\relax 
\citation{Moore:1994}
\citation{FloresPrimack:94}
\citation{KravtsovCores:1998}
\citation{BoschSwaters:2001}
\citation{Lokas:01}
\citation{deBlokMcGaughRubin:2001}
\citation{KlypinSatellites:99}
\citation{MooreSatellites:99}
\citation{ZhaoMao:96}
\citation{BinneyEvans:01}
\citation{KlypinZS:02}
\citation{DehnenBinney:98}
\citation{NavarroSteinmetz:00}
\citation{HernandezAvila:01}
\citation{EkeNavarroSteinmetz:01}
\citation{KlypinZS:02}
\citation{Weinberg:85}
\citation{HernquistWeinberg:92}
\citation{HernquistWeinberg:92}
\citation{CombesSanders:81}
\citation{SellwoodAthanassoula:86}
\citation{DB:99}
\citation{DB:2000}
\citation{AthanassoulaMisiriotis:02}
\citation{Weinberg:85}
\citation{HernquistWeinberg:92}
\citation{DB:99}
\citation{DB:2000}
\citation{TremainWeinberg:84}
\citation{DB:99}
\citation{DB:2000}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
\newlabel{sec:intro}{{1}{1}}
\citation{DB:99}
\citation{DB:2000}
\citation{AthanassoulaMisiriotis:02}
\citation{Elmegreen:85}
\citation{BlitzSpergel:91}
\citation{Zhao:96}
\citation{Freudenreich:98}
\citation{Gerhard:02}
\citation{DehnenBinney:98}
\citation{Hammersley:99}
\citation{Gerhard:02}
\citation{DB:99}
\citation{DB:2000}
\citation{AthanassoulaMisiriotis:02}
\citation{Weinberg:98}
\citation{DB:2000}
\citation{DB:2000}
\citation{DB:99}
\citation{DB:2000}
\citation{Fux:97}
\citation{KlypinZS:02}
\citation{Fux:97}
\citation{DB:2000}
\citation{NFW:97}
\citation{Fux:97}
\citation{AthanassoulaMisiriotis:02}
\citation{DB:2000}
\citation{Hohl:97}
\citation{OstrikerPeebles:73}
\citation{Miller:78}
\citation{Hernquist:93}
\@writefile{toc}{\contentsline {section}{\numberline {2}Models}{2}}
\newlabel{sec:models}{{2}{2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Initial conditions: densities and velocities}{2}}
\newlabel{sec:IC}{{2.1}{2}}
\newlabel{eq:expdisk}{{1}{2}}
\citation{NFW:97}
\citation{Colin:00}
\citation{KlypinZS:02}
\citation{KlypinZS:02}
\citation{El-ZantShlossman:01}
\newlabel{eq:vertical}{{2}{3}}
\newlabel{eq:radial}{{3}{3}}
\newlabel{eq:radiall}{{4}{3}}
\newlabel{eq:phivelocity}{{6}{3}}
\newlabel{eq:NFW}{{8}{3}}
\newlabel{eq:radialDM}{{9}{3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Choice of parameters}{3}}
\newlabel{sec:parameters}{{2.2}{3}}
\citation{KlypinZS:02}
\citation{KlypinZS:02}
\citation{KlypinZS:02}
\citation{KlypinZS:02}
\citation{KlypinZS:02}
\citation{KlypinZS:02}
\citation{kkk:97}
\citation{kravtsov:99}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Initial and final circular velocities for model {\it  A}$_1$\ (left panels) and for model {\it  B}\ (right panels). Dashed curves show the contribution of the stellar component $\sqrt  {GM(r)/r}$. The dot-dashed curves are for the dark matter. Final models show the total stellar contribution: disk and bar contributions are combined. Initially model {\it  A}$_1$\ has a sub-maximum disk with the density of the disk being close to the density of the dark matter inside the central 3\nobreakspace  {}kpc region. Model {\it  B}\ is more dominated by the disk component: the crossing point of the disk and dark matter is at 9\nobreakspace  {}kpc. }}{4}}
\newlabel{fig:Vc}{{1}{4}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Initial parameters of models}}{4}}
\newlabel{param}{{1}{4}}
\newlabel{table:initial}{{1}{4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Numerical simulations}{4}}
\newlabel{sec:simulations}{{2.3}{4}}
\citation{kravtsov:99}
\citation{knebe_etal:00}
\citation{DB:99}
\citation{DB:2000}
\citation{AthanassoulaMisiriotis:02}
\citation{DB:99}
\citation{DB:2000}
\citation{AthanassoulaMisiriotis:02}
\citation{DB:2000}
\citation{AthanassoulaMisiriotis:02}
\citation{DB:2000}
\citation{DB:2000}
\citation{AthanassoulaMisiriotis:02}
\citation{DB:2000}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Finding the bar}{5}}
\newlabel{sec:bar}{{2.4}{5}}
\newlabel{eq:fourier}{{10}{5}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Distribution of the stellar component at different stages of evolution for model {\it  A}$_1$. Starting from the left bottom panel in the clock-wise direction the panels correspond to the initial moment; 1\nobreakspace  {}Gyr; 2\nobreakspace  {}Gyr; 3.3\nobreakspace  {}Gyr. The disk rotates counter-clockwise. To avoid crowding we show only every fifth particle. At the distance 5\nobreakspace  {}kpc the disk made 20 orbital periods during 3.3\nobreakspace  {}Gyr.}}{6}}
\newlabel{fig:evol}{{2}{6}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Evolution}{7}}
\newlabel{sec:evolution}{{3}{7}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Evolution of fraction of disk mass inside given radius. The top panel is for models {\it  A}$_1$\ (full curves) and {\it  A}$_2$. The bottom panel shows model {\it  B}. The total mass inside 5\nobreakspace  {}kpc practically does not change with time. Most of the mass exchange happens inside the central 1 -- 2\nobreakspace  {}kpc. The disk mass inside the central 1\nobreakspace  {}kpc region increased by a factor 4 by the end of evolution. The time-scale of evolution is about twice shorter in the case of the more disk-dominated model {\it  B}\ and the colder model {\it  A}$_2$.}}{7}}
\newlabel{fig:Massevol}{{3}{7}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Angular momentum}{7}}
\newlabel{sec:Angmom}{{4}{7}}
\citation{DB:2000}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces The baryon-to-dark matter ratios (bottom panels) and the ratio of the rotational velocity to the velocity dispersion (top panels) for model {\it  A}$_1$\ (left panels) and model {\it  B}\ (right panels). The dash curves show the initial models. The final models are shown with full curves. The central growth of the density goes at the expense of the stellar density in the middle 2 -- 8\nobreakspace  {}kpc region. At those radii the final baryon-to-dark matter ratio went down producing dark-matter dominated disk. The top panels show that the heating of the disk preferentially happens in the outer regions outside of the bar. Spiral waves may cause the heating. }}{8}}
\newlabel{fig:profile}{{4}{8}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Evolution of the specific angular momentum of the disk for the {\it  A}$_1$\ (top panel) and the {\it  B}\ (bottom panel) models. The top curves in each panel show that the total angular momentum of disk particles declines very little -- few per cent after 4.5\nobreakspace  {}Gyrs of evolution. The other curves present an average specific angular momentum for disk particles inside spherical shells indicated in the plot. Only the very central region (radius less than 1\nobreakspace  {}kpc) exhibits some decrease (a factor of 1.5) of angular momentum. Outside the very center the specific angular momentum does not change. }}{8}}
\newlabel{fig:AngProfile}{{6}{8}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Evolution of the bar amplitude (bottom panels), the pattern speed (middle panels), and disk angular momentum for the models {\it  A}$_1$\ (left column of panels), {\it  A}$_2$\ (middle column of panels) and {\it  B}\ (right column). In all cases the angular momentum declines due to the dynamical friction with the dark matter. The decline is very small - only few percent for $\sim 5$\nobreakspace  {}Gyrs of evolution. Note the complex behavior of bar amplitude and its correlation with the pattern speed. The pattern speed remains almost constant during periods, when the bar amplitude does not evolve (e.g., $t=2-5$\nobreakspace  {}Gyrs for model {\it  A}$_1$or $t=5-7$\nobreakspace  {}Gyrs for model {\it  A}$_2$). Periods of fast increase of the bar amplitude correlate with the decline of the pattern speed (e.g.,$t=3-5$\nobreakspace  {}Gyrs for model {\it  A}$_2$). }}{9}}
\newlabel{fig:Levol}{{5}{9}}
\citation{DB:2000}
\citation{DB:2000}
\citation{DB:2000}
\citation{DB:2000}
\citation{DB:2000}
\citation{DB:2000}
\citation{DB:2000}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Distribution of the z-component of the angular momentum of the stellar particles for models {\it  A}$_1$\ (top panel) and {\it  B}\ (bottom panel) at different moments of time. Initial distribution is shown by dot-dashed curves. Particles with low angular momentum are preferentially at small radii. Large angular momentum is coming from particles at large distances. Dashed curves are for 1-1.5\nobreakspace  {}Gyrs after the beginning of the evolution. The final distribution (full curves, 4.5-5\nobreakspace  {}Gyrs) is qualitatively the same for both models. The peak at small angular momenta corresponds to the bar. The number of particles with intermediate angular momenta substantially decreases during the evolution. There is an excess of particles with very large angular momentum. The changes in the distribution are much stronger in the case of model {\it  B}, which has less dark matter and has a more massive disk. }}{10}}
\newlabel{fig:Angmom}{{7}{10}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Structure of bars: the pattern speed and the surface density}{10}}
\newlabel{sec:BarStructure}{{5}{10}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces  Distribution of z-component of the angular momentum of dark matter particles at different moments. Dashed and full curves are for initial and advanced moments (3.3 Gyrs for {\it  A}$_1$\ and 4.5 Gyrs for {\it  B}) of evolution. We present results only for 10000 particles, which initially were in a spherical shell centered at 3\nobreakspace  {}kpc. Particles at other radii showed even smaller effects. The changes in the angular momentum are clearly seen in both models: there are more particles with high angular momentum. This indicates that the dynamical friction transfers some angular momentum to the dark matter, but the effect is extremely weak. }}{10}}
\newlabel{fig:dmrotation}{{8}{10}}
\citation{AthanassoulaMisiriotis:02}
\citation{AthanassoulaMisiriotis:02}
\citation{AthanassoulaMisiriotis:02}
\citation{DB:2000}
\citation{AthanassoulaMisiriotis:02}
\citation{Sellwood:02}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Different frequencies in models {\it  A}$_1$, {\it  A}$_2$, and {\it  B}. The full curves show the frequency of rotation of the disk $\Omega _{\rm  rot} \equiv V_{\phi }/R$. The dashed curves present the frequency of rotation for a cold disk $\Omega _{\rm  circ}\equiv \sqrt  {GM/R^3}$. The difference between the two frequencies are due to the asymmetric drift. The dotted horizontal lines show the frequency of rotation of the bars. The extension of the bars in the models is indicated by the thick lines. The distance of a bar from the rotation curves is a measure of how fast is the bar. The bar in the model {\it  B}\ is clearly a very fast bar, which extends almost up to the corotation. The bars in models $A$ rotate slower, but they are still fast bars. }}{11}}
\newlabel{fig:OmegRot}{{9}{11}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Discussion}{11}}
\newlabel{sec:discussion}{{6}{11}}
\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Surface density profiles of the stellar components for models {\it  A}$_1$, {\it  A}$_2$, and {\it  B}. The full curves present the azimuthally averaged profiles. Dashed curves show double exponential fits with parameters presented in the plots. The dotted curves show the surface density along the major axes of the bars. The surface densities along the minor bar axis are shown with the dot-dashed curves. All the curves are obtained by averaging over three time moments covering about 0.5\nobreakspace  {}Gyr. For comparison a large dot shows the surface density of the disk (stars + gas) for our Galaxy at the solar position. }}{11}}
\newlabel{fig:bulge}{{10}{11}}
\citation{AthanassoulaMisiriotis:02}
\citation{AthanassoulaMisiriotis:02}
\citation{AthanassoulaMisiriotis:02}
\citation{AthanassoulaMisiriotis:02}
\citation{AthanassoulaMisiriotis:02}
\citation{AthanassoulaMisiriotis:02}
\citation{AthanassoulaMisiriotis:02}
\citation{AthanassoulaMisiriotis:02}
\citation{DB:2000}
\citation{AthanassoulaMisiriotis:02}
\citation{AthanassoulaMisiriotis:02}
\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Evolution of the pattern speed and the bar amplitude in a simulation with initially cold disk with $Q=0.05$. Other parameters of the simulation are the same as for model {\it  A}$_1$. The simulation was done with a very low resolution of 0.5\nobreakspace  {}kpc to mimic results of Debatista \& Sellwood (2000). In this case the pattern speed quickly decreases with time giving an impression that the bar is slowed down by the dynamical friction with the dark matter. This ``slowing down'' of the bar is an artifact of unrealistically cold disk and grossly insufficient force resolution.}}{12}}
\newlabel{fig:OmegapLR}{{11}{12}}
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Effects of resolution on bar formation in model {\it  A}$_2$. Left panels show stellar particles in the simulation, which reached 20\nobreakspace  {}pc resolution. Right panels show the same model simulated with the resolution limited to 350\nobreakspace  {}pc. The top panels are for 2\nobreakspace  {}Gyrs after initial moment; the bottom panels are for 4.5\nobreakspace  {}Gyrs. The high resolution run has a very short (1\nobreakspace  {}kpc) bar for 3\nobreakspace  {}Gyrs, while the low resolution run has remarkably strong and long bar from the very beginning. Axes are labeled in units of kpc. This figure illustrates that numerical resolution can significantly affect structure of a bar. Lack of resolution results in longer and stronger bars. }}{12}}
\newlabel{fig:pointsRes}{{12}{12}}
\citation{Weinberg:85}
\citation{Weinberg:85}
\citation{LittleCarlberga:91}
\citation{WeinbergKatz:2001}
\@writefile{toc}{\contentsline {section}{\numberline {7}Conclusions}{13}}
\newlabel{sec:conclusions}{{7}{13}}
\bibstyle{mn2e}
\bibdata{bars}
\bibcite{AthanassoulaMisiriotis:02}{{1}{2002}{{{Athanassoula} \& {Misiriotis}}}{{{Athanassoula} \& {Misiriotis}}}}
\bibcite{BinneyEvans:01}{{2}{2001}{{{Binney} \& {Evans}}}{{{Binney} \& {Evans}}}}
\bibcite{BlitzSpergel:91}{{3}{1991}{{{Blitz} \& {Spergel}}}{{{Blitz} \& {Spergel}}}}
\bibcite{Colin:00}{{4}{2000}{{{Col{\' i}n} et~al.}}{{{Col{\' i}n}, {Klypin} \& {Kravtsov}}}}
\bibcite{CombesSanders:81}{{5}{1981}{{{Combes} \& {Sanders}}}{{{Combes} \& {Sanders}}}}
\bibcite{deBlokMcGaughRubin:2001}{{6}{2001}{{{de Blok} et~al.}}{{{de Blok}, {McGaugh} \& {Rubin}}}}
\bibcite{DB:99}{{7}{1998}{{{Debattista} \& {Sellwood}}}{{{Debattista} \& {Sellwood}}}}
\bibcite{DB:2000}{{8}{2000}{{{Debattista} \& {Sellwood}}}{{{Debattista} \& {Sellwood}}}}
\bibcite{DehnenBinney:98}{{9}{1998}{{{Dehnen} \& {Binney}}}{{{Dehnen} \& {Binney}}}}
\bibcite{EkeNavarroSteinmetz:01}{{10}{2001}{{{Eke} et~al.}}{{{Eke}, {Navarro} \& {Steinmetz}}}}
\bibcite{El-ZantShlossman:01}{{11}{2001}{{{El-Zant} et~al.}}{{{El-Zant}, {Shlosman} \& {Hoffman}}}}
\bibcite{Elmegreen:85}{{12}{1985}{{{Elmegreen} \& {Elmegreen}}}{{{Elmegreen} \& {Elmegreen}}}}
\bibcite{FloresPrimack:94}{{13}{1994}{{{Flores} \& {Primack}}}{{{Flores} \& {Primack}}}}
\bibcite{Freudenreich:98}{{14}{1998}{{{Freudenreich}}}{{{Freudenreich}}}}
\bibcite{Fux:97}{{15}{1997}{{{Fux}}}{{{Fux}}}}
\bibcite{Gerhard:02}{{16}{2002}{{{Gerhard}}}{{{Gerhard}}}}
\bibcite{Hammersley:99}{{17}{1999}{{{Hammersley} et~al.}}{{{Hammersley}, {Cohen}, {Garz{\' o}n}, {Mahoney} \& {L{\' o}pez-Corredoira}}}}
\bibcite{HernandezAvila:01}{{18}{2001}{{{Hern{\' a}ndez} et~al.}}{{{Hern{\' a}ndez}, {Avila-Reese} \& {Firmani}}}}
\bibcite{Hernquist:93}{{19}{1993}{{{Hernquist}}}{{{Hernquist}}}}
\bibcite{HernquistWeinberg:92}{{20}{1992}{{{Hernquist} \& {Weinberg}}}{{{Hernquist} \& {Weinberg}}}}
\bibcite{Hohl:97}{{21}{1971}{{{Hohl}}}{{{Hohl}}}}
\bibcite{KlypinSatellites:99}{{22}{1999}{{{Klypin} et~al.}}{{{Klypin}, {Kravtsov}, {Valenzuela} \& {Prada}}}}
\bibcite{KlypinZS:02}{{23}{2002}{{{Klypin} et~al.}}{{{Klypin}, {Zhao} \& {Somerville}}}}
\bibcite{knebe_etal:00}{{24}{2000}{{{Knebe} et~al.}}{{{Knebe}, {Kravtsov}, {Gottl{\" o}ber} \& {Klypin}}}}
\bibcite{kravtsov:99}{{25}{1999}{{{Kravtsov}}}{{{Kravtsov}}}}
\bibcite{KravtsovCores:1998}{{26}{1998}{{{Kravtsov} et~al.}}{{{Kravtsov}, {Klypin}, {Bullock} \& {Primack}}}}
\bibcite{kkk:97}{{27}{1997}{{{Kravtsov} et~al.}}{{{Kravtsov}, {Klypin} \& {Khokhlov}}}}
\bibcite{LittleCarlberga:91}{{28}{1991}{{{Little} \& {Carlberg}}}{{{Little} \& {Carlberg}}}}
\bibcite{Lokas:01}{{29}{2001}{{{{\L }okas}}}{{{{\L }okas}}}}
\bibcite{Miller:78}{{30}{1978}{{{Miller}}}{{{Miller}}}}
\bibcite{Moore:1994}{{31}{1994}{{{Moore}}}{{{Moore}}}}
\bibcite{MooreSatellites:99}{{32}{1999}{{{Moore} et~al.}}{{{Moore}, {Ghigna}, {Governato}, {Lake}, {Quinn}, {Stadel} \& {Tozzi}}}}
\bibcite{NFW:97}{{33}{1997}{{{Navarro} et~al.}}{{{Navarro}, {Frenk} \& {White}}}}
\bibcite{NavarroSteinmetz:00}{{34}{2000}{{{Navarro} \& {Steinmetz}}}{{{Navarro} \& {Steinmetz}}}}
\bibcite{OstrikerPeebles:73}{{35}{1973}{{{Ostriker} \& {Peebles}}}{{{Ostriker} \& {Peebles}}}}
\bibcite{Sellwood:02}{{36}{2002}{{{Sellwood}}}{{{Sellwood}}}}
\bibcite{SellwoodAthanassoula:86}{{37}{1986}{{{Sellwood} \& {Athanassoula}}}{{{Sellwood} \& {Athanassoula}}}}
\bibcite{TremainWeinberg:84}{{38}{1984}{{{Tremaine} \& {Weinberg}}}{{{Tremaine} \& {Weinberg}}}}
\bibcite{BoschSwaters:2001}{{39}{2001}{{{van den Bosch} \& {Swaters}}}{{{van den Bosch} \& {Swaters}}}}
\bibcite{Weinberg:85}{{40}{1985}{{{Weinberg}}}{{{Weinberg}}}}
\bibcite{Weinberg:98}{{41}{1998}{{{Weinberg}}}{{{Weinberg}}}}
\bibcite{WeinbergKatz:2001}{{42}{2001}{{{Weinberg} \& {Katz}}}{{{Weinberg} \& {Katz}}}}
\bibcite{ZhaoMao:96}{{43}{1996}{{{Zhao} \& {Mao}}}{{{Zhao} \& {Mao}}}}
\bibcite{Zhao:96}{{44}{1996}{{{Zhao}}}{{{Zhao}}}}