The energy dependence of the three types of low-frequency quasi-periodic oscillations in the black hole candidate H1743−322 Free

Abstract

INTRODUCTION

It is widely accepted that the spectrum of black hole X-ray binaries (BH XRBs) has two components, i.e. the soft and hard. The soft component involves an optically thick and geometrically thin accretion disc, which radiates ultraviolet and soft X-rays at the typical energies of ∼1 keV. The hard component originates from a corona of hot plasma surrounding the disc, where the soft photons from the disc undergo inverse Compton scattering and produce a power-law spectrum in the hard X-ray band. When the mass accretion rate changes, these two components evolve and the BH undergoes several spectral states, i.e. hard (H), soft (thermal-dominant or TD) and very high (steep power law or SPL) state (Esin, McClintock & Narayan 1997; Belloni et al. 2005) with each state exhibits different variability properties. During the hard state, the power-law component with an index between 1.4 and 2.1 contributes more than 80 per cent of the total 2–20 keV unabsorbed flux, and strong low-frequency quasi-periodic oscillations (LF QPOs) are usually present. In the soft state, the flux is dominated by a disc blackbody from the accretion disc and the disc flux fraction is more than 75 per cent. The QPO is usually absent in this state. During the very high state, the power-law index is more than 2.4, and broad weak QPO may be present (Mendez & van der Klis 1997; Remillard & McClintock 2006; McClintock & Remillard 2006).

A truncated disc model is usually quoted to account for both the X-ray spectral and variability properties found in BH XRBs. In this model, a standard outer accretion disc is truncated away from the central BH and replaced by a hot inner flow near the BH at low luminosity. As the disc moves inwards, it penetrates further into the hot flow then more seed photons from the disc are intercepted by the flow so the Compton spectrum softens. The hot flow collapses and the BH turns into the soft state when the disc reaches the last stable orbit. Also, the decrease in the disc truncation radius leads to higher characteristic frequencies (including QPOs) in the power density spectra (PDS; Yuan, Cui & Narayan 2005; Done, Gierliński & Kubota 2007).

The LF QPOs with centroid frequencies from mHz to tens of Hz have been observed in the X-ray flux of most BH XRBs (see McClintock & Remillard 2006, van der Klis 2006 and references therein). Three main types of LF QPOs have been classified in several sources based on their frequencies, phase lags, quality factors (Q), full width at half-maximum and so on. For example, type A, B and C QPOs are originally identified in the light curve of XTE J1550−564 (Wijnands, Homan & van der Klis 1999; Homan et al. 2001; Belloni, Psaltis & van der Klis 2002; Remillard et al. 2002; Casella et al. 2004). Type A and B QPOs appear in the soft intermediate state, and show different harmonic and phase lags, while type C QPO appears in the hard states (i.e. low-hard and hard intermediate) with strong broad-band-limited noise accompanied in its PDS. The frequency of the type C QPO is known to correlate with some spectral properties in BH XRBs, such as the photon index, disc inner radius, disc temperature and the fluxes of the power-law and disc components (see e.g. Muno, Morgan & Remillard 1999; Remillard et al. 2002). In addition, all these QPOs are observed only when the power-law component contributes more than 20 per cent of the 2–20 keV flux, indicating that both the disc and power-law components are linked to the QPO phenomenon (Sobczak et al. 2000).

The X-ray transient H1743−322 was first discovered with the Ariel V and HEAO-1 satellites by Kaluzienski & Holt (1977) during a bright outburst in 1977. In 2003, another bright outburst was detected with the International Gamma-ray Astrophysics Laboratory (INTEGRAL) and it was observed with Rossi X-ray Timing Explorer (RXTE) almost every day during this outburst. Its spectral and timing features show similarities to those of other, dynamically confirmed, BH transients and therefore it was classified as a BH candidate (McClintock et al. 2009). The 2003 outburst was followed by several weaker outbursts in 2004 (Swank 2004), 2005 (Rupen, Mioduszewski & Dhawan 2005), 2008 (Kalemci et al. 2008), 2009 (Krimm et al. 2009; Chen et al. 2010), 2010, 2011 and also 2012. However, these outbursts are less sampled in X-ray observations and we therefore focus only on the 2003 outburst.

On the other hand, recent studies show that the LF QPO's frequency is strongly correlated with the photon energy in BH XRBs of GRS 1915+105 (Qu et al. 2010; Yan et al. 2012) and XTE J1550−564 (Li et al. 2013), which may shed lights on our understanding of the QPO mechanism. Considering the similarities between XTE J1550−564 and H1743−322 (McClintock et al. 2009), one may expect a similar behaviour in the energy dependence of QPO frequency. In this work, we mainly study the LF QPOs dependence on the photon energy in H1743−322 in detail. The analyses of the observational data and results are given in Section 2, and the discussions are made in Section 3.

OBSERVATIONS AND RESULTS

We have analysed all the available RXTE observations of H1743−322 during its major outburst of 2003, and detected LF QPOs in 76 observations. The daily averaged All-Sky Monitor (ASM) light curve of this outburst is shown in the top panel of Fig. 1. The fundamental QPO frequency evolving with time is given in the bottom panel of Fig. 1. The QPO observation IDs (ObsIDs) and other information are listed in Table 1.

Figure 1.

RXTE observations of H1743−322 during the 2003 outburst. The top panel shows the daily averaged ASM light curve while the bottom shows the fundamental QPO frequency. The blue and green points in the top panel represent the hard to SPL intermediate and SPL state, respectively. The red, green, blue and orange points in the bottom panel stand for the type A, B, C and B’ QPOs, respectively.

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For each of their 76 observations, we first extract the 8 ms time resolution light curve of the full photon energy band, corresponding to PCA Channel 0–255. Secondly, we produce PDSs every 64 s of the 8 ms light curve, and then average them to derive the PDS of the whole observation. The PDS ranges from 0.015 625 to 64 Hz. The Poisson noise is not directly subtracted and the PDS is normalized to squared mean intensity (Miyamoto et al. 1991). Finally, we use the model of a constant plus several Lorentzian functions to fit the PDS and derive the QPO frequency from the fitting parameters. The constant represents the Poisson noise, one Lorentzian function stands for the PDS continuum and the others stand for the fundamental QPO and its harmonics.

In consideration of that the change in PDS fitting range causes far less changes in QPO frequency than its errors (see Li et al. 2013), a minimum reduced χ² method adjusted slightly different from Li et al. (2013) is used during the fitting in this work. First, we fit the PDS of the full energy band of an observation with its fitting range between an arbitrary value and 64 Hz. Then we change the arbitrary value until a minimum reduced χ² is obtained at a certain value. Finally, the PDSs of sub-energy bands of this observation are all fitted between this certain value and 64 Hz. This certain value is different for different observations and they are listed in the 5th column of Table 1. The reduced χ² and the number of Lorentzian function used in fitting the PDS of the full energy band are respectively shown in the 6th and 7th columns in Table 1. After fitting the PDS, we can get the LF QPO properties of the PDS. Also, the QPO frequencies, amplitudes and quality factors for all the 76 observations are listed in the 8th, 9th and 10th columns of Table 1, respectively. During the fitting, the error bars are given with Δχ² = 1. As the spectral properties are investigated in detail by McClintock et al. (2009), we focus on the LF QPO in this work. However, the spectral state and fitting model of each observation cited from McClintock et al. (2009) are also given in the 12th and 13th columns of Table 1, respectively.

As discussed above, type A and B QPOs are associated with the very high state, and type C QPO is usually related to the hard state (including the hard intermediate state). Moreover, type C QPO usually superposes on a strong band-limited noise, while type B QPO accompanies with a weak band-limited noise and type A accompanies without any band-limited noise. Based on these characteristics, we classify the LF QPOs of H1743−322 into three types and the QPO types of all these 76 observations are displayed in the 11th column of Table 1. The results also show that (1) type A QPO's frequency ranges from ∼4 to 6 Hz, with Q between ∼2 and 5, and amplitude mostly at ∼2–5 per cent. (2) Type B QPO's frequency is between ∼4.7 and 5.7 Hz, with Q between ∼3 and 6, and amplitude between ∼3 and 5 per cent. (3) Type C QPO's frequency ranges from ∼1.5 to 8.5 Hz, with its Q varying from ∼5.5 to 14 and amplitude changing between 4 and 14 per cent. (4) Two-thirds of the type C QPOs appear in the intermediate state (i.e. hard to very high state), while A, B and one-third C-type QPOs are found in the very high state. (5) More than half of the type C QPOs are accompanied with an iron line while all the A and B type QPOs not.

Besides, we find another type of QPO, whose frequency is around ∼4 Hz, its amplitude is less than 1 per cent while quality factor is larger than 10. We classify this kind of QPO as the extreme case of the type B, i.e. type B’, because it shows weak band-limited noise and has the same relation between amplitude and frequency as the normal type B QPO does (see Fig. 2). The amplitude–frequency relations of the other QPO-types are shown in Fig. 2 as well. From that figure, we can clearly see that the type C QPO's frequency is negatively correlated with its amplitude while the other LF QPOs show a positive correlation.

Figure 2.

Fundamental QPO amplitude versus its frequency in H1743−322. The red, green, blue and orange points represent the type A, B, C and B’ QPOs, respectively.

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The energy dependence of fundamental QPO frequency is derived too. To improve the statistics, we only derive the energy dependence of the fundamental QPOs whose amplitudes are not less than 3 per cent. However, some observations have strong QPOs but short exposures and we combine the neighbouring two short observations to get a QPO frequency versus photon relation. Also, there are two observations, i.e. 80146-01-43-01 and 80146-01-53-01, that cannot be merged with others, they are therefore discarded for deriving their QPO frequency–energy relations. Finally, we get an entire sample of 48 observations (or merged observations, see the first column of Table 2). The sub-energy bands of each observation (or merged observations) are fixed at PCA Channels 0–10, 11–14, 15–19, 20–26 and 27–255, corresponding to the energy bands of 2–4.49, 4.49–6.12, 6.12–8.17, 8.17–11.04 and 11.04–117.86 keV, respectively. The PDS of individual energy band is produced the same as that of the full energy band. The frequency–energy relations of all the sampled observations are displayed in Fig. 3 with the fundamental QPO types and frequencies marked in each panel of Fig. 3.

Figure 3.

Fundamental QPO frequency versus photon energy in H1743−322. The figures are shown in the QPO frequency sequence.

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Meanwhile, we use a linear function to estimate the correlation between the QPO frequency and photon energy. The reduced χ² of each observation is shown in the 3rd column of Table 2. The constant and slope parameters of the linear function are listed in the 4th and 5th columns of Table 2, respectively. As a result, the QPO frequency versus photon energy relation can be well described by the linear function in 38 out of 48 observations according to the reduced χ² listed in the 3rd column of Table 2. During these 38 observations (reduced χ² less than 1.5), 30 observations show a positive correlation, seven observations show no correlation (see the slopes of 19th, 20th, 21st, 24th, 34th, 38th and 40th rows of Table 2) and only one shows a weak anticorrelation (with the type C QPO frequency of 2.275 Hz, see the 5th panel of Fig. 3). During the 10 other observations, whose frequency–energy relations cannot be well fitted by a linear function (the reduced χ² is more than 1.5, see the 7th, 9th, 14th, 29th, 30th, 35th, 39th, 41st, 42nd and 43rd rows of Table 2), three are A-type QPOs (5.196, 5.471 and 5.508 Hz), four are B-type QPOs (4.847, 5.175, 5.267 and 5.363 Hz) and three are C-type QPOs (4.681, 4.880 and 7.334 Hz). The linear fit to these 10 QPOs’ frequency–energy relation gives a reduced χ² within a range of 1.5–4.02. Apparently, the large reduced χ² values for type A and B QPOs are due to the ambiguous correlation between the QPO frequency and photon energy. Although the linear function works badly for these three C-type QPO observations, the QPO frequency increases clearly with the photon energy (see Fig. 3).

Figure 4.

The slope of the QPO frequency versus energy relation plotted as a function of the QPO frequency in H1743−322. The red, green and blue points represent the type A, B and C QPOs, respectively. The black line is the best-fitted power-law function which models the 1 to 7.5 Hz C-type QPOs well.

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The energy dependence of the QPO amplitude is investigated as well and the results are shown in Fig. 5, where the amplitude increases monotonically with the photon energy at energy below ∼10 keV and flattens at energy above ∼10 keV.

Figure 5.

Fundamental QPO amplitude versus photon energy in H1743−322. The figures are shown in the QPO frequency sequence.

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SUMMARY AND DISCUSSIONS

We investigate the properties of the LF QPOS in H1743−322 and have several interesting findings. Apart from the type A, B and C QPOs, a new sub-class QPO shows up at frequency around ∼4 Hz with amplitude less than 1 per cent and quality factor larger than 10, which is different from the normal type B QPO, whose frequency is between ∼4.7 and 5.7 Hz, with amplitude between ∼3 and 5 per cent, and Q between ∼3 and 6. However, this new sub-class QPO superposes on a weak band-limited noise like the normal B-type QPO dose, and its amplitude follows the same tendency as the normal type B QPO's in the amplitude–frequency figure. As a result, we classify this new sub-class QPO as the extreme case of the normal type B QPO, i.e. type B’, in this work.

The negative correlation between QPO amplitude and frequency is widely found in XRBs of e.g. XTE J1550−564 (Li et al. 2013), GRO J1655−40 (Sobczak et al. 2000), GRS 1915+105 (Muno et al. 1999), H1743−322 (McClintock et al. 2009) and so on. However, both the type B and A QPOs show positive correlation between amplitude and frequency, which may suggest a different mechanism in producing the QPO.

As shown in Fig. 5, the QPO amplitude of H1743−322 increases apparently with photon energy when it is below ∼10 keV but changes a little above ∼10 keV, and this behaviour is independent on QPO types. The energy dependence of QPO amplitude is also investigated in many other XRBs of e.g. GX 339−4 (Belloni, Motta & Muñoz-Darias 2011), Cyg X−1, XTE 1752−223 (Muñoz-Darias et al. 2010), XTE J1650−500 (Gierliński & Zdziarski 2005) and XTE J1550−564 (Li et al. 2013). Besides the positive correlation, a flat and inverted correlation were also reported (Rodriguez et al. 2004; Gierliński & Zdziarski 2005; Sobolewska & Życki 2006). The flat and inverted correlations are usually related to the hard state, however the positive correlation is observed in the intermediate, soft and very high state. Moreover, the positive correlation is usually considered as the evidence of the corona-origin of QPOs. Furthermore, detailed discussions about this can be found in Rodriguez et al. (2004), Gierliński & Zdziarski (2005), Sobolewska & Życki (2006) and so on.

In H1743−322, only in the type C QPOs the QPO frequency shows monotonic/clean correlation with photon energy (see Fig. 3). The positive correlation exists in some of the type A and B QPOs. Also the slope in this correlation is well represented with a power law for only type C QPOs. This behaviour, together with the different QPO amplitude-frequency correlations, may provide a joint diagnostic for discriminating LF QPOs of the different types.

As shown in Qu et al. (2010) and Yan et al. (2012), the centroid frequency of the LF QPOs in GRS 1915+105 decreases with photon energy at frequency of less than ∼3 Hz, but reverses at higher frequency. A similar trend is also present in XTE J1550−564, but with a turn-over QPO frequency at around 0.4 Hz (Li et al. 2013). However, the pattern that the type C QPO frequency depending on the photon energy in H1743−322 is slightly different from that of GRS 1915+105 (Qu et al. 2010; Yan et al. 2012) and XTE J1550−564 (Li et al. 2013) in that H1743−322 shows no apparent turn-over frequency from the negative to positive correlation. However, this difference is likely due to the lack of observational data for H1743−322 in hard state, since the frequency turn-over of XTE J1550−564 happened during the initial hard state of the 1998 outburst (Li et al. 2013).

In summary, we find the properties LF QPOs in H1743−322 are different between type C and the others. These findings provide further phenomena that are helpful for our understanding on the QPO mechanism in BH XRBs.

This work is subsidized by the Natural Science Foundation of China for Young Scientists (Grant No. 11203064), the Program of the Light in Chinese Western Region (LCWR) (Grant No. XBBS201121) provided by Chinese Academy of Sciences (CAS) and the Natural Science Foundation of China for support via NSFC 11073021 and 11173024. We thank S. N. Zhang and F. Yuan for useful discussions. We also thank the referee for helpful comments and valuable suggestions.

REFERENCES