# X-ray spectral and timing evolution during the 2018 outburst of MAXI
J1820+070

YaXing Li1,2, Zhen Yan1, ChenXu Gao1,2, and Wenfei Yu1
1Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan
Road, Shanghai 200030, China
2University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049,
China
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We made use high-cadence observations from the $Insight$-HXMT and $NICER$ to
scrutinize the spectral and timing evolution during the 2018 outburst of the
black hole X-ray binary (BHXRB) MAXI J1820+070. It’s hardness-intensity
diagram (HID) displays a “q”-like track including all the spectral states,
along a unique loop in the hard state. The tracks observed in the HID is
anticipated in the evolution of the components responsible for Compton and
reflection emission. This is substantiated by the relationship between the
X-ray luminosity $L_{\mathrm{X}}$ and photon index $\Gamma$, as well as the
relationship between X-ray luminosity $L_{\mathrm{X}}$ and the ratio of
Compton to disk luminosities $L_{\mathrm{C}}/L_{\mathrm{D}}$. Both of these
relationships exhibit a pattern reminiscent of HID. During the hard state, the
hardness (also $\Gamma$) is determined by either reflection component
($R_{f}>1$ ) or Compton component ($R_{f}<1$) depending on the value
reflection fraction $R_{f}$. So the distinctive evolution of $R_{f}$ leads to
the unique loop in the HID (also in the $L_{\mathrm{X}}$–$\Gamma$ plane) of
hard state. Additionally, we found a negative correlation between frequency of
the type-C quasi-periodic oscillation (QPO) ($\nu_{\mathrm{C,QPO}}$) and the
optical depth of the Compton emission ($\tau$), and a positive correlation
between $\nu_{\mathrm{C,QPO}}$ and $\Gamma$. These correlations strongly
suggest a coupling between the QPO properties and the underlying process
responsible for Comptonization.

###### keywords:

accretion, accretion discs – black hole physics – X-rays: binaries – stars:
individual: MAXI J1820+070

††pubyear: 2024††pagerange: X-ray spectral and timing evolution during the
2018 outburst of MAXI J1820+070–A

##  1 Introduction

The majority of Galactic black hole X-ray binaries (BHXRBs) behave as
transient sources that spend years to decades in a quiescent state.
Occasionally, they undergo outbursts lasting for weeks to months before
returning to quiescence (Yan & Yu, 2015; Corral-Santana et al., 2016). These
outbursts may involve transitions through distinct accretion states, which are
characterized by a variety of X-ray spectral and timing features, along with
associated radio emission (see reviews by Remillard & McClintock, 2006; Done
et al., 2007; Belloni, 2010). Given their proximity at kiloparsec distances
and their dramatic variability on timescales spanning from days to months,
BHXRBs serve as excellent targets for real-time monitoring the accretion flow
and jet behavior. The high-cadence observations yield valuable insights into
the physics of accretion and its interplay with jet across different accretion
states.

The outburst usually starts from the hard state (HS) when the luminosity is
low. The X-ray spectrum of HS is dominated by Comptonized emission produced
from a hot plasma usually called corona (Sunyaev & Truemper, 1979), a weak
thermal component from the accretion disk is also detected. In this state, the
strong low-frequency quasi-periodic oscillations (LFQPOs) and broad line
noises (BLNs) are usually detected in the power density spectrum (PDS, e.g.
Belloni et al., 2002; Casella et al., 2004). As the outburst goes on, the disk
component becomes stronger. When the spectra is dominated by the thermal
component from an optically thick disk extending to the innermost stable
circular orbit (ISCO) of the BH (Novikov & Thorne, 1973; Shakura & Sunyaev,
1973), the outburst enters the soft state (SS). In contrast to HS, SS shows
low X-ray variability amplitude with a few percent fractional root mean square
(RMS), and LFQPOs are rarely detected (Motta et al., 2012). The transition
between the HS and SS is called intermediate state (IMS). During the outburst
decay, the disk temperature and luminosity decrease. At some point, the corona
restrengthens and dominates over the disk component, which indicates the
outburst return to HS.

A large fraction of outbursts experience a transition from the HS to SS state
(H-S) during the outburst rise, and conversely, from SS to HS (S-H) during the
outburst decay (e.g. Yu & Yan, 2009; Tetarenko et al., 2016). Through the
comprehensive X-ray spectral and timing analysis, we can conduct detailed
research on different spectral states and state transitions (e.g. Belloni,
2010). The characteristics extracted from X-ray spectral-timing data reveal
the properties and evolution of the accretion flow across different spectral
states (e.g. Kara et al., 2019; Fabian et al., 2020; Ma et al., 2021; You et
al., 2023a). Notably, the X-ray spectral and timing properties exhibit
pronounced changes during these state transitions, providing valuable insights
into the changes in innermost accretion flow and/or ejection around the BH.

##  2 MAXI J1820+070

In this work, we focus on the evolution of the very bright outburst of MAXI
J1820+070. The X-ray outburst MAXI J1820+070 was first detected by Monitor of
All-sky X-ray Image (MAXI) on March 11, 2018 (MJD 58188, Kawamuro et al.,
2018). The optical counterpart ASASSN-18ey was discovered by the All-Sky
Automated Survey for Supernovae (ASAS-SN) (Shappee et al., 2014) around
several days earlier (Tucker et al., 2018; Denisenko, 2018). Soon after, the
source was classified as a BHXRB according to the follow-up observations in
different wavelengths (Baglio et al., 2018; Bright et al., 2018; Uttley et
al., 2018). Atri et al. (2020) measured the distance of $2.96\pm 0.33$kpc by
using the radio parallax method and a jet inclination angle of $63\pm
3^{\circ}$ with very long baseline interferometry (VLBI) observations. Torres
et al. (2020) estimated the mass of black hole is
$8.48_{-0.72}^{+0.79}M_{\odot}$. The spin of the BH was estimated as 0.14
(Zhao et al., 2021).

Like other transient BHXRBs, MAXI J1820+070 is in HS at the beginning of the
outburst. It is a very long HS, extending until around MJD 58290.
Subsequently, the source enters the IMS. The above two periods are referred to
as rising HS and IMS states. The transient jet ejected around MJD 58306
(Bright et al., 2020; Wood et al., 2021), coinciding with the transition
between hard intermediate state (HIMS) and soft intermediate state (SIMS;
Fender et al., 2004). The SS lasts from MJD 58310 to 58383. At about MJD
58393, the source returns to the HS. In order to distinguish from the outburst
rise phase, the period between MJD 58383 to 58393 and after are referred to as
decaying IMS and HS states, respectively. The time intervals of different
spectral states are shown in Figure 1 (see also Shidatsu et al., 2019).

Due to its high X-ray brightness (see the public lightcurve in Sakamoto et
al., 2016) and low interstellar absorption/extinction (Uttley et al., 2018),
MAXI J1820+070 serves as an ideal source for studying outburst evolution
across multiple wavelengths. Extensive multi-wavelength campaigns, involving
various X-ray missions, have been conducted. By concurrently applying X-ray
spectral and timing analysis during this outburst, it is very helpful to
uncover the properties and evolution of accretion flows around black holes
(e.g. Stiele & Kong, 2020; Wang et al., 2020; You et al., 2021).
$Insight$-Hard X-ray Modulation Telescope (HXMT) is one of the best missions
for performing X-ray spectral and timing study in a very broad energy band
1–250 keV (Zhang et al., 2020). It carries three slat-collimated payloads: low
energy X-ray telescope (LE, 1–15 keV, Chen et al., 2020), medium energy X-ray
telescope (ME, 5–30 keV, Cao et al., 2020) and high energy X-ray telescope
(HE, 20–250 keV, Liu et al., 2020). All three instruments have large
collecting areas and high time resolution, which are beneficial to do X-ray
spectral and timing analysis for bright targets. $Insight$-HXMT observed MAXI
J1820+070 from March 14, 2018 to October 21, 2018, and obtained a total of
more than 310 exposures with an average interval of 0.63 days. The
$Insight$-HXMT observations extensively cover the different spectral states
through almost the entire outburst Figure 1. We also used the data from
Neutron Star Interior Composition Explorer ($NICER$) in some cases. Due to its
high time resolution and large effective area, $NICER$ data can provide X-ray
spectral and timing analysis in the 0.2–12 keV.

Figure 1: $Insight$-HXMT light curve, hardness-intensity diagram and absolute
RMS-intensity diagram of MAXI J1820+070 during the 2018 outburst. (a) Light
curves obtained from LE and HE of $Insight$-HXMT. The colors of the background
represent the spectral states: blue for the hard state, green for the
intermediate state and red for the soft state. The blue dashed lines separate
three phases of the rising hard state: the rise, plateau and bright decline
phases. The red dashed line represents MJD 58305.60 when the transient jet
ejected according to Wood et al. (2021). (b) The $Insight$-HXMT hardness-
intensity diagram, defined as the total 1–10 keV count rate vs. the ratio of
hard (3–10 keV) to soft (1–3 keV) count rates. The three phases of the rising
HS correspond to the three curves of the small “$\eta$”-like track on the
upper right. (c) The absolute RMS-intensity diagram, with the grey lines
corresponding to the values of fractional RMS. Both absolute RMS and
fractional RMS are determined in the 0.1–64 Hz from $Insight$-HXMT/LE PDS. The
color bar on the right corresponds to the observation time.

##  3 Data reduction and data analysis

###  3.1 $Insight$-HXMT data reduction

The $Insight$-HXMT data and products were processed and extracted by using the
$Insight$-HXMT Data Analysis Software package (HXMTDAS). We first screened the
original event data of three instruments by using lescreen, mescreen and
hescreen with the recommended criteria in the user manual
111http://hxmten.ihep.ac.cn/SoftDoc.jhtml. The spectra and light curves were
extracted by using the tools lespecgen, mespecgen, hespecgen, lelcgen, melcgen
and helcgen for the target, and using the tools lebkgmap, mebkgmap and
hebkgmap for the background, respectively. All the spectra were grouped with a
minimum count of 25 per bin.

The net light curves were calculated with lcmath. We then used the powerspec
in XRONOS package to compute the power density spectrum (PDS) in Leahy
normalization (Leahy et al., 1983). The net light curves with a time
resolution of 1/512 seconds were divided into segments with a length of 512
seconds for producing the PDSs. So the frequency resolution of the PDS is
1/512 Hz and the Nyquist frequency is 256 Hz.

###  3.2 $NICER$ data reduction

The raw data were first reprocessed by using task nicerl2 in the $NICER$
software package NICERDAS. The source and background spectra, ancillary
response files (ARFs) and response matrix files (RMFs) were all extracted by
using the pipeline task nicerl3-spect. During the above procedure, the
SCORPEON background model was chosen, and the recommended systematic error
from the calibration file was applied. The spectra were grouped with a minimum
count of 25 per bin.

###  3.3 X-ray timing analysis

We excluded the soft state from MJD 58310 to 58383 for timing analysis of
$Insight$-HXMT data. The PDSs were then logarithmically re-binned with an
increment factor of 0.025 in frequency and formatted to be compatible with
XSPEC (Ingram & Done, 2012). We then used a combination of Lorentzian
functions and a constant to fit the PDSs in XSPEC (v12.12.1): two or four
Lorentzians for the BLNs, two or three Lorentzians for the QPO and its
harmonic and/or subharmonic and a constant for the white noise. The PDS of the
data from LE and ME detectors on the $Insight$-HXMT can be described by a QPO
and two BLN components while the data from HE detectors will use two
additional Lorentzians to supply the BLN components. Some $NICER$ observations
during the IMS were used since $Insight$-HXMT observation is absent during the
period of MJD 58301–58305 (obsID 1200120192–1200120197). Notably, the QPOs in
the observations 1200120196 and 1200120197 exhibited dramatic and rapid
changes (Stiele & Kong, 2020; Homan et al., 2020). Consequently, we divided
the two observations into several segments based on the dynamic power spectra
(Homan et al., 2020), in order to study the timing evolution in detail. The
$NICER$ PDSs consist of one to three BLN components and one or two QPO
components. The uncertainties of all the parameters were calculated from the
Markov Chain Monte Carlo (MCMC) method by the implementation of emcee in XSPEC
222https://github.com/zoghbi-a/xspec_emcee. Using the best-fitting results of
PDSs, we calculated the fractional RMS $=\sqrt{K/\left\langle
x\right\rangle}$, where $K$ is the normalisation of the Lorentzian function
and $\left\langle x\right\rangle$ is the mean count rate(Leahy et al., 1983;
van der Klis, 1989).

###  3.4 X-ray spectral analysis

We performed the spectral fitting through XSPEC v12.12.1 by using the chi
statistic. Different models were applied in different spectral states. During
the hard and intermediate states of the outburst rise phase, we applied the
model constant*TBabs*(diskbb+relxillCp+gaussian) to fit X-ray spectra in the
2–150 keV. The constant factor was used to coordinate calibration differences
between different instruments, where the constant for LE was fixed at 1. The
equivalent hydrogen column density ($N_{H}$) of TBabs was fixed at $0.15\times
10^{22}cm^{-2}$(Uttley et al., 2018). The diskbb is a multi-blackbody
component, which accounts for the accretion disk radiation. The relxillCp
(version 2.3) is a relativistic reflection model that calculates the spectrum
from an accretion disk illuminated by the corona (García et al., 2014; Dauser
et al., 2022). In our spectral fitting, we fixed the black hole spin at a =
0.14(Zhao et al., 2021) and the inclination angle at $i=63^{\circ}$(Atri et
al., 2020). We tied the normalization $N_{disk}$ of the diskbb to the inner
disk radius $R_{\mathrm{in}}$ (in unit of $R_{g}$) in relxillCp as
816$R_{\mathrm{in}}^{2}$ (Gao et al., 2023) by ignoring the uncertainties of
the distance and inclination angle. On the other hand, the real
$R_{\mathrm{in}}$ is affected by the color-correction factor, boundary
condition and disk wind (e.g. Kubota et al., 1998; Zdziarski et al., 2022).
For simplicity, we only used a continuous power-law emissivity and fixed the
index at $q_{1}=q_{2}=3.0$, and a constant ionization (iongrad_type=0 ). The
gaussian was used to account for a narrow component near the iron K emission
line ($\sim$6.4 keV). Finally, we used the cflux to get the flux of the diskbb
and relxillCp in the 0.1–100 keV energy band, then got the flux of reflection
and Comptonization components by setting reflection fraction refl_frac as
zero. During and after the soft state, we applied the model
constant*TBabs*(diskbb+nthComp+gaussian) to fit the broadband X-ray spectrum.
Then, we also used cflux to calculate the flux of the diskbb and nthComp in
0.1–100 keV energy band. The uncertainties of all the parameters were
calculated using the emcee in XSPEC.

Because of the absence of $Insight$-HXMT observation around MJD 58301 to 58305
in the IMS, we used the $NICER$ data as the supplementary. We also generated
the energy spectra for each segment of obsID 1200120196 and 1200120197. Then
we applied the same model as used for $Insight$-HXMT data during this period
to fit the spectra in the 1–10 keV. For simplicity, we fixed the electron
number density $\log N$, iron abundance $A\mathrm{{}_{Fe}}$ and electron
temperature $kT_{e}$ at $10^{20}$ $\mathrm{cm^{-3}}$, 5.0 and 100.0 keV,
respectively.

##  4 X-ray spectral and timing evolution during the 2018 outburst

###  4.1 Unique evolution of rising HS

The count rates of MAXI J1820+070 from LE and HE of $Insight$-HXMT are plotted
in Figure 1a, and the hardness-intensity diagram (HID) and absolute RMS-
intensity diagram (RID) are also shown in Figure 1b and c. The light curve of
MAXI J1820+070 shows a multi-peaked outburst profile (Chen et al., 1997). The
first peak remains in the hard state, while its HID exhibits a small loop,
which looks like a “$\eta$” track (Figure 1b). The rising HS is divided into
three phases: the rise, plateau and bright decline phases (e.g. Stiele & Kong,
2020; De Marco et al., 2021), which roughly corresponds to the three curves of
the small “$\eta$”. The rise phase is from the start of the outburst to MJD
58200 when the count rate reaches the peak and then begins to decrease slowly.
The plateau phase is from MJD 58200 to 58260, and the bright decline phase is
from 58260 to MJD 58290. The absolute RMS and count rate do not follow a
single positive correlation (Figure 1c; see also Stiele & Kong, 2020). This
loop evolution of rising HS in HID/RID has never been shown in other BHXRBs
(Belloni, 2010; Belloni & Motta, 2016). Even in the other outbursts with
multiple peaks, their HID/RID usually do not show a loop trend during the
rising HS, such as the outbursts in XTE J1550$-$564, GX339-4 and GRO
J1655$-$40 (e.g. Sobczak et al., 2000; Debnath et al., 2008; Clavel et al.,
2016).

During the rising HS, our timing and spectral analysis results show a clear
distinction between this special plateau phase with the rise and bright
decline phase. Notably, despite the gradual decline of the count rate during
the plateau phase, the Comptonization Luminosity $L\mathrm{{}_{C}}$ calculated
from model relxillCp remains almost constant (see Figure 3). The reflection
fraction $R_{f}$ is large ($>1$) during the plateau phase, which is the
largest among BHXRBs at this luminosity level (You et al., 2023b). The QPO
frequency $\nu_{\mathrm{C,QPO}}$ exhibits a positive and parallel correlation
with the total X-ray luminosity $L_{\mathrm{X}}$ during the rise and the
bright decline phases while the correlation is negative in the plateau phase
(see Figure 7a).

###  4.2 X-ray luminosity and spectral parameter evolution

Figure 2: Time evolution of spectral parameters. From top to bottom: the
reflection fraction $R_{f}$, the electron temperature $kT_{e}$, the
normalization of the diskbb $N\mathrm{{}_{disk}}$, the inner disk temperature
$T\mathrm{{}_{in}}$, the photon index $\Gamma$. The dots are derived from
$Insight$-HXMT data and the triangles are derived from $NICER$ data. The
colors of the background and dashed lines are the same as in Figure 1. Figure
3: Time evolution of X-ray luminosities in 0.1–100 keV of different spectral
components: the disk luminosity (upper panel), the Comptonization luminosity
and the reflection luminosity (middle panel) and total luminosity (lower
panel). The dots are derived using $Insight$-HXMT data and the triangles are
derived using NICER data. The colors of the background and dashed lines are
the same as in Figure 1.

Based on spectral analysis, we present the evolution of the main parameters of
the models in Figure 2. The hard and intermediate state are applied with a
complex model constant*TBabs*(diskbb+relxillCp+gaussian). The reflection
fraction $R_{f}$ increases in the rise phase of HS and subsequently undergoes
a gradual decline until the SS. Please note that the definition of $R_{f}$
from relxillCp with version older than 1.4.1 is different
333http://www.sternwarte.uni-erlangen.de/d̃auser/research/relxill/index.html.
The electron temperature $kT_{e}$ decreases in the rise phase of HS, increases
slowly until the end of hard state, and drops again in the HIMS. During other
periods of the outburst, it is not well-constrained. The normalization
$N_{\mathrm{disk}}$ initially decreases quickly in the rise phase and
decreases slowly in the plateau and bright decline phase of the HS. Then it
begins to increase during the IMS. The photon index $\Gamma$ manifests
different growth rates between the rise and plateau phases of HS, followed by
a decrease during the bright decline phase and a rapid increase during the
IMS. The inner disk temperature $T\mathrm{{}_{in}}$ increases rapidly in the
rise phase of the HS and increases slowly before the IMS is reached. During
the IMS, $T\mathrm{{}_{in}}$ sharply increases and reaches the level of SS.

During and after the SS, we applied the model
constant*TBabs*(diskbb+nthComp+gaussian) for spectral fitting. Then the
$T\mathrm{{}_{in}}$ starts to decrease exponentially until the end of SS
accompanied by a relatively constant $N\mathrm{{}_{disk}}$, which is
consistent with the standard thin disk (Shakura & Sunyaev, 1973). Due to the
hard X-ray tail in the $Insight$-HXMT spectra, $\Gamma$ at an early stage of
SS is lower than that in SIMS (see also Fabian et al., 2020; Mummery et al.,
2024). $\Gamma$ shows fluctuations until we cannot constrain well and fix it
at $2.4$ for the rest of SS. During the decaying IMS, $\Gamma$ gradually drops
to the HS level. The evolution of the spectral parameters in different
spectral states is also reported in You et al. (2021); Peng et al. (2023); Fan
et al. (2024).

The X-ray luminosity of different spectral components calculated in the energy
range of 0.1–100 keV is presented in Figure 3. In the rise phase of HS,
$L\mathrm{{}_{X}}$, $L\mathrm{{}_{R}}$ and $L\mathrm{{}_{C}}$ all increase.
However, $L\mathrm{{}_{R}}$ reaches peak synchronously with $R_{f}$, and
$L\mathrm{{}_{C}}$ reaches its peak earlier. Subsequently, $L\mathrm{{}_{R}}$
and $L\mathrm{{}_{X}}$ decrease until the end of HS. Notably,
$L\mathrm{{}_{C}}$ remains relatively constant during the plateau phase and
then decreases in the bright decline phase of HS. During the rising IMS, there
is a significant increase in luminosities of different spectral components
except $L\mathrm{{}_{R}}$, particularly around the period of transient jet
ejection (Figure 3). Afterward, $L\mathrm{{}_{D}}$ surpasses
$L\mathrm{{}_{C}}$. During the SS, $L\mathrm{{}_{D}}$ exhibits an exponential
decline. In the decaying IMS, $L\mathrm{{}_{D}}$ continues to decrease at a
steeper rate, while $L\mathrm{{}_{C}}$ experiences a small flare (Figure 3).

####  4.2.1 Relationships between $L_{\mathrm{X}}$ and spectral parameters

Figure 4: (a) The relationship between photon index $\Gamma$ and total
luminosity $L_{\mathrm{X}}$ during the 2018 outburst. Blue dots, green dots,
red dots, green triangles and blue triangles respectively indicate rising hard
state and intermediate state, soft state, decaying hard state and intermediate
state. The black stars mark the transition luminosities in the outburst rise
and decay phases. Arrows indicate the direction of evolution. (b) The
relationship between the ratio of Comptonization luminosity $L\mathrm{{}_{C}}$
to disk luminosity $L\mathrm{{}_{D}}$ and total luminosity $L_{\mathrm{X}}$
during the 2018 outburst. Symbols and colors are the same as in panel (a).
Figure 5: (a) The relationship between the reflection fraction $R_{f}$ and
total luminosity $L_{\mathrm{X}}$ during the hard/hard-intermediate state. The
stars, squares, dots and triangles respectively indicate the rise, plateau and
bright decline phases in the hard state and intermediate state. (b) The
relationship between the electron temperature $kT_{e}$ and total luminosity
$L_{\mathrm{X}}$ during the hard/hard-intermediate state. Symbols and colors
are the same as in panel (a). The color bar on the right corresponds to the
observation time.

The relationship between photon index $\Gamma$ and total X-ray luminosity
$L_{\mathrm{X}}$ is presented in Figure 4a. It is evident that
$L_{\mathrm{X}}$ and $\Gamma$ show almost identical “$\mathrm{q}$”-like
evolution with HID even the small “$\eta$”-like track during the rising HS.
When the reflection fraction $R_{f}$ exceeds 1, the reflection component
surpasses the Compton component below the energy of the reflection hump
($\lesssim$ 30 keV; Dauser et al., 2014). Consequently, the photon index (also
hardness ratio) is primarily influenced by the reflection component rather
than the Compton component in X-ray spectra when $R_{f}>1$. Notably, the slope
of the reflection spectra in the 2–10 keV energy range are always steeper than
that of the Compton spectra (Figure 9), resulting in a larger $\Gamma$ and
also hardness. So the $\Gamma$ (also hardness) is determined by either Compton
($R_{f}<1$) or reflection ($R_{f}>1$) component depending on the $R_{f}$. The
positive correlation observed between luminosity and the photon index in the
bright hard state of other BHXRBs is primarily driven by Compton emission
(e.g. Yang et al., 2015; Yan et al., 2020; You et al., 2023b). As a result,
this behavior is not observed during the rising HS with $R_{f}>1$ in MAXI
J1820+070. So the distinctive evolution of $R_{f}$ leads to the unique
“$\eta$”-like track in $L_{\mathrm{X}}$–$\Gamma$ and HID during the rising HS.

The relationship between the $L_{\mathrm{X}}$ and the ratio of
$L\mathrm{{}_{C}}$ to $L\mathrm{{}_{D}}$ is shown in Figure 4b. At the end of
outburst decay, the diskbb is no longer required for the spectral fitting. So
the $L\mathrm{{}_{C}}/L\mathrm{{}_{D}}$ is calculated by using the last best-
fitting $L\mathrm{{}_{D}}$. This diagram also presents a “q”-like pattern
similar to HID and $L_{X}$-$\Gamma$. Notably, the parameters $\Gamma$ and
hardness follows an “$\eta$”-like track during the rising HS, which is not
observed in $L\mathrm{{}_{C}}/L\mathrm{{}_{D}}$(Figure 4). This result also
highlights that the $\Gamma$ during the rising HS is not always determined by
the Compton component. Since the $\Gamma$ exhibits a monotonically negative
correlation with the $L\mathrm{{}_{C}}/L\mathrm{{}_{D}}$ in the Comptonization
scenario (e.g. Haardt & Maraschi, 1991; Beloborodov, 1999).

The relationships between total X-ray luminosity $L_{\mathrm{X}}$ and both the
reflection fraction $R_{f}$ and electron temperature $kT_{e}$ are respectively
shown in Figure 5a and Figure 5b. During the rising HS, a positive correlation
is observed between $L_{\mathrm{X}}$ and $R_{f}$ (see also You et al., 2023b),
which then inverts to a negative correlation in the IMS. Concurrently,
$kT_{e}$ demonstrates a uniform negative correlation with $L_{\mathrm{X}}$
when it can be accurately constrained by our model during both the HS and HIMS
(e.g. Yan et al., 2020; You et al., 2023b).

###  4.3 Type-C QPO evolution

Figure 6: Time evolution of the characteristic frequencies of the type-C QPO.
The dots are obtained from $Insight$-HXMT LE data and triangles are from
$NICER$ data. The orange dotted lines represent the best-fitting exponential
functions applied to the data of different phases: the rise, plateau, and
bright decline phases in hard state, and two segments separated on MJD 58303
during intermediate state. The colors of the background and dashed lines are
the same as in Figure 1. Figure 7: (a) The relationship between type-C QPO
frequency and total luminosity $L_{\mathrm{X}}$. (b) The relationship between
type-C QPO frequency and photon index $\Gamma$. (c) The relationship between
type-C QPO frequency and optical depth $\mathrm{\tau}$. The black line
indicates the best-fitting linear function. The gray shaded area represents
the error region for the slope and offset. The red dashed lines indicate the
scattering range of the data. Symbols and colors are the same as in Figure 5.
The color bar on the right corresponds to the observation time.

The evolution of centroid frequency of type-C QPO is present in Figure 6. We
could detect the type-C QPO from around MJD 58193.42 until MJD 58305.61 when
the source reaches the SIMS. The centroid frequency of QPO
$\nu_{\mathrm{C,QPO}}$ ranges from 0.01 to 8.05Hz and the values obtained from
the same exposure ID in different detectors (LE, ME and HE) are nearly
identical. The $\nu_{\mathrm{C,QPO}}$ evolution obtained from $Insight$-HXMT
is almost the same as that from $NICER$ data (Stiele & Kong, 2020).

The QPO frequency apparently changes at different rates during different
phases (Figure 6). Buisson et al. (2018) has claimed that the QPO frequency
exponentially increases with time. We also used exponential function
$\nu_{\mathrm{C,QPO}}=p_{0}e^{(t-t_{0})/\tau}$ to fit the
$\nu_{\mathrm{C,QPO}}$ at different phases. The best-fitting $e$-folding time
scales $\tau$ are 7.63 $\pm$ 0.78, 23.99 $\pm$ 0.65, -50.27 $\pm$ 7.86 days
for the rise, plateau and bright decline phases of HS, respectively (Figure
6). The $\nu_{\mathrm{C,QPO}}$ evolution during the IMS obviously experiences
two different increasing rates with $e$-folding time scales of 8.28 $\pm$
0.76, and 1.02 $\pm$ 0.05 days Figure 6.

We also performed timing analysis for the $Insight$-HXMT data during the
decaying IMS and HS. But no significant QPO signals were detected. We noticed
that there are some QPO detections with $NICER$ data reported in Stiele & Kong
(2020). However, only six QPO signals are considered to be significant
($>3\sigma$). Their frequency and fractional RMS vary chaotically.
Consequently, it is difficult to conclusively determine the type and evolution
of the detected QPOs during the decaying IMS and HS.

We then investigated the relationships between type-C QPO frequency
$\nu_{\mathrm{C,QPO}}$ and spectral parameters during the rising HS and HIMS
(Figure 7). The $\nu_{\mathrm{C,QPO}}$ exhibits a complex correlation with the
total X-ray luminosity $L_{\mathrm{X}}$. Two positive correlations parallelly
exist in the rise and bright decline phases of HS and IMS. However, a negative
correlation is observed in the plateau phase of HS (Figure 7a). The
$\nu_{\mathrm{C,QPO}}$ and photon index $\Gamma$ exhibit an overall positive
correlation in the HS and HIMS, with varying slopes across different phases
(Figure 7b). It appears that the slopes during the rise, plateau, and bright
decline phases of HS and HIMS differ. We also calculated the optical depth
$\mathrm{\tau}$ of Compton component from $kT_{e}$ and $\Gamma$ according to
the equation in (Zdziarski et al., 1996). As present in Figure 7c, the
$\nu_{\mathrm{C,QPO}}$ and $\mathrm{\tau}$ follow a single negative
correlation. The best-fitting slope of this correlation is obtained as
$-1.18\pm 0.04$ using the Bayesian method in Buchner (2021). However, the
correlation displays a large scatter, with a value of $0.26\pm 0.01$.

###  4.4 Dramatic changes around the transient jet ejection

Figure 8: (a) AMI-LA radio light curve (15.5 Ghz) from Bright et al. (2020)
around the transient jet ejection. The grey dashed line indicates the best-
fitting model from Homan et al. (2020): an exponential function for the
baseline decay, an additional linear function for the radio flare rise, and an
additional power-law function for the radio flare decay phase. (b) The
concurrent evolution of the X-ray disk luminosity$L\mathrm{{}_{D}}$ and the
Comptonization luminosity $L\mathrm{{}_{C}}$ (0.1–100 keV). (c) The concurrent
evolution of photon index $\Gamma$ and inner disk temperature
$T\mathrm{{}_{in}}$. (d) The concurrent evolution of the centroid frequency of
type-C and type-B QPOs. The red and green shadows mark the ejection times of
two ejected components on MJD 58305.60 $\pm$ 0.04 and 58305.97 $\pm$ 0.02,
respectively (Wood et al., 2021).

We are already aware that significant X-ray spectral and timing changes in the
transition between HIMS and SIMS (see Figure 2, Figure 3 and Figure 6),
coinciding with two transient jet ejections and a radio flare around MJD 58306
(Bright et al., 2020; Homan et al., 2020; Wood et al., 2021). Approximately 4
hours subsequent to the first ejection, a radio flare is observed. The peak of
the radio flare coincides with the second ejection (see Figure 8 and Wood et
al., 2021). It is currently uncertain which ejection the radio flare
corresponds to. Both ejection times are the best-constrained among BHXRBs
(Carotenuto et al., 2024). Due to the extensive coverage of $NICER$
observation, we are able to investigate the spectral and timing variation
before and after the ejection.

We divided the two observations around jet ejection into 11 segments. The
parameters of QPOs detected in each segment are listed in Table 1. Notably,
the type-C QPO is present in every segment except the last one, which occurs
just after the first ejection on MJD 58305.60 $\pm$ 0.04. Additionally, a
type-B QPO around 4 Hz emerges roughly 0.4 days before this ejection. It is
first detected on MJD 58305.22 and persists for approximately 14 hours.
Although the type-B QPOs are not prominently visible in the dynamic PDSs prior
to the ejection (see Homan et al., 2020), they are significantly detected in
the averaged PDS of certain segments (Table 1).

In Figure 8, we also present spectral parameters and X-ray luminosity. Prior
to the first ejection, the spectral parameters, specifically the disk
temperature $T\mathrm{{}_{in}}$ and photon index $\Gamma$, exhibit a sharp
increase. After the first ejection, the $T\mathrm{{}_{in}}$ and
$L\mathrm{{}_{D}}$ reach the SS level, the $\Gamma$ and $L\mathrm{{}_{C}}$
show a decrease.

##  5 Discussion

###  5.1 The “q”-like HID and the evolution of $L_{\mathrm{X}}$-$\Gamma$

Similar evolution tracks are anticipated in both the $L_{\mathrm{X}}$–$\Gamma$
and HID, as the calculated hardness (3–10keV/1–3keV) depends on the slope of
the X-ray spectrum, also known as the photon index. Figure 4a displays a
“q"-like track between $L_{\mathrm{X}}$ and $\Gamma$ when all data from the
entire outburst are included, and a small “$\eta$"-like track during the
rising HS, which is similar to HID (Figure 1). We have also gathered data from
several outbursts with comprehensive observations that span the full duration
of the outburst from the literature (Sobczak et al., 2000; Debnath et al.,
2008; McClintock et al., 2009). We found that $L_{\mathrm{X}}$ and $\Gamma$
follow a roughly “q"-like track in all three outbursts similar to the HID (see
Figure 10). The data in the hard state (right part of the “q") roughly follows
a “v"-like correlation, aligning with previous work. The significant scatter
of the right branch of “v"-like correlation (e.g. Fig.2 in Yan et al., 2020)
is evidently due to the different bend points at the upper right of the “q”
track in different outbursts, i.e., the luminosity where the HS can reach.

In the case of thermal Comptonization, the photon index $\Gamma$ monotonically
decreases with $L_{\mathrm{corona}}/L_{\mathrm{seed}}$ (e.g. Haardt &
Maraschi, 1991; Beloborodov, 1999). In this work, the $L_{\mathrm{corona}}$
and $L_{\mathrm{seed}}$ can be represented by the Compton and disk luminosity,
respectively. The $L_{\mathrm{X}}$ and $L_{\mathrm{C}}/L_{\mathrm{D}}$ indeed
follows a similar “q" track to $L_{\mathrm{X}}$ and $\Gamma$ (see Figure 4b
and also Dunn et al., 2010). So the evolution of the corona, which is
responsible for the Comptonization, determines the “q”-like tracks (Figure 1b
and Figure 4).

The H-S transition luminosity during the outburst rise is usually several
times larger than the S-H transition luminosity during the outburst decay(e.g.
Yu & Yan, 2009; Tetarenko et al., 2016), even the hardness ratio or photon
index is similar. This phenomenon is called hysteresis effect, which is
universal in outbursts experiencing state transitions (e.g. Maccarone, 2003).
According to the definition in Yu & Yan (2009), the transition luminosities of
H-S and S-H correspond to hard X-ray peaks before and after the SS. For MAXI
J1820+070, the H-S transition luminosity is 1.8 $\times 10^{38}$ erg s-1,
which is almost one order of magnitude higher than the S-H transition
luminosity (1.9 $\times 10^{37}$ erg s-1, see also Figure 4). The Compton
luminosity of H-S transition is also roughly ten times higher than that of S-H
transition (1.4$\times 10^{38}$ and 1.5$\times 10^{37}$ erg s-1). So the
discrepancy of the transition luminosity is dominated by the Compton
component.

Non-stationary accretion flow has been proposed to drive the H-S transition
luminosity during outburst rise, i.e. the transition luminosity is higher when
the mass accretion rate increases faster (Yu et al., 2004; Yu & Yan, 2009).
During the outburst decay, the S-H transition luminosity remains in a very
narrow range (e.g. Maccarone, 2003; Vahdat Motlagh et al., 2019), since S-H
transition occurs from a stationary standard accretion disk (Yu & Yan, 2009).
For MAXI J1820+070, the rapid increase of the hard X-ray flux before
transition and the corresponding H-S transition luminosity (Figure 3 and
Figure 4) is consistent with the above scenario. So the hysteresis effect is
mainly driven by the non-stationary accretion flow during the outburst rise,
which produces the Compton emission dominated the hard X-ray.

Hot accretion flow is the predominant model to produce the Compton component
(see reviews by Yuan & Narayan, 2014; Liu & Qiao, 2022). In such a framework,
the hot accretion flows can only exist below the critical luminosity
$L<\alpha^{2}L_{\mathrm{Edd}}$ (e.g. Esin et al., 1997; Xie & Yuan, 2012),
where the $\alpha$ is the viscosity parameter of hot accretion flow and the
$L_{\mathrm{Edd}}$ is the Eddington luminosity. So an increasing $\alpha$ can
maintain the how accretion flow at high luminosity regime, to make the H-S
transition luminosity higher (Begelman & Armitage, 2014; Cao, 2016; Li & Qiao,
2023). As a result, the increasing $\alpha$ may play a similar role as the
proposed non-stationary accretion flow in Yu & Yan (2009). The enhancement of
the magnetic field and/or outflow is able to increase $\alpha$ (Bai & Stone,
2013; Cao, 2016).

Jet or its base is also an alternative origin of the Compton emission. Some
X-ray spectral and timing properties during the state transition can be well
explained by jet-like corona (see the discussions in subsequent sections).
Marcel et al. (2019) has fine-tuned two independent parameters
$r_{\mathrm{J}}$ and $\dot{m}_{in}$ of the jet-accretion disk model to
replicate the “q”-like evolutionary track, where $r_{\mathrm{J}}$ is the
transition radius between jet and accretion disk, $\dot{m}_{in}$ is the mass
accretion at the inner disk radius. This model is quite similar to the
truncated disk model (Esin et al., 1997; Done et al., 2007). However, it is
still unknown what mechanism drives the evolution of $r_{\mathrm{J}}$.

###  5.2 Inner radius of accretion disk/reflected component

We used the multiple blackbody model diskbb to fit the thermal component in
HS, IMS and SS. The square root of the normalization of this model
$\sqrt{N_{\mathrm{disk}}}$ can be used as the proxy of the inner radius of the
accretion disk (Kubota et al., 1998). The nearly constant $N_{\mathrm{disk}}$
and exponential decreasing of $T_{\mathrm{in}}$ during the SS Figure 2 are
consistent with standard accretion disk that the inner radius reaches the
innermost stable circular orbit $R_{\mathrm{ISCO}}$ (Shakura & Sunyaev, 1973).

In the spectral fitting of the rising HS and IMS, we employed the relativistic
reflection model relxillCp and linked the inner radius of the reflected
component to the $N_{\mathrm{disk}}$. During the HS, the $N_{\mathrm{disk}}$
continuously decreases (Figure 2), coinciding with a decrease in the
reverberation time lag between the corona and the reflected component. This
behavior agrees with the expected reflection from a truncated accretion disk
or a contracting corona (Kara et al., 2019; De Marco et al., 2021). However,
the $N_{\mathrm{disk}}$ increases after entering the IMS (Figure 2), which is
also consistent with the evolution of the reverberation time lag (De Marco et
al., 2021; Wang et al., 2021). Wang et al. (2021) proposed that a jet-like
corona vertically contracts/expands resulting in the observed evolution of the
reverberation time lag before and after the state transition (see also Kylafis
et al., 2008; You et al., 2021; Cao et al., 2022; Méndez et al., 2022; Wang et
al., 2022b).

However, the best-fitting $N_{\mathrm{disk}}$ during the IMS are obviously
smaller than those during the SS (Figure 2, see also Motta et al., 2009),
which indicates that the reflected component may not be an accretion disk if
the constant $N_{\mathrm{disk}}$ in the SS represents the $R_{\mathrm{ISCO}}$.
In such a case, the $N_{\mathrm{disk}}$ may be the proxy of the area of the
reflected component. During the HS, the corona contracts, resulting in a
natural decrease in time lag and a reduction in the irradiated area.
Conversely, during the IMS, the corona expands, leading to an increase in both
the time lag and irradiated area. The spectral fitting by Buisson et al.
(2019) also reveals that the height of the upper corona varies in a similar
manner when the two lampposts geometry is applied. On the other hand, the
unusual decreasing of reflection fraction $R_{f}$ after the rise phase of HS
(Figure 2) also can be explained by the jet-like corona (You et al., 2021). So
the spectral evolution during the HS and IMS is consistent with a
contracting/expanding jet-like corona.

However, the nature of reflected component during the plateau and bright
decline of HS remains puzzling, if its size is smaller than the
$R_{\mathrm{ISCO}}$ of the accretion disk. The cold cloud embedded in the hot
plasma is a possible candidate (e.g. Krolik, 1998; Wang et al., 2012). In such
a geometry, the reflection fraction is expected to be large. So the unusually
large $R_{f}$ and the additional narrow iron line also support this conjecture
(see e.g. Malzac & Celotti, 2002; Merloni et al., 2006; Yu et al., 2018).

###  5.3 Type-C QPO frequency, corona geometry and Comptonization

The type-C QPO is a predominant characteristic detected in the HS and HIMS,
the oscillated photons of which are generally believed to originate from the
component producing the Compton emission (e.g. Lee & Miller, 1998; Psaltis &
Norman, 2000; Bellavita et al., 2022; Ma et al., 2021; Gao et al., 2023). So
it is important to investigate the QPO properties and the spectral parameters
of Compton component. The correlation between the QPO frequency
$\nu_{\mathrm{C,QPO}}$ and the photon index $\Gamma$ of the Compton component
has been widely studied (e.g. Vignarca et al., 2003; Shaposhnikov & Titarchuk,
2009; Stiele et al., 2013; Wang et al., 2022a). The $\nu_{\mathrm{C,QPO}}$
usually positively correlates with the $\Gamma$ over two orders of magnitude
frequency range, and the $\Gamma$ becomes saturated above a certain frequency
in few sources (e.g. Vignarca et al., 2003; Shaposhnikov & Titarchuk, 2009).
It is generally believed that the mass accretion rate drives the evolution of
both X-ray spectral and timing properties of BHXRB(see reviews in Done et al.,
2007; Gilfanov, 2010). The $\Gamma$ and the $\nu_{\mathrm{C,QPO}}$ both
increase with X-ray luminosity, resulting in a positive correlation (e.g.
Revnivtsev et al., 2001; Mereminskiy et al., 2019; Wang et al., 2022a).
However, $\nu_{\mathrm{C,QPO}}$ in MAXI J1820+070 displays a complex
correlation with $L_{\mathrm{X}}$ (Figure 7a), and $\Gamma$ exhibits a
“$\eta$”-like track along $L_{\mathrm{X}}$ (Figure 4). These results suggest
that the mass accretion rate is not the only factor influencing the evolution
of the spectral and timing properties of the corona.

MAXI J1820+070 also shows a positive correlation between
$\nu_{\mathrm{C,QPO}}$ and $\Gamma$ with varying slopes across different
phases of HS and HIMS (Figure 7b). The $\nu_{\mathrm{C,QPO}}$ and $\tau$
exhibit a consistent negative correlation across various phases of HS and HIMS
(Figure 7c). These correlations provide compelling evidence that the
Comptonization is the driving force behind the evolution of the QPO frequency.
Recently, some models have been proposed to explain the properties of the
type-C QPO based on the Comptonization process (e.g. Bellavita et al., 2022;
Mastichiadis et al., 2022). Specifically, the interplay between thermal and
Compton components, which influences optical depth and electron temperature
during Comptonization, can produce an oscillation roughly consistent with
type-C QPO (Mastichiadis et al., 2022).

In some other models, the QPO frequency is usually thought to inversely
correlate to the characteristic scale of the corona and/or the inner radius of
the accretion disk (e.g. Ingram et al., 2009; Cabanac et al., 2010; Marcel et
al., 2020; Rawat et al., 2023; Motta & Belloni, 2024). So the increasing of
QPO frequency during the rise and plateau phases of HS (Figure 6) can be
accounted for the shrinking of the inner radius of a truncated accretion disk
(De Marco et al., 2021; Zdziarski et al., 2021) or a contracting corona (Kara
et al., 2019; Wang et al., 2021, 2022b). However, the observed decreasing in
QPO frequency during the bright decline, and its subsequent increasing during
the IMS (Figure 6), is challenging to be explained by the behavior of a
contracting and then expanding jet-like corona inferred from the reverberation
lag and X-ray spectral evolution (Wang et al., 2022b).

The QPO frequency may alternatively be proportional to a characteristic
timescale for ejecting mass as a damped oscillator in a jet-like corona model.
As a result, the $\nu_{\mathrm{C,QPO}}\propto R_{0}^{2}n_{e,0}$ (Kylafis et
al., 2008), where the $R_{0}$ is the jet base, and $n_{e,0}$ is the electron
number density of the jet base. The expanding jet-like corona during the IMS
naturally causes the rapid increase of the QPO frequency. The optical depth in
such corona should also be a function of $R_{0}$ and $n_{e,0}$. However, the
specific relation between $\tau$ and $\Gamma$ in the jet-like corona should be
investigated in order to quantitatively understand the correlations between
$\nu_{\mathrm{C,QPO}}$ and $\tau$/$\Gamma$.

###  5.4 The association between rapid transition and radio ejection

It is widely recognized that transient jet ejections are associated with X-ray
spectral state transitions (Fender et al., 2004), wherein Compton-dominated
spectra shift to thermally dominated spectra. The well-sampled observations of
MAXI J1820+070 offer a unique opportunity to investigate the temporal
connection between ejection events and spectral state transitions. Remarkably,
the last occurrence of type-C QPO coincided precisely with the first ejection
within one hour. Subsequent to this ejection, the Compton luminosity sharply
decreased more than two times within 0.19 days. So the observations of MAXI
J1820+070 establish a temporal connection between the corona and ejection
within timescale of hours (see also Homan et al., 2020), which the corona is
responsible for the Compton emission and the type-C QPO. One plausible
scenario is that the corona or part of the corona is ejected, subsequently
allowing the disk component to dominate the X-ray spectrum. The dominance of
ions in the ejection composition further supports this hypothesis (Zdziarski &
Heinz, 2024). Additionally, the corona transforming into an ejected jet has
been proposed in the microquasar GRS 1915+105 (Mirabel et al., 1998; Méndez et
al., 2022). A similar scenario has been proposed for the active galactic
nuclei (AGNs) harboring super-massive BH, such as 3C 120 (Marscher et al.,
2002) and 3C 111 (Chatterjee et al., 2011), in which the observed X-ray dips
are associated with the radio ejections.

## Acknowledgements

We would like to thanks the helpful discussion with Bei You, Fuguo Xie and
Phil Uttley. This work made use of the data from Insight-HXMT mission, a
project funded by China National Space Administration (CNSA) and the Chinese
Academy of Sciences (CAS). This work was supported in part by the Natural
Science Foundation of China (grants U1838203, U1938114, 12373049, 12361131579
and 12373050).

## Data Availability

The Insight-HXMT and $NICER$ data underlying this article are available in the
public archive http://archive.hxmt.cn/proposal and
https://heasarc.gsfc.nasa.gov/docs/archive.html.

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##  Appendix A Some extra materials

Figure 9: The corresponding Compton (in blue) and reflection (in orange)
components of the best-fitting models under different reflection fractions
$R_{f}$ in $Insight$-HXMT observations. The exposure ID, $R_{f}$ and $\Gamma$
are present on the upper right in the figure. P011466100401, P011466102402 and
P011466104403 are selected from the plateau phase of hard state that have
similar $L_{\mathrm{C}}$. Table 1: The QPO information of each segment in
$NICER$ obsID 1200120196 and 1200120197

$\mathrm{Start}$ | $\mathrm{End}$ | Time | $\nu_{\mathrm{C,QPO}}$ | RMSC,QPO | QC,QPO | $\sigma_{\mathrm{C,QPO}}$ | $\nu_{\mathrm{B,QPO}}$ | RMSB,QPO | QB,QPO | $\sigma_{\mathrm{B,QPO}}$
---|---|---|---|---|---|---|---|---|---|---
(s) | (s) | (MJD) | (Hz) |  |  |  | (Hz) |  |  |
142237907 | 142238873 | 58304.2728 | $2.1063^{+0.0197}_{-0.0180}$ | $0.0366^{+0.0017}_{-0.0018}$ | 5.6347 | 10.314 | – – | – – | – – | – –
142269824 | 142271003 | 58304.6423 | $2.9366^{+0.0201}_{-0.0208}$ | $0.0277^{+0.0011}_{-0.0011}$ | 7.2508 | 12.419 | – – | – – | – – | – –
142275663 | 142276722 | 58304.7098 | $3.2084^{+0.0194}_{-0.0198}$ | $0.0288^{+0.0008}_{-0.0011}$ | 6.0187 | 13.3546 | – – | – – | – – | – –
142292969 | 142294468 | 58304.9101 | $3.8371^{+0.0361}_{-0.0368}$ | $0.0217^{+0.0012}_{-0.0012}$ | 6.05 | 8.7983 | – – | – – | – – | – –
142298630 | 142300026 | 58304.9757 | $4.2509^{+0.0225}_{-0.0268}$ | $0.0206^{+0.0008}_{-0.0008}$ | 8.514 | 12.8107 | – – | – – | – – | – –
142308700 | 142314902 | 58305.0922 | $4.9658^{+0.0324}_{-0.0344}$ | $0.0161^{+0.0009}_{-0.0009}$ | 7.7465 | 8.8628 | – – | – – | – – | – –
142319818 | 142333386 | 58305.2209 | $5.9361^{+0.0284}_{-0.0248}$ | $0.0138^{+0.0004}_{-0.0004}$ | 4.9696 | 18.6406 | $3.9725^{+0.1147}_{-0.1200}$ | $0.0086^{+0.0004}_{-0.0003}$ | 2.7874 | 13.0669
142336496 | 142344002 | 58305.4139 | $6.5140^{+0.0347}_{-0.0367}$ | $0.0099^{+0.0003}_{-0.0003}$ | 7.3527 | 14.2943 | $4.4448^{+0.1583}_{-0.1605}$ | $0.0078^{+0.0004}_{-0.0004}$ | 3.2001 | 10.0584
142347614 | 142350064 | 58305.5426 | $7.1084^{+0.0953}_{-0.0904}$ | $0.0106^{+0.0007}_{-0.0007}$ | 3.3794 | 8.0053 | $4.7946^{+0.1202}_{-0.1442}$ | $0.0070^{+0.0005}_{-0.0005}$ | 5.542 | 6.8117
142353173 | 142355624 | 58305.6069 | $8.0492^{+0.1531}_{-0.1288}$ | $0.0051^{+0.0007}_{-0.0007}$ | 4.4178 | 3.4635 | – – | – – | – – | – –
142358915 | 142383043 | 58305.6734 | – – | – – | – – | – – | $4.1896^{+0.0450}_{-0.0420}$ | $0.0077^{+0.0003}_{-0.0003}$ | 5.6398 | 12.8465

Notes:

$\mathrm{Start}$: the start time of segments; $\mathrm{End}$: the end time of
segments; $\nu$: centroid frequency; RMS: root mean square; Q: quality factor;
$\sigma$: significance. The subscript B and C represent the type-B and type-C
QPOs.

Figure 10: The hardness-intensity diagram (HID) and flux-$\Gamma$ plane during
three outbursts in other sources, with the left panels showing the HID and the
right panels showing the flux-$\Gamma$ plane. The outbursts, in order from top
to bottom, are as follows: the 1998 outburst of XTE J1550$-$564, the 2005
outburst of GRO J1655$-$40 and the 2003 outburst of H1743$-$322\. The HIDs are
defined as the total 2.5–30 keV count rate vs. the ratio of hard (10–30 keV)
to soft (2.5–6 keV) count rates from $RXTE/PCA$. The flux and $\Gamma$ data
are from public data in Sobczak et al. (2000); Debnath et al. (2008);
McClintock et al. (2009), respectively.