Statistics of Compact Objects and Coalescence Rates

We review evolutionary scenarios, population statistics and merging rates of binary systems containing white dwarfs, neutron stars and black holes in the context of their impending detection as sources of gravitational waves. We begin in x1 with a census of the various systems currently known. In x2 we review the evolutionary scenarios which are thought to be the main routes for forming these systems. In x3 we look at the various selection e ects at play in the observed samples, as well as some of the techniques used to correct for these biases in x4. Population syntheses are outlined in x5. In x6, we review recent merger rate determinations for various types of binary systems. We conclude the review with an optimistic look to the future in x7. Statistics of Compact Objects and Coalescence Rates 17 1 The Compact-Object Binary Census This review is concerned with the statistics of compact objects in binary systems. Observationally, our knowledge of white dwarfs (WDs), neutron stars (NSs) and black holes (BHs) is improving all the time as state-of-the-art instruments (optical telescopes, revamped radio telescopes and new high-energy observatories) continue to discover new and exciting systems which can be studied in ever-increasing detail. Since many of these systems are expected to merge due to the emission of gravitational radiation, and emit gravitational waves upon coalescence, they are of great interest to the gravitational wave community given the imminent arrival of new detectors such as LIGO. We review the statistics of these sources and summarize the most recent estimates of the merging rates of the various binary systems. Table 1 summarizes the sample sizes of the various types of binary systems including compact objects, which have been observed so far. For binary systems containing two compact objects, the notation used throughout this review is to list the objects in chronological order of their formation. The only case, so far, where this is in fact required is when we need to distinguish between a WD{NS and a NS{WD binary system (see x2). Type of System We Observe Number WD{WD usually the brighter of the two white dwarfs 13 WD{NS radio pulsar and sometimes the white dwarf 2 NS{WD radio pulsar and sometimes the white dwarf 40 NS{NS (so far) one neutron star as a radio pulsar 5 NS{Main Seq. radio pulsar and the main-sequence star 2 NS{Giant low-mass X-ray bin. ; some QPOs and one XMSP 120 NS{Super Giant high-mass X-ray bin. ; sometimes X-ray pulses 70 BH{Giant low-mass X-ray bin. 3 BH{Super Giant high-mass X-ray bin. 7 Table 1: Compact-object binaries known from radio, optical and X-ray observations. QPO stands for quasi-periodic oscillation seen in some low-mass X-ray binaries and XMSP is shorthand for the X-ray millisecond pulsar SAX J1804.4{3658 discussed in x2. The systems in this table are a mixture of old friends (e.g. the lowand high-mass X-ray binaries), and more recent discoveries. The known population of WD{WD binaries is a good example of a growing sample which is bene ting from improved optical observations [34]. Radio pulsar observations provide a signi cant input to Table 1. The known pulsar population has doubled in the last few years thanks to two major surveys of the Galactic plane carried out using the multibeam system [46] on the Parkes radio telescope [15, 29]. Such a large haul of pulsars inevitably results in a number of interesting individual neutron stars, many of which are members of binary systems. Recent discoveries include a likely NS-NS binary [29], a likely WD{ NS system in a 5-hr relativistic orbit [23] as well as two relativistic NS-WD binaries at intermediate Galactic latitudes [15].