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"The Evolution of Compact Binary Star Systems"
Konstantin A. Postnov and Lev R. Yungelson 
Abstract
1 Introduction
2 Observations of Double Compact Stars
3 Basic Principles of the Evolution of Binary Stars
4 Evolutionary Scenario for Compact Binaries with Neutron Star or Black Hole Components
5 Formation of Double Compact Binaries
6 Detection Rates
7 Short-Period Binaries with White-Dwarf Components
8 Observations of Double-Degenerate Systems
9 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
Indeed, to put a gas element of unit mass with specific volume v at a distance R around mass M from infinity, the work equal to the gravitational potential ϕ should be done; but then one should heat up the gas element, which is equivalent to give it the specific internal energy 𝜖, and also do Pv-work to empty space in the already present gas, hence ϕ+ H is relevant in calculating the binding energy of an isentropic envelope, where dH = Pdv.