Tohline: /* Polytropic Models of Close Binary Star Systems */ swap location of defining relation for R

2010-08-05T17:23:46Z

Polytropic Models of Close Binary Star Systems: swap location of defining relation for R

← Older revision		Revision as of 17:23, 5 August 2010
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	<tr>		<tr>
	<td align="right">		<td align="right">
	<math>R</math>  :		<math>R\equiv [3V/(4\pi)]^{1/3}</math>  :
	</td>		</td>
	<td align="left">		<td align="left">
	Mean stellar radius~~, where <math>R \equiv [3V/(4\pi)]^{1/3}</math>~~		Mean stellar radius
	</td>		</td>
	</tr>		</tr>

Tohline: /* Polytropic Models of Close Binary Star Systems */ Add summary table

2010-08-05T17:17:19Z

Polytropic Models of Close Binary Star Systems: Add summary table

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Tohline: Start entering tabulated information on binary polytropes

2010-07-24T15:45:25Z

Start entering tabulated information on binary polytropes

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{{LSU_HBook_header}}

=Polytropic Models of Close Binary Star Systems=

Over the past half-a-dozen 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 mass-transfer. Various properties of these four SCF-code-generated models are summarized in the following tables; the system mass-ratio is given by the parameter <math>q \equiv M_\mathrm{donor}/M_\mathrm{accretor}</math>.

* Model '''Q13''' (<math>q = 1.323</math>): Table 4 in [http://iopscience.iop.org/0004-637X/643/1/381/pdf/63230.web.pdf publication DMTF06]
* Model '''Q07''' (<math>q = 0.700</math>): First page of the [http://www.phys.lsu.edu/~tohline/clayton/q07.pdf accompanying PDF document].
* Model '''Q05''' (<math>q = 0.500</math>): Table 5 in [http://iopscience.iop.org/0004-637X/643/1/381/pdf/63230.web.pdf publication DMTF06]
* Model '''Q04''' (<math>q = 0.4085</math>): Table 1 in [http://iopscience.iop.org/0004-637X/670/2/1314/pdf/71427.web.pdf publication MFTD07]

All of the parameter values listed in these tables are specified in dimensionless ''polytropic units'', defined as follows:

<table border="1" cellpadding="20" align="center" width="75%">
<tr>
<td align="center">
<font color="blue"><b>Polytropic Units</b></font>
</td>
</tr>
<tr>
<td align="left">
Here, ''Polytropic Units'' are defined such that the radial extent of the computational grid for the self-consistent-field (SCF) model, <math>R_\mathrm{edge}</math>,
the maximum density of one binary component, <math>\rho^\mathrm{max}_\mathrm{Accretor}</math>, and the gravitational
constant, <math>G</math>, are all unity, that is,
<div align="center">
<math>G = \rho^\mathrm{max}_\mathrm{Accretor} = R_\mathrm{edge} = 1</math>.
</div>
</td>
</tr>
</table>

In another [http://www.phys.lsu.edu/~tohline/clayton/PolytropicUnits.pdf accompanying PDF document], we explain how to convert from this set of dimension code units to real (''e.g.,'' cgs) units.

 <br />
{{LSU_HBook_footer}}

User:Tohline/Appendix/PolytropicBinaries - Revision history

Tohline: /* Polytropic Models of Close Binary Star Systems */ swap location of defining relation for R

Tohline: /* Polytropic Models of Close Binary Star Systems */ Add summary table

Tohline: Start entering tabulated information on binary polytropes