\documentstyle{l-aa}
\begin{document}
\begin{center}
Appendix 
\end{center} 

\noindent
The tables included in this appendix summarize the results of the 
nonlinear survey of fundamental and first overtone RR Lyrae models 
computed in this investigation.
The amplitudes and periods listed in the tables are all referred 
to models whose dynamical behavior has approached its full amplitude.  
All model envelopes are characterized by a good spatial resolution
($\approx$ 100-150 zones) and 20 zones have been located above the 
hydrogen ionization region.  
The inner and outer boundary conditions of the static models were 
fixed by adopting the same procedure discussed in BS. 
The equilibrium models adopted in the present survey cover 90\% 
of the stellar radius and include few percents of the stellar mass. 
These conditions ensure a proper location of both the ionization 
regions and the dissipation zone. 

\noindent
The content of the tables is as follows:

\noindent
{\em Column 1)}: model identification number. The symbols enclosed in 
parentheses are referred to the modal stability. Models characterized 
by a stable or an unstable limit cycle are denoted by a plus $(+)$ and 
a minus $(-)$ symbol respectively. The static models are forced out of 
their equilibrium status 
by perturbing the linear radial eigenfunctions with a constant velocity 
amplitude
of 10 km $s^{-1}$. As soon as the nonlinear fluctuations due to the 
superposition of higher order modes settle down, the radial motions 
may approach a periodic pulsation (stable limit cycle, driving of the
pulsation) or the initial equilibrium structure (unstable limit cycle, 
quenching of the pulsation).
The models which show a mode switch (e.g. fundamental toward first 
overtone or viceversa) are denoted by an asterisk ($\ast$), whereas 
the models which present a mixture of different radial modes or 
amplitude modulations are denoted by a hash $(\#)$. 
The reader interested to a detailed discussion concerning the 
pulsation properties dependence on initial velocity perturbations 
is referred to Bono, Castellani \& Stellingwerf (1995). 

\noindent
{\em Column 2)}: static effective temperature (K).  

\noindent
{\em Column 3)}: number of periods covered during the direct time 
integration.  

\noindent
{\em Column 4)}: nonlinear periods (days).  

\noindent
{\em Column 5)}: fractional radial oscillation {\em i. e.} 
$\Delta R/R_{ph}\;=\; (R^{max}\,-\,R^{min}) / R_{ph} $ where
$R_{ph} $ is the photospheric radius. 

\noindent
{\em Column 6)}: radial velocity amplitude (km $s^{-1}$)  {\em i. e.}
$\Delta u \;=\; u^{max}\,-\,u^{min}$.  

\noindent
{\em Column 7)}: bolometric amplitude (mag.) {\em i. e.}  
$\Delta M_{bol} \;=\; M_{bol}^{max}\,-\,M_{bol}^{min}$.  

\noindent
{\em Column 8)}: logarithmic amplitude of the static surface gravity.  
$\Delta log g_s \;=\; log g_s^{max}\,-\, log g_s^{min}$.  

\noindent
{\em Column 9)}: logarithmic amplitude of the effective surface gravity.  
$\Delta log g_{eff} \;=\; log g_{eff}^{max}\,-\,log g_{eff}^{min}$ where 
$g_{eff}  \;=\; GM/R^2\,+\, du/dt$.  

\noindent
{\em Column 10)}: surface temperature amplitude (K).  
$\Delta T \;=\; T^{max}\,-\,T^{min})$ where $T$ is the temperature 
of the outermost zone. 

\noindent
{\em Column 11)}: surface effective temperature amplitude (K).  
$\Delta T_e \;=\; T_e^{max}\,-\,T_e^{min})$ where $T_e$ is 
derived from the surface luminosity.  
The temperature values listed in column 10 and 11 have been rounded to
the nearest 50 K. 
\end{document}
