Measuring Black Hole Spin Using X-Ray Reflection Spectroscopy

I review the current status of X-ray reflection (a.k.a. broad iron line) based black hole spin measurements. This is a powerful technique that allows us to measure robust black hole spins across the mass range, from the stellar-mass black holes in X-ray binaries to the supermassive black holes in active galactic nuclei. After describing the basic assumptions of this approach, I lay out the detailed methodology focusing on “best practices” that have been found necessary to obtain robust results. Reflecting my own biases, this review is slanted towards a discussion of supermassive black hole (SMBH) spin in active galactic nuclei (AGN). Pulling together all of the available XMM-Newton and Suzaku results from the literature that satisfy objective quality control criteria, it is clear that a large fraction of SMBHs are rapidly-spinning, although there are tentative hints of a more slowly spinning population at high (M>5×10⁷ M _⊙) and low (M<2×10⁶ M _⊙) mass. I also engage in a brief review of the spins of stellar-mass black holes in X-ray binaries. In general, reflection-based and continuum-fitting based spin measures are in agreement, although there remain two objects (GRO J1655–40 and 4U 1543–475) for which that is not true. I end this review by discussing the exciting frontier of relativistic reverberation, particularly the discovery of broad iron line reverberation in XMM-Newton data for the Seyfert galaxies NGC 4151, NGC 7314 and MCG–5-23-16. As well as confirming the basic paradigm of relativistic disk reflection, this detection of reverberation demonstrates that future large-area X-ray observatories such as LOFT will make tremendous progress in studies of strong gravity using relativistic reverberation in AGN.     

Mass Measurements of Stellar and Intermediate-Mass Black Holes

We discuss the method, and potential systematic effects therein, used for measuring the mass of stellar-mass black holes in X-ray binaries. We restrict our discussion to the method that relies on the validity of Kepler’s laws; we refer to this method as the dynamical method. We briefly discuss the implications of the mass distribution of stellar-mass black holes and provide an outlook for future measurements. Further, we investigate the evidence for the existence of intermediate-mass black holes i.e. black holes with masses above 100 M_⊙, the limit to the black hole mass that can be produced by stellar evolution in the current Universe.     

The Supermassive Black Hole—Galaxy Connection

The observed scaling relations imply that supermassive black holes (SMBH) and their host galaxies evolve together. Near-Eddington winds from the SMBH accretion discs explain many aspects of this connection. The wind Eddington factor \(\dot{m}\) should be in the range ～1–30. A factor \(\dot{m}\sim 1\) give black hole winds with velocities v～0.1c, observable in X-rays, just as seen in the most extreme ultrafast outflows (UFOs). Higher Eddington factors predict slower and less ionized winds, observable in the UV, as in BAL QSOs. In all cases the wind must shock against the host interstellar gas and it is plausible that these shocks should cool efficiently. There is detailed observational evidence for this in some UFOs. The wind sweeps up the interstellar gas into a thin shell and propels it outwards. For SMBH masses below a certain critical (M–σ) value, all these outflows eventually stall and fall back, as the Eddington thrust of the wind is too weak to drive the gas to large radii. But once the SMBH mass reaches the critical M–σ value the global character of the outflow changes completely. The wind shock is no longer efficiently cooled, and the resulting thermal expansion drives the interstellar gas far from the black hole, which is unlikely to grow significantly further. Simple estimates of the maximum stellar bulge mass M _b allowed by self-limited star formation show that the SMBH mass is typically about 10^?3 M _b at this point, in line with observation. The expansion-driven outflow reaches speeds v _out?1200 km?s^?1 and drives rates \(\dot{M}_{\mathrm{out}}\sim 4000~\mathrm {M}_{\odot }\,\mathrm{yr}^{-1}\) in cool (molecular) gas, giving a typical outflow mechanical energy L _mech?0.05L _Edd, where L _Edd is the Eddington luminosity of the central SMBH. This is again in line with observation. These massive outflows may be what makes galaxies become red and dead, and can have several other potentially observable effects. In particular they have the right properties to enrich the intergalactic gas with metals. Our current picture of SMBH-galaxy coevolution is still incomplete, as there is no predictive theory of how the hole accretes gas from its surroundings. Recent progress in understanding how large-scale discs of gas can partially cancel angular momentum and promote dynamical infall offers a possible way forward.     

Black Hole Spin via Continuum Fitting and the Role of Spin in Powering Transient Jets

The spins of ten stellar black holes have been measured using the continuum-fitting method. These black holes are located in two distinct classes of X-ray binary systems, one that is persistently X-ray bright and another that is transient. Both the persistent and transient black holes remain for long periods in a state where their spectra are dominated by a thermal accretion disk component. The spin of a black hole of known mass and distance can be measured by fitting this thermal continuum spectrum to the thin-disk model of Novikov and Thorne; the key fit parameter is the radius of the inner edge of the black hole’s accretion disk. Strong observational and theoretical evidence links the inner-disk radius to the radius of the innermost stable circular orbit, which is trivially related to the dimensionless spin parameter a _? of the black hole (|a _?|<1). The ten spins that have so far been measured by this continuum-fitting method range widely from a _?≈0 to a _?>0.95. The robustness of the method is demonstrated by the dozens or hundreds of independent and consistent measurements of spin that have been obtained for several black holes, and through careful consideration of many sources of systematic error. Among the results discussed is a dichotomy between the transient and persistent black holes; the latter have higher spins and larger masses. Also discussed is recently discovered evidence in the transient sources for a correlation between the power of ballistic jets and black hole spin.     

Scaling Relations from Stellar to Supermassive Black Holes

Accretion is a ubiquitous phenomenon—it is seen in sources ranging from young stars to accreting supermassive black holes in the centres of galaxies. Here, we present the known empirical connections between stellar mass X-ray binaries and active galactic nuclei. We argue that this implies that both the accretion disc and the jet are scale invariant with respect to the black hole mass. Finally, we show that also accretion discs and jets in sources with a different accretor can be connected empirically to accreting black holes, hinting towards a common mechanism of accretion in all sources.     

Massive Stars: Input Physics and Stellar Models

We present a general overview of the structure and evolution of massive stars of masses ≥12 M _⊙ during their pre-supernova stages. We think it is worth reviewing this topic owing to the crucial role of massive stars in astrophysics, especially in the evolution of galaxies and the universe. We have performed several test computations with the aim to analyze and discuss many physical uncertainties still encountered in massive-star evolution. In particular, we explore the effects of mass loss, convection, rotation, ¹²C(α,γ)¹⁶O reaction and initial metallicity. We also compare and analyze the similarities and differences among various works and ours. Finally, we present useful comments on the nucleosynthesis from massive stars concerning the s-process and the yields for ²⁶Al and ⁶⁰Fe.     

Starburst galaxies

Bursts of massive star formation can temporarily dominate the luminosity of galaxies spanning a wide range of morphological types. This review is concerned primarily with such events in the central 1 kpc region of spiral galaxies which result from bar driven inflows of gas triggered by interactions or mergers. Most of the stellar radiant luminosity of such bursts is absorbed by dust and re-emitted in the far-infrared and is accompanied by radio and X-ray emission from supernova remnants which can also act collectively to drive galaxy scale outflows. Both evolutionary stellar models and estimates of the gas depletion times are consistent with typical burst durations of 10^7–8 yr. Spatially-resolved studies of nearby starburst galaxies reveal that the activity is distributed over many individual star forming complexes within rings and other structures organized by interactions between bars and the disc over a range of scales. More distant and extreme examples associated with mergers of massive spirals have luminosities > 10¹³ L and molecular gas masses > 10¹⁰ M implying star formation rates > 1000 M yr^–1 which can only be sustained for 10⁷ yr. In the most luminous merging systems, however, the relative importance of starburst and AGN activity and their possible evolutionary connection is still a hotly debated issue. Also controversial are suggestions that starbursts in addition to a black hole are required to account for the properties of AGNs or that starbursts alone may be sufficient under certain conditions. In a wider context, starbursts must clearly have played an important role in galaxy formation and evolution at earlier times. Recent detections of high redshift galaxies show that star formation was underway at z 4 but do not support a continuing increase of the strong evolution in the co-moving star formation density seen out to z l. Primeval starburst pre-cursors of spheroidal systems also remain elusive. The most distant candidates are radio galaxies and quasars at z = 4–5 and a possible population of objects responsible for an isotropic sub-mm wave background tentatively claimed to have been detected by the COBE satellite.     

Searching for Black Holes in Space

Although General Relativity had provided the physical basis of black holes, evidence for their existence had to await the Space Era when X-ray observations first directed the attention of astronomers to the unusual binary stars Cygnus X-1 and A0620-00. Subsequently, a number of faint Ariel 5 and Uhuru X-ray sources, mainly at high Galactic latitude, were found to lie close to bright Seyfert galaxies, suggesting the nuclear activity in AGN might also be driven by accretion in the strong gravity of a black hole. Detection of rapid X-ray variability with EXOSAT later confirmed that the accreting object in an AGN is almost certainly a supermassive black hole.     

Evolution into contact of the low-mass close binary systems

We investigated the effect of mass accretion on the secondary components in close binomy systems (M _total ≤ 2.5 M _⊙ M _2,0 ≤ 0.75 M _⊙) exchanging mass in the case A. The evolution of the low-mass close binary systems (M _total ≤ 2.5 M _⊙) exchanging the mass in the case A depends on the three main factors:

-the initial mass ratio (q ₀ = M _2,0/M _1,0), which determines the rate of mass transfer between components;

-the inital mass of the secondary component (M _2,0) and

-the effectiveness of the heating of the photosphere of the secondary component, by infalling matter.

The second factor allows to divide all systems into two essentially different groups:

1. systems in which the secondary component is a star with a radiative envelope, or with a thin convection zone in the uppermost layers;
2. and systems in which secondary component has a thick convective envelope or is fully convective.

The systems from the first group evolve into contact in a characteristic time scale 10⁵ – 10⁷ years, and reach contact after transfering of 0.03 – 0.3 M _⊙. The mass exchange proceeds only in a thermal time scale. For the systems from the group b the effectiveness of the heating of the stellar surface is the most important. In the case when the entropy of the newly accreted matter is the same as the surface entropy of the secondary, a convective star should shrink upon accretion. Then contact binaries are not formed. In the case when the entropy of the infalling matter is greater then that on the surface, the reaction of the secondary is different. The radius of the secondary component grows rapidly in response to accretion, and the systems reaches contact after the 10³ – 3 10⁶ years, and after transfer of 0.002 – 0.2. M _⊙. The reaction of the secondary is determined by the formation of the temperature inversion layer below the stellar surface. Full references in: Sarna, M.J. and Fedorova, A.V. (1988) “Evolutionary status of W UMa-type Binaries — Evolution into contact”, Astron. Astrophys., in press.     

Results of evolutionary computations of primaries of close binaries with different initial composition

The present paper summarizes fundamental evolutionary parameters of primaries of close binaries with initial masses between 9 and 60 M_⊙ and initial composition appropriate for the Galaxy, the LMC and the SMC. The primary timescales and WR binary timescales are compared with corresponding recent single star predictions.     

Large-scale Bright Fronts in the Solar Corona: A?Review of?��EIT waves��

??EIT waves?? are large-scale coronal bright fronts (CBFs) that were first observed in 195 Å images obtained using the Extreme-ultraviolet Imaging Telescope (EIT) onboard the Solar and Heliospheric Observatory (SOHO). Commonly called ??EIT waves??, CBFs typically appear as diffuse fronts that propagate pseudo-radially across the solar disk at velocities of 100?C700 km?s^?1 with front widths of 50?C100 Mm. As their speed is greater than the quiet coronal sound speed (c _s ??200 km?s^?1) and comparable to the local Alfvén speed (v _A ??1000 km?s^?1), they were initially interpreted as fast-mode magnetoacoustic waves ( $v_{f}=(c_{s}^{2} + v_{A}^{2})^{1/2}$ ). Their propagation is now known to be modified by regions where the magnetosonic sound speed varies, such as active regions and coronal holes, but there is also evidence for stationary CBFs at coronal hole boundaries. The latter has led to the suggestion that they may be a manifestation of a processes such as Joule heating or magnetic reconnection, rather than a wave-related phenomena. While the general morphological and kinematic properties of CBFs and their association with coronal mass ejections have now been well described, there are many questions regarding their excitation and propagation. In particular, the theoretical interpretation of these enigmatic events as magnetohydrodynamic waves or due to changes in magnetic topology remains the topic of much debate.     

Observational Appearance of Black Holes in X-Ray Binaries and AGN

Accretion onto black holes powers most luminous compact sources in the Universe. Black holes are found with masses extending over an extraordinary broad dynamic range, from several to a few billion times the mass of the Sun. Depending on their position on the mass scale, they may manifest themselves as X-ray binaries or active galactic nuclei. X-ray binaries harbor stellar mass black holes—endpoints of the evolution of massive stars. They have been studied by X-ray astronomy since its inception in the early 60-ies, however, the enigma of the most luminous of them—ultra-luminous X-ray sources, still remains unsolved. Supermassive black holes, lurking at the centers of galaxies, are up to hundreds of millions times more massive and give rise to the wide variety of different phenomena collectively termed “Active Galactic Nuclei”. The most luminous of them reach the Eddington luminosity limit for a few billions solar masses object and are found at redshifts as high as z≥5–7. Accretion onto supermassive black holes in AGN and stellar- and (possibly) intermediate mass black holes in X-ray binaries and ultra-luminous X-ray sources in star-forming galaxies can explain most, if not all, of the observed brightness of the cosmic X-ray background radiation. Despite the vast difference in the mass scale, accretion in X-ray binaries and AGN is governed by the same physical laws, so a degree of quantitative analogy among them is expected. Indeed, all luminous black holes are successfully described by the standard Shakura-Sunyaev theory of accretion disks, while the output of low-luminosity accreting black holes in the form of mechanical and radiative power of the associated jets obeys to a unified scaling relation, termed as the “fundamental plane of black holes”. From that standpoint, in this review we discuss formation of radiation in X-ray binaries and AGN, emphasizing their main similarities and differences, and examine our current knowledge of the demographics of stellar mass and supermassive black holes.     

Formation and evolution of low-mass Algols

We discuss the origin, evolution and fate of low-mass Algols (LMA) that have components with initial masses less than 2.5 M₀. The semi-major axes of orbits of pre-LMA do not exceed 20–25 R₀. The rate of formation of Algol-type stars is ～ 0.01/year. Magnetic stellar winds may be the factor that determines the evolution of LMA. Most LMA end their lives as double helium degenerate dwarfs with M₁/M₂ ～ 0.88 (like L870-2). Some of them even merge through angular momentum loss caused by gravitational waves.     

Inside and outside of supernovae

A newly formed neutron star in a supernova finds itself in a dense environment, in which the gravitational energy of accreting matter can be lost to neutrinos. For the conditions in SN 1987A, 0.1M may have fallen back onto the central neutron star on a timescale of hours after the explosion, after which the accretion rate is expected to drop sharply. Radiation is trapped in the flow until the mass accretion rate drops to 2×10^–4 M yr^–1 at which point radiation can begin to escape from the shocked envelope at an Eddington limit luminosity. Between this neutrino limit and the Eddington limit, 3×10^–8 M yr^–1, there are no steady, spherical solutions for neutron star accretion. SN 1987A should have reached the neutrino limit within a year of the explosion; the current lack of an Eddington luminosity can be attributed to black hole formation or to a clearing of the neutron star envelope. There is no evidence for newly formed neutron stars in supernovae. Radio supernovae, which were initially interpreted as pulsar activity, probably involve circumstellar interaction; SN 1993J shows especially good evidence for outer shock phenomena.     

Clusters of Galaxies: Setting the Stage

Clusters of galaxies are self-gravitating systems of mass ∼10¹⁴–10¹⁵ h ⁻¹ M_⊙ and size ∼1–3h ⁻¹ Mpc. Their mass budget consists of dark matter (∼80%, on average), hot diffuse intracluster plasma (≲20%) and a small fraction of stars, dust, and cold gas, mostly locked in galaxies. In most clusters, scaling relations between their properties, like mass, galaxy velocity dispersion, X-ray luminosity and temperature, testify that the cluster components are in approximate dynamical equilibrium within the cluster gravitational potential well. However, spatially inhomogeneous thermal and non-thermal emission of the intracluster medium (ICM), observed in some clusters in the X-ray and radio bands, and the kinematic and morphological segregation of galaxies are a signature of non-gravitational processes, ongoing cluster merging and interactions. Both the fraction of clusters with these features, and the correlation between the dynamical and morphological properties of irregular clusters and the surrounding large-scale structure increase with redshift. In the current bottom-up scenario for the formation of cosmic structure, where tiny fluctuations of the otherwise homogeneous primordial density field are amplified by gravity, clusters are the most massive nodes of the filamentary large-scale structure of the cosmic web and form by anisotropic and episodic accretion of mass, in agreement with most of the observational evidence. In this model of the universe dominated by cold dark matter, at the present time most baryons are expected to be in a diffuse component rather than in stars and galaxies; moreover, ∼50% of this diffuse component has temperature ∼0.01–1 keV and permeates the filamentary distribution of the dark matter. The temperature of this Warm-Hot Intergalactic Medium (WHIM) increases with the local density and its search in the outer regions of clusters and lower density regions has been the quest of much recent observational effort. Over the last thirty years, an impressive coherent picture of the formation and evolution of cosmic structures has emerged from the intense interplay between observations, theory and numerical experiments. Future efforts will continue to test whether this picture keeps being valid, needs corrections or suffers dramatic failures in its predictive power.     

Observations of the solar wind from coronal holes

The solar wind emanating from coronal holes (CH) constitutes a quasi-stationary flow whose properties change only slowly with the evolution of the hole itself. Some of the properties of the wind from coronal holes depend on whether the source is a large polar coronal hole or a small near-equatorial hole. The speed of polar CH flows is usually between 700 and 800 km/s, whereas the speed from the small equatorial CH flows is generally lower and can be <400 km/s. At 1 AU, the average particle and energy fluxes from polar CH are 2.5×10⁸ cm^–2 sec^–1 and 2.0 erg cm^–2 s^–1. This particle flux is significantly less than the 4×10⁸ cm^–2 sec^–1 observed in the slow, interstream wind, but the energy fluxes are approximately the same. Both the particle and energy fluxes from small equatorial holes are somewhat smaller than the fluxes from the large polar coronal holes.Many of the properties of the wind from coronal holes can be explained, at least qualitatively, as being the result of the effect of the large flux of outward-propagating Alfvén waves observed in CH flows. The different ion species have roughly equal thermal speeds which are also close to the Alfvén speed. The velocity of heavy ions exceeds the proton velocity by the Alfvén speed, as if the heavy ions were surfing on the waves carried by the proton fluid.The elemental composition of the CH wind is less fractionated, having a smaller enhancement of elements with low first-ionization potentials than the interstream wind, the wind from coronal mass ejections, or solar energetic particles. There is also evidence of fine-structure in the ratio of the gas and magnetic pressures which maps back to a scale size of roughly 1° at the Sun, similar to some of the fine structures in coronal holes such as plumes, macrospicules, and the supergranulation.     

Nucleosynthesis in Supernovae

We present the status and open problems of nucleosynthesis in supernova explosions of both types, responsible for the production of the intermediate mass, Fe-group and heavier elements (with the exception of the main s-process). Constraints from observations can be provided through individual supernovae (SNe) or their remnants (e.g. via spectra and gamma-rays of decaying unstable isotopes) and through surface abundances of stars which witness the composition of the interstellar gas at their formation. With a changing fraction of elements heavier than He in these stars (known as metallicity) the evolution of the nucleosynthesis in galaxies over time can be determined. A complementary way, related to gamma-rays from radioactive decays, is the observation of positrons released in \(\beta^{+}\)-decays, as e.g. from \(^{26}\mbox{Al}\), \(^{44}\mbox{Ti}\), \(^{56,57}\mbox{Ni}\) and possibly further isotopes of their decay chains (in competition with the production of \(e^{+}e^{-}\) pairs in acceleration shocks from SN remnants, pulsars, magnetars or even of particle physics origin). We discuss (a) the role of the core-collapse supernova explosion mechanism for the composition of intermediate mass, Fe-group (and heavier?) ejecta, (b) the transition from neutron stars to black holes as the final result of the collapse of massive stars, and the relation of the latter to supernovae, faint supernovae, and gamma-ray bursts/hypernovae, (c) Type Ia supernovae and their nucleosynthesis (e.g. addressing the \(^{55}\mbox{Mn}\) puzzle), plus (d) further constraints from galactic evolution, \(\gamma\)-ray and positron observations. This is complemented by the role of rare magneto-rotational supernovae (related to magnetars) in comparison with the nucleosynthesis of compact binary mergers, especially with respect to forming the heaviest r-process elements in galactic evolution.     

CCD spectroscopy of the W Serpentis binaries KX And and RX Cas

Initial results are presented from a study of H _γ profiles in the two interacting binaries KX And and RX Cas of W Serpentis type. The used CCD spectra with a resolution of 0.13Å/px were obtained with the 2.2m telescope and the Coudé spectrograph at the German-Spanish Astronomical Center at Calar Alto/Spain. KX And. This star is probably a non-eclipsing member of the W Serpentis type interactive binaries and has a period of P = 38.908 days. Our seven spectra of KX And were obtained at phase 0.54 – 0.75. The P Cyg profiles of the H _γ line during our observations indicate an expanding shell. The asymetry becomes blue-sided at phase 0.67 and increases thereafter. This points toward a strong outflow of matter in the vicinity of the L3 point. RX Cas. According to the model of Andersen et al. (1988) the primary is a mid-B type star with M = 5.8M _⊙ and R = 2.5R _⊙. The star is completely obscured by a geometrically and optically thick disk, which is supplied by mass transfer from the other component. The secondary is a K1 giant with M = 1.8M _⊙ and R = 23.5R _⊙ and fills out his critical Roche lobe. Radiative and geometrical properties of the disk are variable and its structure is probably not homogenous. Five spectra of RX Cas were obtained during the primary eclipse (phase 0.95 – 0.19). The observed double-peak emission is seen only after the eclipse with a separation of ≈ 250 km/s peak-to-peak, while during the eclipse an asymetric line profile can be observed with a red-shifted emission always presented. Also, a central emission at φ = 0.94 should be noticed, probably originating in the vicinity of L1. The observations of both systems indicate that we are dealing with strongly interacting binaries. Further observations are planned for better covering of phase.     

Measuring the Masses of Supermassive Black Holes

Supermassive black holes reside at the centers of most, if not all, massive galaxies: the difference between active and quiescent galaxies is due to differences in mass accretion rate and radiative efficiency rather than whether or not they have nuclear black holes. In this contribution, methods for measuring the masses of supermassive black holes are discussed, with emphasis on reverberation mapping which is most generally applicable to accreting supermassive black holes and, in particular, to distant quasars where time resolution can be used as a surrogate for angular resolution. Indirect methods based on scaling relationships from reverberation mapping studies are also discussed, along with their current limitations.     

TeV emission from close binaries

It is commonly accepted that candidates for very high energy -ray sources are neutron stars, binary systems, black holes etc. Close binary systems containing a normal hot star and a neutron star (or a black hole) form an important class of very high energy -ray sources. Such systems are variable in any region of the electromagnetic spectrum and they enable us to study various stages of stellar evolution, accretion processes, mechanisms of particle acceleration, etc. Phenomena connected with this class of very high energy -ray sources are discussed. Particular emphasis has been placed on the TeV energy region.