User:Tohline/Appendix/PolytropicBinaries
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Polytropic Models of Close Binary Star Systems
Over the past halfadozen years, Patrick Motl, Mario D'Souza, and Wes Even have used the Hachisu SCF technique to construct 3D equilibrium models of synchronously rotating, tidally distorted binary polytropes. To date, four of these models have been used extensively as initial states for our dynamical simulations of binary masstransfer. Various properties of these four SCFcodegenerated models are summarized in the following table; the listed parameters are:
: 
System mass ratio 
M : 
Mass 
a : 
Binary separation 
Ω : 
Orbital angular velocity 
J_{tot} : 
Total angular momentum 
ρ^{max} : 
Maximum (central) density 
K_{n} : 
Constant in the polytropic equation of state, 
V : 
Volume occupied by the star or by the Roche Lobe (RL) surrounding the star 
: 
Mean stellar radius 
: 
Rochelobe filling factor 
Properties of (n = 3 / 2) Polytropic Binary Systems 

Model 
Binary System 
Accretor 
Donor 


q 
M_{tot} 
a 
Ω 
J_{tot} 
M_{a} 


R_{a} 
M_{d} 


R_{d} 
f_{RL} 
Q13 
1.323 
0.0309 
0.8882 
0.2113 

0.0133 
1.0000 
0.0264 
0.2672 
0.0176 
0.6000 
0.0372 
0.3509 
0.968 
Q07 
0.70000 
0.02371 
0.83938 
0.20144 

0.013945 
1.0000 
0.02732 
0.2728 
0.009761 
0.6077 
0.02512 
0.2888 
0.998 
Q05 
0.500 

0.8764 
0.1174 


1.0000 
0.016 
0.2067 

0.235 
0.016 
0.2689 
0.898 
Q04 
0.4085 
0.02399 
0.8169 
0.2112 

0.01703 
1.0000 
0.03119 
0.2918 
0.006957 
0.71 
0.01904 
0.2453 
0.996 
References:

All of the parameter values listed in these tables are specified in dimensionless polytropic units, defined as follows:
Polytropic Units 
Here, Polytropic Units are defined such that the radial extent of the computational grid for the selfconsistentfield (SCF) model, R_{edge}, the maximum density of one binary component, , and the gravitational constant, G, are all unity, that is, . In an accompanying PDF document, we explain how to convert from this set of dimension code units to real (e.g., cgs) units. 
© 2014  2019 by Joel E. Tohline 