Binary systems that are composed of a black hole and a normal star are called blackhole binaries. In this chapter, the observational evidence for black holes and the specific properties of the black-hole binaries are discussed.
A black hole is a singular object in the framework of general relativity. In an early theoretical work based on general relativity, Oppenheimer and Snyder  showed that a sufficiently massive star, when all thermonuclear energy is exhausted, would collapse indefinitely and disappear inside a sphere of a limiting radius from which even photons could not escape (the "event horizon"). This radius is called the Schwarzschild radius Rs = 2Rg, where Rg = MG/c2 is the gravitational radius, and M, G, and c are the mass, the gravitational constant, and the light velocity, respectively. Such an object was later called a black hole. However, black holes had remained only in theoretical interests for a long time.
The real existence of stellar mass black holes came to light with the birth of X-ray astronomy (1962) . It began in early seventies with surprising discoveries that the bright X-ray source Cyg X-1 is a binary system and that its X-ray emitting compact object is much more massive than a neutron star (Sect. 16.2). Since then, many stellar-mass black holes have been found among binary X-ray sources: X-ray binaries (hereafter abbreviated to XBs). It is to be emphasized that X-ray observations have played a unique role in the study of black holes, since X-ray observation is practically the only means to discover black-hole binaries. The presently known stellar-mass black holes were all discovered from XBs. The discovery of black holes was certainly one of the highlights of astronomy in the twentieth century.
The observational identification of black holes is not straightforward. The direct proof for a black hole would be to demonstrate the presence of an event horizon in a compact (gravitationally collapsed) object. This requires (1) to confirm complete absence of a material surface, and (2) to find the general relativistic effects that are genuinely unique near the event horizon, such as particle motion near the speed of light, a large gravitational redshift, bending of the light path. Observed facts in support of these have been accumulating, but not yet established as indisputable evidence.
So far, the most reliable evidence for a black hole has come from the mass determination by showing that the mass of the compact object exceeds 3M0. To the best of our current knowledge, any compact object more massive than 3M0, the firm mass upper limit of a stable neutron star in general relativity, is believed to have no other fate than to collapse into a black hole.
Once the optical counterpart of an XB is identified, optical observation allows mass estimation of the compact object (Sect. 16.3). At present, 20 compact objects in XBs are known to have a mass greater than 3M0 (see Table 16.1). On this basis, they are considered to be "secure" black holes. (Note that black holes can in principle have any mass, hence black holes of <3M0, if they exist, are missed with this criterion.) Even so, the genuine general relativistic tests are not as yet perfect. In this sense, one can say that the presence of stellar mass black holes is virtually solid, though not strictly proven.
A wealth of observational results on XBs has become available in the last few decades. Accordingly, studies of the X-ray properties of XBs have much advanced, and fair understanding of the nature of their X-ray emission has been obtained. In particular, from the study of the secure (>3M0) black-hole binaries, it is found that most of them share common X-ray properties that are distinctly different from XBs containing a neutron star ("neutron-star XBs"), as discussed in Sect. 16.4. On the basis of these properties, one can select black hole "candidates" from the X-ray observations alone. In addition, recent multiwavelength observations from radio through gamma-rays also provide important clues to black holes.
Notably, most of the black-hole binaries are not persistently bright in X-rays, but they are transient sources undergoing an X-ray outburst only for a short while (Sect. 16.4.2). It is, therefore, obvious that many more black-hole binaries exist in our Galaxy, though most of them are X-ray quiet.
The above topics and other relevant topics on stellar-mass black holes are discussed in the following sections, based on the results available as of late 2005. The references are admittedly limited. For more details, we refer to previous reviews, e.g., Tanaka and Lewin , Tanaka and Shibazaki , and a more recent extensive review by McClintock and Remillard , and the references therein.
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