CORRELATIONS IN HORIZONTAL BRANCH OSCILLATIONS AND BREAK COMPONENTS IN XTE J1701-462 AND GX 17+2

We analyzed all 866 observations of XTE J1701-462 obtained by the Proportional Counter Array (PCA) instrument on board RXTE during its 2006–2007 outburst. We chose 63 RXTE observations of GX 17+2 obtained in the period of 1999 October 3–12 (i.e., MJD 51454-51463) for a comparison study. For the reduction, we used the HEASOFT package, version 6.12. Only those data with elevation angles >10°, pointing offsets <0.01, and South Atlantic Anomaly exclusion times of 30 minutes were selected for further analysis.

Type I X-ray bursts were identified and removed from the data. Background-subtracted light curves with 16 s time resolutions were constructed from the "standard 2" mode, using data from Proportional Counter Unit (PCU) number 2 only, without dead-time correction. For both XTE J1701-462 and GX 17+2, we defined two X-ray colors: a soft color (SC) and a hard color (HC), as the ratio of count rates in the ∼4.5–7.4 keV/2.9–4.1 keV bands (PCA channels 10–17/6–9) and the ∼10.2–18.1 keV/7.8–9.8 keV bands (PCA channels 24–43/18–23). Intensity was defined as the count rate in the energy range of ∼2.9–18.1 keV(PCA channel 6–43). The small difference in the energy ranges caused by different epochs were ignored. The colors were used to produce CDs and HIDs. For XTE J1701-462, we divided the data into four time intervals, while all observations of GX 17+2 were combined as one interval. Data selections are listed in Table 1: for XTE J1701-462, intervals A and B correspond to the Cyg-like stage and intervals C and D to the Sco-like stage. Interval E is that from GX 17+2. The HIDs of all these five intervals are plotted in Figure 1.

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Standard, fast Fourier transform (FFT) techniques (van der Klis 1989, 1995) were used to create power density spectra (PDS) from all active PCUs, adopting the rms normalization from Belloni & Hasinger (1990). The high time resolution single-bit and event mode data were used to create PDS, without background-subtraction or dead-time correction. We studied the properties of LFQPOs (in this case, HBOs) and band-limited components by selecting box regions along the HB in the HID, accumulating what are known as Sz-resolved spectra. The boxes for each interval are shown in Figure 1: each box corresponds to >1600 s of data. A rank number Sz was given for boxes to track their positions along the Z track (Hasinger et al. 1990). We set the Sz of the HB/NB vertex as one and the leftmost point of the HB as zero, also marked in Figure 1. The Sz of other boxes are obtained by spline interpolation (Dieters & van der Klis 2000; Lin et al. 2012; Li et al. 2014).

For each box, PDSs are accumulated from 16 s segments and a time bin of 2⁻⁸ s (yielding a frequency range of 0.0625–128 Hz), then averaged to obtain a single PDS per box. Since few photons are detected in very high energy bands, the channel range considered is 0–149, corresponding to energy range of 2–67 keV. We fitted the PDS with a multi-Lorentzian function (Nowak 2000; Belloni et al. 2002). PDSs were plotted as representations of rms² time frequencies (νP_ν). It takes three to four Lorentzians to fit each PDS: the low-frequency noise (LFN, also as known as the band-limited component), the HBO and its second and third harmonics. Figure 2 shows a representative PDS of box 11 from interval A, with best-fit Lorentzians. Each Lorentzian, whether used to fit a QPO or band-limited noise, yields three parameters: a centroid frequency (ν₀), a FWHM, and an integrated fractional rms. Then the characteristic frequency ν_c for a particular component can be calculated by using ${\nu _{{\rm {c}}}} = \sqrt{{\nu _0}^2 + {{(\hbox{FWHM}/2)}^2}}$, as introduced by Belloni et al. (2002). We will indicate the characteristic frequency of the HBO as ν_HBO and that of the band-limited component as ν_break.

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In order to study the energy dependence of the HBO and band-limited components, we further divided the PCA channel 0–149 interval into six sub-channels. The division of energy channels and their corresponding centroid energies are listed in Table 2. The multi-Lorentzian fitting results for all selected boxes are listed in Table 3.

In the PDS corresponding to different boxes, for XTE J1701-462, we found ν_HBO between ∼10 Hz and ∼60 Hz. These HBOs are all accompanied by ν_break between ∼2 Hz and ∼12 Hz. For GX 17+2, ν_HBO between ∼22 Hz and ∼45 Hz are found, with ν_break between ∼2 Hz and ∼5 Hz. We also consider data from Wijnands & van der Klis (1999a) and Altamirano et al. (2012). The corresponding WK correlation is shown in Figure 3. Our points from XTE J1701-462 lie on the main WK track, between the outer edge of atoll sources and the lower edge of Z sources, covering most of the points from the 11 Hz accreting pulsar IGR J17480-2446. Meanwhile, the points from the Sco-like stage, with frequency ranges of ∼30–60 Hz, are blanketed with the points from the Cyg-like stage. It is worth noticing that, based on the data of XTE J1701-462, BHCs and part of the atoll sources are on a straight line. However, our data points for GX 17+2 are distributed in the upper envelop of XTE J1701-462, overlapping the data of typical Z sources, showing a slightly shifted correlation from the main cone. It is worth emphasizing that part of the Z data taken from the literature also belonged to GX 17+2, extracted from earlier observation. Our result for the WK correlation is consistent with what Wijnands & van der Klis (1999a) had found in GX 17+2.

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To study the shifted behavior of Z sources, we further plotted the second harmonic frequencies of HBOs (ν₂) for both sources in the WK correlation. We found that the points of ν₂ from XTE J1701-462 overlap with the points of ν_HBO from GX 17+2 and typical Z sources. Furthermore, the points of ν₂ from GX 17+2 are distributed on the upper side of typical Z sources.

We then tested our identification using the PBK relation using the lower kHz QPO frequency (ν_low) and ν_HBO. We didn't measure the kHz QPO frequencies ourselves. Since Sanna et al. (2010) already found 14 observations with kHz QPO in XTE J1701-462, we further searched the HBO signal in these observations to study the PBK relation. Seven observations are found with both ν_low and ν_HBO in the Sco-like stage, with their IDs and frequencies listed in Table 4. In this case, we only accumulated one PDS per observation in order to directly use the results from Sanna et al. (2010). For GX 17+2, Lin et al. (2012) had measured the kHz QPOs and HBOs on Sz-resolved spectra. Since we chose the same data segment with Lin et al. (2012), we simply used their data, which are also listed in Table 4. In Figure 4, we plot the PBK correlation using the data from Table 4 together with the data from Psaltis et al (1999). The data of GX 17+2 are on the main relation, showing good consistency with atoll sources and part of BHCs. However, as can be seen in the inset of Figure 4, the data of XTE J1701-462 show a larger spread around the correlation than those of GX 17+2, overlapping with the data of GX 17+2 and atoll sources (4U 1608–52 and 4U 1728–34).

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In order to test the hypothesis that the band-limited and HBO components have the same origin, we analyzed the data from the six sub-channels (listed in Table 2, see above). In XTE J1701-462, seven boxes (with six of them in the Cyg-like stage and one in the Sco-like stage) were selected from four intervals, judging by the appearance of HBO signals in all six sub-channels. We also investigated the energy dependence of the rms amplitude of the components (rms_break and rms_HBO). When calculating the rms amplitude, we took into account the background contribution to convert power to rms amplitude. We neglected the background contribution for the total energy band since its effect is negligible, but considered its contribution for all the sub-channel bands. The formula is $\hbox{rms} = \sqrt{({P}/{S + B})} * ({S + B}/{S})$, where S and B stand for source and background count rates, and P is the power normalized according to Leahy. We also considered the systematic uncertainty into the background as introduced by Jahoda et al. (2006). Figure 5 shows the rms–energy correlation for these two components. The values of ν_HBO are indicated in the upper left corner of each sub-figure. The trends of rms_break and rms_HBO with energy are similar in both Cyg-like and Sco-like stages. Both rms_break and rms_HBO increase significantly with photon energy below ∼12 keV, and stay more or less constant after ∼12 keV. We used straight lines to fit the first five data points for both components, respectively. The fitting results are listed in Table 5, with errors given at 1σ level. R-squared represents the coefficient of determination, indicating how well the model fits the data. We found that the slopes for the break component (a1) are consistent with each other within the error (∼0.2) in all seven sub-figures, while those for the HBO component (a2) also have the same value (∼0.1) within the error. However, for GX 17+2, the detection significance of HBOs in six energy bands are not good enough to do the similar work as in XTE J1701-462. We could not give a comparative result in GX 17+2.

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In Figure 6, we plot rms_break and rms_HBO as a function of Sz for all five intervals, to study how the temporal properties change with the different positions in the HID. Our results show that both rms_HBO and rms_break show similar trends in all five intervals, i.e., they all decrease with Sz. However, the rms values change more obviously in Cyg-like intervals than in Sco-like intervals. For instance, rms_break (red crosses) decline from 19% to 4% in both Cyg-like intervals. rms_break changes less in Sco-like intervals, decreasing from 16% to 8% in Sco-like interval C and dropping from 9% to 4% in Sco-like interval D. The values of rms_HBO decline from 9% to 2% in two Cyg-like intervals, while they drop from 6% to 1% in Sco-like interval C. The values of rms_HBO and rms_break in GX 17+2 are close to those of Sco-like interval D in XTE J1701-462, that is, rms_HBO decreases from ∼3% to 1% and rms_break decreases from ∼6% to 5%.

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To further investigate the correlations between HBO and break components in XTE J1701-462 and GX 17+2, we plot the relation between rms_break and rms_HBO in Figure 7(a). It is interesting to notice that the points of the HB/NB vertex from XTE J1701-462 are distributed separately from those of the HB, with the points of GX 17+2 lying between them. To make the correlation more clear, we further rebinned the adjacent points in terms of Δrms_HBO < 0.5 to reduce errors, and plot the result in Figure 7(b). We did not rebin the data of the HB/NB vertex because there are only four of them. We used a power law to fit the data of GX 17+2 and J1701-462 separately (excluding the data of HB/NB vertex because of its different physical origin from HB (Lin et al. 2012)). We obtained rms_break = (6.69 ± 1.17)*rms_HBO^{(0.46 ± 0.04)} for XTE J1701-462 and rms_break = (5.18 ± 0.51)*rms_HBO^{(0.17 ± 0.09)} for GX 17+2, with 1σ errors. The difference between the two power-law indices is different from zero at a 99.5% confidence level (2.8σ).

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XTE J1701-462 is on the main track of the WK relation, together with BHCs, atoll sources, while GX 17+2 is shifted from the main track like other persistent Z sources (Cyg X-2, GX 5–1, GX 340+0, Sco X-1, and an earlier observation of GX 17+2). Wijnands & van der Klis (1999a) suggested that the HBOs observed in shifted Z sources are probably harmonic frequencies. However, according to our results, the HBOs in GX 17+2 and XTE J1701-462 should be the same type of QPO since they have similar frequency and rms values. GX 17+2 is a persistent Sco-like Z source that shows strong similarities in spectral properties with XTE J1701-462 in its Sco-like stage (Lin et al. 2012; Li et al. 2014). In Figure 5, one can also see that the rms_HBO of both GX 17+2 and XTE J1701-462 decreases along the HB, while the values of rms_HBO in GX 17+2 are close to those of the Sco-like interval D in XTE J1701-462. All of these results suggest the HBOs in GX 17+2 have similar properties with those in XTE J1701-462, or even in other types of sources. The HBOs in GX 17+2 should also be fundamental QPOs, not harmonics. Thus, the shifted Z track in WK correlation should be caused by HBOs in persistent Z sources, not harmonics, even the harmonics of HBOs in XTE J1701-462 overlap with the shifted Z track.

XTE J1701-462 has a more scattered distribution than GX 17+2 in the PBK correlation. This could be caused by the existence of two different types of lower kHz QPOs (Psaltis et al. 1999). GX 17+2 is a persistent Z source whose temporal and spectral properties barely change with time, which could explain the consistency with other typical persistent Z sources (Cyg X-2, GX 5–1, GX 340+0, and Sco X-1) in the WK and PBK correlations. XTE J1701-462 and GX 17+2 are both Z sources and exhibit strong similarities in spectral and fast variability properties (Lin et al. 2012; Li et al. 2014). However, they lie on different tracks in the WK and PBK correlations, which makes the physical mechanism behind these correlations more mysterious.

The WK and PBK correlations between these X-ray sources show that the solid surface, the magnetosphere, and absorption along the line of sight do not affect these rapid variability components (Wijnands & van der Klis 1999a). These similarities suggested that the basic frequencies of these systems probably have the same origin and are caused by similar physical mechanisms. Our results show that transient sources like XTE J1701-462, BHCs, and 4U 1608-52 are on the main track, while persistent sources, such as typical Z sources and 4U 1728-34, are shifted from the main track. The persistent and transient sources probably have a similar physical mechanism in producing the basic frequencies, but the difference between these two systems may cause the shifted track in WK/PBK schema.

For a given source, mass and spin do not change significantly, and most likely only the mass accretion rate ($\dot{m}$) determines ν_HBO and ν_break. Extensive work has been done to study the spectral properties of GX 17+2 and XTE J1701-462 (Lin et al. 2009, 2012; Li et al. 2013). These authors suggested that the HBs of both GX 17+2 and XTE J1701-462 be interpreted by the same process acting at constant $\dot{m}$, namely an increase of Comptonization, while a changing $\dot{m}$ led to secular changes between subclasses. Table 3 shows that ν_HBO and ν_break increase along HB in both sources at a constant $\dot{m}$, which suggests that the values of ν_HBO and ν_break may be independent with $\dot{m}$, however, under the assumption of certain spectral models.

Several models have been proposed to study LFQPOs. Ingram et al. (2009) described a promising truncated disk/hot inner flow Lense–Thirring (vertical) model to interpret the characteristic frequencies seen in the broadband PSD of BH and NS. Within this model, the frequencies of LFQPOs are mostly dependent on the inner radius of the disk, while the break frequency is set by the viscous timescale at the outer edge of the flow (inner radius of disk). The ∼1 Hz LFQPOs detected in dipping/eclipsing NS-LMXBs also suggested that LT procession models for LFQPOs are possible in NS-LMXBs (Homan 2012). The LT precession relation (ν∝R⁻³) arose in GX 17+2, as introduced by Lin et al. (2012). However, Li et al. (2014) found that ν_HBO in XTE J1701-462 is positively correlated with an inner disk radius based on using the same spectra model with GX 17+2, which makes the LT model an impossible explanation for the HBOs in XTE J1701-462. They further proposed that HBOs come from a corona. In Figure 3, we show that part of the data from XTE J1701-462 overlap with IGR J17480-2446 (green dot), which was assumed to be a inappropriate candidate for LT precession (Altamirano et al. 2012). This makes LT precession a controversial model for explaining the HBOs in XTE J1701-462 or even in other Z sources. In general, the physical mechanism in WK/PBK correlations cannot be well interpreted with any model thus far.

Table 5 shows rms_break increasing linearly with energy below ∼12 keV at a constant slope (a = 0.200 ± 0.004) for XTE J1701-462 in both Cyg-like and Sco-like stages, while rms_HBO also shows the same trend with energy at a constant slope (a = 0.100 ± 0.001). Both rms_break and rms_HBO stay stable when the energy is above ∼12 keV, which is similar to what has been seen for the kHz QPOs (Berger & van der Klis 1996; Méndez et al. 2001). In addition, Figure 6 shows that both rms_break and rms_HBO decrease along HB, and Figure 7 also shows that these two components correlate with each other. These above results suggest that break and HBO components may come from a similar physical mechanism. Break and HBO signals reach the strongest strength at ∼12 keV indicates that they come from higher energy photons, most likely from non-thermal emission from corona, since thermal emission from the disk could not produce such high energy photons. Li et al. (2014) also suggested that the HBO components in XTE J1701-462 are possibly generated from Comptonization emission in a corona, based on the spectral fitting results. Here, we further suggest that Comptonization emission in the corona contributes to both break and HBO components in XTE J1701-462. These two components could be caused by the same kind of oscillation in a corona with uneven density, and they could be produced in different areas of the corona. If break and HBO components come from different areas, they could differ in oscillation frequencies.

GX 17+2 and XTE J1701-462 are Z sources, and the spectral evolution in GX 17+2 was very similar to XTE J1701-462 in its Sco-like stage (Lin et al. 2012). Our results in Figure 6 also show that these two sources have similar variability properties in the Sco-like stage. Both rms_HBO and rms_break decrease with increased source intensity, with hardness decreasing at the same time. Their power spectra resemble each other and they have similar HBO frequencies. In particular, the variations of rms_HBO and rms_break in interval E (GX 17+2) are similar with that of interval D (Sco-like stage in XTE J1701-462). These evidences indicate that break and HBO components in GX 17+2 probably have a similar origin as in XTE J1701-462.

Figure 7(b) shows that rms_HBO has a power-law relation with rms_break for both sources. The data of GX 17+2 lay between the points of HB and the HB/NB vertex of XTE J1701-462. The spectral properties of GX 17+2 are found to be very similar to those of XTE J1701-462 in its Sco-like stage: the HB is associated with Comptonization of disk emission while at the HB/NB vertex the disk assumes a slim disk solution (Lin et al. 2012; Li et al. 2014). For XTE J1701-462, the different distribution between HB and the HB/NB vertex could be caused by the sudden reduction of Comptonization emission when approaching the HB/NB vertex. The connection of non-thermal emission and HBO was found in XTE J1701-462 and GX 17+2: the strength of Comptonization emission decreases when the HBO frequencies increase from upturn to HB, while the HBO signal disappears when Comptonization emission become undetectable on the NB. As shown in Figure 6, for XTE J1701-462, Cyg-like intervals generally have larger values of rms (break and HBO) than Sco-like intervals, while the range of rms of GX 17+2 is consistent with the Sco-like interval D of XTE J1701-462. We suggest this could be caused by different proportions of Comptonization component in total flux: the proportion of the Comptonization component in the Cyg-like stage is higher than in the Sco-like stage, which causes higher rms in the Cyg-like stage. The proportion of the Comptonization component in the Sco-like stage (GX 17+2) is higher than at the HB/NB vertex, which causes the lowest rms to take place at the HB/NB vertex. Thus, the three distinguishable tracks contributed by HB, GX 17+2, and the HB/NB vertex could be caused by different proportions of Comptonization in the total flux.

The transient properties of some sources can be interpreted by the disk instability model (Lasota 2001), which assumes that the accretion disk gains mass from the mass donor at a constant mass transfer rate. The accretion rate is normally lower than the mass supply rate in the disk, thus mass is accumulated in the disk. When the accumulated mass exceeds a certain critical value, a sudden increase of accretion rate results in an outburst. By contrast, the persistent systems have a relatively stable accretion disk. The accretion disk tends to be more unstable in transient sources when they have an outburst, which would affect the oscillation in corona. This could be a reason why transient sources have a wider variation in ν_HBO and ν_break in WK/PBK schema if they are assumed to arise from different areas of corona. The persistent sources shifted from main track could be caused by the size of corona in persistent sources is different from transient sources. All of these suggestions still require further study.