Study of Timing Evolution from Nonvariable to Structured Large-amplitude Variability Transition in GRS 1915 + 105 Using AstroSat

The top left and right panels of Figure 3 show a 1000 s light curve of χ class in 3.0–5.0 keV and 13.0–60.0 keV energy range, respectively. We may see that X-ray flux level is smaller by a factor of 1.5 in the hard-energy band as compared to the soft energy band. A short time variability of <10 s is seen, but no long-term variability (∼100 s) is observed in the light curve of this class. The PDSs for χ class fitted using Lorentzians in soft (3.0–5.0) and hard (13.0–60.0) energy bands are shown in the bottom left and the bottom right panel of Figure 3. A QPO and harmonic component at ∼3.6 Hz and ∼7.2 Hz is observed in the PDS of χ class for the soft band only. The harmonic component is not significant in 13.0–60.0 keV band. The QPO parameters for all the states and three energy bands (3.0–5.0, 5.0–13.0, and 13.0–60.0 keV) are given in Tables 2–4. Two broad Lorentzian noise components and one subharmonic component are also observed in PDS. As shown in Tables 2–4 a higher value of QPO fractional rms in 5.0–13.0 keV and 13.0–60.0 keV as compared to 3.0–5.0 keV is noticed for all three states.

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In the top left panel of Figure 4, a decrease in the time lag at the higher energy band implies soft lag at the QPO frequency of ∼3.6 Hz. On the other hand, at the harmonic frequency of ∼7.2 Hz, a characteristic hard lag is observed. Although the reason is not clear, the time lag at a given energy band is higher at the harmonic frequency compared to that of the QPO frequency. This implies that the phase lag between two given energy bands is different at the QPO and harmonic frequencies.

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The strength of the QPO and harmonic component also varies with photon energy, as shown in the top right and middle right panels, respectively, in Figure 4. For QPO, the fractional rms rises to ∼7% and attains its maximum value at 9.0–12.0 keV energy band and decreases later to 5.5%. For the harmonic, the rms value reaches its maximum of ∼3.5% in 9.0–12.0 keV band and reduces significantly at higher energies. The reduction in the rms value of harmonic above 12.0 keV is the result of the absence of a harmonic component in hard-energy band (13.0–60.0 keV). In the bottom panels of Figure 4, we see that the time lag increases from the soft lag at the lower frequency and makes a transition to the hard lag at a frequency of ∼5.5 Hz. Two dotted lines are marked at QPO and the harmonic frequency, highlighting the fact that the time lag is negative for QPO and becomes positive for the harmonic component, which is in agreement with the time-lag spectra shown in top panels of Figure 4.

The top left and right panels of Figure 5 show 3 ks light curve of the IMS, with a 2.0 s bin size in two different energy ranges, 3.0–5.0 keV and 13.0–60.0 keV, respectively. To account for the variability in the IMS, we extract PDS in the 3.0–5.0 keV and 13.0–60.0 keV energy ranges. These are shown in the bottom left and bottom right panels of Figure 5, respectively. We fit the PDS with five Lorentzians: the QPO, harmonic, subharmonic, and two broad noise components.

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The time-lag and rms spectra shown in Figure 6 show a similar trend as observed for the χ class. However, the fractional rms values at different energy bands are less than those observed during the χ class. In bottom panels of Figure 6, we observe a soft lag up to 6 Hz and then the lag changes sign and becomes hard lag up to ∼9 Hz. This is similar to the behavior of the χ class and independently observed from LAXPC10 (bottom left panel) and LAXPC20 (bottom right panel), respectively. The dotted lines mark the QPO frequency (∼4.0 Hz) and the harmonic component (∼7.8 Hz) showing the soft lag and the hard lag for the QPO and harmonic component, respectively.

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The top left panel of Figure 7 illustrates ∼1100 s light curve of the HS in 3.0–5.0 keV energy band where a peculiar behavior can be noticed. As the source evolves, a sequence of alternately high and low peak count rate is observed where peak count rate changes by a factor of ∼1.5 in every 100 s. The light curve profile of the same section in 13–60 keV energy range is shown in the top right panel of Figure 7. The high count rate peak followed by a low count rate peak structure is absent in the hard band (13–60 keV). A detailed investigation reveals that the cycle period of the flares decreases from ∼150 s to ∼100 s in ∼20 ks HS observation. Moreover, the peak count rate of flares also increases and the dip count rate decreases. The bottom left and right panels of Figure 7 show the PDS for the HS in the Fourier frequency range of 1 mHz to 2 Hz in the soft and hard bands, respectively. Two QPOs are clearly visible: one due to the large-amplitude cyclic variation observed in light curve with the QPO frequency of ∼5 mHz and another at a frequency of ∼5 Hz, similar to that observed from χ class and IMS. We see that the fractional rms for the millihertz QPO is smaller in the hard band in comparison to the soft band, whereas an opposite behavior is seen for the LF QPO.

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To further confirm the spectral nature of the alternative profiles in the soft band, we plot the light curve, hard color (HR2), and soft color (HR1) as a function of time in Figure 8. A dip in HR2 is observed exactly at the time when the count rate reaches its maxima. This implies that the spike in the light curve is a soft pulse. A time delay of 10–15 s is observed between the peak of HR1 and peak of light curve. The implications of such results are provided in the discussion section. In the HID plot of HS (Figure 2 right panel), we do not observe a loop-like structure as observed by Altamirano et al. (2011) during the ρ class of GRS 1915 + 105 and IGR J17091-3624. However, we can anticipate such behavior from Figure 8 where the peak of the HS light curve profile exactly corresponds to the minimum of the hard color. The anticorrelation between X-ray count rate and the hard color is observed as expected with zero time delay between X-ray count rate and the hard color.

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The left panel of Figure 9 shows PDS of the HS in the frequency range between 550 microhertz and 10 Hz. The PDS during the end of the HS observation (76–82 ks in Figure 1) shows the QPO peak and its harmonic. A zoomed view (right panel of Figure 9) of LF QPO ∼5 Hz in three different times of observation shows that the peak of the QPO frequency does not vary within the HS. However, the shape changes. During the last orbit of HS observation (76–82 ks), we notice a broad, distorted, and asymmetric profile for LF QPO, whereas two peaks in the profile structure of millihertz QPO become more prominent. However, it is not clear whether the distortion and broadening in the QPO profile are caused by changes in QPO frequency with time or the presence of two QPOs separated by a small frequency interval that we cannot resolve.

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Time lag as a function of photon energy for the QPO at ∼5.0 Hz is plotted in the left panel of Figure 10, whereas the right panel shows the fractional rms spectra for the same QPO. Similar to χ class and IMS, the lag spectra show a soft lag, whereas the fractional rms increases with energy. The energy-dependent time-lag spectra and the rms spectra at the Fourier frequency of  5 mHz are shown in the upper middle left and upper middle right panels of Figure 10. The energy-dependent lag spectra show hard lags up to ∼6 keV and soft lags at higher energy. However, the rms spectra show the opposite behavior. During the HS, the fractional rms strictly decreases with energy, whereas the energy-dependent fractional rms during the ρ class either increases with energy or initially increases up to ∼10 keV and then decreases (Mir et al. 2016). The time lag versus frequency plot shows the same behavior at QPO (∼5.0 Hz) and harmonic frequency as observed in χ class and IMS. The bottom left and bottom right panels of Figure 10 show the time lag of the 5.0–13.0 keV energy band with respect to 3.0–5.0 keV band (black data points), 13.0–60.0 keV band with respect to 3.0–5.0 keV band (red data points), and 13.0–60.0 with respect to 5.0–13.0 keV photons (blue data points) as a function of Fourier frequency for LAXPC10 and LAXPC20, respectively, at the QPO frequency ∼5 mHz. For the 13.0–60.0 keV band, a soft lag is observed with respect to both 3.0–5.0 keV and 5.0–13.0 keV bands for millihertz QPO. In contrast, the lag is very small for 5.0–13.0 keV relative 3.0–5.0 keV band at millihertz QPO frequency.

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To check the time-dependent behavior of the QPOs in different states, we computed the dynamic power spectrum (DPS). We plot the DPSs for χ class (left panel), IMS (middle panel), and HS (right panel) in the energy range 3–80 keV and frequency interval 2.5–7.0 Hz in Figure 11. During χ class, we observe the peak of the QPO frequency at ∼3.5 Hz nearly constant in time. However, the rms power of QPO shows some variation with time. In contrast, a systematic variation in the QPO frequency between 3.5 and 4.5 Hz has been observed in the DPS of IMS. Moreover, we also see systematic variations in the strength of the QPO. When the QPO frequency shifts to the highest value, the rms power decreases, whereas the rms power is highest close to the minimum of the QPO frequency. During both cycles, each having a period of ∼1500 s, the rms power changes by a factor of ∼2. Double cyclic change is observed in both QPO frequency and the rms of the QPO in an anticorrelated manner. However, we do not see any cyclic pattern in the DPS when the source transits from the IMS to HS. As observed from the plot, the QPO frequency changes between 5.5 and 4.5 Hz in 2000 s; however, the rms does not change significantly in this timescale. Interestingly, the peak rms power of the HS is smaller by a factor of ∼2 when compared to that of χ class and IMS.

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Using a radio/X-ray joint monitoring program, Rodriguez et al. (2008b) observed that the 15 GHz radio flux density during χ X-ray class gradually changed from a radio-quiet state with a mean level of ∼44.9 mJy to a radio-loud state with a mean level of ∼70.4 mJy. Later Pahari et al. (2013) showed that the radio flux density during the radio-quiet χ class can be as low as 10 mJy or less. Although the classification is based on the radio flux density, the X-ray spectral and timing properties of the radio-quiet and the radio-loud χ class are remarkably different. Although no simultaneous radio observation was performed with the AstroSat observation of the χ class presented here, we observed that the X-ray timing properties, such as the QPO frequencies and strength, the nature of light curve, CCD, HID, and lag spectra of the χ class observation analyzed in this work are remarkably similar to the radio-quiet χ class and dissimilar to the radio-loud χ class. We discuss them below. During the radio-loud χ class (plateau state), no phase reversal is observed between the QPO and the harmonic frequencies in GRS 1915 + 105 when QPOs are observed at a frequency lower than 2 Hz (Trudolyubov 2001; Yadav 2006; Pahari et al. 2013). On the other hand, during the radio-quiet χ class as observed by Pahari et al. (2013), phase reversal is noticed during the QPO and the harmonic frequencies, and QPOs are observed at a frequency similar to that observed during our present χ class observations. We also notice phase reversal in the lag spectra. However, there are differences between the χ class observed here and other subclasses of the χ class. During the χ class, we observe an additional strong LF broad Lorentzian noise component at a frequency of ∼0.25 Hz, which is absent from the PDS of the radio-quiet χ class in GRS 1915 + 105 observed with AstroSat/LAXPC (Yadav et al. 2016b) and RXTE/PCA (Pahari et al. 2013). Second, for the QPO component, the time-lag spectra of the χ class show a soft lag accompanied by sharp upturn at 20 keV, above which it shows a hard lag (Yadav et al. 2016b). In the present analysis, we do not observe any hint of an upturn in the time-lag spectra for the QPO component at higher energies in the χ class. Because of its high efficiency, LAXPC is able to resolve more complex structure in the PDS at different photon energies and is able to constrain lag spectra at harder X-ray band than can RXTE/PCA. Therefore, such differences can be attributed to the high detection efficiency of LAXPC compared to RXTE/PCA, particularly in the harder band. It may be noted that, during the χ class, the 3.0–80.0 keV X-ray intensity using LAXPC10 is ∼860 counts/s, whereas it was much higher(>2000 counts/s) in earlier observed radio-quiet χ class using AstroSat/LAXPC (Yadav et al. 2016b).

At the end of the χ class, marked by the sudden increase and strong variability in the hardness (bottom panel of Figure 1), we note that a long-term, large-amplitude, irregular variability is introduced in the light curve (top left panel of Figure 5). Such variability on the timescale of a few thousands of seconds is observed only in the soft X-ray band (3–5 keV) but is absent from the hard X-ray band light curve (13–60 keV). We termed it as “IMS.” The large-amplitude, long-timescale, irregular variability in the soft X-rays is possibly linked to the onset of an outer disk (>50 R_g) turbulence caused by the fluctuations in the mass accretion rate (Neilsen et al. 2011). Despite large-amplitude fluctuations, it is interesting to note that the PDS of IMS shows the LF QPO at ∼4 Hz and its harmonic, whereas the QPO frequency is slightly higher than that observed during the χ class. The strength of the QPO and its harmonic during both IMS and χ class are similar. Moreover, the time-lag spectra of IMS and χ class are also very similar to each other. The reduced fractional rms values in IMS in comparison to those observed during the χ class may imply that, with the launch of large-amplitude, irregular flares, the strength of the QPO is reduced. Comparing hard X-ray light curve of χ class and IMS, we may note that the hard X-ray HR2 remains the same for both states, whereas HR1 attains the highest value in IMS. From the DPS, we may note that, during IMS, the LF QPO surprisingly disappears during certain time intervals. The time-averaged QPO frequency, rms, and width of the observed LF QPOs are similar to those of type-C QPOs. However, the type-C QPOs are found to be very stable for other X-ray binaries, in contrast to our observations. We speculate that the quasi-appearance and disappearance of type-C QPOs during IMS may be caused by the inner disk perturbation driven by the large-amplitude, slow outer disk variability.

Immediately after the IMS, semiregular periodic fluctuations have been observed during the last phase (∼20 ks) of our observations. We termed it as the “HS” for the following reasons. The variability profile is highly structured and has a significant resemblance to the “ρ” class/heartbeat oscillations in GRS 1915 + 105 (Yadav et al. 1999; Belloni et al. 2000; Neilsen et al. 2011). For example, during the HS in our observation, the ratio of maximum-to-minimum flux, averaged over ten cycles, increases from ∼1.5 to ∼2.1 with time, whereas the same during a typical ρ class changes from ∼1.73 to ∼3.33 with time. Although the trend is the same, the values are different. Because these ratios are instrument-independent, a lower ratio during our observation implies that the light curve variability is not fully evolved to a classical ρ class. A similar trend but difference in the evolution of cycle timescale values are observed between the HS and typical ρ class. During HS, the cycle timescale (∼150 s) in the first few kiloseconds is found to be longer than that during last few kiloseconds of observations (∼100 s), which is shown in the top panel of Figure 8. An evolution of ρ cycles toward faster timescale is also observed from GRS 1915 + 105 (110–40 s) and another black hole X-ray transient IGR J17091-3624 (50–20 s) (Pahari et al. 2014). However, in both cases, the evolution started from a large cycle period and evolved up to about half of its value (Figure 6 and Table 3 in Pahari et al. 2014). Such offset in values with similar trends implies that, given a sufficient time to evolve, the HS state variability will eventually lead to the ρ class. It may also be noted that each flare in ρ class shows two peaks when its time cycle is fast (e.g., the 50 s cycle time for GRS 1915+105; Figure 7 in Pahari et al. 2014). In our observation of HS, it is usually a single peak with a time cycle >100 s. We also observe a variation in the alternate peak count rate as shown in top left panel of Figure 7. Such a behavior is seen for the first time in GRS 1915 + 105. Therefore, we observe here an evolution of the large-amplitude, systematic variability that leads to the onset of the heartbeat oscillations in GRS 1915 + 105. Hence, the HS stage can be considered as the precursor of the heartbeat oscillations. We observe a steady increase in light curve fractional rms from χ class to HS as shown in Table 1. This can be attributed to the long-term variability in the light curve.

Despite few similarities in the evolution trend, a few interesting differences between the HS and the ρ class/heartbeat oscillations are noteworthy. We observe a single-peaked pulse during the HS. However, the flux during the pulse peak changes by a factor of ∼1.4 in alternate peaks shown in the top panel of Figure 8. Such a large and systematic change in flux in alternative peaks has not been reported for typical ρ class observations. The nature of the hard color (HR2) and the soft color (HR1) during single-peaked pulse in ρ class is shown by Neilsen et al. (2012). At the position of the pulse peak, shown in their Figure 1, HR2 shows a sudden dip while HR1 shows a sharp peak. This is expected because the pulse is soft. Although the position of the HR2 dip of the pulse during our HS observation in the middle panel of Figure 8 matches with that from Neilsen et al. (2012), the position of HR1 shows a clear discrepancy by 15–20 s. The energy-dependent lag spectra at the millihertz QPO frequency shown in the upper middle left panel of Figure 10 also exhibits a peculiar trend of hard lag of the order of few seconds up to  6 keV and then a soft lag of the order of few tens of seconds at harder X-ray bands. Similar behavior has also been observed from the RXTE/PCA time-lag spectra of ρ class in GRS 1915 + 105 at the heartbeat frequency (Mir et al. 2016). The rms spectra for the HS show different behavior in comparison to that observed by Mir et al. (2016) for ρ class. The reason for such a discrepancy is not clear. The lag timescale is so large that it can be accounted neither by the reprocessing nor by the Comptonization timescale. Therefore, propagation of fluctuations in viscous timescale (Uttley et al. 2011) and a delayed response of the inner disk radius in response to fluctuating mass accretion rate as observed by Mir et al. (2016) are suitable for explaining the long lag.

Although the long-term, large-amplitude component with the variability timescale of the order of few hundreds of seconds significantly evolves from the χ class to HS, the time-averaged LF QPO properties change marginally, as seen in Tables 2–4. In the 3–5 keV energy band, we observe that from the χ class to HS, the LF QPO changes its frequency from ∼3.6 to ∼5.3 Hz, whereas its fractional rms and the width, averaged over few kiloseconds, changes from ∼5.7% to ∼4.3% and ∼0.56 Hz to ∼1.56 Hz, respectively (Table 2). Similar changes are seen in other energy bands. The time-lag spectra show a soft lag during all three states, and the rms spectra are very similar. Therefore, if we assume that the LF QPO is caused by the inner disk activity in a coupled disk-corona system, then the large-amplitude variability may be an outer disk phenomena, and the long-timescale variability does not perturb short timescale variability originating from the inner accretion disk. Such a scenario is also consistent with Neilsen et al. (2011), who assume that the fluctuation during ρ cycles, which causes the density wave that propagates inward, originates at a disk radius of 30 R_g or higher. Interestingly, the harmonic component, which is strongly detected during the χ class and IMS, becomes relatively insignificant during the HS, as can be seen from Figure 7. We also see from Tables 2 and 3 that the width of the harmonic becomes large in the HS, which would lead to a relatively small Q-factor. During the χ class and the IMS, the time-lag and the rms spectra at the harmonic frequency are found to be similar.