Introduction : The astrophysics of relativistic compact objects

Gravitational collapse of normal matter can produce some of the most exotic objects in the universe -- neutron stars and black holes. Proving that these objects exist in Nature occupied theoretical and observational astrophysicists for much of the 20th century. Most of the detailed debate centered around understanding the possible final states of massive stars. On his now famous sea voyage from India to England in 1930, Subrahmanyan Chandrasekhar considered the structure of white dwarf stars -- compact stellar remnants in which gravitational forces are balanced by electron degeneracy pressure. He realized that, if the white dwarf was sufficiently massive, the degenerate electrons will become relativistic thereby rendering the star susceptible to further gravitational collapse [1,2]. Although hotly debated by Arthur Eddington, Chandrasekhar correctly deduced that a white dwarf would undergo gravitational collapse if its mass exceeded $M_{\rm ch}\approx 1.4\hbox{$\rm\thinspace M_{\odot}$}$ (where $1\hbox{$\rm\thinspace M_{\odot}$}=2.0\times 10^{33}{\rm\thinspace g}$ is the mass of the Sun), a limit now known as the Chandrasekhar limit².

Once gravity overwhelms electron degeneracy pressure, it is thought that neutron degeneracy pressure is the last, best hope for averting total gravitational collapse. Objects in which gravitational forces are balanced by neutron degeneracy pressure are called neutron stars. Although there was initial hope that nuclear forces would always be sufficient to resist gravity, the upper limit to the mass of a neutron star is now believed to be in the range $M\approx 1.8-2.2\hbox{$\rm\thinspace M_{\odot}$}$[4,5]. Uncertainties arising from the equation of state at super-nuclear densities continue to plague our determination of this critical mass, but an absolute upper limit of $M\approx 4\hbox{$\rm\thinspace M_{\odot}$}$ arises from very general considerations, i.e., the validity of General Relativity and the principle of causality[6]. Above this mass, it is thought that complete gravitational collapse cannot be avoided. In particular, Hawking's singularity theorems[7] show that the formation of a spacetime singularity is unavoidable (irrespective of the mass/energy distribution) once the object is contained within the light trapping surface. The result is a black hole, i.e., a region of spacetime bounded by an event horizon and, at its heart, possessing a spacetime singularity.

While the above considerations now have a firm theoretical base, observational astrophysics was, and continues to be, critically important in guiding our understanding of such extreme objects. In the case of both neutron stars and black holes, the very existence of these objects was only widely accepted when compelling observational evidence was forthcoming. For neutron stars, the pivotal observation was the discovery of pulsars by Jocelyn Bell and Anthony Hewish via radio observations taken from Cambridge. Black holes gained wide acceptance after it was demonstrated that the X-ray emitting compact object in the binary star system Cygnus X-1 did, in fact, possess a mass in excess of the maximum possible neutron star mass[8,9,10,11,12]. This made it the first of the so-called Galactic Black Hole Candidates (GBHCs), a class that has now grown to include some two dozen objects.

We now know of another class of black holes -- the supermassive black holes, with masses in the range of $10^5-10^{9.5}\hbox{$\rm\thinspace M_{\odot}$}$, that reside at the dynamical centers of most, if not all, galaxies³. Today, by far the strongest case for a supermassive black hole can be made for our own Galaxy. Modern high-resolution, infra-red imaging reveals that the stars in the central-most regions of our Galaxy are orbiting an unseen mass of $2.6\times 10^6\hbox{$\rm\thinspace M_{\odot}$}$[14,15,16]. Furthermore, studies of the orbital dynamics (which now include measured accelerations as well as velocities; [17,18]) constrain the central mass to be extremely compact. According to conventional physics, the only long-lived object with these properties is a supermassive black hole. Alternatives, such as a compact cluster of neutron stars, would suffer a dynamical collapse on short time scales [19].

Figure 1: Continuum subtracted iron line from the long July-1994 ASCA observation of the Seyfert-1 galaxy MCG-6-30-15 [20]. The dashed line shows a model consisting of iron line emission from a relativistic accretion disk around a non-rotating (Schwarzschild) black hole, with a disk inclination of $i=30^\circ$, and an emissivity profile of $r^{-3}$ extending down to the radius of marginal stability ($6\,{\rm GM/c^2}$).

Having established beyond reasonable doubt that black holes exist, it is obviously interesting to perform detailed observational studies of them. The regions in the immediate vicinity of a black hole bear witness to complex interactions between matter moving at relativistic velocities, electromagnetic fields, and the black hole spacetime itself. Given that the apparent angular scales of even the biggest black hole event horizons are $\sim 10^{-6}{\rm\thinspace arcsec}$, direct imaging studies of these regions will not be possible for many years⁴. In the meantime, we must study these regions using more indirect methods, chief among which are spectroscopic methods.

As we will detail in this review, Nature has provided us with a well-understood and extremely useful spectral diagnostic of matter in the near vicinity of astrophysical black holes. In essence, relatively cold matter in the near vicinity of an astrophysical black hole will inevitably find itself irradiated by a spectrum of hard X-rays [21,22]. The result can be a spectrum of fluorescent emission lines, the most prominent being the K$\alpha$ line of iron at an energy of $6.40-6.97{\rm\thinspace keV}$ (depending upon the ionization state of the iron) [23,24,25]. Ever since the launch of the Advanced Satellite for Cosmology and Astrophysics (ASCA) in February 1993, X-ray astrophysicists have had the capability to identify this emission line and measure its spectral profile. Figure 1 shows the iron line in the X-ray emissions originating near the supermassive black hole in the galaxy MCG-6-30-15 [20]. Bearing in mind that the line is intrinsically narrow with a rest-frame energy of 6.4keV, it can be seen that the line has been dramatically broadened and skewed to low-energies. It is now widely accepted that the line originates from material that is just a few gravitational radii from the black hole, and possesses a profile that is shaped by (relativistic) Doppler shifts and gravitational redshift effects. Investigating these spectral features in X-ray luminous black hole systems has given us the clearest window to date on the physics that occurs in the immediate vicinity of astrophysical black holes.

The intent of this review is to describe our current understanding of black hole astrophysics, with an emphasis on what has been learnt by utilizing these X-ray spectral signatures. We begin by discussing the basic theoretical framework within which we understand the astrophysical environment around black holes. A central and important part of this discussion is an introduction to the modern theory of accretion disks. Hand-in-hand with the theoretical discussion, we will introduce the necessary phenomenology associated with stellar mass and supermassive black holes. We then describe the array of past, current, and future X-ray observatories which have bearing on relativistic studies of black holes before discussing how iron line spectroscopy has dramatically improved our current understanding of black hole astrophysics. We conclude by presenting the prospects for future research in this field.