[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 300)

[cott at tapir.caltech.edu]

User: cott
Date: 2012/03/13 01:27 AM

Modified:
 /
  ET.tex

Log:
 * add text clarifying hybrid EOS

File Changes:

Directory: /
============

File [modified]: ET.tex
Delta lines: +11 -1
===================================================================
--- ET.tex	2012-03-13 06:03:14 UTC (rev 299)
+++ ET.tex	2012-03-13 06:27:49 UTC (rev 300)
@@ -1845,7 +1845,17 @@
   \label{eq:hybrid_eos}
 \end{eqnarray}%
 In this,  the total specific internal energy $\epsilon$
-consists of a polytropic and a thermal contribution. In iron core
+consists of a polytropic and a thermal contribution. The variable $\Gamma$
+assumes one of two values,
+\begin{equation}
+\Gamma = \left\{\begin{array}{ll}
+\Gamma_1 & \mathrm{for}\,\,\rho < \rho_\mathrm{nuc}\,\,,\\
+\Gamma_2 & \mathrm{for}\,\,\rho \ge \rho_\mathrm{nuc}\,\,,
+\end{array} \right.
+\end{equation}
+where $\rho_\mathrm{nuc}$ is typically set to $2\times 10^{14}\,\mathrm{g}\,\mathrm{cm}^{-3}$.
+
+In iron core
 collapse, the pressure below nuclear density is dominated by the
 pressure of relativistically degenerate electrons. For this, one sets
 $K = 4.897 \times 10^{14}$ [cgs] in the above. The thermal index