RMS as a function of the count rate for each observation. The RMS is given in the [FORMULA] Hz frequency range where the VLFN dominates, and between 1-100 Hz where the LFQPO is detected. The RMS of the VLFN component ranges between [FORMULA] 3 and 6%, whereas the RMS above 1 Hz ranges between [FORMULA] 5 and 25%. In the LS, the RMS is high and decreases as the average count rate per observation increases. On the other hand, in the HS, the RMS, after reaching a low threshold, does not significantly vary as the count rate increases. Thus, the timing behaviour of 4U1915-05 is different in its two states.

[FIGURE] Fig. 7. RMS in the [FORMULA] Hz range (small symbols) and in the 1-128 Hz range (big symbols) versus count rate (no background subtraction).

3.2.2. Low frequency quasi-periodic oscillations

To further investigate the properties of the LFQPOs detected between a few Hz and 100 Hz in 4U1915-05 (see Fig. 6), and given their relative weakness in the persistent emission, we searched for them in the persistent and dipping emission combined rather than in the persistent emission alone. Although we note that we may be looking at different signals when combining the persistent and dipping emissions, we aimed to get the best signal to noise ratio. The study of the LFQPOs is carried out in the 5-30 keV energy range in order to make easier the comparison with the HFQPOs detected in that energy range with the best signal to noise ratio (see next section). The dipping is large but not complete in that energy range. So, adding the dipping parts, which represent roughly 40% of the data set, actually increases the signal to noise ratio. This is not negligible because 4U1915-05 is relatively faint in the PCA (2-20 keV background subracted count rate around 35 cts s-1 PCU-1, to be compared with [FORMULA] 30000 cts s-1 PCU-1 for Sco X-1) and observed with only 3 PCUs for more than the half of our observation (see Table 2). Furthermore, the ingress or egress of a dip lasts more than 1 second (typically 40 s). So, above 1 Hz where the LFQPOs are detected, the PDS of the persistent and dipping emission is not contaminated by the dip phenomenon itself. PDS were computed in the range [FORMULA] Hz the same way as for the persistent emission alone. We averaged together PDS of the same observation or the same segment.

The LFQPOs frequency, FWHM, RMS and significance level are listed in Table 4. Their frequency ranges between 5 and 80 Hz. Their FWHM is around 16 Hz but can vary from 0.5 to 45 Hz, so that their coherence (Q=[FORMULA]/FWHM) changes roughly from 0.5 to 26 with a mean value of 4. The designation of QPO is then sometimes improper since this is usually used for signals with Q values greater than 2 (Van der Klis 1995). One of the LFQPOs is shown in Fig. 8. In the second segment of September 6th, we found an excess in the PDS between 1 and [FORMULA] 50 Hz ([FORMULA]). A visual inspection of the PDS indicates that this excess is flat, yet above the noise level. For this reason, we were unable to fit it with a Gaussian, and therefore we do not consider this excess as a LFQPO, as defined above. Interestingly enough, however we note that the centroid of the excess ([FORMULA] 30 Hz) would fall on the correlation between LFQPO frequency and the upper HFQPO frequency, as shown in Fig. 13 (see Sect. 4.4).

[FIGURE] Fig. 8. PDS showing the LFQPO in a segment of the October 29th observation (persistent and dipping emissions combined). The solid line is the best fit of the QPO with a Gaussian.


[TABLE]

Table 4. Properties of the QPOs detected above 3 [FORMULA] (see text) in 4U1915-05 in the 5-30 keV energy range. We list the observation date (month/day) followed by the segment number or by an asterisk if all segments have been summed, the frequency, FWHM, RMS and significance of the LFQPOs (1-100 Hz) and HFQPOs (100-1400 Hz). The last column is the separation between the twin HFQPOs. All the values are inferred from Gaussians used to fit the QPOs. The reduced [FORMULA] are close to 1. The error bars are given for the 90% confidence level ([FORMULA]=2.7 for the variation of a single parameter). When no signal is present above our confidence threshold, we give a 3 [FORMULA] upper limit on the RMS of a signal of FWHM 10 Hz for the LFQPOs and 50 Hz for the HFQPOs. The significances quoted here are for a single trial only. A more detailed assessment of the significance of the detections taking into account the number of trials may be found in the text (see Sect. 2.3.3). a) flags detections at a significance level between 3 and 4 [FORMULA]. The other signals have significance level greater than 4 [FORMULA]. b) The excess could not be fitted as a Gaussian (see text). Approximated values of the frequency, FWHM and RMS are given.


We looked for correlations between LFQPOs and spectral states. The bottom-left panel of Fig. 9 shows the LFQPO frequency versus the 5-30 keV count rate. All but one of the LFQPOs are detected in observations of the LS. For 4U1915-05, the LFQPO frequency seems to roughly correlate positively with the intensity, but the scatter is substantial.

[FIGURE] Fig. 9. Left: LFQPO (bottom panel) and HFQPO (top panel) frequency as a function of the 5-30 keV count rate (no background subtraction). Right: LFQPO (bottom panel) and HFQPO (top panel) RMS as a function of the 5-30 keV count rate. Small symbols are used for detections between 3 and 4 [FORMULA], big symbols for detections above 4 [FORMULA].

The bottom-right panel of Fig. 9 shows the LFQPO RMS as a function of count rate. The RMS ranges from 5 to 20%. For the HS, we have derived upper limits ranging between 3 and 10% (see Table 4). No simple relation seems to connect the two quantities.

Recent works have shown that some timing features of similar systems were better correlated with the position on the color-color diagram than with the count rate (Méndez et al. 1999; Méndez & Van der Klis 1999). We thus examined the QPO properties as a function of the position on the color-color diagram.

Color-color diagrams are sensitive to changes of a few percent in flux ratios between energy bands. Observations allowed to show that during these subtle changes, the X-ray intensity was not a measure of the accretion rate since both positive and negative correlations between the two quantities could occur (Hasinger & Van der Klis 1989; Van der Klis 1994). The position on the color-color diagram is a better indicator of the spectral state and hence the accretion rate than the count rate.

The direction of evolution of the accretion rate on the color-color diagrams was inferred from X-ray luminosities and confirmed by multiwavelength and bursts observations (Hasinger et al. 1990; Van der Klis et al. 1990). In the atoll sources, the accretion rate is believed to increase from the island to the lower and then to upper banana states. For our analysis, we refer to the color-color diagram shown in Fig. 3. The spline shows the approximated track followed by 4U1915-05 during the observations. The direction of evolution of the accretion rate along the track is derived from the X-ray luminosity which globaly increases from the extremity located at the top of the diagram to the extremity located at the bottom (see Bloser et al. (2000) for details about spectral fitting).

Following Méndez et al. (1999), we called Sa the parametrization along this spline. Sa is a measure of the position of the source on the diagram. Sa was choosen to increase from top to bottom so that it is representative of the inferred evolution of the accretion rate. We determined the value of Sa for each segment of observation by projecting the corresponding point of the color-color diagram (inset panel of Fig. 3, where one point corresponds to one segment) on the spline. This value of Sa could then also be attributed to the LFQPO detected in the given segment. For LFQPOs detected in PDS averaged from several segments of the same observation day, we used the mean of the Sa values found for each segment. The bottom-left panel of Fig. 10 shows the LFQPO frequency as a function of Sa. A positive correlation is now clearly visible. In the bottom-right panel of Fig. 10, we show that the LFQPO RMS anticorrelates with Sa. In both plots, the scatter is now much smaller than in the previous plots where the count rate was involved. Note that we have also studied the evolution of the LFQPOs as a function of the hard color (10-30 keV/5-10 keV). We concluded that the hard color was a worse indicator of the timing behaviour than Sa: the evolution of the soft color had to be taken into account.

[FIGURE] Fig. 10. Left: LFQPO (bottom panel) and HFQPO (top panel) frequency as a function of the position Sa on the color-color diagram. The asterisks represent the frequency separation of the twin HFQPOs. The solid line is the average separation. Right: LFQPO (bottom panel) and HFQPO (top panel) RMS versus Sa. Small symbols are used for detections between 3 and 4 [FORMULA], big symbols for detections above 4 [FORMULA].

3.3. Discovery of high frequency quasi-periodic oscillations

Now, we report on the discovery of HFQPOs from 4U1915-05. The analysis has been carried out in the 5 to 30 keV energy range because in other sources, it is known that HFQPOs are more easily detected in this energy band, as in, e.g. KS1731-260 (Wijnands & Van der Klis 1997). The persistent and dipping emission were combined to increase the signal to noise ratio (see Sect. 3.2.2).

The results are reported in Table 4 (either the observations or the segments). The HFQPOs frequency ranges between [FORMULA] 200 and 1300 Hz. Their FWHM is around 70 Hz and coherence around 50. Their RMS amplitude is high ([FORMULA] 17%). One of the strongest HFQPO signals is shown in Fig. 11.

[FIGURE] Fig. 11. PDS for the September 6th observation. The HFQPO is fitted with a Gaussian.

We detect twin HFQPOs in 5 segments or observations (Table 4). For four of them, the frequency separation is consistent with being constant. The mean separation is [FORMULA] Hz. For the fifth, the separation is [FORMULA] Hz, thus inconsistent with the previous value. We note that this pair of QPOs occur at 514 and 224 Hz whereas the four other twin peaks occur above 550 Hz. The twin HFQPOs detected in a segment of the June 1st observation are shown in Fig. 12. HFQPOs were not detected in observations with the largest count rates (February 2nd, March 13rd) with upper limits of [FORMULA] 6% on the RMS (Table 4). HFQPOs were not detected either in the lowest count rate regime (May 18th to May 22nd); this might be due to a lack of sensitivity. Indeed, only 3 PCUs were working during these observations (see Table 2) and the upper limits on the RMS are not constraining ([FORMULA] 20%, see Table 4).

[FIGURE] Fig. 12. The twin HFQPOs fitted with Gaussians detected in a segment of the June 1st observation. For display purposes, two different frequency binnings have been used.

The top-left panel of Fig. 9 shows the HFQPO frequency as a function of count rate. In this diagram, we observe a branch between 700 and 1100 Hz where the frequency strictly correlates with the count rate. A second parallel branch seems to be drawn at lower frequencies. However, some of the HFQPOs of that branch do not have a simultaneous twin peak in the upper branch. In the lowest count rate regime, the frequency does not follow anymore a simple relation with the count rate.

The top-left panel of Fig. 10 shows the HFQPO frequency as a function of Sa. The frequency versus Sa relation appears much simpler than the frequency versus count rate relation. We can now easily identify the upper and lower HFQPOs. The frequency of the upper HFQPO is now well correlated with Sa within its full range. The four twin peaks above 550 Hz are detected within a narrow range of Sa around 3. Their frequency separation is shown with an asterisk on Fig. 10. The pair of QPOs at 224 Hz and 514 Hz appears at the lowest Sa and hence lowest inferred accretion rate. Concerning the HFQPO RMS, we show that, surprisingly, it is better correlated (negatively) with the count rate than with Sa (top-right panel of Fig. 9 and 10 respectively).

3.4. Correlation between low and high frequency quasi-periodic oscillations

Fig. 10 (left panel) shows the parallelism between HF and LF QPOs. Their frequency increases similarly with Sa. In Fig. 13, we show the relation between LFQPO and upper HFQPO frequencies when both QPOs are detected simultaneously and above 4 [FORMULA]. The correlation between the two frequencies is obvious. It can be approximated with a power law of the form [FORMULA]. The first attempt of fitting the data provided a high reduced [FORMULA] because of the point representing the July 15th observation lying off from the fit. We thus made the fit taking out this point. We obtained [FORMULA] and [FORMULA] (reduced [FORMULA] of 1.1) as parameters of the power law drawn as the solid line on Fig. 13.

[FIGURE] Fig. 13. LFQPO frequency as a function of the upper HFQPO frequency. We report signals detected simultaneously above 4 [FORMULA]. The solid line is the powerlaw of index 1.6 fitting the data. The dashed line is the precession frequency (Lense-Thirring and classical contributions (Stella & Vietri 1998)) assuming standard parameters for the neutron star (see text) and a spin frequency of 348 Hz.

3.5. Search for oscillations in bursts

For the bursts recorded in the 122 µs resolution mode, we have computed thirty PDS of 1 second duration so that they covered the rising and decaying parts of the bursts. Each was individually searched for excess power. No such excesses were found either in individual PDS nor in their sum. We therefore conclude that no QPOs were found in those bursts. We have set upper limits on the RMS, assuming a 3 [FORMULA] signal of FWHM 1 Hz in the PDS. We derive a 3 [FORMULA] upper limit of 3.2% for the October 29th burst, and of 2.8% for the August 16th burst.

For the burst catcher mode, the situation is slightly different. The data cover only the first 3.75 seconds of the bursts, and the Nyquist frequency is 256 Hz which is below the typical frequency of a burst oscillation (Van der Klis 1999). Note however that coherent oscillations were found at 7.6 Hz in a burst from Aql X-1 (Schoelkopf & Kelley 1991). For the burst that occured on May 5th, no significant signals were found in PDS computed for different segments durations (ranging from 1.25 to 3.75 seconds). We have derived a 3 [FORMULA] upper limit of 2.8% (FWHM=1 Hz) for the 3.75 seconds burst duration.

For the June 1st burst, we have also computed an FFT from the 3.75 seconds data set. When the PDS so computed is rebinned by a factor of 4 ([FORMULA] Hz), two signals are detected by our algorithm; 117.5 Hz (5.4 [FORMULA], RMS=[FORMULA]%), 225.7 Hz (5.0 [FORMULA], RMS=[FORMULA]%). However, in the case of these PDS, the corresponding significance detection level (taking into account the number of trials; see Sect. 2.3.3) is only 85%, which is insufficient to claim a detection.

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Online publication: September 5, 2000
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