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\@writefile{toc}{\contentsline {chapter}{\numberline {1}The Survival of Bars with Central Mass Concentrations}{1}}
\@writefile{toc}{\contentsline {section}{\numberline {1.1}Introduction}{1}}
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\@writefile{toc}{\contentsline {section}{\numberline {1.2}Model and Simulation Details}{2}}
\newlabel{sec:model}{{1.2}{2}}
\newlabel{eqn:bhmass}{{1.2}{3}}
\newlabel{eqn:halopotential}{{1.3}{3}}
\@writefile{lof}{\contentsline {figure}{\numberline {1.1}{\ignorespaces (a) Snapshots of particle positions showing the evolution of one simulation. The CMC with $M_{\rm  CMC}=2\%$ is grown from $t=700$ to 750 acoording to Eq.\nobreakspace  {}(1.2\hbox {}). Only about 1 out of 500 particles is plotted and the grid extends farther vertically than shown.}}{4}}
\newlabel{fig:snapshots}{{1.1}{4}}
\@writefile{toc}{\contentsline {section}{\numberline {1.3}Results}{4}}
\newlabel{sec:results}{{1.3}{4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.1}A fiducial run}{4}}
\newlabel{sec:fiducial}{{1.3.1}{4}}
\@writefile{lof}{\contentsline {figure}{\numberline {1.1}{\ignorespaces (b) The iso-density contours corresponding to the snapshots in (a). The contours are obtained by smoothing the discrete points with an adaptive kernel (Silverman 1986). The dashed ellipse (red) in each panel is the best fit ellipse with the largest ellipticity over SMA, analyzed with IRAF's isophote-fitting task {\tt  ellipse}. These best-fit ellipses appear to match the neighboring density contours quite well. Contours are separated by a constant factor of $10^{0.4}$.}}{5}}
\@writefile{lof}{\contentsline {figure}{\numberline {1.2}{\ignorespaces The time evolution of the bar amplitude $|A_2|$ (heavy solid line) and ellipticity $e$ measured at SMA=2.0, 1.75 and 1.5 (dotted, dash-dotted and dashed curves), respectively.}}{6}}
\newlabel{fig:ell_t}{{1.2}{6}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.2}Bar amplitude \unhbox \voidb@x \hbox {\relax \mathversion  {bold}$|A|$} vs. \unhbox \voidb@x \hbox {\relax \mathversion  {bold}$t_{\rm  growth}$}}{6}}
\newlabel{sec:A-tgrowth}{{1.3.2}{6}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.3}Bar amplitude \unhbox \voidb@x \hbox {\relax \mathversion  {bold}$|A|$} vs. \unhbox \voidb@x \hbox {\relax \mathversion  {bold}$\epsilon _{\rm  CMC}$}}{6}}
\newlabel{sec:A-ecmc}{{1.3.3}{6}}
\@writefile{lof}{\contentsline {figure}{\numberline {1.3}{\ignorespaces The bar amplitude $|A|$ evolution for runs with the same CMC, but grown with different growth time $t_{\rm  growth}$. The uppermost curve (orange) is a comparison run with no CMC grown. Note that the pattern speed of this initial bar is about 50 time units. }}{7}}
\newlabel{fig:A-tgrowth}{{1.3}{7}}
\@writefile{lof}{\contentsline {figure}{\numberline {1.4}{\ignorespaces The bar amplitude as a function of $\epsilon _{\rm  CMC}$, with other CMC parameters fixed. The bar amplitude is measured 250 time units after the central mass starts to grow. The solid (dark) and dashed (red) curves represent the runs for the weak and strong initial bars, respectively. Both curves show similar trends: smaller CMC scale-length cause significantly more damage to the bar, but this effect converges for some sufficiently small $\epsilon _{\rm  CMC}$.}}{7}}
\newlabel{fig:A-ecmc}{{1.4}{7}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.4}Bar amplitude \unhbox \voidb@x \hbox {\relax \mathversion  {bold}$|A|$} vs. \unhbox \voidb@x \hbox {\relax \mathversion  {bold}$M_{\rm  CMC}$}}{7}}
\newlabel{sec:A-mcmc}{{1.3.4}{7}}
\@writefile{lof}{\contentsline {figure}{\numberline {1.5}{\ignorespaces (a) The final bar amplitude as a function of $M_{\rm  CMC}$, with other CMC parameters fixed, for the weak initial bar. The solid (dark) and dashed (red) curves represent the runs with a ``hard'' ($\epsilon _{\rm  CMC}=0.001$) and ``soft'' CMC ($\epsilon _{\rm  CMC}=0.1$), respectively. The final bar amplitude decreases continuously as $M_{\rm  CMC}$ is increased, and ``hard'' CMCs apparently cause significantly more damage to the bar than ``soft'' ones. A few percent $M_{\rm  disk}$ for ``hard'' CMCs or more than ten percent $M_{\rm  disk}$ for ``soft'' ones is needed to destroy the bar effectively on short timescales. (b) As for (a), but for the strong initial bar.}}{8}}
\newlabel{fig:A-mcmc}{{1.5}{8}}
\@writefile{toc}{\contentsline {section}{\numberline {1.4}Parameter Tests and Numerical Checks}{8}}
\newlabel{sec:tests}{{1.4}{8}}
\@writefile{lof}{\contentsline {figure}{\numberline {1.6}{\ignorespaces (a) The bar amplitude of the same test run as a function of the time step $\Delta t$ adopted, for the weak initial bar. The bar amplitude is measured at some fixed time after the CMC growth stopped. The filled stars (dark) and filled square (red) represent the test runs with the guard annuli scheme and with only the normal time step, respectively. The final bar amplitude might be erroneously found to be weaker than it should be as the time step gets cruder, if without special cares around a large hard CMC, like guard annuli scheme we devised. (b) As for (a), but for the strong initial bar.}}{9}}
\newlabel{fig:timesteptest}{{1.6}{9}}
\@writefile{lof}{\contentsline {figure}{\numberline {1.7}{\ignorespaces The comparison between test runs using a rigid and a ``live'' halo for the nearly same halo potential. The bar-weakening trends of the two runs are very similar, suggesting the use of rigid halo is not a problem for the isothermal halo potential described in Eq.\nobreakspace  {}(1.3\hbox {}). And the bar destruction time scales are very similar in both rigid and live halo simulations.}}{9}}
\newlabel{fig:livehalotest}{{1.7}{9}}
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\@writefile{toc}{\contentsline {section}{\numberline {1.5}Conclusions}{10}}
\newlabel{sec:conclusions}{{1.5}{10}}
\@writefile{toc}{\contentsline {schapter}{{\normalfont  \rmfamily  References}}{10}}