Evolution of X-ray and optical rapid variability during the low/hard state in the 2018 outburst of MAXI J1820$+$070 $=$ ASASSN-18ey

Tomo-e Gozen is an optical wide-field video observation system composed of 84 chips of CMOS image sensors on the 1.05 m Kiso Schmidt telescope (Sako et al., 2018b). This is capable of obtaining consecutive frames with timestamps of 0.2-ms absolute accuracy. The frame rate of Tomo-e Gozen is increased by reducing the fields-of-view of the sensors. We observed MAXI J1820$+$070 with about 67.1 fps in a partial readout mode, where the field of view size was 142.56 arcsec by 71.28 arcsec. The observation log is given in Table E1 in the supplementary information. We performed relative photometry with a neighbor reference star (TYC 444-2244-1) (Gaia Collaboration et al., 2023). The fluxes of both stars were measured by the PSF photometry with Gaussian kernels. We confirmed that time variations of measured flux due to atmospheric fluctuations were negligible in comparison with the variability of this source by the relative photometry method with bright sources in the same frame. The error of the aperture photometry is composed of the photon noise, the atmospheric fluctuations, the readout noise, and the current noise. Since MAXI J1820$+$070 was bright during the outburst, the photon noise was dominant. However, the relative photometry did not work if a thin cloud had passed through the field of view. Then, the brightness fluctuated. We removed this kind of bad data for analyses by the criterion that the flux error divided by the flux is higher than 0.4. All observation times were converted to barycentric Julian date (BJD).¹¹1The BJD is the Julian Date corrected for differences in the Earth’s position with respect to the barycenter of the solar system. We use BJD in terrestrial time (TT). The time system TT established by the international astronomical union (IAU) differs from UTC by 32.184 s plus accumulated leap seconds.

NICER is composed of 56 pairs of silicon drift detectors (SDDs) with a large effective area in soft X-rays ranging between 0.2 and 12 keV (Gendreau et al., 2016). The absolute time tagging accuracy is better than 300 ns. NICER monitored MAXI J1820$+$070 during its 2018 outburst, and we here focus on the low/hard state till BJD 2458304. In this work, we used HEAsoft version 6.32.1 for data reduction and analyses. The data were reprocessed with the pipeline tool nicerl2, which used the NICER Calibration Database (CALDB) version later than 2022 October 31 for producing light curves and time-averaged spectra. Fifty two modules in NICER’s SDDs are operating in orbit, but include two noisy modules, IDs 14 and 34. In our data reduction process with nicerl2, we filtered out the data of the noisy two modules. The light curves were generated by the tool nicer3-lc. The time bin of the NICER light curve is 0.015 s, corresponding to the frame rate of the Tomo-e Gozen light curve. The observation log is given in Table E2 in the supplementary information. All observation times were converted to barycentric Julian date (BJD) by barycorr.

We extracted the overall X-ray light curve during the low/hard state from NICER data and compared it with MAXI and Swift/BAT X-ray light curves. MAXI/GSC data were obtained by the point-spread-function fit method (Morii et al., 2016) using GSC_2, GSC_4, GSC_5, and GSC_7 camera units. The Swift/BAT light curve was the same as displayed in Shidatsu et al. (2019). Figure 1 represents these light curves and the MAXI 4–10 keV / 2–4 keV hardness ratio. Incomplete effective-area correction near the edge of the detector in the above method caused artificial sudden or gradual changes in the flux and the hardness ratio before and/or after the data gaps (camera changes) near BJD 2458206, 2458226, and 2458271. Here, we also plot the optical light curve displayed in Niijima et al. (2021). After the release of the NICERDAS software version 11a, the problem of the telemetry saturation²²2$<$https://heasarc.gsfc.nasa.gov/docs/nicer/data_analysis/nicer_analysis_tips.html#Fragmented-Good-Time-Intervals$>$ is addressed. The baseline of the light curve in the second panel of Figure 1 is at least not discontinuous.

The rising phase to the outburst maximum continued for $\sim$10 d, and the optical and X-ray flux exponentially decreased after the maximum. The optical outburst maximum was delayed to the X-ray outburst maximum by a few days. The hardness abruptly decreased around BJD 2458305, which represents the X-ray spectral transition. According to Shidatsu et al. (2019), the low/hard state continued till BJD 2458304, and the system entered the intermediate state after that.

We investigated the time evolution of MAXI J1820$+$070 during the low/hard state of the 2018 outburst in the hardness-intensity diagram (see the left panel of Figure 2) and the correlation between the NICER hardness ratio and the optical flux (see the right panel of the same figure). There were six different phases named H1, H2, H3, H4, H5, and H6, which are denoted with different colors. The time periods for H1, H2, H3, H4, H5, and H6 are BJD 2458190.0–2458195.0, BJD 2458198.0–2458216.0, BJD 2458218.0–2458236.5, BJD 2458238.0–2458253.0, BJD 2458259.0–2458290.0, and BJD 2458290.0–2458304.0, respectively. These time periods are represented as grey boxes in the first and second panels of Figure 1. During H1, both the X-ray and optical flux increased towards the outburst maximum, and the system became softer. During H2, both the X-ray and optical flux showed a plateau but oscillated. The hardness remained at $\sim$0.18. During H3, the average X-ray flux seemed constant, and the optical flux decreased. The hardness maintained around 0.18 at first and became softer. The boundary between H2 and H3 may be unclear. We set it at the short data gap of the NICER light curve by considering the results of our shot analyses presented in section 3.2.3. The X-ray shot property changed at the boundary between H2 and H3. During H4, the hardness became softer, while the X-ray flux seemed constant. The optical flux increased at first and decreased later. During H5, the X-ray flux suddenly dropped and the hardness slightly increased. The optical flux decreased at first and increased later. The fluctuation of the optical flux became prominent at the latter part. During H6, the system became brighter in X-rays, and the hardness rapidly decreased. The optical flux fluctuated by $\sim$0.5 mag. Niijima et al. (2021) reported the optical periodic modulations called superhumps were observed after H5. The fluctuations of the optical flux during H5 and H6 originated from the superhumps, and the tidal dissipation energy may increase the optical flux in H5 and H6 (Osaki, 1989).

The classification of different phases in the low/hard state similar to ours was performed by Prabhakar et al. (2022) according to the hardness-intensity diagram. Phase II in their classification, in which the central energy of complex iron lines shifted from 6.6 keV to 6.8 keV, was divided into three phases in detail by our investigation. The boundary between H4 and H5 was pointed out by Wang et al. (2020) via their X-ray spectral analyses.

The shot amplitude was the highest at the onset of the outburst, during H1 (see the fourth panel of Figure 6), at which the Comptonization component was dominant in soft and hard X-rays (Shidatsu et al., 2019). Also, X-ray flares suddenly disappeared at the X-ray spectral state transition from the low/hard state to the intermediate state after H6 (see the fourth panel of Figure 6). It was reported that the multi-temperature disk overshined the Comptonization component just after the state transition (Shidatsu et al., 2019; Buisson et al., 2021). It is, therefore, naturally considered that the X-ray rapid variability originated from the advection-dominated accretion flow (ADAF)-like region in the vicinity of the black hole, from which X-ray photons are emitted by inverse Compton scattering (Narayan, Yi, 1994). In fact, it was confirmed by past spectral analyses that the Comptonization component became brighter and its electron temperature became lower during X-ray flares, which suggests that the properties of the Comptonization component changed in flaring events (Shidatsu et al., 2018).

As pointed out by Negoro et al. (1994) for Cyg X-1, two different timescales are involved in the X-ray rapid variability also for MAXI J1820$+$070. One is the timescale of the spectral hardening after the fading of the shot, which continued for $\gtrsim$1 s (see Figure 7 and Figure E4 in the supplementary information). The other one is the timescales of the rising and fading parts of the shot, which was $\sim$0.2 s (see the fifth panel of Figure 6). Also, the increase and decrease of the hardness synchronized with the flaring event occurred on this short timescale. The gas in the ADAF accretes onto the black hole with the velocity of $v_{r}(R)=\alpha(H/R)^{2}v_{\phi}(R)$. Here, $R$, $\alpha$, $H$, and $v_{\phi}$ are the radial distance from the central black hole, the viscosity parameter, the scale height, and the rotation velocity, respectively. Although it is unclear whether the hot flow extended vertically or radially during the low/hard state of the 2018 outburst in MAXI J1820$+$070, it has spacial extension (Buisson et al., 2019; Kara et al., 2019; Xu et al., 2020; Zdziarski et al., 2021). For example, it was reported that the radius of the ADAF-like flow was $\sim$50 $r_{\rm g}$, where the gravitational radius $r_{\rm g}$ is defined as $GM_{1}/c^{2}$ (Xu et al., 2020; Zdziarski et al., 2021). The viscous timescale is $\sim$1 s at $R\sim 50~{}r_{\rm g}$. Here, we applied $H/R\sim 1$ and $\alpha\sim 0.01$ (Narayan et al., 1997), which is consistent with the observed longer timescale. However, some physical processes with the dynamical or thermal timescale would be necessary for explaining the steep shot and accompanying hardening. Even in the case of the vertically-extended hot flow, its height might exceed 10 $r_{\rm g}$ at some points (Kara et al., 2019).

For instance, magnetic reconnection in the innermost region of the black-hole accretion flow occurs on timescales of $1/v_{\rm A}\sim 1/\alpha^{1/3}\Omega$, where $v_{\rm A}$ is the Alfvén velocity (Galeev et al., 1979). This timescale is equivalent to the dynamical timescale of the disk. Random mass accretion from the disk towards the black hole powers magnetic flares (Mineshige et al., 1994; Poutanen, Fabian, 1999). Machida, Matsumoto (2003) performed three-dimensional global resistive magnetohydrodynamic (MHD) simulations and proposed that the accretion of dense gas blobs deposits the energy to the accretion flow, which triggers the magnetic reconnection. Hot electrons and protons are produced by a series of magnetic reconnections, which amplify hard X-ray emission. It is expected that the peak of soft X-ray flares, which would be determined by the timing of the accretion of gas blobs, precedes that of hard X-ray flares and that harder flares are narrower than softer flares. The liberated magnetic energy is converted to heat, and the gas is gradually cooled, which produces spectral hardening lasting for a while after the fading of flares.

A sequence of the processes described in the previous paragraph could explain the three stages of the hardness variations described in section 3.2.3 and the short duration of X-ray shots, though we did not find the delay of the peak of hard shots to that of soft shots. The delay time would be too short to be detected (see Figure 2(c) in Poutanen, Fabian (1999)). Although the expected sharp increase of the hardness at the peak time of X-ray shots was not confirmed in Cyg X-1 (Negoro et al., 1994, 2001; Yamada et al., 2013a), we succeeded in detecting it. Yamada et al. (2013a) reported that the shot was observable at more than 100 keV. Our detected spectral hardening at the steep flare may indicate a sudden increase in the electron temperature due to the abrupt release of magnetic energy. As discussed in Kawamura et al. (2022), if we introduce other types of accretion flows with shorter viscous timescales, which were proposed by Narayan et al. (2012) and Marcel et al. (2018), the short shot duration could be explained. It is common for magnetic activity to be prominent in these flows. Also, only fluctuations of mass accretion rates could not explain the observed shot amplitude of more than 60% (Manmoto et al., 1996).

Suppose the primary source of X-ray rapid variability is the magnetic activity in the hot flow. In that case, it is natural that the amplitude of the soft X-ray shot would be lower than that of the hard X-ray shot during H2–H6 (see the fourth panel of Figure 6), when the emission from the optically-thick accretion disk contributed to the soft X-ray flux (Shidatsu et al., 2019; Xu et al., 2020; Zdziarski et al., 2021). The shot amplitudes in the energy bands softer than $\sim$2 keV were also low for Cyg X-1 (Bhargava et al., 2022). The lower amplitude in the softer shot is consistent with the power spectrum analysis performed by Axelsson, Veledina (2021), in which the power of soft X-ray variations with timescales of less than 1 s was lower than that of hard X-ray variations. The duration of the soft X-ray shot was $\sim$20% longer than that of the hard X-ray shot. This wider profile may originate from the process for launching flares as discussed in the previous paragraph, or may come from the reprocessing of hard X-ray photons at the optically-thick disk. In the latter case, the time delay of soft X-ray variations relative to hard X-ray variations, which is called the soft lag, would be observed. In fact, the soft lag with timescales of $\sim$1 ms was reported by Kara et al. (2019); Wang et al. (2021); De Marco et al. (2021); Kawamura et al. (2022); Omama et al. (2023). Since we used the NICER light curves with a 0.015-s bin, we were not able to detect this kind of very short time lag. The time delay of hard X-ray variations relative to soft X-ray variations, which is called the hard lag, has also been detected in past works. The hard lag was a few seconds, and the variability timescale was larger than 10 s (Kawamura et al., 2022; Omama et al., 2023). This hard lag may be associated with the spectral hardening lasting for $\gtrsim$1 s after the fading from the shot peak. According to Omama et al. (2023), the hard lag became shorter during the low/hard state, and the duration of the spectral hardening after the shot tail, which we detected, also became shorter with time (see Figure 7).

The asymmetry of the shot profile developed since H3 (see the fifth panel of Figure 7). This evolution of the asymmetry may be caused by superposed QPO signals, as mentioned in section 3.2.2, or may reflect some physical mechanisms for producing flares with slow or rapid fading. Machida, Matsumoto (2003) expected that hard X-ray flares show exponential decay since their sources are instantaneous acceleration of electrons by magnetic reconnection (M. Machida, private communication). On the other hand, the density disturbance in the hot flow reproduces flares having an almost symmetric profile to the peak time but showing a slightly deeper dip at the fading stage (Manmoto et al., 1996). Also, Negoro, Mineshige (2002) suggested the temporary depletion of the accreting gas after the flaring, which may be the cause of the luminosity dip after the fading from the shot. The hard X-ray shot profile would be determined by the magnetic event, while the soft X-ray shot would be composed of fluctuations of the accretion rate, the energy dissipation by magnetic reconnection, and the reprocessed emission. The soft X-ray shot profile would easily deviate from the symmetric one in comparison with the profile of hard X-ray shots. Our observations showed that the slower decay was more remarkable in hard X-ray shots and that the faster decay was more remarkable in soft X-ray shots (see the fifth panel of Figure 6), and the above-mentioned physical process may be imprinted in the shot profile.

As possible radiation mechanisms of optical rapid variability, the reprocessing of X-ray photons at the low-temperature outer accretion disk and the synchrotron radiation in the hot flow and/or the jet launching plasma have been proposed (Kanbach et al., 2001; Veledina et al., 2011; Kimura et al., 2016; Gandhi et al., 2016). If the reprocessing is dominant, the optical shot is expected to become a smeared shape in comparison with the X-ray shot. However, the optical shot was less spread than the X-ray shot (see Figures 4 and 6). Our results support the synchrotron radiation rather than the X-ray reprocessing at least for rapid variations with timescales of a few hundreds of milliseconds. The correlation analysis between optical and X-ray variations during the 2018 outburst of MAXI J1820$+$070 showed optical lags with timescales of $\sim$0.2 s and a preceding dip at negative lags in the cross-correlation functions (CCFs), which also suggests that the synchrotron emission from internal shocks within jet plasmas and/or the synchrotron self-Compton emission in the hot flow (Paice et al., 2019b; Kajava et al., 2019; Paice et al., 2021; Thomas et al., 2022). This observational feature was also detected in XTE J1118$+$480 (= KV UMa), another black-hole binary, and a similar interpretation was proposed (Kanbach et al., 2001; Spruit, Kanbach, 2002). We note that the NICER and Tomo-e Gozen light curves analyzed in section 3.2.2 were not completely simultaneous observational data. We, therefore, could not test whether the reported optical lag was detectable or not by our shot analyses. The average duration of the optical shot was 0.32 s as estimated in section 3.2.2, which implies that the size of the emission region was $\sim$7900 $r_{\rm g}$ under the assumption that the optical flare occurs on the dynamical timescale.

The entire time evolution in the NICER hardness vs. the optical flux diagram was similar to that of the hardness-intensity diagram during H2–H4, though the optical flux was more variable than the X-ray one in the same phases (see Figure 2). This suggests that the synchrotron emission from the hot flow significantly contributed to the optical continuum emission during the low/hard state of the 2018 outburst in MAXI J1820$+$070. On the other hand, some physical processes, except for the magnetic activity in the hot flow, would influence the optical rapid variability. If the source of the optical rapid variability is the same as that of the X-ray rapid variability, the time evolution of the optical and X-ray shot properties should be correlated with each other. However, the amplitude of the optical shot decreased during H2, while that of the X-ray shot was almost constant during this period. Also, the duration of the optical shot increased during H3, while the X-ray shot showed the opposite behavior. The simultaneously observed optical and X-ray variability seemed not to necessarily correlate with each other in all time periods (Paice et al., 2019b), which suggests that some optical flares were independent of X-ray flares. We consider that the jet emission contributed to the optical variability, as discussed in the previous paragraph. The multi-wavelength spectral analysis performed by Shidatsu et al. (2018) showed that the jet emission did not significantly contribute to the X-ray flux. On the other hand, the optical flux in the low/hard state was much higher than expected from the reprocessed disk (van Paradijs, McClintock, 1994) according to Shidatsu et al. (2019).

The optical shot seems to have faded at the end of H4 since its amplitude became lower and lower (see Figure 4 and the top panel of Figure 6). The appearance of superhumps in H5 was reported by Niijima et al. (2021). This implies that the emission from the outer disk became dominant at optical wavelengths after H5. There is a possibility that the rapid variability became less conspicuous by the radiation from the accretion disk.

In the hardness-intensity diagram, we found six different phases in the low/hard state of the 2018 outburst in MAXI J1820$+$070 (see the left panel of Figure 2), and the properties of X-ray shots seem to have changed with the evolution of these phases (see Figure 6). This may represent the time evolution of the hot Comptonization component with strong magnetic fields. Zdziarski et al. (2021) and Kawamura et al. (2022) suggested that the hard X-ray emission from this object originated from two different components. The detailed geometry and how many components consist of the hot flow are still unclear; however, the harder Comptonization component would be the closest to the black hole, and the softer Comptonization component would be located outside of the harder one. A similar idea was proposed for Cyg X-1 (Yamada et al., 2013b). Since the energy spectra of these two components were similar to each other, it is difficult to distinguish them only by spectral analyses. Instead, the evolution of the shot property may give the key information for understanding the time evolution of multiple components of hot Comptonization flows.

For example, the duration of X-ray shots increased during H2 and H5 and decreased during H3, H4, and H6. If the size of the emission region becomes larger, the duration becomes larger. If only a part of the hot flow having strong magnetic fields is the source of the rapid X-ray variability, the increase and decrease in the shot duration will represent the expansion and shrinkage of the source region of the rapid X-ray variability. It is suggested by past X-ray timing and spectral analyses that the hot flow contracted in the vertical or horizontal axis during H3–H4 (Kara et al., 2019; Buisson et al., 2019; De Marco et al., 2021; Zdziarski et al., 2021). The decrease in the shot duration during H3–H4 may be consistent with these results. Our shot analyses could not determine whether the disk extended to the ISCO or was truncated. The combination with spectral analyses, which are our future work, may address this problem. On the other hand, the change in the duration of optical shots was not synchronized with that of X-ray shots. As discussed in the previous section, the jet emission was likely dominant at optical wavelengths till H4. In this case, the gradual increase in the optical shot duration during H3–H4 may indicate the expansion of the jet base. This interpretation seems to be consistent with that in Wang et al. (2020). They showed that the delay time of hard X-ray variations to soft X-ray variations increased till H4 and decreased after that, and argued that this result indicates the expansion and shrinkage of jet plasmas.

The amplitude of X-ray shots also increased and decreased during the low/hard state, and the behavior was different between soft and hard shots. The disk emission became dominant in the 0.3–2 keV band after H2. The change in the contribution of the hot flow to the soft X-ray flux would lead to the variation in the amplitude of soft X-ray shots. During H3 and H4, the gap in the amplitude between hard shots and soft shots became larger (see the fourth panel of Figure 6). The spectrum became softer during these phases (see the bottom panel of the same figure), which suggests the more significant contribution of the disk emission with time, as discussed in section 4.1. On the other hand, the amplitude difference between hard and soft shots became smaller during H5. Wang et al. (2020) suggested that this phase was similar to the failed outburst. The disk emission would be less dominant in the 0.3–2 keV band during this phase. Not only the amplitude but also the change in the hardness of X-ray shots during H5 seem to have been similar to those during H1 (see Figure 7).

We need to consider complex physical mechanisms in discussing the time evolution of the amplitude of hard X-ray shots since the mass accretion rate and the magnetic energy do not directly converted into the hard X-ray emission. During H3 and H4, the amplitude of hard X-ray shots gradually increased. More electrons might be accelerated by a series of magnetic reconnections during these phases, which results in more hard X-ray photons via the inverse Compton scattering.

Here, we summarize our proposed picture of the time evolution of the entire accretion flow during the low/hard state in the 2018 outburst of MAXI J1820$+$070. During H1, the rapid increase in mass accretion rates to the hot inner flow abruptly enhanced X-ray and optical emission. The emission from the hard Comptonization component with strong magnetic fields was dominant over wide X-ray energy ranges. During H2, the disk emission became dominant in soft X-rays. The jet was launched, which mainly affected the optical emission. During H3–H4, the source flow for causing X-ray rapid variability might contract, and some components, except for that flow, developed even in hard X-rays. The jet base expanded with time. The total size of multiple Comptonization components would become smaller. During H5, the jet plasma shrank, and the tidal dissipation at the outer disk became the main source of the optical continuum. The hard Comptonization component was dominant again in soft X-rays with the decrease in the temperature of the disk. During H6, the inner accretion disk became hotter again, and the hard Comptonization component kept contributing to hard X-ray emission.