Timing analysis of the black hole candidate EXO 1846–031 with Insight-HXMT monitoring

Black hole low mass X–ray binaries (BH–LMXBs), mostly known as transient systems (black hole transients, BHTs), spend most of their lives in a quiescent state but outburst suddenly for maybe weeks or months. During the quiescent state of BHTs, the luminosity is usually lower than 10³³ erg s⁻¹, however, when it goes into an outburst, the source can reach a peak luminosity very fast, after which the luminosity will gradually decrease to the level of the quiescent state. During the outburst, BHTs usually exhibit four spectral states (Homan & Belloni 2005), namely the low-hard state (LHS), hard-intermediate state (HIMS), soft-intermediate state (SIMS) and high-soft state (HSS). The X-ray observations indicate that BHTs are in a hard state at the beginning of the outburst, and then will evolve into a soft state. Between the hard and soft states, two intermediate states (HIMS and SIMS) are defined based on their spectral and timing properties (Homan & Belloni 2005). The LHS mainly occurs in the early and later stages of the outburst, during which the energy spectra are dominated by a hard component, with a power law photon index varying between 1.5 and 1.7. The variability amplitude in LHS can reach a level higher than 20%. In the HIMS, the variability gets weaker and the fractional root mean square (rms) usually fluctuates between 5%–20%. The SIMS exists for only a small fraction of time during the whole outburst, in which the spectrum becomes softer, and the X-ray variation is weak (rms ≲ 10%). When the source evolves into the HSS, the rms will drop to less than 3%, and the energy spectrum is dominated by the disk components.

Low-frequency quasi-periodic oscillations (LFQPOs), which are defined as narrow peaks in the power spectra, have been observed in most BHTs (see van der Klis 2006 for details). Three types of LFQPOs in BHTs with Fourier frequencies ranging from a few mHz to tens of Hz are classified based on their timing features (fractional rms, quality factor Q = ν₀/(2Δ), where ν₀ is the center frequency, and Δ is the half width at half maximum) in the power density denity, noise component and phase lag properties(Wijnands & van der Klis 1999; Remillard et al. 2002; Casella et al. 2005; Motta et al. 2011). Type–A quasi-periodic oscillations (QPOs) usually appear in the soft state of an outburst when the light curve has rms ≲ 3%. The PDS of type–A QPOs are characterized by low-amplitude, red noise and the absence of harmonics. Type–B QPOs appear in the SIMS when the rms of the light curve is 3% – 5% (Kalamkar et al. 2015), whose PDS are characterized by a weak harmonic and power law noise. Generally seen in LHS and HIMS, type-C QPOs are characterized as a strong narrow peak and associated with strong 'flat-top' noise, harmonics and possible subharmonics in the PDS. During the hard states (LHS and HIMS), the centroid frequencies of type–C QPOs regularly increase with source luminosity.

The origin of the type–C QPOs has been studied extensively. Theoretical models that explain the origin of type–C QPO can be divided into two categories: the instability of accretion flows (Titarchuk et al. 1999; Titarchuk & Fiorito 2004; Varnière et al. 2012) and the geometric effects of general relativity (Stella & Vietri 1998, 1999; Schnittman et al. 2006; Ingram et al. 2009). Considering the instability, physical models such as transition layer (Titarchuk & Wood 2004), corona oscillation (Cabanac et al. 2010) and the Accretion- Ejection Instability (AEI) mechanism (Varnière et al. 2003) have been proposed in recent years. The geometric effect involved is mainly a relativistic precession model, which was first proposed by Stella & Vietri (1998), then modified and improved by Schnittman et al. (2006). This model can explain the main observational characteristics of LFQPOs, for example, the frequency evolution of LFQPOs, energy spectra and their phase-resolved spectra. In recent years, more and more observations by X-ray telescopes support that the type-C QPOs may have a geometric origin, with Lense-Thirring precession of the entire inner flow (Ingram et al. 2009; Pawar et al. 2015; van den Eijnden et al. 2017).

In 1985, the European X-ray Observatory SATellite (EXOSAT) discovered the black hole X–ray binary candidate EXO 1846-031. By analyzing data from the first outburst in 1985, Parmar et al. (1993) proposed that the center of the source is most likely a black hole. The source erupted again and was detected by the Monitor of All-sky X-ray Image (MAXI) on 2019 July 23 and the 4–10 keV flux reached about 100 mCrab on July 28 (Negoro et al. 2019). Insight–HXMT began its observation from 2019 August 2, and the preliminary energy spectral analysis showed that the X-ray spectral properties are typical for outbursts in BH–LMXBs (Yang et al. 2019). The Neutron Star Interior Composition Explorer (NICER) observed EXO 1846-031 between 2019 July 31 and 2019 October 25 (Bult et al. 2019).

In this work, we use the observations by Insight-HXMT, NICER and MAXI to study the temporal features of this source. Section 2 presents an introduction to observations and data reduction. In Section 3, the timing results are described in detail. We provide a summary and some discussions of our results in Section 4.

2.1. Observations

2.2. Data Reduction

2.3. Data Analysis and Methods

The hardness-intensity diagram (HID) and hardness-rms diagram (HRD) are conventional methods for analyzing the spectral properties of X-ray binary transients. In many cases, the shape of the HID from BHTs tracks a 'q'-like pattern, if the source performs a complete outburst. We rely on timing properties and HID of this source to distinguish spectral states. The hardness ratio is defined as the ratio of count rate in 4–10 keV and 2–4 keV for LE and MAXI/GSC in this work respectively.

In order to analyze the timing properties, we employ POWSPEC to create a PDS from each light curve by rms normalization (Miyamoto et al. 1991) and split the extracted light curves into 64 s segments including 2048 bins. We fit the the PDS applying XSPEC V12.10 for different components. For the possible QPO components, we fit the Poisson-extracted PDS utilizing a model consisting of several Lorentzians accounting for the possible broad band noise (BBN), the possible QPO fundamental and (sub) harmonics. Since we use the rms normalization in PDS, the fractional rms of QPO is given by (Bu et al. 2015)

$$\begin{eqnarray}&&{{\rm{rms}}}_{{\rm{QPO}}}=\sqrt{R}\times \displaystyle \frac{(S+B)}{S}.\end{eqnarray} \tag{ 1 }$$

Here R is the normalization of the Lorentzian component of the QPO, S is the source count rate, while B is the background count rate.

3.1. Hardness and Timing Evolution

used for referring to this section from elsewhere Based on the Insight–HXMT data, we plot light curves, hardness and total fractional rms of EXO 1846–031 during this outburst in Figure 1. Throughout the outburst, the light curves of LE and NICER show similar behaviors, which can be seen in the top panel of Figure 1. The count rate in low energy (LE 1–10 keV) increases rapidly during the rise phase until it reaches its peak at 233.39 count s⁻¹ on MJD 58705. As for the high energy (HE 25–150 keV) and medium energy (ME 10–20 keV), the count rate decreases monotonically from 248.85 count s⁻¹ and 51.70 count s⁻¹ to a constant level, respectively. In the middle panel of Figure 1, the hardness decreases sharply at first. After reaching a small peak, the hardness begins to fall again to a stable low level. Correspondingly, the count rate of LE (1–10 keV) also has a small fluctuation. As can be seen from the fractional rms evolution diagram (the bottom panel of Fig. 1), most type-C QPOs (Sect. 3.2) appear in fractional rms > 5%, which is consistent with typical BHT sources, for example, H1743–322 (Zhou et al. 2013).

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In Figure 2, we present the HID and HRD of EXO 1846-031 using Insight–HXMT/LE count rate. The results confirm that no complete HID shape is revealed, because the decrease phase of the outburst is not observed. Therefore, we rely on data from the longer observation period of MAXI to draw a more complete HID in Figure 3, where a complete 'q' shape is presented. Comparing Figure 3 with Figure 3, the observations by LE and NICER only cover a part of the complete 'q' pattern due to low count rate. Throughout the outburst, the hardness decreases from ∼ 1.3 to ∼ 0.3 and the fractional rms of the continuum's PDS decreases from ∼ 25% to ∼ 3%, which indicates that the source undergoes state transitions. Moreover, using QPO positions and spectral evolution in HID, we can identify the different spectral states of the outburst, i.e., LHS, HIMS, SIMS and HSS.

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For the first three observations of Insight–HXMT, the X-ray flux increases but hardness ratio barely changes. At the same time, we compare the position of these three observations in HID of MAXI, which is consistent with the phenomenon that X-ray flux increases rapidly while hardness ratio remains unchanged. Those characteristics demonstrate that the source may be in its LHS. During the LHS, the frequency of QPOs increases from 0.71 Hz to 0.96 Hz, and the total fractional rms decreases from ∼ 23.87% to ∼ 22.03%. Following the LHS, the count rate in low energy enhances from 67.31 count s⁻¹ and gradually reaches its peak at 233.39 count s⁻¹ with the hardness ratio decreasing from 1.3 to 0.7 (see Fig. 2). The frequency of QPOs increases from 0.96 Hz to 6.59 Hz (see Fig. 5), and the total fractional rms decreases from ∼ 22% to ∼ 10%. The evolution of the hardness ratio and the timing properties affirms that the source goes into its HIMS. After the flux peak, the X-ray flux of the source drops steeply to 117.47 count s⁻¹ with a constant hardness ratio. Those characteristics seem to be consistent with the LHS at rise phase of the outburst. However, during this phase, the near constant frequency of the QPOs and the stable total fractional rms indicate that the source is in the HIMS. On about MJD 58713, the outburst enters into the second hump, and the peak value of the LE count rate reaches about 154.16 count s⁻¹. During this hump, the total fractional rms drops to ∼ 3% and the hardness is less than 0.6. Such phenomena are consistent with SIMS, although no type–B QPO is observed. When the source leaves the SIMS, the evolution of the light curve enters the last count hump. The results verify that the hardness is less than 0.3, and the total fractional rms remains near a constant value. The outburst entered the HSS. The rough classification between the four states is marked by vertical dashed lines in Figure 2, while the detailed state analysis is required in combination with the energy spectrum (Ren et al., manuscript in preparation).

To study the fast time-variability properties of EXO 1846–031, the PDS is calculated for each observation. The PDS manifests a broad noise component and one or two narrow peaks at different frequencies. It can be seen from the PDS diagram that the observed QPOs can be classified as type–C QPOs, and no type–B QPO is detected throughout the outburst. The QPOs are observed since the first day (MJD 58697) of the Insight–HXMT observations and last for about 8 days. The NICER observations started from MJD 58695 and the QPO observations last for 19 days. Figure 4 features eight representative examples (one representative observation at LHS and one at HIMS) and the fitting results of PDS for observations with different QPO frequencies. Using the fitting model mentioned in Section 2.3, we fit all the parameters of the QPOs as shown in Tables A1, A2, A3 and A4. The frequency range of the total QPOs observed is between 0.26 Hz and 8.42 Hz.

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Figure 5 presents QPO frequency evolution with time for three energy bands of Insight–HXMT and 1–10 keV of NICER. The Insight–HXMT data indicate that the frequency of most QPOs exhibits no energy dependence as seen by LE/ME/HE, and increases monotonically from 0.26 ± 0.00 Hz to 8.42 ± 0.41 Hz. With more NICER observations, we can see that the frequency of QPOs increases at first and then becomes stable; QPO disappears when the source enters a relatively soft state. During the period when QPOs are observed, the hardness detected ranges from 1.33 to 0.63, with the rms decreasing from 23.8% to 2.66%.

More intriguingly, as featured in the top panel of Figure 6, there is a relationship between fractional rms of QPO and its center frequency. For the QPO detected by LE (energy band: 1–10 keV), the QPOs' fractional rms increases from 6.9% to 12.4% when the frequency is lower than ∼2 Hz, and then decreases, which is similar to the case of GRS 1915+105 (Yan et al. 2013; Zhang et al. 2017). In the middle panel of Figure 6, we plot the QPO frequency (LE) as a function of the hardness. As one can see from this figure, the hardness has a downward trend (from 1.31 ± 0.04 to 0.73 ± 0.02) with the frequency increasing, but we can find there are several flat spots (about 1 Hz, 2 Hz and > 6 Hz). The relationship between the total fractional rms and frequency is depicted in the bottom panel of Figure 6. We show the QPO frequency evolution with the count rate in Figure 7. The QPO frequency increases with the count rate of LE (1–10 keV), in the meantime the ME (10–20 keV) and HE (25–150 keV) count rate decreases.

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We have performed a timing analysis and spectral evolution (hardness) study for the 2019 outburst of EXO 1846–031 by examining the observations with Insight–HXMT, NICER and MAXI. The HID derived from the MAXI/GSC data assumes the typical q-shape. Low frequency Type-C QPOs are detected in the early stage of the outburst. The outburst evolution is consistent with the behaviors observed in other typical BHTs, for example, GX 339-4 (Motta et al. 2011). Considering QPO positions and spectral evolution in HID derived from Insight–HXMT/LE, we have identified the different spectral states of the outburst, i.e., LHS, HIMS, SIMS and HSS. Before MJD 58697, we ascertained that the source was in its LHS and then evolved to the HIMS (about MJD 58697 – MJD 58711). According to our analysis, this outburst appeared in the SIMS for a short time, about a few days. Around MJD 58717, the outburst entered the HSS. Due to the weak X-ray flux when the source returned to its HIMS or LHS, the full deceasing phase of outburst was not totally observed by Insight–HXMT or NICER.

The evolution of the total fractional rms values calculated from Insight–HXMT/LE observations is similar to those observed in other BHTs (Belloni et al. 2005; Rao et al. 2010; Muñoz-Darias et al. 2011a). During the LHS, the maximum value of rms is 24% and remains around 21%, while rms ≲ 21% in HIMS and 5% ≲ rms ≲ 10% in SIMS. In the HSS, the observed rms is between ∼ 1.2% and ∼ 10% with large uncertainties, which seems to be larger than the typical value observed in other BHTs. We obtained a weighted averaged rms value of 3.81% ± 2.28% during HSS, which is consistent with the typical variability amplitude in HSS. A similar behavior in MAXI J1659–152 is reported by Muñoz-Darias et al. (2011b), in which they explained it with a high orbital inclination.

Type–C QPOs were both detected during the LHS and HIMS by Insight–HXMT and NICER. Type–C QPO features are similar to the phenomenon of typical BHTs. The QPO frequency varies from ∼0.1 Hz to ∼8 Hz with increasing X-ray flux (accretion rate). However, no type-B QPO has been detected throughout the 2019 outburst in LE or NICER observation. The relationships of QPO frequency–hardness and frequency–total fractional rms in the middle and bottom panels of Figure 6 have been reported in other BHTs, such as Swift J1658.2-4242 (Xiao et al. 2019), MAXI J1659–152 (Muñoz-Darias et al. 2011b) and MAXI J1820+070 (Stiele & Kong 2019). It is interesting to note that the QPO rms shows a different relationship with the QPO frequency at Insight-HXMT energy bands in the top panel of Figure 6, which is similar to figure 6 in Kong et al. (2020). In the low energy band (LE 1–10 keV), the QPO rms first increases, and then decreases at around 2 Hz, which is similar to the results of GRS 1915+105 reported by Yan et al. (2013). Compared with NICER, Insight–HXMT has a higher effective area at high energies, which can provide the high energy characteristics of QPO. The trend of QPO rms in high (HE 25–150 keV) and medium energy (ME 10-20 keV) continues to rise. The upward trend is slower than the trend in LE energy band before 2 Hz, but after that, the trend remains almost constant. We can see from this figure that at any frequency, the QPO rms at higher energy is greater than that of LE. More detailed discussions of the rms energy spectra of QPO can be seen in GRS 1915+105 (Yan et al. 2012), MAXI 1535-571 (Huang et al. 2018) and H1743-322 (Li et al. 2013), in which they considered that the origin of type-C QPOs comes from the non-thermal corona.

For the LFQPOs, many models have been proposed, most of which can be classified either as geometrical effects – whereby the shape and/or size of something varies quasi-periodically – or intrinsic variations – whereby some fundamental property such as pressure or accretion rate oscillates in a stable geometry (for a review see, e.g., Ingram & Motta 2020). In this work, we are primarily inclined to rely on the Lense-Thirring precession model (Stella & Vietri 1998; Ingram et al. 2009) to explain the observational phenomena, while also discussing our results in the framework of the AEI model (Tagger & Pellat 1999).

In the truncated disk model (Esin et al. 1997), the thin disk truncates at some radius, and is replaced by a hot inner flow (corona) which is thought to produce the non-thermal emission. If the black hole spin misaligns with orbital spin, the inner flow will undergo Lense–Thirring precession, which modulates the flux mainly by the combination of Doppler boosting and projected area effects. According to the definition, rms = Δ F/(TC + PL) (where Δ F is the QPO amplitude, TC is the thermal emission from the thin disk and PL is the non–thermal emission flux produced by the inner hot flow), we know that the rms of QPO is affected by both thermal and non-thermal components. During the state transition, the truncation radius moves in and the inner hot flow contracts to a more central position and becomes more compact (Kara et al. 2019), leading to softening of the spectra and increasing of the QPO frequency. When the QPO frequency is lower than ∼2 Hz (about MJD 58698), the energy spectrum is dominated by the non–thermal component (Ren et al., manuscript in preparation). As the mass accretion rate increases, the optical depth of the inner flow increases, thus giving stronger modulation (Ingram et al. 2009; Schnittman et al. 2006). In addition, the reduction of non-thermal components also leads to the increase of rms of QPO. On the other hand, when the QPO frequency is above ∼2 Hz, as the inner disk approaches the black hole, soft photons from the disk continue to cool hot electrons in the inner hot flow, making the size of inner hot flow decrease, and the thermal component gradually begins to play a major role in the low energy band. As demonstrated in Figure 1, the count rate of LE continues to increase after ∼2 Hz, which leads to the decrease of rms of QPO in the lower energy band. However, the emission of HE and ME comes from non–thermal flow. Therefore, the rms of QPO presents a flattening or even a slightly rising trend later in higher energy.

In addition to the precession models, there is another class that discusses the origin of QPO based on various instabilities occurring in either the disk or the corona. Among these models, we intend to use the AEI model to explain our results. The AEI model (Varnière et al. 2001; Rodriguez et al. 2002; Varnière et al. 2002) suggests that the instability of global spiral on magnetized accretion disk may be the origin of QPO. The rotation frequency of the quasi-steady spiral is the orbital frequency at the co-rotation radius (r_c), which is a few times the orbital frequency at the inner edge of the disk (r_in). Based on this, Mikles et al. (2009) discussed the relationship between QPO frequency and inner disk radius. Using the AEI model, Varnière & Vincent (2017) explained the QPO rms-frequency relationship in the 1998-99 outburst of XTE J1550–564, which is similar to the results of this article, but the maximum rms is at ∼1.5 Hz. They suggested that both the strength of the instability and the unmodulated flux emitted between r_in and r_c should affect the QPO rms. Thus different outbursts from the same source or between sources will have a similar increase and then decrease, but with a different position for its maximum which depends on the local condition in the disk (such as its density, magnetization, etc.).

Recently, Motta et al. (2015) reported such an inclination dependence of QPO properties with statistical relation between the QPO rms and its frequency. They found that the type–C QPO exhibits a systematically larger absolute variability amplitude in edge–on sources, consistent with Lense–Thirring precession as its origin. They also found the rms-frequency relation has a maximum value at around 2 Hz (see fig. 1 in Motta et al. 2015). So, for the phenomenon at 1–10 keV, one speculation is that the rms of QPOs depends on the orbital inclination. This result might suggest that EXO 1348–031 is a high inclination system. However, it is unclear why the above 2 Hz feature is observed in high inclination systems.

This work made use of data from the HXMT mission, a project funded by China National Space Administration (CNSA) and the Chinese Academy of Sciences (CAS). This research has applied MAXI data provided by RIKEN, JAXA and the MAXI team. This work also has acquired data from the High Energy Astrophysics Science Archive Research Center Online Service, provided by the NASA/Goddard Space Flight Center. This work is supported by the National Key R&D Program of China (2016YFA0400800) and the National Natural Science Foundation of China (Grant Nos. 11673023, U1838201, U1838115, U1838111, U1838202, 11733009 and U1838108).