Spectral and Timing Properties of the Galactic X-Ray Transient Swift J1658.2–4242 Using Astrosat Observations

Black hole transients (BHTs) spend most of their lives in quiescence and are primarily discovered when they enter into outbursts characterized by abrupt changes in their X-ray luminosity by several orders of magnitudes. During typical outbursts, BHTs undergo a transition from the low hard state (LHS) to the high soft state (HSS) through short-lived hard and soft intermediate states (HIMS, SIMS), then again back to the LHS via the intermediate states (Remillard & McClintock 2006; Belloni 2010; Belloni et al. 2011). In the LHS, the source is characterized by a hard spectrum with high (∼30%) fractional rms variability (Belloni 2005) and sometimes show low-frequency quasi-periodic oscillations (LFQPOs) in the power density spectrum (PDS). A soft thermal component modeled with multicolor disk blackbody component dominates in the HSS, while the fractional rms reduces down to a few percent and PDS shows weak power-law noise.

The intermediate states identified in the black hole systems are rather complex and the observed behaviors are difficult to interpret. In these states, the energy spectrum contains both disk and power-law components, while the PDS mainly contains LFQPOs with a centroid frequency ranging from a few mHz to ∼30 Hz. LFQPOs are identified in several sources and they are classified into types A, B, and C (Remillard et al. 2002; Casella et al. 2005). Type-C QPOs are mainly identified in the HIMS, while type A and B QPOs are detected in the SIMS (Wijnands et al. 1999; Casella et al. 2005; Motta et al. 2011). Although the origin of the LFQPOs is still under debate, several models have been proposed to explain the origin and evolution of LFQPOs in X-ray binaries. The proposed models are generally based on the two different mechanisms: instabilities (e.g., Tagger & Pellat 1999; Titarchuk & Osherovich 1999; Titarchuk & Fiorito 2004; Cabanac et al. 2010) and geometrical effects (Stella & Vietri 1998; Stella et al. 1999; Ingram et al. 2009; Ingram & Done 2011). LFQPOs are widely detected in BHTs and their detailed studies provide essential information regarding the accretion flow around the black hole and geometry of the system. In addition, it is important to examine the energy-dependent properties of quasi-periodic oscillations (QPOs) such as fractional rms and time lag, which also provide the link between the spectral and timing variability properties of BHTs.

Swift J1658.2–4242 is a new Galactic X-ray transient source discovered by the Burst Alert Telescope instrument on board Swift on 2018 February 16 (Barthelmy et al. 2018). The Imager on Board the INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) Satellite/ISGRI instruments on board INTEGRAL detected the source to be in the hard state during their observations of the Galactic center field performed from 2018 February 13 to 16 (Grebenev et al. 2018). The reported position of the source from the Swift X-Ray Telescope observation is R.A. = 16:58:12.58, decl. = −42:41:55.7 (equinox J2000.0) with an uncertainty of ∼4'' (D'Avanzo et al. 2018). Radio observation with the Australia Telescope Compact Array (ATCA) identified a radio source at a position consistent with the Swift XRT position, and the radio emission was consistent with a flat radio spectrum from a compact jet implying that the source is a black hole X-ray binary (BHXRB) at a distance >3 kpc (Russell et al. 2018). In the positional uncertainty of ATCA, an optical source has been observed in the archival imaging observation and the optical spectroscopy observation with SOAR telescope suggest this source is a normal, mid to late-type K star with no signatures of accretion (Bahramian et al. 2018). The Swift XRT observation taken with Window Time (WT) mode reports the presence of a peak at 0.115 Hz in the power spectrum (Kennea 2018), which was explained as a coherent period of the source rather than a QPO, and the authors suggested that the system may be a Be/X-ray binary with a neutron star compact object.

Xu et al. (2018) presented X-ray timing and spectral studies of this source using simultaneous NuSTAR and Swift observations. The broadband spectral modeling with relativistic reflection models suggested that the source is a BHXRB system that is observed in the bright hard state with a photon index of ∼1.6 and coronal temperature of kT_e ∼ 22 keV. From the relativistic disk reflection features, they suggest a highly spinning black hole for the system with a spin value > 0.96 and the inner accretion disk is viewed at a high inclination angle (∼64°). In addition, a low-frequency (type-C) QPO has been observed in the power spectrum with a shift in the QPO frequency from ∼0.14 to ∼0.21 Hz during the single NuSTAR observation.

Recently, Xu et al. (2019) studied the source in the intermediate state using the NuSTAR, XMM-Newton, and Swift observations. During these observations, the source intensity decreased rapidly by 45%, after which a transient QPO at 6–7 Hz was detected in the low flux state. The authors discussed these observed properties by invoking the accretion disk instability scenario. In addition, the relativistic disk reflection component detected in the bright hard state became weaker and was not significantly detected in these observations. Further, the rapid variation of X-ray flux leads to only subtle changes in the shape of the broadband X-ray spectrum, even though the disk temperature decreases by ∼15%.

These observed properties of the source can further be investigated using Astrosat data.  Swift J1658.2–4242 was observed by Astrosat on 2018 February 20 and the preliminary analysis with the Large Area X-ray Proportional Counter instrument on board Astrosat detected a sharp QPO at 1.6 Hz with an rms value of 16%. The observed centroid frequency increased from ∼1.6 to 2 Hz during the 20 ks observation (Beri et al. 2018).

In this work, we studied the X-ray timing and spectral characteristics of  Swift J1658.2–4242 using Astrosat observations. Astrosat (Singh et al. 2014; Agrawal 2017) is India's first multiwavelength astronomical observatory, which contains five onboard instruments: Soft X-ray Telescope (SXT), Large Area X-ray Proportional Counter (LAXPC), Cadmium Zinc Telluride Imager (CZTI), Scanning Sky Monitor (SSM), an Ultra Violet Imaging Telescope (UVIT). We analyze the simultaneous observations of  Swift J1658.2–4242 using the SXT and LAXPC instruments on board Astrosat. Section 2 describes the observations used in the work and the data reduction techniques. The analysis and results are presented in Section 3. The main results are summarized and discussed in Section 4.

We used three publicly available Astrosat target of opportunity observations of the recently discovered X-ray transient  Swift J1658.2–4242 in the Galactic plane. The first observation (O1; ObsID: T02_004T01_9000001910) was conducted during 2018 February 20–21 for an effective exposure of ∼20 ks. In the second observation (O2), the source was observed for an effective exposure time ∼30 ks during 2018 March 3–4 (ObsID: T02_011T01_9000001940), and the third observation (O3) was performed on 2018 March 28–29 (ObsID: T02_020T01_9000001990) with an effective exposure of 30 ks. The observations considered in the analysis are marked on the MAXI light curve shown in Figure 1.

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2.1. Soft X-Ray Telescope

2.2. Large Area X-Ray Proportional Counter

3.1. Timing Analysis

3.1.1. Observation 1

We extracted the background-subtracted light curve of the source from the LAXPC instrument in the 3–50 keV energy band, which is shown in the top panel of Figure 2. We used the LAXPC10 and LAXPC20 detectors for the light-curve extraction with a time bin size of 50 s. The source intensity appears to be constant with an average count rate of ∼654 count s⁻¹, with a marginal increase in the last part of the observation. The hardness ratio (HR) is calculated using the count rate in the 3–7 and 7–16 keV bands, and plotted in the bottom panel of Figure 2. From the plot, it is clear that the HR is in the range of ∼0.85–0.97 and we do not see any particular trend in the observation. To check the presence of QPOs in the light curve, we extracted the PDS in the 3–15 keV, 15–30 keV, and 30–50 keV energy bands. The extracted PDS in the 3–15 keV band is fitted with six Lorentzians and shown in Figure 3. A QPO is detected at ∼1.6 Hz in the PDS with a second harmonic at ∼3.2 Hz. However, the detected QPO feature cannot be fitted with a single Lorentzian. Thus, we attempted to fit the broad feature with two Lorentzians with centroid frequencies of ∼1.57 and ∼1.71 Hz. Moreover, it is noticed that the second harmonic feature observed in the 3–15 keV band is weak and not clearly detected in the 15–30 keV and 30–50 keV energy bands. The centroid frequency and width of the QPOs and second harmonic are given in Table 1.

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Since the source exhibited an increasing trend in the centroid frequency within the NuSTAR observation (Xu et al. 2018), we tested the time-dependent behavior of the QPO by extracting the dynamic power spectrum (DPS) using the standard LAXPC analysis tools. We used the frequency interval of 0.1–30 Hz to compute the DPS. It is clear from the DPS, which is shown in Figure 4, that the QPO changes its centroid frequency from ∼1.56 to ∼1.74 Hz during the observation. Thus, we split the light curve into two parts with time segments below 20 ks and above 20 ks in the light curve (see also Figure 2). To confirm the QPO frequency change, we again extracted the PDS with these time segments, which are shown in Figure 5. The PDS from the two time segments confirmed the change in the QPO frequency, and the second harmonic feature is strongly detected in both time segments only in the 3–15 keV band.

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We determine the fractional rms as a function of energy for the QPOs using several energy bands. We extracted the PDS for these energy bands and fitted the PDS with five Lorentzians. In the model fit, we fix the centroid frequency and width of all Lorentzians to the values obtained from the fitting the 3–15 keV PDS and vary the normalization. The fractional rms is estimated by taking the square root of the normalization of the Lorentzian representing the QPO feature. We used the same energy bands to estimate the time lag by following the method in Nowak et al. (1999). The calculated fractional rms and time lag for the two QPOs at ∼1.56 and ∼1.74 Hz by considering the respective time segments are plotted in Figure 6. For the time lag estimation, the frequency resolution was taken to be σ/3, where σ is the width of the QPO. The strength of the QPOs showed a clear variation with photon energy in both time segments as shown in the top left panel of Figure 6. For the QPO at ∼1.56 Hz, the fractional rms rises from ∼7% and reaches a maximum of ∼15% at the 27–33 keV energy band, but marginally decreases in the 33–50 keV band. For the QPO at ∼1.74 Hz observed in the second time segment, the fractional rms gradually increases from ∼8% to reach a maximum value of ∼15% in the highest (33–50 keV) energy band. The fractional rms of the second harmonics, detected at ∼3.13 and ∼3.49 Hz, seems to be constant in the different energy bands (see the top right panel of Figure 6). The time lags for the QPOs and second harmonics are not well constrained.

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3.1.2. Observation 2

The extracted light curve in the 3–50 keV energy band from the second observation shows an interesting variation pattern in the intensity (see the top panel of Figure 7). The source intensity increases gradually in the first part of the light curve followed by a drastic change in the intensity from ∼1000 to ∼1500 count s⁻¹ in a few kiloseconds time. The intensity then drops suddenly to reach ∼1100 count s⁻¹, which lasts for a few kiloseconds after which the source again reaches the high intensity level (∼1500 count s⁻¹). The source intensity finally drops by a factor of ∼2 in the last part of the observation. This variation in the intensity confirms the short-term variability behavior of the source. We extracted HR from the 3–7 and 7–16 keV light curves as depicted in the bottom panel of Figure 7. We do see marginal HR variation corresponding to the variation pattern observed in the intensity. In addition, the source intensity in the second observation is higher than the first observation by a factor of ∼3.

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Since the source exhibits significant variability behavior, we extracted flux-resolved light curve by choosing an intensity level of 1300 count s⁻¹ (see also the top panel of Figure 7). Using the flux-resolved light curve, we generated the PDS for the two intensity levels in the 3–15 and 15–30 keV bands. The PDS in low and high intensity levels are shown in the left and right panels of Figure 9. A QPO (∼6.60 Hz) and a subharmonic (∼3.17 Hz) are clearly detected in the PDS for the low flux level. However, it is interesting to note that the PDS in the high flux level is significantly changed compared to the PDS in low flux level and the QPO is weakly detected in the high flux level. We further computed the fractional rms of light curves for high and low flux levels from different energy bands and found that the fractional rms has changed by a factor of ∼3. Since the source exhibited flux drops and intensity-dependent QPO behavior in the course of observation, we further explored the time-dependent behavior of the QPO by extracting the DPS (see Figure 8). In the DPS, significant power is observed at the QPO frequency of ∼6.6 Hz during the low flux level, while the QPO power decreases when the intensity increases to higher values, which is consistent with the PDS (see also Figure 9).

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It is clear that the QPO is detected only in the low intensity level; thus, we estimate the fractional rms and time lag using the data only in the low intensity level. We used different energy bins and computed the fractional rms and time lag at QPO and subharmonic frequencies (see Figure 10). The fractional rms at QPO frequency increases from ∼2.5% to reach ∼12% in the highest-energy band of 28–50 keV, while at the subharmonic frequency, the fractional rms increases from ∼2.5 to ∼7.5%. The time lag at QPO frequency and at the subharmonic frequency decreases as the energy increases and the maximum observed time lags are ∼−7 ms and ∼−35 ms for the QPO frequency and the subharmonic in the 14–19 keV and 19–28 keV energy bands, respectively. This further implies a soft lag at both QPO (∼6.60 Hz) and subharmonic (∼3.17 Hz) frequencies.

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3.1.3. Observation 3

In the third observation, the LAXPC30 detector was no longer operational and the LAXPC10 detector was operating at low gain. Thus, we generated the light curve from the LAXPC20 detector only in the 3–50 keV band with a time bin size of 50 s, which is shown in the top panel of Figure 11. From the plot, it is clear that the source did not significantly vary during the observation and the intensity appears to be constant. Moreover, the calculated HR using the count rates in the 3–7 and 7–16 keV energy bands (see the bottom panel of Figure 11) did not show any significant variation. We extracted the PDS in the 0.01–10 Hz using an energy range of 3–50 keV and fitted the PDS with four Lorentzians (see Figure 12). In the power spectrum, we detected the QPO and subharmonic features at ∼3.98 Hz and ∼2.29 Hz, respectively, along with some broad features. We have not detected any time-dependent behavior in this QPO, as observed in the first observation. We estimated the fractional rms and time lags at the QPO frequency from different energy bands and plotted them in Figure 13. The fractional rms at the QPO frequency marginally increases, from ∼1 to ∼4%, with energy.

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3.2. Broadband X-Ray Spectral Analysis

We used the broadband X-ray spectral coverage of Astrosat from the SXT and LAXPC instruments, and fitted both spectra of the source simultaneously in the 0.7–25.0 keV energy band. The spectral modeling was performed with xspec version 12.9.1p (Arnaud 1996). We used the absorbed multicolor disk blackbody (MCD; diskbb in xspec) plus thermal Comptonization (nthcomp) model components to explain the broadband X-ray spectral features of the source. The absorption is incorporated by Tuebingen-Boulder Inter-Stellar Medium absorption model (tbabs; Wilms et al. 2000). The MCD (Mitsuda et al. 1984) component explains the X-ray emission from the accretion disk and provides the seed photons for the Comptonization. Thus, we kept the MCD temperature and seed photon temperature (in nthcomp model) as the same. The nthcomp model (Zdziarski et al. 1996; Życki et al. 1999) describes the thermal Comptonization in a hot corona. The spectral fitting with this model provides a worse fit in all cases with residuals in soft energies. Thus, we added a partial covering fraction absorption (pcfabs in xspec) model and this model fit resulted in a better fit in all cases with Δχ² = −41.4 to −745.0 for 2 degrees of freedom compared to the absorbed MCD plus thermal Comptonization. In the simultaneous SXT and LAXPC fit, we used a multiplicative constant to address the cross-calibration uncertainties between the instruments. A 3% model systematic error is introduced in the model fitting. The quoted parameter uncertainties are at a 90% confidence level.

Table 1.  QPO, Second Harmonic, and Subharmonic Parameters of  Swift J1658.2–4242 in Different Observations

Obs	Seg	QPO	QPO	Second Harmonic	Width	Subharmonic	Width	χ2/dof
		Frequency (Hz)	Width	Frequency (Hz)		Frequency (Hz)
O1	⋯	${1.566}_{-0.011}^{+0.011}$	${0.182}_{-0.038}^{+0.033}$	${3.211}_{-0.044}^{+0.044}$	${0.653}_{-0.172}^{+0.216}$	⋯	⋯	67.1/73
	⋯	${1.712}_{-0.035}^{+0.042}$	${0.390}_{-0.052}^{+0.043}$
	1	${1.561}_{-0.004}^{+0.004}$	${0.204}_{-0.014}^{+0.014}$	${3.127}_{-0.030}^{+0.031}$	${0.339}_{-0.099}^{+0.109}$	⋯	⋯	82.4/76
	2	${1.740}_{-0.006}^{+0.006}$	${0.294}_{-0.021}^{+0.021}$	${3.489}_{-0.053}^{+0.050}$	${0.522}_{-0.188}^{+0.252}$	⋯	⋯	88.4/ 76
O2	⋯	${6.572}_{-0.052}^{+0.052}$	${2.032}_{-0.203}^{+0.189}$	⋯	⋯	${3.178}_{-0.134}^{+0.116}$	${1.847}_{-0.467}^{+0.509}$	88.3/74
	1	${6.603}_{-0.038}^{+0.038}$	${1.963}_{-0.115}^{+0.119}$	⋯	⋯	${3.170}_{-0.104}^{+0.092}$	${1.773}_{-0.317}^{+0.336}$	80.0/71
O3	⋯	${3.975}_{-0.017}^{+0.040}$	${0.479}_{-0.075}^{+0.062}$	⋯	⋯	${2.287}_{-0.128}^{+0.106}$	${0.204}_{-0.201}^{+0.239}$	91.5/47

Note. (1) Observation; (2) segment used; (3)–(4) centroid frequency and width of QPOs; (5)–(6) centroid frequency and width of the second harmonic; (7)–(8) centroid frequency and width of the subharmonic; (9) ${\chi }^{2}$ statistics and degrees of freedom.

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We fitted the observed spectra from the three observations (see Figure 14), and the best-fit model parameters are given in Table 2. The electron plasma temperature (kT_e) was not constrained and hence fixed at 70 keV. The first absorption column density (N_Htbabs) changed from 2.1 to 5.2 × 10²² cm⁻² between the first and second observations, while the second absorption component exhibits a marginal increasing trend in all three observations. However, the covering fraction and inner disk temperature show a marginal decreasing trend as the time evolves. In addition, the yielded photon index increases from ∼1.9 to ∼2.4 in these observations.

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Table 2.  Broadband X-Ray Spectral Parameters for  Swift J1658.2–4242

Obs	Seg	NHtbabs	NH	f	kTin	Ndiskbb	Γ	Nnthcomp	Fdisk	FTotal	Ratio	χ2/dof
O1	⋯	${2.06}_{-1.09}^{+0.99}$	${9.33}_{-0.56}^{+0.55}$	${0.968}_{-0.028}^{+0.018}$	${1.74}_{-0.22}^{+0.22}$	${7.60}_{-2.32}^{+3.95}$	${1.87}_{-0.11}^{+0.09}$	${0.16}_{-0.04}^{+0.05}$	${1.38}_{-0.35}^{+0.34}$	${5.09}_{-0.21}^{+0.25}$	0.27	235.8/255
	1	${2.41}_{-1.17}^{+1.14}$	${9.66}_{-0.69}^{+0.69}$	${0.960}_{-0.038}^{+0.023}$	${1.68}_{-0.23}^{+0.23}$	${8.28}_{-2.71}^{+5.02}$	${1.89}_{-0.11}^{+0.09}$	${0.17}_{-0.04}^{+0.06}$	${1.31}_{-0.35}^{+0.34}$	${5.11}_{-0.25}^{+0.30}$	0.26	180.9/187
	2	${3.53}_{-2.39}^{+2.47}$	${9.38}_{-1.18}^{+1.79}$	${0.930}_{-0.160}^{+0.056}$	${1.65}_{-0.22}^{+0.22}$	${11.49}_{-4.13}^{+8.42}$	${1.90}_{-0.11}^{+0.09}$	${0.19}_{-0.05}^{+0.07}$	${1.66}_{-0.40}^{+0.41}$	${5.78}_{-0.43}^{+0.61}$	0.29	109.6/101
O2	⋯	${5.20}_{-0.24}^{+0.23}$	${10.72}_{-0.81}^{+0.87}$	${0.829}_{-0.018}^{+0.017}$	${1.10}_{-0.06}^{+0.06}$	${362.16}_{-93.79}^{+139.57}$	${2.25}_{-0.06}^{+0.06}$	${0.61}_{-0.10}^{+0.12}$	${9.73}_{-0.86}^{+1.06}$	${16.96}_{-1.21}^{+1.50}$	0.57	504.5/535
	1	${5.06}_{-0.33}^{+0.31}$	${9.43}_{-1.01}^{+1.13}$	${0.796}_{-0.032}^{+0.029}$	${1.10}_{-0.07}^{+0.07}$	${270.70}_{-80.04}^{+129.01}$	${2.21}_{-0.06}^{+0.06}$	${0.46}_{-0.08}^{+0.10}$	${7.33}_{-0.76}^{+0.99}$	${12.93}_{-1.05}^{+1.36}$	0.57	436.44/462
	2	${4.92}_{-0.42}^{+0.42}$	${10.25}_{-0.86}^{+0.99}$	${0.861}_{-0.029}^{+0.025}$	${1.23}_{-0.08}^{+0.08}$	${251.33}_{-67.61}^{+105.74}$	${2.25}_{-0.07}^{+0.07}$	${0.66}_{-0.12}^{+0.15}$	${10.69}_{-0.91}^{+1.11}$	${19.40}_{-1.31}^{+1.67}$	0.55	408.62/404
O3	⋯	${5.06}_{-0.18}^{+0.18}$	${12.16}_{-1.01}^{+1.07}$	${0.786}_{-0.023}^{+0.022}$	${1.04}_{-0.07}^{+0.07}$	${287.14}_{-85.35}^{+138.44}$	${2.40}_{-0.07}^{+0.06}$	${0.46}_{-0.08}^{+0.10}$	${6.19}_{-0.69}^{+0.89}$	${10.97}_{-0.98}^{+1.26}$	0.56	498.45/537

Note. (1) Observation; (2) segment used; (3) neutral hydrogen column density in units of ${10}^{22}\,{\mathrm{cm}}^{-2}$ from tbabs model; (4) neutral hydrogen column density in units of ${10}^{22}\,{\mathrm{cm}}^{-2}$ from pcfabs model; (5) covering fraction; (6) inner disk temperature in keV (7) diskbb normalization; (8) photon index; (9) nthcomp normalization; (10)–(11) the unabsorbed disk flux and total flux in units of 10⁻⁹ erg cm⁻² s⁻¹ in the 0.7–25 keV band derived using cflux; (12) ratio of the disk flux to the total flux; (13) χ² statistics and degrees of freedom.

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The source showed time-dependent and intensity-dependent QPO behaviors in the first and second observations, respectively. Thus, we extracted the spectra from different time segments to study the spectral characteristics of the source related to these behaviors. The spectral modeling of two spectra from the different time segments in the first observation suggests no clear variations between the best-fit model parameters (see Table 2). However, in the second observation, the partial covering fraction and inner disk temperature increase between low and high intensity levels, while the change in the power-law index is marginal.

We also computed the unabsorbed flux in the 0.7–25 keV band using the convolution model cflux. The flux increases by a factor of ∼3 in the second observation compared to the first, while the flux dropped by a factor of ∼2 in the third observation. It is also noted that the disk fraction increases from ∼30% to ∼60% in these observations, which suggests a more dominant disk emission in the later observations.

3.3. Fitting the Energy Dependence Timing Properties

The motivation here is to quantify the energy-dependent fractional rms and time lags of  Swift J1658.2–4242 as measured by LAXPC. In order to do so, we invoke a single-zone stochastic propagation model, which is characterized by only three parameters: the normalized variations of the electron temperature of the inner hot flow (δT_e), inner disk temperature (δT_in), and the phase angle between them (ϕ = 2πfτ_D, where f is the QPO frequency and τ_D is the time lag). However, for model fitting we use the three parameters, δT_e, τ_D, and the attenuation parameter, which quantifies the attenuation of propagations from the corona to disk, given by the ratio δT_in/δT_e. A detailed description of the model is presented in Maqbool et al. (2019). The geometry of the system is assumed to be that of a truncated standard disk with a hot inner flow and Maqbool et al. (2019) applied the model to the hard state of Cygnus X–1. While their analysis was for the broadband noise, here we apply the same model for the QPOs observed. Thus, in contrast to the general idea of fluctuation propagating inward, we assume that an oscillation originates in the inner hot region causing variations in the electron temperature, which then propagates outward, and reaches the outer truncated disk causing variations in the inner disk temperature, but after a time delay.

We first fitted the fractional rms and time lag at the QPO frequency and obtained the fit parameters as given in Table 3. For each of the second harmonic frequencies, we successfully fitted the model by fixing the phase parameter at twice the value of the phase of the respective QPO. The model fitting shows similar time lag for the QPO frequency of 1.56 Hz and second harmonic of 3.12 Hz in the first observation. This trend was also seen for the QPO and second harmonic frequencies at 1.70 Hz and 3.48 Hz, respectively. However, in the case of subharmonic frequency (3.17 Hz), we were not able to fit the observed time lag by fixing the phase value at half of the phase of the QPO at 6.6 Hz. However, keeping phase as a free parameter, we were able to fit the time lag for subharmonic frequency. Thus, the model suggests that the fitting of time lag for the subharmonic frequency requires equal phase change rather than equal time delay. In the case of a QPO frequency of 3.97 Hz, we were able to constrain the fractional rms and time lag with a systematic of 17% suggesting that perhaps the temporal behavior is more complex than the simple model assumed here.

Table 3.  Best-fit Parameters from the Fluctuation Propagation Model

Frequency	δTe	τD	δTin/δTe	χ2/dof
(Hz)		(ms)
1.561	${0.29}_{-0.02}^{+0.03}$	$-{1.49}_{-3.66}^{+3.65}$	${0.087}_{-0.006}^{+0.006}$	25.0/18
3.127	${2.27}_{-1.88}^{+0.00}$	$-1.49(f)$	${0.004}_{-0.004}^{+0.000}$	7.5/19
1.740	${0.29}_{-0.03}^{+0.03}$	$-{3.49}_{-4.28}^{+4.28}$	${0.090}_{-0.006}^{+0.006}$	28.1/18
3.489	${1.19}_{-0.75}^{+0.00}$	$-3.49(f)$	${0.008}_{-0.008}^{+0.011}$	14.1/19
6.603	${0.09}_{-0.02}^{+0.02}$	$-{12.74}_{-3.12}^{+3.08}$	${0.061}_{-0.004}^{+0.004}$	17.9/10
3.170	${0.15}_{-0.03}^{+0.03}$	$-{37.98}_{-4.14}^{+4.15}$	${0.041}_{-0.005}^{+0.004}$	12.0/10
3.975	${0.03}_{-0.00}^{+0.08}$	${10.25}_{-0.0}^{+0.0}$	${0.021}_{-0.004}^{+0.005}$	19.9/10

Note. (1) Frequency in Hz; (2) variation in the electron temperature; (3) time lag in ms; (4) ratio of the variation in the inner disk temperature to the variation of electron temperature; (5) ${\chi }^{2}$ statistics and degrees of freedom.

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We have presented the spectral and timing analysis of the new black hole binary candidate  Swift J1658.2–4242 using Astrosat observations. The main results of the study are as follows.

• 1.  
  We detected QPOs at frequencies of ∼1.7, ∼6.6, and ∼4.0 Hz.
• 2.  
  The QPO detected at ∼1.56 Hz drifts to a higher centroid frequency of ∼1.74 Hz in the course of the first observation.
• 3.  
  We observed a peculiar behavior in the second observation, where the QPO detected at ∼6.6 Hz becomes weak or disappears at high intensity levels.
• 4.  
  The fractional rms of the QPOs increases with photon energy and soft time lag of the order of ∼35 milliseconds were detected for the QPO at 6.6 Hz and its subharmonic.
• 5.  
  The doubly absorbed disk plus thermal Comptonization model successfully explains the observed broadband spectra and the best-fit spectral parameters vary between the observations.
• 6.  
  We quantified the frequency-dependent fractional rms and time lag using a single-zone stochastic propagation model. Variation of the temperature of the corona and the disk with a time lag between them can explain the energy-dependent temporal behavior.

Type-C QPOs are mainly detected in the HIMS of BHXRBs (Wijnands et al. 1999; Casella et al. 2005; Motta et al. 2011). Their centroid frequencies have a range of 0.1–15 Hz with a Q factor (Q = ν/FWHM) of 7–12 and a typical rms of 3%–16% (Casella et al. 2004, 2005). The detected LFQPOs at ∼1.7, ∼6.6, and ∼4.0 Hz from the Astrosat observations are consistent with the above-mentioned values. Thus, these LFQPOs most likely belong to the type-C QPOs (Casella et al. 2004, 2005; Motta et al. 2015). The QPO detected at 1.56 Hz drifts to a slightly higher centroid frequency in the course of observation (see Figure 4). Similar behavior has been reported in the hard state of the source using NuSTAR observation, where the QPO frequency drifts from 0.14 to 0.20 Hz (Xu et al. 2018). In addition, a transient QPO at 6–7 Hz has been reported for the source from the NuSTAR and XMM-Newton observations in the intermediate state, where the QPO appeared only in the low flux level (see Figures 2 and 4 of Xu et al. 2019). We have observed similar behavior in the Astrosat observation, where the QPO at ∼6.6 Hz is strongly detected in the low intensity level, while the QPO becomes weak when the source exhibits flaring (see also Figure 7).

Rapid flux transitions have been detected in some black hole X-ray binaries in their very high states and such behavior has been proposed to have a jet origin (e.g., Miyamoto et al. 1991; Takizawa et al. 1997; Casella et al. 2004; Belloni 2005). Moreover, these flux transitions are associated with the fast transition between the different types of QPOs. However, the observed scenario in the case of  Swift J1658.2–4242 is phenomenologically distinct compared to other sources, where the QPO becomes weak or is not detected during the hard flaring. The disappearance of the QPO associated with rapid flux transition has never been observed in other BHXRBs. This confirms the results from the NuSTAR, Swift, and XMM-Newton observations, where they observed a transient QPO in the low flux state alone (Xu et al. 2019). Thus, the origin of the rapid changes in the observed properties may be due to thermal and viscous instabilities (Shakura & Sunyaev 1973) in the accretion disk as has been reported earlier for this source (Xu et al. 2019).

For the first time we have studied the fractional rms and time lag as a function of photon energy up to 50 keV for  Swift J1658.2–4242 (see Figures 6, 10, and 13). It is noted that the fractional rms at the QPO and the subharmonic frequencies increase with photon energy, while at the second harmonic frequencies the rms seems to be constant. The observed energy dependence of the fractional rms at the QPO frequencies clearly suggests that these LFQPOs are associated with the high-energy component, i.e., the corona. In addition, we have observed soft time lag at QPO and subharmonic frequencies. However, at the second harmonic frequencies there is weak/zero time lag.

In order to quantify the frequency-dependent fractional rms and time lags, we invoke a single-zone stochastic propagation model. The model fitting provides physical measures of the time the fluctuation takes to travel from the inner hot region to the outer truncated disk and successfully explains the time lags observed in the source. We observe a similar time lag for the QPO (1.56 and 1.74 Hz) and second harmonic (3.17 and 3.49 Hz) frequencies, while the model fitting provides different time lags for QPO and subharmonic frequencies at 6.6 and 3.17 Hz, respectively. Thus, the model suggests that the fitting of time lag for the subharmonic frequency requires equal phase change rather than equal time delay.

It is interesting to compare the energy-dependent timing properties of  Swift J1658.2–4242 with Cygnus X-1. For a QPO frequency of 1.56 Hz, the time lag between the δT_in and δT_e is about −1.5 ms, implying that the variation δT_e occurs first. For Cygnus X-1, the time lag is similar for the same frequency, but is positive, implying that the variation δT_in occurs first (Maqbool et al. 2019). Thus, while for Cygnus X-1, the corona responds to a stochastic perturbation that occurs in the disk, for  Swift J1658.2–4242 it is opposite, such that the QPO originates in the corona and the fluctuation propagates outward toward the disk. Nevertheless, the time lags for both systems are of the same magnitude implying that the speed of the fluctuations and the distance traveled are of the same order. For  Swift J1658.2–4242, the primary driver δT_e induces a small fluctuation δT_in and thus the attenuation ratio is small, δT_in/δT_e ∼ 0.09. On the other hand, for Cygnus X-1, since the driver is δT_in, the ratio turns out to be an order of magnitude larger (Maqbool et al. 2019).

The hard-intermediate state of BHXRBs is characterized by the decrease in the HR in the hardness-intensity diagram along with the soft spectra, where the index increases up to ∼2.5, and the presence of the disk component. In addition, the total fractional rms decreases with softening and the type-C QPOs are widely detected in this state (Belloni 2010). During the Astrosat observations, we observed a drop in the HR by a factor of ∼2, the photon index significantly changed from ∼1.9 to ∼2.4, the disk fraction increased steadily to ∼60%, and type-C QPOs were detected. Thus, based on the timing, hardness ratio, and spectral analysis, we have identified the source to be mainly in the HIMS of BHXRBs.

The column density varies between the observations, and the inferred values are generally consistent with previous studies with Swift and NuSTAR observations (Xu et al. 2018). Thus, our analysis with Astrosat confirms the highly absorbed nature of  Swift J1658.2–4242. The inner disk temperature increased by ∼12% when the flux increased during the second observation, which is consistent with earlier studies by Xu et al. (2019), where they observe a decrease in disk temperature by ∼15% when the flux dropped. The observations conducted with Swift and NuSTAR on 2018 February 16 identified the source in the hard state with an index of ∼1.63 (Xu et al. 2018), while the Astrosat observation conducted on 2018 February 20–21 identified the source in the hard-intermediate state with an index of ∼1.9. The joint XMM-Newton and NuSTAR observations conducted on 2018 February 25 identified the source to be in the hard-intermediate state with an index of ∼2.1. Thus, it seems that the observed spectral evolution of  Swift J1658.2–4242 is similar to the other Galactic BHXRBs (Belloni 2010; Belloni et al. 2011).

Previous studies of  Swift J1658.2–4242 with Swift and NuSTAR observations found a strong reflection component in the bright hard state (Xu et al. 2018). In the following observations after ∼8 days, the source was identified to be in the intermediate state of BHXRBs, where the reflection feature becomes weak. One possible explanation for the observed scenario is related to the truncation of accretion disk, where the disk reached the innermost stable circular orbit (ISCO) in the bright hard state and a strong reflection component is detected, while the accretion disk receded from the compact object in the intermediate state, which leads to the detection of the weak reflection component (Xu et al. 2019). However, such a reflection component is not apparent in the Astrosat observations, where the source is mostly identified in the intermediate state. Thus, the nondetection of reflection features in the Astrosat spectra may be because of the intrinsic weakness of the reflection component in the intermediate state. Such a weak component may be hard to detect with the current uncertainties in the response matrix of Astrosat.

We thank the anonymous referee for the constructive comments and suggestions that improved this manuscript. This work was started in the IUCAA-APT Mini School on X-ray Astronomy Data Analysis held at Providence Women's College, Kozhikode, and we thank the organizers for the hospitality. A.R.T. and G.M. acknowledge the IUCAA Visitors Program. The research is based on the results obtained from the Astrosat mission of the Indian Space Research Organization (ISRO), archived at the Indian Space Science Data Centre (ISSDC). This work has used the data from the LAXPC and SXT instruments. We thank the LAXPC Payload Operation Center (POC) and the SXT POC at TIFR, Mumbai for providing the data via the ISSDC data archive and the necessary software tools.

Facilities: ADS - , HEASARC. -

Software: LaxpcSoft, SXT Software, HEASOFT (v 6.22), XSPEC (v 12.9.1p; Arnaud 1996).