"The Evolution of Compact Binary Star Systems"
Konstantin A. Postnov and Lev R. Yungelson 
1 Introduction
1.1 Formation of stars and end products of their evolution
1.2 Binary stars
2 Observations of Double Compact Stars
2.1 Compact binaries with neutron stars
2.2 How frequent are NS binary coalescences?
2.3 Black holes in binary systems
2.4 A model-independent upper limit on the BH-BH/BH-NS coalescence rate
3 Basic Principles of the Evolution of Binary Stars
3.1 Keplerian binary system and radiation back reaction
3.2 Mass exchange in close binaries
3.3 Mass transfer modes and mass and angular momentum loss in binary systems
3.4 Supernova explosion
3.5 Kick velocity of neutron stars
3.6 Common envelope stage
3.7 Other notes on the CE problem
4 Evolutionary Scenario for Compact Binaries with Neutron Star or Black Hole Components
4.1 Compact binaries with neutron stars
4.2 Black-hole–formation parameters
5 Formation of Double Compact Binaries
5.1 Analytical estimates
5.2 Population synthesis results
6 Detection Rates
7 Short-Period Binaries with White-Dwarf Components
7.1 Formation of compact binaries with white dwarfs
7.2 White-dwarf binaries
7.3 Type Ia supernovae
7.4 Ultra-compact X-ray binaries
8 Observations of Double-Degenerate Systems
8.1 Detached white dwarf and subdwarf binaries
9 Evolution of Interacting Double-Degenerate Systems
9.1 “Double-degenerate family” of AM CVn stars
9.2 “Helium-star family” of AM CVn stars
9.3 Final stages of evolution of interacting double-degenerate systems
10 Gravitational Waves from Compact Binaries with White-Dwarf Components
11 AM CVn-Type Stars as Sources of Optical and X-Ray Emission
12 Conclusions
Figure 10
Figure 10: Limits of different burning regimes of accreted hydrogen onto a CO WD as a function of mass of the WD and accretion rate ˙ M [535]. If ˙ ˙ ˙ Mstable ≲ M ≲ MRG, hydrogen burns steadily. If M˙ ≲ M˙stable, H-burning shells are thermally unstable; with decrease of M˙ the strength of flashes increases. For M˙ ≳ M˙RG, hydrogen burns steadily but the excess of unburnt matter forms an extended red-giant–sized envelope. In the latter case white dwarfs may lose matter by wind or due to Roche lobe overflow. A dotted line shows the Eddington accretion rate M˙ Edd as a function of MWD. The dashed lines are the loci of the hydrogen envelope mass at hydrogen ignition. Image reproduced with permission from [535], copyright by AAS.