# Freeze-out surfaces

Huichao Song, 05/17/2008

Freeze-out surface (T_dec = 130 MeV) for ideal and viscous hydro (HS+UH, VISH2+1 with full I-S eqns.):

The figure above was updated on 08/04/2008 by H.S. to include an comparison between different full I-S eqn:

• full I-S eqn-(R&R): ${\displaystyle \Delta _{j}^{m}\Delta _{k}^{n}{\dot {\pi }}^{jk}=-{\frac {1}{\tau _{\pi }}}(\pi ^{mn}{-}2\eta \sigma ^{mn})+{\frac {1}{2}}\pi ^{mn}\left(5D(\ln T)-\partial _{k}u^{k}\right)}$
• full I-S eqn-(S&H):${\displaystyle \Delta _{j}^{m}\Delta _{k}^{n}{\dot {\pi }}^{jk}=-{\frac {1}{\tau _{\pi }}}(\pi ^{mn}{-}2\eta \sigma ^{mn})-{\frac {1}{2}}\pi ^{mn}{\frac {\eta T}{\tau _{\pi }}}d_{k}\left({\frac {\tau _{\pi }}{\eta T}}u^{k}\right)}$

The figure above was updated on 7/23/2008 by H.S. to include an ideal hydro curve (light blue) from AZHYDRO which differs from VISH2+1 by an additional time splitting step in the transport algorithm (which should make it more accurate).

Other formats and data tables for this figure can be downloaded here: Au-global-0508.tar