Unveiling the Temporal Properties of MAXI J1820+070 through AstroSat Observations

We have analyzed ∼93 ks simultaneous data from SXT and LAXPC on board AstroSat spanning over a period of 2 days starting from 2018 March 30. Observed data consisted of 15 continuous segments corresponding to 15 individual orbits of the satellite. Level 1 photon counting mode data of SXT was processed through the official SXT pipeline AS1SXTLevel2-1.4b⁴ to produce Level 2 files.

The HEASoft version 6.24 tool XSELECT was used to extract spectra and lightcurves between the source regions of 4' (inner radius) and 16' (outer radius). These regions were chosen to account for pile-up effect in the charged coupled device (CCD) due to high flux rate (∼1 Crab) of the source in SXT energy range (0.3–8.0 keV). The response matrix file (RMF) "sxt_pc_mat_g0to12.rmf," standard background spectrum "SkyBkg_comb_EL3p5_Cl_Rd16p0_v01.pha" and an ancillary response file (ARF) appropriate for source location on the CCD created using SXT ARF generation tools⁵ were used for the analysis.

Each of the 15 images was visually examined to ensure that drift corrections of the satellite were applied and a single point source was seen. Following this, we used the SXT event merger tool (see footnote 5) to merge all 15 individual Level 2 files into one single merged event file. The merged file was later used for spectral analysis.

The official LAXPC software⁶ was used to process Level 1 event mode data to obtain Level 2 files. The sub-routines of LAXPC software (Antia et al. 2017) were used to generate a good time interval file, total spectrum, RMF, and background spectrum for proportional counters 10, 20, and 30, respectively. However, data from LAXPC10 and LAXPC30 were not used for this work as the POC team reported abnormal gain change in LAXPC10 on 2018 March 28 and LAXPC30 was not operational during this observation.

We have performed a combined spectral fitting of SXT and LAXPC20 spectra using XSPEC 12.9.1p in the energy range 0.7–80 keV. Lower energies (<0.7 keV) were not considered due to the uncertainties in the effective area and response of the CCD. A 3% systematic error was incorporated during analysis to account for uncertainties in response calibration. Background uncertainty was taken to be 3%. Gain correction was applied to the SXT data using the XSPEC command gain fit with slope unity and the best-fit offset value was found to be 23 eV. Relative normalization was allowed to vary between SXT and LAXPC data.

The source spectrum was found to be dominated by thermal Comptonization component along with disk emission and reflection component (Figure 1, left panel). We used XSPEC models nthcomp (Życki et al. 1999), diskbb (Mitsuda et al. 1984; Makishima et al. 1986), and ireflect (Magdziarz & Zdziarski 1995) to fit the thermal Comptonization, disk emission, and reflection component, respectively. We also added model tbabs (Wilms et al. 2000) to account for interstellar absorption. Interstellar hydrogen column density (N_H) was frozen at 0.15 × 10²² cm⁻² (Uttley et al. 2018). Disk emission was considered to be input seed photons for Comptonization, and thus the parameters T_in and nthcomp temperature (kT_bb) were tied together and treated as a single parameter during the fitting. For the reflection model, the abundance was fixed to solar values while the inclination was taken to be ∼30° (Bharali et al. 2019). The temperature of the reflector was tied to the inner disk temperature. The electron temperature of the Comptonizing cloud (kT_e) was not constrained by the data and hence was fixed at a fiduciary value of 100 keV. The disk ionization parameter was frozen at 10 erg cm s⁻¹. The best-fit spectral parameters are listed in Table 1. The spectral index (Γ = 1.61 ± 0.01) obtained indicated that the source was in a hard spectral state (Titarchuk & Shaposhnikov 2005). The disk temperature was found to be 0.22 ± 0.01 keV, suggesting a cool disk truncated at a large distance (∼526 km; Kubota et al. 1998). Spectra also showed the presence of a Compton hump around 30 keV, indicating disk reflection. Note that the parameters obtained here are an approximation due to the large systematic error (3%) considered while fitting SXT and LAXPC spectra, which did not allow for more precise spectral modeling. We also tried using a few other reflection models like reflionX to further constrain the reflection parameters. However, we did not find any significant improvement in the fit or obtain a better estimate of the parameters.

Table 1.  Spectral and PDS Parameters

Spectral Parameters
Model parameters	rel_refl	Γ	Ncomp	kTin	Ndisk	χ2/degree of freedom (dof)
(Description)	(Relativistic	(Asymptotic	(Normalization	(Temperature	(Normalization
	reflection)	power law)	factor)	at inner disk	factor)
				radius) keV	×105
Best-fit value	0.17${}_{-0.05}^{+0.04}$	1.61${}_{-0.01}^{+0.01}$	3.42${}_{-0.06}^{+0.05}$	0.22${}_{-0.01}^{+0.01}$	2.4${}_{-0.6}^{+0.6}$	696/578
PDS parameters
Feature	QPO	Weak	Noise hump 1	Noise hump 2	Noise hump 3	${\chi }^{2}$/dof
		oscillation
Centroid frequency (Hz)	${47.7}_{-2.0}^{+1.6}$ × 10−3	${109.4}_{-1.2}^{+2.8}$ × 10−3	0a	0a	1.04${}_{-0.20}^{+0.13}$
Width (Hz)	${11.9}_{-3.6}^{+5.0}$ ×10−3	$\lt 1.7\times {10}^{-3}$	${10.7}_{-1.3}^{+2.3}$	${0.24}_{-0.02}^{+0.02}$	1.6${}_{-0.6}^{+0.7}$	123/114
Norm ×10−3	${2.5}_{-0.6}^{+0.6}$	${0.3}_{-0.1}^{+0.2}$	${10.3}_{-1.1}^{+0.8}$	${11.1}_{-0.6}^{+0.6}$	2.1${}_{-0.9}^{+1.9}$

Note.

^aParameter frozen during fitting.

Download table as:  ASCIITypeset image

A PDS was generated in the energy range 3–80 keV using LAXPC20 data by averaging segments of 282.64 s with 0.0045 s time resolution. It was then binned logarithmically in frequency to obtain the PDS shown in the right panel of Figure 1 in the frequency range 0.004–30 Hz. The spectrum shows a prominent QPO at 47.7 mHz and three broadened noise humps, which can be represented by Lorentzians. There is also a weak feature at 109.4 mHz, and modeling this component with a Lorentzian resulted in a decrease of χ², i.e., Δχ² = 12 for three additional degrees of freedom (dof). The final χ²/dof was found to be 123/114 after taking into account 2% systematic error. The best-fit parameters are listed in Table 1.

Zoom In Zoom Out Reset image size

Following this, we studied energy dependent temporal behavior by adopting the methodology discussed in Maqbool et al. (2019). The complete event mode data available from LAXPC for the computation of fractional rms and time lag for a large number of finer energy bins integrated over a certain frequency range allows one to compare the results directly with models.

We studied energy-dependent fractional rms and time lag in the energy range 3–80 keV for a range of frequencies using the data from LAXPC20. Nowak et al. (1999) and Miyamoto et al. (1988) have shown that the energy dependence of the time lag is logarithmic in nature. Hence, following the procedure discussed in Maqbool et al. (2019) the observed time lag and fractional rms were fit empirically using Equations (1) and (2), respectively.

$$\begin{eqnarray}&&\delta t(E,f)={T}_{d}(f)\times \mathrm{log}(\displaystyle \frac{E}{{E}_{\mathrm{ref}}})\end{eqnarray} \tag{ 1 }$$

where E is the energy (keV), f is the frequency (Hz) under consideration, E_ref = 4.76 keV is the reference energy, and T_d(f) is a constant.

$$\begin{eqnarray}&&F(E,f)=A(f)\times {E}^{p(f)}\end{eqnarray} \tag{ 2 }$$

where A(f) and p(f) are constants. We have computed the time lag with respect to the reference energy band 4.15–5.37 keV for a wide range of frequencies. Figure 2 shows the energy-dependent time lag and fractional rms for three representative frequencies of 0.1, 1.0, and 10.0 Hz. The rms decreases with energy depending on the frequency whereas the time lag increases with energy, implying that they are hard lags where the hard energy photons lag the softer ones. Figure 3 (top panel) shows the variation of the best-fit parameters A(f), T_d(f), and p(f) with frequency.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Although Figure 3 (top panel) gives an idea about temporal behavior of the system in frequency and energy, they neither provide an interpretation of physical behavior of the system nor its association to the time-averaged PDS. Hence, to make such an association we modeled the observed fractional rms and time lag using the stochastic propagation model developed by Maqbool et al. (2019). We present this result along with a comparison of the results of Cygnus X-1 in the following sections.

The onset of this millennium has seen several ongoing efforts in the development of stochastic propagation models to explain energy-dependent continuum variability observed in most X-ray binaries. Most of these models are built upon the fundamental idea that the perturbations originate at the outer annuli of the disk and propagate toward the central object (Kotov et al. 2001; Ingram & Done 2011, 2012; Ingram & van der Klis 2013; Rapisarda et al. 2016, 2017; Axelsson & Done 2018; Mahmoud & Done 2018). Primarily, these models are aimed at making quantitative predictions of PDS, energy-dependent time lags, and rms variability. Time lags are associated with perturbation propagation time (of the order of viscous timescales), and the prognosis of such studies could provide insights about the geometry of the system in this scenario (Böttcher & Liang 1999; Misra 2000; Kotov et al. 2001).

Kotov et al. (2001) considered the radial profile of the emissivity index and explained the frequency dependency of the time lag. Rapisarda et al. (2017) and Axelsson & Done (2018) linked the production of hard X-rays to the existence of several different Comptonization regions and the origin of photons of various energies with different regions of the accretion disk. However, it is difficult to comprehend the existence of such multi-Comptonization regions, if high-energy photons are indeed produced in the corona having optical depth ∼1. Most importantly, this raises questions about the radial profile of emissivity index. On the other hand, Misra (2000) explained the frequency-dependent time lag by attributing the origin of hard X-ray photons to an optically thick disk with a rapidly varying temperature profile.

Recent work carried out by Cowperthwaite & Reynolds (2014), Hogg & Reynolds (2016), and Ahmad et al. (2018) have shown that for standard optically thick and geometrically thin disks the propagation timescales are frequency dependent and are different from the viscous ones. Maqbool et al. (2019) quantified this behavior for hot, optically thin, geometrically thick flows considering the propagation time from the transition region onward. They also considered the Comptonized spectrum as arising from a single Comptonizing zone as opposed to the multi-Comptonizing zones assumed in previous works. They showed that the observed frequency-dependent time lag between various energy bands may be due to an underlying time lag between seed photon fluctuations and subsequent variation of heating rate of the hot inner flow.

The primary goal here is to quantify fractional rms and time lag measured by LAXPC as described in Section 2.3 in terms of the model discussed in Maqbool et al. (2019). This model is characterized by three parameters: photon index (Γ), electron temperature (T_e), and blackbody temperature (T_bb), which are obtained from the spectral fitting described in Section 2.2. Interestingly, this model uses the same number of parameters as in the empirical fitting described in Section 2.3. We were able to quantitatively explain the observed variability using only three parameters (the normalized amplitudes of temperature of the truncated disk (δT_s), hot inner flow (δT_e), and the time lag between them (τ_D)). The results of the model fitting are shown in Figure 3 (bottom panel), where δT_e, τ_D and the ratio δT_s/δT_e are plotted against frequency. The variation of δT_e shows three broadened humps, which reflect the features exhibited in the PDS described in Section 2.3. Time delay or time lag (τ_D) between the variation of disk temperature and that of the Comptonizing cloud is a function of frequency. At frequencies <2 Hz the lags are of the order of 100 ms, whereas at frequencies >2 Hz one sees a time delay of the order of 10 ms. The ratio δT_s/δT_e represents the attenuation of propagation from the disk to corona. This ratio is about 1.2 at lower frequencies (<0.2 Hz) and roughly flattens out until 2 Hz, just before dropping slightly at higher frequencies (>2 Hz). The results of the modeling showed good agreement with the empirical fit. The reduced χ² in both cases (empirical and model fit) were around 2 and showed a similar trend (Figure 4), thereby making the empirical functions defined in Section 2.3 adequate.

Zoom In Zoom Out Reset image size

Most BHXBs in their hard state show similar spectro-timing characteristics (Uttley et al. 2014). Cygnus X-1, being the most studied X-ray source by generations of X-ray missions, spends most of its time in a hard state (Zhang et al. 1997). The spectro-timing features of Cygnus X-1 are relatively well known as compared to other BHXBs, thus making it suitable for comparative studies.

Maqbool et al. (2019) studied six AstroSat observations of Cygnus X-1 in its hard state, spread out between 2016 January and October. Spectral analysis of these observations revealed a cooler disk (∼0.46 keV) with large diskbb normalization (∼2400) for 2016 January as compared to the other months. Moreover, the PDS of January was found to have only two broadened noise humps, whereas the other months showed three humps (Figure 1, right panel). In this work, we have compared our temporal analysis results with 2016 January and June data of Cygnus X-1 (Figure 3).

The hard-state power spectra for Cygnus X-1 and MAXI J1820+070 show broadband noise features in the frequency range ∼5 mHz to ∼20 Hz, but their detailed spectral shapes are different (Figure 1, right panel). This is also reflected in the model fit parameters such as the variation of δT_e as a function of frequency (Figure 3, bottom-middle panel). The detailed shapes of the variation is different for the two Cygnus X-1 observations and for MAXI J1820+070. However, one sees that the attenuation factor (δT_s/δT_e) for MAXI J1820+070 is remarkably similar to the January observation of Cygnus X-1 for frequencies greater than ∼2 Hz (Figure 3, bottom-left panel). The time delay (τ_D) between the variation of the soft inner disk temperature (δT_s) and the inner region one (δT_e) seems to have the same general frequency dependence for both the Cygnus X-1 observations and the MAXI source, although the time delay for the MAXI source is lower at high frequencies (Figure 3, bottom-right panel).

The temporal behavior of the system, especially at high frequencies, should depend on the geometry of the inner region, which in turn would be characterized by physical parameters such as the inner disk radius and accretion rate. The different temporal behaviors seen for different Cygnus X-1 observations may be related to changes in these parameters. Differences between MAXI J1820+070 and Cygnus X-1 could be additionally due to the systems having different black hole masses, the latter being a transient while Cygnus X-1 is a persistent source. Thus, it is interesting to note the qualitative similarity between the two sources, especially the frequency dependence of the time delay τ_D, which seems to be similar for both sources and for different Cygnus X-1 observations, although the lower values seen at high frequency for MAXI J1820+070 may imply a lower black hole mass than Cygnus X-1. The attenuation factor for the MAXI source is similar to the January observation at high frequencies, implying that perhaps they were having similar geometries, but one should keep in mind the differences in the low frequency behavior and the overall PDS.