# The INTEGRAL view on Black Hole X-ray Binaries

S. E. Motta  J. Rodriguez  E. Jourdain  M. Del Santo  G. Belanger  F. Cangemi
V. Grinberg  J. J. E. Kajava  E. Kuulkers  J. Malzac  K. Pottschmidt  J.P.
Roques  C. Sanchez-Fernandez  J. Wilms  INAF–Osservatorio Astronomico di
Brera, via E. Bianchi 46, 23807 Merate (LC), Italy  Department of Physics,
Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, OX1
3RH Oxford, UK  Dépt. of Astrophysics, lab AIM, CEA/IRFU, CNRS/INSU,
Université Paris-Saclay & Université de Paris, Orme des Merisiers F-91191,
Gif-sur-Yvette, France  IRAP, Université de Toulouse, CNRS, CNES, UPS,
(Toulouse), France
INAF, Istituto di Astrofisica Spaziale e Fisica Cosmica, via Ugo La Malfa 153,
90146 Palermo, Italy  European Space Astronomy Centre (ESA/ESAC), Science
Operations Department, Villanueva de la Cañada (Madrid), Spain;  CNRS,
Laboratoire de Physique Nucléaire et des Hautes Energies (LPNHE), Sorbonne
Université, 4 place Jussieu, Paris 75005, France  Institut für Astronomie und
Astrophysik, Universität Tübingen, Sand 1, 72076 Tübingen, Germany  Department
of Physics and Astronomy, FI-20014 University of Turku, Finland  European
Space Agency (ESA), European Space Research and Technology Centre (ESTEC),
Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands  CRESST, Department of
Physics and Center for Space Science and Technology, UMBC, Baltimore, MD
210250, USA  NASA Goddard Space Flight Center, Code 661, Greenbelt, MD 20771,
USA  Dr. Karl Remeis-Sternwarte & Erlangen Centre for Astroparticle Physics,
Friedrich-Alexander-Universität Erlangen-Nürnberg, Sternwartstr. 7, 96049
Bamberg, Germany

###### Abstract

INTEGRAL is an ESA mission in fundamental astrophysics that was launched in
October 2002. It has been in orbit for over 18 years, during which it has been
observing the high-energy sky with a set of instruments specifically designed
to probe the emission from hard X-ray and soft $\gamma$-ray sources. This
paper is devoted to the subject of black hole binaries, which are among the
most important sources that populate the high-energy sky. We present a review
of the scientific literature based on INTEGRAL data, which has significantly
advanced our knowledge in the field of relativistic astrophysics. We briefly
summarise the state-of-the-art of the study of black hole binaries, with a
particular focus on the topics closer to the INTEGRAL science. We then give an
overview of the results obtained by INTEGRAL and by other observatories on a
number of sources of importance in the field. Finally, we review the main
results obtained over the past 18 years on all the black hole binaries that
INTEGRAL has observed. We conclude with a summary of the main contributions of
INTEGRAL to the field, and on the future perspectives.

###### keywords:

black hole physics , X-rays: general , gamma-rays: general , accretion disc ,
jets , binary stars

††journal: Journal Name

##  1 Introduction

X-ray binaries (XRBs) are binary systems consisting of an ordinary star and a
compact object, which can be a stellar-mass black hole (BH) or a neutron star
(NS). Those containing a BH are referred to as black hole binaries (BHBs). The
compact object is formed by the collapse of the core of a massive star at the
end of its (relatively quick) evolution. The gas from the companion star is
stripped away and forms an accretion disc around the compact object, where the
gas is heated up through viscosity to millions of degrees, causing the gas to
emit X-rays. The presence of an accretion disc, coupled with the deep
gravitational potential well around the compact object, gives rise to
different kinds of outflows, streams of matter launched from different regions
of the accretion flow. Outflows are able to carry away from the system a
significant fraction of the matter and energy, which could have potentially
fallen onto the compact object, so that XRBs act to heat their environment
rather than behaving only as sinks. Outflows can take the form of
relativistic, transient or persistent collimated jets, but also warm or cold,
poorly collimated winds (and essentially anything in between), and are
observed in different portions of the electromagnetic spectrum, from the radio
wavelengths up to the X-rays.

With their fast evolution, which takes place on humanly accessible time-
scales, BHBs, together with NS binaries [369], constitute the best
laboratories where to study the extremes of physics in real time: around
collapsed objects one can probe the behaviour of matter in the presence of
extremely curved space-time, which is at the base of the accretion process,
but also the physics underlying the particle acceleration behind the launch of
relativistic jets and winds.

There are approximately 60 known BHBs in our Galaxy. Of these, around 20 host
black holes dynamically confirmed via spectro-photometric observations [64].
Another $\sim$40 systems are referred to as BH candidates: they share a strong
phenomenology with the confirmed black holes (e.g. [493, 336]). In the
following, we will not differentiate between candidate and confirmed BHs, and
we shall refer to these systems collectively as the BHBs. The BH discovery
rate is currently limited by the X-ray outburst rate of BHBs (the number of
persistent systems being so dramatically lower than that of transient ones),
which is relatively small - on average 2 outbursts per year - due to the
typically low duty cycles of these systems. Most transient BHBs are X-ray
bright for only a small fraction of the time that is on the order of a few
percent, and most of the time, they are in a quiescence state, i.e. very X-ray
dim or (more typically) invisible to observers from Earth [53]. Therefore, the
total of $\sim$60 known BHBs in the Galaxy is necessarily only a minute
fraction of the actual Galactic BHB population, which is thought to be greater
than $\sim 10^{4}$ [511]. In turn, the Galactic BHB population represents an
equally minute fraction of the total number of stellar mass BHs in the Milky
Way, estimated to be in the range of 108–109 [489, 44].

###  1.1 History

The first BHB, Cygnus X-1 (Cyg X-1), was discovered in 1964 [40, 146], at the
dawn of X-ray astronomy, via sounding rockets carrying X-ray sensitive
instruments. Cyg X-1 became the first candidate for systems hosting a BH when
optical observations revealed its binary nature, thus allowing an estimate of
the mass of the compact object [35, 503]. Cyg X-1 is one of the few known
persistent BHB systems in the Galaxy, which are relatively rare in the local
Universe as it was established decades after its discovery. We now know that
most BHBs are transients, and thus only visible during rare outbursts. A
0620$-$00 was the first transient system which was also classified as a BHB
[286], with a lower limit to the mass of the compact object of 3.2 $M_{\odot}$
[117]. A few additional transient BHBs were later discovered, including two
X-ray sources in the Large Magellanic Cloud (LMC X-1 and LMC X-3), which were
afterwards classified as BH candidates, and GX 339$-$4, one of the most
extensively studied BHBs [273].

With the launch of the Ginga satellite and its all-sky monitor, the number of
known BHBs started to increase. Among these, a notable case is that of GS
023+338 in 1989 [261], which was quickly connected with the optical source
V404 Cygni, and also linked to an optical transient observed over 50 years
earlier [184]. Casares et al. [63] obtained the first determination of the
system’s mass function ($f$(M) = 6.26 $\pm$ 0.31 $M_{\odot}$), making GS
2023+338 what is considered the first dynamically-confirmed BHB (even though
Bolton [35] already claimed such record for Cyg X-1).

This era of early observations began to elucidate some of the basic properties
of BHBs, namely that they vary on relatively-short timescales, and show
significant flux changes, which led to the definition of a BHB’s high and low
states [475]. Such states are largely based on observations of Cyg X-1, which
were initially performed in a limited X-ray band only extending up to 10 keV.
More detailed studies based on several observations—in particular of the
transient GX 1124$-$683 (also known as Nova Muscae 1991), GX 339$-$4 and Cyg
X-1—showed that the complex behaviour of BHBs could not be reduced to two
states, and additional states were defined, based on the complex spectral and
timing properties of these systems [see, e.g., 312, 181, 288, 106]. In
particular, the first spectral studies based on the modelling of the accretion
disc emission opened the way to techniques aimed at measuring the inner disc
radius [310].

The hard X-ray/soft $\gamma$-ray sky has been notably explored in the 1980’ by
the CGRO and Granat observatories, which both carried instruments covering a
large energy domain, from a few keV to a few MeV (and even more in the case of
CGRO/EGRET). The study of accreting BHBs took a jump forward with the launch
of the Rossi X-ray Timing Explorer (RXTE) satellite in 1995. RXTE carried an
All Sky monitor (ASM) that allowed a lot more outbursts of old and new
transients to be detected. RXTE also carried two high time-resolution
instruments with large effective areas, which could operate in a very flexible
way while accumulating high signal-to-noise data for timing and spectral
studies in the 2-200 keV energy band. The INTErnational Gamma-Ray Astrophysics
Laboratory (INTEGRAL) was launched in 2002, just few years after the XMM-
Newton and Chandra X-ray satellites (both launched in 1999). It contributed
significantly to the field of BH research by improving the knowledge of the
high-energy emission from accreting XRBs, thanks to its sensitive high-energy
instruments. These four observatories brought on an explosion of information,
which led to new insights into the emission properties of BHBs that resulted
in a much clearer understanding of the process of accretion onto compact
objects [491, 492, 287, 106, 28].

Since their discovery, stellar-mass accreting BHs in Galactic binaries have
been studied in comparison with the super massive black holes (SMBH) in Active
Galactic Nuclei (AGN), with which they share a number of fundamental
properties, reflecting the fundamentally similar physics underlying their
emission [140, 295, 122, 377, 161]. Of course, Galactic BHBs have also been
largely compared with other types of accreting binaries, first and foremost NS
XRBs. Such systems in many respects show the same properties and
characteristics of their BH counterparts, and thus provide the best control
sample to test which of the fundamental processes governing the inflow/outflow
of matter and energy around all accreting objects may be unique to BHs.

Another type of systems typically compared with BHBs is that of the enigmatic
Ultra-Luminous X-ray (ULX) sources, a class of very bright, unresolved, extra-
galactic X-ray sources, generally located at some distance from the centre of
their host galaxies, and currently believed to be powered by accreting compact
objects [206]. The compact object hosted in these systems have been proposed
to be either a stellar mass BHs or (more likely) NS accreting either
significantly above the Eddington accretion rate or non-isotropically (see
e.g. [193]); or an intermediate mass black holes (IMBHs) accreting at much
lower accretion rates [115].

A final type of BH-powered system that is being compared to BHBs especially in
the late years is that of the tidal disruption events (TDEs), where a star is
gravitationally captured by a (typically quiescent) SMBH and is partially or
completely torn apart by tidal forces [400, 160, 178]. When such an encounter
takes place, a relatively short-lived accretion disc forms around the SMBH
from the stellar matter of the captured star. Such an accretion disc would
then power the production of radio jets in many ways similar to those produced
in BHBs and in the AGN [232]. This further strengthens the idea that the
accretion/jet generation process occurs according to the same principles in
many systems that share one key property: the combination of a deep
gravitational potential well and an accretion disc.

###  1.2 In this paper

This review focuses on the systems identified as BHBs (candidates or
dynamically confirmed), with an emphasis on the contribution that INTEGRAL has
made to improve our understanding of these systems. We will restrict ourselves
to the science of these systems, while the details relating to the INTEGRAL
mission and its instruments are reviewed in Kuulkers and et al. [238, and
reference therein], and the data reduction is discussed in the INTEGRAL user
manuals111See https://www.isdc.unige.ch/integral/analysis.

INTEGRAL is an ESA medium size mission dedicated to the spectroscopy and
imaging of celestial hard X-ray/soft $\gamma$-ray sources, in the energy range
15 keV to 10 MeV with concurrent source monitoring in the X-ray (3-35 keV) and
optical (V-band, 550 nm) energy ranges. The INTEGRAL payload consists of the
two main soft $\gamma$-ray instruments, both using a coded mask imaging
technique, with a field of view of $\sim 30^{\circ}$: SPI, a spectrometer that
operates in the 18 keV–8 MeV energy range with an energy resolution of 2.2 keV
(FWHM) at 1.33 MeV; and the imager IBIS, with a spatial resolution of 12
arcmin, operating between 15 keV and 10 MeV. INTEGRAL carries also two
monitors, JEM-X (formed by two coded-mask units), sensitive to the X-rays
(3–35 keV) with a field of view of 5∘, and the optical monitor OMC, equipped
with a Johnson V-filter to cover the wave-length in the 500–600 nm range. All
instruments are co-aligned, and thus are able to cover simultaneously a very
broad energy range.

INTEGRAL has permitted several important leaps forward in the understanding of
BHBs and various aspects of accretion-ejection mechanisms. This progress has
not been due to specific instrumental capabilities - even if at the time of
launch in 2002, SPI featured the best spectral resolution and IBIS the best
spatial resolution above 20 keV, compared to the other X-ray missions
operational back then. Instead, advances have been made possible by the
combination of many unique properties of the INTEGRAL mission, such as: a very
wide field of view of 30∘ by 30∘ (900 square degrees); the ability to perform
long uninterrupted observations of up to 3 full days; and a high sensitivity
above 20 keV. These capabilities are also what made INTEGRAL ideal for the
study of BHBs. Specifically, early stages of outbursts in the hard state could
be detected serendipitously, so that simultaneous multi-wavelength observing
campaigns could be promptly organised, and surveys and monitoring observations
— especially of the Galactic plane and Centre — could be planned as core
programs and encouraged as guest observers programs. All the above allowed for
spectral transitions to be observed and probed in detail, and important
connections between the X-rays (accretion flow)/soft $\gamma$-rays (’hard
tails’) and the radio (jets) emission to be investigated.

This paper is organised as follows: Section 2 describes the typical outburst
evolution of BHBs, the states and transitions that characterise them and their
properties. Section 3 looks at the different types of outflows that can be
observed from BHBs, and reviews the current understanding of the connection
that exists between accretion and outflows. Section 4 examines the properties
of the hard X/soft $\gamma$-ray emission probed by INTEGRAL, and briefly
reviews the interpretations and models that have been put forward since the
beginning of the mission. Section 5 details the main results obtained from
INTEGRAL observations of BHBs. We first focus on a few sources of historical
importance, which were most relevant for the understanding of BHBs in general,
and to the understanding of which INTEGRAL particularly contributed (Section
5.1 to Section 5.6). Then we will briefly review the sources that have been
discovered thanks to INTEGRAL (Section 5.7), and finally all the sources that
INTEGRAL observed since its launch (Section 5.8 and Section 5.9).

##  2 Outbursts

In BHBs, the X-ray emission arises from the inner portion of the accretion
flow, and possibly from the base of the jets (observed primarily in radio),
which may or may not coincide with part of the accretion flow itself [274].
While a few BHBs are persistent sources, like the archetypal BH system Cyg
X-1, (which is a persistent accretor and shows a luminosity consistently above
$10^{37}ergs^{-1}$), most of them are of transient nature. With a recurrence
period that varies between several months and decades [53], the accretion rate
onto the central objects increases by orders of magnitude and the sources
enter their outburst phases, which are interleaved by (typically much longer)
quiescence phases. During outbursts, the X-ray luminosity of XRBs increases,
peaks and then decays, roughly tracing the changes of accretion rate onto the
BH.

While active, most BHBs show significant luminosity variations that take them
from the low quiescent luminosity of the order of $L\sim 10^{30-31}\,{\rm
erg\,\,s^{-1}}$ [409]), to values of the order of $L\sim 10^{38-39}\,{\rm
erg\,\,s^{-1}}$ or more, and through marked spectral and fast time-variability
changes. For most BHBs, outbursts—historically referred to as X-ray novae—last
between a few weeks and a few months (although a few systems have shown
decades-long outbursts, like GRS 1915+105), and generally recur on the
timescale of years to decades [474].

###  2.1 Accretion states

The different properties observed during the outbursts of transient BHBs are
generally associated with different accretion states, but even restricting
ourselves to the two original accretion states identified in Cyg X-1 [475],
the (low) hard and (high) soft states, the details of the emission are rather
complex [e.g., 149], and have led to a number of state classifications [513,
179, 287]. In this review, we will arbitrarily follow the classification
originally proposed by Homan et al. [179] (see also [29, 28]).

The various physical components that contribute to the energy spectra, as well
as the various fast time-variability properties of the emission from BHBs,
vary quickly (in $\sim$hours or faster) and in a correlated fashion, in ways
that vary in different states and/or across certain state transitions.
Outbursts of different sources, and even different outbursts from the same
systems, show time evolution that can differ considerably. Fortunately, these
variations follow repeating cyclical patterns of behaviour that become
apparent in a so-called X-ray hardness-intensity diagram, or HID [28] (see
Fig. 1), where accretion states and transitions can be identified as specific
regions of a q-shaped track. HIDs have been commonly used to describe the
behaviour of accreting stellar mass BHs for over two decades now [28], but
they have been used also in the case of NS binaries [336], and even in AGN
[233, 471]. The HID is the X-ray equivalent of the Hertzsprung–Russell diagram
used in stellar astrophysics, but instead of being populated by several
sources at different evolutionary phases spanning several million years, the
HID shows the same source evolving quickly (over weeks to years) through
different states. An HID shows the X-ray intensity in units of (instrumental)
count rate, luminosity, or flux as a function of a hardness ratio, calculated
as a ratio of count rates (or luminosity, or fluxes) measured in two energy
bands (hard over soft is typically used).

Figure 1: A sketch of a typical Hardness Intensity Diagram (HID). All the
accretion states sampled during an outburst—save for the ultra-luminous
state—occupy 4 different vertical bands in the HID. The name of each each
state is marked on the plot. During an outburst, the “q-shaped” loop is
travelled anti-clockwise from the bottom right corner. All or only some of
accretion states are sampled. Hard-only and failed outbursts are also marked
on the figure. As noted in the text, the qualifications “low” and “high”
attached to the hard and soft state denominations have an historical origin
and and do not hold a physical meaning.

The general evolution of a transient BHB during an ordinary (as opposed to
failed, see below) outburst is roughly always the same: a “q-shaped” track is
travelled counterclockwise in the HID from the bottom right, which corresponds
to the initial phase of an outburst, just above the quiescence, which is in
general not included as most X-ray telescopes are not sensitive enough to
detect sources at such low luminosity. The (Low) Hard State (LHS), which is
observed at the beginning and at the end of an outburst, can be roughly
identified with the right-hand vertical branch; the (High) Soft State (HSS),
generally including or following closely the peak of the outburst, corresponds
to the left-hand side vertical branch222Note that the right and left-hand side
branches are not exactly vertical. This is an effect of the logarithmic scale
typically used to display HIDs, which minimises the significant softening
observed as sources brighten.  of the q-loop. We note that the qualifications
“low” and “high” attached to the hard and soft state denominations are a
legacy of the original state classification based on the first observations of
Cyg X-1, and thus have an historical rather than physical meaning.

The transition between the two main states takes place at two different flux
levels: at high flux, as the source moves from the LHS to the HSS, and at low
flux, when it transitions back from the HSS to the LHS completing an
hysteresis cycle [313]. Along the two horizontal branches that complete the
q-track, lie the Intermediate States, which are often split in two states -
the Hard Intermediate State (HIMS) and Soft Intermediate State (SIMS). These
two intermediate states can be distinguished from each other thanks to their
different timing properties [28]. In a few sources a fifth state has been
observed, the so-called Ultra-Luminous State (ULS), or anomalous state [320].
Such a state shares some characteristics with the two intermediate states, and
is characterised by a high luminosity, which can reach or even exceed the
Eddington Limit [488].

Over the decades of X-ray monitoring of several BHBs with, a general pattern
has emerged, according to which a source moves around the hardness-luminosity
plane following the sequence LHS-HIMS-SIMS-HSS-SIMS-HIMS-LHS. Occasional brief
excursions back and forth from and to the HIMS and SIMS have been observed in
a few systems, as well as transitions all the way back to one of the main
states (LHS or HSS) in rare cases (see [125] and, e.g, [319, 320] for GX
339$-$4 and GRS 1655$-$40, [43] for XTE J1859+226).

Despite the general pattern followed by many transient BHBs in outbursts, a
relatively small number of unusual outbursts has been observed over the past
decades, in which sources do not show all the main accretion states. A number
of sources never leave the LHS during the outburst [42], and show hard-state-
only outbursts. Other sources proceed to an intermediate state before
returning to the HS and quiescence, without, however, completing a full
transition to the HSS and back ([58, 129, 460], see Sec. 5.7.4, 5.8.6, 5.8.8).
Such outbursts are generally referred to as failed outbursts, even though the
same term is also sometimes improperly used in the literature to indicate
hard-state-only outbursts (see below). It is worth noting that some sources
have undergone both canonical outbursts and failed outbursts [467]. Since most
of the failed outbursts are under-luminous, it has been argued that the lack
of a transition to the HSS might be connected with a premature decrease of the
mass accretion rate, as during the 2008 outburst of H1743$-$322 [60] (see Sec.
5.7.4).

Weaker outbursts can follow the initial outbursts by some weeks to a few
months [e.g., 208]. These events, referred to as re-flares or re-brightenings,
are very similar to the hard-state-only outbursts mentioned above, so much so
that it is not clear whether these two types of outbursts are physically
distinct. During re-flares, a source temporarily rises out of quiescence to a
higher luminosity, but no transition to a softer state is observed, so that
the system remains in the hard state, thus only travelling up and down the
right-hand side vertical branch of the HID. Analogous secondary outbursts are
also seen in systems hosting a white dwarf (see, e.g., [240]) or a neutron
star (e.g., [251, 373]), suggesting a disc instability origin, or reflecting
an increase in the mass released from the companion star, perhaps induced by
X-ray heating of its outer layers during the primary outburst (e.g., [474,
245]).

The accretion states are defined based on specific properties, which emerge
both from the analysis of the X-ray spectra of the source considered, as well
as on their fast-time variability properties. The latter play a crucial role
especially when it comes to the definition of the two intermediate states (see
Section 2.3). In the following sections, we will give a brief overview of the
main spectral and fast-time variability properties typically observed in
transient BHBs.

###  2.2 Spectral properties of BHBs

The typical X-ray ($\sim$0.1 –200 keV) spectrum of a BHB is characterised by
two main components (unlike the more complex spectra from accreting NSs),
which play a different role in the different accretion states. A geometrically
thin, optically thick disc [445] truncated at a certain radius - the inner
disc truncation radius - generally larger than the innermost stable circular
orbit (ISCO, [13]), is responsible for black-body-like emission below $\sim$6
keV, and takes the form of a multi-colour disc black body in the spectrum
[445]. The emission from such a disc peaks at a few keV and is scarcely
variable on time-scales of hours and shorter, thus does not contribute
significantly to the overall variability of BHBs on such time-scales.

A cloud of electrons located close to the BH is believed to be primarily
responsible for the non-thermal emission due to Comptonisation of disc seed
photons, appearing typically above 5–10 keV [470, 162]. Such a cloud of
electrons has been historically referred to as the corona, in analogy with the
solar corona, although it is now clear that the BH coronae have little to do
with stellar coronae, and a lot to do with the accretion flow itself, which
the corona is most likely part of. The geometry of the corona is still
debated, but it seems that at least part of it coincides with to what is
generally referred to as hot flow. This is the central part of the accretion
flow, which puffs up into a relatively geometrically thick, optically thin
accretion flow. The hot flow is believed to replace or sandwich the razor-thin
Shakura-Sunyaev disc that exists further out [446, 343, 118, 106, 271, 272,
270], so that the accretion flow from the inner disc truncation radius inwards
is best described by a geometrically thick disc. The electrons in the hot flow
(which are thermalised) up-scatter the disc photons (or seed-photons) giving
rise to hard X-ray emission above 6 keV. Such photons produce a power law-like
component in the X-ray spectra featuring a high-energy cut-off that reflects
the temperature of the Comptonising electrons [114, 470, 514, 199, 106]. Such
non-thermal emission, unlike the disc emission, is highly variable, and it is
responsible for the marked fast time variability typical of accreting BHBs.

In the soft state, where the electrons have cooled down by the increasing
amount of seed photons being up-scattered, this hard X-ray component does not
show any cutoff below MeV energies. Therefore, a small population of electron
with a non-thermal/powerlaw distribution, has been proposed to be responsible
for the up-scattering of the seed photons [83, 388, 147, 293, 522].

Besides the emission from photons Comptonised by thermally-distributed
electrons, an additional non-thermal component may also be present, depending
on the accretion state a source is sampling. This type of emission appears as
a second power law like tail, which does not show any cut-off and extends up
to the MeV region [38]. The physical origin of this high-energy tail is not
clear, even though it has been explained in terms of a contribution of the
jets, or as the result of the Comptonisation of the seed photons on a
population of non-thermal electrons. This topic has been largely investigated
by INTEGRAL, and more details on the issue of the origin of this soft
$\gamma$-ray emission in BHBs is treated in more detail below, in Section 4.

A third component - the reflection - can appear in the spectra as well,
superimposed to the spectral continuum determined by the aforementioned
components. The reflection emission is believed to arise from the hot flow
emission reflecting off the geometrically thin disc, and takes the form of a
number of lines around 6.4 keV (including the Fe K$\alpha$ line and a number
of lines attributed to several Fe ionization states) and a high-energy hump
peaking at around 30 keV [145]. In some sources, where the presence of a local
absorber significantly affects the X-ray emission (see, e.g. V404 Cyg, Sec.
5.3, [331]), what is called reflection includes the radiation reprocessed in
the local absorber (including up- and down-scattering in a cool, possibly in-
homogeneous, nearly optically-thick medium), and should be more correctly
referred to as reprocessed emission [e.g., 329, and Sec. 5.3.2].

The contributions of all these components vary in the different accretion
states, and determines the overall spectral shape in the X-ray band
($\sim$1–200 keV) and fast time-variability properties of BHB in outburst. The
accretion disc dominates the X-ray emission in the HSS, which is thus
characterised by a soft X-ray spectrum and very little to no thermal (i.e.
Comptonised) emission in the $\sim$1–200 keV energy band, and very limited
fast-time variability ($<5\%$). The non-thermal emission from the hot flow
dominates the LHS, which shows hard spectra extending up to several tens and
sometimes even hundreds of keV, with little to no contribution of a thermal
disc-blackbody, and a large fraction of fast time-variability (up to 30%). In
the HIMS and SIMS (and during the ULS, when sampled), both the thermal and non
thermal emissions are present, with the contribution of each component
smoothly decreasing/increasing in the spectrum depending on the outburst
phase: as a source moves from the LHS to the HSS, the inner disc truncation
radius decreases, the hot flow emission decreases, and the thermal emission
rises. The opposite trend is observed when a source moves from the soft to the
hard state, with the disc emission progressively decreasing and the hot-flow
emission increasing, as a consequence of an increase in the inner disc
truncation radius [106]. These trends drive changes in the fast time
variability, which decreases along the LHS to HSS transition (from above 20%
to 10% in the HIMS, and between 5% and 10% in the SIMS), and increases along
the opposite direction. This is due to both the decrease/increase of the
number of non-thermal and variable photons, and the increase/decrease of
thermal/non-variable photons which dilute the integrated variability.

###  2.3 Fast time variability properties of BHBs

Black hole X-ray binaries have been known to be variable on short timescales
since the very first observations of Cygnus X-1 [475]. When the available
X-ray instrumentation became sufficiently sophisticated to allow detailed
variability studies on short (sub-second) time-scales, the definitions of
states and transitions were refined to include fast timing properties [493,
287, 28].

While the long-term (days to years) variability of transient BHBs in outburst
is most commonly described through the HID, the shorter time-scales cannot as
easily be appreciated by the same means, and even the inspection of a source’s
light curve can be unpractical. Hence, the fast (i.e., sub-minute) time
variability in accretion binaries is best studied in the Fourier domain, and
the Power Density Spectrum (PDS) - the modulus squared of the Fourier
transform of the light curve - is a tool commonly employed to study the
emission from X-ray binaries. The PDS from BHBs typically displays several
different features, ranging from various types of broad-band noise spanning
several decades in frequency (i.e. essentially scale-free), to much more
narrow features, called quasi-periodic oscillations (QPOs).

QPOs have been discovered in the late ’70s in the BHB GX 339$-$4 [440], and
have been observed since then not only in virtually all BH and NS X-ray
binaries, but also in a number of ULXs and AGN [206, 2]. QPOs reflect the
oscillations of the accretion flow in the strong field regime, and yield
accurate centroid frequencies linked to the motion of matter and/or accretion-
related timescales. Thus, the study of variability in general and QPOs in
particular provides a way to explore the accretion flow around BHs in ways
which are inaccessible via the spectral analysis alone. The association of
QPOs with specific spectral states and transitions indicates that they could
be a key ingredient in understanding the details of the physical conditions
underlying the accretion states. Furthermore, being produced in the vicinity
of relativistic objects such as BHs and NSs, QPOs are expected to carry
information about the condition of matter in the strong field regime, thus
providing powerful probes of the predictions of the Theory of General
Relativity.

Most of the components found in a typical PDS, and in particular QPOs, have
been studied in great detail by fitting the Poisson noise subtracted PDS of
many observations with various empirical models, the most commonly used
consisting of a sum of Lorentzian functions. From Parseval’s theorem, the PDS
can be normalised such that its integral over all positive frequencies is
equal to the square of the fractional root mean square deviation (or rms) of
the corresponding time series (this results in a PDS fractional rms
normalisation). The rms essentially quantifies how variable a given time
series is in a given Fourier frequency range. The typical frequency range
sampled by the recent X-ray instruments is from a few mHz to a few kHz (ms to
ks).

QPOs in BHBs are normally divided into two large groups, based on the
frequency range where they are usually detected: the low frequency QPOs and
the high-frequency QPOs. The former in BHBs have traditionally been classified
into three types: A, B and C.

Type-C QPOs are by far the most common type of QPO in BH systems. Type-C QPOs
can be detected in all accretion states (perhaps except the SIMS), although
they are most prominent in the HIMS and at the bright end of the LHS, where
the overall variability is large - up to 30% rms in the 0.1–100 Hz band. The
centroid frequency of type-C QPOs is highly sensitive to the state of the
source, rising from a few mHz in the LHS at low luminosities to $\sim$10 Hz in
the HIMS, and up to $\sim$30 Hz in the ULS. Type-C QPOs have also been
observed at optical (e.g. [318, 189, 143]), ultraviolet [185] and infrared
[211] wavelengths. Type-B QPOs have been detected in a large number of BHBs
and they appear during the SIMS, which is in fact defined by the presence of a
Type-B QPO [28], and by a rms level of $\sim$5-10% in the 0.1-100 Hz band.
They are characterised by a relatively high amplitude (up to $\sim$5% rms) and
narrow ($Q\gtrsim 6$) peak, and generally show centroid frequency at 5-6 Hz
(even though type-B QPOs with significantly lower centroid frequencies have
been also reported [322]). Being associated to a short-lived accretion state,
type-B QPOs are comparatively much less frequent than Type-C QPOs. The same is
true for type-A QPOs, which are the least common type of LF QPO in BHBs: the
entire RXTE archive only contains $\sim 10$ significant Type-A QPO detections.

High Frequency QPOs (HFQPOs) are rare features in BHBs (but much more common
in NS XRBs, [e.g., 331]), and to date most of the confirmed detections have
been made by RXTE (but see also [27]). The first HFQPO was detected in 1997 in
GRS 1915+105 (at $\sim 67$ Hz [317]) which is the source where the vast
majority of HFQPOs come from. Other sources who have been claimed to show
HFQPOs - all at frequencies significantly higher than in GRS 1915+105 - are
XTE J1550$-$564, GRO J1655$-$40, XTE J1859+226, H 1743$-$322 , GX 339$-$4, XTE
J1752$-$223, 4U 1630$-$47, IGR J17091$-$3624 (which also shows a high-
frequency QPO at $\sim$67Hz, [4]). However, most detections have been proven
to be not statistically significant, leaving only a handful of detections from
two sources (XTE J1550$-$564, GRO J1655-40, see [30]).

Many models have been proposed for both LFQPOs and HFQPOs, some of which have
been developed for years and largely tested against data, while others are
little more than ideas mentioned in a few papers at most. Dwelling on the
details of the theoretical models for QPOs is beyond the scope of this work,
and therefore we refer the interested reader to [192] and references therein
for a recent review on the topic. Here we will only mention that the only type
of QPO that has a relatively widely accepted explanation is the type-C.Type-C
QPOs have been ascribed to the Lense-Thirring precession of particles within
the accretion flow, a General relativity effect that arises from the frame
dragging occurring in the vicinity of spinning massive compact objects [248,
191, 326].

##  3 The accretion-ejection connection.

The ’90s saw a leap forward in the knowledge of accreting BHBs thanks to a
remarkable increase in the X-ray data available. These years were also marked
by the discovery of relativistic jets from the BHBs GRS 1915+105 [308] and
1E1740.7–2942 [309], to which followed the discovery of more jets from a
number of other X-ray binaries hosting either BHs (see e.g. [166, 164, 86]) or
NSs [133, 296]. BHBs began to be referred to as micro-quasars, in analogy to a
jetted sub-class of Active Galactic Nuclei (AGN) - the quasars - where radio
jets had been already observed frequently in radio for at least a few decades.
Such a discovery opened a new path to the study of accretion and its
connection with the generation of jets, and of outflows in general, which is
often referred to as to disc-jet coupling333Even if this term has been
initially coined to describe the connection that exists between the accretion
disc and the generation of jets, it is now more broadly used to describe the
connection between the accretion flow and all the outflows that the disc is
capable of generating. , or accretion-outflow connection.

Similarly to what happened for the radio jets, which were observed much
earlier around SMBHs than around stellar mass BHs, powerful winds,
relativistic and not - already observed in a number of AGN - were also
discovered initially only in BHBs [378] and later in NS systems as well [379].
Unlike jets, which are believed to be mildly to highly collimated and
approximately orthogonal to the accretion disc, winds appeared to be flowing
in an almost equatorial direction with respect to the accretion disc, and are
thus detected mainly in sources observed at high inclination (i.e. close to
edge-on) [378]. Probably due to the low number of simultaneous multi-band
observations available, it initially seemed that disc winds and jets were
mutually exclusive, with the first being launched in the radio-free HSS, where
the radio activity was generally thought to be quenched. It must be noted that
in the past observations were carried out mainly in the X-ray band, which
prevented to fully grasp the contribution of some components of accreting
systems (such as jets and winds), which can be energetically very important.
It has now become clear that the full picture is significantly more complex
than that available only a decade ago, and new observations, more and more
often carried out simultaneously in several energy bands (primarily in the
soft and hard X-rays and radio, but also in optical, infra-red, and sub-mm
band) are continuously unveiling unknown properties of jetted accreting
systems that highlight how the connection between the accretion process and
the generation of outflows is far from being fully understood.

The general picture which started to emerge in the early ’00s remains overall
true. During the LHS, steady, compact (i.e., generally not resolved in high-
resolution radio images) and mildly relativistic jets dominate the radio
emission. Simultaneous X-ray and radio observations of BHBs in the LHS have
evidenced the existence of a non-linear correlation between the X-ray and the
radio luminosity, originally observed in GX 339$-$4 [165] and then found in
many other BHBs by several authors in the last two decades. This correlation
was initially considered universal [140] \- which led to a number of works on
the fundamental plane of black hole activity [e.g., 295, 122, 377, 161]. More
recently it became clear that most transient BHBs are considerably less
luminous in the radio band than GX 339$-$4 [89, 331], and populate a second
track in the radio-X-ray plane, which effectively includes the majority of the
known BHBs [325].

During the intermediate states, and in particular close to the HIMS-SIMS
transition, powerful relativistic radio ejections are observed, which are
often resolved as synchrotron emitting blobs in radio Very Long Baseline
Interferometry (VLBI) high-resolution images. Jets—both the steady compact
jets, and the transient relativistic one—are believed to transport an enormous
amount of (kinetic) energy, which is transferred to the BH surrounding.
Observational evidence exists that the power output of low-luminosity – i.e.
the overwhelming majority of – stellar mass BHs is dominated by the kinetic
energy of ‘dark’ outflows, whose key signature is the eventual energising of
the ambient medium [137].

In the soft states, highly ionised winds - the presence of which is determined
via the detection of characteristic X-ray absorption lines - are launched on a
quasi-equatorial direction at up to relativistic velocities. Winds are thought
transport a huge amount of matter away from the accretion disc, possibly
comparable with the amount of mass accreting onto the black hole, and perhaps
enough to trigger a return to the hard state [333]. Occasionally, cold winds
(i.e., consistent with being not ionised), which appear to co-exist with the
radio jets (either the compact steady jets, or the discrete, relativistic
ones), have also been observed in the optical band during the hard and hard
intermediate states [333]. Such finding was among the first pieces of
observational evidence to cast doubts on the idea according to which jets and
winds are associated with different accretion states, and therefore cannot co-
exist.

A different sort of cold outflow has been observed in a limited number of
systems, all believed to erratically or persistently accrete at or above the
Eddington limit: a non-homogeneous, optically-thick mildly relativistic
outflow which arises from the inner part of the accretion flow as a result of
radiation pressure forces, which develop at high accretion rates. In a rather
spectacular way, V404 Cyg displayed the best example of such an outflow
observed to date (see Sec. 5.3), but other sources show a similar property,
albeit in a less extreme way (see e.g. [300, 350, 228, 327] for the case of
GRS 1915+105, [408] for V4641Sgr, and [170, 332] for Swift J1858.6$–$0814).
Interestingly, again similarly to the case of both jets and winds, outflows of
this sort have been already observed - although not frequently - around SMBHs,
in those AGN which are generically referred to as obscured (see e.g., [331]
for a discussion on the topic).

##  4 The high-energy emission from BHBs in the INTEGRAL era

Understanding the mechanisms of production of high-energy photons by XRBs is
crucial for understanding the physical processes at work in the regions
surrounding the central compact objects. The properties and evolution of the
two main components constituting the energy spectra of BHBs - the cool,
geometrically thin disc, and the hotter, geometrically thicker hot flow (see
Sec. 2.2) - explain well the spectral shape evolution from the sub-keV region
up to $\sim$100–200 keV. As already mentioned above, the $\sim$10–200 keV
spectrum is well understood in terms of Comptonisation of soft photons from
the disc by the Maxwellian-distributed electron population in the hot flow
[514].

As soon as the signal to noise ratio became high enough thanks to improved
instrumental sensitivity, it also became clear that the BHB emission above
$\sim$100–200 keV deviates from the spectral shape expected in the presence of
a thermal Comptonisation continuum. The earliest observations of Cyg X-1 (see
Sec. 5.2) in its hard state, revealed the first hints of spectral hardening
above a few hundreds of keV (see [254] and references therein) as well as the
presence of possible annihilation line features [353]. More robust results
followed at the beginning of the ‘90s, with the launch of space-bound missions
covering a broader energy domain, which featured improved sensitivity that
started to shed light on the soft $\gamma$-ray emission from BHBs. Instruments
such as OSSE & COMPTEL on CGRO, and SIGMA on Granat, which observed the sky
from 15 keV up to few MeV, really opened the way to the exploration of the
high-energy emission from BHBs.

A soft $\gamma$-ray tail, in excess of a thermal Comptonisation and in the
form of a simple power law, was confirmed in Cyg X-1, both in the soft and in
the hard states [291, 293]. A similar component was also tentatively detected
in the transient BHB GX 339$-$4 [502] and in Nova Persei (GRO J0422+32), a
bright X-ray transient discovered in 1992 by CGRO/BATSE [159, 200, 255]. Such
findings have emphasised the need to explore the high-energy sky above a few
hundreds keV.

Thanks to INTEGRAL, more and more observations covering the high-energies have
become available over the years, revealing a more complex configuration. The
INTEGRAL mission was specifically designed to investigate in greater detail
the hard X-ray/soft $\gamma$-ray domain, in particular thanks to two
instruments - IBIS and SPI - featuring high sensitivity in the energy band
from 20 keV to a few MeV. INTEGRAL observations of Cyg X-1 assessed the
presence in the hard states of a spectral component extending to the MeV,
beyond the Comptonised emission observed in all the known BHBs [38, 52, 267,
203, 100]. Thereafter, the presence of such a soft $\gamma$-ray tail was
revealed by INTEGRAL in several BHBs, when in hard or hard-intermediate states
(e.g. GX 339$-$4 [102], GRS 1758-258, [381], 1E 1740 [37], V404 Cyg [428],
Swift J174510.8–262411 [98], MAXI J1820+070 [427], GRS 1716–249 [17]) and also
in a few systems harbouring a neutron star (e.g., GS 1826$-$238, [412]). After
the launch of INTEGRAL, it started to become clear that if the presence of the
second component (referred to in the literature as the “hard tail” or the
“soft $\gamma$-ray tail”) is omitted in the model description of a BHB broad-
band spectrum, the temperature of the Comptonising medium may be affected and
will be overestimated. Furthermore, variations in the soft $\gamma$-ray
component may mimic an evolution of the apparent temperature and/or optical
depth of the Comptonised continuum. This is particularly important for
instruments with limited sensitivity in the corresponding energy domain (i.e.,
above 200 keV), which would not be able to properly probe the soft
$\gamma$-ray tail and its variations.

Various works were dedicated to the study of the variability of this high-
energy emission and to its correlation with other spectral components (see the
individual source sections below), and evidence was found that the soft
$\gamma$-ray tail evolves independently from the thermal Comptonisation
emission [109]. However, none of these works has allowed the validity of one
particular scenario over the others to be confirmed [e.g., 199, 268, 375,
204]. Various hypotheses on the nature of the soft $\gamma$-ray tail have been
put forward: a second Comptonisation region (or a gradient of temperature in
one single emission region), a pair plasma [e.g., 37, 353] or - probably the
most popular one - an hybrid thermal/non-thermal electron population [e.g.,
83, 387]. It has also been suggested that the high-energy tail could be at
least partially explained in terms of a jet contribution to the X-ray emission
(see also Section 3), but the level of this contribution is the subject of
intense controversies.

INTEGRAL detected a strong polarisation of the soft $\gamma$-rays (0.4–2 MeV)
from Cyg X-1 ([247, 202], see Section 5.2), which indicates that the jet
synchrotron emission likely dominates at these energies, in particular in the
hard states [422]. Polarisation measurements on other BHBs proved to be
difficult mainly due to low number statistics limitation, as polarisation
measurements based on IBIS and SPI data require the accumulation of an
important number of photons above $\sim$100 keV, which is often challenging in
sources not as bright as Cyg X-1. Therefore, the vast majority of the
polarisation measurements from XRBs made by INTEGRAL come from observations of
Cyg X-1, even though tentative polarisation detections exist for two extreme
transients (V404 Cyg, [246] and MAXI J1348$-$630, [Cangemi, F, PhD thesis,
2020]).

At low energies (i.e. below a few tens of keV), the measured polarisation is
limited ($<$10 percent in the case of Cyg X-1, [257, 71]), which seems to
favour Comptonisation in an extended hot flow for the bulk of the observed
X-ray emission below $\sim$200 kev [71, 72]. However, some authors have
pointed out that Comptonisation, or hybrid Comptonisation, may also arise in
the jets [e.g., 275, 244], but for this component to dominate the X-ray
emission, the energy budget requires the ejected plasma to be dominated by
electron-positron pairs [264, 259]. A highly polarised emission in the soft
$\gamma$-rays, instead, points at the presence of a synchrotron emission
arising from an ordered medium, most probably a jet. It seems therefore
possible that the (polarised) soft $\gamma$-ray emission arises from the same
population of electrons that generate the synchrotron emission in radio, and
that the jet produces most of the photons observed above 300–400 keV. The fact
that the polarisation fraction increases with energy (from less than 20% below
$\sim$230 keV, to greater than 75% above $\sim$400 keV) is consistent with a
scenario where the jet contributes marginally to the emission below $\sim$100
keV - where instead inverse Compton is responsible for the bulk of the emitted
photons - and dominates above $\sim$400 keV in a form of a power law-like
spectrum with photon index $\sim$1.6 [247, 202].

Theoretical studies performed by Zdziarski et al. [521] demonstrated that jet
models can in fact explain the soft $\gamma$-ray-energy emission assuming
continuous particle acceleration along the jet. However, standard jet models
usually require rather extreme parameters in order to reproduce the observed
MeV spectrum of X-ray binaries [e.g., 521, 17, 214], such as a very hard
electron energy distribution (electron index $\sim 1.5$) and strong
constraints on the magnetic field. Therefore, on the one hand, the spectrum
observed above the high-energy cut-off is more easily interpreted in terms of
inverse Compton emission from a small population of non-thermal particles
located near the BH [e.g., 387, 265, 389]. On the other hand, the problem in
this scenario is that the degree of polarisation expected from these hybrid
thermal/non-thermal Comptonisation models would be much weaker than that
observed, e.g., by INTEGRAL in Cyg X-1 above 300 keV [21].

Even though more and better data are necessary to further investigate the
nature of the soft $\gamma$-ray tails in BHBs in order to solve the above
discrepancy, the high degree of polarisation observed in the very hard tail
makes a jet origin quite plausible.

##  5 Galactic Black Holes

System | Coordinates | References
---|---|---
| J2000 | (based on INTEGRAL results)
GRS 1915+105 | 19 15 11.55 +10 56 44.90 |  [110] [135] [167] [168] [423] [424] [417]
Cygnus X-1 | 19 58 21.67 +35 12 05.78 |  [18] [38] [47] [52] [55] [100] [201] [202]
|  |  [203] [247] [258] [268] [383] [385] [422]
V404 Cyg | 20 24 03.82 +33 52 01.90 |  [1] [128] [204] [207] [236] [237] [328] [329]
|  |  [333] [344] [413] [415] [428] [441] [452]
GX 339$-$4 | 17 02 49.38 -48 47 23.16 |  [26] [46] [50] [97] [102] [198]
1E 1740.7$-$2942 | 17 43 54.83 -29 44 42.60 |  [37] [36] [95] [96] [101] [67]
IGR J17091$-$3624 | 17 09 07.61 -36 24 25.70 |  [59] [241] [260] [418]
IGR J17098$-$3628 | 17 09 45.93 -36 27 57.30 |  [60] [73] [150] [151] [392]
IGR J17177$-$3656 | 17 17 42.62 -36 56 04.5 |  [134] [367]
IGR J17464$-$3213 | 17 46 15.60 -32 14 00.86 |  [60] [61] [199] [371] [407]
IGR J17454$-$2919 | 17 45 27.68 -29 19 53.45 |  [74] [75] [363] [366]
IGR J17497$-$2821 | 17 49 38.04 -28 21 17.50 |  [239] [458]
GRO J1655$-$40 | 16 54 00.14 -39 50 44.90 |  [45] [105] [199] [449]
GRS 1716$-$249 | 17 19 36.93 -25 01 03.43 | [17]
GRS 1758$-$258 | 18 01 12.40 -25 44 36.10 |  [382] [381]
GS 1354$-$64 | 13 58 09.70 -64 44 05.80 | [362]
MAXI J1828$-$249 | 18 28 58.07 -25 01 45.88 |  [130] [131] [152]
MAXI J1836$-$194 | 18 35 43.45 -19 19 10.48 | [153]
Swift J1745$-$26 | 17 45 10.85 -26 24 12.60 |  [98] [212]
Swift J1753.5$-$0127 | 17 53 28.29 -01 27 06.22 |  [49] [210] [411]
XTE J1550$-$564 | 15 50 58.70 -56 28 35.20 | [467]
XTE J1720$-$318 | 17 19 58.99 -31 45 01.11 | [51]
XTE J1752$-$223 | 17 52 15.09 -22 20 32.36 | [82]
XTE J1817$-$330 | 18 17 43.53 -33 01 07.80 | [439]
XTE J1818$-$245 | 18 18 24.43 -24 32 17.96 | [48]
MAXI J1348$-$630 | 13 48 12.79 -63 16 28.48 |  [54] [56] [249]
MAXI J1631$-$479 | 16 31 14.22 -47 48 23.44 |  [132] [358]
MAXI J1820+070 | 18 20 21.94 +07 11 07.19 | [427]
SS433 | 19 11 49.56 +04 58 57.82 |  [76] [77] [78] [79] [80]
Cygnus X$-$3 | 20 32 25.78 +40 57 27.90 |  [20] [57] [175] [472]
Table 1: A list of the black hole X-ray binaries in this work.

In this section, we will briefly review the results that have been obtained
thanks to INTEGRAL on BHBs. With no pretence of being exhaustive, we aim to
give an overall view of the contribution of INTEGRAL to the field, focusing on
the results that we consider most relevant. We will concentrate on a few
sources that we judge particularly relevant because of their historic
importance, as well as of their specific characteristics and behaviour, i.e.,
GRS 1915+105 (Section 5.1), Cyg X-1 Section 5.2, V404 Cyg (Section 5.3), GX
339$-$4 (Section 5.5), 1E1740.7$-$2942 (Section 5.6). In Section 5.7, we will
go through the sources that were discovered by INTEGRAL, in Section 5.8, we
will review other BH systems that INTEGRAL observed over its 18 years of
activity. Finally, we will briefly overview SS 433 and Cyg X-3, which may host
a stellar-mass BH (Section 5.9.1 and Section 5.9.2). Table 1 lists all the
sources covered in this work, along with their coordinates, and the references
to the most relevant works reporting findings obtained based on INTEGRAL data.

###  5.1 GRS 1915+105

####  5.1.1 A short resume of a very peculiar source

GRS 1915$+$105 was discovered in 1992 with the WATCH instrument on-board
Granat [68]. It is considered a transient source, although it has always been
active since its discovery. Contrary to most other sources, and until quite
recently [e.g., 349, 180, 417, 327], GRS 1915$+$105 has always been found in a
bright X-ray state, and is most likely one of the brightest BHBs in our
Galaxy.

Infrared observations made with X-shooter allowed the orbital period to be
refined to P$\sim$33.85 days [461], and to obtain a mass measurement of
M${}_{\mathrm{BH}}\sim$10.1 M⊙ and M${}_{\mathrm{Star}}\sim$0.47 M⊙ for the BH
and its K-M III companion star, respectively. A distance of $\sim$9 kpc was
obtained by Reid et al. [401] from VLBA radio parallax measurements, which
allowed the mass to be re-evaluated and refined (M = 12.4${}_{-1.8}^{+2.0}$
M⊙), and the jet inclination and average speed to be accurately estimated -
$\sim$60o and between 0.65c and 0.81c, respectively [401].

GRS 1915$+$105 is amongst the few microquasars that do not behave like the
vast majority of Galactic black hole systems (a-la GX 339$-$4)444See also V404
Cyg and Cyg X-3 as two more obvious ’outliers’, although likely for different
reasons (Sec. 5.3 and 5.9.2). Among its most obvious peculiarities:

  * •

it has been in outburst for almost $\sim$30 years, most likely because of its
large accretion disc, the largest among all the known Galactic BHs, which
provides an extremely large mass reservoir;

  * •

its outburst is characterised by extreme variability on seconds to years
timescales (see Fig. 2), with X-ray flares appearing randomly either isolated
or in series, interspersed by longer phases of bright but steadier X-ray
emission (Fig. 2);

  * •

it is highly variable at all wavelengths on short time-scales: in particular,
on sub-second time scales shows both LF & HFQPOs [e.g., 317, 338, 421], and on
seconds-minutes time-scales it displays large oscillatory repetitive patterns
(including the so-called heartbeats) [e.g., 307, 24, 224]

  * •

it does not clearly follow the common ’Q-shape’ pattern in the HID, which is
typical of the vast majority of BHBs (Sec. 2), but shows transitions between
three accretion states in many ways similar to the canonical ones [24] (see
below).

  * •

besides major relativistic discrete jets and the LHS compact jet, which are
also observed in other BHBs, it also shows another type of jet, characterised
by repeated small ejections in fast succession (tens of minutes, with fluxes
of the order 30-100mJy [e.g., 380]).

####  5.1.2 The largest display of variability patterns

The RXTE satellite monitored GRS 1915+105 intensively over its 16-years long
life-time, generating one of the largest soft X-rays dataset at high time
resolution for this system. Based on $\approx$8 years of data, Belloni et al.
[24] identified 12 distinct variability patterns in the 1-s resolution X-ray
light curve of GRS 1915+105. Such variability classes repeat randomly in time,
tracing specific patterns in a colour-colour diagram555A colour-colour diagram
is similar to the HID, but the intensity is replaced by a second hardness
ratio (or colour), obtained from intensities measured in two extra energy
bands., and are believed to reflect transitions among three accretion states,
labelled A, B, and C. Such states are roughly equivalent to - but not
coincident with - the HSS (state A), a bright SIMS (state B), and a bright
HIMS (state C), with which they share common fast temporal properties, in
particular in terms of the presence and behaviour of QPOs [e.g 338, 339, 421,
419, 424].

Two additional variability patterns were added to the original 12 a few years
after Belloni et al. [24], one thanks to the longer, quasi-uninterrupted
observation possible with INTEGRAL [167]. All the variability patterns have
been named using Greek letters, and are widely used to describe essentially
any new X-ray dataset obtained on GRS 1915+105. The 2–20 keV X-ray spectral
analysis also indicated that the transitions between states could be due to
rapid emptying/refilling of the inner disc [25], which evolves on either the
viscous time-scales, or on faster/(quasi-)dynamical time-scales [114]. With
the exception of IGR J17091$-$3624 (see Sec. 5.7.1), GRS 1915+105 is the only
system showing such a large number of variability patterns. No Galactic BHBs
continuously shows the variability typical of GRS 1915+105, although a few
other sources have shown at times a handful of classes. Such an example is the
NS XRB MXB 1730$-$335, also known as the Rapid Burster [6], which has been
recently shown to display two variability classes observed in GRS 1915+105
(namely, the $\rho$ and $\theta$ class). A second example is the ULX system
4XMM J111816.0$-$324910 in the galaxy NGC 3621, which might host a stellar
mass BH or a NS, and has also clearly shown the heartbeats typical of GRS
1915+105 [330].

####  5.1.3 A lab for studying the accretion-ejection connections

While GRS 1915+105 is in many ways unique, it also shares several properties
with more conventional transient BHBs (e.g GX 339$-$4, [107, 459]), and also
with some AGN (and in particular some quasars, [280, 69, 395]), which are
thought to display mass-scaled versions of GRS 1915+105’s correlated X-ray and
radio behaviour close to jet ejection events. Therefore, comprehending the
coupling between inflow and outflow in GRS 1915+105 is important for the
understanding of XRB systems, but has also a broader relevance for studies of
AGN, and potentially of all the jetted systems powered by accretion on compact
objects [123].

GRS 1915$+$105 is considered the archetypal galactic source of relativistic
jets, and as such has been for many years the source of choice for the study
of the physics of jets. Radio observations performed early after its discovery
revealed the presence of large scale radio jets making GRS 1915$+$105 the
second microquasar (see Sec. 1.1) after 1E 1740.7$-$2942 [309]. Such radio
jets were seen to evolve on the plane of the sky with an apparent superluminal
motion [308], and - as it was clarified later - correspond to the transient
relativistic ejections observed also in other BHBs during the LHS to HSS
transitions. GRS 1915$+$105 also shows a rather steady radio emission,
associated with harder and less variable X-ray emission, which has been
ascribed to the presence of a compact jet of smaller extension [104]. GRS
1915$+$105 and the high-mass BHB Cyg X-1 (Sec. 5.2) are the only sources where
compact radio jets have been resolved with interferometric radio observations
performed using Very Long Baseline Interferometry (VLBI) [104, 464, 135].

In addition to the radio emission associated with transient and compact,
steady jets, GRS 1915$+$105 also shows smaller amplitude radio and infrared
oscillations [380, 127, 307], which simultaneous multi-wavelength observations
in radio, IR, and X-ray observations have associated with X-ray oscillations
on the same time-scales [116, 307]. The radio/IR oscillations were interpreted
as the signature of small discrete ejections of material from the system
occurring on a rapid succession, possibly associated with certain disc
instabilities developing in the accretion flow. This particular radio/IR and
X-ray correlated variability made GRS 1915$+$105 the first and still in many
ways the best source where the disc-jet coupling can be probed in detail. For
this reason, GRS 1915$+$105 has been the target of numerous multi-wavelength
observing programs, many involving INTEGRAL, over the past 19 years, and is
also being currently monitored regularly, as simultanously as possible, by
INTEGRAL, Insight-HXMT and Nicer in the X-rays, the Sardinia and Medicina
radio telescopes in Italy, and AMI-LA in the UK666We note that monitoring
observations are not restricted to these facilities, but we mention here only
those that are in tentative simultaneity with the long-term INTEGRAL
monitoring.

The main questions at the core of most of the observing programs that have
targeted GRS 1915$+$105 over the years revolve around the interplay that
exists between the inner accretion flow and the generation of various types of
outflows, which not only includes the jets observed in radio, but also the
disc winds seen during the soft(-ish) states [351]. The advent of INTEGRAL
allowed the spectral window to be extended to energies above 20 keV, and thus
to study the behaviour of the Comptonised emission, probe the presence of an
additional soft $\gamma$-ray tail, and explore the potential connections of
such spectral components end their properties with the presence of jets [e.g.,
135, 423, 110].

####  5.1.4 18 years of INTEGRAL observations: long-term light curve and
selected results

Figure 2 shows the GRS 1915$+$105’s RXTE/ASM, MAXI and INTEGRAL/IBIS/ISGRI
30–80 keV light curves from 2002, October 17th (INTEGRAL’s launch) to 2020,
December 31st. The ISGRI light curve was obtained from all the available
pointings between revolution 48 (MJD 52704.523, or 2003 March, 6th) and 2298
(MJD 59170.195 or 2020, Nov. 17th), where we selected data with an ISGRI
exposure greater than 500 s. We further restrained to data where GRS
1915$+$105 was observed with an off-axis angle of less than 10o. This results
in a total of 7609 good pointings.

Figure 2: Long term light curves from GRS 1915+105. From the top: AMI-LA
(circles) and MeerKAT (diamonds) data (panel a), MAXI data (panel b) covering
the 4–20 keV energy band, BAT data (panel c) covering the 15–50 keV energy
band, IBIS/ISGRI data (panel d), covering the 30–50 keV energy band. In panel
(d), red- and blue-edged points mark data reduced using OSA 10.2 and OSA 11.1,
respectively. Each point in panel (d) comes from one INTEGRAL revolution
($\approx$300 hr). In July 2018 ( MJD 58300) GRS 1915+105 started a slow
decline towards an X-ray plateau, which still continues at the time of
writing. A marked change in the radio behaviour of the source is visible
around MJD 58600. Figure adapted from Motta et al. [327].

The very first dedicated INTEGRAL observation made during revolution 48 was
reported by [168]. Analysis of these data allowed a ’new’ source, IGR
J19140$+$0951, to be discovered. The JEM-X, IBIS/ISGRI, and RXTE/PCA light
curves permitted to identify a new variability class to be added to the 12
already defined by Belloni et al. [24]. This new class, labelled $\xi$ [167],
is characterised by a flaring behaviour (Fig. 3) composed of a main,
relatively hard pulse, followed by smaller amplitude softer ones, recurring on
a typical time-scale of about five minutes. The JEM-X, ISGRI, and SPI spectra
obtained at the flare peaks and in correspondence with the minima between
consecutive flares are well fitted by a model consisting of a bright disc and
hybrid thermal/non-thermal Comptonisation above $\sim$ 10 keV, compatible with
the source being in a soft state (state A) during class $\xi$. Unlike other
classes, where flares sign transitions between states A-B-C, the flares in
class $\xi$ are purely isothermal and the overall variability is attributed to
limit-cycle oscillations, possibly resulting from delayed feedback in the
inner accretion disc.

Figure 3: The upper plots show the JEM-X 3–35 keV light curve of GRS 1915+105
obtained during the first half of the rev. 48 observation (left), and the
spectra obtained from both the peak and at the minima in between flares in
this observation obtained combining JEM-X, ISGRI and SPI data (right). Adapted
from Hannikainen et al. [167]. The lower plots represent the radio (panels
(a)), X-ray (panels (b) for JEM-X and (d) for RXTE/pca), and hard X-ray
(IBIS/ISGRI, panels (c)) light curves of 3 variability classes showing radio
ejections. Adapted from Rodriguez et al. [423].

Fuchs et al. [135] reported the very first simultaneous multi-wavelength
observations of GRS 1915$+$105, which happened during revolution 57 (MJD
52731, 2003 Apr. 2nd). Less than a month after the discovery of class $\xi$,
the source was found in a ’steady’ state, associated with class $\chi$ (state
C). Benefiting from one of the largest frequency coverage ever obtained for
this system, Fuchs et al. [135] could observe (i) a strong steady optically
thick radio emission, resolved with the VLBA as a strong compact jet; (ii)
bright near-IR emission (probably associated with the jet); (iii) a strong QPO
at 2.5 Hz in the X-rays; (iv) a power law spectrum without any cutoff in the
3–-400 keV range. This was the first time that all these ’hard’-state
properties were observed simultaneously, thus reinforcing the suspected links
among the hard accretion state, the presence of a compact jet as well as of a
high-energy tail, and X-ray QPOs.

The detection of hard X-ray/soft $\gamma$-ray tails above $\sim$100 keV was
studied by Droulans and Jourdain [110] with SPI. The analysis of 20
observations (19 of which have exposures larger than $\gtrsim$45 ks) with data
covering the 20–500 keV energy range clearly shows the need for an additional
power law component beside the standard thermal Comptonisation used to
represent the $\sim$20–100 keV spectra. An hybrid Comptonisation model also
adequately represents the spectra, and Droulans and Jourdain [110] argue that
the 20–500 keV emission in GRS 1915$+$105 might be due to a combination of
thermal and non-thermal Comptonisation. The comparison between the emission in
the 1-12 keV (RXTE/ASM) energy range, and the 20-50 keV energy range (SPI)
showed that the emission in the two bands vary in a correlated fashion. This
property led the authors to conclude that the emission in these two bands
arises from the same spectral component, but has no link with the hard
spectral tail above 50 keV, which is rather stable and does not follow the
variations of the other two components. The X-ray variability classes in GRS
1915$+$105 most likely reflect changes within the accretion flow (e.g.,
accretion rate changes, variations of the viscosity). Instead, the emission
above 10 keV reflects the properties of the electron population(s). The fact
that the parameters of the population of thermalised electrons may vary, but
not in a correlated fashion with the variability pattern observed in the light
curves of GRS 1915$+$105, suggest that the macroscopic properties of the
Comptonising electrons evolve independently from those of the (inner)
accretion flow.

####  5.1.5 An X-ray signal precursor to small ejections: is the corona the
source of ejected material?

The possibility to follow GRS 1915$+$105 on long continuous observing window
with INTEGRAL allowed observers to nicely monitor the variability patterns for
long periods of time [e.g. 168], thus accumulating data during several
distinct accretion states [167, 110]. The long X-ray observations possible
with INTEGRAL also allowed simultaneous multi-band observing campaigns to be
organised more easily, which resulted in a better understanding of the source
[e.g., 135]. With the aim to study the interplay and causal relations between
the main emission components in GRS 1915$+$105 (jets, disc, corona), Rodriguez
et al. [423] presented the results of a long term radio to X/$\gamma$-ray
monitoring performed with the Ryle telescope, RXTE, and INTEGRAL. From the 11
INTEGRAL observations, these authors observed the source in 9 different
variability classes. Radio observations were made during of 8 of these, and in
particular allowed the intervals during which the source was displaying the
variability classes $\lambda$, $\nu$, and $\beta$ to be covered.

Rodriguez et al. [423] adopted a model-independent approach, based on the
inspection of light curves and colour diagrams, which allowed to witness
transitions between specific multi-wavelength states on short ($\sim$100 s)
time-scales (Fig. 3). This allowed Rodriguez et al. [423] to discover small
amplitude ejections in a new class ($\lambda$) correlated to a specific hard-
dip/soft flare X-ray behaviour. This is reminiscent of what is seen during
classes $\beta$, $\nu$ (confirmed in this same study), and $\alpha$. The
authors conclude that, in GRS 1915$+$105, small amplitude ejections
systematically occur in response to a phase of a hard X-ray dip ended by a
short, intense, and soft X-ray spike (bottom of Fig. 3). This proposition is
reinforced by the potential correlation between the amplitude of the radio
flare and the length of the preceding hard dip. These results were later
confirmed by the analysis of the entire sample of simultaneous RXTE/Ryle
observations [394].

Rodriguez et al. [424] presented both the spectral and temporal analysis of
the INTEGRAL and RXTE data of these 4 different variability classes. In the
case of the three ’cyclic’ classes, they performed a state-resolved
JEM-X/ISGRI spectral analysis. For each class, all cycles were separated into
3 ($\beta$), 4 ($\nu$), or 6 ($\lambda$) spectra based on their count rates
and hardness. The resultant phase-dependent spectra were modelled with a
common model consisting of an absorbed thermal/disc emission and a Comptonised
component. In all cases, the spectral analysis shows a comparable behaviour:
the inner disc radius and temperature increase from the hard dip to the soft
X-ray flares, with a relative disc contribution to the 3–200 keV flux that
increases monotonically over the sequence. Meanwhile the contribution of the
Compton ’corona’ first increases from the bottom of the dip to the rising part
of the first X-ray spike, and then shrinks at the spike’s maximum. It should
be noted that this spike is not necessarily the main obvious flare in this
sequence, but is the one that is easily seen ’half’ way through the dip in
class $\beta$. It is interesting to note that it is also at this moment that
the LFQPO observed up to this point disappears (as clearly visible in classes
$\beta$ and $\nu$). The main conclusion here is that the soft spike is the
true moment of the ejection (later seen in radio), and that the corona is the
source of the ejected material. The same conclusion was drawn by [420] in the
case of XTE J1550$-$564, and later discussed for other sources as well [414].

The spectral analysis of class $\chi$ revealed the presence of an additional
power law component beside the disc and thermal Comptonisation component.
While the low energy components (disc and thermal corona) show little
variations over the course of this observation, the high-energy power law
varies in apparent correlation with the radio flux. This led to the suggestion
that this ’hard-tail’ was somehow related to the jet emission, and thus was
akin to that observed in Cyg X-1 and a handful of other sources.

####  5.1.6 The recent low luminosity state: when GRS 1915$+$105 finally
behaves like other Galactic black holes (for a while)

On July 2018, based on MAXI/GSC data (Fig. 2), Negoro et al. [349] reported
the faintest X-ray state observed since 1996 (i.e., the start of daily
monitoring of the source with RXTE/ASM) from GRS 1915$+$105\. The observations
analysed were taken between 2018 July 7 and 8 (MJDs 58306-58307), and follow a
nearly exponential $\sim$100 days decrease [349]. Also the radio flux from the
source appeared to be relatively low (even though not significantly so)
compared with the historical data. Unfortunately, at the time of the main
decline observations with INTEGRAL were not possible.

On 2019 May Homan et al. [180] and Miller et al. [297] reported a sudden,
further X-ray dimming as observed by Chandra and Nicer. An active
Swift+INTEGRAL monitoring of the source allowed Rodriguez et al. [417] to show
that the source was in a state very similar to the a canonical BH LHS, i.e.
significantly harder and fainter that the typical C state (during class $\chi$
in particular), typically observed in GRS 1915$+$105\. Unlike the usual anti-
correlated soft-hard X-ray behaviour, a significant hard X-ray dimming was
also reported from the 2019, May, 13th (MJD 58616) Swift +INTEGRAL
observation, leading to the suggestion that the source was maybe slowly
decaying to quiescence. This hypothesis was refuted quickly by Iwakiri et al.
[195], who observed a flare with both Maxi and Swift/BAT. Since then, as can
be seen in the long term light curve in Fig. 2, although the source is indeed
in a long, slightly decreasing, low flux state, it still appears to have quite
regular X-ray flares, and an extremely marked radio flaring, in all
qualitatively similar to what has been observed over the many years of the
outburst of GRS 1915$+$105 [323, 327]. This recent period certainly attracted
great interest in this source as testified by the number of Astronomer’s
Telegrams reporting on the changing phenomenology observed from the source
(and numerous papers published over the following year), including brief
transitions to faint states, sudden flares, and brief episodes during which
some of the several known variability classes of GRS 1915$+$105 manifested.
The origin of this possibly new state remained unclear for some time, although
reports of obscuration episodes interleaved by short and intense flares
started to highlight significant similarities between GRS 1915$+$105 and
systems displaying phases of strong, variable local absorption: all such
systems tend to show high-amplitude flares. Some noteworthy examples are V4641
Sgr [408], Swift J1858.6$-$0814 [170, 332], and even some Seyfert II galaxies
[316], and - perhaps the clearest and most recent example - V404 Cyg.

Radio observations of GRS 1915$+$105 during the long X-ray plateau finally
solved the conundrum: while during approximately half of the X-ray plateau GRS
1915$+$105 was remarkably quiet in radio, after a month-long multi-band
flaring period, its radio activity resumed and continued after the multi-band
flaring ceased. In this phase, absorption was a constant characteristic of the
X-ray energy spectra of GRS 1915+105 [231, 300, 350, 10, 228], indicating the
presence of an obscuring in-homogeneous absorbing medium located close to the
source. The radio emission, instead, was characterised by marked flaring
activity qualitatively very similar to that observed in the past. This
provided evidence for two important facts: first, that the correlation between
radio and X-ray emission (which for many years characterised GRS 1915+105
[123]) ceased to exist during the latest evolution of GRS 1915$+$105; and
second, that the X-ray behaviour alone—in the absence of such radio-X-ray
correlation—is very misleading, as it offers only a partial view of the
current state of the source. It thus appears that GRS 1915+105 has not entered
quiescence yet, and might not be approaching it either (but see [350] and
[228]). Continued observations of this intriguing source will show what path
the outburst evolution will take this time.

Based on the results obtained with the dense monitoring of this unusual phase
in the life of this iconic X-ray binary, it seems now clear that the decline
preceding the long-lived X-ray plateau observed starting from mid-2018 was a
transition to a truly dim state, very similar to the canonical LHS typical of
many transient BHBs [417, 327]. Such a state, characterised by low X-ray and
radio flux, as well as low long-term variability in both bands, is certainly
unusual for GRS 1915+105, which has never been observed before in a low-
luminosity canonical LHS [but see 140]. The second half of the long X-ray
plateau, following the multi-band aforementioned flaring period, despite
having been dubbed ‘the obscured state’, it is not really a state, but rather
a condition directly dependent on the presence of local absorption along our
the line of sight [327].

The accretion processes that must be feeding the markedly variable jet
observed in radio must be happening beneath a complex layer of material local
to the source, which shields the inner portion of the accretion flow, and thus
blocks a large fraction of the X-ray emission. Behind this Compton-thick
curtain of material, GRS 1915+105 is most likely evolving through various
states and transitions (as shown by Motta et al. [327]), consistent with what
it had been doing for 25 years until June 2018. This means that, perhaps, GRS
1915+105 did not really enter the outburst phase in 1992, when it was
discovered, but simply emerged from an obscured phase similar to the one we
are witnessing at the time of the observations presented in Motta et al.
[327], as suggested by Miller et al. [300].

As to what is the reason behind the change in the behaviour of GRS 1915$+$105,
as in many other ways this systems remains a mystery, despite having been
scrutinised with essentially any instrument that could ever observe it, from
the radio radio to the $\gamma$-rays. A change in the accretion flow must have
happened to trigger such a remarkable change in the emission from the source,
but whether this was due to a change in the companion star, or in the
properties of the accretion flow itself remains unclear. Certainly GRS
1915$+$105 remains one of the most important BHBs we know, and a lot has to be
learned still from this system. INTEGRAL, which has greatly contributed to the
understanding of GRS 1915$+$105, will be crucial to the continuation of the
studies of this system, especially if the obscured phase will continue for
much longer. Instruments sensitive to the lower energies will not be able to
monitor the activity of this source (currently best studied in the hard
X-rays), which are much less affected by absorption, and are easily within the
reach of INTEGRAL.

###  5.2 Cygnus X-1

####  5.2.1 A key source for understanding black hole XRBs

Discovered during a rocket flight in 1964 [40], and identified to be a massive
source in orbit with the O9.7 Iab star HDE226868 [35, 503], Cyg X-1 was the
first BH candidate (see Oda [356] for a review of the early observations). As
also discussed in Sect. 1.1, Cyg X-1 is one of only a handful of persistent
stellar-mass BHs in our Galaxy. The newest VLBI parallax measurements place
the source at a distance of $2.22^{+0.18}_{-0.17}$ kpc, and yield a mass of
the BH of $21.2\pm 2.2M_{\odot}$ [301].

Figure 4: IBIS/ISGRI long-term light curve of Cyg X-1 since 2004 [55]. Colours
indicate the state of the source (blue: hard, green: intermediate, red: soft).
The dashed lines separate the time intervals included in the earlier analysis
[415] and the data from newer programmes. Figure taken from Cangemi et al.
[55].

With a 5.6 d long, circular orbit and an orbital separation of $40\,R_{\odot}$
between the two binary members, the BH is close enough to the donor that the
stellar wind is focused towards it [148]. Therefore, accretion occurs mainly
via a wind, although the presence of a small accretion disc dampens the short
term fluctuations typical of pure wind accretors. The result is that Cyg X-1
spends a significant fraction of the time in the LHS. In fact, Cyg X-1 has
been considered for long the prototype of the BHB in the LHS, although
excursions into the HSS are possible and have been often observed. In
particular, the source has spent more time in the HSS in the last decade [156,
55]. As the BH is deeply embedded in the stellar wind, strong orbital
variability is seen in the soft X-rays; there are both an overall orbital
modulation due to line of sight effects through the wind [390, 157] as well as
short-term absorption dips caused by density fluctuations in the stellar wind
and/or the accretion flow passing through our line of sight [e.g., 252, 12,
299, 311, 173]. In addition, a strong broadened Fe K$\alpha$ fluorescence line
has been observed, which might suggest that the BH has a high to extreme
intrinsic angular momentum [120, 121, 483, 370, 112, 527].

Cyg X-1 has been subjected to deep observations with virtually any available
X-ray missions, past and present. A comprehensive review of all of its
properties is therefore not possible nor appropriate here. We will instead
concentrate on the areas where INTEGRAL contributed the most, including the
studies of the broad band X-ray spectrum and of the radio through X-ray and
$\gamma$-ray spectral energy distribution, the hard X-ray variability, and the
question of the soft $\gamma$-ray tails and its polarisation.

####  5.2.2 Spectral behaviour and short-term variability

In the hard state, the X-ray spectrum of Cyg X-1 can be well described by a
Comptonisation continuum (see [383, 100] for studies using INTEGRAL), together
with a Compton reflection hump [112]. Phenomenologically speaking this
corresponds to a power law continuum with an exponential cutoff. Above a few
hundreds keV, deviations from this continuum become apparent, indicating the
presence of a soft $\gamma$-ray tail. We will discuss this spectral component
and its polarisation – which was first measured with INTEGRAL– in Sect. 5.2.3
below.

In order to study the broad-band long-term variability of the source, INTEGRAL
has performed an extensive monitoring of the source since launch, accumulating
more than 15 Ms of exposure on this system. Figure 4 shows the long-term light
curve of the source obtained from this campaign [55], also encoding the source
state, determined following the prescription of Grinberg et al. [156]. These
observations are part of an unique long-term observing campaign with multiple
instruments that started in the late 1990s. The aim of these observations was
to study the evolution of the broad-band spectral energy distribution from 1
keV to ${\sim}$2 MeV, the short-term X-ray timing behaviour, and the
relationship between the X-rays and the radio emission of the source. The
campaign consisted of INTEGRAL key programme observations, bi-weekly 5–10 ksec
RXTE pointings, and dedicated simultaneous observing campaigns with Chandra,
Suzaku, NuSTAR and XMM-Newton, which have been accompanied by extended
monitoring observations in the radio (AMI-LA, VLA) and in the optical bands
[384, 386, 504, 505, 52, 268, 163, 113, 34, 100, 483, 112, 298, 156, 158, 157,
422, 311, 484, 173, 258, 55].

The main emphasis of the spectroscopic analysis of the campaign concentrates
on the statistics and interpretation of the continuum emission of the source,
as other missions are better suited for studies of the soft X-ray spectrum and
the relativistic reflection. Statistical analysis of the hard and intermediate
states of Cyg X-1 showed that the source behaviour on these states is more
complex than previously assumed. For example, Lubiński et al. [258] used IBIS
data in the 22–100 keV range to constrain the correlations between hard X-ray
flux, spectral shape expressed by the photon index, and variability
properties. The X-ray flux and photon index show a multi-mode behaviour, with
multiple clusters of typical parameter configurations, corresponding to
different flavours of the states, especially during the LHS. These clusters
show different X-ray and radio variability properties and are possibly related
to different accretion geometries. Similar indications of different hard state
flavours had been seen by Pottschmidt et al. [385] in the short-term
variability behaviour of Cyg X-1 in the $\sim$3–20 keV energy range of RXTE
data, and by Jourdain et al. [203] in the 20-200 keV energy band in the
INTEGRAL SPI data. For what concerns the intermediate state, INTEGRAL
observations also revealed similar bi-modal spectral variability [268].

INTEGRAL also offers an unique opportunity to extend short-term variability
(“timing”) studies to the hard X-rays, and to probe the short-term variability
of the hard X-ray emission in different spectral states. Pottschmidt et al.
[383] were able to obtain 15–70 keV PDS using ISGRI, focusing on a flaring
episode, while Cabanac et al. [47] used SPI up to 130 keV, concentrating on
long-term averaged PDS for the LHS and the HSS. The power spectral shapes are
generally consistent with those seen at lower energies with RXTE [385, 157,
and references therein] and can be described by a sum of several Lorentzian
components which show a characteristic dependency on the spectral hardness of
the source [158]. These studies showed that Cyg X-1 varies significantly up to
at least 130 keV.

####  5.2.3 SED, disc-jet connection, and polarisation

The major impact that INTEGRAL has had on our understanding of Cyg X-1 has
been on the behaviour of its hard tail and its polarisation (see Sect. 4 for a
general overview of the hard tail). The elusive soft $\gamma$-ray tails, i.e.,
excesses in the hard band above the rollover of the Comptonisation component,
have first been detected in Cyg X-1 with CGRO/COMPTEL [292, 293]. INTEGRAL was
crucial in confirming the detection of the tail with SPI [38, 52, 202] and
IBIS [247, 415], and in studying its possible dependency on the spectral state
[498]. Cangemi et al. [55] reported the analysis of the full data set of Cyg
X-1, in which the presence of a hard tail component also in the average soft
state spectrum was confirmed.

The modelling of the broad band radio to MeV and even TeV spectrum of Cyg X-1
results in two equally plausible explanations for its hard emission. One
explanation is that the hard tail is due to a non-thermal particle population
in the Comptonising medium [e.g., 426, 71, and references therein], while an
alternative explanation is that the hard tail is formed by synchrotron
emission from a jet [e.g., 268, 100, 375, 214]. The latter explanation, as
already mentioned above, would provide a direct connection between the hard
X-ray and $\gamma$-ray emission and the jets observed in radio (see also Sect.
3).

Cyg X-1 is an ideal source for tackling this question, since it is essentially
always located in the region of the HID sometimes referred to as the “jet-
line”[29], where transitions from the hard states to the soft states result in
energetic, relativistic ejection events, and subsequent jet quenching. For
this reason, the coupling between the disc and the jet can be studied
exceptionally well. The only other Galactic quasi-persistent hard state
sources, 1E 1740.7$-$2942 (see Sec. 5.6) and GRS 1758$-$258, both show
$<$5–10% of the typical X-ray flux of Cyg X-1. This makes their observation
more challenging, since it is much harder than in Cyg X-1 to accumulate enough
photons to study the emission above $\sim$300 keV. The other bright quasi-
persistent BH, GRS 1915+105, is (almost uniquely) operating in a very
different accretion regime, and thus is not particularly suited for
polarisation studies (see Sec. 5.1).

Del Santo et al. [100] analysed 6 years of INTEGRAL observations of Cyg X-1
using two hybrid thermal/non-thermal Comptonisation models. Besides the
largely used eqpair, for the first time these authors performed a spectral
fits with the belm model (Fig. 5) which takes into account the effects of the
magnetic field in the corona of BHBs [264]. They found that while in the soft
states the emission is dominated by Comptonisation of the disc photons, while
in the hard states, the data are consistent with a pure synchrotron self-
Compton model, which means that the synchrotron photons could be the only
source of seed photons for the Comptonisation process. Finally, Del Santo et
al. [100] provided important constraints on the intensity of the magnetic
field in the X-ray corona, which are in agreement with previous analytic
results [501].

Figure 5: Joint JEM-X, IBIS and SPI energy spectra of Cyg X-1 during four
different spectral states fitted with the belm model with pure non-thermal
acceleration, plus diskline and reflect (figure taken from Del Santo et al.
[100]).

Breaking the degeneracy between hybrid Comptonisation models and models where
the tail is explained through synchrotron radiation requires additional
diagnostics beyond the mere spectra analysis. INTEGRAL provides unique
capabilities to help clarifying the above issue, in particular thanks to the
data yielded by IBIS (ISGRI and PICsIT), as well as by the SPI instrument,
used as polarimeters (see Sect. 4). Based on IBIS data of the first years of
INTEGRAL, Laurent et al. [247] found that above 400 keV - where the hard tail
dominates the emission - a high degree of polarisation is observed, with hints
that the degree increases with increasing energy. These results were later
independently confirmed thanks to SPI [202] (Fig. 6).

The limited availability of data required these initial analyses to use all
available observations, and thus precluded a state-dependent analysis of the
data. It should be noted, however, that during the initial years of the
mission Cyg X-1 was predominantly observed in the LHS. The accumulation of
more data allowed Rodriguez et al. [422] to perform a state-resolved
polarisation analysis of the data, which confirmed a high degree of
polarisation in the LHS. However, only high upper limits could be placed in
the HSS, mainly owing to the lower flux of source in this state in the high
energies, combined with lower exposure accumulated during the HSS at the time
of the analysis.

The high degree of polarisation of the hard tail in Cyg X-1 makes it very
likely that the emission detected above 400 keV is due to synchrotron
radiation, as no other process is known that could produce such a high degree
of polarisation. The emission below 200 keV is not polarised, as one would
expect from Comptonisation. This result therefore strongly suggests that the
soft $\gamma$-ray tail emission originates in the jet, as is also suggested by
the Fermi satellite detection of a very high energy component [512] and by the
broad band spectral energy distribution of the source [375]. The fact that the
degree of polarisation is so high also means that the magnetic field
configuration in the source must be very simple and uniform, since only minor
de-polarisation must have occurred to randomise the starting polarisation.
This is particularly important because it sets strong constraints on
synchrotron models. For example, as argued by Zdziarski et al. [515], the
shape of the hard tail implies a rather hard electron energy spectrum ($p\sim
1.3$–1.6, where the electron energy distribution is $\propto E^{-p}$), i.e.,
significantly harder than what one would expect from standard electron
acceleration mechanisms, which would instead give $p\sim 2$. In addition,
there must be highly energetic electrons relatively far away from the BH
[375]. If the hard tail comes from the jet, then the observed Compton
component may be associated to the jet base, as postulated, e.g., by Markoff
et al. [275].

Figure 6: Spectrum and polarisation results from SPI. Figure adapted from
Jourdain et al. [202].

###  5.3 V404 Cygni

Figure 7: Swift/XRT (red for the source, orange for the dust scattering halo
spectrum) + INTEGRAL/JEM-X (purple) + INTEGRAL/ISGRI (clear blue) spectrum of
V404 Cyg fitted with model based on MYTORUS [507], as described in [329].
Upper panel: the thick black line marks the best fit to the data. The thin
black line indicates the illuminating Compton continuum, the dashed and
dotted-dashed lines mark the various components of MYTORUS, the dotted line
marks the fluorescent Fe line spectra and a Gaussian line at $\sim$7.5 keV.
Finally, the solid grey line indicates the model component accounting for a
dust scattering halo emission. Figure taken from Motta et al. [329].

####  5.3.1 A brief history of the first dynamical black hole

The transient system V404 Cyg harbours one of the first dynamically confirmed
stellar-mass BHs [63] (see also Bolton [35], McClintock and Remillard [286]).
It is located at a distance d = 2.39 $\pm$ 0.14 kpc [304], and is well known
by its bright and extremely variable outbursts. The system was detected as a
powerful X-ray source (GS 2023+338) by the Ginga satellite in 1989 ([261], and
promptly identified with the recurrent recurrent Nova Cygni 1938 [262, 281]
with recorded outbursts in 1938 and 1956 [410]. The 1989 outburst was
characterised by rapid and erratic flaring activity in X-rays in any time
scale down to 2 ms [473]: in some flares, drops in flux of $\sim$ 20 Crab in
less than one hour [473, 222] were observed. Despite the high fluxes exhibited
by the system, which might have reached the Eddington limit during the peak of
the outburst [473], the source energy spectra (well-described by a power law)
and PDS (mostly consisting of steep red noise) were consistent with V404 Cyg
being in the LHS during the entire outburst [473, 359], which suggested that
the source did not transition to the HSS (or intermediate states), as many
other transient BHBs do. It was also observed that the spectral parameters
were strongly influenced by changes in the local absorption, which had values
in the range $5\times 10^{21}-4.5\times 10^{23}$ cm-2 [473, 359, 190]. As the
outburst decayed, the average flux became less variable and the absorption
episodes were less frequent, until the source reached quiescence, the level of
which is notoriously higher ($L_{\textrm{x}}\sim 10^{34}\,{\rm
erg\,cm^{-2}\,s^{-1}}$) than for other BHBs in the case of V404 Cyg [137].

After $\sim$26 yr in quiescence, the onset of a new outburst was detected by
Swift/BAT, MAXI and Fermi/GBM on 15 June 2015 [15, 346, 510], although optical
data suggest that the outburst actually started one week earlier [32]. The
peak of the outburst was reached on 26 June 2015, and the flux dropped
abruptly immediately afterwards [128, 499]. Following this drop, V404 Cyg
slowly faded to quiescence over the subsequent weeks [453]. The outburst
triggered an intense multi-wavelength monitoring campaigns, which provided
data over the entire electromagnetic spectrum, generating one of the richest
(largely coordinated) multi-band campaign ever performed on a BHB. INTEGRAL
played a key role in providing X-ray and optical coverage as continuously as
possible between June 17th and July 13th 2015 [236, 237], yielding crucial
pieces of information which helped piecing together the most important
properties of this important system.

####  5.3.2 INTEGRAL observations of V404 Cyg

Intense flaring activity was observed by INTEGRAL between $17-28$ June 2015
[415, 344, 428, 441], as well as hardness variations on second time-scales
[344]. In some major flares, V404 Cyg reached peak fluxes around 50 and 40
Crab in soft and hard X-rays, respectively, and peak-to-peak flare recurrence
times as short as 20 min [415]. The extraordinary brightness of the source
allowed spectral studies with unprecedented time resolution for coded-mask
instruments such as those on-board INTEGRAL. Sánchez-Fernández et al. [441]
analysed 602 IBIS/ISGRI spectra of V404 Cyg during the intense flaring period
($17-28$ June 2015) with integration times as short as 8 seconds in the
brightest flares. All the 20–200 keV IBIS/ISGRI spectra were compatible with a
Comptonised model, which in most cases required an absorption component to fit
the data. The measured absorption columns were so high ($N_{\rm H}\gtrsim
10^{24}$ cm-2) - especially during the plateaus observed in the IBIS/ISGRI
light curves - that the effects of absorption were evident up to $\sim$ 30
keV. The absorption column density and the X-ray flux were anti-correlated in
most of the flares, suggesting that the observed variability was partly - but
not exclusively - due to variations in the absorption column. Sánchez-
Fernández et al. [441] studied the correlations between the parameters derived
from the fits of the IBIS/ISGRI spectra, and concluded that V404 Cyg had been
in the LHS during most of the outburst, but with clear indications for softer
spectra observed during some of the brightest flares.

The detailed analysis of the broad-band spectrum of V404 Cyg during one of the
June 2015 X-ray plateaus showed an energy spectrum reminiscent of that of
obscured/absorbed active galactic nuclei (AGN) [329] (see Fig. 7). The joint
spectral analysis of strictly simultaneous Swift/XRT, JEM-X and IBIS/ISGRI
spectra revealed a Comptonised spectrum ($N_{\rm H}\sim 1-3\times 10^{24}$
cm-2) heavily absorbed by a partial covering material, and a dominant
reprocessed component, which included a narrow Iron $K_{\alpha}$ line (see
Fig. 7). This finding indicated the presence of a geometrically thick
accretion flow as the likely responsible of both the high intrinsic absorption
and the intense reprocessed emission.

####  5.3.3 Other X-ray and multi-wavelength observations

A complete, time-resolved, spectral analysis of the available Swift/XRT data
[328] found that the XRT spectra could be fitted with a partially-covered,
absorbed power law. A blue-shifted Iron $K_{\alpha}$ line appears together
with the signature of high column densities. In these fits, changes in column
density relate with fast ($\sim$minutes) but moderate flux changes, while
variations in the covering fraction would be responsible for the most dramatic
flux and spectral changes observed during the outburst [328]. Interestingly,
despite the intense flares observed (sometimes exceeding the Eddington
luminosity), none of the spectra showed the unambiguous presence of soft disc-
blackbody emission. These findings were ascribed to the presence of a slim
disc in the vicinity (a few hundreds of Gravitational radii) of the central
BH, which both hides the innermost (and brightest) regions of the accretion
flow, and produces a cold, fragmented, high-density outflow that introduces
the high-absorption and fast variability observed. Such a slim disc was
possibly sustained by erratic or even continuous at Eddington/Super-Eddington
accretion, and as a consequence the central BH was partly or completely
obscured by the inflated disc and its outflow.

Similar extreme and variable absorption was also detected by NuSTAR during
observations close to the peak of the outburst [500]. A strong relativistic
reflection component was found in the NuSTAR flare spectra, which was
interpreted as the result of illumination of the accretion disc (truncated at
a small distance from the BH) by transient jet activity [500].

During the flares of V404 Cyg INTEGRAL/SPI detected high-energy excesses [428,
204] with respect to the thermal Comptonisation continuum that describes the
ISGRI and SPI data well up to 200 keV [441, 344]. This excess is reminiscent
of the one seen in Cyg X-1 up to about 1 MeV, which has been interpreted
either as the result of Comptonisation by a hybrid (i.e., thermal plus non-
thermal) electron population in both the LHS and the HSS [517], or as
synchrotron emission from the jet based on the presence of a significant
polarisation fraction (see Sec. 5.2). Noticeably, since the GeV detection by
FERMI/LAT [256] came from the very same V404 Cyg flares where the 200 keV - 1
MeV excess was seen by SPI [204], it is possible that both originate in the
jet. Figure 8 displays the behaviour of V404 Cyg along the brightest (and
last) flare observed by INTEGRAL. Jourdain et al. [204] ascribed the 20–50 keV
flux to the corona and the 100–300 keV flux to the jet, and pointed out that
the two components evolve independently, following two distinct evolution
patterns. The flux-flux relation shows two different slopes, which can be
interpreted as two regimes where the source emission is driven by the corona
and the jet contributions, respectively. A third (horizontal) track,
reflecting a stable ’jet’ emission with a decreasing corona flux, corresponds
to the transition between the two.

Figure 8: Flux-flux relation observed in V404 Cyg during the brightest flare,
as seen by INTEGRAL/SPI. Figure adapted from Jourdain et al. [204]

The soft $\gamma$-ray tail detected in V404 Cyg could be in principle ascribed
to a third mechanism, the production of electron-positron pair plasma during
the brightest, Eddington-limited flares. Siegert et al. [452] reported
evidence of a 511 keV annihilation line associated to a pair plasma in the SPI
data. However, independent studies have failed to confirm this 511 keV line
detection [204, 427]. Such a discrepancy was likely caused by the event
selection of the SPI data, which is a particularly important issue for bright
sources [427].

In the radio VLBA monitoring, Miller-Jones et al. [306] found that the jet
orientation was changing significantly in time scales ranging from minutes to
hours. Their interpretation was that the Lense-Thirring precession of the slim
disc that forms due to the super-Eddington accretion – which is also likely
responsible for the rapid changes in the cold absorption [328] – is driving
the changes in the jet orientation.

####  5.3.4 Rapid multi-wavelength variability

Rapid variability in the emission from V404 Cyg was also omnipresent at longer
wavelengths. Perhaps the most surprising feature of was the detection of
heartbeat-type oscillations in the optical [219], which are reminiscent of the
X-ray light curves of GRS 1915+105 (Sec. 5.1). A particularly fascinating
aspect of V404 Cyg was the complexity of how the X-ray and optical emissions
were correlated (see [354] for a study of correlated variability in UV and
X-rays, performed using Swift/UVOT and XRT data). An incredible plethora of
examples of correlated behaviour was observed within the 2 central (i.e. most
active) weeks of the outburst. The detailed study by Rodriguez et al. [415]
and Alfonso-Garzón et al. [1] showed that on 1-minute and longer time scales,
the INTEGRAL OMC, JEM-X and ISGRI light curves showed: (i) flares where the
optical emission was delayed by minutes up to an hour following and strong
X-ray flare, (ii) flares where the optical and X-ray emissions were
practically simultaneous (i.e. almost the exact same variations were observed
), and 3) flares during which enhanced optical and soft X-ray emissions
preceded a hard X-ray flare [209]. Moreover, simultaneous NuSTAR and optical
observations taken on sub-second time scales showed that the optical emission
lagged the X-rays by roughly 100ms [142, 186]. This lag was interpreted as the
delay between fluctuations generated in the hot corona around the BH, that
propagate up to the relativistic jet base about 1000 $R_{\rm g}$ away, which
is responsible for part of the optical emission [e.g., 266]. The correlated
1-minute time scale optical lags correspond to the light travel time delays
from the BH to the outer disc, were instead likely produced by the re-
processing of the X-rays in the outer accretion disc, or by the illuminated
binary companion [220, 1, 186].

Longer optical time lags of up to an hour were attributed to interactions
between distinct relativistic ejecta in the form of blobs of plasma [1],
although on these long time scales the association of a given X-ray flare to
its optical counterpart may be in some cases ambiguous given the stochastic
nature of the light curves. The few cases where INTEGRAL/OMC/JEM-X/ISGRI
detected negative lags, i.e., where the optical (and soft X-ray) emission
leads the (hard) X-rays [1, 209], remain a puzzle yet to be solved, which
could be explained in terms of mass accretion rate fluctuations propagating
inwards through the accretion disc.

Optical emission line profiles showed significant changes minutes after major
X-ray flaring detected by INTEGRAL [333]. Such lines showed broad and deep
P-Cyg profiles, from which outflow velocities up to 3000 km/s were estimated.
The presence of an outflow in optical with such a velocity is consistent with
the strong disc wind observed in X-rays by Chandra, likely radiation or
thermally driven as V404 Cyg approached the Eddington limit [221]. As
suggested by Motta et al. [328], the two outflows could be two portions of the
same disc wind, which likely feature a temperature/ionisation stratification.
Over the course of the 2 most active weeks of the outburst, more than
$10^{-8}\,M_{\odot}$ was lost in these variable disc winds, as well as in the
Compton-thick outflow responsible for the variable partial covering, such that
the suggestion was made that the outburst itself may have ceased prematurely
due to excessive mass loss [333].

####  5.3.5 The December 2015 re-flare

On 23 December 2015, only four months after the end of the primary outburst,
the Swift/BAT telescope detected a re-brightening of V404 Cyg [14]. Follow-up
X-ray, optical, and radio observations confirmed the onset of a new outburst
[334]. This December event was a re-flare, it was in many respects a fainter
analogue of the first week in the June 2015 activity, with weaker flares and
lower non-flaring emission in between them. The INTEGRAL and Swift spectra
were compatible with a Comptonised continuum modified by a Compton-thick
partial covering absorber [207]. Optical photometry [220] and spectroscopy, as
well as monitoring in radio [334] also showed a behaviour comparable to what
was observed in June, including similar, though less pronounced, P-Cyg optical
lines and radio variability.

###  5.4 Fast time variability

The X-ray timing studies by INTEGRAL [413] and NuStar [142] did not show signs
of QPOs, but instead the dominating feature was the presence of strong low-
frequency (bending) power law noise, and the complete absence of high-
frequency variability. PSD featuring these properties are characteristic of
heavily absorbed sources like Cyg X-3 [229], GRS 1915+105 in its obscured
state [228] as well as GRO J1655$-$40 in its ultrasoft state [488]. By analogy
with these sources, it appeared that the high frequency noise in V404 Cyg was
not intrinsically absent, but was instead smeared out or suppressed by the
disc wind via heavy scattering. Timing analyses of Chandra, FERMI/GBM and
Swift on the other hand did show only weak and short-lived mHz QPOs [183]. The
absence of the strong type-C QPOs typically expected in a BH in its LHS or
HIMS was interpreted as a consequence of the peculiar properties of V404 Cyg:
the rapid evolution of either the truncation radius or the radius of a ring
where the anisotropies responsible for the generation of QPOs occur [192]
would make the accretion flow might be much more turbulent than it would
otherwise be, so much so that the conditions for the precession of the inner
accretion flow that would give origin to a Type-C QPO are not met, if not for
very short times.

###  5.5 GX 339$-$4

GX 339$-$4 was discovered in 1973 by OSO-7 [273] and, based on the luminosity
upper limit of the stellar companion, it was classified 28 years later as a
low-mass XRB [444]. Soon afterwards, observations in the optical band [187]
revealed the motion of the companion star, based on which an orbital period of
$\sim 1.7$ d was derived, as well as a mass function of $5.8\pm 0.5$ M⊙. Later
on, based on high-resolution optical spectra, a distance to the source in the
range 6–15 kpc was proposed [188], which, however, is still to be confirmed.

Over the years after its discovery, GX 339$-$4 has shown a number of outbursts
that have been extensively monitored in several multi-wavelength observations,
and the properties of this system - which is considered the prototypical
transient BHB - have been probed via a vast number of analysis techniques. The
long-term spectral behaviour of the source, evidenced in the data collected
from 1987 until 2004 - mostly by RXTE but also Ginga and CGRO \- was presented
in Zdziarski et al. [514]. This study showed that GX 339$-$4 had already
undergone 15 outbursts in the period analysed, sampling several times all the
known accretion states, occurring along pronounced hysteresis cycles, with the
hard-to-soft state transitions occurring at much higher (and variable)
luminosity than the soft-to-hard transitions.

The outburst which occurred in 2002/2003 was studied in detail through timing
and colour analysis [23], and provided the prototype for the HID (see Sec. 2).
The state classification based on the HID proposed by [179] has since then
been the main framework to describe the outburst evolution of transient BHBs,
featuring two extra states - the HIMS and SIMS - with respect to the two
historical LHS and HSS. This state classification has been refined over the
years to incorporate the increasing amount of information acquired on the more
and more BHBs that were being observed and discovered, and started to include
multi-band observations, in primis coming from the radio band. Indeed, radio
observations performed during the 2003/2004 outburst revealed a large-scale
relativistic radio jet from GX 339$-$4[136], which was then associated with
the HIMS-SIMS transition [125] reported previously by Nespoli et al. [352].

In 2004, a new outburst occurred, and it was extensively observed by INTEGRAL
as well as by RXTE and other observatories. A simultaneous RXTE and INTEGRAL
campaign was performed on 2004 August 14-16, when the transition HIMS-to-SIMS
was expected [26]. Belloni et al. [26] observed a state transition shorter
than 10 hr, and performed the first simultaneous timing and and broad-band
spectral analysis (3–200 keV) across a hard-to-soft state transition. These
authors observed in the HIMS a steeper power law ($\Gamma\sim$1.9) and a lower
value of the high-energy cut-off ($\sim 70$ keV) than in the LHS. They also
observed the disappearance of the cut-off in the 3–200 keV energy band at the
transition to the SIMS. This confirmed a behaviour previously observed in
other sources (e.g., GRO J1655$-$40 [199]), where it was argued that the cut-
off might not disappear at the transition to the SIMS, but move to
significantly higher energies, i.e., beyond the energy band covered by RXTE,
but within the reach of INTEGRAL.

A similar finding was reported later on by Del Santo et al. [102] and Motta et
al. [319], who analysed INTEGRAL and RXTE data from the 2007 outburst of the
source, and observed in greater detail the evolution of the high-energy cut-
off across the long-lived ($\approx$ 10 days) hard-to-soft transition. A much
denser monitoring with RXTE of this outburst allowed Motta et al. [319] to
confirm that the evolution of the cut-off is non-monotonic: it decreased
monotonically from 120 to 60 keV during the luminosity increase in the LHS,
started increasing again at the LHS-to-HIMS transition reaching approximately
100 keV just before the transition to the SIMS. The cut-off further increased
to $\sim$130keV, and was no longer detected in the HSS.

The non-monotonic evolution of the high-energy cutoff observed in GX 339$-$4
has been later reported in a number of sources (e.g. [98]). As observed in GX
339$-$4 for the first time, and with an unprecedented clarity, the changes in
the high-energy cutoff are observed to be as fast as the timing properties (in
particular in the behaviour of the LFQPOs observed in the RXTE PDS), while
other spectral properties appear to be evolving much more smoothly over the
state transition.

The use of a phenomenological model such as a cut-off power law provides a
useful qualitative description of the data and of the evolution of the
spectral shape at a time where the energy spectrum undergoes pronounced and
relatively fast changes. However, it is worth noticing that by using such an
empirical model, not much can be said on the evolution of the plasma physical
parameters, as the energy cut-off is only roughly correlated to the electron
temperature of the Comptonising plasma, and it may not reflect the evolution
of the electron temperature of the corona. Additional components play a role
in the complex X/$\gamma$-ray spectra of BHBs (e.g., non-thermal
Comptonisation and Compton reflection), which has to be investigated by means
of more accurate, physically motivated spectral models. In this context, Del
Santo et al. [102] investigated the spectral variability of GX 339$-$4 across
the different states by using the hybrid thermal/non-thermal Comptonisation
model eqpair [83] on the INTEGRAL spectra collected during the period August-
September 2004 (see Fig. 9). These authors found that the spectral transition
HIMS-SIMS-HSS was driven by changes in the soft photon flux responsible of the
cooling of the hot plasma (the corona, or hot flow). Simultaneously, the
increase in the disc temperature and the decrease of the inner disc radius
were also observed. Such properties and behaviour are consistent with the
truncated disc model [118, 106], although other models such as dynamic
accretion disc corona models cannot be in principle ruled out.

Thanks to the high-energy coverage of the INTEGRAL telescopes, in all spectral
states of GX 339$-$4, a significant contribution from a (sometimes variable
[109]) high-energy tail above 200 keV, (see Sec. 4), was observed [198, 102,
46]. During the 2007 outburst a peculiar spectral transition was observed by
INTEGRAL and RXTE [97], with multiple transitions back and forth from/to the
HSS and LHS, across the SIMS, while during the 2010 outburst a number of
simultaneous multi-wavelength observations confirmed the jet quenching over
the transition in many wavebands [50].

Figure 9: Joint JEM-X, IBIS and SPI energy spectra of GX 339$-$4 collected in
different spectral states, from hard (violet) to soft state (orange). The data
were fitted with the hybrid thermal/non-thermal Comptonisation model eqpair
plus discline (from Del Santo et al. [102]).

###  5.6 1E1740.7$-$2942: the great annihilator

Discovered by the Einstein satellite in 1984 [172], the bright hard X-ray
source 1E 1740.7$-$2942 (hereafter 1E 1740) is located less than one degree
away from the Galactic Centre. It was classified as candidate BHB by Sunyaev
et al. [468] because of the spectral similarities with Cyg X-1, based on
results obtained with the Franco-Russian hard X-ray/soft $\gamma$-ray
satellite Granat. 1E 1740 is the prototype of the microquasar class, thanks to
its double-sided radio jets reaching large angular distances from the core
($\sim 1^{\prime}$), which were discovered in 1991 by Mirabel et al. [309].

This source takes its nickname from a claim that was made soon after the first
observations in the soft $\gamma$-ray domain. In 1990, the SIGMA telescope,
on-board Granat, observed 1E 1740 and found a spectrum characterised by a
transient (less than 3 days) broad feature around the electron-positron
annihilation energy at 511 keV [39, 468]. This finding attracted the attention
of the community and a great deal of studies were dedicated to investigate the
possibility that the aforementioned feature could be due to the electron-
positron annihilation line (the search of which is among the main aims for the
INTEGRAL mission). The “line” was speculated to be connected with the
spectacular bipolar jet seen in radio, which could be formed by leptons rather
than by baryons. Alternatively, it could be the result of productions of
positrons (which would therefore annihilate the electrons) by a hot plasma
with a temperature much lower than 1 MeV via photon-photon absorption, for
example when the accretion flow is able to interact with a wind [495]. Bouchet
et al. [37] performed a deep analysis based on the SPI data searching for any
feature around 511 keV associated with 1E 1740, but did not find evidence for
a line at 511 keV, either narrow or broad, transient or persistent. Later on,
De Cesare [95] searched for such an emission from any point sources with the
IBIS telescope, and found no evidence of Galactic 511 keV point sources, but
estimated a 2 $\sigma$ upper limit annihilation flux of 1.6$\times
10^{-4}ph/cm^{2}/s$, consistent with a diffuse electron-positron annihilation
scenario, where electrons and positrons could be produced in compact objects,
and propagate in the interstellar medium before annihilation. Thus, the
annihilation scenario for 1E 1740 was never confirmed, but the evocative name
of this source stuck to it, so that 1E 1740 is often still affectionately
referred to (rather erroneously) as the Great annihilator.

Smith et al. [455] measured a periodic modulation of $\sim 12.73\pm 0.05$ days
which, if interpreted as the orbital period of the system, would suggest a
red-giant as donor. However, the upper limit for the IR counterpart derived
with the VLT seems to exclude such a nature [284]. The high hydrogen column
density toward the source (see e.g. [138]) does not allow any firm
identification of the companion star, the characteristics of which remain
unclear.

INTEGRAL observations performed throughout several years have revealed that
most of the time 1E 1740 is found in either one of two main states: the
canonical LHS, with a mean flux of $\sim$ 50 mCrab, and a dim state, with a
much lower flux level of a few mCrab [101, 37]. In particular, XMM-Newton and
INTEGRAL provided the arguably highest quality broadband spectrum of the
source in the LHS [67]. In a few occasions, soft spectra have been observed,
testifying occasional transitions to a softer state [456]. In particular,
simultaneous INTEGRAL and RXTE broad-band spectra taken in 2003 showed that an
intermediate/soft spectral state occurred just before one of the long dim
states shown by 1E 1740 [96]. This behaviour was interpreted as the effect of
a drop in the accretion rate, which is expected to affect both the thin disc
and the hot flow (corona). While such a change would propagate through the hot
flow immediately, it might take up to several weeks to propagate through the
thin accretion disc. Thus, the hot flow is temporarily drained of matter
compared to the disc, therefore an accretion flow configuration very similar
to that observed in the HSS of other BHBs can be temporarily observed (see
also [456]).

Bosch-Ramon et al. [36] applied a jet model to the 1E 1740 SED (which include
INTEGRAL data) to investigate the possibility that the hard X-ray emission in
1E 1740 was to be ascribed to the jet. They concluded that synchrotron
emission from the jet seemed in fact to be able to explain the low-hard state
X-ray spectrum of the source, but it exceeded largely the observed core radio
fluxes. Bosch-Ramon et al. [36] therefore concluded that although accretion
and jet phenomena are probably linked - in 1E 1740 (and in any other source),
the dominant component in the (hard) X-rays can be either the jet or the
disk/corona depending on the system considered.

###  5.7 Black holes discovered by INTEGRAL

Figure 10: A zoom-in to the Galactic Bulge region as seen by INTEGRAL, based
on the IBIS/ISGRI (18–40 keV) data obtained through the Galactic bulge program
(from 2005 to 2009). Transient BHBs are marked in red, persistent BHBs are
marked in white. All source names are annotated above the source X-ray
position, except 1E1740.7$-$2942 (annotated at the right of the position), and
IGR J17497$-$2821 and GRS 1758$-$258 (both annotated below their position).
All the sources that are not labelled are NS X-ray binaries.

The bulge of our Galaxy (Galactic Bulge) contains a variety of high-energy
point sources [see, e.g., 225, 22, 242, 33], including persistent and
transient (candidate) BHBs. While persistent sources offer the opportunity to
probe the accretion process at play at any time, in transient BHBs the
accretion rate varies by larger factors than in the persistent sources, thus
offering the opportunity to study accretion in regimes not accessible in the
persistent sources. The regular and long-term monitoring of persistently
bright BHBs allowed by the Galactic Bulge monitoring program enables a
systematic study of the hard X-ray states of BHBs (e.g., [96, 345] for 1E
1740.7$-$2942), which is difficult or impossible for other missions to
accomplish due to a limited sensitivity at high energies and/or the lack of
wide-field imaging instruments as well as of orbits wide enough to allow long,
uninterrupted observations of a particular region of the sky. Furthermore, by
probing the hard X-ray spectra of the sources over a wide luminosity range,
the Galactic Bulge monitoring allowed the dependence of the X-ray spectrum on
the (total) luminosity to be investigated.

Since February 2005, whenever the Galactic Bulge region was visible, it has
been monitored approximately every 2–3 days with 3.5 hours snapshots, thanks
to a dedicated INTEGRAL program [242]. The wide-field imagers at high-energies
that are key to the INTEGRAL payload allowed the monitoring of the variability
of the variety of sources in this region to be performed all at once in a
broad energy range over the past 15 years. Various bright ($\gtrsim$100 mCrab)
well-known X-ray transients were active during the several years of the
Galactic bulge monitoring program (e.g. GRO J1655$-$40, [448] and H1743$-$322,
[393]), as well as new ones, some of which were discovered by INTEGRAL during
routine observations of the Galactic Bulge region. INTEGRAL is ideally suited
to detect such hard spectral state outbursts: transient and persistent BHBs
account for about half of the total detections in the 150–300 keV band (e.g.,
[19, 235]).

In this section, we will briefly review the results obtained on BHBs which
have been discovered by INTEGRAL, focusing in particular on the discoveries
and findings made possible thanks to INTEGRAL.

####  5.7.1 IGR J17091$-$3624

INTEGRAL discovered IGR J17091$-$3624 on 2003 April 14, during a routine
observation of the Galactic Centre region [241]. Follow-up observations were
immediately performed by RXTE, which confirmed the presence of an hard
spectrum well-fitted by an absorbed power law and fast time variability on
time scales from several tenths of a second to several tens of seconds,
typical of a BHB in the LHS [260]. Archival searches revealed that IGR
J17091$-$3624 was also detected by the Roentgen observatory aboard KVANT
module of the MIR space station in 1994 October, and by BeppoSAX in 1996
September and 2001 September [260]. XMM-Newton observed the field of IGR
J17091$-$3629 in 2006 August, and 2007 February, but while IGR J17098$-$3628 -
located 9.6 arcminutes away from it was observed in a relatively bright state,
IGR J17091$-$3624 was not detected. In 2011 January, Swift/BAT observed
renewed activity of this system, which raised from a flux of $\sim$20 mCrab to
$\sim$60 mCrab in about a week [234].

Capitanio et al. [59] followed the evolution of IGR J17091$-$3624 throughout
its 2011 outburst with INTEGRAL and Swift. Unlike the previous outbursts of
this source, which were relatively short (weeks) and faint, the 2011 outburst
was significantly longer and brighter. The initial evolution of the source
followed the standard state evolution of most BHBs, with a LHS followed by a
HIMS and a transition to the SIMS and HSS. Radio observations of this system
confirmed the presence of a flat radio spectrum in the LHS, and the detection
of a radio flare during the hard to soft transition, likely associated with
relativistic ejections [418]. Shortly after the HSS was reached, IGR
J17091$-$3624 started showing a variability pattern very reminiscent of the
heartbeats [3, 90] observed in GRS 1915+105 and a handful of other sources
[see, e.g., 330, and references therein].

The long and bright outburst started in 2011 ended in 2013, with a return of
the source to the LHS, a number of short re-flares during the LHS, and a final
descent into a very low-luminosity LHS, or a bright quiescence [376]. In 2016
February, IGR J17091$-$3624 showed another outburst, which, however, only
lasted approximately 2 months with no sign of the heartbeat variability shown
during the previous outburst [376].

####  5.7.2 IGR J17098-3628

IGR J17098$-$3628 was discovered by INTEGRAL on 2005 March 24th during deep
Open Program observations of the Galactic Centre region. The discovery was
made thanks to IBIS/ISGRI data, which revealed a new X-ray transient located
9.4 arcmin off IGR J17091$-$3624 [151]. Follow-up INTEGRAL and RXTE
observations of the Galactic centre region revealed a variable source, which
was tentatively classified as a new transient BHB due to its properties
typical of the sources of such a class [150]. A tentative radio counterpart
was identified shortly after the discovery by Rupen et al. [434] in VLA
observations, which showed a relatively bright radio source well within the
IBIS/ISGRI error circle.

INTEGRAL and RXTE observed the field of IGR J17098$-$3628 several times in the
period between 2005 and 2007, during which the target was regularly detected
[60, 73]. Targeted observations performed with XMM-Newton and Swift also