2. Observations and data analysis
2.1. The RXTE/PCA observations
4U1915-05 was observed by RXTE on 19 occasions in 1996: on February 10th, March 13th, May 5-6th, May 14th to 23rd, June 1st, July 15th, August 16th, September 6th and October 29th. The log of the observations is presented in Table 2. An observation has an exposure time of roughly 8000 seconds and is provided as typically three data files with gaps between files. These files are refered as segments of observation in our analysis. We report on the data collected in the 2-60 keV range with the PCA. It consists of 5 nearly identical large area Proportional Counter Units (PCU 0 to 4) corresponding to a total collecting area of cm2 (Jahoda et al. 1996). For safety reasons, PCUs are switched on and off in the course of an observation. During our observations, the data were mainly obtained in three different PCU configurations: all PCUs on, first four on and first three on. Furthermore, our observations cover two PCA gain epochs: the February 10th and March 13th observations belong to the first one whereas the following observations belong to the third one. Different response matrices were used for each set. More than 138 ks of good data are available after recommended screening (elevation angle above the Earth's limb greater than 10 degrees and pointing offset angle less than 0.02 degree).
Table 2. Observation log. We list the name assigned to the observation, its start and stop times (day and UT hour), the number of PCUs working (P), the high time resolution data modes M available (G, E and CB designate the E_125us_64M_0_1s, GoodXenon_16s and CB_2ms_64M_0_249 (Binned Burst Catcher) configurations respectively), the total exposure time () in seconds after screening (on elevation and offset), the number of bursts (B) and dips (D) present, the exposure time in seconds of the persistent light curve after filtering out the bursting and dipping parts (T) and the 2-20 keV background subtracted count rate in units of cts s-1 PCU-1 (R) of the persistent emission. (1) Gain epoch 1 data (the other observations are gain epoch 3). a) Two small observations were carried out on May 23rd, we merged them together for clarity.
The all-sky monitor (ASM) aboard RXTE consists of three coded-aperture cameras mounted on a motorized rotation drive, allowing to view different regions of the sky during a satellite orbit (Levine et al. 1996). The instrument is sensitive in the energy range 2-12 keV. Fig. 1 is the ASM light curve of 4U1915-05 during 1996. The binning time is one day. The times of the PCA observations are flagged with arrows. Four X-ray bursts were recorded during the PCA observations: on May 5th, June 1st, August 16th and October 29th. With the exception of the first one, they began during a dip. A total of 58 primary or secondary dips (or parts of dips) were observed, lasting typically 400 seconds. Dips are thought to be due to occultation of the internal emitting region by vertical structure at the outer edge of the accretion disk (Walter et al. 1982; White & Swank 1982). Primary dips occur at intervals consistent with an orbital period of 50 minutes. Secondary dips are "anomalous" dips, narrower than the primary ones. They occur irregularly at 180o out of phase with the primary dips (Chou et al. 1999). Dipping is almost 100% in the 3-5 keV energy range, but only 65% in the 5-30 keV range.
2.2. Data modes
The Standard 2 mode is available for each observation. This mode provides counts integrated during 16 seconds in 128 energy channels covering the 2-60 keV energy range. The high time resolution data were provided in two different modes, depending on the observations (see Table 2): the E_125s_64M_0_1s mode with 122 µs resolution or the GoodXenon_16s mode with s resolution. The bursts that occured on October 29th and August 16th were recorded in the 122 µs resolution mode. The bursts that occured on May 5th and June 1st were recorded during 3.75 seconds in a burst catcher mode with 2 ms resolution.
2.3. Data analysis
2.3.1. Light curves, color-color and hardness-intensity diagrams
For the light curves, color-color and hardness-intensity diagrams, we have used the Standard 2 mode data. We made light curves in adjacent energy bands. The bursts and dips were then filtered out after visual screening of the light curves to generate the color-color and hardness-intensity diagrams for the persistent emission. The soft color was calculated as the 3-5 keV/1.7-3 keV count rate ratio, and the hard color as 10-30 keV/5-10 keV.
As all the PCUs have different energy responses, the absence of a PCU can mimic spectral variations. Thus, we used the data collected with the first three PCUs since they were continuously operating during all our observations.
Differences between response matrix of gain epoch 1 and 3 introduce differences in the boundaries of the energy channels used. This instrumental effect introduces shifts between the colors or count rates obtained from different epochs. We quantified these shifts using the Crab nebula which is a steady source. We find that the correction factors to apply to gain epoch 1 data in order to make them match the epoch 3 region are +10.1%, -1.5%, -1.1% and +2.8% for the count rates in the energy bands 1.7-3, 3-5, 5-10 and 10-30 keV respectively. The correction factors are -10.5% and +4.0% for the soft and hard colors respectively. We applied these correction factors to 4U1915-05 data.
2.3.2. Power density spectra
To investigate the variability of 4U1915-05, we computed PDS using the FTOOLS powspec . We treated separately the data obtained from the different high time resolution modes.
To reach timescales ranging from roughly 10 ms to 4 minutes, the data were rebinned to a ms resolution. Then, each continuous set was divided into segments of 65536 bins. A fast Fourier transform (FFT) of each segment was computed yielding a low frequency PDS in the range Hz.
To reach timescales ranging from roughly 0.25 ms to 1 second, the data were rebinned to a s resolution. Each continuous set was divided into segments of 8192 bins. A FFT of each segment was computed leading to high frequency PDS in the range 1-4096 Hz. Then, the low or high frequency PDS obtained from a given set of observations, a given observation or a given segment of observation were averaged together to obtain a final PDS representative of the set, observation or segment.
The PDS were normalized according to Leahy et al. (1983) so that the average power expected from a Poisson distribution is 2. We have checked in the high frequency PDS that the average white noise level above 1500 Hz was indeed 2, indicating that deadtime corrections were not needed.
The error on each PDS bin has been set to where M is the number of raw PDS averaged together, W the number of raw frequency bins averaged together (Van der Klis 1989). is set to the Fourier power at the point considered for low frequency PDS (where the power can differ significantly from the white noise level 2 because of the source aperiodic variability) and to 2 for the high frequency PDS. Both logarithmic and linear rebinnings were applied.
Different components were summed to fit the resulting PDS: a constant for the white noise level (C), a power law for the VLFN (PL), a cutoff power law for the HFN (CPL). The functional shapes used for the latter components are and respectively, where A is the normalization, the power law index, the frequency and the cutoff frequency. C is a free parameter for the high frequency PDS and is set to 2 for the low frequency PDS. We used Gaussians (G) to describe the QPO features. Note that Lorentzians are also currently used (Van der Klis 1995).
All the fits were performed using a minimization technique. The errors on the analytic model parameters correspond to a variation of 2.7, equivalent to the 90% confidence region for a single interesting parameter.
To compute the RMS, the PDS were normalized according to Belloni and Hasinger (1990) taking into account the total and background count rates. The RMS was then obtained by integrating the normalized PDS in the appropriate frequency range.
We have also computed PDS of data from the bursts. For the bursts recorded in the 122 µs resolution mode, we have calculated an FFT power spectrum using 4096 bins lasting 244 µs, so that one PDS corresponds to a segment of the burst of 1 sec duration and the Nyquist frequency is 2048 Hz. For the other bursts, the time resolution is only 2 ms, yielding a Nyquist frequency of 256 Hz.
2.3.3. Search technique for quasi-periodic oscillations
To look for weak QPOs in the PDS (as in the case of 4U1915-05), we developed an algorithm which computes for each PDS the width of the window which maximises the signal to noise ratio (SNR) within the window. Assuming that a given window of width w contains N frequency bins, the error on the binned points becomes and the SNR can be computed as:
where Pj are the N PDS points contained in the window of width w and Pref is the reference power. For the low frequency PDS, given the weakness of the VLFN component above 1 Hz, we looked for excesses above =2, the theoretical level expected from Poissonian noise. PDS have been processed through the algorithm and searched for excesses of widths from 1 to 50 Hz in the frequency range 1-100 Hz. For the high frequency PDS, we looked for excesses of widths 5-200 Hz in the frequency range 100-1500 Hz. We used the noise level averaged above 1500 Hz ( 2.0) as the reference for the search of excesses in the PDS. In both cases, we first selected the positive detections above 3.5 . A new significance level inferred from the fit was then attributed to each excess in order to take into account the excess shape. We report here on the LFQPOs and HFQPOs which have a significance level greater than 3 . This significance level is reported in Table 4 with the properties of the QPOs detected in 4U1915-05. We do mention either the observation or the segments, so that no overlapping is possible.
This algorithm does not take into account the number of trials in determining the significance level. To determine the real significance of the detections, we follow Van der Klis (1989) and define the confidence level Pdetect as the power level that has only the small probability /Ntrial to be exceeded by a noise power. Ntrial is the number of different power values that one wishes to compare with Pdetect. It may be the total number of bins in the PDS, or less if only a given frequency range is looked for excesses. The number of different PDS looked at may also be included in the number of trials but we did not take it into consideration. In our case, the high frequency PDS are scanned over a frequency range of 1400 Hz. The exposure time of a raw PDS is 1 second (corresponding to a frequency resolution of 1 Hz). The typical exposure time for a segment of observation is 3000 seconds so that M=3000 raw PDS are averaged together to create the PDS representative of the segment. Assuming that the algorithm finds a maximum excess of width 20 Hz (corresponding to a final rebinning factor NW of 20) at 5 , then Ntrial=70 and the actual significance level of the signal is 99.998%. In the worst case of an excess of width 5 Hz (ie the minimum width considered) found at 3.5 (ie the minimum level obtained from the algorithm considered), Ntrial=280 and the actual significance level is 92.7%. The low frequency PDS are scanned over a frequency range of 100 Hz. The exposure time of a raw PDS is 256 seconds (corresponding to a frequency resolution of Hz). A PDS representative of a 3000 seconds segment is obtained from M=12 raw PDS. In the worst case of an excess of width 1 Hz (e.g NW=256) at 3.5 , then Ntrial=100 and the true significance level is 97.0%.
© European Southern Observatory (ESO) 2000
Online publication: September 5, 2000