# Highly-coherent quasi-periodic oscillations in the ‘heartbeat’ black hole
X-ray binary IGR J17091–3624

Jingyi Wang11affiliationmark:  , Erin Kara11affiliationmark:  , Jeroen
Homan22affiliationmark:  , James F. Steiner33affiliationmark:  , Diego
Altamirano44affiliationmark:  , Tomaso Belloni55affiliationmark:  ,∗, Michiel
van der Klis66affiliationmark:  , Adam Ingram77affiliationmark:  , Javier A.
García 88affiliationmark:  99affiliationmark:  , Guglielmo
Mastroserio1010affiliationmark:  , Riley Connors1111affiliationmark:  , Matteo
Lucchini66affiliationmark:  , Thomas Dauser1212affiliationmark:  , Joseph
Neilsen1111affiliationmark:  , Collin Lewin11affiliationmark:  , Ron A.
Remillard11affiliationmark:  11affiliationmark:  MIT Kavli Institute for
Astrophysics and Space Research, MIT, 70 Vassar Street, Cambridge, MA 02139,
USA
22affiliationmark:  Eureka Scientiﬁc, Inc., 2452 Delmer Street, Oakland, CA
94602, USA
33affiliationmark:  Harvard-Smithsonian Center for Astrophysics, 60 Garden
St., Cambridge, MA 02138, USA
44affiliationmark:  School of Physics and Astronomy, University of
Southampton, Highfield, Southampton, SO17 1BJ
55affiliationmark:  INAF-Osservatorio Astronomico di Brera, via E. Bianchi 46,
I-23807 Merate, Italy
66affiliationmark:  Astronomical Institute, Anton Pannekoek, University of
Amsterdam, Science Park 904, NL-1098 XH Amsterdam, Netherlands
77affiliationmark:  School of Mathematics, Statistics and Physics, Newcastle
University, Herschel Building, Newcastle upon Tyne, NE1 7RU, UK
88affiliationmark:  X‐ray Astrophysics Laboratory, NASA Goddard Space Flight
Center, Greenbelt, MD 20771
99affiliationmark:  Cahill Center for Astronomy and Astrophysics, California
Institute of Technology, Pasadena, CA 91125, USA
1010affiliationmark:  INAF-Osservatorio Astronomico di Cagliari, via della
Scienza 5, I-09047 Selargius (CA), Italy
1111affiliationmark:  Villanova University, Department of Physics, Villanova,
PA 19085, USA
1212affiliationmark:  Remeis Observatory & ECAP, Universität Erlangen-
Nürnberg, 96049 Bamberg, Germany

###### Abstract

IGR J17091–3624 is a black hole X-ray binary (BHXB), often referred to as the
‘twin’ of GRS 1915+105 because it is the only other known BHXB that can show
exotic ‘heartbeat’-like variability that is highly structured and repeated.
Here we report on observations of IGR J17091–3624 from its 2022 outburst,
where we detect an unusually coherent quasi-periodic oscillation (QPO) when
the broadband variability is low (total fractional rms $\lesssim 6\%$) and the
spectrum is dominated by the accretion disk. Such spectral and variability
behavior is characteristic of the soft state of typical BHXBs (i.e. those that
do not show heartbeats), but we also find that this QPO is strongest when
there is some exotic heartbeat-like variability (so-called Class V
variability). This QPO is detected at frequencies between 5 and 8 Hz and has
Q-factors (defined as the QPO frequency divided by the width) $\gtrsim 50$,
making it one of the most highly coherent low-frequency QPO ever seen in a
BHXB. The extremely high Q factor makes this QPO distinct from typical low-
frequency QPOs that are conventionally classified into Type-A/B/C QPOs.
Instead, we find evidence that archival observations of GRS 1915+105 also
showed a similarly high-coherence QPO in the same frequency range, suggesting
that this unusually coherent and strong QPO may be unique to BHXBs that can
exhibit ‘heartbeat’-like variability..

accretion, accretion disks — black hole physics

##  1 Introduction

BHXBs provide us with opportunities to study different accretion states of
accreting black holes in a single source (see e.g., Méndez & van der Klis,
1997; Remillard & McClintock, 2006; Belloni et al., 2011, and Kalemci et al.,
2022 for a recent review). In a typical outburst, the BHXBs rise from
quiescence through a hard state where the X-ray emission is dominated by
emission from the ‘corona’ (the hot plasma with temperature on the order of
$100$ keV). Then, the BHXBs make a transition in days to weeks, through what
is known as the intermediate state, into the soft state where the disk
emission dominates. Finally, they return to the hard state and then recede
again into quiescence. ††∗We dedicate this paper to the late Tomaso Belloni,
who contributed significantly to this paper before his untimely passing on 26
August 2023. Tomaso was a pioneer in the study of X-ray timing since his early
days working on EXOSAT, and in particular, awakened the community to the
beautiful puzzle that is GRS 1915. In this work, on GRS 1915’s ‘little
sister’, IGR J17091, we build upon the legacy of a trailblazer in our field.
We will miss him for his energy, his insights, his humor and his unwavering
passion for science. Ad astra, Tomaso.

Figure 1: The time evolution of NICER count rate (0.3–12 keV, normalized for
52 FPMs), the fitted disk temperature with a baseline model (W24a), and the
fractional rms (0.01–10 Hz in 1–10 keV). There are 305 data points, each
representing a 500 s NICER segment. The gray shaded regions indicate when the
highly-coherent QPO was detected (Epochs 1–10 in Table 1). Besides MJD, the
calendar dates are shown on the top x-axis. Classes V and X are termed
‘exotic’ because exotic ‘heartbeat’-like variability (structured and repeated)
is present in the lightcurves. See Section 2 and W24a for more details on the
state identifications.

In the lightcurves of BHXBs, we observe various types of low-frequency quasi
periodic oscillations (LFQPOs; see the reviews Belloni & Motta, 2016; Ingram &
Motta, 2019, and references therein). The LFQPOs in BHXBs are usually
categorized with an A/B/C classification scheme (see e.g., Wijnands et al.,
1999; Remillard et al., 2002b; Casella et al., 2005; Motta et al., 2011). The
classification is based on the properties of the QPO including e.g., its
frequency, strength, and Q factor (frequency divided by the full width at half
maximum, FWHM), the type of the underlying noise component, and the spectral
state in which the QPO is detected.

Figure 2: The unfolded spectra using a model where reflection and absorption
lines are included (see W24a for more details). For each state, when a
simultaneous NuSTAR spectrum is available, we show that for coverage at high
energies; in the Hard state, HIMS, and Transition to Class V, the NICER
spectra are shown. The highly coherent QPO detected are in the Soft State and
Class V, which are both disk-dominated, consistent with a high disk
temperature as illustrated in Fig. 1.

  * •

Type-C QPOs are seen commonly in the hard state and hard-intermediate state
(HIMS). The QPO frequency ranges between a few mHz to $\sim 10$ Hz. They are
strong ($\lesssim 20\%$ rms), narrow ($Q\gtrsim 8$), and accompanied by a
flat-top noise. In addition to the fundamental (usually defined as the
component with the highest rms amplitude), there are often second and even
third harmonics and the sub-harmonic (half of the frequency). The frequency of
Type-C QPO was found to be correlated with the spectral properties of both the
disk and the corona, albeit with some spread. For instance, correlations have
been seen with e.g., the disk flux (Markwardt et al., 1999; Sobczak et al.,
2000; Remillard & McClintock, 2006), the photon index of the coronal spectrum
(Vignarca et al., 2003; García et al., 2022), and the coronal electron
temperature (Méndez et al., 2022). Compared with other timing properties, the
QPO frequency is also correlated with the low-frequency break of the flat-top
noise (Wijnands & van der Klis, 1999; Psaltis et al., 1999), and is
anticorrelated with the total fractional rms (Motta et al., 2011). There is
evidence that Type-C QPOs have inclination dependency of their amplitudes
(Motta et al., 2015) and the time lags at the QPO frequencies (van den Eijnden
et al., 2017). This may suggest that they are produced by some geometrical
effects involving Lense-Thirring precession (e.g, the Relativistic Precession
Model, Stella & Vietri, 1998; the solid-body Lense-Thirring precessing model,
Ingram et al., 2009; precession of the base of a jet, Ma et al., 2021).
However, recently, Marcel & Neilsen (2021) show that not all models of the
inner accretion flow can produce precession. Besides geometrical models, there
are also models involving intrinsic luminosity changes of the system including
e.g., accretion ejection instability model (Tagger & Pellat, 1999), and
variable Comptonization (Bellavita et al., 2022).

  * •

Type-B QPOs are seen in soft-intermediate state (SIMS), and they are narrow
($Q\gtrsim 6$) but weaker compared to Type-C ($\lesssim 5\%$ rms), found
usually at 5–6 Hz and sometimes 1–3 Hz, and appear on top of weak red noise
(few percent rms). The QPO frequency is not anticorrelated with the total
fractional rms as observed for Type-C QPOs (Motta et al., 2011). The
appearance of the Type-B QPO has been suggested to be linked to discrete jet
ejections (Fender et al., 2004; Stevens & Uttley, 2016; Kylafis et al., 2020;
García et al., 2021; Liu et al., 2022; Ma et al., 2023). The best example is a
Type-B QPO in MAXI J1820+070 that appeared at a time consistent with that of a
jet ejection event (Homan et al., 2020; Wood et al., 2021).

  * •

Type-A QPOs also normally appear in the SIMS. They are the least common type
as there were only $\sim$10 detections in the entire RXTE archive. The QPO
frequency is between 6 and 8 Hz. They are weak (a few percent rms), broad
($Q\lesssim 3$), and they are accompanied by very weak red noise (Homan et
al., 2001; Motta et al., 2011, 2015). As they are rare, weak, and broad, the
phenomenology and nature of Type-A QPOs are the least understood.

IGR J17091–3624 and GRS 1915+105 are extraordinary BHXBs because they are the
only two known BHXBs that, in addition to LFQPOs, exhibit a variety of exotic
variability classes, usually consisting of flares and drops that are highly
structured and have high amplitudes (e.g., Belloni et al., 2000; Altamirano et
al., 2011; Court et al., 2017). Because of a famous ‘heartbeat’ class when the
lightcurve resembles an electrocardiogram (Class IV in IGR J17091–3624 and
Class $\rho$ in GRS 1915+105), in this work, we refer to variabilities that
are structured and repeated as ‘exotic’ or ‘heartbeat-like’. We observe LFQPOs
in the X-ray light curves of these two BHXBs, mostly in the hard state and
intermediate state without exotic variabilities (Morgan et al., 1997; Reig et
al., 2000; Altamirano et al., 2011; Pahari et al., 2014; Wang et al., 2024).
LFQPOs are sometimes also detected in the states showing exotic
variabilitites, and the QPO changes in frequency and even type along with the
exotic variabilities (Markwardt et al., 1999; Muno et al., 1999; Rodriguez et
al., 2002; Fender & Belloni, 2004; Soleri et al., 2008; Neilsen et al., 2011;
Court et al., 2017).

Besides the LFQPOs, there are also high-frequency QPOs (HFQPOs) in BHXBs but
these are detected less frequently. In the RXTE archive, HFQPOs were only
detected in a handful of BHXBs, and some detections are statistically marginal
(see Belloni et al., 2012 and references therein). The QPO frequency is
usually a few hundred Hz, while it is at only $\sim 67$ Hz in both GRS
1915+105111We note that Motta & Belloni (2023) recently suggested that the 67
Hz QPO in GRS 1915+105 may in fact be a Type-C QPO, rather than a HFQPO. and
IGR J17091–3624 (Morgan et al., 1997; Altamirano & Belloni, 2012). The Q
factor is in the range of 5–30, with an amplitude of 0.5–6%. HFQPOs sometimes
show up as two peaks with a frequency ratio close to an integer ratio of 3:2,
but with rare exception, the pair are not simultaneous or appear in different
energy bands (Strohmayer, 2001; Remillard et al., 2002a; Remillard &
McClintock, 2006).

In Wang et al. (2024) (hereafter W24a), we presented the spectral-timing
analysis of IGR J17091–3624 in its 2022 outburst using NICER, NuSTAR, and
Chandra data. We found that, as in typical BHXBs, the outburst began in the
hard state, then the intermediate state, but then transitioned to a soft state
where we identified two types of heartbeat-like variability (Class V and a new
Class X; see also Fig. 1). We observed Type-C QPOs in the hard state and HIMS,
Type-B QPOs in the SIMS, as in normal BHXBs, and a highly-coherent QPO in the
soft state and Class V. In this paper, we focus on the highly-coherent QPO,
including its evolution and properties in Section 3, and discuss its nature in
Section 4.

Figure 3: The time evolution of (a) the count rate in 0.3–12 keV (normalized
to 52 FPMs), and (b) the QPO centroid frequency. The purple data points are
measurements from the 10 data epochs corresponding to the PSDs in Fig. 4, and
the gray underlying data points are single-segment measurements. The dashed
line indicates Epoch 7 when two QPO components are detected. The star and
triangle markers represent the two QPO components respectively, and the color
scale represents the Q factor of the QPO. In (b), all the QPOs in purple (from
the 10 data epochs) are also significantly detected above $3\sigma$ in single-
segment PSDs, except for the QPOs in Epochs 1, 2, which are also the least
significant QPOs (below $6\sigma$) as shown in Table 1. Figure 4: The PSDs
that show the highly-coherent QPOs. The PSDs are raw, as the Poisson noise are
not subtracted. For each epoch, a zoom-in of the PSD at the QPO frequency band
is shown on the right. The solid line shows the best-fit with multiple
Lorentzians, the dashed line shows the Poisson noise level, and the dotted
lines show the other noise components. The Lorentzian components for the QPOs
are not shown for clarity. The gray arrows indicate the fitted QPO centroid
frequencies (corresponding to the values in Table 1). Representative
corresponding lightcurves can be found in W24a.

##  2 Observations and data reduction

After its last outburst in 2016, IGR J17091–3624 entered a new outburst in
March 2022 (Miller et al., 2022). When this outburst began, we triggered our
NICER and NuSTAR GO Program (PI: J. Wang). We analyzed all 136 NICER
observations taken at a near-daily cadence from 2022 March 27 to Aug 21 in
W24a. Readers are referred to W24a for data reduction and state
classification. In summary, we identify the different states by the broadband
spectral shape, the power spectral densities (PSDs), and the shape of the
lightcurves. From the analysis of the broadband spectral shape (Figs. 1 and 2)
and PSDs, we conclude that IGR J17091–3624 transitions between spectral and
timing characteristics of typical BHXBs (the Hard State, HIMS, SIMS, Soft
State and IMS Return). Then, the shape of the lightcurves revealed that there
was a transitional phase termed Transition to Class V, and that sometimes in
the soft state when the disk dominates over the coronal emission, instead of
showing very little variability (as in most BHXBs), IGR J17091–3624 can
demonstrate exotic (structured and repeated) variability. Therefore, we also
identified exotic variability classes Class V and a new class that we labeled
Class X. To be self-contained, we included two figures modified from W24a.
Fig. 1 presents the time evolution of the count rate, fitted disk temperature,
and fractional rms, with the gray-shaded regions highlighting the data in
which the highly coherent QPO was detected. We found the highly coherent QPO
was detected in the Soft State and Class V when the disk temperature was high
(1.5–2 keV; middle panel), the coronal spectrum was soft (photon index $\sim
2.7$; see W24a), and the broadband variability was weak (low rms $\lesssim
6\%$ in 0.01–10 Hz; bottom panel). Fig. 2 shows the unfolded spectra using a
model where disk and coronal emission, reflection, and absorption lines are
included (see W24a for more details). We see that IGR J17091–3624 transitioned
from a hard and corona-dominated state to a soft and disk-dominated state. The
highly coherent QPO was detected in disk-dominated states (Soft State and
Class V).

In this paper, we compute PSDs in 1–10 keV using a segment length of 500 s and
a time bin of 1 ms (Nyquist frequency of 500 Hz). This allows us to capture
both the LFQPOs and the exotic variability in a single PSD. However, due to
our 500 s segment length requirement, several short ObsIDs with significant
LFQPOs were excluded. We therefore also produced PSDs from segments with a
length of 64 s. The results from these shorter-segment PSDs are presented in
Appendix A. We use the ‘rms-squared’ normalization and the PSDs are binned
geometrically in frequency, i.e., from frequency $\nu$ to $(1+f)\nu$, where
$f$ is called the f factor (see e.g., Section 2.2 in Uttley et al. 2014 for
more details). For single-segment PSDs, we use an f factor of 0.01. For PSDs
with multiple segments, from 0.002 to 500 Hz, we choose 10 frequency ranges in
logarithmic space where the f factor decreases logarithmically from 0.8 to
0.0008. This results in an f factor $\sim 0.008$ in the frequency range where
the highly-coherent QPOs are detected (5–8 Hz). We note that for single-
segment PSDs, the errors on the PSD approach Gaussian at frequencies $\gtrsim
3$ Hz ($\gtrsim 20$ Foutier frequencies per frequency bin). When combining
$\sim 10$ segments, the PSD errors approach Gaussian at frequencies as low as
$\sim 0.01$ Hz, and these are the PSDs that the conclusions are ultimately
made from. We fit the raw (Poisson noise included) PSDs with a model including
multiple Lorentzian components and a constant for the Poisson noise.
Lorentzians are used to describe both the broadband noise and the QPOs.

All the uncertainties quoted in this paper are for a 90% confidence range
unless otherwise stated. We use XSPEC 12.12.1, and $\chi^{2}$ fit statistics
for the power spectral fits.

##  3 Results

Figure 5: The fitted Lorentzian centroid frequencies in the single-segment
PSDs versus the fractional rms (0.01 to 10 Hz). In (a), we show the Lorentzian
components for all the 8 states we identified in W24a; in (b), we only show
the Lorentzian components representing the Type-C and Type-B QPOs in the hard
state and intermediate state, and the highly coherent QPOs (in Class V and
Soft State) that are the focus on this paper. The NICER energy band used is
1–10 keV.

We first fit the single-segment PSDs. The frequencies of the QPOs detected
above $3\sigma$ are shown as underlying gray points in Fig. 3b. We find that
the QPO can evolve in frequency on a timescale of a day. There are 62 segments
of the length of 500 s between Apr 19 and June 26. We combine successive
segments into 10 data epochs. The PSDs, the best-fit models and the QPO
profiles are shown in Fig. 4. The time evolution of the frequencies of the
QPOs detected above $3\sigma$ among the 10 epochs is shown by the purple
points in Fig. 3. The corresponding information of the NICER observations, the
QPO properties including its frequency, Q factor, fractional rms amplitude,
and detection significance are summarized in Table 1. All the QPOs detected
above $3\sigma$ in multiple-segment PSDs are also detected in all single-
segment PSDs, except for the QPOs in Epochs 1 and 2. These two QPOs are also
the least significant ones (below $6\sigma$) in Table 1.

The QPO can be highly coherent as the Q factor is extremely high in Epochs 3–9
($\gtrsim 50$). This is also one of the highest coherence detected for LFQPOs
in BHXBs; a LFQPO at 11 mHz has been detected in the hard state of a BHXB
H1743–322 with a Q factor as high as $\sim 100$ (Altamirano & Strohmayer,
2012). The QPO amplitude is several percent fractional rms. The QPO frequency
is in the range of 5–8 Hz. In Epochs 1–6, the QPO frequency is positively
correlated with the count rate (Fig. 3). In Epoch 7, we detect two QPO
components in the PSD (Fig. 4g), which are both extremely narrow (Q factor
$\gtrsim 60$). The lower-frequency component is stronger in terms of the
fractional rms amplitude. The QPO frequency ratio is
$1.314^{+0.008}_{-0.010}$, indicating that the two components are not in a 2:1
harmonic relationship, which is usually seen for LFQPOs (see Section 4.2 for
the discussion). If we identify the lower-frequency component as the
fundamental, in Epochs 7–10, the QPO frequency is also positively correlated
with the count rate (Fig. 3).

Table 1: The data epochs and the detected highly-coherent QPOs when we fit the
PSDs in Fig. 4.

Epoch | Obs.IDs | Date | Expo. | Total frac. | QPO Freq. | Q factor | Frac. rms | Significance
---|---|---|---|---|---|---|---|---
|  |  | (ks) | rms (%) | (Hz) |  | (%) |
1 | 5618010302–5618010403 | 04/19–04/23 | 8.0 | 4.6 | $7.1^{+0.3}_{-0.1}$ | $6^{+6}_{-2}$ | $2.0^{+0.5}_{-0.4}$ | $4.4\sigma$
2 | 5618010404–5618010406 | 04/24–04/26 | 3.5 | 4.5 | $6.69\pm 0.09$ | $15^{+8}_{-5}$ | $2.3^{+0.3}_{-0.4}$ | $5.9\sigma$
3 | 5618010502–5618010503 | 05/20–05/21 | 3.0 | 7.2 | $6.69\pm 0.01$ | $44^{+11}_{-8}$ | $4.1\pm 0.2$ | $16.5\sigma$
4 | 5618010504–5618010506 | 05/22–05/24 | 1.0 | 6.8 | $6.81\pm 0.02$ | $52^{+16}_{-12}$ | $4.1^{+0.3}_{-0.4}$ | $9.6\sigma$
5 | 5618010507–5618010508 | 05/25–05/26 | 4.5 | 7.2 | $7.07\pm 0.01$ | $46^{+5}_{-4}$ | $4.6\pm 0.2$ | $22.5\sigma$
6 | 5618010601 | 05/27 | 1.5 | 6.3 | $7.22^{+0.01}_{-0.02}$ | $59^{+14}_{-10}$ | $4.2\pm 0.3$ | $12.5\sigma$
7 | 5618010602–5618010603 | 05/28–05/29 | 1.5 | 6.1 | $5.69\pm 0.01$ | $63^{+18}_{-16}$ | $3.0\pm 0.3$ | $9.8\sigma$
|  |  |  |  | $7.48^{+0.03}_{-0.04}$ | $58^{+50}_{-26}$ | $1.9\pm 0.4$ | $4.8\sigma$
8 | 5618010704–5618010708 | 06/07–06/11 | 4.0 | 5.2 | $6.36\pm 0.01$ | $49\pm 9$ | $2.8\pm 0.2$ | $14.5\sigma$
9 | 5618010903–5618010905 | 06/21–06/23 | 2.5 | 4.2 | $7.10^{+0.02}_{-0.01}$ | $59\pm 12$ | $2.4\pm 0.2$ | $10.0\sigma$
10 | 5618010907–5618010908 | 06/25–06/26 | 1.5 | 5.0 | $6.89\pm 0.03$ | $31^{+12}_{-8}$ | $2.8\pm 0.3$ | $8.4\sigma$

Notes.
The total fractional rms is in 0.01–10 Hz. The Q factor is defined as the QPO
centroid frequency divided by the width. The fractional rms quoted is the
square root of the integrated power density (i.e., for our fits using XSPEC,
it is computed as the square root of the normalization of the Lorentzian used
to fit the QPO), as we adopt the rms-squared normalization for the PSDs and
the normalization of the Lorentzian means the integrated power. The
significance of the QPOs is given as the ratio of the integrated power of the
Lorentzian used to fit the QPO (i.e., the Lorentzian normalization) divided by
the negative $1\sigma$ error on the integrated power. All the uncertainties
quoted in this table are for a 90% confidence range.

In addition to the Poisson noise (PSD is flat over frequency), we also observe
red noise in all epochs (an empirical description for the power is PSD
$\propto f^{-2}$). In addition, a flat-top noise component is required in
Epochs 1–2 and 8–10, which can be modeled with a Lorentzian with the centroid
frequency fixed at 0, and the FWHM is in a range of 1–2 Hz. In Epochs 3–7, the
centroid frequency of the Lorentzian for the additional noise component is
non-zero. It increases from 0.34 to 0.57 Hz through Epochs 3 to 6, as the
count rate and the QPO frequency increase. In Epoch 7 where the two QPO
components are present simultaneously, the noise centroid frequency decreases
to 0.43 Hz. The corresponding Lorentzian FWHM ranges between 0.4 and 0.6 Hz.
It is worth noting that the highly-coherent QPO is the strongest and narrowest
when the noise component with the non-zero centroid frequency is present. We
show in Fig. 6 the frequency of this noise component in Epochs 3–7 and the
corresponding QPO frequency. In Epochs 3 to 6, the centroid frequency
($\nu_{0}$) of the noise component is correlated with the QPO frequency; the
characteristic frequency ($\sqrt{\nu_{0}^{2}+\Delta^{2}}$ where $\Delta$ is
the half width at half maximum) of the noise component is less constrained but
the correlation is consistent. This noise component could be the low-rms
extension of the Lorentzian component representing heartbeat-like exotic
variability in Class V (see Fig. 5a). Therefore, although the highly-coherent
QPO is always present along with characteristics of a soft state including the
low total rms and a disk-dominated spectrum, data with the non-zero-centered
noise component is classified as Class V rather than the soft state. However,
exotic (structured and repeated) variability is too weak to be identified
directly in the lightcurves.

Figure 6: The noise frequency vs the QPO frequency in Epochs 3–7 where one
noise component with non-zero centroid frequency is required. The stars are
for the centroid frequencies, and the triangles are for the characteristic
frequencies (see Section 3 for more details).

We also performed an analysis of the rms-dependence on energy. In addition to
the 1-10 keV band, PSDs were created in the 0.5–1 keV, 1–2 keV, 2–4 keV, 4–7
keV, and 7–12 keV bands. All power spectra were rms-normalized. For
observations and epochs with the strongest QPOs the PSDs from all energy bands
(including 1–10 keV) were fitted simultaneously with a constant and one or two
Lorentzians. QPO frequency and width were linked between all power spectra,
while the underlying noise level and QPO rms were left to vary. In Figure 7 we
show several representative examples of the rms-dependence on energy. As can
be been, the rms has a steep dependence on energy. Note that the QPO was never
detected in the 0.5–1 keV band and only upper limits could be determined that
were not very constraining; therefore these upper limits are not shown. The
QPO typically had a fractional rms values of $\sim$1–2% in the 1–2 keV band,
increasing to $\sim$12–20% in the 7–12 keV band.

Figure 7: Four representative examples of the energy dependence of the QPO’s fractional rms. The red dashed line marks the fractional rms in the 1–10 keV band. Figure 8: Previously detected Type-C QPOs in the soft state of BHXBs using RXTE data including (a) XTE J1550–564 (Homan et al., 2001), (b) H1743–322 (Homan et al., 2005), and (c) GRO J1655–40 (Remillard et al., 1999; Motta et al., 2012). The RXTE PSDs are the same as in those references. The Poisson noise is subtracted to see the QPOs more clearly. The solid line shows the best-fit with multiple Lorentzians, the dotted lines show the noise components, and the dot-dashed lines are the QPOs. The segment length to generate the PSDs is 128 seconds in (a) and (c), and is 16 seconds in (b). The f factor is 0.025. See Table 2 for the observation information and measurements of the fitted QPOs. Table 2: The QPOs previously detected in the soft state of 3 BHXBs using RXTE data.  Source | Energy (keV) | Expo. (ks) | QPO Frequency (Hz) | Q factor | Frac. rms (%) | Significance
---|---|---|---|---|---|---
XTE J1550–564 | 2–60 | 30.7 | $17.7\pm 0.2$ | $15^{+12}_{-6}$ | $0.27\pm 0.05$ | $5.1\sigma$
H1743–322 | 3.7–27.4 | 13.6 | $14.7\pm 0.4$ | $10^{+10}_{-5}$ | $0.8\pm 0.2$ | $4.0\sigma$
GRO J1655–40 | 2–60 | 487.3 | $27.2\pm 0.3$ | $11^{+4}_{-3}$ | $0.47\pm 0.05$ | $8.3\sigma$

##  4 Discussion

In the following, we will discuss several possibilities for the nature of the
highly coherent QPO we detected in the BHXB IGR J17091–3624 that can show
‘heartbeat’-like variability .

###  4.1 Under the A/B/C classification scheme for LFQPOs

Conventionally, when the spectrum is dominated by the accretion disk, the QPO
classified and the corresponding accretion state are either Type-B QPO in the
SIMS, or Type-C QPO in the soft state.

In the soft state, the PSDs usually contain only a weak (broken) power-law
noise and no QPOs. Soft state QPOs have only been detected in a few BHXBs,
including XTE J1550–564 (Homan et al., 2001), H1743–322 (Homan et al., 2005),
and GRO J1655–40 (Remillard et al., 1999; Motta et al., 2012). All detections
were made in RXTE data. After the detections in these three sources, Franchini
et al. (2017) performed a systematic search of QPOs in soft states and found
them in three additional sources (GX 339–4, 4U 1543–47, and XTE J1817–330). In
Fig. 8 we show soft state PSDs exhibiting QPOs of the initial three sources in
which soft state QPOs were found. Their corresponding observation information
and the properties of the QPOs are shown in Table 2. The QPOs are at
$\sim$15–27 Hz with a Q factor $\sim 10$, and their fractional rms amplitudes
are $<1$% (in the hard energy band; see Table 2). These QPOs were classified
as Type-C based on the relationship between the noise break frequency and the
QPO frequency (Homan et al., 2005), and/or the total fractional rms versus QPO
frequency relation (Motta et al., 2012) where the QPO frequency increases and
total rms decreases as the source evolves through the outburst.

In Fig. 5b, we show the QPO frequency versus the integrated fractional rms for
IGR J17091–3624 for the highly-coherent QPOs, as well as for the Type-B and
Type-C QPOs detected in the same outburst (see W24a for more details). We find
that Type-B QPOs lie below the branch traced out by the Type-C QPOs, as found
in Motta et al. (2011); the highly coherent QPO could either be a low-
rms/high-frequency extension of the Type-C QPOs detected in this outburst in
the hard state and HIMS, or it could be a horizontal extension (with a gap in
frequency) of the Type-B QPOs detected in the SIMS. In addition, we find that
the QPO frequency is correlated with count rate, which is similar to its
correlation with the disk flux previously found for Type-C QPOs (Sobczak et
al., 2000; Remillard & McClintock, 2006; Motta et al., 2011).  The highly-
coherent QPOs in IGR J17091–3624 show steep energy dependence of their rms,
increasing by factors of almost 10 between 1 and 12 keV. This was also
observed for the soft state QPOs in XTE J1550-564 (Homan et al., 2001), albeit
at higher energies. We note, however, that a steep rms dependence on energy
has also been observed for some Type-B QPOs (Homan et al., 2001).

If this highly coherent QPO is a Type-C QPO in the soft state, as in the
aforementioned 6 BHXBs, the QPO frequency would correspond to the Lense-
Thirring precession frequency at the innermost stable circular orbit (ISCO)
radius (Motta et al., 2014a, b). In the solid-body precession model (Ingram et
al., 2009), this means the disk extends very close to the ISCO, leaving only a
tiny inner flow ‘ring’ to precess and produce the QPO; it then becomes unclear
how the frame dragging effect could drive such a precession for such a tiny
ring of inner flow (see also results and discussion in Nathan et al. 2022). In
the framework of the Relativistic Precession Model (Stella & Vietri, 1998),
this means that there is a hot spot or some over-density at the ISCO producing
the QPO. However, we note that this is the limiting case of the processing
flow when the radial extent of the processing flow is very small (Motta et
al., 2018), so a similar challenge is encountered in this model.

However, there are some discernible differences between the soft-state QPO
properties in IGR J17091–3624 compared to other sources (the three
representatives in Fig. 8 and those in Franchini et al., 2017): (1) the Q
factor is much higher ($\gtrsim 50$ compared to $\sim 10$), (2) the QPO
frequency is lower (5–8 Hz compared to 10–27 Hz), and (3) the QPO is much
stronger (fractional rms of the QPO is several percent compared to $<1$%).

###  4.2 A new type of LFQPO in BHXBs that can show ‘heartbeat’-like
variability?

The extremely high coherence of the QPO we detected is in IGR J17091–3624;
this BHXB is special in some regards as it is one of the only two BHXBs known
to exhibit heartbeat-like variabilities. This suggests that the QPO could also
be a new type of LFQPO that is only present in BHXBs that can show
‘heartbeat’-like variability, perhaps some sort of resonance is amplified by
exotic variability.

The first piece of evidence for this is that in the other source that can show
‘heartbeat’-like variability, GRS 1915+105, the LFQPOs observed along with
exotic variabilities (e.g., Markwardt et al., 1999) can also be highly
coherent. One example is shown in Fig. 9, where a QPO detected in the
frequency bin 4.75–5 Hz has a Q factor $>20$. Markwardt et al. (1999) also
found that above 4 Hz, the QPO frequency depends nearly linearly on the disk
flux, consistent with the dependency of the QPO frequency on the count rate
found in Section 3.

Figure 9: Highly-coherent QPO (Q factor $>20$) in GRS 1915+105. The PSD is
computed using two continuous segments of length of 4 seconds, which is a part
of the RXTE data 20402-01-45-03 when the lightcurve exhibited heartbeat-like
variability (see Markwardt et al., 1999). The QPO was detected therein, but
here, we show it is also highly coherent. The PSD is not rebinned in frequency
and is in Leahy normalization. The gray arrow indicates the QPO in the
frequency bin 4.75–5 Hz.

Another piece of information is that in Section 3, we found the highly-
coherent QPO is the strongest and narrowest when accompanied by a Lorentzian
component peaking at $\sim 0.3$–0.6 Hz (Epochs 3–7). Without this Lorentzian
component, the QPO properties (the Q factor and fractional rms amplitude) are
more in line with those of the Type-C QPOs in the soft state in other sources.
This Lorentzian component is likely an extension of the component representing
the heartbeat-like exotic variability (see Fig. 5a), even though we cannot
identify any exotic (structured and repeated) variability in the light curves.
The centroid frequency of the noise component also correlates with the
frequency of the highly-coherent QPO (Fig. 6).

There are two other properties of the highly-coherent QPO worth discussing:
the overall PSD shape, and the QPO pair with a frequency ratio inconsistent
with 2:1 that is usually observed for LFQPOs. The PSDs in Epochs 3–7 (red
noise, the noise component peaking at $\sim 0.3$–0.6 Hz, and the highly-
coherent QPO on top of Poisson noise) are very similar to the ones in which
HFQPOs are detected at $\sim 67$ Hz in both IGR J17091–3624 and GRS 1915+105
(see Fig. 2 in Altamirano & Belloni, 2012). The HFQPOs are detected in the
variability class $\gamma$ as defined in Belloni et al. (2000) , so the low-
frequency ‘bump’ is due to exotic variability. In this variability class,
there are occasional flares and drops in the lightcurves (see e.g., Fig. 4 in
Altamirano & Belloni, 2012), which are not observed in the data where we
detect the highly-coherent QPO.

We detect two QPO components in Epoch 7, with a frequency ratio of
$1.314^{+0.008}_{-0.010}$. We tried various selections on count rate and/or
hardness ratio, but found the two QPOs are always simultaneously present. In
the ObsID-based PSD analysis with a shorter segment length, the QPO pair is
detected in four ObsIDs including the two ObsIDs combined in Epoch 7 (Fig. A1;
see also Appendix A for more details). When both QPO frequencies increase with
count rate, the QPO frequency ratio is $1.310\pm 0.003$, consistent over the
four ObsIDs. This indicates a close relation between the two QPO components.
This frequency ratio is inconsistent with the 2:1 harmonic relationship
usually seen for LFQPOs. It is closer to a small integer ratio of 4:3 but
still inconsistent with it by $4\sigma$ and $13\sigma$. Although a frequency
ratio of 4:3 has not been observed for either LFQPOs or HFQPOs before, a 3:2
frequency ratio has been observed merely for HFQPOs (Strohmayer, 2001;
Remillard et al., 2002a; Remillard & McClintock, 2006). A possible mechanism
for these harmonic relations (rather than 2:1) is some sort of resonance in
the system (e.g., Abramowicz & Kluźniak, 2001). It is also plausible that the
two QPOs are not harmonically related, as the frequency ratio is inconsistent
with 4:3 by $>3\sigma$. In this case, the two QPOs could be produced in two
different regions with the same physical mechanism as both QPO frequencies are
correlated with the count rate. The two regions evolve in e.g., the size,
resulting in the QPO frequency evolution. Nevertheless, it is unclear how to
sustain a constant frequency ratio when the two QPOs evolve in frequency.

##  5 Summary

We discovered a highly-coherent QPO in the BHXB IGR J17091–3624 that can show
‘heartbeat’-like variability in its 2022 outburst in NICER. Our major findings
are as follows:

  1. 1.

The Q factor reaches $\gtrsim 50$, indicating a high coherence of the QPO.
This is also one of the highest coherence of LFQPOs detected in a BHXB.

  2. 2.

The QPO frequency is in the range of 5–8 Hz, and is positively correlated with
the count rate.

  3. 3.

The QPO amplitude is several percent fractional rms in 1–10 keV. The QPO
amplitude also increases with energy, reaching $\sim 12$–20% fractional rms in
the 7–12 keV band.

  4. 4.

The highly-coherent QPO is detected when the spectrum is dominated by the
accretion disk emission. Therefore, under the conventional A/B/C
classification scheme for LFQPOs, this QPO could either be a Type-C QPO in the
soft state or a Type-B QPO in the SIMS. With the total fractional rms vs QPO
frequency plot, both possibilities are viable. However, the extremely
narrowness of the QPO still hints at a nonidentical origin compared to
conventional LFQPOs.

  5. 5.

This QPO could also be a new type of LFQPO that is only present in sources
that can exhibit ‘heartbeat’-like variability. The hints we see include,
first, highly-coherent LFQPOs are also detected in the other heartbeat source,
GRS 1915+105. Second, the QPO is strongest when accompanied by a noise
component that is likely an extension of the component representing the exotic
variability; the QPO frequency also correlates with the centroid frequency of
this noise component.

  6. 6.

In four observations, we observe two simultaneous QPO components, with a
frequency ratio of $\sim 1.3$ that is inconsistent with a normal 2:1 ratio
observed for LFQPOs, but closer to a ratio of 4:3. We also find the frequency
ratio is constant over the four observations when the QPO frequencies evolve.

We thank Keith Gendreau, Zaven Arzoumanian, and Elizabeth Ferrara for
scheduling and performing the NICER observations. JW acknowledges support from
the NASA FINESST Graduate Fellowship, under grant 80NSSC22K1596. JW thanks
Gibwa Musoke, Megan Masterson, Mason Ng, Navin Sridhar, and Yerong Xu for
useful discussions. JW, EK, JAG, GM, and ML acknowledge support from NASA ADAP
grant 80NSSC17K0515. AI and DA acknowledge support from the Royal Society. TMB
acknowledges the financial contribution from PRIN INAF 2019 n.15.

##  Appendix A PSD analysis on individual observations

As mentioned in Section 2, besides a segment-based PSD analysis, we also
performed a PSD analysis for individual ObsIDs. For each ObsID we created
time-averaged PSDs using segment lengths of 64 s (instead of 500 s), allowing
for more ObsIDs to be included in our analysis. Notably, there are four ObsIDs
in which a LFQPO pair is detected: 5618010602–5618010605. In the segment-based
analysis, only a single QPO pair was detected in Epoch 7 (which combined
ObsIDs 5618010602 and 5618010603), and 5618010604 and 5618010605 were excluded
owing to their short exposure times. The time evolution of the QPO frequency
is shown in the upper panel of Fig. A1. Only QPOs detected with a significance
of $>3\sigma$ are shown, with the exception of the $\sim$7.6 Hz QPO in ObsID
5618010605 (which was only detected at 2.5$\sigma$). The data points are
color-coded according to the fractional rms amplitude of the QPO.

As in the segment-based anaylsis, a clear increase in QPO frequency is
observed starting around MJD 59720. When the second (lower) QPO appears, on
MJD 59727, it increased in frequency along with the upper QPO, while
maintaining a frequency ratio of 1.310$\pm$0.006 (see lower panel of Fig. A1.
While this ratio is close to 4:3, it is not consistent with that value. The
upper QPO showed a sudden drop in rms when the lower peak appeared, from
$\sim$3.5–4.7 % to $\sim$1.7–2.9. After MJD 59731 the upper QPO was no longer
detected, while the lower QPO continued to increase in frequency until MJD
$\sim$59750\. The fact that 1) the two QPOs had a constant frequency ratio
(albeit in a narrow frequency range) and 2) the upper QPO became significantly
weaker when the lower QPO appeared, suggests a connection between the
mechanisms responsible for the two QPOs.

Figure A1: The time evolution of the QPO frequency (upper panel) and QPO
frequency ratio (lower panel, when applicable) for individual NICER ObsIDs.
Data points in the upper panel are color-coded according the their fractional
rms value (for rms scale, see color bar on the right side). The frequency
error uncertainties are generally smaller than the symbol size. The best fit
with a constant to the frequency ratios is depicted by the dashed red line
(value of 1.310); for reference we also show the a 4:3 ratio with a dotted
blue line.

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