Universitá di Cagliari Dipartimento di Fisica High-Energy Astrophysics Group
Dottorato di Ricerca in Fisica ciclo XXX
Settore scientifico disciplinare di afferenzafis/05
Multiband studies of Neutron Stars in Low
Mass X-ray Binary systems
&
the HERMES project
Presentata da: Fabiana Scarano
Coordinatore Dottorato: Prof. Alessandro De Falco Tutor:
Prof. Luciano Burderi
Esame finale Anno Accademico 2016-2017
Fabiana Scarano
Multiband studies of Neutron Stars in Low Mass X-ray Binary systems &
the HERMES project
Tutor: Prof. Luciano Burderi High-Energy Astrophysics Group
Universitá di Cagliari - Dipartimento di Fisica SS.P. Monserrato - Sestu Km 0.700
Summary
Although historically the observation of the sky from the Earth surface has been limited to the visible band of the electromagnetic spectrum, thanks to the advent of satellites it has been extended farther to the other regions of the spectrum, giving the opportunity to detect high-energy radiations coming from celestial objects.
While the X-ray emission mainly comes from the accretion of matter onto a compact object, i.e. neutron star or black hole in binary systems, Gamma Ray Bursts are originated from exotic phenomena such as magnetars and supernova remnants and the merging of two compact objects. The observation of these phenomena is extremely important since makes it possible to probe matter in extreme physical conditions of high density, temperature and strong magnetic field, which cannot be reproduced on the Earth.
The spectral analysis of the X-ray emission of these objects offers the opportunity to obtain relevant information about the physical processes that occur onto, or in proximity, of the compact object surface (if it exists), where the general relativistic effects become predominant. The first part of the present thesis aims at contributing to the understanding of these processes. To this end, the X-ray spectra of two atoll sources (GX 3+1 and GX 9+9) have been analysed, with the emphasis on the component produced when the cold matter of the accretion disc is irradiated by the hard photons in the proximity of the compact object. These spectra are often characterised by a continuum and by the presence of emission lines and absorption edges due to the most abundant elements present in the disc. The most intense ones among these discrete features is the fluorescence iron line at 6.4–6.9 keV. This line appears broadened and distorted, probabily owing to the Doppler and relativistic effects due to the high-velocity of the plasma in the disc. From the study of these features it is possible to obtain important information about the disc matter (its chemical composition and its ionisation state), the inclination of the system with respect to the line of sight, the inner radius of the accretion disc, and it also provides an upper limit of the neutron star radius.
Because of the multiple spectral components and many parametres, the spectral fittings performed in this thesis are complex and the evaluation of the uncertainties required a large amount of computing time, up to a month, in addition to the fact that it was necessary to evaluate different models.
The broad-band spectrum (0.9–50 keV) of the source GX 3+1 has been acquired by means of the ESA satellites INTEGRAL and XMM-Newton, whereas the source GX 9+9 has been observed by different satellites XMM-Newton, BeppoSAX and Suzaku. The aim was the characterisation of their X-ray spectrum with particular attention to the discrete features which are typical of the reflection spectrum. The first source is characterised by a complex spectral
shape with asymmetrically broadened emission features associated with the transitions of iron, calcium, argon and sulphur. The spectrum has been analysed using different models that confirmed the results obtained in previous works. In particolar the inclination angle of the system of 35° and the logarithm of the ionisation parameter of the accretion of 2.8, have been inferred. Owing to the self-consistent model a more physical interpretation of the X-ray emission from GX 3+1 has been obtained, such as the radius to which the reflection component is produced. Furthermore, it has been detected for the first time for GX 3+1, the presence of a powerlaw component at energies higher than 20 keV, probabily related to an optically thin component of non-thermal electrons.
On the contrary, in the case of GX 9+9, the broad-band (0.7–35 keV) spectrum showed the absence of the fluorescence iron line, the most intense discrete line in these spectra, and other discrete features. Also for GX 9+9 spectra, different models have been adopted to analyse the data. In particular, using the self-consistent model it has been possible to infer an upper limit to the relative reflection normalisation of about 0.1, that does not exclude a weak presence of a reflection component. The lack of the reflection component, with its predominant iron line, could be explained by means of different scenarios which suggest that the accretion geometries or the chemical properties of the source GX 9+9 are different compared to other atoll sources. The second half of this thesis regards the HERMES project, an Italian Space Agency’s project in collaboration with different universities and INAF institutes, which proposes to launch a network composed of 6–8 nanosatellites in the next two years. The ensemble of these detectors represents an extraordinary instrument to estimate, using the trilateration method, the position of the intense astrophysical phenomena, such as the Gamma Ray Bursts, with unprecedented accuracy. Since the project is still in a preliminary stage, it has been necessary to verify the feasibility of the scientific goals of this mission and to determine the most suitable technology for the detector. To do this, different simulations of GRB light curves have been carried out and owing to the use of the cross-correlation techniques between these curves, has been possible to evaluate the delays received from different units, in order to establish the GRB position in the sky. Although still preliminary, the results obtained are very promising. Furthermore, the modularity approch of the HERMES project represents a major progress in the space missions field. As a matter of fact, each nanosatellites on board of HERMES is an independent detector, this will allow an incremental growth of the satelllites constellation until a complete constellation is reached.
In conclusion, the work presented in this thesis could be of importance both in the field of the spectroscopy analysis and in the detection of Gamma Ray Bursts positions, two important astrophysical aspects in which many open questions still remain.
Contents
I
X-ray binary systems description
11 X-ray binary systems 5
1.1 Formation and Evolution. . . . 5
1.1.1 Low-mass X-ray binary systems (LMXBs) . . . . 6
1.1.2 High-mass X-ray binary systems (HMXBs) . . . . 8
1.2 Compact objects. . . . 9
1.2.1 Neutron stars . . . . 11
1.2.2 Black holes . . . . 14
1.3 Accretion process . . . . 16
1.3.1 From the accretion disc to the compact object . . . . 17
2 Physics of X-ray binary systems 19 2.1 Different components . . . . 19
2.1.1 The accretion disc . . . . 20
2.1.2 The corona . . . . 23
2.2 Physical processes in the accretion disc-corona system . . . . 24
2.2.1 Photoelectric absorption . . . . 24
2.2.2 Compton scattering . . . . 25
2.2.3 The reflection component. . . . 28
2.3 The states of a source . . . . 31
2.3.1 The soft state . . . . 31
2.3.2 The hard state. . . . 32
2.3.3 Spectral transitions . . . . 32
3 Study of the reflection spectrum of the accreting neutron star GX 3+1 using XMM-Newton and INTEGRAL * 35 3.1 Introduction . . . . 35
3.2 Data Reduction . . . . 37
3.3 Spectral Analysis. . . . 38
3.3.1 Self-consistent models . . . . 42
3.4 Discussion and Conclusions . . . . 45
4 Broad-band spectral analysis of GX 9+9: a surprisingly featureless spectrum * 49 4.1 Introduction . . . . 49
4.2.1 XMM-Newton . . . . 51 4.2.2 BeppoSAX . . . . 52 4.2.3 Suzaku . . . . 52 4.3 Spectral analysis . . . . 53 4.3.1 Self-consistent model . . . . 54 4.4 Discussion . . . . 56 4.5 Conclusions . . . . 59 5 Results 61
II
The HERMES project
63 6 Originality and innovation of the experiment 67 6.1 Gamma Ray Bursts phenomenology . . . . 676.1.1 GRBs classification . . . . 68
6.1.2 Fireball model . . . . 69
6.2 Introduction to Quantum Gravity . . . . 70
6.2.1 Quantum Gravity experiments performed with GRB detectors . . . . 70
6.3 Description of the HERMES project . . . . 71
6.3.1 Description of the proposed detector. . . . 72
6.4 Multimessanger Astronomy . . . . 75
6.4.1 What if HERMES already existed?. . . . 76
7 Simulations and Results 79 A Spectral analysis 89 B Scientific instrumentation 91 B.1 BeppoSAX . . . . 91 B.2 INTEGRAL . . . . 92 B.3 Suzaku. . . . 92 B.4 XMM-Newton . . . . 93 Bibliography 97
Part I
X-ray binary systems description
Introduction
High-energy Astronomy, in particular in the X-ray and γ-ray bands, which regards the study of high energy processes releasing electromagnetic radiation, is a branch of Astronomy. These systems consist of a dead star, i.e. a neutron star or a black hole, formed in the final stages of the evolution of massive stars, and a companion star, usually a main sequence star. When the two stars are close enough, a mass transfer towards the compact object occurs, which gives rise to accretion. The gravitational energy released during this process, makes compact objects powerful sources of energy. Therefore, the spectral analysis of the X-ray photons provided by these systems, offers an important tool to understand their physics and investigate these fascinating objects.
The main aim of the first part of this thesis is to describe the analysis of the X-ray spectra of Low Mass X-ray Binary systems that host a neutron star. In particular, the study has been focused on the reflection spectra of bright sources, known as atoll sources. The study of the discrete features (in emission and absorption), observed in the X-ray spectra of neutron star Low Mass X-ray Binaries, provides important information about the geometry and the physical processes that occur onto, or in proximity, of the compact object surface, where the general relativistic effects become predominant.
Chapter1and2are devoted to the study of the X-ray binary systems; in particular on their formation, the role that the mass accretion plays and the physical processes that occur in these systems.
Chapter3describes the spectral analysis of the source GX 3+1. The observations of XMM-Newton and INTEGRAL made in 2010, have allowed to examine the spectrum in an energy range of 0.9–50 keV. This spectrum is characterised by broadened emission features associated with the transition of iron, calcium, argon and sulphur. Moreover, it has been detected, for the first time for GX 3+1, the presence of a powerlaw component dominating at energies higher than 20 keV.
Chapter4concerns the results of the spectral analysis performed on the source GX 9+9. It was observed by BeppoSAX, XMM-Newton and Suzaku satellites in different periods (from 2000 to 2010). The different energy bands covered by the instruments on board of these satellites, have allowed to determine the continuum spectrum with great accuracy and to verify the surprising absence of the iron emission line. An anomalous behaviour for a bright atoll source.
1
X-ray binary systems
Contents
1.1 Formation and Evolution. . . . 5 1.2 Compact objects. . . . 9 1.3 Accretion process . . . . 16
Around two thirds of all stars in our galaxy are in binary stellar systems. In a small fraction of these systems, the two stars are close enough to significantly condition the evolution of each other. Discovered in the 1960s (Giacconi et al.,1971, Giacconi et al.,1972, Tananbaum et al., 1972), these systems are named X-ray binary systems and they are the most luminous objects in the X-ray sky. At the moment, more than 400 X-ray binaries have been detected.
1.1
Formation and Evolution
X-ray binary system consists of two objects: a compact object (Neutron Star or Black Hole, hereinafter referred to asNSandBH, respectively) and a companion star, which both orbit around the common centre of mass of the system. In these systems, the matter that leaves the companion star (also calleddonor star) is accreted onto the compact object. The X-ray emission originates from the conversion of the gravitational energy of the accreted matter into light, through viscous processes or shocks occurring in the accretion disc.
Depending on the mass of the donor star, X-ray binary systems are divided into two classes (see e.g. Bradt et al.,1983): Low-Mass X-ray Binaries and High-Mass X-ray Binaries (hereinafter referred to asLMXBsorHMXBs, respectively). Table1.1summarises the main differences of these systems.
In the LMXBs the accretion process takes place by Roche lobe overflow, whereas in the HMXBs the accretion mainly occurs via stellar wind. Figure1.1shows an illustration of both LMXBs and HMXBs classes.
An interesting point, concerning X-ray binary systems, is their evolution history, from their origin until their final stages. It is difficult, indeed, to investigate the origin of these systems, mainly because of the mass exchange between the two stars of the system (Karttunen et al., 2007). For this reason, the star evolution will not depend only on its initial mass, but will also be affected by the interactions with each other.
The presence of a compact object means that the progenitor was a massive star that underwent a supernova explosion. During this catastrophic event a large amount of mass is expelled from the system, causing a probable break of the binary system. To maintain the binary system, different explanations have been proposed, as discussed by Verbunt,1993.
Table 1.1.:Classification of NS X-ray binaries
Properties LMXBs HMXB Donor star K-M or WD (M ≤ 1 M ) O-B (M > 5 M )
Population II (109years) I (107years)
LX/Lopt 100–1000 0.001–10
Optical spectrum reprocessing stellar-like
Orbital period 10 min - 10 days 1–100 days
Accretion disc yes sometimes, small
Magnetic field weak (108–109G) strong (∼ 1012G)
X-ray spectrum soft (kT < 10 keV) hard (kT > 15 keV)
X-ray eclipse rare common
X-ray pulsations rare (0.001–100 s) common (0.1–1000 s)
X-ray QPOs common (1–1000 Hz) rare (0.001–1 Hz)
Type-I X-ray burst common absent
Figure 1.1.:Artistic view (top) and schematic view (bottom) of the LMXB and HMXB systems to explain the different accretion modes: Roche lobe overflow via an accretion disc for the LMXB and by stellar wind for HMXB.
1.1.1 Low-mass X-ray binary systems (LMXBs)
Most of LMXB systems have been observed in the galactic bulge and Magellanic clouds (Liu et al.,2007). In these systems the companion star is a low-mass star (with M ≤ 1M ), generally
a late-type star of population II (> 109years), with a weak magnetic field, B ∼ 108–109G. This low value of B is probably due to the fact that being these old systems, they dissipated the magnetic field during the accretion process (Taam et al.,1986, Geppert et al.,1994, Konar et al., 1997, Cumming et al.,2001).
Formation
The formation of a LMXB system can be occurred by two different processes: two stars are gravitationally bound from their birth, or the system is formed by capture of a second star.
In the first case, the most massive star evolves quickly and reaches the giant phase during which a large amount of its envelope is either transferred to the companion, lost from the binary as the spiral-in of the companion, or lost from the binary via stellar wind. Then, a supernova explosion takes place. If the loss mass during this explosion is less than half of the binary mass, the system survives. Otherwise, the system can only survive if a kick velocity from the explosion happens in the right direction. In conclusion, if the binary system remains bound, it will contain the new-born compact object and the companion star. Figure1.2shows this scenario. In the second case, a massive star lives alone and becomes a compact object. Because of a high-star density environment, a star can be captured (in a close encounter). This happens mainly in globular clusters.
Roche lobe overflow
In a LMXB the companion star is usually a main-sequence star, much smaller than itsRoche lobe. The Roche lobe is defined as the quasi-sphere influence within which the matter is gravitationally bound. The point of intersection between the two Roche lobes is called inner Lagrangian point,L1. Because in the Lagrangian points the effective force (gravity plus centrifugal) vanished. When for evolution issues one of the two stars expands to fill its Roche lobe, the pressure gradient pushes the gas through L1. The matter, no longer gravitationally bound to the star, can be accreted by the compact object (with a transfer rate of about 10–9
M /year).
The effective gravitational potential of the two stars, which are in circular orbits (this is a good approximation because the tidal effects tend to circularise their orbits in a small time), is given by the Roche potential. In a reference frame, a test mass m in a gravitational potential is subjected to a force F = –m∇ΦR, which is expressed in terms of Roche potential ΦRas:
ΦR= – GM1 | r – r1| – GM2 | r – r2| – Ω2 (r – rc)2 2 , (1.1)
where r1and r2are the positions of the masses M1 and M2, respectively, r is the position of the test mass m, rcis the position of the centre of mass, Ω is the angular velocity of the rotation about the centre of mass of the system, Ω =
r
G(M1+M2)
a3 , and a is the binary separation.
A representation of the Roche potential is shown in Figure1.3.
This result corresponds to the sum of the equipotential surfaces for each star and a centrifugal potential associated with the stars rotation around the common centre of mass. As mentioned above, when a star fills its Roche lobe, a matter transfer starts through the point L1 to the
Figure 1.2.:An illustration of the star evolution in a binary system leading to the formation of a LMXB (Tauris et al.,2003).
compact object. The accreted matter will have a large amount of angular momentum, therefore it will not accrete radially onto the compact object but it will rotate around it to form an accretion disc. During the accretion process the mass of the two stars can change considerably, leading to a modification in the star separation and orbital period.
This accretion mode is calledRoche lobe overflowand it is typical of the LMXB.
1.1.2 High-mass X-ray binary systems (HMXBs)
The first X-ray sources observed by the UHURU mission in 1970s were HMXBs. These systems consist of a young (< 107years) and high-mass companion star (with M > 5M ) of spectral type O or B. These stars produce a strong wind, part of which is captured by the compact object, that orbits around the massive star, and its energy is transformed into X-ray emission (e.g. Nagase et al.,1986). In this case, the Roche lobe overflow may represent a small fraction
Figure 1.3.:Illustration of the Roche potential in a binary system. The bottom of the figure represents the equipotential surfaces plotted in the equatorial plane. L1, L2and L3are the Lagrangian points, where the gravity effects vanish.
Credits: Marc van der Sluys, 2006
of the accretion in addition to the wind accretion. Figure1.4shows a possible scenario for the formation of the HMXB systems.
Depending on the spectral type of their companion, the HMXBs can be divided into two subgroups: Be/X-ray binary andSG/X-ray binaries.
In the first group, the companion is a B-emission (Be) star and the compact object is a NS (Reig,2011). These systems present eccentric orbits, their periods tend to be long, and they are highly variable. Indeed, in some of these systems, outbursts have been observed because of the increase of the accretion rate when the star passes close to the Be star. Because of the large size of the companion star, Be/X-ray systems usually show eclipses, as a direct evidence of the binary nature of the system. The magnetic field of the NS is often higher than 1011G, much stronger than the magnetic field of NSs in the LMXB, and it originates an accretion disc truncated at large radius around the NS star.
In the second group, SG-X, the companion star is an evolved supergiant (SG) of O or B spectral type.
1.2
Compact objects
For most of its life, a star is in equilibrium with a perfect balance between its gravitational and thermal pressure of gas. The major source of energy derives from nuclear fusion processes in the central regions. The more massive is the star, the faster is its life and the heavier will be the elements synthesised by different nuclear reactions (H, He, C, Ne, O, Si and Fe). When the star exhausts its nuclear fuel, the reactions are no longer possible and its core collapses into a compact object. Compact objects are the last stage of the star life, and their nature depends on the initial mass of the star.
Figure 1.4.:An illustration of the star evolution in a binary system leading to the formation of an HMXB (Tauris et al.,2003).
Compact objects can be classified in order of increasing compactness in: white dwarf (WD), NS and BH. The ratio MR of an object increases with its compactness and it can be calculated using the compactness parameter RSchR , where RSch is the Schwarzschild radius defined as:
RSch = 2GM c2 = 3 M M km. (1.2)
This compares the object radius with that of static BH of the same mass.
In WD and NS the density is so high that they are stuck by electron and neutron degeneracy pressure, respectively, which counterbalances gravity. BHs represent the most exotic objects in the Universe since no force can support their gravity. Table 1.2 summarises the main characteristics of compact objects.
Table 1.2.:Main characteristics of typical white dwarfs, neutron stars and black holes.
White Dwarf Neutron Star Black Holes Progenitor Mass (M ) 0.1–8 8–25 ≥ 25
End stage of star red giant supernova supernova
Mass M (M ) 0.1–1.4 1–3 ≥ 3
Radius R (km) 104 10 RSch
Density ρ (kg m3) 109–1010 1018
-Compactness parameter 10–4 0.2–0.4 1
Since the first part of this thesis focuses on LMXB systems, only NSs and BHs will be discussed in the following sections.
1.2.1 Neutron stars
NSs are the densest objects known in the Universe. These objects represent ideal astrophysical laboratories for dense matter physics and provide connections among nuclear physics, particle physics and astrophysics.
With typical masses of M ∼ 1.4M and radii of R ∼ 10 km, NSs have a gravitational energy
Egrav:
Egrav ∼ GM
R2 , (1.3)
where G denotes the gravitational constant.
Their mass is similar to the solar mass but the radius is 105 times smaller than the solar radius, the mass density is:
ρ = 3M
4πR3 ∼ 6 · 10 17
kg m–3∼ 5ρn, (1.4) with ρnis the mass density of nucleon matter and is defined as:
ρn= 4mn 3πr3n
= 1.2 · 1017kg m–3, (1.5)
where rnand mnare the radius and the mass of a neutron, respectively. The central density of a NS is even larger, about 10–25 ρn.
The huge density of a NS and the degeneration of its electron levels encourage the free electrons to combine with protons in the nuclei of atoms to form neutrons through the inverse
β-decay:
p + e–−→ n + ν
e.
Depending on their age, NSs show different temperatures and magnetic fields. Young NSs can achieve temperatures of the order of 1010K and magnetic field of about 1015G, whereas old NSs have generally much lower values of about T ∼ 107K and B ∼ 108G.
NS formation
The formation of a NS can be due to two different scenarios: the final stage of a massive star or a WD with a mass that exceeds the Chandrasekhar limit (MCh = 1.4M ).
In the first case, the NS corresponds to the final product of a stellar evolution. When a massive star is in the giant or supergiant stage and finishes its fuel, its core is subjected to a gravitational collapse and becomes a NS, while the outer layers are washed away by an expanding shock wave. This event is defined as a supernova explosion of type II (see e.g. Imshennik et al.,1988, Arnett,1996).
In the second case, the NS is formed via accretion-induced collapse of an accreting WD in a binary system. If the WD reaches, during the mass transfer, the critical mass of Chandrasekhar, the star becomes unstable and collapses to form a NS (Bhattacharya et al.,1991).
Equation of state and NS structure
Understanding the relationship between pressure and density at different stages in the NS interior is important to determine the structure of these objects. These relations are called Equations of State (hereinafter referred to asEOS) (Shapiro et al.,1983, Haensel et al.,2007). Since NS are mainly composed of degenerate fermions (electrons, neutrons and protons), the temperature dependence is negligible and the EOS can be calculated at T=0.
Although its internal structure is not totally known, a NS is thought to be composed of four zones of different density, plus a gaseous atmosphere of about 10 cm thick forming a surface layer (Zavlin et al.,2002, see Figure1.5). For this reason, different methods are used to calculate the EOS from the NS surface to centre.
• The first zone, also namedouter crust, is a thin (∼ 300 m) outer layer that extends from the atmosphere to the layer with density ρ ∼ 4 · 1014kg m–3. The matter is similar to the one found in WD, composed mainly of heavy nuclei and degenerate electrons. The increase of the density produces an electron energy large enough to induce β-decay by increasing the neutrons number in nuclei.
• The second zone, called inner crust, extends from the layer with density of ρ ∼ 4 · 1014kg m–3to ρ ∼ 4 · 1017kg m–3 with a thickness about 600 m. This shell is com-posed of neutron-rich nuclei, free degenerate neutrons and a degenerate gas of relativistic electrons. When the density increases, the number of free neutrons increases providing most of the pressure.
• Theouter coreorneutron liquid phase, is the largest zone with a thickness of about 9.7 km. Here, the matter reaches density of ρ ∼ 1018kg m–3 and it is composed of neutrons with a little percentage of protons, electrons and muons, all strongly degenerate. Electrons and muons form ideal Fermi gases, whereas protons and neutrons (interacting via nuclear forces) create the Fermi liquid and can be in a superfluid state.
• The central region of massive NS (in case of low-mass the outer core extends until the cen-tre), calledinner core, is charaterised by an extremely high density ρ ∼ 3 · 1018kg m–3 and a radius of several kilometres. Different exotic models have been proposed to
Figure 1.5.:Structure of a neutron star (Gendreau et al.,2012).
describe its dense matter composition. The implications of exotic forms of matter on the structure and stability of neutron stars are discussed by Camenzind,2007.
Mass and radius
The orbital motion of the companion star offers the possibility to directly measure the mass of the NS. The mass function gives a lower limit on the mass of the compact object:
Mx= K3 optP(1 – e2)3/2 2πGsin3i 1 + 1 q 2 , (1.6)
where Kopt is the semi-amplitude of the radial velocity curve, P is the orbital period, e is the eccentricy of the orbit, i is the inclination of the orbital plane to the line of sight and q is the mass ratio of the compact object and the companion star.
The typical mass of a NS is estimated to be 1.4 M , which corresponds to the Chandrasekhar limit on mass for a WD, whereas the minimum and maximum mass limit of a stable NS are
M < 1M and 3M , respectively. As a matter of principle, a larger mass than 3M should not exist, because nuclear and degeneracy pressures could not counterbalance the gravity force. This is called Oppenheimer-Volkoff limit and is the akin to the Chandrasekhar limit for WD stars. Exceeded this limit the NS would collapse to form a BH.
• from the density of nuclear matter, RNS = 3M 4πρ 1/3 ; (1.7)
• from the neutron degeneracy pressure:
Pdeg = h 2 2π2 Z A 5/3 ρ5/3 m8/3n , (1.8)
by equating Pdeg = Pgrav, the mass-radius relation gives:
RNS = 2 π 3 4π 5/3Z A 5/3h2M–1/3 Gm8/3n , (1.9)
where Z is the atomic number, A is the mass number and h is the Planck constant. • from the inner disc radius which provides an upper limit on the NS radius via the iron
line profile, or from measurement of X-ray bursts or X-ray binaries containing an old and weakly magnetised NS. X-ray bursts are associated with a brief thermonuclear flash (∼ 1 min), which occur when the matter accumulated onto the NS surface reaches a critical mass. The burst provides the possibility to measure the NS radius, which radiates like a spherical blackbody of luminosity of:
Lburst= 4πR2σT4
= 4πfxd2 (1.10) where d is the distance to the NS, fxis the flux of the burst, T is the temperature from the peak wavelength of the burst spectrum and σ is the Stefan-Boltzmann constant. The models explained above provide comparable results. The typical value for a NS radius is
RNS∼ 10 km, but it can vary with the mass of the compact object.
1.2.2 Black holes
BHs are the most mysterious objects in the Universe but paradoxically they can be considered to be very simple. Indeed, a BH is characterised by only the mass M, the angular momentum
J and the electric charge Q. Any other information is lost during the BH formation.
Depending on their mass, BHs can be classified into three categories: supermassive, interme-diate and stellar BHs.
Characterised by a mass of M > 106M , the supermassive BHs are present in the centre of most (or probably all) galaxies (King,2003). However, their origin is still an open issue and a lot of simulations are needed in order to understand their formation and their role in the galaxies. The second class, the intermediate BHs, includes BHs with a mass larger than the stellar BHs but smaller than the supermassive ones (M =102–104 M ). Such BHs are expected to be found in some ultraluminous X-ray sources (ULXs) (Miller et al.,2004, Roberts,2007).
Lastly, stellar BHs which are associated with the end of life of a supermassive star. They are created by the gravitational collapse when the star does not have enough nuclear fuel to
counterbalance gravitation forces. The stellar BHs in our galaxy have a mass smaller than ∼ 20 M .
Event horizon
A BH is defined as an object exhibiting strong gravitational effects that nothing (particles or electromagnetic radiation such as light) can escape from inside it. BHs are delimited by an event horizon, which represents the radius of the sphere surrounding the collapsed mass, where the escape speed equals the speed of light. It is defined as:
RH = GM c2 + s GM c2 2 – a2 (1.11)
where a denotes the BH spin and reads as:
a = Jc
GM2 (1.12)
The event horizon is usually expressed in units of the Schwarzschild radius RSch. This zone
defines the region of space-time from which is impossible to get any information, since any event taking place in it, cannot be observed. Because the matter can fall in but never leave, the BH mass can only increase.
Schwarzschild BH
A non-rotating BH, with J and Q null, is named Schwarzschild BH. It is formed when a mass M collapses in a sphere of radius RSch; this means that a Schwarzschild BH has an event horizon of RH = RSch.
Below a certain radius the particle orbit around the BH is not periodic anymore and the particle will eventually fall into the BH. This radius defines the last stable orbit (Shapiro et al., 1983, Kato et al.,1998) and reads as:
RLSO= 6GM
c2 (1.13)
For a Schwarzschild BH, RLSOis three times farther than the event horizon, that is RLSO= 3RSch.
Kerr BH
Compact objects with an angular momentum (J 6= 0) and rotating around one of their axes of symmetry are called Kerr BH (Kerr,1963). For these objects the spin affects the characteristics of the inner disc in two ways (Bardeen et al.,1972).
First, the radius of a Kerr BH horizon is smaller than a non-spinning BH. Indeed, rewriting the equation (1.11) as follows:
RH = Rg 1 + q (1 – a2∗) , (1.14)
where Rg = GMc2 and a∗=
a
Rg, which varies from –1 to 1, it easy obtains:
RH (a∗= ±1) = Rg = 1
2RH (a∗ = 0). (1.15) Second, the radius of the last stable orbit of the accretion disc is a function of the BH spin. If the BH and the accretion matter rotate in the same direction (a∗ > 0) RLSO= Rg = 12RSch; whereas if they rotate in the opposite direction (a∗< 0), RLSO = 9Rg = 92RSch.
1.3
Accretion process
Accretion of matter onto the compact objects is an important concept in astrophysics as it is an efficient and natural mechanism to explain the X-ray emission of objects among the most luminous in the galaxy.
This phenomenon represents the accumulation of the matter onto a compact object under the effect of gravity. The matter approaching the compact object, releases gravitational potential energy, making the accreting object a powerful source of energy (Frank et al.,1992).
Accretion luminosity
The gravitational potential energy released at the surface of a compact object of mass M and radius R, by the accretion of a mass m situated at distance r is:
Egrav(r) = –GMmr . (1.16) The mass m M moves from an infinite distance, r → ∞, to the surface of the object, r = R, therefore the energy difference will be:
∆Egrav= Egrav(r → ∞) – Egrav(R) = GMm
R . (1.17)
Since the central object accretes matter continuously at a rate M in the time interval ∆t˙ (∆M =M∆t) it will liberate the energy:˙
∆Egrav = GM∆M
R . (1.18)
If the energy is radiated away at the same rate at which it is liberated, the luminosity of the object due to the accretion process is:
Lacc = GM ˙M
R ; (1.19)
Laccis called accretion luminosity and can be written in terms of rest energy of the accreted mass as:
Lacc= ηMc˙ 2
, (1.20)
where c is the light speed and η = GMRc2, is the efficiency of the conversion of accreted mass into
which represents the compactness of the accreting object. In the case of a NS with R =10 km and M = 1.4M , the efficiecy will be η ' 15%; for a WD with radius R=5 · 103km and
M = M , η = 10–4 , whereas for a Schwarzschild BH and a Kerr BH, the accretion efficiency is estimated to be η = 5.7% and η = 32%, respectively.
Finally, to determine the accretion disc luminosity, is necessary add a factor 12 to take into account the fact that half of the gravitational energy is converted into kinetic energy whereas the other half is available to be radiated away by the disc itself:
Lacc = 1 2
GM ˙M
R . (1.21)
Eddington luminosity
The luminosity of the binary system depends on the accretion rate M, but it cannot grow˙ indefinitely. In fact, the high luminosities caused by the accretion matter onto the compact object can be reduced by the radiation pressure: the photons emitted by the source interact with the matter through scattering and absorption processes, resulting in an upper limit on the luminosity of these systems. The limiting luminosity is calledEddington luminosity. This occurs when the inward gravitational forces, extended on the protons, balance the outward radiation pressure:
Fgrav= Frad⇔ GMmp
D2 =
LEddσT
4πD2c , (1.22) where D denotes the stellar centre distance and σT is the Thomson scattering cross-section of
the electron.
The Eddington luminosity is therefore:
LEdd= 4πGMmpc σT ' 1.3 · 10 38 M M erg s –1 , (1.23)
from which the mass accretion rate that corresponds to the Eddington luminosity can be deduced: ˙ MEdd= LEdd ηc2 = 1.3 · 10 38 R GM . (1.24)
As is clear from the equation (1.24),M˙Edddoes not depend on the mass of the star but only on its
radius. For instance, the accretion rate of a NS of radius R = 10 km isM˙Edd=1.5 · 10–8M yr–1.
1.3.1 From the accretion disc to the compact object
Because of the conservation of angular momentum, the accreting matter from the companion star does not directly fall on the compact object but it spirals around it to form a flat structure, so-called accretion disc. The accretion disc plasma follows Keplerian orbits around the compact object with speed vK =
q
GM
R . The orbit of a blob of plasma in the accretion disc
slowly decrease until reaches the compact object, losing gravitational potential energy but gaining kinetic energy.
Depending on the nature of the compact object, the matter can arrive more or less close to the compact object. In the case of a BH, the matter reaches the last stable orbit whereas for
a NS the magnetic field plays an important role in the way the matter comes and falls onto the compact object. If the magnetic field is strong, the matter follows the field lines and falls onto the magnetic poles genereting pulses. In this configuration, the inner accretion disc is truncated at the magnetosperic radius, named Alfven radius. Concerning low magnetised NSs, the matter can reach the surface of the compact object. The boundary layer represents the region which does the connection between the accretion disk and the neutron star surface, and is an important source of luminosity.
2
Physics of X-ray binary systems
Contents
2.1 Different components . . . . 19 2.2 Physical processes in the accretion disc-corona system . . 24 2.3 The states of a source . . . . 31
The compact object is surrounded by a hot plasma, which is namedcorona(see Figure2.1).
Figure 2.1.:Artistic view of a LMXB system.
Corona and accretion disc play an important role in the X-ray emission of LMXBs. In the following sections, the crucial role of the corona, the different types of interactions occurring between photons and matter, the geometry of the disc and corona and the states observed in X-ray binary sources will be discussed.
2.1
Different components
X-ray spectra of accreting binary systems are usually characterised by two states of emission: the soft and the hard state. During soft states the spectrum can be described by a soft-thermal component, usually a blackbody or a multi-colour blackbody disc, associated with the accretion disc component. Whereas, the hard state is probably due from soft photons emitted by the accretion disc that get Compton up scattered by high-energy electrons which
form a corona. These components can be fitted by a blackbody or by a powerlaw with a high-energy cutoff when the source is in the soft or in the hard state, respectively. In these spectra a reflection component is usually detected and is thought to be due to the interaction between the Comptonised photons and the cold matter in the accretion disc.
The components illustrated above are shown in Figure2.2.
Figure 2.2.:Schematic picture of the interactions between the disc and the corona. The three main components of the emission corresponding to an accreting BH (top) and a plausible geometry of the accretion flow in the hard spectral state (bottom), where the black point, the blue slabs, and the pink points represent the compact object, the accretion disc, and the corona of electrons, respectively (Gilfanov,2010).
2.1.1 The accretion disc
The accretion disc is a structure formed by stellar plasma, that is ionised gas coming from the envelope of the companion star. Depending on the temperature, the accretion disc can be totally ionised or recombined to form neutral atoms at lower temperature. The mass accretion rate and viscosity play an important role in the accretion disc structure and geometry. It is possible to distinguish different classes of models, such as accretion flows radiatively efficient and radiatively inefficient, depending mainly on three parameters: the ratio between the heating rate and cooling rate, the gas opacity and the dominant pressure (gas or radiation). Regardless of the configuration, all of these involve an optically thick and geometrically thin accretion disc.
Standard model of the accretion disc
One of the solutions among the others is the standard accretion disc. Developed by Pringle et al.,1972and Shakura et al.,1973, it is a geometrically thin and optically thick disc (with
H r, where H is the disc thickness and r is the radius). It corresponds to the radiatively
efficient case, where the disc is dominated by the gas pressure. To determine the accretion disc structure it is important to infer the type and the influence of the viscous forces, this is possible through the Reynolds number:
Re∼ l 2ν
t ∼ vl
ν (2.1)
where l, t and v are the typical dimensions of length, time and viscosity of the flow, and ν is the kinematic velocity. If Re < 1, viscous forces play a central role, whereas if Re > 103 the flow becomes turbulent (Landau et al.,1987).
In the case of an accretion disc around a NS, R ∼ 1012(Longair,2011); this means that the turbulent viscosity plays an important role; the flow is strongly turbulent and the momentum transport depends on the turbulence in the plasma. An optically thick accretion disc entails the photons scatter many times before escaping from the disc, in this way particles and photons continuously share their kinetc energies.
In the equilibrium conditions, the average particle kinetic energy is equal to the average photon energy and it is possible to define a single temperature T. Thus, the disc irradiates from its top and bottom surfaces and the heat dissipated between r and r + ∆r can be approximated by a blackbody emission from the surfaces, such as:
2σT4· 2πr∆r −→ σT4= 3G ˙mM
8πr3 , (2.2)
where σ is the Stefan-Boltzmann constant, M is the accreting object mass, r is the radial distance from the centre and ˙m = 2πvrΣ is the mass transfer rate through the disc with density Σ at
the velocity vr (Frank et al.,1992).
Every annulus of the disc radiates like a blackbody of temperature T depending on the radius r, as T ∼ r–3/4. The disc temperature increases towards the compact object. The total intensity of the disc is proportional to the surface area at temperature T and to the blackbody intensity at that temperature, and can be written as:
I(ν) = Z 2πrB(T, ν)dr, (2.3) where: B(T, ν) = 2hν 3 c2 · 1 ehν/kT– 1 (2.4)
is the Planck function. At low frequencies, below the peak (hν kT), this function can be approximated by: B(T, ν) = 2ν 2kT c2 ∼ ν 2T, (2.5)
the latter is called Rayleigh-Jeans approximation. On the other hand, if the frequencies are above the peak (ehν/kT 1), the spectrum decreases exponentially:
B(T, ν) = 2hν
3
c2 e –hν/kT
. (2.6)
This is known as the Wien approximation.
Therefore, the accretion disc spectrum is usually fitted by a blackbody peaked at ∼ 1 keV (Tdisc∼ 107K) or by a multi-colour blackbody which approximates the blackbody emission at each radius of the disc, as shown in Figure2.3.
Figure 2.3.:Spectrum obtained by the overlapping of the blackbody components originated by the single rings in the optically thick accretion disc Hanke,2011.
Accretion flow dominated by radial energy transport (advection)
Since the standard model did not reproduce the spectral energy distribution of some sources, such as low rate accreting source (Esin et al.,1996), the Advection Dominated Accretion Flow (hereinafter referred to asADAF) model was proposed (Ichimaru,1977). This model assumes that the inner region of the accretion disc is close to the compact object and is replaced by a hot flow (Narayan et al.,1994, Narayan et al.,1995a, Narayan et al.,1995b, Abramowicz et al., 1995, Chen et al.,1995). The assumption of the ADAF model is that the photons accumulate energy from the viscous processes, this energy is stored in the gas as thermal energy and it is radiated with the flow onto the compact object (Ichimaru,1977). Only a small fraction of the energy is radiated away (Narayan,1996), therefore the radiation efficiency is significantly lower than that of the standard accretion disc (Narayan et al.,1998, Kato et al.,1998).
Other models based on the ADAF have been proposed, such as ADIOS (Advection Dominated Inflow-Outflow Solution) the average energy does not cross the event horizon as in the case of the ADAF but it is expelled in outflow (Yuan,2001), LHAF (Luminous Hot Accretion Flow) that consists of an efficient accretion flow, or CDAF (Convection Dominated Accretion Flow), the convection transports angular momentum towards the inner part of the flow (Quataert et al., 2000). Currently, it is still not obvious which of the different configurations is the correct one.
2.1.2 The corona
Contrary to the cool accretion disc, thecoronais composed of hot electrons (T > 109K) and it is responsible for production of the high-energy spectrum by Comptonisation. Energetic electrons occupy the region above and below the accretion disc, but not substitute it as occurs in the case of ADAFs, where the corona is the inner part of the accretion flow.
Different models have been proposed to explain of the corona existence. The first model suggests that the corona is formed by evaporation of hot material from the accretion disc surface (Shakura et al.,1973). Another one suggests that the hot corona is formed by the injection of energy from the accretion disc into a thin layer (Liang,1977). This would lead to a very hot corona similar to the observed structure of the solar corona (Galeev et al.,1979).
Moreover, also the corona geometry is still uncertain. For this reason different models are proposed:
• aslaborsandwichgeometry, the corona is placed top and bottom the disc;
• aspheregeometry, the corona is around the compact object;
• apatchyor apill boxcorona.
All models above mentioned are illustrated in Figure2.4
Figure 2.4.:Possible geometries of the accretion disc (red) and corona (yellow). From the top: slab or sandwich geometry, sphere geometry, and patchy geometry Stern et al.,1995.
Accretion disc corona
The Accretion Disc Corona (hereinafter referred to as ADC) is the simplest model able to reproduce the spectral features in the X-ray binary systems (White et al.,1982). It adopts the standard model of an optically thick and geometrically thin accretion disc, which extends close to the compact object (Shakura et al.,1973) and a sandwich geometry for the corona.
Truncated disc model
An alternative of the ADC model is the truncated disc model, where the thin accretion disc is truncated and substituted by an ADAF (Esin et al.,1997, Done et al.,2007).
The configuration of the thin accretion disc, the inner hot flow and the corona changes with the mass accretion rate. If the mass accretion rate is low, the ADAF is radiatively inefficient and the thin disc is found at large radii. If the mass accretion rate is high, the ADAF becomes radiatively efficient and the system more luminous. The ADAF get smaller whereas the thin accretion disc moves closer the compact object. The truncated disc model explains the spectral changes in the X-ray sources.
2.2
Physical processes in the accretion disc-corona
system
As mentioned above, the accretion disc and the corona form a complex system. Since some regions of the hot corona are in contact or in the close vicinity of the cold matter of the disc, important interactions occur. Among the main processes that deal with the interaction between the high-energy photons and atoms, nuclei and electrons, are Compton scattering and electron-positron pair production but also a third important process, external to the disc-corona system, takes place: the photoelectric absorption.
These processes dominate the X-ray spectra of AGN and binary sources and they will be discussed in the following (for more details see Rybicki et al.,1979, Bradt,2008, Longair,2011).
2.2.1 Photoelectric absorption
Thephotoelectric absorption(orphotoabsorption) consists in the absorption of some of the X-ray photons by the interstellar medium, between the source and the observer. This process is observed in the spectra of X-ray sources with low energy. Moreover, the X-ray binaries may be subject to extra absorption from the companion star or from material in the accretion disc. It is the dominant process at low photon energies (E <1–10 keV).
The photoabsorption consists in the absorption of a photon with energy hν by an atom or an ion with the subsequent ejection of a bound electron. Indeed, incident photon transfers its total energy to the atom. If the photon energy is greater than the energy of the atomic energy level EI, the atom-electron bond breaks, and the electron is ejected from that level. A large amount of energy Eeis carried out as the kinetic energy by the ejected electron:
Ee = hν – Enlj (2.7)
where Enlj is the bond dissociation energy of the electron in the atom.
The probability of absorbing photons depends on the energy: X-rays of low energy are absorbed more than X-rays of high energy, since the cross section for photoabsorption decrease as ∼ ν–3. Furthermore, the absorption cross sections depends on the atomic number Z of the element (such as H, He, C, O, ...). Hence, although heavier elements are less abundant than
hydrogen, their contribution to the total absorption cross section is more significant at X-ray energies. σK = 4 √ 2σTα4Z5 mec2 hν !7/2 ∝ Z5 (hν)7/2, (2.8) where α = e 2
4πε0~c is the fine structure constant and σT = 8π 3 e2 mec2 2
is the Thomson cross section (Klein et al.,1929).
This is the analytic solution for the absorption cross section for photons with energies
hν EI and hν mec2due to the ejection of electrons from K-shells of atoms. (For more details about the calculations of these cross sections see Karzas et al.,1961).
Absorption cross sections are then summed, weighted by the cosmic abundance of the different elements: σe(E) = n1 H X i niσi(E). (2.9)
Because the hydrogen is the most abundant element, the observed absorption is usually expressed as NH (the equivalent number of neutral atoms per cm2 in a column between the
source and the observer), that is the usual quantity used to parametrise X-ray extinction due to photoelectric absorption in astrophysical sources.
2.2.2 Compton scattering
Scattering is the simplest interaction between photons and free electrons. According to the initial energy of the photon with respect to that of the electron, it is possible to distinguish different regimes, such as Thompson scattering, direct Compton scattering and inverse Compton scattering.
Direct Compton scattering
If a photon with an initial energy low hν mec2, interacts with an electron at rest, the photon is scattered in a random direction and its radiation frequency does not change. This is the classic case ofThompson scattering.
If the photon energy is comparable to, or greater than the electron energy, non-classical effects have to be taken into account. This process is calleddirect Compton scattering. When the photon interacts with the rest electron, it loses a fraction of momentum and energy. Indeed, direct Compton scattering is not elastic since a recoil is observed and a transfer of energy occurs. This implies that initial and final energy of the photon are different.
Let us consider that the incident photon has an energy hν and momentum hνc , and the scattered photon has an energy hν0 and a momentum
hν0
c . The initial energy of the rest
electron is mec2, its recoil energy is γmec2and its momentum associated is p = γβmec = γmev,
where me is the electron mass, v is its recoil speed, β = vc is the speed parameter and γ is the Lorentz factor, γ =
q
1 – β2. Calling θ the photon scattering angle (angle between the old and new direction of the photon), φ the angle of the scattered electron and assuming
the conservation of the energy and the momentum, it is possible write three equations (two equations are required for the momentum, along the x and the y axis):
hν + mec2= hν0+ γmec2 hν c = hν0 c cos θ + γβmec sin φ 0 = hν 0 c sin θ + γβmec sin φ. (2.10)
The initial (i.e. before the interaction) momentum and energy are on the left sides, the final ones in the right sides. By combining these equations, the energy of the Compton scattered photon is obtained: hν = hν 0 1 +mhν ec2(1 – cos θ) . (2.11)
This change of energy can be converted in an increase of the photon wavelength, as:
λ – λ0= mh
ec(1 – cos θ) (2.12)
where the quantity mhec is known as the Compton wavelength λC.
Inverse Compton scattering
In the high-energy astrophysics contest, the electron is not at rest but it has an energy greater than the photon. Therefore, when a collision between photon and electron takes place, the energy is transferred from the electron to the photon. This process is known as inverse Compton scattering.
Here again, there are two regimes, called Thomson and Klein-Nishina regimes, which depend on the energy of the photon with respect to mec2. If the energy of the incoming photons is smaller than mec2, the Thomson regime is considered. In this case the recoil of the electron is small and can be neglected. On the contrary, if the photon energy is larger than mec2, the Klein-Nishina regime occurs and the recoil cannot be neglected. In both regimes, typically photon gains energy.
In the case of an isotropic distribution of photons, the power emitted by Compton scattering by an electron of the Lorentz factor γ is (Rybicki et al.,1979):
PC = 4
3σTUradγ 2β2
, (2.13)
where Uradis the radiation energy density of the photon field.
Comptonisation
When the spectrum is dominated by Compton processes (direct and inverse Compton scattering) it is said to be Comptonisation. In this situation the plasma is thin enough so that other processes, as bremsstrahlung, do not dominate the spectrum.
If the photons have an energy hν mec2and the electrons are non-relativistic, the relative change in photon energy is:
∆E E =
hν
mec2(1 – cos θ). (2.14) The average energy increase of the electrons is defined as:
∆E E =
hν
mec2 (2.15)
because, in the frame of reference of the electrons, the scattering is Thomson and therefore symmetric around the incident direction of the photons.
On the contrary, when the energy is transferred from the electrons to the photons (hν
mec2), the energy gain of the photons per inverse Compton scattering is: ∆E E = 4 3 v c 2 . (2.16)
When the process of multiple scattering of a photon is due to a thermal or quasi-thermal plasma of electrons, thethermal Comptonizationoccurs.
The thermal plasma is characterised by a thermal distribution of velocities at temperature
Te: 3 2kTe= 1 2mev 2 , (2.17)
with v the typical electron velocity. Hence, the equation (2.16) becomes: ∆E
E =
4kTe
mec2. (2.18)
As a consequence, the relation of the photon energy change (gain or loss) at each collision, both in the high and low-frequency regimes, reads as:
∆E E =
4kTe– hν
mec2 . (2.19)
If hν = 4kTe there is no energy transfer, if hν > 4kTe electrons gain energy whereas if
hν < 4kTephotons gain energy.
Another determinant parameter for the spectral shapes is the optical depth:
τ = neσtR, (2.20)
where neis the electron density, σT the Thomson cross section and R the radius of the source. When τ < 1, the photon leaves the source without any scattering. When τ > 1, the photon will suffer, on average, τ2 scatters before it leaves the source.
Considering that the number of scattering events, given by the random walk theory, is
nscat = max(τe, τe2), the total energy change of the photon for a non-relativistic temperature
and photons at low energy, is defined by:
y = 4kTe
mec2 max(τe, τ 2
This parameter, named Compton parameter, measures the importance of the inverse Compton process.
For y 1 the total energy does not change significantly, whereas for y ≥ 1, the Comptonised spectrum has more energy than the spectrum of the seed photons, so the Comptonisation process becomes very important (for more details see Ghisellini,2012).
In conclusion, photons from the disc gain energy by the multiple Compton scattering with the electrons of the corona. This leads to a powerlaw spectrum whose shape depends on the temperature and the optical depth of plasma. The spectral slope becomes harder when these parameters increase.
2.2.3 The reflection component
The Compton reflection is observed when the cold matter forming the accretion disc interacts with the hard photons. Photons with energies below 15 keV are absorbed by the cold matter rather than reflected. On the other hand, photons with energies ≥ 15 keV are Compton scattered. The result is a reflection spectrum whose most important signature is the iron K-α line at 6.4–7 keV. This emission line provides an useful spectral diagnostic for matter in the innermost regions of the accretion flow around the compact object (Fabian et al.,1989). Other important features are the emission lines at lower energy, the iron absorption edges and a Compton hump at ∼ 30 keV, as shown in Figure2.5.
Figure 2.5.:Monte Carlo simulation showing the reflection spectrum obtained assuming as incident spectrum a powerlaw (dashed line) on a cold gas. The main reflected features are the Fe K-α at 6.4 keV and the Fe absorption edge at 7.1 keV (Reynolds,1996).
Iron line
A useful tool to desume properties of the innermost regions of the accretion disc is the study of the iron emission lines shape. It provides a direct way to investigate the physics of the strong gravity region in the close vicinity of the compact object.
The irradiation of the cold matter in the proximity of the compact object produces the fluorescent and recombination emission lines. The photoabsorption of high-energy X-ray photons from a K-shell removes the inner shell electron of an atom or an ion. The ion becomes highly unstable, and the electron cascades from ion higher shells will fill the vacancy. This process can be followed either by a radiative transition, such a K-α line photon (fluorescence), or by radiationless transfer of energy to an electron (Auger effect). The probability that the ion de-excites via fluorescence or Auger effect is given by the fluorescence yield, which depends on the nuclear charge (∝ Z4). Iron and heavier elements strongly tend towards fluorescence. The combination of high fluorescent yield (ωK,Fe= 34% probability, Kaastra et al.,1993) and its high cosmic abundance, make the Fe K-α fluorescent line, emitted at ∼ 6.4 keV, the most evident line in the X-ray spectrum. Depending on the ionisation state of the plasma that forms the accretion disc, highly ionised line can be detected at 6.67–6.70 keV associated with FeXXV (He-like) and at 6.95–6.97 keV associated with FeXXVI (H-like).
Due to the fact that the line is probably originated in the inner regions of the accretion disc, where the Doppler effects and gravitational redshift produce strong distortions on its profile (see Figure2.6), the iron line appears broadened and distorted towards low energy. Each ring of disc
Figure 2.6.:Left panel: representation of the accretion disc with matter approaching (blue) and receding (red).
Right panel: from the top, the three squares represent the effects produced on the emission line. The
two lines profile indicate the emission from the radii represented on the disc (dashed line). The sum of the Doppler and relativistic effects gives rise to a broad and distorted iron line shape, as shown in the fourth square (Fabian et al.,2000).
the line produced by the matter moving in the direction of the observer undergoes a blushifted and an intensity boost, while the line produced by the matter moving in opposite direction undergoes a redshift and an intensity suppression. The result is a broad and asymmetric line shifted at low energy (see Figure2.6). The study of the iron line profile is therefore fundamental to obtain information on the inner radius of the emitting region in the disc, the inclination angle of the system with respect to the line of sight and the radial dependence of the line emissivity. Moreover, the emission line depends on the ionisation state of the disc. The ionisation parameter is:
ξ(r) = 4πFX(r)
ne (2.22)
where FX(r) is the X-ray flux received by unit area of the disc and neis the electron density (Reynolds et al.,2003). Depending on the value of this parameter it is possible to distinguish four regimes (Matt et al.,1993, Fabian et al.,2000):
• ξ < 100 erg cm s–1: neutral regime, known as cold reflection. In this regime the iron line at 6.4 keV is combined with a weak Fe absorption edge at 7.1 keV.
• 100 erg cm s–1< ξ < 500 erg cm s–1: intermediate ionisation regime. The FeXVII FeXXIII and a moderate absorption edge should be visible in the reflection spectrum. The fluorescence emission is followed by resonant absorption until the photons are destroyed by the Auger effect. Only a few photons can escape the disc, as a result the iron line appears weak.
• 500 erg cm s–1 < ξ < 5000 erg cm s–1: high ionisation regime. The ions are too highly ionised to permit the Auger effect. Consequently, the lack of a destruction mechanism implies that photons can escape the disc and produce the iron line. FeXXVand FeXXVI are emitted at 6.67 keV and 6.97 keV respectively, in addition to a large iron absorption edge.
• ξ > 5000 erg cm s–1: full ionisation regime. Being the disc highly ionised, no iron line emission or edges are produced.
Other emission lines
Additionally to the strong Fe line, other emission lines can be detected at lower energies (see Figure2.5). It is believed that these lines are originated from the inner part of the accretion disc as is the case for the Fe. Their detection depends on their fluorescent yield and on the ionisation state of the disc.
Compton hump
As previously stated, photoabsorption and Compton scattering are the two processes in com-petition in the accretion disc. Depending on their energy, photons will be subject one or the other process. If the photon energy is smaller than 15 keV, photons will be absorbed in the cold medium, whereas if the photon energy is greater than 15 keV, photons will be mostly Compton scattered until they either leave the system or are photoabsorbed. Both processes
originate a broad hump in the spectrum at ∼ 30 keV, also known as Compton reflection hump (see Figure2.5).
Absorption edge
The probability of absorbing photons of a particular energy increases when the energy corre-sponds to the ionisation state of an absorbing element, such as H, He, C, etc. The absorption edge will be produced and visible in the X-ray source when the incident photon energy is equal to the ionisation energy, hν = EI. A strong edge detected in the X-ray spectra of binary
sources is the Fe K-edge a ∼ 7.1 keV.
2.3
The states of a source
A variety of spectral shapes can be shown by an X-ray binary source if it is observed at different moments. The X-ray emission is, indeed, variable on time scale of minutes, months or years. Depending on the type of sources, sequences of outbursts, which correspond to a high X-ray luminosity, are generally observed and they are separated by periods of low X-ray luminosity. According to the spectral properties of the source, two different spectral states are identified (McClintock et al.,2006, Homan et al.,2005). Thehigh-soft state, dominated by the thermal emission from the accretion disc, during the outbursts and thelow-hard state, dominated by the emission from the corona, during the low X-ray luminosity periods. The intermediate state defines the transition between both states.
It is thought that different states are connected to the changes in the accretion physics (Hameury et al.,1986), such as the mass accretion rate, the instabilities in the disc or the way in which the matter move toward the compact object. Nevertheless, processes that produce these variabilities are not yet well understood. Observations at different wavelengths (radio, IR, optical, UV, X- and γ-ray) give a more complete view helping in the comprehension of state transitions.
2.3.1 The soft state
When a source is bright in soft X-rays and softness in hard X-rays, it is said that it is in the high-soft state or, simply, in the soft state. The spectrum is dominated by the thermal component (associated with the geometrically thin and optically thick accretion disc), which can be fitted by a blackbody or by a multi-temperature blackbody. The disc is thought to extend down to the compact object, i.e. the surface of the compact object for a NS or the last stable orbit in the case of a BH.
At higher energy, the spectrum is dominated by a non-thermal component that it is fitted by a weak steep powerlaw with a photon index Γ ∼ 2.1–3. This powerlaw is associated with the inverse Compton scattering among the soft photons of the disc and the hot electrons of the corona. This component illuminates the disc and gives rise to strong reflection features (Done et al.,2007).
To study the sources during the soft state allows to prove the existence of the last stable orbit in BH and to estimate its spin. In the case of NS, it is also important to understand the role of
