11institutetext: Emrah Kalemci 22institutetext: Sabancı University, Faculty of
Engineering and Natural Sciences, Tuzla, Istanbul, 34956, Turkey, 22email:
<EMAIL_ADDRESS>33institutetext: Erin Kara 44institutetext: MIT Kavli
Institute for Astrophysics and Space Research, Cambridge, MA, 02139, USA,
44email<EMAIL_ADDRESS>55institutetext: John A. Tomsick 66institutetext: Space
Sciences Laboratory, 7 Gauss Way, University of California, Berkeley, CA
94720-7450, USA, 66email<EMAIL_ADDRESS>
# Black holes: Timing and spectral properties and evolution

Emrah Kalemci and Erin Kara and John A. Tomsick corresponding author

###### Abstract

We review the timing and spectral evolution of black hole X-ray binary
systems, with emphasis on the current accretion-ejection paradigm. When in
outburst, stellar mass black hole binaries may become the brightest X-ray
sources in the sky. Analysis of high signal to noise data has resulted in a
general framework of correlated X-ray spectral and fast timing behavior during
an outburst. We utilize recent data from small but powerful observatories
launched in the last decade supported by multi-wavelength ground-based
observations. Coordinated observations showed that outflows (in the form of
jets and winds) are an integral part of this evolution, providing a coherent
phenomenological picture that we discuss in terms of the hardness-intensity
diagram and spectral states. We pay particular attention to the evolution of
broad and narrow emission and absorption lines and hard tails in the energy
spectrum, quasi-periodic oscillations, lags and reverberation from fast timing
studies, making the connections with multi-wavelength observations when
relevant. We use the bright outburst of MAXI J1820$+$070 as a recent test case
to discuss different aspects of spectral and timing evolution, but the data
and results are not limited to this source. In the second part of the review,
we discuss competing theoretical models that can explain different aspects of
the rich phenomenology. Data from future missions and simulation results will
have the power to resolve discrepancies in these models and black hole binary
research will continue to be an exciting field that allows for tests of
fundamental physics and studies of the properties of matter in strong
gravitational fields.

##  1 Keywords

black hole physics, accretion, accretion disks, X-rays: binaries, jets

##  2 Motivation

Galactic black hole (BH) research is in the midst of an era of frequent
discoveries thanks to the maturation of data from small, yet powerful space
observatories launched in the last decade, as well as flurry of activity from
bright transients lighting up the X-ray and $\gamma$-ray sky (see Fig. 1).
These new observatories, namely, _Nuclear Spectroscopic Telescope Array_
(_NuSTAR_ Harrison et al. (2013)), _Neutron Star Interior Composition
Explorer_ (_NICER_ Gendreau et al. (2016)), and _Hard X-ray Modulation
Telescope_ (_Insight-HXMT_ Zhang et al. (2014)) provided exciting new results
over those presented in the seminal review of timing and spectral evolution in
X-rays by Remillard and McClintock (2006), and subsequent reviews of different
aspects of the subject Belloni (2010); Gilfanov (2010); Belloni and Motta
(2016); Bambi (2018); Bambi et al. (2020).

Multi-wavelength campaigns have become the norm, with unprecedented
cooperation between groups all over the world to coordinate ground- and space-
based observations to probe the physics of accretion and ejection around BHs.
One of these campaigns for transient source MAXI J1820$+$070 utilized all the
active X-ray observatories at the time with multi-wavelength support. This
source was not only extremely bright, but also extremely rich in terms of
phenomenology observed in other sources which resulted in the publication of
many interesting articles. We used MAXI J1820$+$070 as a case study here for
the discussion of different aspects of spectral and timing evolution of BHs to
highlight contributions of the new observatories on top of the established
framework based on the pioneering research done in the _Rossi X-ray Timing
Explorer_ (_RXTE_ Bradt et al. (1993)) era.

Figure 1: MAXI light curves of four bright outbursts observed between MJD
57600 and MJD 59000.

The review starts with an overview of spectral and timing observational
results in §3 that provides the rich phenomenology of black hole research.
Next, deeper information is provided on the important aspects of the
phenomenology on the observational level, leaving the discussion of the
underlying models in §4. The review finishes with a discussion of what we can
expect in the future with the future observatories in §5.

##  3 Galactic black holes: an observational view

Black hole binary (BHB) systems consist of a black hole and an ordinary star.
Together with neutron star binaries they form a larger class of objects called
X-ray binaries (XRB) in which matter accreted from the companion star may form
an accretion disk around the compact object. The inner parts of the accretion
disk heat up to millions of degrees in the deep gravitational potential well
of the compact object resulting in X-ray emission. XRBs, especially the BHBs
provide natural laboratories where one can, among other things, can study the
effects of General Relativity in strong gravitational field through spectral
and timing studies. In this review, BHB denotes systems with stellar mass
black holes, intermediate mass black hole candidates are not considered.

The first ever discovered BHB is Cyg X$-$1, which is a persistent system and
has a high mass companion (therefore it is a high mass X-ray binary). Since
then, many other BHBs have been discovered. Currently, the number of BHBs
reported is close to 70 (see https://www.astro.puc.cl/BlackCAT/ (Corral-
Santana, J. M. et al., 2016) for an up to date list and references). Most BHBs
turned out to include low mass companions (hence most are low mass X-ray
binaries). Moreover, most BHBs are transients, normally their luminosities are
very low ($L_{\rm x}<10^{33}$ erg/s), and they can only be detected for a
limited amount of time (typically weeks to months) when the mass accretion
rate increases (see Fig. 1). One can compare this luminosity with the
Eddington Luminosity $L_{Edd}$, which is the maximum luminosity for which the
radiation pressure balances the gravitational force towards the compact
object. The Eddington Luminosity is proportional to mass of the object, and
for one solar mass ($M_{\odot}$) it is 1.26 $\times 10^{38}$ erg s-1 (Bambi,
2018). Note that dynamically measured masses of BHBs are typically between
5-10 $M_{\odot}$ (Corral-Santana, J. M. et al., 2016).

A full historical account of the discoveries regarding BHBs and their main
properties is out of scope of this review, interested readers can consult
Remillard and McClintock (2006); Belloni and Motta (2016), and references
therein. The launch of _RXTE_ in 1995 deserves a special mention, as it
revolutionized the field thanks to the large effective area detectors with
unprecedented time resolution, and an all sky monitor (ASM) that allowed many
new outbursts to be detected. Its scheduling flexibility, together with
improved signal-to-noise led to many discoveries and established a
phenomenological landscape that is used in this review as well. In the _RXTE_
era, one of the most important discoveries about the BHBs has been the overall
accretion - ejection paradigm; relativistic outflows detected as jets in the
radio band (§3.3), and winds detected in X-rays (§3.2) were found to be
closely related to X-ray spectral and temporal behavior in an outburst.

The fast timing properties of BHBs are studied in the Fourier domain through
the power spectral density (PSD), frequency-dependent lags and coherence
techniques (§3.4, §3.5). The PSD show both broad and narrow features, and the
narrow features are called quasi-periodic oscillations (QPOs).

Most of the time, BHBs are in a very low mass accretion regime called the
_quiescence_ , or the _quiescenct state_. But in an outburst, they may span
eight orders of magnitude in luminosity, with typical quiescence levels of
below $10^{-5}L_{\rm Edd}$ (Plotkin et al., 2013) to maximum levels of a few
$L_{\rm Edd}$ (Motta et al., 2017). This places them amongst the brightest
X-ray emitters in the sky. During outbursts, BHBs often follow a well known
track when the intensity is plotted against the X-ray hardness called the
“Hardness Intensity Diagram” (HID) Belloni and Motta (2016) as shown in Fig.
2. In this track, sources show distinct and correlated X-ray spectral and fast
timing properties called states. Moreover, the behavior in other wavelengths
(especially in radio and near infrared) is also closely related to the X-ray
spectral states.

Figure 2: The hardness intensity diagram of MAXI J1820$+$070, illustrating the
four main accretion states of a low mass X-ray binary outburst. For each
state, we provide a short description of the key observables. Figure credit:
Jingyi Wang and authors.

Galactic BHs tend to travel counterclockwise in the HID, from the bottom
right, completing a sequence of states before fading into quiescence (see §3.7
for a discussion of sources not following the usual sequence). The outbursts
start in the _hard state_ in which the X-ray spectrum (the navy blue curve in
Fig. 3) is dominated by a hard component associated with inverse
Comptonization of seed photons from inner parts of the disk in a hot electron
corona (see §4.4; §4.3 for a discussion of the origin and geometry) with a
distinct break at tens to hundreds of keV (§3.6). While a softer component
associated with blackbody emission from the disk may exist (§4.1), its
contribution to the X-ray luminosity is low.

A component due to the reflection of hard photons by the disk is often
present, and part of this component is an emission line due to fluorescence of
iron. The shape of the line provides a means to study the effects of strong
gravity on the inner accretion disk material. A broad and often asymmetric
iron line from reflection of disk material close to the black hole is often
seen at higher luminosities but can turn into a narrow iron line at low
luminosities (§3.1).

The power spectral density (PSD) reveals strong broad-band noise (tens of %
RMS) and quasi-periodic oscillations (QPOs, see §3.4 for details). The
observations in the hard state for MAXI J1820$+$070 are shown in navy blue
color in the HID (Fig. 2). The radio spectrum in this state is consistent with
compact, self absorbing jets (Fender, 2001) (§3.3).

Figure 3: The X-ray and $\gamma$-ray spectra of MAXI J1820$+$070 at two times
during its 2018 outburst shown in log-log scale. The red and blue points show
the spectrum of the source in the soft and hard states, respectively.

As the outburst evolves with increasing accretion rate, the soft emission
associated with the disk increases, and a transition to the _hard intermediate
state_ (HIMS) is observed. The emission from the corona becomes softer as well
(if modelled with a power-law spectrum, the spectral index increases compared
to those in the hard state). Type C QPOs are still present and the overall
root mean square variability (RMS) is still high, but the RMS drops with
increasing disk flux (see Fig. 6).

In some sources, there is a sudden transition to a softer state called the
_soft intermediate state_ (SIMS) manifested with a radio flare, a decreased
continuum RMS amplitude of variability and appearance of a Type B QPO (see
Fig. 6, §3.3, and §3.4). Some sources show rapid transition back and forth
between the HIMS and the SIMS Belloni et al. (2011). The observations in HIMS
and SIMS for MAXI J1820$+$070 are shown in blue and orange, respectively, in
the HID (Fig. 2)

As the disk emission becomes more dominant, another transition takes place to
the _soft state_. In this state, the emission from the corona is very weak
(the contrast can be seen in Fig. 3). The soft $\gamma$-ray spectrum extends
without a break up to a few MeVs Grove et al. (1998). The RMS variability is
very low (a few % RMS, see Fig. 6) and QPOs are absent. The observations in
the soft state for MAXI J1820$+$070 are shown in red in the HID (Fig. 2).
Radio emission is quenched by 3.5 orders of magnitude (Russell et al., 2019),
indicating that the jets are absent; however, high resolution X-ray spectral
observations indicate presence of an equatorial wind in high inclination
sources (Ponti et al., 2012) (§3.2).

As the disk flux starts to decrease, the source may go through the SIMS and
HIMS and eventually ends up at the hard state again Belloni and Motta (2016).
The transition back to the hard state takes place at a much lower flux
compared to the transition to the softer states during the outburst rise
(sometimes this behavior is called ”hysteresis”). There are also indications
that the transition back to the hard state occurs at a fixed bolometric
luminosity (Maccarone, 2003; Vahdat Motlagh et al., 2019). As the luminosity
goes even lower, some sources show a softening in their spectrum before they
fade to quiescence (Kalemci et al., 2013; Plotkin et al., 2013).

A few important additional items should be noted at this point. For papers
before and in the early _RXTE_ era, the hard state and the soft state were
denoted as the low state and the high state, respectively. While using
”high/low” instead of ”soft/hard” state could be justified if only the soft
X-rays are considered, when X-ray bolometric luminosities are used, the hard
state rise luminosities can exceed the soft state luminosities Dunn et al.
(2010). This is also evident in Fig. 3. Sometimes terms like high soft state
and low hard state are used as well Belloni and Motta (2016). A few sources
divert to a very luminous (close to or exceeding the Eddington Luminosity) and
soft state called the ultra-luminous, hyper-soft or anomalous state Belloni
(2010). For in depth discussion of different definitions of states, see
Belloni (2010).

While the hardness intensity diagram is extremely useful to see the big
picture in terms of spectral states, it does not provide the details that may
be very important to characterize the source behavior. For example, it is not
clear how fast the evolution takes place in different states; while the
intermediate states span a wide range in hardness in MAXI J1820$+$070 (see
Fig. 2), they lasted for 20 days. In contrast, the source spent more than 100
days in the initial hard state Shidatsu et al. (2019). For other useful
diagrams utilized in describing especially the timing properties of states,
see references in Belloni and Motta (2016).

###  3.1 Iron lines

The X-ray spectra of accreting BHs often show a reflection component that is
formed when hard X-rays irradiate the disk. This component includes a
fluorescent iron emission line, an iron absorption edge, and a broad excess
peaking at tens of keV (Lightman and White, 1988; Fabian et al., 1989).
Relativistic velocities of the disk material and a redshift from the BH’s
gravitational field distort the reflection component (Laor, 1991). Although
the the entire reflection component is affected, the distortion is most
apparent in the iron K$\alpha$ emission line, and this is clearly seen in both
Active Galactic Nuclei (Tanaka et al., 1995) and stellar mass black holes
(Miller, 2007).

Although sources do not show reflection components at all times, and some
sources do not show them at all, the presence of reflection is common. The
majority of sources have reflection components, and they can occur in a
variety of spectral states. For example, Cyg X$-$1 exhibits a strong
reflection component in its hard state (Nowak et al., 2011; Parker et al.,
2015), its soft state (Walton et al., 2016), and its intermediate state
(Tomsick et al., 2018). GX 339$-$4 is an active BH transient with a well-
studied reflection component in multiple spectral states (e.g., Zdziarski et
al., 1998; Parker et al., 2016).

Figure 4: A possible physical scenario for the X-ray production based on the
model used to fit hard state spectra of MAXI J1820$+$070 in Buisson et al.
(2019). We thank Dr. Javier Garcia for providing a first version of this
figure.

The velocities in the inner portions of the disk can exceed 10% of the speed
of light, producing a symmetric distortion of close to 1 keV at the 6.4 keV
energy of the iron emission line. The gravitational effect produces an
asymmetric distortion, which leads to a red wing of the emission line. A main
goal of modeling the iron line and reflection component is to measure the
location of the inner edge of the accretion disk ($R_{\rm in}$). If the disk
extends to the innermost stable circular orbit (the ISCO), then measuring
$R_{\rm in}$ provides a measurement of the BH spin. Even if the disk is
slightly truncated and does not reach the ISCO, the $R_{\rm in}$ measurement
still provides a lower limit on the BH spin.

Some spectral and timing measurements can be interpreted as the disk becoming
highly truncated for sources in the hard state (Tomsick et al., 2009; Plant et
al., 2015; De Marco and Ponti, 2016; Xu et al., 2020), while other
measurements are not indicative of truncation (Miller et al., 2015). Most
observations that suggest a high level of truncation have occurred for sources
that are at low luminosities near 0.1% Eddington. At these low luminosities,
the iron line profile changes from having a relativistic profile to a
relatively narrow line, which provides a low limit on $R_{\rm in}$ (Tomsick et
al., 2009; Plant et al., 2015; Xu et al., 2020). However, the relativistic
iron line seen at high luminosities in the hard state leaves it unclear
precisely when the disk becomes truncated. Determining the location of $R_{\rm
in}$ and characterizing its evolution in the hard state is an active area of
research (e.g., Wang-Ji et al., 2018).

The iron line and other spectral components are illustrated in Fig. 4. The
spectrum shown of MAXI J1820$+$070 in the hard state is based on modeling of a
_NICER_ and _NuSTAR_ spectrum. The two direct components are the thermal disk
emission at low energies and the coronal emission, which is modeled as being
produced by Comptonization by high-energy electrons in the jet with a thermal
distribution. Fig. 4 illustrates the source geometry used in work by Buisson
et al. (2019). We discuss possible source geometries, which are likely state-
dependent, in §4.3. The properties of the reflection component provide
motivation for the double-lamppost since many sources have reflection
components that combine relativistic reflection from the inner disk and non-
relativistic reflection from the outer disk.

_NuSTAR_ has enabled advances in reflection and iron line studies for a number
of reasons. _NuSTAR_ ’s 3–79 keV bandpass is very well-matched to measuring
the reflection component. Its advantages over _RXTE_ are its much better
energy resolution as well as improved sensitivity (especially at the high-
energy part of the bandpass) due to lower background. _NuSTAR_ also provides
advances over CCD instruments like those on _XMM-Newton_ and _Suzaku_ by
providing sensitive measurements at higher energies. In addition, photon pile-
up can lead to spectral distortion in CCD instruments (Done and Diaz Trigo,
2010; Miller et al., 2010) which is not trivial to account for. Although pile-
up can often be mitigated by using certain detector modes or by modeling the
pile-up effects, it is a significant source of systematic uncertainty for
bright sources. However, _NuSTAR_ has a triggered readout system that is not
susceptible to pile-up. The _NuSTAR_ advances in bandpass and avoiding pile-up
have occurred along with advances in reflection modeling by making the models
more physically realistic (García et al., 2014). These advances have increased
the reliability of the modeling technique as a tool to measure the properties
in the inner accretion disk, including the inner disk radius and the spins of
black holes.

###  3.2 Absorption lines and winds

High resolution spectral observations of BHBs revealed the presence of
absorption lines (see Fig. 5, Left) blue shifted by up to a few thousand km
s-1, showing that these sources not only produce collimated jets but can also
drive winds. The lines are mainly hydrogen- and helium-like iron K${\alpha}$,
indicating material that is strongly photoionized by the X-ray illumination
from the central source (see reviews by Ponti et al. (2012, 2016); Díaz Trigo
and Boirin (2016)).

The wind is an important component in the accretion flow as the mass outflow
rate in this component can exceed the mass accretion rate through the disk
(Ponti et al., 2012; King et al., 2012). It is also one of the determining
factors in the general outburst profile and duration (Dubus et al., 2019;
Tetarenko et al., 2020). Winds are observed across the black hole mass scale
(King et al., 2013, and references therein), and a comparison of their
properties in supermassive BHs and Galactic BHs can provide clues about the
driving mechanisms of the winds.

Figure 5: Left: Chandra grating spectrum of GRO J1655$-$40 in the soft state.
Figure credit: Adapted, NASA/CXC/U.Michigan/J.Miller et al. Miller et al.
(2006). Right: The hardness luminosity diagram of high inclination LMXBs,
combined with detection (circles) and upper limits (triangles) of key wind
absorption feature. Gray circles show all observations from all sources, and
colored circles and triangles are from high inclination BHBs. Figure credit:
Ponti et al. Ponti et al. (2012).

Whether we can observe evidence of winds in X-rays depends on the spectral
state and disk inclination: wind signatures are preferentially detected in
soft states for high inclination sources (see Fig. 5, Done et al., 2007; Ponti
et al., 2012). The inclination effect indicates that the plasma has a flat,
equatorial geometry above the disk providing large amount of material in the
line of sight. Wind signatures are also imprinted in the optical emission
lines of He and H as P Cygni profiles and broad emission line wings (Muñoz-
Darias et al., 2019, and references therein). These “cold winds” are detected
in the hard state. In fact, similar near infrared line features obtained by
VLT/X-Shooter indicate that the cold winds are present throughout the outburst
in both soft and hard states (Sánchez-Sierras and Muñoz-Darias, 2020). See
§4.2 for a discussion of competing models to explain the origin of winds in
BHBs.

###  3.3 Radio and near infrared emission and jets

In addition to the accretion disk, corona and winds observed in the X-ray
band, XRBs are also known to launch powerful jets that are most clearly
observed through synchrotron emission in the radio to infrared (IR). These
jets are capable of carrying away a significant amount of the accretion energy
and depositing large amounts of energy into their surrounding environments
Gallo et al. (2005); Russell et al. (2007); Tetarenko et al. (2017). Radio
emission is only detected in the hard state and during the state transition.
Thus, it is clear that the launching mechanism is somehow related to the
accretion process, but the causal connection between accretion and ejection
and how these relativistic jets are launched, collimated and accelerated
remain open questions. Here we describe the properties of the radio and IR
emission during a the black hole outburst, and observational efforts to probe
the disk-jet connection.

At the beginning of an outburst, when the X-ray emission is spectrally hard,
the radio and IR show a steady, compact (AU-sized) jet Dhawan et al. (2000);
Corbel et al. (2000); Fender (2001); Stirling et al. (2001); Fender et al.
(2004). The radio-to-mm spectral energy distribution (SED), shows a flat or
inverted spectrum that extends up to $\sim 10^{13}$ Hz, beyond which the jet
becomes optically thin, and the spectrum steepens. This frequency of the
spectral break is thought to be set by the location in the jet where particle
acceleration begins: higher frequencies correspond to an acceleration zone
that is closer to the black hole. In a typical outburst, as the accretion rate
increases throughout the hard state, the spectral break is observed to evolve
to lower frequencies (down to the radio band), which has been interpreted as
being due to the particle-acceleration region moving further from the black
hole.

During the transition from hard to soft state, the steady, compact jet turns
off, but that is not the end of the story for the jet. In several cases where
high-cadence radio monitoring was possible, the end of the state transition
was marked by rapid flaring in radio before completely shutting down in the
soft state. The flares have been associated with the ejection of discrete
knots of plasma moving away from the black hole at relativistic velocities
(e.g. Mirabel and Rodríguez (1994); Fender and Belloni (2004); Bright et al.
(2020)). No compact radio core is observed in the soft state, but one can
observe residual and spatially extended radio emission from ejecta launched
during the state transition. In some cases, these knots can reach separations
of tens of thousands of times farther than the jet core. In the remarkable
case of MAXI J1820$+$070, Bright et al. (2020) discovered that during the
state transition, an isolated radio flare from the compact core expanded to a
spatially extended, bi-polar, relativistic outflow that was also detected in
the X-rays, likely due to shocks from the jet ejecta interacting with the
interstellar medium (Corbel et al., 2002; Espinasse et al., 2020).

The dramatic change in both the jet (as observed in radio) and the inner
accretion flow (as probed in X-rays) during an outburst motivated studies
correlating these two wavelengths in order to better understand their
connection. Indeed, the strong correlation between X-ray and radio luminosity
suggests that an increase in the mass accretion rate onto the black hole
results in an increase in mass loading in the jet Hannikainen et al. (1998);
Corbel et al. (2002); Gallo et al. (2003). This same correlation is even seen
in supermassive black holes when scaled properly for black hole mass Merloni
et al. (2003); Falcke et al. (2004). While early studies suggested X-ray
binaries in outburst exist on a single track, such that
$L_{\mathrm{radio}}\propto L_{\mathrm{X}}^{\sim 0.7}$ Corbel et al. (2002), in
a large population study, Gallo et al. (2012) showed that there were two
populations: one that is “radio-loud” and another “radio-quiet”, which may be
related to changes in the radiative efficiency of the accretion flow
throughout the outburst Casella and Pe’er (2009); Koljonen et al. (2018);
Espinasse and Fender (2018) and/or variations in observed luminosity due to
inclination affects Zdziarski et al. (2016); Motta et al. (2018); Muñoz-Darias
et al. (2013); Heil et al. (2015); Motta et al. (2015).

Beyond correlations in population studies, cross-correlation between the X-ray
band and radio/IR/optical bands on timescales as short as milliseconds, have
revealed insights into the causal connection between these emitting regions.
Several systems show a rapid IR/optical lag of $\sim 0.1$ s behind the X-rays
Gandhi et al. (2008, 2017); Vincentelli et al. (2019); Paice et al. (2019),
which has been interpreted as being due to the propagation delay between the
X-ray corona and the first IR/optical emission zone in the jet, and thus
constrains the physical scale over which plasma is accelerated and collimated
in the inner jet Jamil et al. (2010); Malzac (2013, 2014). This model can also
explain the observed lag on a timescale of $\sim$minutes between radio and
sub-mm bands, as the propagation front moves outwards in the jet. In addition
to these lags, other tantalizing broadband timing properties are observed in
several sources, but their origins remain a topic of debate, including: an
anti-correlation of the X-ray and optical/IR at zero-lag (e.g., Veledina et
al. (2011); Paice et al. (2021)) and quasi periodic oscillations (QPOs) at
same temporal frequency in both X-ray and optical/IR Vincentelli et al.
(2021). Simultaneous, fast photometry observations in X-rays and longer
wavelengths are challenging to coordinate, and the field is relatively young.
Future coordinated campaigns at several points in the outburst have the
potential to be a powerful tool for probing disk-jet connection in X-ray
binaries.

###  3.4 Quasi-periodic oscillations

QPOs are a tantalizing phenomenology commonly observed during black hole
outbursts, where variability power is concentrated in a narrow frequency range
(Fig. 6). Their origin is still debated, but much progress has been made in
the last decade to understand the physics behind these striking features. QPOs
broadly take the form of “low-frequency QPOs” (LFQPO, in the temporal
frequency range of $\sim 0.005-40$ Hz) and “high frequency QPOs” (HFQPO,
observed at $\sim 40-450$ Hz). There is a rich phenomenology and an admittedly
confusing nomenclature, which we attempt to distill below. We refer readers to
more thorough descriptions of QPOs in Casella et al. (2005), Belloni (2010)
and Ingram and Motta (2019).

Figure 6: The power spectral density of MAXI J1820$+$070 in four spectral
states. The colors match the spectral types in Fig. 2. Figure credit: Jingyi
Wang.

#### Low-Frequency QPOs

As the source emerges in the hard state (dominated by the hard Comptonization
component), the variability is very strong over a wide range of timescales
(resulting in a broadband noise PSD that is often phenomenologically modelled
as several broad Lorentzian components with fractional RMS of $\sim 30$%).
Just as the spectra are observed to change dramatically, so too do the
variability properties. As the source flux increases in the hard state, the
variability becomes more rapid, resulting in a shifting of the broad
Lorentzians to higher frequencies. Often the variability becomes more
concentrated at particular frequencies, resulting in the appearance of
coherent QPOs. These particular hard and HIMS state QPOs are known as “Type C
QPOs,” and are by far the most common type of QPO observed in black hole XRBs.
They occur in a frequency range of $\sim 0.05-30$ Hz, often accompanied by
their higher order harmonics.

Type C QPOs have been known for decades (first seen with Ariel 6 observations
of GX 339$-$4; Motch et al. (1983)), and their origin remains elusive, but a
major break-through came in 2015 when Motta et al. (2015) and Heil et al.
(2015) discovered that the strength of the Type C QPO is dependent on the
inclination of the binary orbit. More edge-on systems show stronger Type C QPO
amplitudes. This suggests that the origin of Type C QPOs is geometric rather
than due to intrinsic resonances in the accretion flow. Moreover, Ingram et
al. (2016) found in one source, H1743-322, that the iron line centroid energy
shifts with QPO phase, which gives stronger credence to geometric models.
Possible origins of Type C QPOs are discussed in detail in Section 4.6.

Entering the HIMS, more power is concentrated in the QPOs and the broadband
noise level diminishes to a fractional RMS value of $\sim 10$%. The frequency
of the Type C QPOs continues to increase throughout the HIMS, until suddenly
the Type C QPO vanishes and is replaced by a Type B QPO, which typically
occurs in a narrower frequency range (1–6 Hz) and generally has a lower
variability amplitude than Type C QPOs. The presence of the Type B QPO marks
the transition to the SIMS. Type B QPOs are less commonly observed than Type C
QPOs, but this may simply be due to the fact that they are short-lived. In
MAXI J1820$+$070 the Type C QPO (and harmonics) were observed for $\sim 100$
days, while the Type B QPO was seen in half of one observation for just a few
hundred seconds. The Type B QPO has long been suspected to be associated with
the transient ballistic jet seen in the SIMS, and in MAXI J1820$+$070 Homan et
al. (2020) showed the clearest connection to date between these phenomena. The
Type B QPO was detected 1.5–2.5 hours before the radio jet flare. Type B QPOs
also show an inclination dependence (again suggesting a geometric origin), but
unlike Type C QPOs, they are stronger in face-on systems.

The soft state, when the accretion disk dominates the spectrum, shows very
little variability on the $\sim$hour timescale of a typical observation (i.e.
a fractional RMS of $<3$%). The PSD is often described by a single broad
Lorentzian or broken powerlaw, usually with no low-frequency QPOs, though in
the RXTE era, a handful of so-called Type A QPOs were found (Wijnands et al.,
1999). No Type A QPOs have been seen by NICER, and (Casella et al., 2005)
suggest Type A QPOs are, in fact, a subset of Type B QPOs. As the source
transitions back to the hard state, at the end of the outburst, the Type C
QPOs return, and the broadband variability increases again.

#### High-Frequency QPOs

HFQPOs have properties that are distinct from LFQPOs. In addition to having
higher frequencies, they tend to appear near certain characteristic values,
such as the 67 Hz HFQPO seen from GRS 1915$+$105 (Morgan et al., 1997) and the
66 Hz signal from IGR J17091$-$3624 (Altamirano and Belloni, 2012). They are
relatively weak with typical RMS amplitudes of several percent or less;
however, their strength often increases strongly with energy (Morgan et al.,
1997; Remillard and McClintock, 2006; Strohmayer, 2001). They have been
detected at high significance by _RXTE_ from at least four accreting BH
systems (the two mentioned above, GRO J1655$-$40, and XTE J1550$-$564), and at
lower significance for five or six more (Remillard and McClintock, 2006;
Belloni et al., 2012). They have also been detected by AstroSat for GRS
1915$+$105 (Sreehari et al., 2020).

For GRO J1655$-$40, by searching the 13–30 keV band, Strohmayer (2001) found a
signal at 450 Hz, which is the highest frequency that has been observed. When
combined with the measured mass of the BH in this system, the frequency
corresponds to an orbital time scale at a radius smaller than the ISCO of a
non-rotating BH, providing evidence that the GRO J1655$-$40 BH must have non-
zero spin (Strohmayer, 2001; Motta et al., 2014). Thus, these signals are of
high interest as they probe the innermost regions of the accretion disk. The
origin of these signals is not known, but theoretical models have been
developed to explain why systems with multiple signals have frequencies that
cluster around a 3:2 ratio, such as the 41 and 67 Hz HFQPOs in GRS 1915$+$105,
the 300 and 450 Hz HFQPOs in GRO J1655$-$40, or the 180 and 280 Hz HFQPOs in
XTE J1550$-$564\. However, while the 3:2 ratio was originally thought to be a
defining characteristic of HFQPOs, further analysis has shown that at least
some (and perhaps most) of the 3:2 ratios are spurious (Belloni et al., 2012;
Ingram and Motta, 2019).

HFQPOs are relatively rare, and, in most cases, they were found only by
intense monitoring of sources with _RXTE_. Belloni et al. (2012) find that the
XTE J1550$-$564 HFQPOs are most often seen when the source is in the SIMS, but
they conclude that HFQPOs are not only seen in the SIMS. However, the
detection of HFQPOs does appear to require that the source has strong thermal
and power-law components (Remillard and McClintock, 2006). _RXTE_ ’s
combination of hard X-ray bandpass and large effective area enabled it to
obtain HFQPO detections. NICER’s soft X-ray bandpass is not as well-suited,
and it is also difficult for _NuSTAR_ to detect HFQPOs due to its smaller
effective area than _RXTE_ ’s Proportional Counter Array and its relatively
high level of deadtime for bright sources. _Insight-HXMT_ , with its broad
energy band, large detection area and favorable pile-up properties is well
suited for HFQPO detection (Zhang et al., 2014), however, no HFQPO detection
from BHBs has been reported with this observatory at the time of writing this
review.

###  3.5 Lags and reverberation

Figure 7: Left: The frequency-dependent time lags between the ‘soft band’
(0.3–1 keV) and the ‘hard band’ (1–4 keV) for MAXI J1820$+$070 in one hard
state observation and the HIMS. By convention, the soft lag is defined to be
negative, and is the feature interpreted as due to reverberation lags between
the coronal continuum and reflection off the accretion disk. The colors match
the spectral types in Fig. 2. The soft lags become larger in amplitude and
lower in frequency during the state transition. Figure credit: Jingyi Wang.
Right: The results of a systematic search for soft reverberation lags in 10
black hole LMXBs (Wang et al. (2022)), where the HID for all sources has been
linearly scaled to that of MAXI J1820$+$070 . The colored markers indicate
sources where soft lags were detected, and the color and marker size indicate
the amplitude of the lag. The lags are shortest in the bright hard state, and
become significantly longer during the state transition.

While the power spectrum is the amplitude of the Fourier transform of a given
light curve, much information is also contained in the phase, and in
particular the phase difference between different energy bands (see Fig. 7).
For a detailed review on Fourier-resolved time lag techniques and modeling, we
encourage readers to see Uttley et al. (2014). Here, we provide a short
history of the field, with particular focus on new results from XRBs and how
the lags evolve with spectral state.

Fourier-resolved time lags in stellar-mass black holes were first discovered
with _RXTE_ in the hard state of the high-mass X-ray binary, Cyg X$-$1
Miyamoto et al. (1988); Nowak et al. (1999); Pottschmidt et al. (2000). In
this source, hard photons were observed to lag soft photons on long timescales
(low Fourier-frequencies $<1~{}Hz$). Indeed, similar low-frequency hard lags
have also been seen in Active Galactic Nuclei (first in Papadakis et al.
(2001)), and during the hard state in low-mass X-ray binaries Uttley et al.
(2011), but are not typically observed in the soft state of LMXBs, when
variability amplitudes are too low. The low-frequency hard lags are typically
0.1 s or longer, and thus are unlikely to arise from a light travel time lag,
which would imply that the corona is thousands of gravitational radii ($R_{\rm
g}$ = $GM/c^{2}$) Nowak et al. (1999). Thus the prevailing interpretation is
that these lags are related to the radial inflow (i.e. viscous) timescale
Kotov et al. (2001), as mass accretion rates propagate inwards through the
accretion disk Lyubarskii (1997). As such, these lags are often referred to as
propagation lags or continuum lags.

More recently, time lag studies have expanded to higher Fourier frequencies,
revealing a new phenomenology: the high-frequency soft lag. First discovered
with _XMM-Newton_ in the hard state of GX 339$-$4 Uttley et al. (2011), these
lags are interpreted as due to the light travel time between the X-ray corona
and the accretion disk, though how the observed lags translate to the exact
truncation radius of the disk or the height of the corona is still debated
(see Section 4.3). De Marco et al. (2015) expanded these studies of GX 339$-$4
in the rise in the hard state, and found that the lag amplitude decreased
during the hard state, which was interpreted either as the truncation radius
of the disk moving inwards or the corona contracting before the state
transition. Pile-up in _XMM-Newton_ timing mode precluded the spectral
confirmation of this picture by simultaneous mapping of the iron line profile.

Now NICER has revolutionized spectral-timing studies thanks to its high
throughput, good energy resolution with virtually no pile-up that allows us to
measure both the time lags and spectra simultaneously. Kara et al. (2019)
studied the luminous hard state of the bright XRB MAXI J1820$+$070 and
discovered that before the state transition, the reverberation lags evolved to
higher frequencies with a smaller amplitude lag. During this same period, the
broad iron line profile remained constant, suggesting that the truncation
radius did not change, and rather, the vertical extent of the corona
decreased. Recently, Wang et al. (2021) and De Marco et al. (2021) discovered
that during the state transition, days before the detection of a radio flare
and a Type B QPO, the reverberation lag suddenly increased in amplitude (and
decreased in Fourier frequency; Fig. 7-left). Both papers suggest this result
indicates that the hard-to-soft transition is marked by the corona expanding
vertically and launching a jet knot that propagates along the jet stream at
relativistic velocities. Most recently, Wang et al. (2022) performed an
automated NICER search for time lags in black hole LMXBs, and discovered that
the longer reverberation lags during the state transition is not only observed
in MAXI J1820+070, but is common behaviour in black hole transients (Fig.
7-right).

Not only are time lags associated with the broadband noise, but also
distinctive lags are observed in Type C Altamirano and Méndez (2015);
Karpouzas et al. (2021); Méndez et al. (2022); Zhang et al. (2022) and Type B
QPOs Stevens et al. (2018); García et al. (2021). Some sources show hard QPO
lags, while others show soft lags, which may be determined simply by
inclination effects (low orbital inclination sources show hard lags, while
high-inclination sources show soft lags; van den Eijnden et al. (2017)) or
perhaps is indicative of time-dependent radiative properties of the corona
Méndez et al. (2022), where the balance of heating and cooling of the corona
can lead to hard or soft QPO lags Karpouzas et al. (2021); Zhang et al.
(2022). The latter model was recently applied to $Insight-HXMT$ observations
of the low-frequency QPOs of MAXI J1535$-$571 during the transition from HIMS
to SIMS, and inferred that the corona extends vertically during the state
transition (similar to inferences from the broadband reverberation lags
described above; Wang et al. (2021); De Marco et al. (2021); Wang et al.
(2022)). Méndez et al. (2022) recently compared the inference from this
variable Comptonization model to the radio jet luminosity in GRS 1915$+$105,
which also suggests a connection between the powering of the corona and the
relativistic jet.

High-throughput instruments with moderate energy resolution are
revolutionizing our understanding of LMXBs, allowing for modeling of both the
timing and spectral products. Time lags are an example of one such technique
where the energy and time-dependence of the photons are accounted for in the
models. Frequency-resolved spectroscopy is another technique that allows
obtaining the energy spectrum of the X-ray flux variations on different time
scales. It has been applied to very bright sources to probe the geometry of
the black hole vicinity (Revnivtsev et al., 1999; Baby and Ramadevi, 2022), as
well as to study the origin of QPOs (Axelsson and Done, 2016). Other examples
of important spectral-timing techniques include: phase-resolved spectroscopy
(e.g. Stevens et al. (2018); Ingram et al. (2016)), cross-spectral analysis
(e.g. Mastroserio et al. (2019)), and the bispectrum (e.g. (Arur and
Maccarone, 2022)).

###  3.6 Soft $\gamma$-rays and Polarization

The observations with the OSSE instrument on the _Compton Gamma-ray
Observatory_ provided the first evidence of the distinct hard X-ray (from
$\sim$10 keV to a few hundred keVs) - soft $\gamma$-ray (from a few hundred
keVs to a few MeVs) behaviour in the hard and the soft states of BHBs. In Cyg
X$-$1, the hard state shows a break at around 100 keV while the soft state
emission has no break up to the MeV range Grove et al. (1998). This behavior
has been seen in many sources, and can also be observed for MAXI J1820$+$070
in Fig. 3. The spectra are consistent with thermal Comptonization in the hard
state, thereby providing a measure of the electron temperature and the optical
thickness in the corona, and non-thermal Comptonization in the soft state from
electrons with an initial power-law energy distribution Coppi (1999).

The game changer in understanding the high energy emission behavior of BHBs
has been the $INTEGRAL$ Observatory with a combination of sensitive
instruments operating in the hard X-ray and soft $\gamma$-ray bands (as well
as a softer X-ray instrument) and its ability to perform uninterrupted
observations with a large field of view. A recent review by Motta et al.
(2021) discusses the contribution of the $INTEGRAL$ observatory in BHB
research in detail, and only a few highlights are presented here.

One of the most important contributions of $INTEGRAL$ has been the
confirmation and detailed investigations of a soft $\gamma$-ray tail in the
spectra of several BHBs in the hard and the hard intermediate states extending
up to the MeV energies. Equally important discovery made by $INTEGRAL$ is the
polarization measurement of Cyg X$-$1 in the soft $\gamma$-ray band showing
that the polarisation fraction increases with energy (from less than 20% below
$\sim$230 keV, to greater than 75% above $\sim$400 keV, Laurent et al. (2011);
Jourdain et al. (2012)). Soft X-ray (at 2.6 keV and 5.2 keV) polarization
measurements of Cyg X$-$1 performed with $OSO-8$ indicate a relatively low
(compared to soft $\gamma$-ray measurements) polarization level of 2-5% with
low significance Long et al. (1980), consistent with the decreased
polarization fraction with decreasing energy.

Historical soft $\gamma$-ray band observations also claimed narrow and broad
features associated with positron annihilation; a broad feature in Cyg X$-$1
measured with $HEAO1$ Nolan and Matteson (1983), a narrow line for Nova Muscae
Sunyaev et al. (1992) and a broad and variable feature in 1E1740.7–2942
Bouchet et al. (1991) measured with SIGMA on $GRANAT$. Recently, using the SPI
instrument on $INTEGRAL$, a detection of a broadened 511 keV annihilation line
during a strong flaring activity in the 2015 outburst of V404 Cyg has been
claimed Siegert et al. (2016), yet other groups failed to detect the same
feature in the same dataset Roques and Jourdain (2019); Jourdain et al.
(2017). Comprehensive searches for annihilation line features with IBIS and
SPI on $INTEGRAL$ did not find any point source, and the emission in the
associated band is consistent with diffuse positron-annihilation De Cesare
(2011); Tsygankov and Churazov (2010). MAXI J1820$+$070 is no exception as a
detailed analysis of the soft $\gamma$-ray region extending up to 2 MeV with
PICSiT and SPI on $INTEGRAL$ only provided a strong upper limit to an
annihilation line feature. The non-detection, together with the Comptonization
model parameters allowed a calculation of the electron-positron pair density
which is turned out to be low Zdziarski et al. (2021b).

Finally, observational campaigns have been performed during the state
transitions with $RXTE$ as well as with $INTEGRAL$ in the hard X-ray band to
characterize the evolution of the break frequency (or cut-off frequency
depending on the spectral model used) and other spectral parameters to
understand the possible physical changes in the accretion environment during
transitions. GX 339$-$4 in the 2004 outburst showed a rapid transition ($<$10
hrs) from the HIMS to SIMS with significant changes happening in the break
frequency and the timing properties Belloni et al. (2006). The evolution of
the break energy during the transitions are quite complex, decreasing during
the hard state to the HIMS, and then increasing, disappearing, or moving
beyond the detection range towards the transition to SIMS Motta et al. (2021).

###  3.7 Outliers in hardness intensity diagram evolution

There are a significant number of exceptions to the standard path taken by BH
transients in the HID. For example, there are many cases of “failed outbursts”
that do not reach the SIMS and soft state, and there are also “hard-only”
outbursts that do not even make it into the HIMS (Motta et al., 2021). These
differences in the HIDs occur on an outburst-by-outburst basis, and Fig. 8
shows different outburst types for the same source. While some sources may
more often have one type or another type of outburst, a single BH transient
can exhibit regular, failed, and hard-only outbursts. Thus, the difference may
be related to different mass accretion rates between outbursts or perhaps
different properties of the disc (e.g., magnetic field) or jet.

There are also some interesting accreting BH sources that have unusual aspects
of their HID behavior. Cyg X$-$1 is a persistent source and makes transitions
between the hard and soft states, but its luminosity remains unchanged to
within about 15% (Zhang et al., 1997). Thus, it occupies a relatively narrow
range of intensity in the HID. GRS 1915$+$105 can show extremely rapid flux
oscillations with distinctive and repeating patterns. At times, these
oscillations occur while GRS 1915+105 is restricted to the bright and soft
part of the HID. Combining X-ray, radio, and near-IR measurements provides
evidence for a connection between the X-ray oscillations, which are presumably
related to disk instabilities, and jet production (Fender and Belloni, 2004).

Although less common, there are also cases where the hardness-intensity path
differs from regular outbursts. Low-soft states have been seen in the
persistent BH systems 1E 1740.7–2942 and GRS 1758–258. Both of these sources
spend the vast majority of their time in the hard state, but they will
occasionally decrease in flux and transition to the soft state (Smith et al.,
2001). This has also been seen in the BH transient Swift J1753.5–0127, which
showed a very similar behavior at one point during an outburst that lasted
over a decade (Shaw et al., 2016). It has been suggested that this phenomenon
may be due to the presence of two accretion flows, a thin disk and a hot halo
(Smith et al., 2002). The low-soft states can be naturally produced if the
time scale for changes in mass accretion rate to propagate through the disk
are different in the two flows.

Figure 8: HIDs from the BH transient 4U 1630–47 during a regular outburst from
1998 and during a clockwise outburst in 2002-2003. The data are from _RXTE_ ,
and the hardness ratio is the 9-20 keV count rate divided by the 3-9 keV count
rate. The count rate on the vertical axis is the 3-20 keV count rate. Adapted
from (Tomsick, 2006).

Another BH transient that shows low-soft states is 4U 1630–47 (Tomsick et al.,
2014). Approximately 20 outbursts have been seen from this source going back
to 1969. In 1998, it showed a regular outburst rising in the hard state and
moving in a counter-clockwise direction through the HID (Fig. 8). However,
most of the 4U 1630–47 outbursts show the opposite pattern with the source
taking a clockwise path through the HID. Although the reason for this
difference is not known, it has some relationship to the the strength of the
jet because 4U 1630–47 typically shows weak or undetectable radio emission
during outbursts, but the strongest radio emission seen from 4U 1630–47
occurred during the 1998 outburst (Hjellming et al., 1999).

##  4 Modelling and Interpretation

In this section, the emphasis will be on the physical explanations and the
models put forward to explain different aspects of observations discussed
earlier. Due to page limitations, only major models have been discussed.
However, references to recent reviews for more comprehensive coverage are
provided in each section.

###  4.1 Thermal disc modelling

Accreting black holes often have a strong thermal component in their spectra
(see Fig. 3), especially (but not exclusively) when they are emitting at high
luminosities. This component is very well-described by a multi-temperature
disk, which is approximated by adding the contributions of blackbody emission
from many annuli in the disk. A theoretical temperature vs. radius profile
(Shakura and Sunyaev, 1973) can be used to determine the temperature for each
annulus. The simplest and often used version of this model is the “disk-
blackbody” model (Mitsuda et al., 1984), and it is specified by the inner disk
temperature and a normalization. The normalization depends on the apparent
inner radius, the distance to the source, and the inclination of the disk.
With corrections described in Kubota et al. (1998), a physical value for the
inner radius ($R_{\rm in}$) can be estimated. Measuring $R_{\rm in}$ is of
great interest since it is a key disk geometry parameter, having implications
for what happens during state transitions as well as providing an opportunity
to measure the spin of the BH, $a_{*}$ (Middleton, 2016).

Using the measurement of $R_{\rm in}$ to determine $a_{*}$ is only justified
if the inner edge of the optically thick disk is at the innermost stable
circular orbit (ISCO). In addition to the properties of the thermal component,
there are other observational lines of evidence that the disc reaches near to
or to the ISCO. The red wing of the iron emission line (see §3.1) shows that
the emission reflected from the disc comes from the direct vicinity of the BH.
Similarly, the HFQPOs must originate from very close to the ISCO. Measurements
of $R_{\rm in}$ obtained by modeling the thermal component (“continuum
fitting”) often show constant $R_{\rm in}$ values over large ranges of
luminosity, strongly suggesting that the inner edge reaches a limiting value
(Steiner et al., 2010), which is naturally interpreted as the ISCO.

Using continuum fitting to determine $a_{*}$ requires a significant amount of
additional knowledge of the binary BH system. To determine $R_{\rm in}$ in
physical units requires knowledge of the distance to the system as well as the
disk inclination, which is usually assumed to be the same as the binary
inclination. Once $R_{\rm in}$ is determined in physical units, then the mass
of the BH is needed to calculate $R_{\rm g}$, and determine $R_{\rm
in}$/$R_{\rm g}$, which determines $a_{*}$. Measurements of $a_{*}$ using the
continuum fitting technique was accomplished for ten sources (McClintock et
al., 2014) with a range from $a_{*}=0.12\pm 0.19$ (A 0620–00) to $>$0.95 (Cyg
X$-$1). Recently, an update of the Cyg X$-$1 distance (Miller-Jones et al.,
2021) has led to a revision of the spin estimate to $a_{*}>0.9985$ (Zhao et
al., 2021).

While improved distances and masses for more systems will lead to more
opportunities for $a_{*}$ measurements from continuum fitting, the systematic
uncertainties need to be considered carefully. For example, spectral hardening
of the disc continuum by the disc atmosphere leads to a higher observed
temperature than the effective temperature of the disc. A correction using the
spectral hardening factor, $f_{\rm col}$, is typically made when using the
continuum fitting technique, but it has been argued that the uncertainty in
$f_{\rm col}$ is large enough to lead to significant uncertainty in $a_{*}$
(Salvesen and Miller, 2021). In addition, there have been challenges to the
assumption of spin-orbit alignment (Walton et al., 2016; Salvesen and
Pokawanvit, 2020). One avenue to further improvements is the joint
measurements of $a_{*}$ with the continuum fitting and reflection (iron line
modeling) techniques (Parker et al., 2016). Spectro-polarimetry is another
type of measurement that is expected to provide advances in this area (see
Chapter 5).

###  4.2 Origin of winds

The two main unresolved discussion points regarding the winds in BHBs are the
driving mechanism of the wind (thermal, magnetic or radiation pressure) and
the disappearance of X-ray absorption lines in the hard state.

The bright soft state provides ample, possibly unobscured ionizing radiation
to lift matter from the disk surface through Compton heating (Begelman et al.,
1983). For this thermal driving mechanism the wind is launched at large
distances (104 \- 105 $R_{g}$) from the central black hole. The launch radius
will be a fraction of the Compton radius (the distance such that escape speed
equals the isothermal sound speed at the inverse Compton temperature, Woods et
al., 1996), and the exact value of the fraction depends on properties of the
illuminating X-rays Done et al. (2018).

The other possible mechanisms to drive winds are radiation pressure and
magnetic processes. For Galactic BHs, line driving is not efficient due to low
UV flux, and high ionization (Done et al., 2007); however, under certain
conditions radiation pressure can transfer momentum to free electrons
(Reynolds, 2012; Done et al., 2018). On the other hand, magnetic wind
launching mechanisms are viable possibilities. In fact, for GRO J1655$-$40, a
single observation revealed a rich series of absorption lines (see Fig. 5)
from a dense, highly ionized wind, initially interpreted as magnetically
driven (Miller et al., 2006) as the calculated wind launch radius was much
smaller than the Compton radius inferred for the given source luminosity
prohibiting thermal winds. Magnetically driven winds close to the black hole
are implied in other sources such as IGR J17091$-$3624 (King et al., 2012;
Miller et al., 2012) and 4U 1630$-$47 (King et al., 2014). However, the
magnetic origin in the single GRO J1655$-$40 observation has been challenged
by multiple authors. If the wind is optically thick, the luminosity will be
underestimated (it could be close to Eddington) leading to complications in
the interpretation of the data due to radiative mechanisms (see (Done et al.,
2018) for additional discussion regarding arguments against magnetic origin).
Perhaps both origins are possible within a magneto-thermal hybrid wind, with
magnetic launching from the inner parts of the disk and thermal launching from
the outer parts of the disk in the same source (Neilsen and Homan, 2012;
Trueba et al., 2019).

The disappearance of the X-ray absorption features in the hard state has been
linked to the over-ionization of the material, photoionization instabilities,
geometrical obscuration of the outer disk by a large scale-height corona, and
the details of the driving mechanism Ponti et al. (2012); Chakravorty et al.
(2013, 2016). Over-ionization in a static absorber is ruled out by detailed
photoionization computations (Neilsen and Homan, 2012), and observationally
the hard state luminosity during the rise of the outburst is similar to the
soft state luminosities with wind features (see Fig. 5).

Perhaps the lack of winds in the hard state and the origin of the driving
mechanism of the wind are interlinked. The hard states show ubiquitous jets,
and an analysis of accretion ejection behavior in GRS 1915$+$105 led to the to
claim that both jets and winds are part of the same magnetic system and the
degree of collimation determines whether we see a jet or wind (e.g. “jet-wind
dichotomy” Neilsen and Lee, 2009). However, winds and optically thin jets are
known to coexist (Kalemci et al., 2016; Homan et al., 2016), and cold winds
may be present in all states. Some magnetohydrodynamic simulations indicate
that that the inclusion of magnetic fields into a thermally driven wind has
the effect of suppressing the wind in low-plasma beta regions Waters and Proga
(2018). There are rare claims of hard state wind features in the X-ray spectra
such as for Swift J1658.2-–4242 with _NuSTAR_ (Xu et al., 2018) and for V404
Cyg and GRS 1915$+$105 with Chandra (Homan et al., 2016). Perhaps more
sensitive instruments (such as Xrism and later Athena) will provide more
insight to the properties and the origin of the hard state winds.

###  4.3 Hard state accretion geometry

While the general picture for the soft state is a non-truncated optically
thick disc extending to the ISCO, there is no consensus on the accretion
geometry in the hard state. In the context of the advection-dominated
accretion flow (ADAF) model, a paradigm emerged where the disc begins to
truncate in the intermediate state, $R_{\rm in}$ increases further in the hard
state, and then reaches $10^{2}$ to $10^{4}$ Schwarzschild radii below
Eddington ratios of $\sim$0.01 (Esin et al., 1997). Some measurements, such as
the drop in the temperature of the thermal disc component and the drop in the
QPO frequencies as the luminosity drops support this picture (Dinçer et al.,
2014). In addition, other measurements can be explained by the truncated disc
picture, including the size and evolution of the X-ray lags (De Marco and
Ponti, 2016) as well as changes in the iron line, which has been found to
change from a relativistic profile to a narrow line at Eddington ratios of
0.001-0.003 (Tomsick et al., 2009; Xu et al., 2020). An analysis of the
frequency-resolved spectra of MAXI J1820$+$070 also indicated a reflector
moving closer to the inner edge of the accretion disk in the hard-to-soft
transition (Axelsson and Veledina, 2021). However, the relativistic iron lines
that are seen in the bright ($\sim$0.01-0.1 $L_{\rm Edd}$) hard states (Miller
et al., 2015; García et al., 2015) strongly contradict the idea that disc
truncation is necessary for sources to show hard state properties.

Another critical addition to our understanding of BHB spectral states in the
last two decades is that a compact jet is present in the hard state. The jet
dominates the spectrum at radio wavelengths (Fender, 2001) and can dominate up
to at least the near-IR (Corbel and Fender, 2002; Gandhi et al., 2011).
Although it very likely extends to X-rays and perhaps gamma-rays, it is
unclear what fraction of the X-ray and gamma-ray emission we see comes from
the jet (see also §4.5). The question of how much X-ray emission comes from
the jet compared to a more extended corona is important since the reflection
modeling that is used to derive the inner radius of the disc depends on the
source geometry (Dauser et al., 2013).

As described in §3.1, narrow and broad iron line components are often seen in
hard state spectra, and one explanation that has been advanced for MAXI
J1820$+$070 is that there is X-ray emission coming from different heights in
the jet that illuminate both the inner and outer parts of a non- or mildly-
truncated disc (Kara et al., 2019; Buisson et al., 2019). However, it has been
shown that the MAXI J1820$+$070 can also be described by other geometries. The
narrow and broad iron line components have also been modeled with a moderately
truncated disk and illumination by multiple X-ray components (Zdziarski et
al., 2021a). Within the reflection interpretation, the broad iron line does
not allow for a highly truncated disc, but these two analyses show that
complex models can lead to different numerical answers for $R_{\rm in}$.

In addition to the questions of disc truncation, high-energy emission from the
jet, and source geometry in general, another question is regarding the disc
inclination and whether the inner disc is aligned with the binary orbit, if it
is set by the BH spin, or if the inner disc precesses, which has been
suggested as a QPO mechanism (Ingram et al., 2017) (see also §4.6). Overall,
there are still many open questions related to geometry of accretion in hard
state, and answering the open questions related to the hard state accretion
and source geometry is likely to require a combination of observations,
theory, and numerical simulations.

###  4.4 Corona origin / jet connection

In Section 3, we described several key observations that demonstrate a
connection between the hot, optically thin corona at $R<100R_{\rm g}$ and the
relativistic jet observed at much larger distances ($10^{7-8}R_{\rm g}$).
These include:

  * •

The X-ray/radio flux correlation in Active Galactic Nuclei and XRBs, known as
the ‘fundamental plane’ (Merloni et al. (2003); §3.3)

  * •

The low reflection fraction observed in the hard state, which has been
interpreted as due to the corona/jet base accelerating away from the accretion
disk. This beams much of the X-ray emission away from the disk (Markoff et al.
(2005); §3.1).

  * •

The close temporal coincidence of the Type B QPOs during the state transition,
and radio flares from the jet (Homan et al. (2020); §3.4).

  * •

The correlation between the size of the X-ray corona (probed by X-ray
reverberation), and the radio luminosity (Wang et al. (2021); De Marco et al.
(2021); §3.5).

Because of these and other observables, several models have been proposed that
relate the corona and the jet. For instance, Markoff et al. (2005) suggest
that the X-ray corona is the base of the relativistic jet. Thermal seed
photons (and possibly also synchrotron photons from electrons in the jet) will
be inverse-Compton upscattered in the jet base to produce the observed hard
X-ray photons. This model maintains a spatially compact corona/jet-base that
is required to explain the broad reflection features. Kylafis et al. (2008)
and Reig et al. (2018) suggest a similar model where disk photons are
upscattered in a jet, though require that the low-frequency hard lags (Section
3.1.6) are due to light travel time delays in the jet, and therefore require a
much larger, extended jet. Petrucci et al. (2008) also suggest a connection
between the hard X-ray emitting region and the relativistic jet, but propose
that the hard X-rays originate in the plane of the accretion disk, in the so-
called jet-emitting disk (JED), a highly magnetized, low-density inner
accretion flow. The large large-scale jets then tap the mechanical energy
released in the JED, via the Blandford-Payne mechanism Blandford and Payne
(1982). The observational implication of the JED model is a truncated thin
disk in the hard state, which is distinct from the jet-base model where the
thin disk can extend to the ISCO. Because of these different observational
predictions, future mutli-wavelength spectral-timing observations, paired with
improved numerical simulations will reveal how the corona and jet are coupled.

###  4.5 Origin of gamma-ray tail

The most popular models that have been put forward to explain the origin of
the high-energy tail in the hard and hard intermediate states of BHBs are
Comptonization from a non-thermal electron population and synchrotron emission
from a compact jet. The energy dependent polarization measurement for Cyg
X$-$1 above 400 keV nearly reaches the theoretical maximum for synchrotron
radiation with ordered magnetic fields and strongly favors a jet origin beyond
this energy as neither thermal nor non-thermal Compton scattering would
provide polarization fractions close to the observed 75%. A jet origin for Cyg
X$-$1’s MeV emission has interesting physical implications as it implies
magnetic field strengths above the equipartition and a very efficient particle
acceleration Zdziarski et al. (2014). There are no other reports of
polarization measurement in hard X-rays/soft $\gamma$-rays for any other BH
sources, and whether the high polarization is a peculiarity of Cyg X$-$1, or a
common phenomena in all BH sources remains to be seen. A future MeV
polarimeter such as the future Compton Spectrometer and Imager (COSI) (Tomsick
et al., 2021) will allow for sensitive polarization measurements of BH
transients.

The case for Compton scattering from a non-thermal population of electrons
have already been put forward to explain the tail in the soft state, and also
have been invoked in the hard state as well. For lower quality data (e.g.
during the outburst decays with lower luminosity) the presence of non-thermal
or hybrid Comptonization is implied by poor fits with thermal only
Comptonization models, and a significant improvement in reduced $\chi^{2}$
with addition of a non-Maxwellian electron energy distribution (using the
$eqpair$ model Coppi (1999), for example). With the much higher quality data,
such as the case for MAXI J1820$+$070, the picture becomes more complicated.
The analysis of SPI data at different energy bands indicated a two component
emission, modeled as a thermal Comptonization plus a cut-off power-law with a
claim that the power-law has possibly a jet origin as it is only prevalent at
high energies (100 - 300 keV) in the hard state. On the other hand, an
analysis including lower energies using $NuSTAR$ and higher energies using SPI
and PicSIT on $INTEGRAL$ led to an alternative picture with two Comptonizing
regions, one closer to the BH which is producing both thermal and non-thermal
Comptonization, and the other possibly over the disk at a larger radii with
thermal Comptonization, without the need of a separate power-law component
Zdziarski et al. (2021b).

Non-thermal tails in the electron energy distribution invoked to explain the
hard tails would also invoke enhanced synchrotron radiation by the same
electrons, possibly not only altering the seed photon energy distribution
(much less than the disk photon energies in the hard state), but may also be
producing near-infrared emission at the same energies where the jets could
also contribute Veledina et al. (2013).

###  4.6 Origin of QPOs

Many models have been forward to explain the origin of QPOs (for both HFQPOs
and LFQPOs, even extending same models to explain the QPOs in neutron star
systems), but in general, the models can be classifies as “geometrical”, or
“intrinsic”. In the geometrical models, one of the accretion/ejection
component’s shape varies, and in the intrinsic models, the geometry is stable
within the QPO oscillation timescale, however, the disk or the corona emission
changes due to changes in the local properties. An extensive list of both
geometrical and intrinsic models and their principles have been given in a
recent review, Ingram and Motta (2019)), and here only models relevant to
general evolution of X-ray spectral and timing will be discussed.

The Type C QPOs are observed almost every state, and currently the leading
model to explain the origin of this QPO is the Lense-Thirring Precession (LTP)
model arising from the frame dragging in the vicinity of a spinning BH Ingram
et al. (2009). This model assumes a thick accretion flow (or a corona) inside
a truncated disk misaligned with the equatorial plane of the BH causing a
nodal precession of the entire inner flow due to the inequality between the
orbital and vertical epicyclic frequencies. The epicyclic frequencies are the
natural frequencies of a test mass disturbed slightly from the black hole
equatorial plane, and in Kerr metric the orbital, radial and vertical
frequencies are slightly different (Ingram and Motta, 2019). There are strong
observational evidences for geometrical origin through the inclination
dependence on the QPO RMS, and the iron line centroid frequency dependence on
the QPO phase, both consistent with the predictions of LTP (though the latter
is observed only in one source). There are also supporting arguments in favor
of LTP, and against some of the intrinsic models. First of all, there is no
sign of direct QPO modulation in the emission from the disk through frequency-
resolved spectroscopy Sobolewska and Życki (2006), in contrast, the Type C
QPOs can be observed beyond 200 keV Ma et al. (2021), therefore the modulated
emission is coming from the corona. The LTP predicts a highest QPO frequency
based on the spin, therefore this highest frequency should vary from source to
source which is the case so far. It is important to stress that if LTP is
indeed the correct model for Type C QPOs, most BH disk axis should be
misaligned with the spin axis, and should stay misaligned (with at least 5∘)
for a long time as the accretion brings them back to alignment. There are
observational and theoretical arguments in favor of misalignment which can be
found in Ingram & Motta 2019 Ingram and Motta (2019) and references therein.

Type B QPO properties also depend on inclination, pointing to a geometrical
origin, yet their RMS is higher for the lower inclinations systems whereas the
opposite is observed for Type C QPOs Motta et al. (2015). One model associates
Type B QPO to the precession of the jet Motta et al. (2015), as opposed to the
precession of the thick flow in Type C QPOs.

For the HFQPOs, the 2:3 ratio in GRO J1655$-$40 (and weaker detection claims
in other sources) suggested models invoking resonances related to test
particle orbits, and for the case of GRO J1655$-$40, with the accompanying low
frequency QPOs, a simple relativistic precession model has been suggested in
which the LFQPO fundamental frequency, the lower, and the higher HFQPOs are
the Lense-Thirring precession, periastron precession, and the orbital
frequency at a characteristic radius, respectively Motta et al. (2014).
Knowing all three frequencies allowed to determine the spin, characteristic
radius and mass of the black hole, and the inferred mass is in agreement with
the mass determined through optical observations. The HFQPO pair can also be
explained within the framework of a precessing torus with frequencies
corresponding to the breathing mode and vertical epicyclic frequency of the
inner flow Fragile et al. (2016).

##  5 Future of black hole research in X-ray and Gamma-ray domain

Our understanding of the accretion and ejection mechanisms around BHBs
increased substantially in the last 25 years, with major contributions from
_RXTE_ followed by $Chandra$, _XMM-Newton_ , $INTEGRAL$ in X-rays and
$\gamma$-rays, accompanied with multiwavelength observing campaigns to link
the accretion processes to the launch of relativistic jets. In the last 10
years, we had another huge leap with _NICER_ , _NuSTAR_ , and _Insight-HXMT_ ,
resulting a deeper understanding of X-ray spectral components and their
relation to the timing properties.

We appear to be approaching yet another milestone to put the controversial
issues discussed in §4 to rest with the upcoming approved and concept
missions, and perhaps opening up new and exciting discoveries to be solved in
the future. Specifically, the Imaging X-ray Polarimetry Explorer ($IXPE$,
Weisskopf et al. (2016)) launched at the end of 2021 and enhanced X-ray Timing
and Polarimetry ($eXTP$, Zhang et al. (2019)) to be launched in late 2027 will
allow polarization measurements in X-rays, providing an opportunity to test
specific predictions of QPO models and accretion geometry in the hard state De
Rosa et al. (2019). Even measuring stochastic polarization variability in
short time scales may be possible in the near future with $IXPE$ (together
with a large area instrument, such as $STROBE-X$) or directly with the $eXTP$
utilizing Polarimetry Focusing Array with the Large Area Detector (Ingram and
Maccarone, 2017). In addition, COSI (to be launched in 2025, (Tomsick et al.,
2021)) will measure polarization at soft $\gamma$-ray energies, to determine
if the MeV and X-ray emission has a different origin as has been suggested by
$INTEGRAL$ measurements of Cyg X$-$1.

In addition to polarimetry, studies of highly ionized outflows via absorption
line spectroscopy will be revolutionized by the launch of $XRISM$, a high-
resolution X-ray microcalorimeter, set to launch in 2023 (XRISM Science Team,
2020). $XRISM$’s energy resolution at hard X-rays will be unparalleled until
the launch of $Athena$ in 2034. High-resolution spectroscopy is also expected
to clarify the multi-component line profiles often seen as part of reflection
components.

$eXTP$, and $STROBE-X$ (Ray et al. (2019) if recommended for implementation)
would provide plenty of photons thanks to an order of magnitude increase in
their effective areas compared to _RXTE_ to study physics of accretion in
strong gravity in unprecedented detail. The other advantages of these new
generation large observatories over _RXTE_ will be their low energy coverage
extending well below that of _RXTE_ , and better energy resolution allowing
relating variability in absorption and emission lines to changes in fast
variability properties without a need for coordinated observations with other
satellites. These two missions offer complimentary characteristics to study
BHBs, the $eXTP$ with capability allowing simultaneous polarimetric
measurements with great timing and spectral coverage and $STROBE-X$ with
excellent coverage in less than 2 keV with the X-ray Concentrator Array with
an area an order of magnitude larger than _NICER_. Both instruments will carry
a very large area, very large field of view Wide Field Monitor (WFM) (Hernanz
et al., 2018) allowing not only detecting new transient sources when they are
still dim, but also allowing following state transitions in detail with the
WFM data only.

In addition to future advancements in X-ray instrumentation, the last decade
has shown the importance of coordinated multi-wavelength campaigns, especially
pairing with fast photometric instruments in the optical, IR and sub-mm. While
often challenging to coordinate, these campaigns help us probe the causal
connection between the accretion disk, corona and relativistic jet. Finally,
just as we improve telescope technology, we continue to see fast improvement
in numerical simulations of accretion flows in X-ray binaries, including the
effects of general relativity and radiation in the magneto-hydrodynamics. As
GPU-accelerated simulations continue and improve in the future (e.g. Liska et
al. (2018); Dexter et al. (2021)), we will better be able to connect disk
theory to observations.

##  6 Cross-References

Volume 1: History of X-ray Astrophysics, Astrosat, ATHENA, Chandra, eXTP,
Insight-HXMT, MAXI, NICER, Swift, IXPE The Imaging X-ray Polarimetry Explorer,
XMM-Newton, Study Concepts for future mission in High Energy Astrophysics.

Volume 2: History of Gamma-ray Astrophysics, The COMPTEL instrument on the
CGRO mission, The INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL),
Low mass X-ray binaries, High mass X-ray binaries, Overall accretion disk
theory, Black holes: Accretion processes, Fundamental physics with black
holes, Probing black-hole accretion through time variability, Tests of General
Relativity using black hole X-ray data, X-ray polarimetry-timing, Soft gamma-
ray polarimetry with COSI using maximum likelihood analysis.

##  7 Acknowledgements

The authors thank Jingyi Wang for providing data and making plots of MAXI
J1820+070 found in Figures 2, 6 and 7. The authors thank Dr. Douglas Buisson
for providing MAXI J1820+070 energy spectra, which were used in the making of
Figures 3 and 4. The authors thanks Dr. Javier Garcia for providing a first
version of Fig. 4.

JAT acknowledges partial support from NASA under grant 80NSSC20K0644. EAK
acknowledges partial support from NASA ADAP grant 80NSSC17K0515.

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