# Transitions and Origin of the Type-B Quasi-Periodic Oscillation in the Black
Hole X-ray Binary MAXI J1348–630

H.X.Liu  Key Laboratory for Particle Astrophysics, Institute of High Energy
Physics, Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049,
People’s Republic of China  University of Chinese Academy of Sciences, Chinese
Academy of Sciences, Beijing 100049, People’s Republic of China
<EMAIL_ADDRESS>Y. Huang<EMAIL_ADDRESS>Q.C.Bu<EMAIL_ADDRESS>tuebingen.de Y. Huang  Key Laboratory for Particle Astrophysics, Institute of
High Energy Physics, Chinese Academy of Sciences, 19B Yuquan Road, Beijing
100049, People’s Republic of China  University of Chinese Academy of Sciences,
Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
Q.C.Bu  Institut für Astronomie und Astrophysik, Kepler Center for Astro and
Particle Physics, Eberhard Karls Universität, Sand 1, 72076 Tübingen, Germany
W. Yu  Key Laboratory for Particle Astrophysics, Institute of High Energy
Physics, Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049,
People’s Republic of China  University of Chinese Academy of Sciences, Chinese
Academy of Sciences, Beijing 100049, People’s Republic of China  Z.X.Yang  Key
Laboratory for Particle Astrophysics, Institute of High Energy Physics,
Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049, People’s
Republic of China  University of Chinese Academy of Sciences, Chinese Academy
of Sciences, Beijing 100049, People’s Republic of China  L. Zhang  Key
Laboratory for Particle Astrophysics, Institute of High Energy Physics,
Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049, People’s
Republic of China  L.D.Kong  Key Laboratory for Particle Astrophysics,
Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan
Road, Beijing 100049, People’s Republic of China  University of Chinese
Academy of Sciences, Chinese Academy of Sciences, Beijing 100049, People’s
Republic of China  G.C.XIAO  Purple Mountain Observatory, Chinese Academy of
Sciences,Nanjing 210034, People’s Republic of China  J.L.Qu  Key Laboratory
for Particle Astrophysics, Institute of High Energy Physics, Chinese Academy
of Sciences, 19B Yuquan Road, Beijing 100049, People’s Republic of China
University of Chinese Academy of Sciences, Chinese Academy of Sciences,
Beijing 100049, People’s Republic of China  S.N.Zhang  Key Laboratory for
Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of
Sciences, 19B Yuquan Road, Beijing 100049, People’s Republic of China
University of Chinese Academy of Sciences, Chinese Academy of Sciences,
Beijing 100049, People’s Republic of China  S.Zhang  Key Laboratory for
Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of
Sciences, 19B Yuquan Road, Beijing 100049, People’s Republic of China
University of Chinese Academy of Sciences, Chinese Academy of Sciences,
Beijing 100049, People’s Republic of China  L.M.Song  Key Laboratory for
Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of
Sciences, 19B Yuquan Road, Beijing 100049, People’s Republic of China
University of Chinese Academy of Sciences, Chinese Academy of Sciences,
Beijing 100049, People’s Republic of China  S.M.JIA  Key Laboratory for
Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of
Sciences, 19B Yuquan Road, Beijing 100049, People’s Republic of China
University of Chinese Academy of Sciences, Chinese Academy of Sciences,
Beijing 100049, People’s Republic of China  X.MA  Key Laboratory for Particle
Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences,
19B Yuquan Road, Beijing 100049, People’s Republic of China  University of
Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100049,
People’s Republic of China  L.TAO  Key Laboratory for Particle Astrophysics,
Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan
Road, Beijing 100049, People’s Republic of China  University of Chinese
Academy of Sciences, Chinese Academy of Sciences, Beijing 100049, People’s
Republic of China  M.Y.GE  Key Laboratory for Particle Astrophysics, Institute
of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan Road, Beijing
100049, People’s Republic of China  University of Chinese Academy of Sciences,
Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
Q.Z.LIU  Purple Mountain Observatory, Chinese Academy of Sciences,Nanjing
210034, People’s Republic of China  J.Z.YAN  Purple Mountain Observatory,
Chinese Academy of Sciences,Nanjing 210034, People’s Republic of China  R.C.MA
Key Laboratory for Particle Astrophysics, Institute of High Energy Physics,
Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049, People’s
Republic of China  University of Chinese Academy of Sciences, Chinese Academy
of Sciences, Beijing 100049, People’s Republic of China  X.Q.REN  Key
Laboratory for Particle Astrophysics, Institute of High Energy Physics,
Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049, People’s
Republic of China  University of Chinese Academy of Sciences, Chinese Academy
of Sciences, Beijing 100049, People’s Republic of China  D.K.ZHOU  Key
Laboratory for Particle Astrophysics, Institute of High Energy Physics,
Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049, People’s
Republic of China  University of Chinese Academy of Sciences, Chinese Academy
of Sciences, Beijing 100049, People’s Republic of China  T.M.LI  Key
Laboratory for Particle Astrophysics, Institute of High Energy Physics,
Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049, People’s
Republic of China  University of Chinese Academy of Sciences, Chinese Academy
of Sciences, Beijing 100049, People’s Republic of China  B.Y.WU  Key
Laboratory for Particle Astrophysics, Institute of High Energy Physics,
Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049, People’s
Republic of China  University of Chinese Academy of Sciences, Chinese Academy
of Sciences, Beijing 100049, People’s Republic of China  Y.C.XU  Key
Laboratory for Particle Astrophysics, Institute of High Energy Physics,
Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049, People’s
Republic of China  University of Chinese Academy of Sciences, Chinese Academy
of Sciences, Beijing 100049, People’s Republic of China  Y.F.DU  Key
Laboratory for Particle Astrophysics, Institute of High Energy Physics,
Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049, People’s
Republic of China  University of Chinese Academy of Sciences, Chinese Academy
of Sciences, Beijing 100049, People’s Republic of China  Y.C.FU  Key
Laboratory for Particle Astrophysics, Institute of High Energy Physics,
Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049, People’s
Republic of China  University of Chinese Academy of Sciences, Chinese Academy
of Sciences, Beijing 100049, People’s Republic of China  Y.X.XIAO  Key
Laboratory for Particle Astrophysics, Institute of High Energy Physics,
Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049, People’s
Republic of China  University of Chinese Academy of Sciences, Chinese Academy
of Sciences, Beijing 100049, People’s Republic of China  G.Q. Ding  Xinjiang
Astronomical Observatory, Chinese Academy of Sciences,150, Science 1-Street,
Urumqi, Xinjiang 830011, China  X.X. YU  Key Laboratory for Particle
Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences,
19B Yuquan Road, Beijing 100049, People’s Republic of China  University of
Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100049,
People’s Republic of China

###### Abstract

The fast transitions between different types of quasi-periodic oscillations
(QPOs) are generally observed in black hole transient sources (BHTs). We
present a detailed study on the timing and spectral properties of the
transitions of type-B QPOs in MAXI J1348–630, observed by _Insight_ -HXMT. The
fractional rms variability–energy relationship and energy spectra reveal that
type-B QPOs probably originate from jet precession. Compared to weak power-law
dominated power spectrum, when type-B QPO is present, the corresponding energy
spectrum shows an increase in Comptonization component and the need for
xillverCp component, and a slight increase of height of the corona when using
relxilllp model. Therefore, we suggest that a coupled inner disk-jet region is
responsible for the observed type-B QPOs transitions. The time scale for the
appearance/disappearance of type-B QPOs is either long or short (seconds),
which may indicate an instability of disk-jet structure. For these phenomena,
we give the hypothesis that the Bardeen-Petterson effect causes disk-jet
structure to align with BH spin axis, or that the disappearance of small-scale
jets bound by the magnetic flux tubes lead to the disappearance of type-B
QPOs. We observed three events regarding the B/C transitions, one of which
occurred in a short time from $\sim 9.2$ Hz (C) to $\sim 4.8$ Hz (B). The
energy spectral analysis for the other two transitions shows that when type-C
QPO is present, the Comptonization flux is higher, the spectrum is harder and
the inner radius of disk changes insignificantly. We suggest that type-C QPOs
probably originate from relatively stronger jets or corona.

Black hole binaries, X-Ray, QPO, jet

##  1 Introduction

Most of the black hole X-ray binaries (BHXBs) in the Galaxy are discovered as
transients whose spectral and timing properties change with time. During a
typical outburst, a BHXB goes through a transition from the low/hard (LHS) to
the high/soft (HSS) state through relatively short–lived intermediate states,
which are known as hard intermediate state (HIMS) and soft intermediate state
(SIMS) (Belloni, 2010; Remillard & McClintock, 2006; Motta et al., 2009). The
rapid flux variations found in the X-ray light curves of BHXBs are generally
considered to be a feature of the inner accretion flow in the vicinity of
black holes. Low frequency Quasi Periodic Oscillations (LFQPOs), characterized
by discrete peaks in the Power Density Spectra (PDS), are commonly observed in
the 0.01–30 Hz range in BHXBs. Based on the properties of PDS in several
typical BHXBs, XTE J1550–564, GX 339–4, and XTE J1859+226 (Wijnands et al.,
1999; Homan et al., 2001; Motta et al., 2011; Casella et al., 2005), LFQPOs
are classified into three types, namely type-A, B, and C. Type-A QPOs are
rarely detected during the HSS, and they are characterized by a weak and broad
peak in the PDS. During the transition state—SIMS, type-B QPOs are usually
observed, and typically have a rather high amplitude in the PDS of a power law
shape with a centroid frequency around 4–6 Hz. Generally seen in the LHS and
HIMS, type-C QPOs are characterized as a strong narrow peak with broadband
noise in the PDS, which may be accompanied by harmonics and possible sub-
harmonics (Casella et al., 2004).

Through timing analysis, rapid transitions between two types of QPOs (type-B
QPOs transit to other types or disappear), have been observed in a few BHXBs.
As reported by Miyamoto et al. (1991), Nespoli et al. (2003) and Motta et al.
(2011), the transitions of type-B QPOs are often observed in GX 339–4. In XTE
J1550–564 (Homan et al., 2001; Sriram et al., 2016), transition events related
to type-B/A QPOs variations were observed along with the change of energy
spectra. Similar rapid transitions involving type-B QPOs and spectral
variations in XTE J1859+226 were reported by Casella et al. (2004) and Sriram
et al. (2013). In XTE J1817–330, Sriram et al. (2012) found that a type-B QPO
$\sim$ 6 Hz QPO switches to a type-A QPO with a decrease in flux. Among all
the outbursts of H1743-322 observed by Rossi X-ray Timing Explorer (_RXTE_),
not only were type B/A QPOs transitions observed, (Homan et al., 2005) but
also three B/C transitions (Sriram et al., 2021). For MAXI J1535–571, Huang et
al. (2018) found type-B QPOs $\sim$ 10 Hz in correspondence with flux changes
in X–ray, and Stevens et al. (2018) reported a weak type A/B QPO transition
with no sudden flux change. The type C/B QPO transitions were also found in
GRS 1915+105 (Soleri et al., 2008) and MAXI J1820+070 (Homan et al., 2020).

Although LFQPOs have been discovered for decades, there is still no consensus
for their physical explanations. Some promising models have been proposed
based on observational data, which can be divided into two categories: the
geometric effects of the hot inner/outer flows and the instability of
accretion flows. The relativistic precession model was firstly proposed by
Stella & Vietri (1998) to explain the origin and the behaviour of the LFQPO
and kHz QPOs in neutron star X-ray binaries. This model has been continuously
modified (Ingram et al., 2009; Pawar et al., 2015; van den Eijnden et al.,
2017; Ma et al., 2021) later and applied to BHXBs. In these improved models,
the QPOs are from Lense-Thirring (L-T) precession of a hot inner flow (a
radially extended corona or jet). These observational evidences support the
geometric explanations for LFQPOs (Schnittman et al., 2006; Ingram et al.,
2009, 2016). In the other kind of model, the QPOs come from intrinsic
instabilities in the accretion flow, for example, magneto-acoustic wave
propagation (Titarchuk & Fiorito, 2004; Cabanac et al., 2010), or the
accretion-ejection instability (AEI)—a product of instability accretion model
(Tagger & Pellat, 1999).

It is thought that the different types of QPOs observed in the BHXBs systems
are associated with different physical mechanisms in the inner region of the
accretion disk. However, the inner disk variation could not be conclusively
demonstrated previously, which may be due to the energy band of _RXTE_.
Therefore, the transition mechanism between different types of QPOs has not
been clear. Using the data of _Insight_ -HXMT, with a wider energy band (1
keV–250 keV), it is now possible to obtain more information and to better
understand the changes that occur in the inner disk regions as well as in the
high-energy radiation regions where the LFQPOs and their transitions are
observed.

MAXI J1348–630 was discovered as a X-ray binary by the X-ray telescope
MAXI/GSC on January 26, 2019 (Yatabe et al., 2019). Jana et al. (2020)
estimated the mass of the BH to be $9.1^{+1.6}_{-1.2}$ $M_{\sun}$. They also
found that the viscous timescale in this outburst is $\sim$3.5 days. The
distance of the source was estimated as $\sim$2.2 kpc by Chauhan et al.
(2020). Tominaga et al. (2020) proposed that the black hole is more massive if
the disk is inclined and the black hole is spinning. These results suggest
that MAXI J1348–630 may host a relatively massive black hole among the known
BHXBs in our Galaxy. Carotenuto et al. (2019) reported that a radio source is
detected at a position consistent with the location of MAXI J1348–630,
displaying, on 2019-02-09, a preliminary flux density of 520.3 $\pm$ 5.0 mJy.

The QPOs transitions between different typical QPOs were also observed in the
2019 outburst of MAXI J1348–630. For this outburst, Zhang et al. (2021) have
analyzed four fast appearance/disappearance of type-B QPO using the data from
_NICER_ , in the energy band of 0.5–10 keV.

_Insight_ -HXMT has observed several transitions involving the type-B QPOs
with its three main detectors: LE, ME, and HE, covering a broad-band energy
(1–250 keV). Using the data from _Insight_ -HXMT, the detailed timing and
spectral analyses for the transitions given in this work may provide more
information to understand the underlying physical processes. The paper is
organized as follows: the data reduction is introduced in Section 2, and we
present the timing and spectral results in Section 3; in Section 4, we present
the summary and discussions; finally, we present conclusions in Section 5.

##  2 Observations and Data Reduction

_Insight_ -HXMT, China’s first X-ray astronomical satellite which was
successfully launched on June 15, 2017, carries three sets of main instruments
(LE/ME/HE, short for the Low/Medium/High Energy X-ray Telescope respectively).
More details about _Insight_ -HXMT can be found in Zhang et al. (2020), Chen
et al. (2020) (LE), Cao et al. (2020) (ME) and Liu et al. (2020) (HE). MAXI
J1348–630 was observed regularly with _Insight_ -HXMT from January 27 2019 to
May 15. We analyzed the observations in the SIMS around the peak of this
outburst (see the Figure 1) in this work.

The _Insight_ -HXMT Data Analysis software (HXMTDAS, v2.04) is used to process
and filter the data. Since the background and some particle events do not have
significant influences on the PDS, the screening criteria of good time-
intervals (GTIs) in timing analysis can be loosened. Therefore, the light
curves to produce dynamic power spectra (DPS) are generated with the following
criteria: the offset for the point position $<0.06^{\circ}$, the elevation
angle (ELV) $>10^{\circ}$. The selection of GTIs is more demanding when
extracting the energy spectra: ELV $>10^{\circ}$; the geometric cutoff
rigidity (COR) $>6^{\circ}$; the offset for the point position
$<0.04^{\circ}$; data are used at least 300 s before and after the South
Atlantic Anomaly (SAA) passage. The backgrounds are estimated with the
official tools: LEBKGMAP (Liao et al., 2020a), MEBKGMAP (Guo et al., 2020)
(ME)and HEBKGMAP Liao et al. (2020b) in version 2.0.6.

The energy bands, adopted for energy spectral analysis are 1–1.8, 2–10 keV
(LE), 10–35 keV (ME) and 35–100 keV (HE) in this work. The XSPEC software
package v12.11 (Arnaud, 1996) is used to fit the spectra. Uncertainty
estimated for each spectral parameter is for 90% confidence level, and a
systematic error of 1% is added. Detailed discussions of its calibrations are
given in Li et al. (2020).

##  3 Data Analysis and Results

###  3.1 Timing Analysis and Results

Using the archived data of _Insight_ -HXMT observations of MAXI J1348–630, we
plot the evolution of its light curves and hardness in Figure 1, with each
point in the diagram representing an observation. The top panel represents the
count rate of LE (1–10 keV), while the bottom panel shows the hardness ratio
that is defined as count rates ratio between 4–10 keV and 2–4 keV. According
to the the spectral analysis, Zhang et al. (2022) have defined four states for
this outburst. Huang et al. (2022) (In prepation) studied in detail the timing
properties in the 2019 outburst. They found that the observational properties
are consistent with BHXBs and the type-C QPOs frequency varied between 0.26
and 7.31 Hz with decreasing hardness.

The appearance of the type-B QPO indicates the source was in its SIMS, as
shown in the shaded area of Figure 1. In this work, we focus on studying the
transitions of QPOs during the SIMS of this outburst, while the detailed
information are listed in Table 1. For our timing analysis, we compute the
power density spectra (PDS) with a time resolution of 1/128 s using 16 s data
segments (corresponding to a Nyquist frequency of 64 Hz) for the observation
listed in Table 1.

In order to search for the QPOs, the PDS is normalized according to Leahy
normalization (Leahy et al., 1983). In Figure 2, we show the light curves from
three energy bands (LE:1–10keV; ME:10–35 keV; HE: 35–100 keV), hardness and
DPS with a time interval of 16 s for part of SIMS I (from MJD 58523.8 to MJD
58527.8) and SIMS II (MJD 58539.1–MJD 58540.2). The results show that in the
bottom panel of Figure 2, type-B QPOs often disappear or transit into other
types of QPOs when the counts rate change.

Based on the occurrences of QPOs and variations of rate shown in Figure 2, we
divide the whole SIMS into 7 epochs and mark them by different colors, which
are also referred in the last column of Table 1. Epoch 1 is the period from
MJD 58522.60 to MJD 58524.25, during which no intermittent QPO and no
significant changes in flux are observed. Therefore it is not shown in Figure
2. During Epoch 2 (MJD 58524.27–58524.41), a fast transition between type-B
and type-C QPOs is detected. The fast re-occurrence of type-B QPOs on short
time-scale is found during Epoch 3 (MJD 58524.77–58524.94). For Epoch 4 (MJD
58525.06–58525.87) and Epoch 5 (MJD 58526.19–58527.10),there are long time
transition intervals between the appearance and disappearance of type-B QPOs.
To clarify, the corresponding DPS are plotted in Figures 4 and 5. In Epoch 6
and Epoch 7, the transitions between type-B and type-C QPOs are observed,
accompanied by significant changes in the X-ray flux (also see Figure 5).

Based on the DPS, the average PDS is produced according to Miyamoto
normalization (Miyamoto et al., 1991) in units of (rms/mean)2Hz-1 after
subtracting the Possion noise, in order to get the characteristics of QPOs for
the different ObsIDs. The PDSs are fitted by a model consisting of multiple
Lorentzians (Belloni et al., 2002). The background contribution to the QPO
fractional rms are corrected according to (Belloni & Hasinger, 1990; Bu et
al., 2015)

${\rm rms}=\sqrt{R}\times\frac{(S+B)}{S},$ (1)

here _R_ is the power calculated with the integration of the QPO Lorentzian
function over the frequency range 0.01–64 Hz, _S_ is the source count rate,
while _B_ is the background count rate. We fit the PDS of all QPOs and the
results are given in Table 1. The frequency of type-B QPOs varied within a
narrow range of 4.3–4.7 Hz and 4.0–4.2 Hz in SIMS I (MJD 58522.7–58527.8) and
SIMS II (MJD 58539.1–58540.2), respectively.

In order to investigate the energy dependence of the type-B QPOs, type-B QPOs
observations are divided into 12 energy bands from 1–100 keV: 1–2.5, 2.5–3.5,
4.5–5.5, 5.5–7.0, 7.0–10.0, 10.0–14.0, 14.0–18.0 18.0–30.0, 30.0–40.0,
40.0–50.0 and 50.0–100.0 keV. The corresponding centroid frequencies and the
rms of type-B QPOs from all epochs are plotted in Figure 3. The results show
that rms increased with energy from 1 keV and reached a plateau above 10 keV.
Meanwhile, the frequency of QPO remains unchanged with the energy.

####  3.1.1 The temporary characteristics of Type-B QPOs

In this work, we perform spectral analysis for these observations using two
different models mentioned above in the energy band 1–100 keV. When source was
in its SIMS, the QPOs frequently appeared or disappeared as shown in Figure 2.
When the source entered Epoch 3 from Epoch 2, the count rates of ME, HE and
the hardness decrease abruptly, while the DPS show that there are multiple
rapid transitions between no QPO (hereafter NO-Q) and type-B QPOs (hereafter
B-Q, also see in Table 1). In order to show the temporary nature of the type-B
QPOs clearly, the DPS and PDS of partial Epoch 3 observations is shown in the
top panel of Figure 4. We can see that type-B QPOs disappeared suddenly on a
shorter time scale (about ten seconds), while no significant changes are
observed in the flux. The PDS of NO-Q is characterized by a weak power-law
noise. Unfortunately, the LE data is not available during this period, but
previous studies using _RXTE_ and _NICER_ ’s data have shown that the
disappearance of type-B QPOs are often accompanied by a flux decrease in low
energy band (Sriram et al., 2013, 2021; Zhang et al., 2021).

Type-B QPOs can also be present or disappear for a few hours. In Epoch 1,
type-B QPO are observed continuously for more than 3 days. In Epochs 4 and 5,
QPOs are more likely to disappear completely at the relatively lower hardness
and flux of the high energy bands (i.e. ME, HE), as shown in Figure 2 (MJD
58525.1-58525.7 and MJD 58526-58526.8), which is consistent with the results
of Zhang et al. (2021). In the bottom panels of Figure 4, we show examples of
DPS and PDS for a long-time scale transition between B-Q and NO-Q and find
that the PDS of NO-Q show a weak power-law noise at low frequencies. We will
discuss the possible physical causes of this transition in combination with
information on time variation and energy spectrum in section 3.2.

####  3.1.2 Transitions between type-B and type-C QPOs

Several obvious transitions between type-B and type-C QPOs are observed in
this outburst, as shown in Figure 5. The first one is observed on $\sim$ MJD
58524.4 (in Epoch 2), which occurred in a short period of $\sim$ 2000 s.
During the first $\sim$ 1800 s, the averaged PDS show appearances of a QPO
with two peaks of $\sim$ 2.8 Hz (rms $\sim$ 8.6%) and $\sim$ 9.3 Hz (rms
$\sim$ 10.3%). Depending on the characteristics of type-C QPOs ($\sim$ 7 Hz
with small rms $\leq$ 10% in Huang et al.(In preparation)) at the HIMS of this
source, it can be inferred that the QPO with frequency of $\sim$ 9.3 Hz is
type-C. A type-B QPO with central frequency of $\sim$ 4.8 Hz (rms $\sim$ 8.1%)
is detected in the last $\sim 200$ seconds. It is likely that a type-C QPO
appeared subsequently, though this is hard to confirm because of its short
duration. This transition occurred in a particularly short period of time as
we can see from the DPS shown in the top panel of Figure 5.

The second transition (denoted as Epoch 6) is accompanied by a significant
decrease in the count rate of LE and increase in the count rates of ME and HE
(see the Figure 2 and the middle panel of Figure 5), when a significant
evolution of this type-C QPO is observed. The middle panel of Figure 5
demonstrates that this QPO has two peaks and evolves over time; in particular,
the lower frequency peak evolved from $\sim$ 2.9 Hz to $\sim$ 3.2 with a
slight change in rms from 8.1% to 8.2%, while the higher peak evolved from 7.6
Hz to 10.0 Hz (rms $\sim$ 10.5%-11.2%).

During the SIMS II, the transition of a type-B at frequency of $\sim$ 4.3 Hz
to a type-C QPO at frequency of $\sim$ 7.8 Hz is detected (denoted as Epoch
7), accompanied by a smaller low-energy rate (1–10 keV) and a larger high-
energy rate ($\geq$ 10 keV), as shown in the bottom panel of Figure 5. The
last two type-C QPOs also exhibited energy-dependent properties, i.e., the PDS
exhibit different shapes for different energy bands.

###  3.2 Spectral Analysis and Results

Due to the limitation of LE GTIs, only data from Epoch 4 to Epoch 7 are used
for the energy spectrum study. In order to study the energy spectral
characteristics regarding different types of QPOs, we first combine the energy
spectra based on PDS (i.e., NO-QPO, type-B QPO, and type-C QPO) that are
observed in Epochs 4, 5, 6, and 7, namely NO-Q, B-Q, and C-Q, to increase the
signal-to-noise. Before fitting the spectra, we first compare the spectra
between the segments of NO-Q (C-Q) and B-Q qualitatively. The energy spectrum
ratio between the B-Q and NO-Q observations is shown in the top panel of
Figure 6. The ratios between B-Q and NO-Q indicate differences at both low and
high energy bands. At energies below 3 keV, the ratio approaches 1, which
indicates that the energy spectrum shape has slightly changed. However, the
ratio is more or less constant above 10 keV, and the flux of B-Q is
significantly higher than that of NO-Q at energies above 3 keV. These results
are consistent with the phenomenons that type-B QPOs appear in the high energy
bands.

The energy spectra ratio between the type-C QPOs and type-B QPOs is shown in
the bottom panel of Figure 6. We find that even after the source re-entered
the SIMS II for 12 days, the trend of the energy spectra ratio remains the
same when the QPO transitions occurred. The ratio (C-Q/B-Q) is appreciably
less than 1 at energies <10 keV (maximum value $\sim$ 0.8 at 4–5 keV), which
indicates that the spectral shapes have significantly changed at low energy
bands. At energies $>$ 10 keV, the ratio increases with energy with a value
$>1$, which indicates that the C-Q flux is larger at higher energies. These
agree with the fact that the spectra of type-B QPOs are softer than those of
type-C QPOs in a transition.

To quantitatively study the evolution of spectral parameters, different models
are applied to the observations in Epoch 5. As shown in Figure 7, the first
trial of fitting is with a model consisting of a multi-color disk component
and a Compton component (Zdziarski et al., 1996; Życki et al., 1999), i.e.,
tbabs$\times$(diskbb+nthcomp). The nthcomp is the thermally comptonized
continuum model that may arise from a hot corona associated with accretion
disc in the BHTs. Therefore, during the fitting, we link the seed photon
temperature ($T_{\rm bb}$) of the nthcomp model with the inner disc
temperature ($kT_{\rm in}$) of the $diskbb$ component. The goodness of fit
($\delta\chi^{2}>2$) are mostly attributed to an obvious asymmetry of the
broadened iron line. Accordingly, we add an extra gaussian component to fit
the spectra and the residuals are shown in the 4-5th panels of Figure 7.
However, a hint of a narrow iron line seems to be present in the residuals.
Therefore, we add another non-relativistic reflection model xillverCp with the
inclination angle fixed at $36.5^{\circ}$, $\Gamma$ and $kT_{\rm e}$ linked to
the parameters of nthcomp and we calculate the significance using $F-{\rm
test}$ in XPSEC. The best-fitting parameters of model 1, i.e,
tbabs$\times$(diskbb+gaussian+nthcomp+xillverCp), are shown in Tables 2 and 3.
Although the fitting is significantly improved, the centroid line energy of
Gaussian is less than the typical 6.4–7.1 keV iron regime, and the profile is
extremely wide (1–2 keV). The values are un-physical, which is similar to the
result in Cygnus X-1 reported by Tomsick et al. (2014). The broad emission
feature is normally seen in the reflection spectra.

An accretion disk with a lamppost geometry corona (the relativistic reflection
model), as model 2, tbabs$\times$(diskbb+relxilllp) is introduced to fit the
spectra. For the relxilllp components of all spectra, an extreme spin value of
0.8 and an inclination angle of $36.5^{\circ}$ (given in Jia et al. 2022) are
chosen and fixed during spectral fittings. We show the best-fitting parameters
in Tables 5 and 6. In the relxilllp model, the reflection fraction $R_{\rm f}$
is defined as the ratio of the incident photon intensity that illuminates the
accretion disc to that observed directly, $\Gamma$ and $E_{\rm cut}$ denote
the initial spectral index and its deviation energy from a simple power-law
shape. Other parameters in relxilllp provide information about the accretion
disk: the inner radius of disk $R_{\rm in}$, ionization of the accretion disk
log($\xi$) and iron abundance of the material $A_{\rm Fe}$. However, the iron
abundance is very high and often pegs at its limit during our fitting,
probably because the reflection comes from a high-density disk, which can be
referred to Chakraborty et al. (2021) for specific studies. An example (NO-Q
in Epoch 4) of the MCMC (Markov Chain Monte Carlo) analysis for this model is
present in Figure 9.

####  3.2.1 The spectral results of B-Q and NO-Q

To study the recurrences of type-B QPOs, we compare the segment NO-Q and B-Q
energy spectra in Epochs 4 and 5 (also see Table 2). By using model 1,
tbabs$\times$(diskbb+gaussian+nthcomp+xillverCp), to fit the spectra in Epoch
4 and Epoch 5, we find that the disk temperature remains almost the same at
$kT_{\rm in}\sim$ 0.74–0.75 keV along with the power-law index at $\Gamma\sim$
2.20; the change in the normalization of diskbb is also negligible within the
error range.

However, compared to NO-Q, the thermal flux is lower and the Comptonization
flux is higher in B-Q. Especially for Epoch 5, the thermal flux is reduced by
5.3% and the Comptonization flux increases by 58.3%, which coincides with the
direct energy spectrum comparison in Figure 6. To investigate which spectral
parameter is responsible for the spectral changes, we perform a simultaneous
fit, using NO-Q and B-Q spectra following the method of Sriram et al. (2013).
First we fix the adjacent NO-Q and B-Q spectral parameters together and free
them one by one to obtain the corresponding residuals and the changes of the
parameters. For each epoch, the values of the segment B-Q spectrum are set to
the best-fit parameters of segment NO-Q spectrum and the $\chi^{2}/d.o.f$ can
be seen in the Table 4. For Epochs 4 and 5, we free the nthcomp, Gaussian, and
diskbb normalization parameter and find that the fitting are improved
significantly. Therefore, it can be assumed that some changes occurred in the
corona and disk at this time.

In the same way as in model 1, the smallest set of parameters is listed in
Table 5 for Epoch 4 and Epoch 5. A relatively small variation in $N_{\rm
diskbb}$ is observed in Epoch 4, whereas in Epoch 5 both $N_{\rm diskbb}$ and
$kT_{\rm in}$ are found to be variable. Compared to the spectral results using
the simple model, little change in photon index $\Gamma$ are observed for
NO-Q/B-Q during this fitting. During the fitting of the four spectra, the
corona height $h$ seems to be larger, while the change in $R_{\rm in}$ is
insignificant $\sim 1R_{\rm ISCO}$ (Radius of the innermost stable circular
orbit). The inner disk radius can also be calculated from disk normalization
parameter as outlined by Mitsuda et al. (1984), whereby $R_{\rm
in}^{2}=f^{4}D_{10}^{2}(N_{\rm diskbb}/{\rm cos}\theta)$, where $f$ is the
color correction factor (Kubota et al., 1998), $D_{10}$ is the distance to the
source in units of 10 kpc, and $\theta$ is the disk inclination. We adopt the
best-fit $N_{\rm diskbb}$ values with their uncertainties from Table 5.
Assuming a canonical value for color correction of $f=1.5$, a fixed disk
inclination of $36.5^{\circ}$ and a fixed distance of 2.2 kpc, $R_{\rm in}$ is
found to be $87.4\pm 0.3$ km, $85.1^{+0.4}_{-0.8}$ km, for NO-Q and B-Q,
respectively, in Epoch 4, and $91.3\pm 0.1$ km, $81.5\pm 0.3$ km in Epoch 5.
The inner disk radius increases slightly in NO-Q if the assumption of $R_{\rm
in}^{2}\propto N_{\rm diskbb}$ is considered.

####  3.2.2 The spectral results of B-Q and C-Q

Intuitively, it can be seen from the bottom panel of Figure 6 that the disk
component of B-Q is remarkably stronger compared to that of C-Q. In order to
understand the change of accretion disk configurations in SIMS (B-Q) and HIMS
(C-Q), we fit the energy spectra of Epoch 6 and Epoch 7 with models 1 and 2,
respectively. From the best fitting results of the two models (see Table 3 and
Table 6), it can be inferred that for both B-Q and C-Q epochs, the parameters
of the disk have changed significantly.

For both model 1 and model 2, the C-Q spectra had a relatively lower disk
temperature $kT_{\rm in}$ and a larger inner disk radius ($N_{\rm diskbb}$)
compared to the B-Q spectral state, meanwhile $\Gamma$ is slightly smaller in
C-Q, suggesting a harder spectra. Correspondingly, the thermal component flux
is weaker and the Comptonized component is stronger in C-Q.

For Epochs 6 and 7, after freeing $kT_{\rm in}$, $\Gamma$ and $N_{\rm
diskbb}$, the residuals are improved significantly (4). These results suggest
that the accretion disk moved inward when the source entered the SIMS from the
HIMS, i.e, B-Q has a smaller inner radius than C-Q. This is consistent with
the standard accretion disk model (Esin et al., 1997).

Using model 2 (see Table 6), it is also suggested that the normalization of
the diskbb is larger at C-Q. Using the parameters in Table 6, $R_{\rm in}$ is
found to be $77.1\pm 0.7$ km, $83.7\pm 0.9$ km, $82.9\pm 0.6$ km, for B-Q,
C-Q, and B-Q, respectively, in the SIMS I. After 12 days in the SIMS II,
$R_{\rm in}$ is found to be $82.9\pm 0.3$ km, $87.5\pm 0.2$ km, $85.3\pm 0.3$
km for B-Q, C-Q, and B-Q. However, $R_{\rm in}$ in relxilllp of C-Q is found
to be the same as that of B-Q: $\sim 1R_{\rm ISCO}$ for Epochs 6 and 7. We
also find that the height of the corona $h$ is slightly larger in B-Q. For
both epochs (see Table 7), after freeing the parameters $kT_{\rm in}$, the
chi-squared value are improved significantly. However, for Epoch 7, all the
parameters need to be free except for log($\xi$). Furthermore, an improvement
of fitting for Epoch 6 is also present after freeing $h$, which indicates that
the height of the corona indeed changed.

From the above results, we conclude that after the source MAXI J1348–630
entered the SIMS (B-Q), it may have returned to the HIMS (C-Q) again, or
returned to the SIMS (SIMS II) after HSS, suggested by changes in PDS and
energy spectrum.

##  4 Summary and Discussions

In this paper, we focus on studying the timing and spectra properties of the
QPO transitions observed in MAXI J1348–630 using data from _Insight_ -HXMT
during its 2019 outburst. The results can be summarized as follows:

  * •

The type-B QPOs ($\sim$ 4.2 – 4.7 Hz) in this source are recurrent, on
timescales from seconds to hours;

  * •

The variation amplitude (rms) of QPOs has a same relation with energy, i.e.,
rms increases with energy below 10 keV and remains constant above 10 keV to
100 keV.

  * •

When type-B QPOs disappear

    * –

the PDS show a weak power-law noise;

    * –

the flux of the Comptonization component decreases, while the spectral index
$\Gamma$ remains unchanged;

    * –

the inner disk radius increases slightly when inferred from disk component
($N_{\rm diskbb}$);

    * –

the corona height of type-B QPOs observation is larger than that of NO-Q when
including an additional reflection model xillver by need for the continuum
fitting.

  * •

Three transitions are found between the type-C and type-B QPOs with the
following results:

    * –

a transient timescale as short as $\sim$ 10 seconds;

    * –

the Comptonization flux is higher and the spectral index is smaller in C-Q;

    * –

the inner radius of the accretion disk is moderately larger for C-Q as
inferred from the disk component, while it remains constant $\sim 1R_{\rm
ISCO}$ using reflection model;

    * –

the corona height is larger in B-Q using the reflection model.

The above results suggest that the type-B and C QPOs are associated with
different physical mechanisms within the inner region of the accretion disk.
In the next sub-sections, we will discuss those results and possible physical
mechanisms of the QPOs.

###  4.1 LFQPOs and Models

When the last type-C QPO at $\sim 7.35$ Hz in the HIMS disappeared, a
subsequent type-B QPO detection means that MAXI J1348–630 entered SIMS. The
spectral fitting results show that throughout the SIMS, the inner radius of
the disc was very close to the ISCO, which is consistent with the results of
Zhang et al. (2022). The same results have been found in several other BHTs,
such as H1743-322 (Sriram et al., 2021), XTE J1859+226 (Sriram et al., 2013),
etc.

The model proposed for type-B QPOs is not as comprehensive as for type-C, but
there is much evidence that they may have originated from a jet-like
structure. The most convincing evidence is that type-B QPOs and jet ejections
(or radio flares) are observed to occur close in time (Fender et al., 2009;
Russell et al., 2019, 2020; Homan et al., 2020). Recently, observations on
MAXI J1820+070 (Homan et al., 2020) have given strong evidence that there is a
connection between the appearance of type-B QPOs and the launch of discrete
jet ejections because the short time delay ($\sim$ 2-2.5 hr) between the
transition and a strong radio flare. During the current outburst of MAXI
J1348–630, two radio flares, considered to be associated with the discrete
ejection of the same radio knot (Carotenuto et al., 2021), were detected in
MJD 58523.2 and MJD 58527.7, which is reported by Carotenuto et al. (2019) and
Chauhan et al. (2020) respectively. The first flare was about 0.6$\sim$0.8 day
from the start of the SIMS. About $\sim 0.1$ day before the start of the
second one, we observe a sharp drop in the count rate of LE and a slight rise
in the count rate of ME/HE, while the averaged-PDS shows type-C QPOs. A type-B
QPO with frequency $\sim 4.5$ Hz appeared almost simultaneously with the
second radio flare, which started at MJD 58527.5 and peaked with flux $252\pm
13$ mJy at MJD 58527.66, suggesting a strong connection between the type-B
QPOs and the ejection.

For the type-B QPOs observed in this source, using the observations obtained
with the _NICER_ observatory, Belloni et al. (2020) computed the energy
dependence of the rms and the phase lags at the QPO frequency, sampling for
the first time at energies below 2 keV. Concentrating on the phase lags,
García et al. (2021) successfully used a two-component Comptonization model to
fit them and explained the radiative properties of the type-B QPOs in 0.8–10
keV energy range by two physically connected Comptonization regions.

Our result shows that the fractional rms of type-B QPOs increase with energy
up to 10 keV and stay more or less constant above 10 keV in all observations,
which implies a Comptonization origin of the type-B QPO. In the jet precession
model, the jet velocity can be measured by the QPO amplitude (Ma et al.,
2021). Assuming the QPOs rms of $\sim 15\%$ (see Figure 3; B-QPO rms), an
observed inclination angle of $\sim 30^{\circ}$, and the jet half-opening
angle of $\sim 3^{\circ}$, the jet velocity can be determined as $0.55-0.9c$.
Assuming $v=\beta\times c$ to be the escape velocity of the black hole, the
height of the ejection knot can be calculated as $\sim 6.6-2.5r_{\rm g}$
($\beta=0.55-0.9c$) , which is consistent with the emitting scale height of
the hard component (Table 5). Recently Marcel et al. (2020) also have found
that type-B QPOs require a small transition radius ($r_{J}$, truncation radius
due to a jet in the inner region) around 2.5 $r_{\rm g}$. These results
indicate that type-B QPOs are produced very close to the BH.

Furthermore, the similar rms–energy correlations for different LFQPOs in the
2-30 keV range are found with _RXTE_ in XTE J1859+226 (Casella et al., 2004),
GRS 1915+015 (Rodriguez et al., 2004; Yan et al., 2012, 2013; Yadav et al.,
2016), H1743–322 (Li et al., 2013b), and XTE J1550–564 (Li et al., 2013a), ),
in which a corona origin of type-C QPOs is considered. Thanks to the large
effective area of _Insight_ -HXMT at high energies, the similar rms–energy
correlations above 30 keV have been found in MAXI J1535-571 (Huang et al.,
2018), MAXI J1820+070 (Ma et al., 2021) and MAXI J1631-479 (Bu et al., 2021).
Their results all suggest a geometric origin of the type-C QPOs, while Ma et
al. (2021) proposed that the type-C QPOs originate from jet rather than
corona.

Therefore, whether the origin of type-C QPOs lies in the corona or the jet is
still an open issue. A recent study in GRS 1915+105 (Méndez et al., 2022)
proved that the X-ray corona can morph into a jet. They found that the corona
is hot and extended, and covers the inner parts of the disk when the type-C
QPO frequency is in the 2–6 Hz range. Then the corona will become a jet as the
type-C QPO frequency decreases below $\sim 2$ Hz. A similar conclusion was
also proposed by Alabarta et al. (2022) for MAXI J1348–630, who suggested that
there are differences in the geometry of the system at the different phases of
the outburst according to the relationship between QPOs frequency and their
phase lags.

During the the SIMS in MAXI J1348–630, three transitions from type-B QPO to
type-C and then to type-B are observed by _Insight_ -HXMT. One of them is only
detected by ME and HE, but it is a continuous transition from a type-C QPO at
$\sim$ 9.2 Hz to a type-B QPO at $\sim$ 4.8 Hz in a short period of $\sim 10$
s (see the top panel of Figure 5), which also occurred in MAXI J1820+070
(Homan et al., 2020). However, the flux at the high energy band changed very
slightly in our observation. This may indicate that both the type-C and B QPOs
are either generated in different regions located at different radii or in
same region with different modulations.

For the other two occurrences of type-C QPOs between type-B QPOs, we can
present not only the differences in the power spectra but also the differences
in the energy spectra. The bottom panel of Figure 6 clearly shows that the
type-C QPOs have harder spectra than type-B in energy above 10 keV, and less
flux at low energies. Furthermore, it can be inferred from Tables 3 and 6 that
the energy spectra of C-Q have less disc contribution and low disk temperature
($kT_{\rm in}$). The non-relativistic model seems to be less significant at
C-Q in the fit of model 1, probably because of the contraction of the jet
structure. This hypothesis is consistent with the $h$ parameter change in
model 2. The inner disk radius of C-Q is moderately larger as inferred from
the disk normalization parameter: $\sim 1.71R_{\rm ISCO}$, $\sim 1.86R_{\rm
ISCO}$, $\sim 1.84R_{\rm ISCO}$ for B-Q, C-Q, and B-Q, respectively, in the
SIMS I. However, $R_{\rm in}$ given by the reflection model remains at $R_{\rm
ISCO}$. One possible reason for this is that the broad iron line leads to a
small radius when applying the reflection model, even in the hard state (Reis
et al., 2010; Ren et al., 2022). A recent simulation study reported by Liska
et al. (2022), assuming cold, optically thick, clumps of gas falling into the
black hole, also suggested that a broader iron line usually appears in the
harder spectral states. Another reason could be that the inner radius varied
so little during the transitions that the reflection model is insensitive to
it. We test this by fixing $R_{\rm in}$ to the radius value derived from
$N_{\rm diskbb}$ and find that the effect on the other parameters is
insignificant.

We consider the L-T precession under the truncated disc/corona (hot inner
flow) geometry (Ingram et al., 2009), assuming that both QPOs $\sim$ 7–9 Hz
and $\sim$ 4–5 Hz originate from the precession of an inner flow, a $\sim$ 7–9
Hz QPOs spectrum should have a smaller inner radius than the latter. The
observations reveal the difference of quality factor ($Q$), suggesting that
the precessions of different morphological structures leads to different $Q$.
The type-B QPOs appear when the disk is close to the ISCO, which may indicate
that the motion of the disk caused a deformation of the Comptonization region,
and thus the flux modulation of different properties is observed in MAXI
J1348–630. Kylafis et al. (2020) quantitatively explained that the type-B QPOs
in GX 339–4 come from the precession of non-solid structures, while type-C
QPOs originate from the precession of solid inner flow. In the simulation
results of Liska et al. (2018), a solid-body-like precession of the tilted
disk-jet system can explain type-C QPOs. Nevertheless, it is also difficult to
explain the difference between type-C and B QPOs using solid/non-solid body
behavior, which requires better simulations and higher quality observations.

Based on the above, we find that both type-B and C QPOs may be related to the
so-called jet. Nevertheless, it is clear that types C and B QPOs have
significantly different timing and spectral features as summarized in GX 339–4
by Motta et al. (2011) as well as in MAXI J1348–630. Their common
Comptonization origin properties and the short transition time scale suggest
that a rapid change in physical properties or morphology of the Comptonization
results in their differences.

The jet/corona in low-luminosity states (hard states) is suggested to be
formed in the BP mechanism (Blandford & Payne 1982. see also e.g. Blandford &
Begelman 1999; Meier 2001). Meier (2001) further suggested that during very
high accretion states, the more relativistic jet rather than the ‘BP’ jet may
be associated with the BZ mechanism (Blandford & Znajek, 1977). This jet has a
higher Lorentz factor, causing the propagation of an internal shock through
the slower-moving outflow in front of it, which may lead the observation of
discrete ejection Fender et al. (2004). Therefore, we argue that the compact
and steady ‘BP’ jet in low accretion phases is associated with type-C QPOs,
while the fast ‘BZ’ jet in SIMS is associated with type-B QPOs. As the
accretion rate increases, the truncation radius moves inward, resulting in an
increase in the frequency of type-C QPOs (Ferreira et al., 2006; Liska et al.,
2022). Broadband noise in PDS during hard states are assumed to arise from the
propagation of magneto-rotational instability (MRI; Balbus & Hawley 1991)
fluctuations of the inner hot flow (Ingram et al., 2009; Ingram & Done, 2011;
Yang et al., 2022). During the SIMS phase, the frequency range of type-B QPOs
varies narrowly, which may be related to a particular radius and a detailed
discussion is given in sub-section 4.2. The noise weakness during SIMS may be
due to the magnetic field of ‘BZ’ jet emanating from the black hole, meanwhile
the MRI originating with the disk is suppressed.

###  4.2 The disappearances of Type-B QPOs

The disappearance of type-B QPOs (NO-Q/B-Q) has been studied using archival
data from the _RXTE_ , for example, on XTE J1817–330, XTE J1859+226, and
H1743–322 (Sriram et al., 2012, 2013, 2021). From the energy spectra
comparisons (Figure 6), it can be seen that the difference is very small at
energies below 2 keV where the emission is dominated by the thermal component.
The most noticeable difference is in the energies above 2 keV, suggesting that
the disappearance of type-B QPOs may be related to changes in the Comptonized
component. The same result has been found in this source on the results of
Zhang et al. (2021) and several of the above sources. The observed transient
properties of type-B QPOs can occur on timescales of seconds to hours, which
implies that the Comptonization radiation region is unstable. When type-B QPOs
appeared, the increase in the high-energy flux indicates that there is either
an extra Comptonized region contributing to the energy spectra, or the flux in
the same region increases for some reasons. Our results give that the height
of the corona is greater at B-Q, although the difference in the spectral shape
is insignificant (small change in $\Gamma$). For the type-B QPOs observed in
this source, using the observations obtained with the _NICER_ observatory,
Zhang et al. (2021) gave a hint that an additional component involving the
transitions of type-B QPOs may be related to the base of jet.

In section 4.1, we discussed that the type-B QPOs originating from the jet
near the BH and the disk is also very close to the ISCO at this time.
Therefore, we suggest that a coupled inner disk-jet region is responsible for
the observed type-B QPOs transitions.

Although the jets powered by BZ and BP effect are continuous and steady, the
magnetic field lines close to the BH can be complicated by the strong gravity.
However, the simulation results of different ways of Yuan et al. (2019a, b)
and Liska et al. (2021) allow us to understand the precessing jet near the BH
and its instability from two perspectives.

Theoretical studies show that the jet with transient properties can only exist
when the accretion disk is very close to the BH and the magnetic fields on the
accretion disk are quite in-homogeneous (Yuan et al., 2022; Lin & Ye, 2021;
Wu, 2009; Yuan et al., 2019a, b, 2009). The small-scale magnetic flux tube
model proposed by Yuan et al. (2019a, b) argue that a closed zone with a size
of a few gravitational radii is formed by the magnetic flux tubes, which may
arise due to magnetorotational instability or magnetic buoyancy. This zone
connecting the central compact object and the accretion disc may be able to
produce strong X-ray emission and can be seen as the small-scale jet, which
precesses and modulates X-ray emission (LFQPOs) as the BH rotates. Considering
that the type-B QPOs arise from the precession of small-scale jets that are
produced only when the disk is close to the BH, it is natural that the
frequency of the type-B QPOs varies within a narrow range. Obviously, the
field lines in and around this closed structure are actually continuously
reconnecting i.e. the field lines connecting a point of the BH to a point on
the disk only maintain the connectivity for a short time, and the rotation of
the BH increases the toroidal twist of this field line, which eventually
breaks. After that, open field lines are formed on the disk. As a result, the
field lines on the accretion disk around the closed region alternate between
closed and open configurations, leading to the sporadic type-B QPOs observed
as well. The Comptonization emission still observed in NO-Q may be due to the
remaining symmetric corona or a collimated smaller-scale jet (smaller height
in NO-Q).

In addition to the small-scale magnetic tube model, another mechanism
involving titled disks can explain the rapid transitions of type-B QPOs.
Because the accreted material is most likely independent of the BH spin, its
angular momentum is expected to be misaligned with respect to the BH spin,
resulting in a titled accretion disc. Liska et al. (2019) performed 3D general
relativistic magnetohydrodynamics (GRMHD) simulations of tilted discs around
rapidly spinning BHs. They suggested that such disk undergo L-T precession and
can launch relativistic jets that propagate along the disc rotation axis. As
we discussed above, the flux modulation produced by such jets that precess
with discs allows us to observe type-B QPOs. Bardeen & Petterson (1975)
predicted that in the presence of realistic magnetized turbulence, the inner
part of the disk ($<r_{\rm BP}$, Bardeen-Petterson radius) can align with the
BH spin axis, while the outer disc is titled. Recently, Liska et al. (2021)
found a smaller ($\lesssim 5-10r_{\rm g}$ ) alignment radius than predicted by
analytic models through GRMHD simulations, which is consistent with our energy
spectral fitting results.

When the disk reaches the Bardeen-Petterson transition radius, the jet is
parallel to the spin axis of the BH due to the dragging effect, and type-B
QPOs generated by the jet precession will not appear. The observed PDS noise
at this time is very small, probably due to the collimation of the jet.
However, the Comptonization component is observed at this time, indicating
that it is different from the HSS. Therefore, it is highly likely that there
is a parallel jet generating Comptonization radiation, but without obvious
modulations in its flux. The results show that the Comptonization flux
decreases when the disk tears, probably because the outer disc cannot maintain
a sufficient gas supply (Liska et al., 2021). Conversely, disk flux less than
2 keV increases slightly, which is also seen in recent simulations of Musoke
et al. (2022), although their main research is not type-B QPOs. They suggested
that the absence of a warp in the aligned portion of the disk reduces the
inflow speed of the gas, which increases the density. Furthermore, the
obtained rms-spectra are more or less the same regardless of how much the flux
of the hard component increases when type-B QPOs are present, suggesting that
type-B QPOs are more likely to arise from the overall behavior of one
component.

It is accepted that the transient jets (discrete ejection) on large-scales
could be the result of the ejection of the corona at state transitions
(Rodriguez et al., 2003; Vadawale et al., 2003) and are associated with
presence of type-B QPOs. In addition, the radio flares in XRBs are proposed to
be produced by the adiabatic expansion of ejected plasma blobs (Fender et al.,
2004; Miller-Jones et al., 2012); hence the ejection components should be
launched before strong radio flares are observed. If the ejections of the
corona (Comptonization part) are associated with the absence of type-B QPOs,
although type-B QPOs occasionally disappear before or after ejections, it is
possible that the opened magnetic field lines (parallel to the BH axis) can
accelerate the plasma to a very large distance, leading to the in radio band
discrete ejections.

###  4.3 Unified model for type-C and type-B QPOs

More and more observational results in the BHT family indicate that LFQPOs may
be a geometrical effect, which is also supported by our findings in MAXI
J1348–630. However, in the geometrical effect models, explaining the
transition between different type QPOs, as well as the transient properties of
type-B QPOs remain open issues.

Based on the above results in BHT MAXI J1348–630, we propose a scenario
illustrated in Figure 8 to explain the timing and spectral evolution as
observed in the BHTs. In the LHS and HIMS (panel (a) of Figure 8), the L-T
precession of the corona/jet in the inner regions of the disk (or titled disk)
produces type-C QPOs due to the misalignment with BH spin axis. With the
increase of accretion rate, the inner edge of the accretion disk gradually
approaches the BH, while the corona/jet becomes smaller and its precession
frequency increases. Although the jet-structure shown in top panel of Figure
8, considering frequency ($\sim 7-10$) Hz and the variation in spectra of
type-C QPO, we argue that it may be possible that the vertical-jet becomes a
corona structure during the QPO transitions, or vice versa (B-C-B), as
suggested in GRS 1915+105 (Méndez et al., 2022).

In the SIMS, the inner radius of the accretion disk approaches its ISCO (panel
(b) of Figure 8) and the precessing jets parallel to the titled disc produce
type-B QPOs. The innermost parts of the accretion disk align with the BH
equator due to the Bardeen-Petterson effect, while the outer parts remain
tilted and the disc forms a smooth warp in between (panel (c) of Figure 8).
Since the jets are launched along the direction of the BH spin axis, type-B
QPOs disappear due to the absence of precession effect on the modulation of
the flux. Alternatively, we can also explain the absence of type-B QPOs by the
disappearance of small-scale jets bound by the magnetic flux tubes near the
BH. In SIMS, possibly for some reason, inner disc may subsequently recede,
when the larger scale Comptonisation component (corona/strong-jet) dominates
the radiation and therefore the appearance of type-C QPOs may be observed. But
what causes the outward movement of the disk is not yet precisely conclusive.

##  5 Conclusions

In this work, we investigate the spectral and timing properties of the type-B
QPOs transitions found in the BHT source MAXI J1348–630. An additional xillver
component is required in the modelling of the continuum of type-B QPO, while
the reflection modelling also suggests a larger height of the corona. Combined
these with other results, we suggest that type-B QPOs probably originate from
the precession of the weak-jet in a titled disk-jet structure located
relatively close to the BH. However, due to the Bardeen-Petterson effect, the
misaligned inner-disk in the high spin BH system can tend to be parallel to
the direction of the BH spin axis, which can explain the disappearance of
type-B QPOs in the BHXBs. We can also explain the absence of type-B QPOs by
the disappearance of small-scale jets bound by the magnetic flux tubes. In
this source, _Insight_ –HMXT observed a type-C/B transition that occurs within
a very short time scale. It is still unclear whether type-C QPOs originate
from the jet or the corona precession. Based on our results, there is only a
slight increase in the inner disk radius when type-C QPO appears. However, due
to the limitation of the observation time, it is not clear whether the disc is
moving outward or the reasons for the type-C/B QPO transitions in SIMS.

This work made use of the data from the mission,a project funded by China
National Space Administration (CNSA) and the Chinese Academy of Sciences
(CAS).This work is supported by the National Key R&D Program of China
(2021YFA0718500). This work is supported by the National Natural Science
Foundation of China (Grant No. 11733009, 11673023, U1838202, U1838201,
U1938102, U2038104 and U2031205.), the CAS Pioneer Hundred Talent Program
(grant No. Y8291130K2) and the Scientific and technological innovation project
of IHEP (grant No. Y7515570U1).

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Figure 1: _Insight_ -HXMT/LE (1–10 keV) light curve (top panel) and the
hardness (bottom panel) for MAXI J1348–630 during its 2019 outburst. Each
point corresponds to one exposure. Hardness is defined as the ratio of LE
count rate in 4–10 keV and 1–4 keV. Green points correspond to observations
with a type-C QPO in the PDS, red points correspond the observations with a
type-B QPO and black points mark all the other observations that do not show
low-frequency QPOs. Figure 2: The detailed light curve and hardness (16 s bin)
of the parts of SIMS I and SIMS II for this outburst. _Panel (a), (b) and (c)_
: light curves in three energy bands respectively: 1–10 keV (LE), 10–35 keV
(ME) and 35–100 keV (HE). _Panel (d)_ : hardness between 4–10 keV (LE) and 1–4
keV (LE) count rate. _Panel (e)_ : dynamical power spectra (DPS) in the energy
band 35–100 keV (HE) with a time resolution of 16 s. We separate the all SIMS
into thirteen epochs. The label ‘C-Q’ means type-C QPO are detected.
Similarly, ‘B-Q’ corresponds to type-B QPO, ‘NO-Q’ corresponds to NO-QPO ,
‘TR-B’ corresponds to the time interval when the transitions of type-B QPO are
detected. Figure 3: The relationship between type-B QPOs frequency/fractional
rms and energy. Figure 4: The detailed light curves (16 s bin), dynamical
power spectra (DPS) of transition between NO-QPO and type-B QPOs and the
corresponding average PDSs are shown on the right. The black and red lines
represents the light curve of two energy bands: 1–10 keV (ME), 35–100 keV
(HE). _Top panel_ : Fast transitions in Epoch 3 and the start time is MJD
58524.779. _Bottom panel_ : An example of long-time scale transitions
involving B-Q and NO-Q. The start time is MJD 58526.763 (Epoch 5).  Figure 5:
The detailed light curves and dynamical power spectra (DPS) (16 s bin) of the
transitions between type-B and type-C QPOs are shown on the left. The black
and red lines represents the light curve of two energy bands: 1–10 keV (ME),
35–100 keV (HE). The corresponding average PDSs are shown on the right. _Top
panel_ : The transition between a type-B QPO and a type-C QPO in Epoch 2. The
start time is MJD 58524.372. _Middle panel_ : Epoch 6 and the start time is
MJD 58527.44. _Bottom panel_ : Epoch 7 and the start time is MJD 58539.75
Figure 6: _Top panel:_ The spectral ratio defined as the ratio between the
merged spectrum with the type-B QPO and that without the QPO (B/NO-Q), plotted
in light-blue for Epoch 4 and dark-blue for Epoch 5. _Bottom panel:_ The
spectral ratio defined as the ratio between the merged spectrum with the
type-B QPO and type-C (C/B), plotted in green for Epoch 6 and light-green for
the Epoch 7. Figure 7: An example (The NO-Q and B-Q in Epoch 5) of fitting
energy spectrum with four models. _Top panel:_ The total model (solid lines)
is plotted together with contributions from the thermal disk (dotted lines)
and the reflection component (dash-dot lines). _The rest panels:_ Spectral
residuals from tbabs$\times$(diskbb+nthcomp),
tbabs$\times$(diskbb+gaussian+nthcomp),
tbabs$\times$(diskbb+gaussian+nthcomp+xillverCp) as Model 1, and Model 2,
tbabs$\times$(diskbb+relxilllp). The spectra are plotted in dark-orange and
dark-cyan for the B-Q and NO-Q section, respectively. Black, red, and green
represent the spectra of the three detectors LE, ME, and HE, respectively
Figure 8: A sketch of the different states during an outburst. _Panel (a)_
illustrates the Comptonization component dominated states: LHS and HIMS, where
type-C QPOs originate from the L-T precessing of the corona or jet. However,
it cannot be determined if the disk is truncated. _Panel (b) and (c)_ show
SIMS when type-B QPOs are present or absent and the radius of the disk is
close to $R_{\rm ISCO}$. _Panel (b)_ depicts a jet in the same direction as
the titled disc. Due to the flux modulation caused by the precession effect,
we observe type-B QPOs. When the jet is parallel due to Bardeen-Petterson
effect to the BH spin axis, the modulation effect on the flux disappears, as
shown in _panel (c)_ , where the type-B QPO disappears. Figure 9: An
illustration of one and two dimensional projections of the posterior
probability distributions derived from the MCMC analysis for the parameters in
model 2, tbabs$\times$(diskbb+relxilllp). This illustration corresponds to the
spectral fitting of NO-Q in Epoch 4. Table 1: QPO types classification and
variability parameters.

ObsID | Start-Time | End-Time | QPO Typea | Frequencyb | ${{\rm FWHM}_{\rm QPO}}^{c}$ | ${{\rm rms}_{\rm QPO}}^{d}$ | Epoche
---|---|---|---|---|---|---|---
| MJD | MJD |  | (Hz) | (Hz) | (%) |
P021400201101 | 58522.607 | 58522.756 | B | $4.66\pm 0.02$ | $0.54\pm 0.05$ | $13.9\pm 0.1$ |
P021400201102 | 58522.808 | 58522.889 | B | $4.49\pm 0.02$ | $0.41\pm 0.05$ | $14.0\pm 0.1$ |
P021400201103 | 58522.943 | 58522.955 | B | $4.46\pm 0.04$ | $0.38\pm 0.07$ | $14.6\pm 0.2$ |
P021400201201 | 58523.314 | 58523.449 | B | $4.61\pm 0.09$ | $0.60\pm 0.14$ | $13.4\pm 0.2$ | EP 1
P021400201501 | 58523.801 | 58523.948 | B | $4.54\pm 0.02$ | $0.41\pm 0.05$ | $14.3\pm 0.1$ |
P021400201502 | 58524.072 | 58524.114 | B | $4.69\pm 0.06$ | $0.43\pm 0.09$ | $13.0\pm 0.2$ |
P021400201503 | 58524.136 | 58524.246 | B | $4.57\pm 0.07$ | $0.36\pm 0.17$ | $9.7\pm 0.6$ |
P021400201504 | 58524.275 | 58524.345 | B | $4.55\pm 0.04$ | $0.45\pm 0.13$ | $13.2\pm 0.3$ |
P021400201504 | 58524.372 | 58524.393 | C | $9.23\pm 0.32$ | $7.21\pm 0.93$ | $15.9\pm 2.1$ | EP 2
P021400201504 | 58524.393 | 58524.396 | B | $4.81\pm 0.15$ | $1.24\pm 0.32$ | $12.3\pm 3.1$ |
P021400201505 | 58524.407 | 58524.743 | B | $4.56\pm 0.02$ | $0.59\pm 0.05$ | $13.5\pm 0.1$ |
P021400201506 | 58524.779 | 58524.799 | NO-Q |  $\cdots$ |  $\cdots$ |  $\cdots$ |
P021400201506 | 58524.799 | 58524.805 | B | $4.47\pm 0.13$ | $0.79\pm 0.32$ | $9.5\pm 2.3$ |
P021400201506 | 58524.805 | 58524.808 | NO-Q |  $\cdots$ |  $\cdots$ |  $\cdots$ |
P021400201506 | 58524.848 | 58524.856 | B | $4.33\pm 0.07$ | $0.43\pm 0.12$ | $9.1\pm 1.1$ |
P021400201506 | 58524.856 | 58524.861 | NO-Q |  $\cdots$ |  $\cdots$ |  $\cdots$ |
P021400201506 | 58524.861 | 58524.865 | B | $4.46\pm 0.05$ | $0.43\pm 0.08$ | $13.1\pm 1.2$ | EP 3
P021400201506 | 58524.865 | 58524.875 | NO-Q |  $\cdots$ |  $\cdots$ |  $\cdots$ |
P021400201507 | 58524.917 | 58524.922 | NO-Q |  $\cdots$ |  $\cdots$ |  $\cdots$ |
P021400201507 | 58524.922 | 58524.931 | B | $4.35\pm 0.04$ | $0.35\pm 0.11$ | $10.3\pm 0.4$ |
P021400201507 | 58524.931 | 58524.933 | NO-Q |  $\cdots$ |  $\cdots$ |  $\cdots$ |
P021400201507 | 58524.933 | 58524.941 | B | $4.45\pm 0.05$ | $0.44\pm 0.09$ | $13.5\pm 0.7$ |
P021400201508 | 58525.064 | 58525.176 | NO-Q |  $\cdots$ |  $\cdots$ |  $\cdots$ |
P021400201509 | 58525.198 | 58525.239 | NO-Q |  $\cdots$ |  $\cdots$ |  $\cdots$ |
P021400201510 | 58525.386 | 58525.468 | NO-Q |  $\cdots$ |  $\cdots$ |  $\cdots$ |
P021400201511 | 58525.500 | 58525.601 | NO-Q |  $\cdots$ |  $\cdots$ |  $\cdots$ | EP 4
P021400201512 | 58525.632 | 58525.737 | B | $4.35\pm 0.04$ | $0.57\pm 0.09$ | $13.0\pm 0.1$ |
P021400201513 | 58525.787 | 58525.869 | B | $4.33\pm 0.03$ | $0.49\pm 0.07$ | $13.3\pm 0.1$ |
P021400201601 | 58526.195 | 58526.232 | NO-Q |  $\cdots$ |  $\cdots$ |  $\cdots$ |
P021400201602 | 58526.379 | 58526.455 | NO-Q |  $\cdots$ |  $\cdots$ |  $\cdots$ |
P021400201603 | 58526.495 | 58526.595 | NO-Q |  $\cdots$ |  $\cdots$ |  $\cdots$ |
P021400201604 | 58526.625 | 58526.730 | NO-Q |  $\cdots$ |  $\cdots$ |  $\cdots$ |
P021400201605 | 58526.781 | 58526.815 | NO-Q |  $\cdots$ |  $\cdots$ |  $\cdots$ | EP 5
P021400201605 | 58526.815 | 58526.863 | B | $4.45\pm 0.06$ | $0.44\pm 0.07$ | $13.7\pm 0.2$ |
P021400201606 | 58526.913 | 58526.995 | B | $4.57\pm 0.04$ | $0.69\pm 0.09$ | $14.6\pm 0.1$ |
P021400201607 | 58527.022 | 58527.096 | B | $4.49\pm 0.03$ | $0.47\pm 0.08$ | $13.6\pm 0.1$ |
P021400201701 | 58527.372 | 58527.448 | B | $4.56\pm 0.04$ | $0.51\pm 0.08$ | $13.2\pm 0.1$ |
P021400201702 | 58527.487 | 58527.525 | C | $7.42\pm 0.07$ | $4.13\pm 0.32$ | $18.6\pm 3.1$ |
P021400201702 | 58527.551 | 58527.588 | C | $10.21\pm 0.16$ | $6.23\pm 0.51$ | $19.2\pm 3.4$ | EP 6
P021400201703 | 58527.618 | 58527.723 | B | $4.44\pm 0.02$ | $0.41\pm 0.03$ | $14.1\pm 0.2$ |
P021400201704 | 58527.774 | 58527.856 | B | $4.34\pm 0.03$ | $0.52\pm 0.07$ | $14.3\pm 0.1$ |
P021400202501 | 58539.134 | 58539.161 | B | $3.98\pm 0.08$ | $0.45\pm 0.15$ | $11.9\pm 0.2$ |
P021400202502 | 58539.171 | 58539.534 | B | $4.16\pm 0.02$ | $0.47\pm 0.04$ | $12.6\pm 0.1$ |
P021400202503 | 58539.559 | 58539.663 | B | $4.15\pm 0.04$ | $0.55\pm 0.08$ | $13.1\pm 0.1$ |
P021400202504 | 58539.741 | 58539.795 | B | $4.33\pm 0.31$ | $0.71\pm 0.86$ | $11.2\pm 0.3$ |
P021400202504 | 58539.795 | 58539.804 | C | $7.78\pm 0.40$ | $9.34\pm 1.03$ | $20.1\pm 6.8$ | EP 7
P021400202505 | 58539.828 | 58539.955 | C | $7.43\pm 0.36$ | $11.77\pm 0.88$ | $22.1\pm 6.3$ |
P021400202505 | 58539.955 | 58539.940 | B | $4.08\pm 0.02$ | $0.52\pm 0.05$ | $12.7\pm 0.4$ |
P021400202506 | 58539.993 | 58540.004 | B | $4.13\pm 0.08$ | $0.39\pm 0.18$ | $10.4\pm 0.2$ |
P021400202507 | 58540.125 | 58540.463 | B | $3.96\pm 0.03$ | $0.56\pm 0.09$ | $11.3\pm 0.1$ |

Note. — a The label ‘C’ means type-C QPO are detected. Similarly, ‘B’
corresponds to type-B QPO, ‘NO-Q’ corresponds to NO-QPO.

b Centroid frequency of the Lorentzian component.

c Width of the Lorentzian component.

d Fractional rms of the LFQPO.

e The divided epochs.

Table 2: Best-fit spectral parameters of epochs with B-QPO and NO-QPO using
model 1 tbabs$\times$(diskbb+gaussian+nthcomp+xillverCp)

Component | Parametes | EP 4 | EP 5
---|---|---|---
|  | NO-Q | B-Q | NO-Q | B-Q
TBabs |  $N_{\rm H}(\times 10^{22}\rm cm^{-2}$) | $0.913\pm 0.009$ | $0.901\pm 0.003$ | $0.908\pm 0.006$ | $0.893_{-0.007}^{+0.009}$
Diskbb | $kT_{\rm in}({\rm keV})$ | $0.758\pm 0.003$ | $0.752_{-0.005}^{+0.004}$ | $0.743\pm 0.003$ | $0.734_{-0.007}^{+0.006}$
| norm | $27555_{-571}^{+621}$ | $27987_{-672}^{+421}$ | $30067_{-525}^{+582}$ | $28496_{-1007}^{+1203}$
Gaussian | $E_{\rm line}({\rm keV})$ | $5.0_{-0.3}^{+0.2}$ | $4.3_{-0.4}^{+0.3}$ | $4.8_{-0.3}^{+0.2}$ | $3.7_{-0.6}^{+0.4}$
| $\sigma({\rm keV})$ | $1.47_{-0.17}^{+0.16}$ | $1.87_{-0.15}^{+0.13}$ | $1.66_{-0.12}^{+0.13}$ | $2.03_{-0.19}^{+0.21}$
| norm | $0.27_{-0.07}^{+0.09}$ | $0.62_{-0.13}^{+0.16}$ | $0.38_{-0.07}^{+0.08}$ | $1.06_{-0.28}^{+0.31}$
Nthcomp | $\Gamma$ | $2.26\pm 0.02$ | $2.22_{-0.02}^{+0.03}$ | $2.21_{-0.02}^{+0.01}$ | $2.23_{-0.02}^{+0.03}$
| $kT_{\rm e}(\rm keV)$ | $105.1_{-34.9}^{+59.9}$ | $61.3_{-8.8}^{+20.1}$ | $102.9_{-27.5}^{+94.6}$ | $54.7_{-8.4}^{+20.1}$
| norm | $3.47_{-0.26}^{+0.19}$ | $3.86_{-0.13}^{+0.15}$ | $2.64_{-0.10}^{+0.11}$ | $4.80_{-0.14}^{+0.19}$
Xillver | $A_{\rm Fe}$ | $2.40_{-1.02}^{+1.47}$ | $10.00_{-6.28}^{*}$ | $10.00_{-6.29}^{*}$ | $10.00_{-6.15}^{*}$
| log($\xi$) | $3.85_{-0.37}^{+0.29}$ | $3.47_{-0.37}^{+0.43}$ | $3.61_{-0.57}^{+0.44}$ | $3.84_{-0.29}^{+0.28}$
| norm | $0.017_{-0.008}^{+0.010}$ | $0.025_{-0.001}^{+0.003}$ | $0.002_{-0.001}^{+0.003}$ | $0.007_{-0.002}^{+0.008}$
| probability | 3.24e-07 | 7.02e-08 | 0.0065 | 2.351e-07
| $\chi^{2}/d.o.f$ | 730.3/728 | 726.3/746 | 670.0/733 | 590.6/675
Flux | Total | $16.68$ | $16.66$ | $15.50$ | $16.59$
| Diskbb | $12.78$ | $12.36$ | $12.51$ | $11.35$
| Gaussian | $0.29$ | $0.43$ | $0.31$ | $0.64$
| Nthcomp | $3.61$ | $3.87$ | $2.68$ | $4.60$

Note. — Error bars are of 90% confidence limit.

∗ means that the parameter pegs at its limit.

Flux unit is $10^{-8}\rm ergs/\rm cm^{2}/\rm s$ in the energy band 1–100 keV.

Table 3: Best-fit spectral parameters of epochs with B-QPO and C-QPO using
model 1 tbabs$\times$(diskbb+gaussian+nthcomp+xillverCp)

Component | Parametes | EP 6 | EP 7
---|---|---|---
|  | B-Q | C-Q | B-Q | B-Q | C-Q | B-Q
TBabs |  $N_{\rm H}(\times 10^{22}\rm cm^{-2}$) | $0.899_{-0.017}^{+0.018}$ | $0.870\pm 0.011$ | $0.894\pm 0.007$ | $0.859\pm 0.006$ | $0.856_{-0.011}^{+0.004}$ | $0.867_{-0.007}^{+0.008}$
Diskbb | $kT_{\rm in}({\rm keV})$ | $0.759_{-0.046}^{+0.010}$ | $0.683_{-0.007}^{+0.006}$ | $0.737_{-0.006}^{+0.005}$ | $0.689\pm 0.004$ | $0.646_{-0.004}^{+0.007}$ | $0.685\pm 0.004$
| norm | $23662_{-1425}^{+4510}$ | $32228_{-1289}^{+1376}$ | $28206_{-797}^{+923}$ | $28437_{-617}^{+676}$ | $31670_{-734}^{+747}$ | $28920_{-681}^{+757}$
Gaussian | $E_{\rm line}({\rm keV})$ | $4.6_{-3.8}^{+0.4}$ | $3.5_{-0.4}^{+0.4}$ | $3.9_{-0.5}^{+0.4}$ | $3.5_{-0.4}^{+0.3}$ | $3.4_{-0.3}^{+0.3}$ | $3.5_{-0.5}^{+0.3}$
| $\sigma({\rm keV})$ | $1.13_{-0.36}^{+1.77}$ | $2.07_{-0.18}^{+0.18}$ | $1.96_{-0.16}^{+0.17}$ | $2.10_{-0.11}^{+0.13}$ | $2.24_{-0.10}^{+0.10}$ | $2.02_{-0.20}^{+0.16}$
| norm | $0.26_{-0.12}^{+1.56}$ | $1.16_{-0.27}^{+0.31}$ | $0.81_{-0.20}^{+0.28}$ | $0.87_{-0.14}^{+0.20}$ | $1.04_{-0.14}^{+0.16}$ | $0.69_{-0.19}^{+0.22}$
Nthcomp | $\Gamma$ | $2.31_{-0.06}^{+0.02}$ | $2.15\pm 0.02$ | $2.25_{-0.02}^{+0.03}$ | $2.20\pm 0.01$ | $2.10\pm 0.01$ | $2.22\pm 0.02$
| $kT_{\rm e}(\rm keV)$ | $121.2_{-20.4}^{+23.1}$ | $84.3_{-18.1}^{+32.2}$ | $111.3_{-29.2}^{+108.1}$ | $108.5_{-23.9}^{+49.3}$ | $84.1_{-14.7}^{+22.8}$ | $142.2_{-48.8}^{+339.6}$
| norm | $4.86_{-4.86}^{+4.86}$ | $5.52_{-0.27}^{+0.30}$ | $4.19_{-0.16}^{+0.17}$ | $3.18_{-0.09}^{+0.09}$ | $2.90_{-0.11}^{+0.12}$ | $2.77_{-0.17}^{+0.13}$
Xillver | $A_{\rm Fe}$ | $4.92_{-3.27}^{+4.88}$ |  $\cdots$ | $6.53_{-3.85}^{+-6.53}$ | $4.03_{-1.47}^{+2.81}$ |  $\cdots$ | $3.82_{-1.18}^{+1.95}$
| log($\xi$) | $4.15_{-1.24}^{+0.49}$ |  $\cdots$ | $3.50_{-0.29}^{+0.33}$ | $3.65_{-0.19}^{+0.19}$ |  $\cdots$ | $3.95_{-0.18}^{+0.30}$
| norm | $0.034_{-0.025}^{+0.012}$ |  $\cdots$ | $0.007_{-0.002}^{+0.006}$ | $0.006_{-0.002}^{+0.003}$ |  $\cdots$ | $0.011_{-0.004}^{+0.006}$
| probability | 0.006882 |  $\cdots$ (0.75) | 2.25e-10 | 1.19e-21 |  $\cdots$ | 4.29e-23
| $\chi^{2}/d.o.f$ | 307.5/322 | 344/309 | 660.2/736 | 974.4/1017 | 682/615 | 792.0/919
Flux | Total | $16.63$ | $15.35$ | $15.90$ | $12.04$ | $11.02$ | $11.60$
| Diskbb | $11.32$ | $9.03$ | $11.41$ | $8.47$ | $7.34$ | $8.45$
| Gaussian | $0.60$ | $0.66$ | $0.51$ | $0.49$ | $0.57$ | $0.42$
| Nthcomp | $4.71$ | $5.67$ | $3.98$ | $3.08$ | $3.12$ | $2.73$

Note. — Error bars are of 90% confidence limit.

∗means that the parameter pegs at its limit.

Flux unit is $10^{-8}\rm ergs/\rm cm^{2}/\rm s$ in the energy band 1–100 keV.

Table 4: Results of simultaneous spectral fits using model
tbabs$\times$(diskbb+gaussian+nthcomp)

| EP 4 | EP 5 |  | EP 6 | EP 7
---|---|---|---|---|---
| NO-Q | B-Q | NO-Q | B-Q |  | B-Q | C-Q | B-Q | C-Q
Parameters |  $\cdots$ | ${\chi^{2}_{red}/d.o.f}^{d}$ |  $\cdots$ | $\chi^{2}_{red}/d.o.f$ | Parameters |  $\cdots$ | $\chi^{2}_{red}/d.o.f$ |  $\cdots$ | $\chi^{2}_{red}/d.o.f$
All tied |  $\cdots$ | 6326.3/1502 |  $\cdots$ | 100662.1/1436 | All tied |  $\cdots$ | 32532.22/656 |  $\cdots$ | 81580.34/1657
${N_{\rm nthcomp}}^{a}$ |  $\cdots$ | 3712.9/1501 |  $\cdots$ | 13564/1435 | $N_{\rm diskbb}$ |  $\cdots$ | 7403.7/655 |  $\cdots$ | 16945.38/1656
${N_{\rm diskbb}}^{b}$ |  $\cdots$ | 1867.9/1500 |  $\cdots$ | 5265.4/1434 | $\Gamma$ |  $\cdots$ | 5312.17/654 |  $\cdots$ | 16403.51 /1655
${N_{\rm gaussian}}^{c}$ |  $\cdots$ | 1610.7/1499 |  $\cdots$ | 1658.7/1433 | $kT_{\rm in}$ |  $\cdots$ | 1443.28/653 |  $\cdots$ | 2797.47/1654
|  |  |  |  | $N_{\rm nthcomp}$ |  $\cdots$ | 763.98/652 |  $\cdots$ | 2604.69/1653
$N_{\rm nthcomp}$ | $3.46_{-0.10}^{+0.11}$ | $3.72\pm 0.01$ | $2.56_{-0.08}^{+0.09}$ | $4.23\pm 0.01$ | $N_{\rm diskbb}$ | $28089_{-1922}^{+3099}$ | $34772_{-347}^{+353}$ | $29730_{-815}^{+884}$ | $34052_{-154}^{+155}$
$N_{\rm diskbb}$ | $27663_{-448}^{+485}$ | $26967_{-26}^{+25}$ | $29914_{-467}^{+516}$ | $28036_{-31}^{+32}$ | $\Gamma$ | $2.22_{-0.02}^{+0.02}$ | $2.15\pm 0.01$ | $2.16\pm 0.01$ | $2.108\pm 0.003$
$N_{\rm gaussian}$ | $0.34_{-0.04}^{+0.05}$ | $0.41\pm 0.01$ | $0.40_{-0.05}^{+0.06}$ | $0.72\pm 0.01$ | $kT_{\rm in}$ | $0.747_{-0.020}^{+0.013}$ | $0.684\pm 0.002$ | $0.84\pm 0.01$ | $0.684\pm 0.002$
|  |  |  |  | $N_{\rm nthcomp}$ | $1.22_{-0.09}^{+0.11}$ | $1.51\pm 0.02$ | $0.87\pm 0.02$ | $0.931_{-0.007}^{+0.008}$

Note. — Error bars are of 90% confidence limit.

∗ means that the parameter pegs at its limit

abc Normalization of _nthcomp_ , _diskbb_ and _gaussian_ , respectively.

d The chi-squared obtained after freeing the parameters.

_Last row_ presents results obtained after freeing the above parameters.

Table 5: Best-fit spectral parameters of epochs with B-QPO and NO-QPO using
model 2 tbabs$\times$(diskbb+relxilllp)

Component | Parametes | EP 4 | EP 5
---|---|---|---
|  | NO-Q | B-Q | NO-Q | B-Q
TBabs |  $N_{\rm H}(\times 10^{22}\rm cm^{-2}$) | $1.04_{-0.01}^{+0.02}$ | $1.02\pm 0.01$ | $1.007\pm 0.001$ | $1.03\pm 0.01$
Diskbb | $kT_{\rm in}({\rm keV})$ | $0.762_{-0.002}^{+0.001}$ | $0.763_{-0.002}^{+0.003}$ | $0.746\pm 0.001$ | $0.759\pm 0.001$
| norm | $25078_{-142}^{+234}$ | $23760_{-413}^{+212}$ | $27333_{-58}^{+85}$ | $21770_{-178}^{+166}$
Relxilllp | $h(GM/C^{2})$ | $2.95_{-0.12}^{+0.08}$ | $3.18_{-0.12}^{+0.09}$ | $2.86_{-0.20}^{+0.04}$ | $3.21_{-0.07}^{+0.04}$
|  $R_{\rm in}$ (ISCO) | $1.00_{*}^{+0.16}$ | $1.00_{*}^{+0.13}$ | $1.00_{*}^{+0.09}$ | $1.00_{*}^{+0.07}$
| $\Gamma$ | $2.40_{-0.02}^{+0.03}$ | $2.35\pm 0.01$ | $2.39\pm 0.01$ | $2.36\pm 0.01$
|  $a^{*}$ ($c{\rm J}/GM^{2}$) | 0.80 (fixed)
|  $\theta$ (deg) | 36.5 (fixed)
| log($\xi$) | $3.77_{-0.06}^{+0.21}$ | $4.25_{-0.11}^{+0.07}$ | $4.23_{-0.04}^{+0.01}$ | $4.36_{-0.01}^{+0.01}$
| $A_{\rm Fe}$ | $6.03_{-1.24}^{+0.94}$ | $10.00_{-1.76}^{*}$ | $9.67_{-0.44}^{+0.03}$ | $10.00_{-0.71}^{*}$
| $E_{\rm cut({\rm keV}})$ | $241.1_{-30.2}^{+61.8}$ | $219.1_{-24.5}^{+14.8}$ | $500.0_{-121.9}^{*}$ | $204.3_{-14.4}^{+12.3}$
| $R_{\rm ref}$ | $0.62\pm 0.03$ | $0.63\pm 0.03$ | $0.74_{-0.03}^{+0.01}$ | $0.67_{-0.02}^{+0.02}$
| norm | $1.43\pm 0.15$ | $0.98_{-0.09}^{+0.08}$ | $1.06_{-0.04}^{+0.06}$ | $1.40_{-0.01}^{+0.12}$
| $\chi^{2}_{red}/d.o.f$ | 786.5/729 | 755.2/747 | 724.6/734 | 617.1/676
Flux | Total | $17.49$ | $17.46$ | $16.14$ | $17.53$
| Diskbb | $11.77$ | $11.22$ | $11.59$ | $9.97$
| Relxilllp | $1.41$ | $1.72$ | $1.42$ | $2.22$
| Cutoffpl | $4.32$ | $4.48$ | $3.18$ | $5.32$

Note. — Error bars are of 90% confidence limit.

∗ means that the parameter pegs at its limit.

Flux unit is $10^{-8}\rm ergs/\rm cm^{2}/\rm s$ in the energy band 1–-100 keV.

Table 6: Best-fit spectral parameters of epochs with B-QPO and C-QPO using
model 2 tbabs$\times$(diskbb+relxilllp)

Component | Parametes | EP 6 | EP 7
---|---|---|---
|  | B-Q | C-Q | B-Q | B-Q | C-Q | B-Q
TBabs |  $N_{\rm H}(\times 10^{22}\rm cm^{-2}$) | $1.022_{-0.004}^{+0.007}$ | $1.004_{-0.012}^{+0.009}$ | $1.026_{-0.007}^{+0.008}$ | $0.975_{-0.003}^{+0.001}$ | $0.938_{-0.006}^{+0.003}$ | $0.969_{-0.007}^{+0.003}$
Diskbb | $kT_{\rm in}({\rm keV})$ | $0.777_{-0.003}^{+0.004}$ | $0.710_{-0.003}^{+0.004}$ | $0.756\pm 0.002$ | $0.706\pm 0.001$ | $0.669_{-0.004}^{+0.002}$ | $0.699_{-0.002}^{+0.001}$
| norm | $19467_{-400}^{+336}$ | $22968_{-560}^{+532}$ | $22533_{-323}^{+326}$ | $22565_{-158}^{+139}$ | $25110_{-188}^{+102}$ | $23894_{-210}^{+100}$
Relxilllp | $h(GM/C^{2})$ | $4.06_{-0.31}^{+0.23}$ | $2.99\pm 0.08$ | $4.54_{-0.11}^{+0.04}$ | $2.61_{-0.04}^{+0.03}$ | $2.51_{-0.03}^{+0.04}$ | $2.68_{-0.05}^{+0.03}$
| Rin (ISCO) | $1.0_{*}^{+0.9}$ | $1.0_{*}^{+0.4}$ | $1.0_{*}^{+0.1}$ | $1.00_{*}^{+0.02}$ | $1.00_{*}^{+0.06}$ | $1.00_{*}^{+0.04}$
| $\Gamma$ | $2.37_{-0.02}^{+0.01}$ | $2.30_{-0.02}^{+0.01}$ | $2.40\pm 0.02$ | $2.38_{-0.01}^{+0.02}$ | $2.30_{-0.01}^{+0.02}$ | $2.38\pm 0.01$
|  $a^{*}$ ($c{\rm J}/GM^{2}$) | 0.80 (fixed)
|  $\theta$ (deg) | 36.5 (fixed)
| log($\xi$) | $4.28_{-0.13}^{+0.18}$ | $4.21_{-0.04}^{+0.03}$ | $4.28_{-0.11}^{+0.13}$ | $4.28_{-0.03}^{+0.02}$ | $4.27_{-0.04}^{+0.02}$ | $4.27_{-0.06}^{+0.07}$
| $A_{\rm Fe}$ | $6.83_{-1.65}^{+0.96}$ | $5.01_{-0.33}^{+0.02}$ | $8.12_{-0.75}^{+1.42}$ | $8.03_{-0.37}^{+0.29}$ | $10.00_{-0.28}^{*}$ | $7.52_{-0.72}^{+0.82}$
| $E_{\rm cut({\rm keV}})$ | $350_{-60}^{+25}$ | $500_{-51}^{*}$ | $372_{-63}^{+93}$ | $500_{-60}^{*}$ | $500_{-11}^{*}$ | $500_{-62}^{*}$
| $R_{\rm ref}$ | $0.64_{-0.12}^{+0.08}$ | $0.73_{-0.01}^{+0.09}$ | $0.63_{-0.04}^{+0.03}$ | $0.88_{-0.06}^{+0.08}$ | $1.05_{-0.01}^{+0.04}$ | $0.96_{-0.06}^{+0.04}$
| norm | $0.70_{-0.09}^{+0.08}$ | $0.52_{-0.05}^{+0.01}$ | $1.40_{-0.12}^{+0.11}$ | $1.75_{-0.10}^{+0.12}$ | $1.13_{-0.02}^{+0.01}$ | $1.17_{-0.08}^{+0.07}$
| $\chi^{2}_{red}/d.o.f$ | 310.7/323 | 335.1/307 | 711.2/737 | 1120.3/1018 | 737.9/613 | 867.5/920
Flux | Total | $17.51$ | $16.13$ | $16.77$ | $12.61$ | $11.47$ | $12.12$
| Diskbb | $10.03$ | $7.41$ | $10.21$ | $7.45$ | $6.41$ | $7.51$
| Relxilllp | $2.25$ | $2.57$ | $1.81$ | $1.96$ | $2.09$ | $1.88$
| Cutoffpl | $5.24$ | $5.79$ | $4.78$ | $3.22$ | $2.96$ | $2.72$

Note. — Error bars are of 90% confidence limit.

∗ means that the parameter pegs at its limit.

Flux unit is $10^{-8}\rm ergs/\rm cm^{2}/\rm s$ in the energy band 1-–100 keV.

Table 7: Results of simultaneous spectral fits using model 2
tbabs$\times$(diskbb+relxilllp)

| EP 4 | EP 5 |  | EP 6 | EP 7
---|---|---|---|---|---
| NO-Q | B-Q | NO-Q | B-Q |  | B-Q | C-Q | B-Q | C-Q
Parameters |  $\cdots$ | ${\chi^{2}_{red}/d.o.f}^{c}$ |  $\cdots$ | $\chi^{2}_{red}/d.o.f$ | Parameters |  $\cdots$ | $\chi^{2}_{red}/d.o.f$ |  $\cdots$ | $\chi^{2}_{red}/d.o.f$
All tied |  $\cdots$ | 8460.37/1502 |  $\cdots$ | 111803.8/1436 | All tied |  $\cdots$ | 29227.48/656 |  $\cdots$ | 64119.46/1658
$\Gamma$ |  $\cdots$ | 4063.71/1501 |  $\cdots$ | 14354.44/1435 | $kT_{\rm in}({\rm keV})$ |  $\cdots$ | 3404.34/655 |  $\cdots$ | 4316.91/1657
${N_{\rm diskbb}}^{a}$ |  $\cdots$ | 1742.65/1500 |  $\cdots$ | 8201.09/1434 | $h(GM/C^{2})$ |  $\cdots$ | 1235.55/654 |  $\cdots$ | 4022.04/1656
$h(GM/C^{2})$ |  $\cdots$ | 1628.05/1499 |  $\cdots$ | 3552.20/1433 | $N_{\rm diskbb}$ |  $\cdots$ | 983.54/653 |  $\cdots$ | 2569.73/1655
$kT_{\rm in}({\rm keV})$ |  $\cdots$ | 1571.34/1498 |  $\cdots$ | 2096.51/1432 |  $\Gamma$ ;$E_{\rm cut}$ |  $\cdots$ | 700.66/651 |  $\cdots$ | 2102.18/1653
${N_{\rm relxilllp}}^{b}$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1980.67/1431 | $R_{\rm ref}$ |  $\cdots$ | 655.98/650 |  $\cdots$ | 2084.41/1652
$E_{\rm cut}$;$R_{\rm ref}$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1378.33/1429 |  |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
$\Gamma$ | $2.40_{-0.02}^{+0.03}$ | $2.38_{-0.02}^{+0.01}$ | $2.39\pm 0.01$ | $2.32\pm 0.01$ | $kT_{\rm in}$ | $0.777_{-0.003}^{+0.004}$ | $0.707\pm 0.002$ | $0.706\pm 0.001$ | $0.661\pm 0.001$
$N_{\rm diskbb}$ | $25078_{-142}^{+234}$ | $23474_{-123}^{+119}$ | $27333_{-58}^{+85}$ | $21383_{-221}^{+135}$ | $h$ | $4.42_{-0.11}^{+0.33}$ | $3.77_{-0.15}^{+0.14}$ | $2.61_{-0.04}^{+0.03}$ | $2.47_{-0.01}^{+0.02}$
$h(GM/C^{2})$ | $2.95_{-0.12}^{+0.08}$ | $3.33\pm 0.01$ | $2.86_{-0.20}^{+0.04}$ | $3.51_{-0.02}^{+0.03}$ | $N_{\rm diskbb}$ | $19467_{-400}^{+336}$ | $23232_{-398}^{+406}$ | $22565_{-158}^{+139}$ | $26296_{-144}^{+152}$
$kT_{\rm in}({\rm keV})$ | $0.762_{-0.002}^{+0.001}$ | $0.765\pm 0.001$ | $0.746\pm 0.001$ | $0.763\pm 0.001$ | $\Gamma$ | $2.37_{-0.02}^{+0.01}$ | $2.33_{-0.01}^{+0.01}$ | $2.38\pm 0.01$ | $2.34\pm 0.01$
$N_{\rm relxilllp}$ |  $\cdots$ |  $\cdots$ | $1.06_{-0.04}^{+0.06}$ | $1.59_{-0.18}^{+0.11}$ | $E_{\rm cut}$ | $350_{-60}^{+25}$ | $500^{*}$ | $500^{*}$ | $500^{*}$
$E_{\rm cut}$ |  $\cdots$ |  $\cdots$ | $500^{*}$ | $159_{-10}^{+11}$ | $R_{\rm ref}$ | $0.64_{-0.12}^{+0.08}$ | $0.92_{-0.11}^{+0.14}$ | $0.88_{-0.06}^{+0.08}$ | $1.12_{-0.05}^{+0.06}$
$R_{\rm ref}$ |  $\cdots$ |  $\cdots$ | $0.74_{-0.03}^{+0.01}$ | $0.62_{-0.02}^{+0.04}$ |  |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$

Note. — Error bars are of 90% confidence limit.

∗ means that the parameter pegs at its limit.

ab Normalization of _diskbb_ and _relxilllp_.

c The chi-squared obtained after freeing the parameters.

_Last row_ presents results obtained after freeing the above parameters.