Figure 30

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"The Evolution of Compact Binary Star Systems"

Konstantin A. Postnov and Lev R. Yungelson

	Abstract
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
	Acknowledgments
	References
	Footnotes
	Updates
	Figures
	Tables

Figure 30: Dependence of the dimensionless strain amplitude for a WD + WD detached system with initial masses of the components of $0.6M ⊙ + 0.6 M ⊙$ (red line), a WD + WD system with $0.6M + 0.2M ⊙ ⊙$ (blue line) and a NS + WD system with $1.4M + 0.2 M ⊙ ⊙$ (green line). All systems have an initial separation of components $1 R ⊙$ and are assumed to be at a distance of 1 Kpc (i.e., the actual strength of the signal has to be scaled with factor $1∕d$ , with $d$ in Kpc). For the DD system, the line shows an evolution into contact, while for the other two systems the upper branches show pre-contact evolution and lower branches – a post-contact evolution with mass exchange. The total time-span of evolution covered by the tracks is 13.5 Gyr. Red dots mark the positions of systems with components’ mass ratio $q = 0.02$ , below which the conventional picture of evolution with a mass exchange may be not valid. The red dashed line marks the position of the confusion limit as determined in [519].