Advances in Understanding High-Mass X-ray Binaries with INTEGRAL and Future Directions
Peter Kretschmar, Felix Fürst, Lara Sidoli, Enrico Bozzo, Julia Alfonso-Garzón, Arash Bodaghee, Sylvain Chaty, Masha Chernyakova, Carlo Ferrigno, Antonios Manousakis, Ignacio Negueruela, Konstantin Postnov, Adamantia Paizis, Pablo Reig, José Joaquín Rodes-Roca, Sergey Tsygankov, Antony J. Bird, Matthias Bissinger né Kühnel, Pere Blay, Isabel Caballero, Malcolm J. Coe, Albert Domingo, Victor Doroshenko, Lorenzo Ducci, Maurizio Falanga, Sergei A. Grebenev, Victoria Grinberg, Paul Hemphill, Ingo Kreykenbohm, Sonja Kreykenbohm né Fritz, Jian Li, Alexander A. Lutovinov, Silvia Martínez-Núñez, J. Miguel Mas-Hesse, Nicola Masetti, Vanessa A. McBride, Andrii Neronov, Katja Pottschmidt, Jérôme Rodriguez, Patrizia Romano, Richard E. Rothschild, Andrea Santangelo, Vito Sguera, Rüdiger Staubert, John A. Tomsick, José Miguel Torrejón, Diego F. Torres, Roland Walter, Jörn Wilms, Colleen A. Wilson-Hodge, Shu Zhang
AAdvances in Understanding High-Mass X-ray Binaries with
INTEGRAL andFuture Directions
Peter Kretschmar a , Felix F¨urst b , Lara Sidoli c , Enrico Bozzo d , Julia Alfonso-Garz´on e , Arash Bodaghee f , SylvainChaty g,h , Masha Chernyakova i,j , Carlo Ferrigno d , Antonios Manousakis k,l , Ignacio Negueruela m , KonstantinPostnov n,o , Adamantia Paizis c , Pablo Reig p,q , Jos´e Joaqu´ın Rodes-Roca r,s , Sergey Tsygankov t,u , Antony J. Bird v ,Matthias Bissinger n´e K¨uhnel w , Pere Blay x , Isabel Caballero y , Malcolm J. Coe v , Albert Domingo e , VictorDoroshenko z,u , Lorenzo Ducci d,z , Maurizio Falanga aa , Sergei A. Grebenev u , Victoria Grinberg z , Paul Hemphill ab ,Ingo Kreykenbohm ac,w , Sonja Kreykenbohm n´ee Fritz ad,ac , Jian Li ae , Alexander A. Lutovinov u , SilviaMart´ınez-N´u˜nez af , J. Miguel Mas-Hesse e , Nicola Masetti ag,ah , Vanessa A. McBride ai,aj,ak , Andrii Neronov h,d , KatjaPottschmidt al,am , J´erˆome Rodriguez g , Patrizia Romano an , Richard E. Rothschild ao , Andrea Santangelo z , VitoSguera ag , R¨udiger Staubert z , John A. Tomsick ap , Jos´e Miguel Torrej´on r,s , Diego F. Torres aq,ar , Roland Walter d , J¨ornWilms ac,w , Colleen A. Wilson-Hodge as , Shu Zhang at Abstract
High mass X-ray binaries are among the brightest X-ray sources in the Milky Way, as well as in nearby Galaxies.Thanks to their highly variable emissions and complex phenomenology, they have attracted the interest of the highenergy astrophysical community since the dawn of X-ray Astronomy. In more recent years, they have challenged ourcomprehension of physical processes in many more energy bands, ranging from the infrared to very high energies.In this review, we provide a broad but concise summary of the physical processes dominating the emission from highmass X-ray binaries across virtually the whole electromagnetic spectrum. These comprise the interaction of stellarwinds with the high gravitational and magnetic fields of compact objects, the behaviour of matter under extrememagnetic and gravity conditions, and the perturbation of the massive star evolutionary processes by presence in abinary system.We highlight the role of the INTEGRAL mission in the discovery of many of the most interesting objects in thehigh mass X-ray binary class and its contribution in reviving the interest for these sources over the past two decades.We show how the INTEGRAL discoveries have not only contributed to significantly increase the number of highmass X-ray binaries known, thus advancing our understanding of the population as a whole, but also have opened newwindows of investigation that stimulated the multi-wavelength approach nowadays common in most astrophysicalresearch fields.We conclude the review by providing an overview of future facilities being planned from the X-ray to the very highenergy domain that will hopefully help us in finding an answer to the many questions left open after more than 18years of INTEGRAL scientific observations.
Keywords:
X-rays: binaries, accretion, stars: neutron, pulsars: general, gamma rays: observations, INTEGRAL observatory
Preprint submitted to New Astronomy September 8, 2020 a r X i v : . [ a s t r o - ph . H E ] S e p European Space Astronomy Centre (ESA / ESAC), Operations Department, E-28692 Villanueva de la Ca˜nada (Madrid), Spain b Quasar Science Resources S.L for ESA, European Space Astronomy Centre (ESA / ESAC), Operations Department, E-28692 Villanueva de laCa˜nada (Madrid), Spain c INAF – IASF, Istituto di Astrofisica Spaziale e Fisica Cosmica, Via A. Corti 12, I-20133 Milano, Italy d Department of Astronomy, ISDC, University of Geneva, Chemin d’Ecogia 16, CH-1290 Versoix, Switzerland) e Centro de Astrobiolog´ıa – Departamento de Astrof´ısica (CSIC-INTA), E-28692 Villanueva de la Ca˜nada (Madrid), Spain f Department of Chemistry, Physics and Astronomy, Georgia College and State University, Milledgeville, GA 31061, USA g AIM, CEA, CNRS, Universit´e Paris-Saclay, Universit´e de Paris, F-91191 Gif-sur-Yvette, France h Universit´e de Paris, CNRS, Astroparticule et Cosmologie, F-75006 Paris, France i School of Physical Sciences and CfAR, Dublin City University, Dublin 9, Ireland j Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2, Ireland k Department of Applied Physics & Astronomy, University of Sharjah, Sharjah, UAE l Sharjah Academy of Astronomy, Space Sciences, and Technology (SAASST), Sharjah, UAE m Department of Applied Physics, University of Alicante, E-03080 Alicante, Spain n Sternberg Astronomical Institute, Moscow State University, 119234, Moscow, Russia o Kazan Federal University, Kazan, Russia p Institute of Astrophysics, Foundation for Research and Technology-Hellas, 71110 Heraklion, Crete, Greece q University of Crete, Physics Department & Institute of Theoretical & Computational Physics, 70013 Heraklion, Crete, Greece r Department of Physics, Systems Engineering and Signal Theory, University of Alicante, E-03690 Alicante, Spain s University Institute of Physics Applied to Sciences and Technologies, University of Alicante, E-03690 Alicante, Spain t Department of Physics and Astronomy, FI-20014 University of Turku, Finland u Space Research Institute of the Russian Academy of Sciences, Profsoyuznaya Str. 84 /
32, Moscow 117997, Russia v School of Physics and Astronomy, Faculty of Physical Sciences and Engineering, University of Southampton, Southampton SO17 1BJ, UK w Erlangen Centre for Astroparticle Physics (ECAP), Erwin-Rommel-Strae 1, 91058 Erlangen, Germany x Universidad Internacional de Valencia - VIU, C / Pintor Sorolla 21, 46002, Valencia, Spain y Aurora Technology B.V. for ESA, European Space Astronomy Centre (ESA / ESAC), Operations Department, E-28692 Villanueva de la Ca˜nada(Madrid), Spain z Institut f¨ur Astronomie und Astrophysik, Universit¨at T¨ubingen, Sand 1, 72076 T¨ubingen, Germany aa International Space Science Institute (ISSI), Hallerstrasse 6, CH-3012 Bern ab MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA ac Dr. Karl Remeis-Sternwarte, Friedrich-Alexander-Universit¨at Erlangen-N¨urnberg, Sternwartstr. 7, D-96049 Bamberg, Germany ad Franz-Ludwig-Gymnasium, Franz-Ludwig-Strasse 13, 96047 Bamberg ae Deutsches Elektronen Synchrotron DESY, D-15738 Zeuthen, Germany af Instituto de F´ısica de Cantabria (CSIC-Universidad de Cantabria), E-39005, Santander, Spain ag INAF – OAS, Osservatorio di Astrofisica e Scienza dello Spazio, Area della Ricerca del CNR, via Gobetti 93 /
3, I-40129 Bologna, Italy ah Departamento de Ciencias F´ısicas, Universidad Andr´es Bello, Fern´andez Concha 700, Las Condes, Santiago, Chile ai South African Astronomical Observatory, Observatory Road, Observatory, 7925, Cape Town, RSA aj Inter-University Institute for Data-Intensive Astronomy, Department of Astronomy, University of Cape Town, Private Bag X3, Rondebosch7701, South Africa ak IAU-O ffi ce of Astronomy for Development, P.O. Box 9, 7935 Observatory, South Africa al CRESST, Department of Physics, and Center for Space Science and Technology, UMBC, Baltimore, MD 21250, USA am NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA an INAF – Osservatorio Astronomico di Brera, Via E. Bianchi 46, I-23807 Merate, Italy ao Center for Astrophysics and Space Sciences, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 920093-0424, USA ap Space Sciences Laboratory, 7 Gauss Way, University of California, Berkeley, CA 94720-7450, USA aq Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans s / n, E-08193 Barcelona, Spain; Institut d’Estudis Espacials deCatalunya (IEEC), Gran Capit`a 2-4, E-08034 Barcelona, Spain ar Instituci´o Catalana de Recerca i Estudis Avan¸cats (ICREA), E-08010 Barcelona, Spain as ST12 Astrophysics Branch, NASA Marshall Space Flight Center, Huntsville, AL 35812, USA at Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan Road, ShijingshanDistrict, 100049, Beijing, China ontents1 Introduction 32 Physics and observable phenomena 4 ff ect 102.5.2 Quasi-spherical accretion: su-personic (Bondi) vs subsonic(settling) . . . . . . . . . . . . 112.5.3 Magnetic and centrifugal inhi-bition of accretion in wind-fedNS HMXBs . . . . . . . . . . . 112.5.4 Accretion regimes in SFXTs . . 132.6 Continuum spectrum . . . . . . . . . . 162.7 Cyclotron Resonant Scattering Features 182.7.1 Luminosity dependence of theCRSF energy . . . . . . . . . . 192.7.2 Pulse phase dependence of theCRSF profile . . . . . . . . . . 202.7.3 Secular changes of the CRSFenergy . . . . . . . . . . . . . . 202.8 X-rays from black hole HMXB systems 202.9 Gamma-ray binaries . . . . . . . . . . . 212.10 Ultraluminous X-ray sources . . . . . . 22 INTEGRAL ’s role in HMXB studies 22
INTEGRAL . . 313.6 Gamma-ray binary studies with
INTE-GRAL . . . . . . . . . . . . . . . . . . 32
INTEGRAL
In High-Mass X-ray Binaries (HMXBs) a compactobject – most frequently a neutron star (NS) – ac-cretes matter from a binary companion star with a massabove ∼ (cid:12) . They form a sub-class of X-ray Binaries(XRBs), hosting very massive donors ( M donor ≥
10 M (cid:12) ).Galactic HMXBs were among the earliest sources de-tected by the new field of X-ray astronomy in the 1960’s(see, e.g., Giacconi et al., 1962; Chodil et al., 1967;Schreier et al., 1972; Webster and Murdin, 1972) andhave remained an intense subject of study ever since.These systems can form during the joint evolution of apair of massive stars in a sequence involving mass trans-fer between the companions also before the first super-nova explosion (van den Heuvel and Heise, 1972; Tauriset al., 2017). Massive stars influence their environmentsignificantly, through their strong, ionizing ultravioletradiation, as well as by their strong winds and final ex-plosions which provide a significant input of energy andchemically enriched matter into the interstellar medium(Kudritzki, 2002). Some of these systems may developfurther into double compact objects, i.e., future sourcesof gravitational wave events (see, e.g., van den Heuvel,2019, and references therein).Accretion in HMXBs can occur in di ff erent ways,as described in Section 2. Observationally, one usu-ally distinguishes between disc-fed systems, showingRoche-Lobe overflow, wind-accreting Supergiant X-rayBinaries (sgHMXBs), with stellar type O or B massdonors – including the sub-class of peculiar SupergiantFast X-ray Transients (SFXTs) – and Be X-ray Binaries(BeXRBs), in which accretion is driven by the interac-tion between the compact object and the decretion discaround the mass donor. Another, special class are theWolf-Rayet X-ray Binaries with only 7 known exam-ples, 6 of which are in other galaxies (Esposito et al.,2015). The very well-known, but peculiar X-ray binaryCyg X-3 is the only example in our Milky Way and hasbeen studied frequently by INTEGRAL (e.g. Beckmannet al., 2007; Zdziarski et al., 2012a,b).3 igure 1: Spin-period ( P s ) over binary ( P b ) period diagram (“Cor-bet diagram”) for HMXBs. The di ff erent classes are distinguished bycolour and symbol shape: SFXTs, disc-fed (sgDF) supergiant binaries(including ultra-luminous X-ray sources (ULXs)), wind-fed (sgWF)supergiant binaries, as well as Be X-ray Binaries (BeXRB). The verti-cal line indicates the binary period at which a 20 R (cid:12) , 22 M (cid:12) supergiantfills its Roche lobe. Below the blue lines quasi-spherical accretionfrom the stellar wind for two di ff erent dipole magnetic field strengths B is inhibited by the centrifugal barrier (see Section 2.5), assuming awind speed of 800 km s − . Updated from Fig. 4 in Grebenev (2009). Due to the large field of view of the
INTEGRAL in-struments and their sensitivity, especially in the hard X-ray band, as well as an observing programme concen-trating in particular on regions in the Galactic disc, thenumber of known HMXBs has grown very significantlywith
INTEGRAL and new types of HMXBs have beenidentified. Specifically,
INTEGRAL observations ledto the detection of very highly absorbed sources (seeSect. 3.2) and to the identification of SFXTs as a newclass (see Sect. 3.4). In addition,
INTEGRAL observedalmost all major outbursts from BeXRBs and discov-ered eight new such systems (see Sect. 3.5). Studiesof accreting X-ray pulsars with long pulse periods, havealso benefited from the long, uninterrupted observationspossible due to the highly-elliptic orbit of
INTEGRAL .The relatively high fraction of sgHMXBs among thesources found with
INTEGRAL (see also Table A.1)has led to a more even distribution of known sourcetypes and allowed us to fill the parameter space in thespin-period ( P s ) over binary ( P b ) period diagram (Fig-ure 1), often referred to as “Corbet-Diagram”. While for obvious reasons detections of new HMXBsystems were especially frequent in the early years of INTEGRAL , when certain areas of the sky where cov-ered in depth for the first time by its instruments (seeTable A.1 and its references), the number of identifiedsources has been steadily growing, also due to the tran-sient nature of many systems. For catalogues of
IN-TEGRAL surveys see Revnivtsev et al. (2004); Birdet al. (2006, 2007, 2010); Krivonos et al. (2010, 2012),while results from the Optical Monitor Camera havebeen published by Alfonso-Garz´on et al. (2012). Anextensive review of HMXBs in the Milky Way and
IN-TEGRAL ’s contribution was published by Walter et al.(2015).In the following, we first summarize in Section 2the physics and observable phenomena which are be-hind the rich phenomenology seen in HMXBs by
IN-TEGRAL and other satellites. Section 3 summarizeskey results obtained for the di ff erent classes of sourcesand specific example cases. In Section 4 we discuss thedistribution of HMXB systems in the Galaxy and theircontribution to the overall luminosity of the Galaxy inthese wavelengths. Finally, Section 5 focuses on the fu-ture of HMXB observations with INTEGRAL and otherobservatories.
2. Physics and observable phenomena
In this Section, we give a short overview of themost important observable phenomena and their phys-ical interpretation. We discuss flux variability, whichis linked to variations in the accretion rate (Sects. 2.1,2.2, 2.3), super-orbital variability (Sect. 2.4), interac-tions at the magnetosphere (Sect. 2.5), X-ray contin-uum emission properties of neutron stars (Sect. 2.6),the formation of Cyclotron Resonant Scattering Fea-tures (CRSFs, Sect. 2.7), and X-rays from black holesystems (Sect. 2.8).
In the majority of sgHMXBs, the compact objectaccretes directly from the stellar wind of its compan-ion. Therefore the physical state, structure, and den-sity of the wind has an immediate e ff ect on the ac-cretion rate and hence on the observed X-ray luminos-ity. A large fraction of the observed aperiodic variabil-ity can be qualitatively explained by accretion from a“clumpy” stellar wind; however, quantitative calcula-tions are more di ffi cult to obtain, as outlined below.4 .1.1. Acceleration of stellar winds The winds of hot luminous stars are mainly drivenand accelerated by ultra-violet (UV) resonance lines(like ions of C, N, O, Fe, etc), therefore they are knownas line driven winds. The theory of radiatively drivenstellar winds was first developed by Castor et al. (1975)(CAK hereafter) and refined in many subsequent publi-cations, see e.g. Kudritzki and Puls (2000); Puls et al.(2008). The acceleration depends on the ionization, ex-citation, and chemical composition of the stellar wind(see e.g., Eq. 7 in Castor et al., 1975). The amount ofionization is strongly a ff ected by the stellar parameters(e.g. e ff ective temperature, T e ff ) and in X-ray binarysystems also by the X-ray emission of the compact ob-ject (see e.g., Sander et al., 2018; Krtiˇcka et al., 2018,for recent studies).From the phenomenological point of view, the stel-lar wind can be characterized by two parameters: i) themass loss rate ( ˙ M ) per unit of time and ii) the termi-nal velocity ( υ ∞ ) at large distances from the star, wherewind acceleration becomes insignificant. Typical massloss rates of massive stars are of the order of ˙ M ∼ − M (cid:12) yr − . Typical values of the terminal velocity inmassive stars are of the order of υ ∞ ∼
500 – 2000 km s − (Kudritzki and Puls, 2000; Puls et al., 2008).Assuming a spherically symmetric (non-rotating)stellar wind, the mass loss rate can be derived from˙ M = π r ρ ( r ) υ ( r ), where r is the distance from thecenter of the star, ρ ( r ) is the density and υ ( r ) is the ve-locity at that distance. The radial density profile is com-monly parametrized assuming a so-called β -velocitylaw (CAK): υ ( r ) = υ ∞ (cid:0) − R (cid:63) / r (cid:1) β , (1)where R (cid:63) is the stellar radius and β describes the steep-ness of the wind velocity profile. Both wind terminalvelocity ( υ ∞ ) and the β -parameter are obtained mainlythrough spectral fitting of optical / UV data. Typical val-ues of β parameters are in the range between 0 . It was recognized early (Lucy and Solomon, 1970;Lucy and White, 1980) that line driven wind accel-eration is likely to be unstable, leading to the forma-tion of shocks and inhomogeneous regions in the wind,commonly referred to as clumps (Owocki and Rybicki,1984; Owocki et al., 1988). This phenomenon is usuallydescribed as line-deshadowing (or just line-driven) in-stability (LDI), which will lead to a very unstable outerwind, but which may be damped close to the stellar sur-face, although Sundqvist and Owocki (2013) also found an unstable wind in near photospheric layers. For mostof the wind mass, the dominant overall e ff ect of the in-stability is to concentrate material into dense clumps,leading to a density contrast up to 10 (Puls et al.,2008).Accounting for clumpy winds can a ff ect the interpre-tation of observable quantities for the stellar wind (e.g.mass-loss rates derived from spectral line fits) by largefactors. LDI simulations tend to favour relatively smallclump sizes and masses, compared to some values as-sumed in studies of X-ray binaries, see Mart´ınez-N´u˜nezet al. (2017) for a detailed discussion. Figure 2: Top: an example of a single-arm CIR presented by Bozzoet al. (2017a) and obtained from the hydrodynamic code developedby Lobel and Blomme (2008). In this case, the CIR is generated by abright spot on the stellar surface and it has a period of 10.3 days. Thecolors code the wind density of the CIR model relative to the densityof the supergiant star unperturbed, smooth wind. The maximum over-density in the CIR is by a factor 1.22 (red colors). The black solidlines show 20 overplotted contours of equal radial velocity in the hy-drodynamic rotating wind model. Bottom: Simulated long-term lightcurve of IGR J16493 − ∼
20 days is produced by a single-arm CIR in the top figure.
The existence of large structures in OB supergiantwinds, beyond the typical size expected for the clumps,was suggested already in the 1980s by Mullan (1984),and confirmed later by the observational detection of so-5alled discrete absorption components (DACs; see, e.g.,Underhill, 1975, and references therein). These DACsare understood to be generated by corotating interac-tion regions (CIRs) induced by irregularities on the stel-lar surface, related either to dark / bright spots, magneticloops, or non-radial pulsations (Cranmer and Owocki,1996). CIRs are spiral-shaped density and velocity per-turbations in the stellar wind that can extend outward upto several tens of stellar radii, and the physical proper-ties of such structures (thickness, inclination, velocityand density profiles, number of spiral arms, rotationalperiod) can be determined from the characteristics as-sumed for the irregularity(ies) from which they origi-nate (see also Fig. 2). Unfortunately, there is a paucityof observational data on DACs in supergiant stars, withall evidence obtained with the IUE satellite (Boggesset al., 1978), due to the lack of an UV facility withcomparable or better sensitivity. But their existence isfurther supported by modulations of the X-ray emissionobserved in single OB stars (Oskinova et al., 2001; Naz´eet al., 2013; Massa et al., 2014). Figure 3: Snapshot of a hydrodynamic simulation of a model of theVela X-1 system using the VH1 code developed by John Blondin.Originally Fig. 7.5 in Manousakis (2011).
In wind accreting HMXBs, the presence of the com-pact object moving through the dense stellar wind closeto the massive star significantly influences the windflow. The gravity of the compact object will focus thewind towards the orbital plane and the position of theaccretor; the orbital movement of the companion willlead to the formation of a bow shock and a trailing ac-cretion wake; and finally the X-ray emission will ionizethe local environment, changing the availability of res-onance lines for acceleration. The ionization state ofthe wind is defined as ( ξ ( r ) = L X / Nr ), where L X isthe average X-ray luminosity and N is the gas density atthe distance r from the NS (Tarter et al., 1969). X-rayphotoionization and heating can lead to the formation ofa Str¨omgren sphere, where the wind is not accelerated anymore. At the boundary of this a shock is formed andsheets of gas trailing the X-ray source result (Franssonand Fabian, 1980). In extreme cases, wind accretionmight be inhibited, leading to a feedback process (e.g.Blondin et al., 1990; Krtiˇcka et al., 2018).In general, in a sgHMXB system an accretion wakedevelops around and behind the compact object andevolves with time, showing fluctuations. Even when as-suming a smooth wind as starting condition, the wind islikely to be heavily disrupted due to the hydrodynami-cal e ff ects, accounting for high X-ray variability even inthe absence of clumps (Manousakis and Walter, 2015a).First steps to model the accretion of clumps from a real-istic clumpy wind model (Sundqvist et al., 2018) weredone by El Mellah et al. (2018), but without includingthe ionizing feedback e ff ect on the incoming matter.We note that most studies relating wind density andX-ray emission e ff ectively assume immediate Bondi-Hoyle accretion of the matter reaching the vicinity ofthe NS. As shown in Section 2.5, the detailed physicsof accretion close to or at the magnetosphere will fur-ther modulate the variability, e.g., by “magnetic gating”,possibly dampening or enhancing the intrinsic densityfluctuations. Simulations combining all these multi-scale, multi-physics e ff ects are still in the future. While wind accretion is the main mechanism to feedX-ray emission in HMXBs, for a limited subset of thesesources the presence of an accretion disc is inferredfrom their substantially higher luminosity, their positionin the spin period over orbital period (Corbet) diagram(Corbet, 1986), marked trends in their spin periods,or their optical lightcurves. Well-known examples areLMC X-4 (Heemskerk and van Paradijs, 1989), Cen X-3 (Tjemkes et al., 1986) and SMC X-1 (Hutchings et al.,1977). Other systems in which transient discs have beenreported and / or strongly suggested due to observation-ally indirect evidences include OAO 1657 −
415 (Jenkeet al., 2012; Sidoli and Paizis, 2018), 4U 0114 +
650 (Huet al., 2017), GX 301 − − P s ) over binary ( P b ) period di-agram (a.k.a. “Corbet diagram”, Figure 1) a groupof bright X-ray binaries occupies a distinct position inthe lower left part of the diagram and these are gener-ally considered to be accreting from a disc. The veryhigh and persistent X-ray flux has an e ff ect on the massdonors, which are “bloated” – their luminosity class andbrightness is higher than expected for their mass (which6as been accurately measured, unlike in almost all otherHMXBs). There may even be X-ray heating of the stel-lar surface, and this may have an e ff ect on wind accel-eration, connected to, but not quite the same as, the ef-fects discussed in Section 2.1.4 above for fainter X-raysources.The disc formation has often been ascribed to Roche-lobe Overflow (RLO). Fully-developed RLO will leadto mass transfer on the thermal timescale of the donor,at a rate of about 10 − M (cid:12) yr − , which will completelyextinguish the X-ray source. However, it was shownby Savonije (1978, 1983) that prior to filling the Rochelobe, already a phase of beginning atmospheric RLOmay set in, which in the case of a core-hydrogen-burning donor may last many thousands of years andsupply mass-transfer rates below 10 − M (cid:12) yr − . In ad-dition, Quast et al. (2019) showed that a stable RLOphase with mass-transfer rates below 10 − M (cid:12) yr − – asobserved in ULXs – may last for >
200 000 yrs, beforefull thermal-timescale RLO sets in. On the other hand,recent theoretical publications (El Mellah et al., 2019;Karino et al., 2019) indicate that under certain condi-tions, especially for slower wind speeds than assumedin the past, also accretion discs may form at least tem-porarily in wind-accreting systems without the need toinvoke Roche-lobe Overflow.We only briefly mention the well-known X-ray binarySS 433, discussed in its own review as part of this col-lection (Cherepashchuk et al., 2019). The accreting X-ray pulsar Her X-1 (e.g. Staubert et al., 2017), an inter-mediate mass system and disc accretor, is also discussedin another review in this volume (Sazonov et al., 2020,Sect. 6.1).
When the optical counterpart in an HMXB is not anevolved (supergiant) star but a Be star, then the sys-tem is called Be / X-ray binary (BeXRB, Maraschi et al.,1976; Reig, 2011; Paul and Naik, 2011). The Be com-ponents are early-type B (earlier than B3) or late-type O(later than O8) stars with masses in the range 8 – 15 M (cid:12) whose most prominent property is the presence of a discaround the star’s equator. The disc is formed by mate-rial ejected from the photosphere, due to the star’s rapidrotation in addition to stellar activity (e.g., Balona andOzuyar, 2020) and not by accretion from an externalsource. Since material is transported outwards by thesame viscosity mechanism that drags matter inwards inan accretion disc, the disc is referred to as a decretiondisc. The disc provides the reservoir of material thatis accreted by the compact object, in contrast to thestellar wind in sgHMXBs, and is ultimately responsible for the variability observed in these systems at all fre-quency bands. In the optical and infrared, Be stars showemission lines in their spectra, excess flux that increaseswith wavelength (with respect to a canonical B star ofthe same spectral type), and polarization. The emissionlines and infrared excess are formed by recombinationin the disc. Linear polarization results from Thomsonscattering, when photons from the Be star scatter withelectrons in the Be disc (Poeckert et al., 1979; Woodet al., 1996; Yudin, 2001; Halonen et al., 2013; Hauboiset al., 2014). In the X-rays, BeXRBs show two distincttypes of outbursting behaviour: an orbitally-modulatedincrease in X-ray flux, normally coincident with peri-astron passage (type I), and giant and long-lasting out-bursts (type II). During type I outbursts, the X-ray lu-minosity is generally below a few 10 erg s − , while intype II outbursts the luminosity may reach a few 10 erg s − , close to the Eddington value (Stella et al., 1986;Okazaki and Negueruela, 2001)The Be phenomenon, i.e., the presence of a circum-stellar disc, was first observed in isolated Be stars, with-out NS companions. In principle, one could turn tothe vast amount of studies on classical Be stars to shedlight on the properties of BeXRBs since the variabilityin BeXRBs is closely linked to the evolution of the de-cretion disc. The disc forms, grows and dissipates ontime scales of years. However, it turns out that the pres-ence of a compact companion a ff ects the characteristicsand evolution of the disc. Discs in BeXRBs are smallerand denser than in isolated systems (Reig et al., 1997;Zamanov et al., 2001; Okazaki et al., 2002; Reig et al.,2016). The reason is that discs in BeXRBs are trun-cated at the outer rim (Okazaki and Negueruela, 2001;Okazaki et al., 2002). Disc truncation was also pro-posed as a natural explanation for the existence of thetwo di ff erent types of outbursts (Okazaki and Negueru-ela, 2001).Observational evidence for disc truncation stemsfrom the various correlations of disc parameters with thesize of the orbit, expressed as the orbital period P b , ec-centricity e , or orbital separation a . Circumstellar discsin narrow-orbit systems are naturally more a ff ected bythe tidal torque exerted by the NS than systems withlonger orbital periods. Thus, we expect faster and largeramplitude variations of the observables in systems withtighter orbits. The following correlations support thedisc truncation idea: – Orbital separation and disc size . The correlation be-tween the orbital period and the highest historical valueof the equivalent width of the H α line (EW(H α )) wasthe first to be suggested as evidence for disc truncation(Reig et al., 1997) and confirmed in subsequent stud-7es (Reig, 2007; Antoniou et al., 2009; Coe and Kirk,2015; Reig et al., 2016). Because the equivalent widthis directly related to the size of the disc (Quirrenbachet al., 1997; Grundstrom and Gies, 2006), these correla-tions imply that large discs can only develop in systemsin which the two components are far apart. In systemswith small orbital separation, the tidal torque exerted bythe NS prevents the disc from expanding freely. – Orbital period and variability . Systems with smallorbital periods are more variable both in the continuumand line optical emission (Coe et al., 2005; Reig et al.,2016). A similar result was found by analysing the vari-ability in the X-ray band (Reig, 2007). Because thediscs in systems with short orbital periods su ff er strongtidal torques exerted by their NS, they cannot reach astable configuration over long timescales. – Disc recovery after dissipation . Systems withshorter orbital periods display larger growth rates af-ter a disc-loss episode. Owing to truncation, the discbecomes denser more rapidly in shorter orbital periodsystems, and so the equivalent width of the H α line in-creases faster. Not only the disc formation, but alsothe entire formation and dissipation cycle appears tobe faster in systems with short orbital periods, whilelonger timescales are associated with longer orbital pe-riods (Reig et al., 2016).Disc truncation has implications for theories that ex-plain type II (giant) outbursts. X-ray outbursts arecaused by the mass transfer from the Be star’s discto the NS. But if the disc is truncated, how can largeamounts of matter be transferred to the NS? The cur-rent idea is that the giant outbursts occur when the NScaptures a large amount of gas from a warped and ec-centric Be disc, highly misaligned with respect to theorbital plane (Okazaki et al., 2013; Martin et al., 2011,2014). The models show that highly distorted discs re-sult in enhanced mass accretion when the NS gets acrossthe warped part. Observational evidence for misaligneddiscs comes from optical spectra (Moritani et al., 2011,2013) and polarization (Reig and Blinov, 2018).In Be stars, the H α line can display very di ff erentshapes, from single peaked to double-peaked. Thesevaried flavours in the emission line appearance are at-tributed to the di ff erent inclinations of the line of sightwith respect to the circumstellar disc (Hanuschik, 1995;Hummel, 1994). Single-peaked profiles are seen (gener-ally showing flank inflections due to non-coherent scat-tering, producing the wine-bottle profile) in low incli-nation systems. For intermediate inclinations, Dopplerbroadening gives rise to double-peaked profiles. Forlarge inclination systems, the outer cooler regions of thedisc intercept the line of sight and produce shell pro- files (deep narrow absorption cores that go below thecontinuum level). But, what if all the types of pro-files described above are seen in the same source, asin the BeXRB 4U 0115 +
63 (Negueruela et al., 2001;Reig et al., 2007)? Because the spin axis of the Bestar cannot change on time scales of days, the appear-ance of di ff erent profiles in the same star can only im-ply that the disc axis is changing direction. This phe-nomenon is then interpreted as evidence for a precess-ing and warped disc. A similar interpretation has beenused to explain the complex, three-peaked H α profilesshown by 1A 0535 +
262 and AX J0049.4-7323 (Mori-tani et al., 2011; Ducci et al., 2019a). The warping ofthe disc may be caused by the tidal interaction with theNS (Martin et al., 2011) or by radiation from the centralstar (Porter, 1998)Further evidence for warped discs comes from po-larization. The light coming from a Be star is polar-ized. The net polarization is perpendicular to the scat-tering plane (the plane containing the incident and scat-tered radiation). Since the photons that get scatteredcome from the Be star and the scattering medium is thedisc, the polarization angle is expected to be perpen-dicular to the major elongation axis. Therefore, if thedisc precesses, we should expect the polarization angleto change. Changes in the optical polarization angle ontime scales comparable to the orbital period were re-ported for the first time during a giant X-ray outburst inthe BeXRB 4U 0115 +
63 and were interpreted as vari-ation in the orientation of the disc (Reig and Blinov,2018).As with the supergiant systems, BeXRBs in the MilkyWay are generally a ff ected by heavy extinction. Ad-vances in our understanding of the class have comethrough the detailed analysis of a few representative sys-tems (e.g. Reig et al., 2007; Monageng et al., 2017, andreferences therein). In contrast, the Small MagellanicCloud (SMC) contains a very large number of BeXRBs(approaching 100), almost free of interstellar absorp-tion (at a moderately large distance, though), which canbe used to perform population studies (Coe and Kirk,2015). This large number of BeXRBs is unexpected insuch a small galaxy, and likely related to a recent burstof star formation due to interaction with the Large Mag-ellanic Cloud (LMC) (Antoniou et al., 2010). Thanksto these properties, the SMC has become the prime lab-oratory for the study of BeXRBs (Haberl and Sturm,2016). Optical properties (McBride et al., 2008) and X-ray properties (Galache et al., 2008) can be studied sta-tistically, providing valuable input for the investigationof the accretion process (e.g. Yang et al., 2017), forma-tion mechanisms (e.g. Townsend et al., 2011a) or even8trict constraints on models for the production of grav-itational wave emitting systems (e.g. Vinciguerra et al.,2020). Superorbital modulations are periodic variations ofthe X-ray luminosity observed from several HMXBson time-scales longer than their orbital period (typ-ically a factor of 3–10 longer; see, e.g., Kotze andCharles, 2012, and references therein). In a few disc-fed HMXBs, as SMC X-1 and LMC X-4, superorbitalvariations have been known for decades, and have beenclearly detected in all long-term monitoring data col-lected with
RXTE , INTEGRAL , and
Swift (see, e.g.,Dage et al., 2019, and references therein). These modu-lations can be interpreted as being caused by irradiationfrom the X-rays emitted by the compact object onto atilted and / or warped accretion disc, which is then forcedto precess and periodically obscures the X-ray source(see, e.g., Pringle, 1996; Ogilvie and Dubus, 2001).Superorbital modulations have also been more re-cently discovered in several wind-fed sgHMXBs,mainly by using Swift data and then confirmed in afew cases also in the
INTEGRAL and
RXTE data (seeCorbet and Krimm, 2013; Corbet et al., 2018); in someoccurrences, only promising indications are found andconfirmations are expected in the future when more datawill be available. The interpretation of super-orbitalmodulations in wind-fed systems is less straightforwardthan in disc accreting binaries. It is unlikely that thepresence of temporary accretion discs in wind-fed sgH-MXBs could be the cause of the super-orbital modu-lations, as these periodicities require a mechanism sta-ble over years to produce variations that are detectedby folding the decade-long data-sets collected with
IN-TEGRAL , Swift , and
RXTE . The interpretation putforward to explain the super-orbital variability in sgH-MXBs involves either the variability of the mass-lossrate from the donor star induced by tidally-regulated os-cillations of its outer layers (Koenigsberger et al., 2006),or the presence of a third star in a hierarchical system(Chou and Grindlay, 2001). The problem with these twointerpretations is that the first has been shown to workonly for strictly circular orbits, while a stable triple hi-erarchical system implied by the second interpretationwould require the presence of a third body in a very dis-tant orbit that is not compatible with the fact that super-orbital modulations in sgHMXBs have a period that isin general not longer than roughly three times the orbitalperiod of these sources (Corbet and Krimm, 2013).More recently, Bozzo et al. (2017a) proposed an alter-native idea according to which superorbital modulations could be related to the interaction between the CIRs ofthe supergiant (see Sect. 2.1) and the NS orbiting thecompanion. When the NS encounters the CIR, the dif-ferent velocity and density of this structure comparedto the surrounding stellar wind produces the requiredlong-term variation of the mass accretion rate to giverise to a super-orbital modulation with the observed in-tensity. As the CIRs do not necessarily have the samerotational period of the supergiant star and their num-ber as well as geometrical properties are not yet wellknown, di ff erent combinations of a single or multipleCIR arms can be invoked in the di ff erent sgHMXBs inorder to obtain the observed super-orbital periods. Fig. 2shows an example of applying this idea to interpret the ∼
20 days-long superorbital modulation observed fromthe sgHMXB IGR J16493 − − Swift
BAT with a broad-band spectral analysis combining twoquasi-simultaneous
Swift
XRT and
NuSTAR observa-tion at the maximum and minimum phase of the su-perorbital modulation within a single 20 days cycle.They did not observe any significant di ff erences be-tween the spectral parameters of the two sets, apart fromthe overall flux change and could not firmly identify themechanism causing the modulation. Despite the lim-itation of the short amount of time during which thebroad-band spectral properties are measured, mecha-nisms where a significant change in the neutral hydro-gen column density would be expected were consideredunlikely. More observations covering much longer in-tegration time scales, e.g., folding data covering manysuperorbital cycles, are clearly needed in order to ad-vance our understanding on the intriguing superorbitalvariability of wind-fed sgHMXBs. In the case of accreting NSs their usually strong mag-netic fields add another level of complexity to the ac-cretion physics. Note that this is often happening at thescale of a single pixel within the grids of models de-scribing the system at a whole and thus tends to be han-dled in a very simplified manner in the kind of modelsdescribed previously.Interaction of plasma accreting onto a magnetizedNS is usually described using an ideal magneto-9ydrodynamic (MHD) approximation. In this approx-imation, the accreting plasma flow is significantly dis-turbed by the NS magnetic field at the radius (the Alfv´enradius, R A ) determined by the balance between accret-ing plasma pressure (thermal and dynamical) and mag-netic pressure. For example, for a spherically symmet-ric flow characterized by a mass accretion rate ˙ M onto aNS with mass M x and dipole magnetic moment µ , oneobtains (Elsner and Lamb, 1977): R A = (cid:32) µ ˙ M √ (2 GM x ) (cid:33) / (2)This is a convenient reference formula to which real val-ues of the magnetospheric boundary R m , di ff erent bydi ff erent factors in each particular source, can be nor-malized. It is convenient to write R m = ζ R A , wherethe coe ffi cient ζ is generally a function of ˙ M , µ andother parameters and geometry of the flow (see, e.g., Lai2014 but also the criticism to this approach expressed byBozzo et al. 2009b, 2018). Note that the dependence ofthe Alfv´en radius on accretion rate R A ∝ ˙ M − / was in-directly checked by the analysis of aperiodic X-ray vari-ability of bright accreting NSs (Revnivtsev et al., 2009)and is confirmed by the disc accretion torque-luminositydependence in transient X-ray pulsars with Be compo-nents (Sugizaki et al., 2017; Filippova et al., 2017).Magnetospheric interaction di ff ers for disc or quasi-spherical accretion. The type of accretion (disc or quasi-spherical) is determined by the specific angular momen-tum of captured matter j m at the magnetospheric bound-ary R m . A disc is formed around the magnetosphere if j m exceeds the specific Keplerian value at the magneto-spheric boundary, j m ( R m ) > j K ( R m ) = √ GM x R m . Thisis always the case for Roche-lobe overflow, but morerarely occurs in wind-fed systems (see above in Section2.2). In the opposite case, the accretion flow arriving atthe magnetosphere is quasi-spherical. ff ect In the case of disc accretion, the inner disc radius R d = ζ d R A is the key parameter directly related to ob-servational phenomena (spin-up / spin-down transitionsin HMXB X-ray pulsars, the propeller e ff ect, etc.).Presently, there are a number of models e ff ectively de-scribing R d , which is determined by plasma micro-physics and the model of plasma-magnetospheric inter-action. For example, assuming a purely diamagneticShakura-Sunyaev α − disc (Shakura and Sunyaev, 1973),one readily finds ζ d ≈ α / (Aly, 1980). In other mod-els (see, e.g., Ghosh and Lamb (1979a,b); Lovelaceet al. (1995); Klu´zniak and Rappaport (2007), among many others), di ff erent e ff ective values of ζ d are ob-tained (Bozzo et al., 2009b; Lai, 2014).From an observational point of view, the plasma-magnetospheric interaction can be probed by spin-up / spin-down studies of X-ray pulsar spin periods andby analysis of non-stationary phenomena (X-ray out-bursts). The torques acting on a NS are usually splitinto spin-up ( K su ) and spin-down ( K sd ) parts so that theangular momentum balance implies I ˙ ω (cid:63) = K su − K sd ,where ω (cid:63) = π/ P s is the NS spin frequency, I is the NSmoment of inertia. The spin-up torque can be written as K su = ˙ M ω m R , where ω m is the angular frequency ofmatter at the magnetospheric boundary. The spin-downtorque includes the magnetic part ∼ µ / R (which gen-erally may have di ff erent sign depending on the twistingof the magnetic field lines) and the part due to the possi-ble mass outflow from the inner disc radius ∼ ˙ M ej R ω (cid:63) .Note that adding the matter ejection part provides an ex-planation for the observed strong spin-down episodes inHer X-1 (Klochkov et al., 2009).A widely accepted approach is to consider, in thefirst approximation, an equilibrium spin period P eqs ob-tained from the balance K su = K sd . Obviously, this isa model-dependent quantity, P eqs ( ˙ M , µ, ζ d , ... ). The no-tion of an equilibrium spin period is frequently used forindirect estimation of the NS magnetic field from obser-vations of P s and the X-ray luminosity produced nearthe NS surface – the latter is related to ˙ M as L x ≈ ˙ Mc .This period is close (but not identical) to the criticalNS spin period derived from the condition for accre-tion to be centrifugally allowed, which is obtained byequating the corotation radius to the inner disc radius: R c = ( GM x /ω ∗ ) / = ζ d R A . In the first approxima-tion by assuming ζ d = const, we get P crits ∝ ˙ M − / . Inother words, with decreasing ˙ M the inner disc radiusincreases, and once at a given P s it reaches the corota-tion radius, accretion is centrifugally inhibited, and theNS enters the so-called ‘propeller’ state (Illarionov andSunyaev, 1975). At this stage, the matter can be cen-trifugally expelled along open magnetic field lines, andmagnetically dominated Poynting jets can be formed(Lii et al., 2014). Nevertheless, a residual, stronglyreduced X-ray luminosity (compared to the accretionstate), can still be sustained by an ine ffi cient plasmaentry rate into the magnetosphere caused by di ff usion,cusp instabilities, etc., as discussed e.g. by Elsner andLamb (1984), or can be due to thermal emission fromthe magnetospheric accretion with L x , m (cid:39) GM x ˙ M / R m ,as in the model developed for γ Cas stars by Postnovet al. (2017a).Variable accreting X-ray sources o ff er the possibil-ity to probe the accretion-propeller transitions during10ise and decay of outbursts. The propeller mecha-nism is frequently invoked to explain a variety of tran-sient phenomena in HMXBs, including SFXT outbursts(Grebenev and Sunyaev, 2007; Bozzo et al., 2008a),luminosity changes in bright transient X-ray pulsars(Tsygankov et al., 2016a; Lutovinov et al., 2017; Tsy-gankov et al., 2018) and in ultra-luminous X-ray pulsars(ULXPs) (Tsygankov et al., 2016b). In the case of quasi-spherical accretion, interac-tion of plasma at R m can be responsible for di ff erentsteady-state and non-stationary phenomena in wind-fedHMXBs (see Section 3.4 below). Here a new impor-tant parameter appears – the plasma cooling time at themagnetospheric boundary, which determines the type ofmagnetosphere inflow and the torques that apply to theNS.It has long been recognized that plasma entry into theNS magnetosphere in accreting X-ray binaries occursvia an interchange instability – Rayleigh-Taylor (RT) inthe case of slowly rotating NSs (Arons and Lea, 1976;Elsner and Lamb, 1977) or Kelvin-Helmholtz (KH) inrapidly rotating NSs (Burnard et al., 1983). In the caseof disc accretion, the plasma entry into the magneto-sphere via the RT instability was compellingly demon-strated by multi-dimensional numerical MHD simula-tions (Kulkarni and Romanova, 2008). However, globalMHD simulations of large NS magnetospheres ( ∼ cm) have not been performed as yet, and informa-tion about physical processes near NS magnetospheresshould be inferred from observations.During quasi-spherical wind accretion onto slowlyrotating NSs, there is a characteristic luminosity, L ∗ (cid:39) × erg s − , that separates two physically distinctaccretion regimes: the free-fall Bondi-Hoyle supersonicaccretion occurring at higher X-ray luminosity, whenthe e ff ective Compton cooling time of infalling plasma t cool is shorter than the dynamical free-fall time t ff (El-sner and Lamb, 1984), and subsonic settling accretion atlower luminosities, during which a hot convective shellforms above the NS magnetosphere (Shakura et al.,2012, 2018). In the latter case, a steady plasma entryrate is controlled by plasma cooling (Compton or radia-tive) and is reduced compared to the maximum possiblevalue determined by the Bondi-Hoyle-Littleton gravi-tational capture rate from the stellar wind of the opti-cal companion, ˙ M B (cid:39) ρ w R / v , by a factor f ( u ) − ≈ ( t cool / t ff ) / >
2. Here ρ w and v w are the stellar winddensity and the velocity relative to the NS, respectively,and R B = GM x / v is the Bondi gravitational capture radius. The necessary conditions for settling accretionare met at low-luminosity states in HMXBs (Postnovet al., 2017b).Settling accretion, unlike supersonic Bondi-Hoyle ac-cretion, enables angular momentum transfer from themagnetosphere, which makes it possible to find anequilibrium NS spin period from the torque balance K su = K sd . However, unlike in the disc case, theequilibrium period for a standard NS magnetic fieldturns out to be proportional to the binary orbital pe-riod P b , and can be very long: P eqs ≈ P b ( R m / R B ) ≈ P µ / L − / v . Here P = P b /
10 d, L = L x / (10 erg s − ), v = v w / (1000 km s − ). This can ex-plain the existence of very long-period X-ray pulsarswithout invoking a superstrong magnetic field for theNSs (Marcu et al., 2011; Sidoli et al., 2017a). Fur-ther implications and population synthesis modeling ofHMXBs at the settling accretion stage are discussed inPostnov et al. (2018).At the settling accretion stage, in a rather narrow X-ray luminosity range between ∼ a few × erg s − and L ∗ , Compton cooling is still e ff ective enough to enablesteady plasma entry at a rate ˙ M x = f ( u ) Comp ˙ M B viathe RT instability. The classical persistent X-ray pul-sars Vela X-1 and GX 301-2 provide suitable examples(Shakura et al., 2012). With decreasing X-ray lumi-nosity, radiative cooling becomes more e ff ective thanthe Compton one. However, it is unclear whether theRT-mediated plasma entry into the magnetosphere canbe steadily sustained by radiative cooling. Indeed, ob-servations of ‘o ff ’-states in Vela X-1 show abrupt de-creases in the observed X-ray flux by more than anorder of magnitude during which X-ray pulsations areclearly visible, suggesting a temporary transition to theradiative cooling regime (Shakura et al., 2013). Similarchanges were observed in the SFXT IGR J11215 − Bozzo et al. (2008a) proposed a di ff erent approachto identify the diverse accretion regimes in NS HMXB,especially SFXTs, expanding on Burnard et al. (1983),Davies et al. (1979), and Davies and Pringle (1981).Compared to the previous sub-section, this also con-siders the case of fast rotating NSs, for which plasmapenetration into the magnetosphere through the KH in-stability can be more e ff ective than the RT instability.This description is based on the relative sizes of threeessential radii defined in wind acrretion (see Bozzo11t al., 2008a, for detailed equations and definitions): • the accretion radius: R a is the distance at which theinflowing matter is gravitationally focused towardthe NS; • the magnetospheric radius: R M , at which the pres-sure of the NS magnetic field ( µ / (8 π R ), with µ the NS magnetic moment) balances the ram pres-sure of the inflowing matter; • the corotation radius: R co , at which the NS angularvelocity equals the Keplerian angular velocity.Assuming typical values for the NS and the stellar wind,these three radii are all of the order of a few times10 cm.Changes in the relative position of these radii resultinto transitions across di ff erent regimes for the NS.In particular, the accretion radius and magnetosphericradius depend on the wind parameters ( R a ∝ v − , R a ∝ v − / , with the wind velocity v w ), which canvary on a wide range of timescales (from secondsto months) and are usually assumed to trigger thetransition between the di ff erent regimes, together withthe corresponding variations in the X-ray luminosity.Below the di ff erent regimes of a magnetic rotating NS,subject to a varying stellar wind, are summarised (seealso Bozzo et al., 2008b). Outside the accretion radius: magnetic inhibition ofaccretion (R M > R a ) .In systems with R M > R a the mass flow from thecompanion star interacts directly with the NS magneto-sphere without significant gravitational focusing, form-ing a bow shock at R M . The power released in this re-gion L shock is estimated to be relatively low luminosity –a few times 10 erg s − – and is mainly radiated in theX-ray band. Two di ff erent regimes of magnetic inhibi-tion of accretion can be distinguished:1. The super-Keplerian magnetic inhibition regime ( R M > R a , R co ): In this case the magnetosphericradius is larger than both the accretion and corota-tion radii. Matter that is shocked and halted closeto R M cannot proceed further inward, due to the ro-tational drag of the NS magnetosphere which is lo-cally super-Keplerian. Since magnetospheric rota-tion is also supersonic, the interaction between theNS magnetic field and matter at R M results in rota-tional energy dissipation and thus, NS spin down.This process releases energy at a rate L sd , again of the order of a a few times 10 erg s − for typicalparameters, which adds to the shock luminosity.2. The sub-Keplerian magnetic inhibition regime ( R a < R M < R co ): In this case the magnetosphericdrag is sub-Keplerian and matter can penetrate theNS magnetosphere through the KH instability. Themass inflow rate across the magnetospheric bound-ary R M resulting from this instability depends onthe e ffi ciency factor η KH ∼ .
1, the shear velocity v sh at R M , and the densities ρ i and ρ e inside andoutside R M , respectively. The luminosity releasedby accretion of this matter onto the NS is estimateddi ff erently (see Bozzo et al., 2008a, for details), de-pending on the choice of the post shock gas veloc-ity or the rotational velocity of the NS magneto-sphere, but is estimated to be of the order of a afew times 10 erg s − for typical parameters. Inside the accretion radius: R M < R a .Once R M is inside the accretion radius, matter flow-ing from the companion star is shocked adiabaticallyat R a and halted at the NS magnetosphere. In the re-gion between R a and R M this matter redistributes itselfinto an approximately spherical configuration (resem-bling an “atmosphere”), whose shape and properties aredetermined by the interaction between matter and NSmagnetic field at R M . A hydrostatic equilibrium ensueswhen radiative losses inside R a are negligible; the at-mosphere is stationary on dynamical timescales, and apolytropic law of the form p ∝ ρ + / n can be assumed forthe pressure and density of the atmosphere. The valueof the polytropic index n depends on the conditions atthe inner boundary of the atmosphere, and in particularon the rate at which energy is deposited there. Threedi ff erent regimes can be distinguished:1. The supersonic propeller regime ( R co < R M < R a ):In this case the rotational velocity of the NS mag-netosphere at R M is supersonic; the interaction withmatter in the atmosphere leads to dissipation ofsome of the star’s rotational energy and thus spin-down. Turbulent motions are generated at R M ,which convect this energy up through the atmo-sphere, until it is lost at its outer boundary. Matterthat is shocked at ∼ R a , reaches the magnetosphericboundary at R M , where the interaction with the NSmagnetic field draws energy from the NS’s rota-tion. According to Pringle and Rees (1972), thisgives the largest contribution to the total luminos-ity in this regime, L sd , of the order of a a few times10 erg s − for typical parameters.12. The subsonic propeller regime ( R M < R a , R co ,˙ M w < ˙ M lim ): The break down of the supersonicpropeller regime occurs when the magnetosphererotation is no longer supersonic with respect to thesurrounding material. The structure of the atmo-sphere changes and the transition to the subsonicpropeller regime takes place. Since the rotationof the magnetosphere is subsonic, the atmosphereis roughly adiabatic ( n = / R M < R co , but the energy input at thebase of the atmosphere is still too high for matterto penetrate the magnetosphere at the capture rate˙ M capt at which it flows towards the magnetosphere.Nevertheless, a fraction of the matter inflow at R a isexpected to accrete onto the NS, mainly due to theKH instability, leading to a luminosity L KH > erg s − for typical parameters. The rotational en-ergy dissipation at R M gives a small contribution L sd of order of 10 erg s − under the same assump-tions.The subsonic propeller regime applies until thecritical accretion rate ˙ M lim is reached, at which thegas radiative cooling completely damps convec-tive motions inside the atmosphere. If this coolingtakes place, direct accretion at the rate ˙ M capt ontothe NS surface becomes possible.3. The direct accretion regime ( R M < R a , R co , ˙ M w > ˙ M lim ): If R M < R co and matter outside the mag-netosphere cools e ffi ciently, accretion onto the NStakes place at the full capture rate ˙ M capt . The cor-responding luminosity L acc = GM NS ˙ M capt / R NS (cid:39) × ˙ M erg s − , (3)where ˙ M = ˙ M capt / g s − . This is the standardaccretion regime, identified in some of the previoussections as the Bondi-Hoyle accretion. Supergiant Fast X-ray Transients (SFXT) have beenestablished as a class by
INTEGRAL and are discussedin detail in Section 3.4 later. Their behaviour is char-acterized by transient emission and a huge dynamicalrange during outbursts. This suggests inhibition of ac-cretion between the flares, which can be due to phys-ically di ff erent mechanisms. Chronologically, the firstmodel invoked the magnetospheric gating due to themagnetic and / or centrifugal propeller e ff ect in a wind-fed system discussed above in Section 2.5 (Grebenevand Sunyaev, 2007; Bozzo et al., 2008a). Indeed, for a fixed value of the mass accretion rate ˙ M , if a NS spinsfast enough and / or if its magnetic field strength is suf-ficiently intense, the magnetospheric radius can end upbeing either larger than the corotation radius but insidethe accretion radius, or larger than both the accretionand corotation radii. Under these circumstances, thesystem might end up either in the supersonic propellerregime or even in the super-Keplerian propeller regime,where the largest inhibition of accretion occurs due tothe magnetic and centrifugal gate. In this regime, thesystem is expected to be characterized by a low lumi-nosity state ( (cid:46) erg s − ). Temporary increases in ˙ M ,for example related to the clumps in the winds of OB-supergiants (Bozzo et al., 2016b, 2017a), can ‘open’ themagnetopsheric / centrifugal gates and induce transitionsto the other di ff erent accretion regimes introduced ear-lier in this section. Among them, the subsonic propelleror the direct accretion regimes allow a much higher ac-cretion rate onto the compact object to take place, thusexplaining the brightest X-ray states observed from theSFXTs ( (cid:38) –10 erg s − ).A first attempt to simulate the transitions betweendi ff erent accretion regimes in SFXTs using an hydro-dynamically calculated supergiant clumpy wind modelhas been presented by Bozzo et al. (2016b). The au-thors have shown that the e ff ect of the NS rotation cou-pled with a strong magnetic field can significantly re-duce the average luminosity of a sgHMXB and qualita-tively explain the di ff erence between classical systemsand SFXTs. This is shown in Fig. 4.The system parameters adopted in the simulation areshown on the top of each figure (for the parameters andcircular orbits assumed in this work a separation of 5 R (cid:63) corresponds to an orbital period of 25.6 days). The topfigures both on the left and on the right report the windvelocity and density as a function of time, and all rele-vant radii to be determined in the gating accretion model(see Sect. 2.5). The bottom figures show the luminosityin each regime that is achieved by the system triggeredby the variations of velocity and density in the stellarwind.The top panel of the top figures shows the instan-taneous density of the supergiant wind, while the sec-ond panel displays the corresponding density. The reddashed line in these panels represents a critical value ofthe wind density above which the mass inflow rate to-ward the compact object becomes large enough to trig-ger the switch to the direct accretion regime.In the other panels, RM RM RM L shock is as13 igure 4: Results of the simulations of the accretion onto a NS using an hydrodynamically calculated supergiant clumpy wind model and takinginto account the gating accretion mechanisms described in Sect. 2.5. This figure combines Figures 7 and 8 of Bozzo et al. (2016b). See text fordetails. L sd1 corresponds to the spin-down luminosityin the super-Keplerian magnetic inhibition regime, L sd2 and L sd3 to those in the supersonic and subsonic pro-peller regimes, respectively. L kh1 and L kh2 are the twosomewhat di ff erent estimates for the KH-fueled accre-tion luminosity in the sub-Keplerian magnetic inhibi-tion regime, while L kh3 is the corresponding luminosityin the subsonic propeller regime.The bottom panels of the bottom figures show thesummed X-ray luminosity (red solid line) compared tothe luminosity that a system would have if it was alwaysin the direct accretion regime (solid magenta line). Thetop and bottom figures on the left di ff er from the cor-responding ones on the right only for the assumed NSmagnetic field strength. The figures on the left show arepresentative case of a classical sgHMXB, where theNS magnetic field as a “standard” value close to 10 Gand the system in virtually always in the direct accre-tion regime. The figures on the right show the casewhere a much stronger NS magnetic field is assumed(“magnetar”-like, 10 G) and how this leads to a verydi ff erent behaviour in the X-ray domain with a more ex-treme variability that is closer to what is observed in theSFXTs. With this stronger magnetic field, the veloc-ity and density variations of the stellar wind are able tocause frequent switches among the di ff erent accretionregimes due to the fact that the magnetospheric radius,the accretion radius, and the corotation radius are closerto one another.In a wind-fed system there are also di ff erent modelsto explain the instability of the accretion flow onto thecompact object and to interpret the correspondingly in-duced X-ray variability. As discussed earlier in this sec-tion, if we assume the specific case of a “slow” rotatingNS, it can be shown that subsonic (settling) accretiononto the NS magnetosphere occurs at X-ray luminosi-ties below ∼ erg s − . In this regime, the entry rateof accreting plasma into the NS magnetosphere is de-termined by plasma cooling. At low accretion rates, thecooling is radiative (ine ffi cient compared to Comptoncooling operating at higher ˙ M ), which hampers the de-velopment of the RT instability at the magnetosphericboundary. Neglecting the KH instability due to the slowrotation, the mass accretion rate drops down to low val-ues corresponding to luminosities of ∼ − ergs − , which are comparable to those recorded during theSFXT ‘low’ states.It is quite possible that in the low-luminosity states ofSFXTs no RT-mediated plasma entry into the NS mag-netosphere occurs at all. This could be the case if theplasma cooling time is longer than the time a plasmaparcel spends near the magnetosphere because of con- vection in the magnetospheric shell: t cool > t conv ∼ t ff ( R B ) ∼ − XMM-Newton
EXTraS project can natu-rally be explained by the development of RT instabilityat low accretion rates (Sidoli et al., 2019).Additionally, within the context of the settling accre-tion model, in SFXTs the magnetospheric boundary it-self can be made unstable for di ff erent reasons. For ex-ample, it was conjectured (Shakura et al., 2014) that gi-ant flares in SFXTs are due to a sudden break of themagnetospheric boundary caused by the magnetic fieldreconnection with the field carried along with stellarwind blobs. This can give rise to short strong outburstsoccurring in the dynamical (free-fall) time scale duringwhich the accretion rate onto the NS reaches the maxi-mum possible Bondi value from the surrounding stellarwind. A tentative evidence for the presence of magneticfields in the OB supergiant in IGR J11215-5952 wasfound from ESO-VLT FORS2 spectropolarimetric ob-servations (Hubrig et al., 2018). Another reason for theinstability can be due to stellar wind inhomogeneitieswhich can disturb the settling accretion regime and evenlead to free-fall Bondi accretion episodes.So far, only one outburst observed from the SFXTsis di ffi cult to be reconciled with a wind-fed accretionscenario. Independently of the specific assumptionsconsidered for the plasma penetration inside the mag-netosphere, the giant outburst observed in 2014 fromthe SFXT IGR J17544-2619 (Romano et al., 2015)reached an unprecedented X-ray peak luminosity of3 × erg s − that is virtually impossible to achieve ina wind-fed system due to the limitations on the amountof material captured by the NS for any reasonable valueof the supergiant companion mass loss rate. Romanoet al. (2015) suggested that this event resulted fromthe temporary formation of a short-lived accretion discaround the NS hosted in this system. Accretion from aneven temporary accretion disc can, indeed, lead to muchhigher luminosities than those achieved in a wind-fedsystem due to the larger mass accretion rate that can betransported through the disc by viscosity. As of today,this was the only case in which a disc accretion scenariowas adopted for an SFXT, but short-lived accretion discshave also been invoked to explain bright X-ray lumi-nosity states in classical sgHMXBs (see, e.g., the caseof OAO 1657-415; Xu and Stone, 2019, and referencestherein)15 .6. Continuum spectrum Soon after the discovery of X-ray binaries, it be-came clear that Compton scattering in the hot and densemedium close the compact object leads to the shap-ing of X-ray radiation (Davidson and Ostriker, 1973).In neutron-star high-mass X-ray binaries, plasma flow-ing from the limit of the magnetically dominated re-gion (the magnetosphere) is funneled along the mag-netic field lines and then falls onto the NS on the mag-netic poles forming two or more “accretion columns”.The accretion column radius depends on the magneticfield strength and on the accretion rate as (Lamb et al.,1973) r ac ≈ L / B − / m, where we have assumeda one solar mass NS with radius of 10 km, luminosityis expressed in units of 10 erg s − , and the magneticfield in units of 10 G. The spectrum emerging from ahot, dense plasma with a more rarefied medium above isdominated by Compton scattering of some thermal seedphotons. At first approximation it has, thus, the spec-tral shape of an absorbed power-law with an exponentialroll-over at high energy. Several empirical functionalshapes have been used to describe the spectral energydistribution of these systems (cuto ff power law, Fermi-Dirac cuto ff , NPEX, etc.; see Coburn et al., 2002, fora collection of model shapes). However, in all of them,the cuto ff energy is indicative of the plasma temperaturein the accretion column and is of the order of 10 keV ormore. At lower energy, for most systems, photoelec-tric absorption in the local and Galactic medium pre-vents the investigation of the spectrum. However, forless absorbed systems, such as Her X-1, additional com-ponents due to the accretion disc may appear (e.g. F¨urstet al., 2013).Basko and Sunyaev (1976) realized that a high accre-tion rate would naturally lead to a halt of the infallingmaterial by radiation in the column and identified a crit-ical luminosity at which the formation of a radiatively-induced collisionless shock at some height above the NSsurface is unavoidable: L (cid:63) ≈ × r ac cm σ T σ s cm R MM (cid:12) erg s − , (4)where r ac is the accretion column radius, σ s is the crosssection in the vertical direction, and M is the neutronstar mass. At first approximation, below this critical lu-minosity, the plasma is stopped very close to the sur-face and radiation can escape vertically forming a “pen-cil beam”, while for brighter systems plasma will sinksubsonically below the shock and radiation is emittedfrom the sides of the accretion column in a “fan beam”. In that seminal work, it was noted that a crucialrole is played by the value of the opacity due to elec-tron scattering, which is strongly energy dependent ina magnetized plasma, especially at energies comparableto the cyclotron energy in the magnetic field ( E cyc ∼ . B keV, see Sect. 2.7). If we indicate with σ (cid:107) the cross section for electron scattering parallel to themagnetic field lines and with σ ⊥ the cross section com-ponent perpendicular to it, for E << E cyc one finds σ ⊥ ∼ σ T and σ (cid:107) << σ ⊥ (Canuto et al., 1971). Whenapproaching the cyclotron energy, resonances in thecross section play a crucial role and the extraordinarymode polarization dominates with an angle-dependentcross section which can exceed 10 times the Thomp-son value. Around the cyclotron energy, we thus expectfeatures in the spectrum: the ones that are most knownare the cyclotron resonant scattering features, describedin Sect. 2.7, which appear in absorption. However, alsothe continuum formation is influenced by such a strongenergy dependency of the cross section.With the high-sensitivity of the Rossi X-ray Tim-ing Explorer proportional counter array ( RXTE / PCA),it was noted that there were wiggles appearing around10 keV on the top of a smooth continuum. However, itwas with the giant outburst of EXO 2030 +
375 in 2007that the issue of whether a broad absorption or emis-sion feature is most appropriate became evident. Asdepicted in Fig. 5, Klochkov et al. (2007) showed thatduring a giant outburst, the continuum of this sourcecould be equally described by adding a broad Gaussianfeature centered at ∼
14 keV (a “bump”) or by two ab-sorption lines at ∼
10 and ∼
20 keV. Spin-phase-resolvedanalysis revealed a possible absorption feature at muchhigher energy ( ∼
60 keV; Klochkov et al., 2008). Sincethen, more cases arose with such a behaviour: particu-larly relevant is that of 4U 0115 +
63, for which M¨ulleret al. (2013) showed that the simultaneous presence ofemission and absorption features is important for the cy-clotron line centroid energy determination. However,the emission feature in this source is centered at ∼ ff ering between each other (see alsoFerrigno et al. 2009).The energy di ff erence between emission and absorp-tion features in 4U 0115 +
63, but also in EXO 2030 + EM−X
ISGRIBAT 10 + XRT b)c)d)a)
Figure 5: The broad band spectrum of EXO 2030 +
375 from simulta-neous fits of
INTEGRAL and
Swift data of the 2007 giant outburstwith highecut (a) and residual plots after fitting it without additionalfeatures (b), adding a “bump” around 15 keV (c), or alternatively in-cluding two absorption lines at ∼
10 and ∼
20 keV (d) (from Klochkovet al., 2007). See Camero-Arranz et al. (2005) for a broadband spec-trum from an earlier, normal outburst.
Pioneering works by Meszaros and Nagel (1985a,b)described the spectrum of magnetized accreting NSs asa function of the pulse phase. They exploited the maininteractions between matter and radiation in the columnto produce the first energy-dependent beam patterns thatcould qualitatively reproduce the observed properties ofpulse profiles and spectra of pulsating HMXBs. Fur-ther refinements were focused on the light bending inthe strong gravity regime (Ri ff ert and Meszaros, 1988;Meszaros and Ri ff ert, 1988; Leahy and Li, 1995).A breakthrough in understanding of the spectral char-acteristics came from the work by Becker et al. (2005)and Becker and Wol ff (2007) who managed to find ananalytical model to describe the spectral continuum ofmagnetized XRBs. To understand their work, it shouldbe first noted that there are two regions of the sys-tem where photons can be originally generated: thebase of the column, where an optically thick thermalmound emits as a black body at 1–2 keV, and the ac-cretion column in which the flowing plasma, in an opti-cally gray regime, emits bremsstrahlung radiation witha temperature of several keV. However, in presence ofa magnetic field with cyclotron energy of the order ofthe plasma temperature, the collisional excitation of theLandau levels around the magnetic field lines strongly modifies the emission spectrum with a prominent angle-dependent spike at the cyclotron energy produced atthe expense of higher-energy photons (Ri ff ert et al.,1999). This spectrum is very complex, but it can besimplified by assuming that the cyclotron emission is adelta function and the bremsstrahlung is not modified.In this approximation, seed photons are thus of threekinds: black-body from the base of the column, thermalbremsstrahlung and cyclotron emission (delta-function)from the vertical column body.Seed photons are then up-scattered in the Comptonprocess. In the presence of a strong magnetic field, theCompton cross section is heavily modified because pho-tons have two polarization states and these interact dif-ferently with the electrons bound to the magnetic fieldlines. To make the problem viable it can be noted that,below the cyclotron energy, the cross section parallelto the magnetic field is heavily suppressed, while per-pendicularly it remains essentially the Thompson one.The e ff ective cross section can thus be treated in themodel as an angle-average. With these assumptions,it is then possible to compute the transfer function forseed photons as they di ff use along the accretion column:which is a Green function (Becker and Wol ff , 2007).The model is substantially analytical and it can be usedto fit the spectra of accreting X-ray binaries. This wasdone by Ferrigno et al. (2009) for 4U 0115 +
63 using
BeppoSAX data, where it was necessary to introduce anadditional emission component at low energy, and byWol ff et al. (2016) for Her X-1 using NuSTAR data.Model limitations include the assumption of a cylin-drical shape of the accretion column, of an analyticalplasma velocity profile decoupled from radiation, of aconstant magnetic field and electron temperature in thecolumn. Farinelli et al. (2016) managed to relax the as-sumptions on the vertical dependency on the magneticfield and on the plasma velocity profile; they also intro-duced a Gaussian profile of the cyclotron emission in-stead of a delta function. This allowed them to describethe spectra of three X-ray binaries (4U 0115 +
63, CenX-3 and Her X-1) without the need for any additionalcomponent.Despite these theoretical e ff orts, a comprehensive de-scription of the X-ray spectrum of pulsating HMXBsstill eludes our complete understanding, due to the in-herent di ffi culties in treating the coupled MHD problemof a plasma that is emitting near the local Eddingtonlimit. However, with the models proposed so far, it hasbecome clear that the commonly used power law withexponential rollover can only describe the thermal partof the emission, i.e. the Compton upscattering of ther-mally produced photons. Additional components in the17 igure 6: Averaged cyclotron cross-sections in units of the Thomson cross-section calculated by Schwarm et al. (2017b,a). The di ff erent colorsindicate di ff erent angles ϑ between the photon path and the magnetic field, where µ = cos ϑ . The calculations were done for a magnetic fieldstrength of B = × G and a plasma temperature of kT = emission are thought to be due to the Compton broaden-ing from collisional excitation of the Landau level (cy-clotron emission). Once a continuum is formed, there isa transition from an optically gray regime to free stream-ing. In this phase, scattering features, mainly in ab-sorption, can be imprinted on the spectrum (see the nextsection). These features are quite broad and sometimesit becomes impossible to disentangle between emissionand absorption (see Bozzo et al., 2017b; Ferrigno et al.,2019, for recent cases). Electrons moving in a magnetic field are forced ontocyclic paths in the direction perpendicular to the mag-netic field. If the magnetic field is strong enough,their cyclotron energy becomes comparable to their restmass, requiring a quantum mechanical and relativistictreatment (e.g., Daugherty and Harding, 1986; Canutoet al., 1971; Harding and Daugherty, 1991). In fieldsthat are strong, the movement of the electrons perpen-dicular to the magnetic field axis can be described by quantized Landau levels, whose energies are the Eigen-values of the electron’s Hamiltonian and can be approx-imated when integrating over all angles and polarizationas E Landau , n = n (cid:126) eBm e (5)These quantized levels change the cross-section be-tween electron and photons, and hence strongly influ-ence the observed X-ray spectrum. Calculating thesecross-sections, however, requires detailed fully rela-tivistic QED-based calculations. The most recent workon this topic was presented by Schwarm et al. (2017b,a),building on work by, e.g., Sina (1996); Harding andDaugherty (1991); Isenberg et al. (1998); Araya andHarding (1999); Sch¨onherr et al. (2007).The cross-sections show two important properties:first of all, they are very strongly peaked close to theLandau level energies, implying that the plasma be-comes optically thick at these energies. Secondly, be-cause the energy of the electrons is only quantized inthe direction perpendicular to the magnetic field, the an-18le between the magnetic field and the photon becomesrelevant. For large angles, the cross-sections becomethermally broadened and shift to higher energies for theharmonic levels, as shown in Fig. 6.Because the optical depth is so large at the resonantenergies for cyclotron scattering, photons with the ex-act amount of momentum in the direction perpendicularto the magnetic field cannot escape the line forming re-gion, and we can observe absorption like features in thehard X-ray spectrum. These features are referred to asCyclotron Resonant Scattering Features (CRSFs) or cy-clotron lines for short. The CRSF central energy candirectly be related to the magnetic field strength in theline forming region via E CRSF , n = E Landau , n + z ≈ n + z . × B keV (6)where B is the magnetic field strength in 10 G and z is the gravitational redshift. Equation 6 is commonlyknown as the “12-B-12”-rule and works well for di ff er-ent geometries in the case of B (cid:46) G.CRSFs are the only way to directly measure the mag-netic field strength close to the surface of a NS. Cur-rently, 36 CRSF are known. For a recent in-depth re-view about them and their history, see Staubert et al.(2019, and references therein).Among the open questions in CRSF research is thefact that model calculations (Araya and Harding, 1999;Schwarm et al., 2017b,a) tend to predict asymmetricallines, frequently showing ”emission wings” at energiesbelow and above the central energy, while observed fea-tures tend to be broad and without a marked asymmetry.In order for discrete CRSFs to be observable, thesample magnetic field has to be confined to a very nar-row range, indicating a closely confined region withinthe accretion column, possibly a shock region in the col-umn or close to the poles (Becker et al., 2005; Beckerand Wol ff , 2007, and references therein). Broad andshallow observed CRSF might be caused by multipleline forming regions contributing (Nishimura, 2008).Another possibility is that CRSFs are formed due to re-flection of the downwards beamed radiation from theaccretion column on the NS surface around the poles(Poutanen et al., 2013). It is observationally clearly established that the CRSFenergy may change as function of luminosity. Thesources exhibiting such behaviour can be divided intotwo groups: the first, where the centroid energy ofCRSF is positively correlated with accretion luminosity,
Figure 7: Upper panel: Energy spectra of V0332 +
53 measured with
INTEGRAL for two di ff erent brightness states, with an immediatelyvisible shift of the cyclotron lines. Lower panel: Dependence of thecyclotron line energy on the source luminosity (3–100 keV); Trian-gles and squares mark INTEGRAL and
RXTE results, respectively.(Originally Figures 3 and 4 of Tsygankov et al. (2006a)). and the second, where an anti-correlation is observed.The sources with detected positive correlation tend tobe less bright than the sources with negative correlation(Becker et al., 2012; Mushtukov et al., 2015a). Di ff er-ent models which are able to explain the observed CRSFenergy behaviour have been proposed.Becker et al. (2012) defined three di ff erent accretionregimes, depending on luminosity and magnetic fieldstrength. At the lowest luminosities the infalling ma-terial is only stopped at the NS surface and the line isformed there. In this case, no change of the line energywith luminosity is expected. At intermediate luminosi-ties a Coulomb-dominated shock is formed in which theline is formed. With increasing luminosity the shock is19xpected to move closer to the NS surface, samplinghigher magnetic field strengths and increasing the ob-served line energy. At the highest luminosities, above acritical luminosity, the infalling material is deceleratedin a radiation dominated shock (Inoue, 1975; Basko andSunyaev, 1976). This shock is expected to rise in heightwith increasing luminosity, decreasing the observed lineenergy (see Sect. 2.6).In the line formation model of Poutanen et al. (2013)a higher luminosity leads to a higher accretion columnand a larger fraction of the NS surface being illumi-nated by this column. A larger area includes regions ofa lower magnetic field closer to the NS equator, result-ing in a decrease of the observed cyclotron energy withincreasing luminosity. Mushtukov et al. (2015b) explainthe case of positive correlation for sub-critical luminosi-ties via the Doppler e ff ect of a mildly relativistic fallingplasma in the column. The observed line profiles and energies dependstrongly on the angle under which we see the lineforming region. Because the rotational axis is typi-cally not aligned with the magnetic field axis (or withour line-of-sight), our viewing angle of the CRSF re-gion changes as function of pulse phase. The possi-ble changes are very complex and predictions dependstrongly on the assumptions about the magnetic fieldgeometry and emission pattern of each column. Energyshifts of the CRSF could for example be explained bydi ff erent observed relativistic boosting factors of the in-falling plasma (F¨urst et al., 2018).In case of a perfectly symmetric accretion geometry,with two opposed accretion columns, a lot of the ex-pected variability as function of pulse phase is consid-erably suppressed (Falkner, 2018). Because of the rela-tivistic light-bending, at most phases both columns arevisible and their flux variations as function of the view-ing angle almost cancel each other.The beaming function, and therefore flux and CRSFprofile variations with the pulse phase, can be stronglya ff ected by the material moving from the accretion discto the NS surface. The influence of magnetospheric ac-cretion flow is expected to be stronger in the case ofsuper-critical accretion, when the gravitationally lensedflux from the accretion columns passes the regions ofrelatively high density of magnetospheric flow (Mush-tukov et al., 2018). Because accretion is a dynamic process during whichthe NS gains mass, it is also expected that the accretion geometry might slowly change over time. Because theCRSF is so sensitive to the magnetic field, we might ex-pect a secular change of the CRSF energy, for exampleif the magnetic field slowly decays. However, expecteddecay times of magnetic fields are of the order of 10 years (e.g., Bhattacharya et al., 1992), much longer thanthe history of CRSF science. However, other e ff ects,like screening or burying of the surface magnetic fielddue to accumulation of the accreted material might oc-cur, but a clear theoretical picture has so far not emerged(see also the discussion in Staubert et al., 2014). The
INTEGRAL view on Galactic black-hole (BH)binaries is discussed elsewhere in a dedicated chapter,and we refer the reader to this for a more detailed discus-sion (Motta et al., this volume). Most of these sourcesare in low-mass X-ray binaries (e.g., McClintock andRemillard, 2006). Only a few confirmed BH HMXBsare known, but among them is one of the most promi-nent X-ray sources in the sky, Cygnus X-1, that has beenobserved by
INTEGRAL for over 11 Ms of dead-timecorrected exposure (Cangemi et al., 2019). Althoughthought to be wind-accretors, BH HMXBs usually ex-hibit a stable accretion disc.Observationally, BHs in XRBs can be found in twomain states: hard state , where the total energy out-put is driven by a hard power law component above10 keV with an exponential cuto ff at a few hundredkeV, and soft state , where soft thermal emission from a ∼ ff above ∼
500 keVmay be present. Changing between the states, the sourceevolves through the hard / soft intermediate state thatshows intermediate spectral characteristics (e.g. Fenderet al., 2004; Belloni, 2010). Radio emission is de-tected in the hard state but it is strongly suppressedor absent in the soft one; radio jets can be resolvedin several sources and radio flares are often associ-ated with state transitions. The states further show dis-tinct X-ray timing characteristics (e.g. Belloni, 2010).BH X-ray binary states correspond to di ff erent accre-tion / ejection geometries, but in particular the exact ori-gin of the Comptonized hard emission is still controver-sial (Nowak et al., 2011; Zdziarski et al., 2014). Addi-tionally, sources sometimes show an excess beyond thehard cuto ff , the so-called hard tail.Cygnus X-1 is a key source to understanding BH X-ray binaries: as a HMXB, it is a persistent accretor andthus easy to observe. Additionally, it often transits be-tween the states, crossing the so-called ‘jet line’ where20e expect the strongest changes in accretion geome-try to take place (Grinberg et al., 2013). INTEGRAL ’sunique capabilities at highest energies have contributedin several ways to a better understanding of this system:in particular, the hard tail above 400 keV in Cygnus X-1 has been shown to be polarized (Laurent et al., 2011;Jourdain et al., 2012; Rodriguez et al., 2015), hintingat a jet origin for this component. For the spectrumof the hard tail, see also Walter and Xu (2017). Ca-banac et al. (2011) analyzed power spectra and time lagsup to ∼
130 keV, for the first time assessing the energy-dependence of variability properties at such high ener-gies, giving strict constrains on models that try to repro-duce properties of hard X-ray emission.
The population of Galactic X-ray sources above2 keV is dominated by the X-ray binaries, see e.g.Grimm et al. (2002). At gamma-ray energies, how-ever, the situation is drastically di ff erent. Whilecurrent Cherenkov telescopes have detected around80 Galactic sources (see the TeVCat catalogue at http://tevcat2.uchicago.edu/ ), less than 10 bi-nary systems are regularly observed at TeV energiesas non-extended gamma-ray sources (Dubus, 2013;Chernyakova et al., 2019). The properties of PSRB1259 −
63, LS 5039, LS I + ◦ + − + −
093 (Eger et al., 2016; Mart´ı-Devesa andReimer, 2020), 4FGL J1405.1 − ffi ciently is not known yet.These systems are called gamma-ray binaries as thepeak of their spectral energy distribution lies in thegamma-ray range above 1 MeV, sometimes in the GeV–TeV range.All gamma-ray binaries host compact objects orbit-ing around massive young stars of O or Be spectraltype. This leads to the suggestion that the observedgamma-ray emission is produced as the result of inter-actions between the relativistic outflow from the com-pact object and the non-relativistic wind and / or radia-tion field of the massive companion star. However, nei-ther the nature of the compact object (BH or NS?) northe geometry (isotropic or anisotropic?) of the relativis-tic wind from the compact object are fully understood.Only in PSR B1259 −
63 and PSR J2032 + −
63 (Abdo and (Fermi LAT Collaboration),2011; Chernyakova et al., 2015; Caliandro et al., 2015;Johnson et al., 2018).In all other cases the source of the high-energy ac-tivity of gamma-ray binaries is uncertain. It can be ei-ther dissipation of rotation energy of the compact ob-ject (e.g. Dubus, 2006; Sierpowska-Bartosik and Tor-res, 2008; Torres et al., 2012), or emission from a jet(e.g. Bosch-Ramon and Paredes, 2005; Zimmermannand Massi, 2012a). In these other systems the orbitalperiod is much shorter than in PSR B1259 −
63 and PSRJ2032 + + ◦
303 in Acker-mann and (Fermi LAT Collaboration) (2013); we refermore about this below.Massi et al. (2017) tried to deduce the nature of thecompact source in LS I + ◦
303 by studying the rela-tion between the X-ray luminosity and the photon in-dex of its X-ray spectrum. It turned out that existingX-ray observations of the system follow the same anti-correlation trend as BH X-ray binaries. Under the hy-pothesis of a microquasar nature for LS I + ◦ + ◦ + ◦
303 tobe a magnetar and implies a change from a propellerregime at periastron to an ejector regime at apastron.During the periastron the pressure of matter from theBe star outflow compresses and disrupts the magneto-sphere of the NS, which leads to the disappearing ofthe pulsar wind. In this case electrons are acceleratedat the propeller shock, which accelerates electrons tolower energies than the inter-wind shock produced bythe interaction of a rotationally powered pulsar and thestellar wind of the Be star. A magnetar-like short burstcaught from the source supports the flip-flop model andthe identification of the compact object in LS I + ◦ + ◦
303 demonstrated the presence of a few,several second long, flares (Smith et al., 2009), whichwere compared by those authors to the flares typicallyfound in the accretion-driven sources; see also Li et al.(2011b) for a further analysis covering a wider range oforbital cycles. In principle, neither BAT nor RXTE ob-servations can exclude the possibility that the observedflares are coming from another source located close tothe line-of-sight (Smith et al., 2009), although similarobservations of instruments with better spatial resolu-tion indicate that it is likely they are from the gamma-ray source (Paredes et al., 2007; Rea et al., 2010).Other possible scenarios for the super-orbital mod-ulation in LS I + ◦
303 are related to the precessionof the Be star disc (Saha et al., 2016), or to a non-axisymmetric structure rotating with a period of 1667days (Xing et al., 2017).During its orbital motion around the optical compan-ion, the environment of the compact source changes alot from periastron to apastron. This leads to the ob-served spectral variability on very di ff erent time scales,from hours to the orbital and superorbital periodicities.The typical X-ray flux from gamma-ray binaries is at thelevel of few mCrabs, so it is not possible to study with INTEGRAL the spectral variability on short time scales(few hours). Still,
INTEGRAL is sensitive enough tostudy the properties of gamma-ray binaries on longertime scales.
Ultraluminous X-ray sources (ULXs) have been de-fined as a class of extragalactic point-like objects, out-side the nucleus of their respective galaxies and with aluminosity exceeding the Eddington limit for a 10 M (cid:12) black hole. Originally often thought to be intermediate-mass black holes with masses > (cid:12) , further stud-ies rather indicated “stellar mass” compact objects ac-creting at super-Eddington rates for at least most ULXs(e.g., Sazonov et al., 2014). The discovery of X-raypulsations from the ULX M82 X-2 (Bachetti et al.,2014) demonstrated that ULXs can host accreting neu-tron stars and further examples have been found subse-quently. Due to their distance, the nature of the massdonor is not well determined for most ULXs and onlyfor NGC 7793 P13 (Israel et al., 2013) this has beenclearly identified as a high mass star (Motch et al.,2011). A few more pulsating ULX have been tenta-tively identified as HMXBs, but, for example, in thecase of NGC 300 ULX1, Heida et al. (2019) reclassi-fied the mass donor as red supergiant. As noted alsoin Bachetti et al. (2014), very luminous outbursts ofBeXRB systems can also reach super-Eddington lumi-nosities and di ff erent Be transients like SMC X-3 (Tsy-gankov et al., 2018) or the recently found transient SwiftJ0243.6 + INTEGRAL ’s role in HMXB studies
Persistent wind-accreting supergiant HMXBS (sgH-MXBs) are systems with an early type (O or B-star)supergiant companion, losing large amounts of massthrough a stellar wind. The compact objects in thesesystems accrete from this dense wind, and, while theytend to show a large variability (up to a factor of 100),they are always active and some were among the firstHMXBs discovered.
INTEGRAL contributed to theknowledge about this source class by the merit of longobservations of fields containing these sources – fre-quently not directly targeting the sources themselves.22
NTEGRAL data in the hard X-ray band have also beenimportant to disentangle intrinsic variations of the X-raysource flux from the e ff ects of absorption when study-ing X-ray variability. For eclipsing systems, the accu-mulated long-term data has allowed to refine eclipse pa-rameters and thus derive new constraints on the massesof the binary companions, as detailed in Section 3.3. Inthe following, we give a few specific examples of IN-TEGRAL results for this source class. C oun t r a t e ( c oun t s / s ) −0.85−0.80−0.75−0.70−0.65 H a r dn e ss R a ti o
27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 a)b) Flare 1 Flare 2 Flare 3Flare 4 Flare 5Rev 137 Rev 138 Rev 139 Rev 140 Rev 141Offstates
Figure 8: Variability of Vela X-1 for the complete Vela region obser-vation from Revolution 137 to 141. a) ISGRI 20–40 keV light curve(time resolution 1 SCW, i.e. ∼ INTEGRAL ’s perigee passages, during which the instrumentsare switched o ff . The long dashed vertical lines show the eclipseingress and egress times. The dotted vertical line indicates the de-rived eclipse center, while the dash-dotted line indicates the time ofmean longitude T90. Originally Fig. 2 in Kreykenbohm et al. (2008). The sgHMXB Vela X-1 is among the best studiedobjects in the X-ray sky and often taken as a pro-totype supergiant X-ray binary in order to study thephysics of HMXB or as baseline case for modeling andsimulation e ff orts (see Kretschmar et al., 2019, for anoverview). Long-term X-ray monitor data show on av-erage a clear orbital profile (F¨urst et al., 2010; Falangaet al., 2015), driven by the mean absorption in thedense material present in the system, especially in theaccretion and photoionization wakes (Grinberg et al.,2017, and references therein). Erratic flux variationson timescales from days to minutes have been reported since early deep observations of the system (e.g., For-man et al., 1973; Watson and Gri ffi ths, 1977; ¨Ogelmanet al., 1977). During an extended observation of theVela region for five consecutive INTEGRAL revolu-tions in November / December 2003 (Fig. 8), coveringalmost two orbital periods of Vela X-1,
INTEGRAL found especially intense flaring, as well as o ff -states,which during the flux dropped below the detection limitof INTEGRAL for 1–2 rotations of the neutron star(Staubert et al., 2004; Kreykenbohm et al., 2008). F¨urstet al. (2010) found that the
INTEGRAL flux distribu-tion closely followed a log-normal distribution. Earlystudies of the accretion flow (Taam and Fryxell, 1988)identified strong time-dependent behaviour as well asindications of a highly asymmetric flow. Other stud-ies (starting with Blondin et al., 1990) revealed indeedhighly asymmetric structures caused by the photoion-ization and accretion wakes. Pushing these studiesfurther, Manousakis and Walter (2015a,b) found time-dependent holes in the simulated mass flow, which mayexplain the o ff -states observed by Kreykenbohm et al.(2008) and others, without requiring intrinsic clumpi-ness of the wind. P e r i od [ s ec ] MJD
MAM J J A S OND J FMAM J J A S OND J FMAM J
Figure 9: A torque reversal of 4U 1907 +
09 found in
INTEGRAL observations. Originally Fig. 6 in Fritz et al. (2006).
4U 1907 +
09 is a less studied source, a wind-accretingsgHMXB on a moderately eccentric, close orbit.
INTE-GRAL observations (Fritz et al., 2006) found a clearspin-down after almost 20 years of constant spin-upand confirmed CRSFs at ∼
19 and ∼
40 keV, consistent23ith earlier results (Figure 9). The spin-down trend re-versed again later (S¸ ahiner et al., 2012). Long-term spinperiod change trends like in this source contrast withthe “random walk” changes in pulse period observed,e.g., in Vela X-1. This source also shows dips or o ff -states. Using a Suzaku observation, Doroshenko et al.(2012a) found that the source continues to pulsate inthe o ff -state and that the transitions may be explainedby “gated accretion” (see Section 2.5.3), which mightmake 4U 1907 +
09 an interim source between SFXTsand ordinary accreting pulsars.The somewhat unusual system 2S 0114 +
650 har-bours one of the slowest spinning pulsars ( P s ≈ .
65 h)in a close orbit ( P b ≈ . INTEGRAL observations (Bonning and Falanga, 2005;Wang, 2011) have confirmed the previously observedlong-term spin-up trend with shorter variations. Notingstronger short-term variations and super-orbital varia-tions, Hu et al. (2017) propose the formation of a tran-sient disc (see also Section 2.2), while Sanjurjo-Ferrr´ınet al. (2017) consider quasi-spherical settling accretion(see Section 2.5) on a magnetar to explain the observedbehaviour.
Highly absorbed systems do not define a class them-selves: the physics and the nature of the sources areclearly the same as non-absorbed ones. It is, how-ever, worth pointing out that due to its unprecedentedcoverage, and, at that time, the best angular resolu-tion at hard X-rays, we could hope that
INTEGRAL could see sources otherwise undetected at lower ener-gies, for various reasons: sensitivity, hard spectra, con-fusion, high absorption, etc. On 2003 January 29 th ,during the first Galactic Plane Scan of the Norma re-gion (after a few weeks spent on the other side of theGalaxy in the Cygnus region), INTEGRAL detected itsfirst such system, and one of the most extreme of all
INTEGRAL sources (IGRs): IGR J16318 − −
37 or GX 301 −
2) with N H in excess of10 cm − (Walter et al., 2003). This results in a fea-tureless, continuumless spectrum below 4 – 5 keV, hugeFe K α , K β and Ni K β lines in the soft X-ray spectrum(Matt and Guainazzi, 2003; Walter et al., 2003), andvariable hard X-ray emission (Barragan et al., 2010),see Figure 10. Multi-wavelength follow-ups (mainlyfrom near-to-mid infra-red spectroscopy) have shownthe companion to be a peculiar supergiant (a so-calledsgB[e]), while the system is enshrouded in a dense co-coon (Filliatre and Chaty, 2004). This material also shows up in the X-rays, where the strongly absorbedspectrum can be self-consistently explained with a com-bination of gas and dust absorber (Ballhausen et al.,2020). Later observations with the ESO-VLT VISIR in-strument suggested that the compact object (of unknownnature) is orbiting within or behind the rim of a torus ofmatter encircling the supergiant star (Chaty and Rahoui,2012). Recently, Fortin et al. (2020) presented newESO-VLT X-shooter broad-band spectroscopic obser-vations from optical to near infra-red of this source, andcompared it with models made with the POWR code foratmospheres of massive stars. Figure 10: XMM-Newton and ISGRI unfolded photon spectra ofIGR J16318–4848, the first new source detected by
INTEGRAL andan extremely absorbed HMXB. From Walter et al. (2003).
It was still surprising that the following IGRs(e.g. IGRT J16320 − − − − N H ∼ cm − (Rodriguezet al., 2003; Bodaghee et al., 2006; Zurita Heras et al.,2006; Walter et al., 2006; Tomsick et al., 2008), morein line, however, with older sources. The strength ofthe absorption can vary as function of the orbital phase.Garc´ıa et al. (2018) followed the spectral evolution andchanges in column density of IGR J16320 − XMM-Newton observations,describing the changes in a simple geometrical model.
After the highly absorbed archetypeIGR J16318 − INTEGRAL found some more24ources with similar X-ray spectral properties. Someof these systems seem to be persistent sources, such asIGR J16320 − − − INTEGRAL , the small number of sgHMXBswas explained by the short-lived supergiant phase. Thedistribution of this kind of systems was reproduced wellby population synthesis models. However, the
INTE-GRAL survey of the Galactic plane and central regionshas revealed the existence of more than 900 sources inthe energy range 17–200 keV (Bird et al., 2016), with alocation accuracy of 0.5 (cid:48) –4 (cid:48) , depending on count rate,position in the field of view and exposure. The ob-serving strategy of INTEGRAL allowed the detectionof new kinds of sources that had been missed in the pastdue to the very short transient nature (see Section 3.4) orthe very high absorption. A large fraction of these newlydiscovered sources belongs to the sgHMXB class, re-sulting in a substantial increase of its members. Oftenthe highly absorbed sources are not accessible in the op-tical band due to the high interstellar extinction or wouldrequire extremely long exposure times on large opticaltelescopes.Under these circumstances, infrared spectroscopy isan alternative tool to characterize these systems in amultiwavelength context. The detection and study ofcounterparts in the infrared is possible with the IR in-strumentation on a 4-m class telescope. Combining itwith available IR photometry and the X-ray properties,the nature of the binary system can be established un-ambiguously. Follow-up X-ray observations by
XMM-Newton (e.g. Bodaghee et al., 2006; Rodriguez et al.,2006; Bozzo et al., 2012b),
Chandra (e.g. Tomsick et al.,2008; Paizis et al., 2011; Nowak et al., 2012) or
Swift (e.g. Kennea et al., 2005; Rodriguez et al., 2009; Pavanet al., 2011) lead to the reduction of the error circle toa few arcseconds and, consequently, the correct identi-fication of the IR counterpart (e.g. Chaty et al., 2008).To establish or constrain the nature of the compan-ions through IR spectroscopy, IR atlases of Hanson et al.(1996, 1998, 2005) are used for comparing the spectralfeatures present in the IR spectrum. The IR counterpartof IGR J19140 + + − − Suzaku observations confirmed that this object belongs to theclass of absorbed HMXB (Bodaghee et al., 2010). Pel-lizza et al. (2011) obtained optical and IR observa-tions of the field of IGR J16283 − − − − I , J , H and K bands with JHK photometry. They con-cluded that this IGR source is a persistent X-ray sourcewith a B1 Ib companion, i.e. a highly absorbed sgH-MXB system (see also Pradhan et al., 2019; Aftab et al.,2016).Although Walter et al. (2006) did not use IR spec-troscopy, they studied 10 IGR sources (8 persistent and2 transient systems), obtained follow-up observationswith
XMM-Newton and proposed IR counterparts fromexisting catalogues. They confirmed or demonstratedthat 8 out of the 10 sources are intrinsically absorbedand 7 of them are persistent sources. Moreover, theysuggested that the companions of these persistent sys-tems are very likely supergiants.AX J1910.7 + INTEGRAL inthe hard X-ray band. Pavan et al. (2011) analysedall archival
INTEGRAL , ASCA,
XMM-Newton and
Chandra observations around the position of this ob-ject. These authors associated the IR counterpart of thesource with 2MASS J19104360 + ff erentcomponents (see Fig.11). Their conclusion was that thecompanion of this source is most likely an early B su-pergiant located at a distance of ∼ igure 11: Left panel : 1.2 (cid:48) × (cid:48) K finding chart for 2XMM J191043.47 + XMM-Newton position of 2XMM J191043.47 + (cid:48)(cid:48) positional error. Right panel : 50 (cid:48)(cid:48) × (cid:48)(cid:48) in the Outer arm. This system would also belong to theclass of obscured HMXBs containing the slowest pulsarfound to date (Sidoli et al., 2017a).Overall, INTEGRAL has increased the number ofsgHMXB systems dramatically. The proportion of con-firmed sgHMXB related to HMXBs is now around 42%,and so, almost ten times higher than before
INTEGRAL (Coleiro et al., 2013).
Only in a few sources among more than one hundredHMXBs is the inclination of the system high enoughfor the compact star to be periodically occulted alongour line of sight by the companion, giving rise to X-rayeclipses. For these eclipsing HMXB systems, LMC X-4, Cen X-3, 4U 1700 − − − − − − INTEGRAL and
RXTE / ASM, the ephemeris, including the durationof the eclipse, orbital decay, and for eccentric systemsthe angle of periastron and the apsidal advance has beenderived (Falanga et al., 2015). Additionally, updatedvalues for the masses of the NS hosted in these tenHMXBs were also provided, as well as the long-termlight curves folded on the best determined orbital pa-rameters of the sources. The energy-dependent profileof the X-ray light curve during the eclipse ingress and O • )LMC X-4Cen X-34U 1700-3774U 1538-522SMC X-1SAX J1802.7-2017XTE J1855-026Vela X-1EXO 1722-363OAO 1657-415 Figure 12: Masses of the ten eclipsing HMXBs. The NS masses de-termined using 10 years
INTEGRAL data are shown with solid lines.Values from the literature are represented with dashed lines. The errorbars correspond to uncertainties at 1 σ c.l. The dashed vertical lineindicates the canonical NS mass of 1.4 M (cid:12) (see Falanga et al., 2015,for more details). M (cid:12) range(this occurs when the NS core is made of exotic mat-ter such as kaons, hyperons, and pions), whereas sti ff EoSs can reach up to 2.4–2.5 M (cid:12) . More massive NSscan thus provide stronger constraints on the EoS mod-els. As discussed by Rappaport and Joss (1983), eclips-ing HMXBs hosting X-ray pulsars provide a means tomeasure the NS mass and thus place constraints on theirEoS. INTEGRAL data at high energy band measuredsemi-eclipse angle smaller than the values reported inthe literature, and thus for the ten eclipsing HMXBsNS masses we estimated are generally higher, see Fig-ure 12.
INTEGRAL has proved an excellent tool for the dis-covery of transients. Its combination of large fieldof view, fine angular resolution and excellent instanta-neous sensitivity, coupled with long exposures as partof regular monitoring of the Galactic Plane, makes itfar superior to classical all-sky monitors at this task.In particular, one of the major outcomes of the missionhas been the detection of several unidentified fast X-raytransients (Sguera et al., 2005, 2006). Although some ofthese objects were already known at the time of launch,they had not been studied in depth (Figure 13). Sev-eral more fast transients were quickly discovered, char-acterised by strong activity on very short time-scales.Their identification with OB supergiant counterparts(Negueruela et al., 2006b) changed our view of the over-all HMXB population, by adding a new, distinct class ofwind-accreting sources: a totally unanticipated result.
While classical wind-fed supergiant HMXBs are,as described in Sect. 3.1, persistent or mildly variable in X-rays, but always detectable aroundL X ∼ erg s − , these new sources werecharacterised by their transient nature. Early inthe mission, 5 such objects had been identified,namely XTE J1739 −
302 (IGR J17391 − − − − − −
302 had been characterised with
RXTE (Smith et al., 2006). An accurate localisationby
Chandra allowed the identification of its counter-part, and follow-up optical spectroscopic observationsobtained in May 2004 with VLT / FORS1 showed it to bean O8 Iab(f) star, at a distance of ∼ . INTEGRAL during the first few yearsof operation had already permitted the discovery andcharacterization of a handful of new systems. Inten-sive work by di ff erent groups (e.g. Masetti et al., 2006a,2008; Negueruela and Schurch, 2007) led to the local-isation of counterparts to many of these sources, bothpersistent and transient.One of the new transient sources, IGR J17544 − XMM-Newton and
Chandra positions,allowing Pellizza et al. (2006) to take spectra withNTT / EMMI, and identify the counterpart as an O9 Ibsupergiant, at a distance of ∼ − XMM-Newton error circle,containing only one star. NTT / EMMI spectra of thisobject taken in 2005 and VLT / X-shooter spectra ob-tained in 2012 allowed its identification as an early B0.5to 1 Ib star with moderate mass loss and very broadlines, indicating a high rotational velocity of 320 km s − ,far higher than in most supergiant stars (Chaty et al.,2016). In a few other cases, the infra-red (IR) counter-parts of the fast IGR transient sources were identifiedthanks to the fast repointing and positional capabilitiesof Swift / XRT (see, e.g., Romano et al., 2016, and refer-ences therein).This serves to illustrate that subsequent follow-up op-tical / infrared spectroscopy in most cases showed thatthese sources are associated with blue OB supergiantdonor stars, just like the majority of sgHMXBs, with avariable amount of absorbing material, though. It wasthus proposed to name this new class of sgHMXB as27 oun t s / s ec Time (s)
Figure 13: Top panel: IBIS / ISGRI pointing-by-pointing image sequence (20–60 keV) of a fast X-ray outburst from the SFXT XTE J1739 − ff erence in sigma from the mean reconstructedflux. A weaker persistent source (1E 1740.7 − Supergiant Fast X-ray Transients (SFXT; Sguera et al.,2005; Negueruela et al., 2006b; Smith et al., 2006),because of the fast outbursts and supergiant compan-ions. This new subclass of sgHMXBs, sharing manysimilarities with other wind-fed sgHMXBs, comprisesabout 20 sources (including both firm members and can-didates), a population size comparable with persistentsgHMXBs.Although most SFXTs were discovered in the firstyears of the
INTEGRAL mission, new members havebeen uncovered recently (e.g., AX J1949.8 + − After the association of SFXTs with early-type super-giant companions, it became evident that these HMXBsare characterized by a remarkable hard X-ray activ-ity: their sporadic high-energy emission caught by
IN-TEGRAL only during short duration (a few thousandseconds) flares, put into question the accretion mecha-nism driving them (see the next subsection), comparedwith the classical population of supergiant HMXBs (likeVela X-1), known to persistently emit X-rays.On the timescales typical of SFXT flares ( ∼ / ISGRI occurs at fluxes greater thana few 10 − erg s − cm − (18 – 50 keV). This implies lu-28inosities above 10 – 10 erg s − at the known SFXTdistances (see Sidoli and Paizis 2018 for a systematicanalysis of the INTEGRAL archival observations of asample of 58 HMXBs, from 2002 to 2016). In thisbright flaring state, SFXTs spend less than 5% of thetime (their duty cycles at hard X-rays range from 0.01%in IGR J17354 − − INTEGRAL ) show power-law like dis-tributions, possibly indicative of a fractal structure ofthe supergiant wind matter (Sidoli et al., 2016b).An important observational e ff ort involved several X-ray missions operating at soft X-rays, to investigate theSFXT behaviour outside these outbursts. It consisted ofa twofold approach: deep, sensitive pointings at soft X-rays (below 10 keV; from the first studies by in’t Zand2005; Gonz´alez-Riestra et al. 2004; Walter et al. 2006with Chandra and
XMM-Newton , to the most recent
XMM-Newton overviews by Bozzo et al. 2017b andPradhan et al. 2018), alongside long-term monitoringcampaigns aimed at characterizing the X-ray propertiesoutside outbursts and at catching new luminous flares(we refer the reader to Romano (2015) and Bozzo et al.(2015) for the most recent reviews of the
Swift / XRTmonitoring of a sample of SFXTs, and to Smith et al.(2012) for the
RXTE results).These investigations found that the most extremeSFXTs span a large dynamic range in X-ray luminos-ity, from quiescence (L X ∼ erg s − , e.g. Drave et al.2014) to the peak of the flares (L X ∼ -10 erg s − ,reaching 10 erg s − in IGR 17544 − X ∼ -10 erg s − and L X ∼ erg s − (Sidoli and Paizis, 2018), with a time-averaged X-rayluminosity L X (cid:46) erg s − (Sidoli et al., 2008;Bozzo et al., 2015). The comparison of the SFXTsand classical sgHMXBs duty cycles carried out withSwift / XRT highlighted even more the strikingly di ff er-ent behaviours of the two classes of systems in the X-ray domain (see, e.g., Bozzo et al., 2015, and refer-ences therein). The SFXT emission is indeed very vari-able (flaring) at all X-ray luminosities (already evidentfrom the first XMM-Newton observation of the SFXTIGR J17544 − X ∼ erg s − ) of SFXTs remain poorly known, al-though from Swift / XRT monitoring it can be esti-mated as the most frequent state in some members ofthe class (IGR J08408 − − − ∼ − INTEGRAL (Sidoliet al., 2006), later refined to ∼
165 days with
Swift / XRT(Sidoli et al. 2007, Romano et al. 2009b) and likely as-sociated with the orbital period of the system. This isthe longest one, while for other SFXTs the orbital cy-cle ranges from 3.3 days (Jain et al., 2009a) to 51 days(Drave et al., 2010). Most periodicities have been dis-covered from the modulation of their long-term lightcurve observed with
INTEGRAL (Bird et al., 2009; Zu-rita Heras and Chaty, 2009; Clark et al., 2009, 2010;Drave et al., 2010; Goossens et al., 2013),
Swift / BAT(Corbet et al., 2006b; La Parola et al., 2010a; D’A`ıet al., 2011) and
RXTE (Levine and Corbet, 2006; Cor-bet et al., 2010d). SFXTs display both narrow circularorbits and wide, very eccentric ones, with orbital eccen-tricities ( e = .
63 in IGR J08408 − e > . − / X-ray tran-sients (see the discussion in Sidoli and Paizis 2018). InIGR J17544 − − − − − − − ∼ Γ be-tween 0 and 1), modified by a high energy cuto ff in therange of energies 10–30 keV (e.g. Walter et al. 2006;Sidoli et al. 2006; G¨otz et al. 2007; Filippova et al. 2007;Romano et al. 2008; Sidoli et al. 2009; Zurita Heras andWalter 2009; Ducci et al. 2010). The few SFXTs whereboth spin and orbital periods are detected are spread29ver a vast area of the Corbet diagram, overlapping (andbridging) persistent sgHMXBs and Be / X-ray transients.In a few SFXTs a soft X-ray spectral component hasbeen detected during outbursts (as observed in many ac-creting pulsars; see e.g. La Palombara and Mereghetti2006) and was modeled using a hot blackbody with ra-dius of a few hundred meters, compatible with the NSpolar caps (e.g. Sidoli et al. 2012). To date, only in thecase of the SFXT pulsar IGR J11215 − − XMM-Newton plus
NuSTAR spectrumacross di ff erent luminosity states (from 6 × erg s − up to the peak of a flare, 1600 times brighter): the com-bination of a hot (blackbody with kT ∼ ∼
40 keV, showed evidence of a moreprominent contribution from the blackbody at fainterfluxes (Bozzo et al., 2016a), similar to what is usuallyobserved in HMXB pulsars.Sometimes the soft excess detected in the same X-ray observation can be accounted for equally well bydi ff erent models, besides a blackbody: either a partialcovering absorption or a ionized absorber (Sidoli et al.,2012, 2017b). The specific case of IGR J08408 − cm − ) out of all SFXTs. This al-lowed Sidoli et al. (2009) to uncover two distinct photonpopulations (during outburst): one with a temperatureof ∼ ∼ L X ∼ – 10 erg s − ) are usually softer, althoughstill well described by a power law (with photon index Γ ∼ ∼ erg s − ) can be very soft ( Γ ∼
6; in’t Zand 2005),probably due to thermal X-ray emission from the super-giant wind.In some sources the local absorbing column densityis variable: an increase in the absorption during the riseto the peak of a flare is interpreted as due to and en-hancement of the accreting wind matter (Sidoli et al.,2009; Bozzo et al., 2011b, 2016a), otherwise it can besimply due to the passage of a foreground dense clump(Rampy et al., 2009; Boon et al., 2016; Bozzo et al.,2017b). A drop in the column density at the peak of abright flare is explained with the ionization of the localmaterial (Bozzo et al., 2011b, 2016a, 2017b).SFXTs have overall lower absorbing column densi-ties than persistent sgHMXBs (Gim´enez-Garc´ıa et al.,2015; Pradhan et al., 2018). Some exceptions exist, likeSAX J1818.6 − N H ∼ × cm − wasobserved, similar to what is seen in obscured HMXBs(Boon et al., 2016; Bozzo et al., 2017b). Another di-agnostic of the circumsource material is the iron lineemission (Bozzo et al., 2011b; Gim´enez-Garc´ıa et al.,2015; Pradhan et al., 2018), contributed by the super-giant wind illuminated by the X-ray source. The equiv-alent width (EW) of the 6.4 keV line measured out-side eclipses correlates with the absorbing column den-sity and can reach much higher values (EW > ff erence in the donor wind between some mem-bers of the two subclasses: in the persistent sourceVela X-1 a slower supergiant wind than in the SFXTIGR J17544 − . σ ) in the supergiant companion of theperiodic SFXT IGR J11215 − B ∼ G) has been found in IGR J18483 − B ∼ Ghas been measured with
NuSTAR in IGR J17544 − NuSTAR observation (Bozzo et al., 2016a). In the187 s pulsar IGR J11215 − NuSTAR spec-trum of a flare (Sidoli et al., 2017b), but was not con-firmed during a second
NuSTAR observation (Sidoli30t al., 2020).As a final remark, we note that the classification ofa source as an SFXT or a classical sgHMXB is by nomeans clear-cut, and there exist several sources dis-playing a behaviour which is intermediate between thetwo subclasses (see, e.g., Walter et al. 2015; Sidoli andPaizis 2018). Thus, we should not expect lists of SFXTsor sgHMXBs produced by di ff erent groups to agree ex-actly. INTEGRAL
The large field of view and high sensitivity of theinstruments on-board
INTEGRAL allowed this mis-sion to play a leading role in the detection and studyof transient sources, and particularly transient X-raypulsars (XRPs) in Be-binary systems (BeXRBs; seeSect. 2.3). For over 15 years, almost all major out-bursts from systems already known were observed,while eight new Be binaries were discovered by
IN-TEGRAL , representing an increase in the total num-ber of such sources up to 60 in our Galaxy (Walteret al., 2015). Pulsations with periods ranging from ∼ ∼
700 s were detected in several new systems: IGRJ01583 + + + + + ff erentmass accretion rates is essential to understand physicalprocesses at the accretion disc - magnetosphere borderand in the vicinity of the NS surface. A giant (type II)outburst from the BeXRB V 0332 +
53 starting late in2004 (Swank et al., 2004; Kreykenbohm et al., 2005)became the first such an event studied with the
INTE-GRAL observatory in great detail. About 400 ks of ex-posure time were invested to cover the whole outburstand investigate the properties of the source at very dif-ferent mass accretion rates. As a result of this monitor-ing, an unexpected negative correlation of the cyclotronenergy (see Sect. 2.7) with source luminosity was re-vealed (Tsygankov et al., 2006b; Mowlavi et al., 2006;Tsygankov et al., 2010; Ferrigno et al., 2016). Thisdiscovery led to a surge of interest in the study of cy-clotron lines, especially using the
INTEGRAL obser-vatory in view of its good energy resolution and broadenergy coverage (see e.g., Filippova et al., 2005, forthe review of spectral properties of XRPs with
INTE-GRAL ). Another pulsar possessing a possible negativecorrelation of the cyclotron energy with luminosity is4U 0115 +
63, where such a trend was suggested by Mi-hara et al. (1998). Later, this correlation was confirmed using the
INTEGRAL and
RXTE averaged and pulse-amplitude-resolved spectra (Nakajima et al., 2006; Mi-hara et al., 2004; Tsygankov et al., 2007; Klochkovet al., 2011). On the other hand, some authors explainedthis behaviour of the cyclotron energy in 4U 0115 + L X (cid:46) erg s − ), a pos-itive correlation of the cyclotron energy with luminositywas discovered using di ff erent observations, includingsome by INTEGRAL (Staubert et al., 2007; Yamamotoet al., 2011; Klochkov et al., 2012). For the well knownsource 1A 0535 + INTEGRAL and
RXTE observa-tions of the first observable outburst after a long periodof quiescence fixed the previously debated magneticfield strength and found no correlation with luminosityover the observed range (Kretschmar et al., 2005; Ca-ballero et al., 2007). These and many other results ob-tained with di ff erent X-ray missions (e.g. RXTE , NuS-TAR , Suzaku ) substantially improved our knowledge inthe field of cyclotron lines formation and evolution (seeSect. 2.7 and the recent review by Staubert et al. 2019).The good time resolution of the
INTEGRAL maininstruments also permitted studies of temporal proper-ties of emission from XRPs in hard X-rays. In partic-ular, a comprehensive investigation of the pulse pro-file shapes and pulsed fraction as a function of energyband and flux from the source was performed by Lu-tovinov and Tsygankov (2009). These authors showedthat the pulsed fraction systematically increases withenergy and has local peculiarities near the cyclotron en-ergy. Phase-resolved spectral analysis also revealed asignificant variability of the emission properties overthe pulse phase in several sources. Particularly in EXO2030 + ∼
63 keV in a very narrowphase interval covering less than 10% of the whole spinperiod (Klochkov et al., 2008).In addition to transient sources, the BeXRB fam-ily contains a few persistent X-ray pulsars (Reig andRoche, 1999). Such objects are characterized by rel-atively low luminosity (10 − erg s − ) and wideorbits ( P b (cid:38)
200 days). Due to the high sensitivity ofthe IBIS telescope some of these systems were detectedand studied in the hard energy range with great detail.For instance, RX J0440.9 + ∼
120 keV (Tsygankov et al., 2012) and ∼
160 keV (Lutovinov et al., 2012), respectively, whichis not typical for X-ray pulsars. In the case of X Persei,the high quality of the spectrum allowed Doroshenkoet al. (2012b) to interpret the broad absorption-like fea-ture around 30 keV not as a cyclotron line (Coburn et al.,31001), but as an artificial deficit of photons between twodistinct spectral components (see also Di Salvo et al.,1998). The latter interpretation was recently confirmedfor two other BeXRBs, GX 304 − + V [ m ag ] V [ m ag ] V [ m ag ] Figure 14: OMC light curves of BeXRBs. Top: 1A 0535 + − −
1. The apparent dispersionwithin the observation windows is due to intrinsic low-amplitude vari-ability, typical of Be systems.
Another contribution to BeXRB research with
INTE-GRAL is from the Optical Monitoring Camera (OMC),which provides photometry in the Johnson V –band si-multaneously with the high-energy observations (Mas-Hesse and (INTEGRAL OMC Consortium), 2003). Inthis way long-term OMC optical light curves of manyHMXBs, along with light curves of many other vari-able objects (Alfonso-Garz´on et al., 2012), are avail-able through the OMC archive (Guti´errez et al., 2004;Domingo et al., 2010). Long-term optical variabilityhas been observed in the OMC light curves of someBeXRBs, with examples shown in Fig. 14.Beyond the Milky Way, INTEGRAL has made a sig-nificant contribution to identifying the BeXRB popula-tion in the nearby Magellanic Clouds. A series of deepobservations has led to the discovery and identificationof several new systems (McBride et al., 2007; Coe et al.,2010a). A good example of the power of the
INTE-GRAL wide field of view is shown in this map of ob- http://sdc.cab.inta-csic.es/omc/ jects detected during one set of observations - see Fig-ure 15. Identifying all the BeXRB systems in externalgalaxies like the Magellanic Clouds provides us with avery e ff ective tool for understanding recent star forma-tion and X-ray luminosity functions in these galaxies –see, for example, Shtykovskiy and Gilfanov (2005). INTEGRAL
Joint
INTEGRAL and
XMM-Newton observationsof LS I + ◦
303 demonstrated that the overall spectrumof the system in the 0.5–100 keV energy band is wellfit with a featureless power law both at high- and low-flux states, see, e.g., Fig. 16 and Chernyakova et al.(2006); Zhang et al. (2010); Li et al. (2014). Non-observation of a cut–o ff or a break in the spectrumat 10–100 keV energies, typical of accreting NSs andBHs, favours the scenario in which the compact objectis a rotation-powered pulsar. INTEGRAL observationsdemonstrated that in the hard X-rays LS I + ◦
303 isfollowing the overall orbital modulation trend of softX-rays (Zhang et al., 2010) and also showed hints of avariability similar to the change of the orbital lightcurveon the superorbital time scale observed in the 3–20 keVrange (Chernyakova et al., 2012; Li et al., 2014). A jointstudy of the LS I + ◦
303 spectral variability at hard X-rays with
INTEGRAL and in the radio band was doneby Zimmermann and Massi (2012b) and Li et al. (2014)to test the possible microquasar nature of the system. Liet al. (2014) showed that, for most of the
INTEGRAL observations, LS I + ◦
303 had a hard spectrum with Γ ∼ . α <
0, whichis inconsistent with the predictions of the microquasarmodel (Zimmermann and Massi, 2012b). Still, moreobservations are needed to reach any firm conclusionon the nature of the compact source in the system.The study of
INTEGRAL observations of anothergamma-ray binary, LS 5039, revealed that that thesource significantly emits at hard X-rays (25–200 keV);this emission varies with the orbit in phase with the veryhigh energy gamma-rays detected with HESS (Ho ff -mann et al., 2009) and is fully anti-correlated with theGeV emission (Abdo and (Fermi LAT Collaboration),2009). The spectrum at the inferior conjunction is welldescribed by a power law, while at the superior con-junction the hard X-ray emission is below the sensitiv-ity of INTEGRAL . This result indicates that accretionmight not be the mechanism for the production of thehard emission in the system, since, in this case, onewould expect a rather sharp flux maximum near peri-astron (Ho ff mann et al., 2009). An investigation of the32 igure 15: Sources detected by IBIS on INTEGRAL overplotted on the SMC H I column density map. Figure from Coe et al. (2010a). The sourcesin red are definite source detections. The two sources in black are candidate sources.
Figure 16: Broad-band spectrum of LS I + ◦ orbital light curve in a broad energy range from classi-cal X-ray to TeV energies revealed a transition energyrange of tens to hundreds MeV, in which the dominantemission moves from around apastron region to aroundperiastron (Chang et al., 2016).A similar behaviour is observed in1FGL J1018.6 − INTEGRAL data available at that time. The totale ff ective exposure extracted on the source amounted to5.78 Ms, and led to a credible detection of the source athard X-rays (18–40 keV). The count rate of the sourceis very low, but hints at an anti-correlation with the100 MeV–200 GeV emission detected by Fermi-LAT.In 2004 INTEGRAL performed the first imaging ob-servations of PSR B1259 −
63 in the hard X-ray range ( >
20 keV) (Shaw et al., 2004), which allowed separatingthe emission of PSR B1259 −
63 from the emission of thenearby pulsar 2RXP J130159.6 − ff power law spectrum inthe 20–200 keV energy range served as invaluable inputfor further broad band spectral modeling. INTEGRAL also traced the hard X-ray behaviour of PSR B1259 − igure 17: The distribution of INTEGRAL -IBIS-detected HMXBs is shown for an observer situated outside the Milky Way. The closed trianglesrepresent 91 HMXBs whose distances are known. The open triangles denote 21 HMXBs whose distances are not known, so they are placed at thegalactocentric distance of 7.6 kpc used in the spiral arm model of Vall´ee (2002). The largest circles indicate the most active sites of massive starformation (Russeil, 2003). The shaded bands in the background indicate the number of HMXBs per bin of 15 ◦ in Galactic longitude, as viewedfrom the Sun (star symbol). This is an update of the study by Bodaghee et al. (2012b). o r m a LMC
SMC
BeXRBSFXT sgWF
UXT
Figure 18: Sky distribution in Galactic coordinates of HMXBs for which
INTEGRAL played a significant role (see Table A.1). The overlaycontours indicate the fully-coded and maximum fields of view of the
INTEGRAL instruments.
4. Population overview and distribution in theGalaxy (and beyond)
All-sky surveys by
INTEGRAL -IBIS have loweredthe sensitivity limit to 2 . × − erg cm − s − for a5 σ source detection above 20 keV (Krivonos et al.,2017). This is equivalent to an X-ray luminosity of2 × erg s − for a source located at a distance of20 kpc, i.e., at the far side of the Milky Way. As a result, INTEGRAL doubled the number of HMXBs detectedin hard X-rays in the Galaxy, and tripled the number ofthose with supergiant donor stars (Walter et al., 2015).These HMXBs feature column densities in excess of10 or even 10 cm − . The nature of the compact ob-ject in these new systems is known, or suspected, to bea NS in almost every case. Many of them exhibit longpulsation periods expected from wind accretors. There-fore, the catalog of INTEGRAL -detected HMXBs pro-vides a large (in number), uniform (in exposure), andnearly complete (in luminosity) population for statisti-cal analysis.
Figure 17 presents the Milky Way as viewed by anoutside observer with the locations of 112 HMXBsdetected by
INTEGRAL -IBIS, as well as active sitesof massive star formation (Russeil, 2003). There arenow 91 HMXBs whose distances, as reported in the literature, place them somewhere within our Galaxy.The previous version of this map had 79 such objects(Bodaghee et al., 2012b). Distances to 47 HMXBswere either refined or collected for the first time thanksto measurements of the optical counterpart as part ofthe 2nd data release from the
Gaia mission (Gaia Col-laboration, 2018; Bailer-Jones et al., 2018). From ourperspective within the Galaxy, the direction tangent tothe Norma spiral arm continues to feature the highestconcentration of HMXBs (the darkest band in Fig. 17).That particular wedge of 15 ◦ in longitude contains 16HMXBs which has motivated X-ray surveys by Chandra and
NuSTAR (Fornasini et al., 2014; Fornasini, 2016;Fornasini et al., 2017) to uncover its faint HMXB pop-ulation. Figure 19 shows a deep mosaic of this region.The spatial distribution of HMXBs traces the recenthistory of massive star formation in the host galaxy.This is because only a few tens of Myr are thought toelapse between the birth of a massive stellar binary inan OB Association (OBA), and the supernova phase thatleaves behind a compact object (Schaller et al., 1992).Studies of longitudinal distributions of HMXBs consis-tently show that they are most abundant near sites wherethe formation of massive stars is most intense, i.e., to-wards the tangents to the Galactic Spiral Arms (Grimmet al., 2002; Dean et al., 2005; Lutovinov et al., 2005a;Bodaghee et al., 2007). The surface density of HMXBsis largest for galactocentric distances of 2–8 kpc, which35 igure 19: Deep mosaic image in the 28–80 keV energy range of the Norma region close to the tangent direction, a zone in the Galaxy rich in hardX-ray sources. The mosaic includes 770 individual
INTEGRAL pointings between 2016 and 2020. is again consistent with the distribution of OBAs (Lu-tovinov et al., 2013).Nevertheless, significant di ff erences emerge betweenthe HMXB and OBA populations when comparingtheir physical locations within the Galaxy. The scaleheight of the HMXB population is larger than thatof the OBA population: ∼
90 pc and ∼
30 pc, respec-tively (Lutovinov et al., 2013). On average, a HMXBis located 0.3 ± ff set in the two-point cross-correlation func-tion increases the significance of the clustering betweenHMXBs and OBAs, which indicates that the HMXBshave moved away from their parent OBAs and from theSpiral Arms as well. Assuming typical HMXB ages,this corresponds to an average migration velocity of100 ±
50 km s − (Bodaghee et al., 2012b). Coleiro andChaty (2013), after computing the distance and absorp-tion to 46 HMXBs by fitting the optical and infraredSED of the donor star, could associate them with theirlikely parent OBAs, deriving a clustering size betweenHMXB and OBA of 0.3 ± ± − , Coleiro and Chaty (2013)constrained age and maximum migration distance of 13HMXBs: 9 BeXRBs and 4 sgHMXBs.These velocities are higher than expected from re-coil due to anisotropic mass loss from the primary tothe secondary (Blaauw, 1961), or via dynamical ejec- tion and outflows from the cluster (Poveda et al., 1967;Pflamm-Altenburg and Kroupa, 2010). Instead, the ve-locity range is consistent with values expected for a na-tal kick acquired during the formation of the NS, whichcan be significant in an asymmetrical supernova (e.g.,Shklovskii, 1970). Empirical evidence of migration ve-locities in HMXBs can help determining the character-istic timescale between the formation of the NS andthe X-ray emission phase, which is still poorly under-stood, as well as constraining models of type II su-pernovae. Unfortunately, there are only a handful ofHMXBs whose proper motions are known well enoughto enable the measurement of a kick velocity away froma specific OBA (e.g., Ankay et al., 2001; Rib´o et al.,2002; Mirabel et al., 2004). Fortunately, the evolution-ary history of massive binary stars is imprinted as ano ff set in the spatial distribution of HMXBs relative totheir birthplaces, and this o ff set yields an average ve-locity for the population. A useful diagnostic of HMXB populations is the lu-minosity function N ( > L ), which is the number distri-bution of sources with luminosities greater than L , plot-ted as a function of L , as shown in Fig. 20. The shapeof the HMXB luminosity function depends on the re-cent star-formation rate of the host galaxy (e.g., Grimmet al., 2002), and on the relations governing the massaccretion rate and luminosity in wind-accreting systems(Postnov, 2003).36 . Doroshenko et al.: Population of the Galactic X-ray binaries and eRosita (RN) . . . . . . . . . a . . . . . . a S w i f t B A T V o ss e t a l . ( ) I N T E G R A L I N TE G R A L e R o s it a . . . . . . . . . a . . . . . . a V o ss e t a l . ( ) L u t ov i nov e t a l . ( ) I N TE G R A L I N TE G R A L / s i m u l a ti on e R o s it a e R o s it a / b e s t Fig. 1.
Simulation results for the LMXB (left) and the HMXB (right) populations. Black contours and points show a 68% probabilitythat the simulated population will have the same flux distribution as observed in
INTEGRAL eRosita
INTEGRAL data.The black and red dotted contours represent results for the synthetic HMXB populations 1) by assuming the XLF parameters reportedby Lutovinov et al. (2013) and observed with
INTEGRAL and 2) by assuming the best-fit XLF parameters with ↵ = . eRosita , which is an optimistic forecast. The XLF parameters as reported by Voss & Ajello(2010) and Lutovinov et al. (2013) are also shown for reference. L x erg s N ( > L ) Voss et al. (2010)Grimm et al. (2002) 10 L x erg s N ( > L ) Voss et al. (2010)Lutovinov et al. (2013)Grimm et al. (2002)
Fig. 2.
Cumulative luminosity functions for LMXBs (left) and HMXBs (right) as derived in this work using the
INTEGRAL data(hatched area). Best-fit estimates by Grimm et al. (2002), Voss & Ajello (2010), and Lutovinov et al. (2013) are also plotted forreference. – For each simulated source we determine whether it would bedetected by
INTEGRAL by comparing its flux with the surveysensitivity in a given direction and obtain the final model fluxdistribution. – We calculate the normalisation of the model XLF by compar-ing the number of sources detected in simulation with numberof sources detected in the
INTEGRAL survey. – Finally, we compare the model and the observed flux dis-tributions at each point on a grid of input XLF parameters L br ,↵ ,↵ using the two-sample Kolmogorov-Smirnov testto calculate the probability P KS ( L br ,↵ ,↵ ) that two samplescome from the same distribution. Setting a threshold on P KS allows the acceptable values for XLF parameters to be re-stricted. To smooth out the variations due to the random nature of simula-tion, we repeat the steps above about ten times for each combina-tion of XLF parameters until the resulting sample of P KS valuesbecome normally distributed and then calculate the mean value.
3. Results and discussion
Taking the previous estimates of the XLF parameters into account,we considered the parameter ranges of 0 . ↵ .
8, 0 . ↵ ↵ .
5, and 10 L br . The results are presentedin Table. 1 and Fig. 1. Here, the contours mark regions wherethe maximum value of P KS for a given ↵ , and any L br exceedsthe selected threshold of P KS Figure 20: Top panel: luminosity function for persistently-emittingHMXBs in the Milky Way (red histogram) fit with a broken powerlaw (dashed curve) as presented in Lutovinov et al. (2013). Volume-limited samples are shown as black histograms. The shaded re-gion corresponds to the luminosity function from
RXTE -ASM data(Grimm et al., 2002). Bottom panel: the same luminosity func-tion (shaded area) as reconstructed through Monte Carlo modeling byDoroshenko et al. (2014). For comparison, the results by Lutovinovet al. (2013) and Voss and Ajello (2010) are shown.
Luminosity functions are relatively easy to build forHMXBs in other galaxies since the entire population islocated at the well-known distance of the host galaxy.Measuring the distances of HMXBs in the Milky Way,however, is more challenging given that the Galacticveil of dust and gas leads to optical extinction of thestellar companion, and photoelectric absorption of thesoft X-rays. So not only are many of the distances un-known but also, for those objects whose distances areknown, the sensitivity of the survey in each region ofthe Milky Way must also be considered.Figure 20 presents the HMXB luminosity function with
INTEGRAL -IBIS data (Lutovinov et al., 2013). Asingle power law does not adequately fit the luminosityfunction over the range of luminosities sampled (10 –10 erg s − ), given that a break in the slope around10 erg s − and a flattening at lower luminosities areevident. That becomes even more clear if the spatialdistribution of early type stars is taken into the account.This is illustrated by an independent reconstruction ofthe HMXB luminosity function using the same data-setby Doroshenko et al. (2014) and shown in Figure 20,where the impact of distance uncertainties to individ-ual objects is minimized through Monte Carlo model-ing under the assumption that the spatial distribution ofHMXBs is roughly known.These results could imply that the IBIS surveys maybe missing a significant number of faint HMXBs. How-ever, a flattening at the faint end was also observed inthe luminosity function of HMXBs in the more uniform Swift -BAT survey (Voss and Ajello, 2010), as well as inthe luminosity function of HMXBs in the Small Magel-lanic Cloud (Shtykovskiy and Gilfanov, 2005). There-fore, an adjustment may be necessary in the universalluminosity function which is expected to follow a sin-gle power law dN / dL ∝ L − α with α = . ± . –10 erg s − ). Sur-veys by INTEGRAL -IBIS and other facilities such as eROSITA will continue to probe the faint end of the lu-minosity function, helping to clarify the recent historyof massive star formation and the relative contributionof HMXBs to the total X-ray luminosity of galaxies.
A long-term systematic analysis of
INTEGRAL data(fourteen year span) has been performed by Paizis andSidoli (2014) and Sidoli and Paizis (2018) who inves-tigated the hard X-ray properties of 58 HMXBs. Thesample, about half of the total number of HMXBsknown in our Galaxy, comprises persistent and transientsystems, including BeXRBs, sgHMXBs and SFXTshosting a NS or a BH. Light-curves of 2 ks time binswere used to derive hard X-ray (18–50 keV) cumula-tive luminosity distributions (CLD) for all the sources.This approach leads to a full quantitative characteriza-tion of the hard X-ray luminosity distributions of thesingle sources, displaying in a concise way the di ff er-ent phenomenologies and patterns at play, the sources’duty cycles, range of variability and the time spent ineach luminosity state. Figure 21 shows the CLDs offour representative sources.In Sidoli and Paizis (2018), the phenomenologyobserved with INTEGRAL is juxtaposed with otherknown source properties in order to obtain a quantitative37 x (10^35 erg/s)11 11 110 101010 100100 100 100100100 100010001000100001 100 101010Lx (10^35 erg/s) Lx (10^35 erg/s)Lx (10^35 erg/s)
Figure 21: Cumulative luminosity distributions (18–50 keV) of four representative sources considering fourteen years of
INTEGRAL
IBIS / ISGRIdata. Each point refers to a source detection in a ∼ INTEGRAL pointing. The highest y-axis values indicate the duty cycles in the given band,while the range of variability can be seen on the x-axis. From left to right, top to bottom: Vela X − − + +
530 (the bimodal shape can be explained by the occurrence of normaland giant outbursts). Adapted from Sidoli and Paizis (2018). igure 22: Cumulative luminosity distributions (2–10 keV) of severalSFXTs and classical sgHMXBs derived from the long term monitor-ing campaigns of these objects performed with Swift / XRT (Bozzoet al., 2015, Romano et al. 2020, in preparation). The figure is adaptedfrom Bozzo et al. (2015) and includes both data previously published(gray lines) and newly obtained data (Romano et al. 2020, in prepa-ration). Solid lines are used for SFXTs and dashed lines for classicalsgHMXBs. The typical “step-like” shape of the SFXT cumulative lu-minosity distributions can be clearly seen in all cases. overview of the main subclasses of accreting massive bi-naries as they tend to cluster in the di ff erent parameterspaces explored.With respect to Lutovinov et al. (2013) who stud-ied the luminosity and spatial properties of persistentHMXBs in our Galaxy with INTEGRAL , Sidoli andPaizis (2018), while considering transient sources aswell, focused on the bright luminosity end. Indeed, theselection criteria chosen (source detection in a single2 ks pointing) resulted in a flux-limited sample with asensitivity of a few 10 − erg s − cm − , about one orderof magnitude worse than what considered by Lutovinovet al. (2013).Motivated by the intriguing INTEGRAL results, thestudy of the HMXB cumulative luminosity distributionspresented by Paizis and Sidoli (2014) was extended inthe soft X-ray energy domain (2–10 keV) by Bozzoet al. (2015). These authors used Swift / XRT data col-lected during the long-term monitoring campaign ofseveral classical sgHMXBs and SFXTs, which regularlyspan a significant fraction of the orbital phases of manyrevolutions of these systems (providing a few 100 ksof e ff ective exposure per source), in order to providean e ffi cient probe of their di ff erent luminosity states.The advantage of the XRT data is that the instrumentis endowed with a high sensitivity and can extend thecumulative luminosity functions down to fluxes as low as ∼ − erg s − cm − , complementing the INTEGRAL curves. We show in Fig. 22 an improved version ofthe fig. 5 of Bozzo et al. (2015), which includes the re-sults of the most recent and partly still ongoing XRT ob-servation campaigns (the gray curves are those alreadypublished previously, whereas the other ones will be re-ported with all details in Romano et al. 2020, in prepa-ration). In agreement with the results found by
INTE-GRAL , the XRT observations revealed that the cumu-lative distributions of the SFXTs have a more complexshape, with multiple “steps” (as opposed to the singleknee curve of the classical systems) marking the pres-ence of di ff erent accretion states. These findings havebeen interpreted by Bozzo et al. (2015) in terms of thedi ff erent accretion regimes introduced in Sect. 2.5.
5. Future perspective
INTEGRAL has now been confirmed to operate atleast until end 2020, with a possible further extensionup to the end of 2022. Other extensions will be decidedfollowing pending reviews of the mission status and op-erations, but are formally possible until 2029, when aplanned maneuver will force the satellite to a controlledre-entry in the Earth atmosphere. As emphasized multi-ple times in this review, the unique combination of sen-sitivity, pointing strategy, and large field of view of the
INTEGRAL instruments will surely lead in the years tocome to the discovery of new transient HMXBs, includ-ing SFXTs. The most recent results in these fields, assummarized in this review, prove that each newly dis-covered IGR source o ff ers new perspectives to under-stand the physics of HMXBs and often poses new theo-retical / observational challenges. The community is thuscertainly looking forward to more years of successful INTEGRAL operations.Following the success of the
INTEGRAL mission, anumber of di ff erent high energy facilities, covering fromthe softer ( (cid:46) Athena mission (see, e.g., Nandra and (AthenaCollaboration), 2013) is set to fly in the early 2030sand, especially thanks to the X-IFU instrument (Bar-ret and (Athena X-IFU Collaboration), 2018), it willopen the possibility of performing high resolution spec-troscopy of HMXBs even at relatively low fluxes. Theseobservations will be able to probe for the first time,among others, the physical processes occurring duringthe accretion of single clumps from the stellar windsonto the compact objects hosted in classical sgHMXBs39nd SFXTs (Bozzo and Athena SWG3. 3, 2015). Thisis something that today is only possible by exploit-ing the grating spectrometers on-board
Chandra and
XMM-Newton for the uniquely bright HMXB Cyg X-1 (Hirsch et al., 2019). High-resolution spectroscopyof wind-fed HMXBs with X-IFU (with a typical accu-racy of a few eV, depending on the specific energy) willalso permit us to investigate in unprecedented detail thephysics of the interaction between the X-rays from thecompact object and material in the stellar wind, finallyproviding a solid measure of the perturbed and unper-turbed stellar wind. This is the key also to likely dis-tinguish between the scenarios proposed to explain thedi ff erent behaviours of classical sgHMXBs and SFXTs.The eXTP mission (Zhang and (eXTP Collabora-tion), 2019) is planned to be at present the next X-ray fa-cility harboring a large field-of-view instrument (WFM;G´alvez et al., 2019) that will cover the full sky every ∼ INTEGRAL / IBIS, but willcomplement the
INTEGRAL discoveries by monitor-ing the sky in the softer energy band. The eXTP / WFMwill provide a good energy resolution of 300 eV on theentire band and a time resolution as accurate as a few µ s. An on-board system will detect and broadcast to theground impulsive events, as for example the outburstsfrom SFXTs. The instrument will thus be capable todiscover many more transient / flaring HMXBs , as wellas flares / outbursts from already known sources, collect-ing for each of these events a uniquely rich amount ofuseful data that will be provided to the community afew hours after the detection. The eXTP / WFM will alsoprovide daily monitoring data for hundreds of sourceswith good timing and spectral resolution, that can beused to verify the evolution of the spectral states, aswell as the spin period and / or the timing state of the dif-ferent HMXBs (including possible evolution over timeof the cyclotron line features and orbital / super-orbitalmodulations). Furthermore, the suite of instruments on-board eXTP (Zhang and (eXTP Collaboration), 2019)will be able to provide an unprecedentedly high statis-tics, good energy resolution, and high timing accuracydata in a broad energy range (2–50 keV) to perform acombined timing-spectroscopy-polarimetry analysis ofmany bright HMXBs . This will open new perspectives See, e.g., Bozzo et al. (2013). These authors estimated the num-ber of SFXT outbursts for the WFM instrument on-board the LOFTmission (Feroci and (LOFT Collaboration), 2012), which has a similardesign as the eXTP / WFM. Preliminary measurements of the X-ray polarimetry in HMXBs to resolve changes of the cyclotron line parameters asa function of the system physical conditions (geometry,luminosity, line of sight) and understand intimate detailsof the physics of accretion in wind- / disc-fed systems,as well as aspects of the microphysics of plasma pen-etration in the NS magnetosphere in a never accessedbefore way(in’t Zand and (eXTP Collaboration), 2019;Santangelo et al., 2019).Improvements over the already exciting results thatwill be provided by eXTP are expected from its succes-sor STROBE-X (Ray and (STROBE-X Collaboration),2019), which will provide yet more e ff ective area to in-crease the statistics and optimize the background in amore extended energy range (0.5–50 keV). STROBE-Xis a mission concept proposed for the NASA decadalsurvey .Flares and outbursts from Galactic and extra-GalacticHMXBs are expected to be among the easiest targets fordetection by the next generation of wide-field X-ray fa-cilities using Lobster-eye telescopes (Angel, 1979), asthose planned onboard the Einstein Probe (Yuan et al.,2018) and the THESEUS mission (Amati and (THE-SEUS Collaboration), 2018; Stratta and (THESEUSCollaboration), 2018). The former mission is led byChina and is planned to be launched as early as 2021,while THESEUS is one of the three candidates com-peting for a launch opportunity in 2032 within the con-text of the ESA M5 call . The advantage of Lobster-eye telescopes is to provide a large field of view (up to60 ×
60 deg in the currently planned configurations) anda low background, achieving a sensitivity able to dis-cover sources as faint as ∼ − erg s − (0.3–6 keV) al-ready in a few tens of seconds. This matches well therange of luminosity of the flares and outbursts observedfrom HMXBs. THESEUS will also be endowed withan infrared telescope (IRT) which will be automaticallyre-pointed toward the sources of interest, and could beused to identify the massive companions of HMXBs.In the gamma-ray domain, the AMEGO missionconcept (McEnery and (AMEGO Collaboration), 2019)is expected in a farther future to provide new insightsabout the emissions from HMXBs in the MeV energyrange, distinguishing between the possibilities that such (Kallman et al., 2015) could be already expected thanks to the NASAmission IXPE (So ffi tta, 2017), currently planned for a launch in 2021. See See . But see also the similar mission concept e-ASTROGAM (de An-gelis and (E-Astrogam Collaboration), 2017). / or “gamma-ray loud bina-ries” (Dubus, 2013; Chernyakova et al., 2019), whichrapidly became subject of major interest. Similarly tothese general classes, in principle SFXTs, as well asother flaring sgHMXBs, could be able to produce HEand VHE emission as well since they are characterizedby the same ingredients in terms of a compact objectand a massive early-type companion star. However,the detection of such emission is nontrivial for currentgenerations of HE and VHE instruments, since itshould likely be in the form of unpredictable flareshaving short duration, small duty cycle and relativelylow flux. To date, only few hints have been reported inthe literature on SFXTs as best candidate counterpartsof unidentified transient HE sources, merely based oncircumstantial evidences (Sguera et al., 2009; Sguera,2009; Sguera et al., 2011). No detection of VHE emis-sion from other sgHMXBs has been reported so far.Hopefully, this situation will change in the near futurethanks to a new generation of ambitious facilities underconstructions, e.g. the Cherenkov Telescope Array,which will o ff er an order of magnitude improvementin the VHE domain in terms of sensitivity and surveyspeed compared to existing facilities, hence holdingthe promise of performing well as a transient detectionfactory (Cherenkov Telescope Array Collaboration,2019). We expect that future studies will likely shednew light by detection or not-detection SFXTs, as wellas other sgHMXBs, as HE and VHE transient emitters.If confirmed, this would open the investigation to acompletely unexplored energy window, allowing adeep study of the most extreme physical mechanisms atwork, which could be tested on very short timescales,not usually investigated. All this could eventually add afurther extreme characteristic to the class of SFXTs, aswell as to other subclasses of HMXBs in general.The INTEGRAL mission has provided an importantimpulse to the study of HMXBs: its large field of viewtogether with its broad spectral range, sensitivity and an-gular resolution has allowed us to peer through the ob-scured as well as fast transient X- / gamma-ray sky. Ourknowledge has grown broader and deeper in the ever-changing source population that traces the star-forming arms of our Galaxy. INTEGRAL plays an importantrole in connecting the soft X-rays to the very high-energy range of the electromagnetic spectrum (MeV toTeV), enriching our view of the physical processes in-volved. It serves as an important springboard for themissions and the knowledge to come.
Acknowledgments
Based on observations with
INTEGRAL , an ESAproject with instruments and a science data centerfunded by ESA member states (especially the PI coun-tries: Denmark, France, Germany, Italy, Spain, andSwitzerland), the Czech Republic, and Poland and withthe participation of Russia and the USA. The
INTE-GRAL teams in the participating countries acknowl-edge the continuous support from their space agenciesand funding organizations: the Italian Space AgencyASI (via di ff erent agreements including the latest one,2019-35HH, and the ASI-INAF agreement 2017-14-H.0), the French Centre national d’´etudes spatiales(CNES), the Russian Foundation for Basic Research(KP, 19-02-00790), the Russian Science Foundation(ST, VD, AL; 19-12-00423), the Spanish State Re-search Agency (via di ff erent grants including ESP2017-85691-P, ESP2017-87676-C5-1-R and Unidad de Ex-celencia Mar´ıa de Maeztu – CAB MDM-2017-0737).IN is partially supported by the Spanish Govern-ment under grant PGC2018-093741-B-C21 / C22 (MI-CIU / AEI / FEDER, UE). LD acknowledges grant 50 OG1902.41 . HMXBs discovered or identified with
INTEGRAL
Table A.1: HMXB discovered or identified with
INTEGRAL . Under System type, sgWF stands for wind-accreting sgHMXB, BeXRB for BeX-ray binary, SFXT for Supergiant Fast X-ray Transient and UXT for Unidentified X-ray Transient. Reference numbers are expanded below thetable. Distance values are taken from Bailer-Jones et al. (2018) for many sources. For sources in the SMC we use the “canonical distance modulus”proposed by Graczyk et al. (2014), which is consistent, e.g., with de Grijs and Bono (2015). For sources in the LMC we use the recent value byPietrzy´nski et al. (2019)Source R.A. Decl. P s P b distance Companion System Referencesname deg deg s days kpc type typeIGR J00370 + / BN0.7 Ib sgWF [1,2,3,4]IGR J00515 − − ± / B0 III BeXRB [5,6]IGR J00569 − − ± − − ± − − ± + − − ± + − − . ± . − − . ± . − − . ± . + − − − − − − − − . + . − . B0.5 Ia SFXT [46,47,48,4]IGR J11305 − − − − ± − − − − − − − − − − − ∼
10 early B III or mid B V BeXRB [62,45]IGR J14488 − − − − − − / B1 Ia sgWF [65,68,69,70]IGR J16283 − − ± ± − − . ± . − − − − . ± . − − − − † sgWF [77,88,89,90,91]IGR J16418 − − − − . ± . / O9.5Ia SFXT [97,98,99,100]IGR J16479 − − ∼ / ∼ − − >
6) B0.5Ib sgWF [104,105,106,107]AX J1700.2 − − − − −
363 261.297 − ‡ O8.5I sgWF [110,111,65,112,113]IGR J17354 − − − − (cid:63) – SFXT [117,118,55]XTE J1739 −
302 264.775 − − − . ± . − − − − † In doubt as [91] found a Chandra position inconsistent with the proposed counterpart. ‡ Various existing distance estimates falling withing the quoted range [112]. (cid:63)
Tentative determination continued on next page . . . able A.1: (continued from previous page) HMXB discovered or identified with
INTEGRAL .Source R.A. Decl. P s P b distance Companion System Referencesname deg deg s days kpc type typeIGR J18027 − − ± − − − − . ± . − − − − ± − − − − − − (cid:63) − − ± − − ∼ ∼
11? – SFXT [158,160]IGR J18483 − − + ±
110 – 16 early B I sgWF [77,164,165]IGR J19140 + + + + ∼
890 or 1056 – ∼ + + >
100 4–5 B0-1 III-Ve BeXRB [176,177,178,179,6] (cid:63)
Tentative determination
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