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\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Image Preparation}{7}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Decomposition Steps}{8}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Choosing the Best Fit Between Stage 2 and Stage 3}{10}}
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\@writefile{toc}{\contentsline {section}{\numberline {4}Extra Tests to Verify Correctness of Fits}{11}}
\newlabel{stests}{{4}{11}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Using $1D$ Decomposition To Generate Guesses for Bulge Parameters}{12}}
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\@writefile{toc}{\contentsline {section}{\numberline {5}Results and Discussion}{13}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Impact of Bars in $2D$ Decomposition }{13}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Mass in Bulges, Disks, and Bars}{14}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Distribution of Bulge Index and $B/T$}{15}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Comparison With Independent Decompositions}{16}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {5.5}Comparison of $B/T$ to Hierarchical Models of Galaxy Evolution}{17}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {5.6}Revisiting Bulge Formation in Hierarchical Models of Galaxy Evolution}{19}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {5.7}Bar Strength}{20}}
\newlabel{sbar2}{{5.7}{20}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.8}Bar Fraction as Function of $B/T$ and Bulge Index}{21}}
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\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces OSUBSGS Galaxies (N=146) }}{29}}
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\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces OSUBSGS Galaxies (N=146) }}{32}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Structural Parameters of 146 OSUBSGS Galaxies }}{33}}
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\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Structural Parameters of 146 OSUBSGS Galaxies }}{34}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Structural Parameters of 146 OSUBSGS Galaxies }}{35}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Structural Parameters of 146 OSUBSGS Galaxies }}{36}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Structural Parameters of 146 OSUBSGS Galaxies }}{37}}
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Checking GALFIT Robustness With Different Input Guesses}}{38}}
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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The distribution of absolute $B$-band magnitudes for the OSUBSGS sample before (unshaded) and after (shaded) the cut to remove highly inclined ($i > 70^\circ $) spiral galaxies. }}{39}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces The distribution of Hubble types for for the OSUBSGS sample before (unshaded) and after (shaded) the cut to remove highly inclined ($i > 70^\circ $) spiral galaxies. The sample is dominated by Hubble types S0/a to Sc. }}{40}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces The OSUBSGS luminosity function is compared the $B$-band Schechter luminosity function (SLF). The former is calculated as described in \S  2.1\hbox {} using equation (1\hbox {}). The parameters for the SLF are $\Phi ^*=5.488\times 10^{-3}$ Mpc$^{-3}$, $\alpha =-1.07$, and $M^*_B=-20.5$, corresponding to $H_0$=70 km/s Mpc$^{-1}$. }}{41}}
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\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Stellar mass distribution of OSUBSGS galaxies as determined in \S  2.2\hbox {}. }}{42}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces An overview of the method of decomposition. All images are subjected to Stages 1-3. Either the output of Stage 2 or Stage 3 is chosen as the best model. }}{43}}
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\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Complete $2D$ decomposition for NGC 4643. Note the prominent bar residuals in the residual for the Stage 1 and Stage 2 bulge-disk decomposition. This is a case where the prominent bar causes the Stage 2 bulge-disk fit to artificially extend the bulge and inflate the $B/T$. The disk fitted in Stage 2 has a low surface brightness and is very extended, well beyond the real disk: the $b/a$ and $PA$ of the fitted disk is shown as contours. Stage 3 bulge-disk-bar decomposition provides the best model. See Table 4\hbox {} for the fit parameters. }}{44}}
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\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces The complete $2D$ decomposition for NGC 4548. This is an extreme example where the prominent bar results in an extended bulge and inflated $B/T$ in the Stage 2 bulge-disk fit. Like NGC 4643 in Figure 6\hbox {}, the disk fitted in Stage 2 has a low surface brightness and is very extended: its $b/a$ and $PA$ are shown as contours. Stage 3 bulge-disk-bar decomposition provides the best model. See Table 5\hbox {} for the fit parameters. }}{45}}
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\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces This plot shows the data image, Stage 2 model, and Stage 3 model for NGC 4902. The Stage 2 bulge is too bright and is extended along the major axis of the bar ($B/T$=31.2\% and $b/a$=0.45). In Stage 3, the bulge and bar are fit with distinct components ($B/T$=6.2\%, bulge $b/a$=0.75, Bar/$T$=10.0\%, bar $b/a$=0.25). }}{46}}
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\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces The data images and Stage 3 bulge-disk-bar decomposition models of NGC 5427 and NGC 7412 are shown. The Stage 3 models each distinctly show a false bar component, which is not present in the data images.The false components can be inspired by prominent spiral arms, such as those present in these galaxies. Such cases are flagged during the visual inspection of fits and the Stage 3 bulge-disk-bar decomposition is discarded in favor of the Stage 2 bulge-disk decomposition. }}{47}}
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\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces The run of $b/a$ and $PA$ are shown from modeling the bulge of NGC 4548 with ten concentric S\'ersic profiles with fixed $r_e$ each separated by 0.75''. The mean $b/a$ and $PA$ are indicated with horizontal lines. The combined $B/T$ from the ten components is 14.5\%, in good agreement with the 13.0\% value from the fit with a single bulge of constant $b/a$. }}{48}}
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\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces  An elementary test is to determine if GALFIT can recover the known parameters of artificial noisy images. Noisy images were simulated by taking parametric model images (left panels) produced by GALFIT, and adding noise and sky background (right panels). The noisy images were then fitted to see if the original known parameters can be recovered. See \S  4.2\hbox {} for details. }}{49}}
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\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces  The top, middle, and bottom panels show stellar mass for bulges, disks, and bars, respectively, along the Hubble sequence. }}{50}}
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\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces The individual and mean $B/T$ (left panels) and bulge S\'ersic index (right panels) are plotted, as a function of Hubble type and galaxy stellar mass. Barred and unbarred galaxies are shown separately. The mean $B/T$ and bulge index in barred galaxies differ systematically from unbarred galaxies, but there is a large overlap in the individual values. The error bars denote the error on the mean. The distribution of $B/T$ shows that bulges with $B/T \leq 0.2$ are pervasive and exist across the whole spectrum of S0/a to Scd. Furthermore, only a small fraction (5.5\%) of bulges have classical S\'ersic indexes ($n\ge $\nobreakspace  {}4): such bulges lie primarily in S0/a to Sab,and have large $B/T > 0.2$. A large fraction (34.4\%) of bulges have \nobreakspace  {}$2<n<4$: they exist in barred and unbarred S0/a to Sd, and their $B/T$ spans a wide range with a mean of 0.23. Finally, a striking 60.2\% of bulges have $n \leq 2$: they exist in barred and unbarred galaxies across all Hubble types; their $B/T$ spans a wide range (0.01 to 0.4) with a mean of 0.10. }}{51}}
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\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces  The relation between $B/T$ and bulge index is shown. In the top panel, galaxies are coded according to bar class. In the lower panel, galaxies are coded according to Hubble type. Only a small fraction (5.5\%) of bulges have classical S\'ersic indexes ($n\ge 4$): such bulges lie primarily in S0/a to Sab,and have large $B/T > 0.2$. A large fraction (34.4\%) of bulges have $2<n<4$: they exist in barred and unbarred S0/a to Sd, and their $B/T$ spans a wide range with a mean of 0.23. Finally, 60.2\% of bulges have $n \leq 2$: they exist in barred and unbarred galaxies across all Hubble types; their $B/T$ spans a wide range (0.01 to 0.4) with a mean of 0.10.}}{52}}
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\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces $B/T$ is plotted against Bar/$T$ and sorted by bulge S\'ersic index. Aside from the eight galaxies with large Bar/$T$ ($\geq 0.3$), most galaxies have moderate Bar/$T$ and a wide range of $B/T$ is seen at each Bar/$T$. }}{53}}
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\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces The top two rows contain barred galaxies, which have early RC3 Hubble types, but yet have $B/T<0.2$. The bottom row contains unbarred galaxies, which have late RC3 Hubble types, but yet have $B/T \sim 0.4$. See $\S  $\nobreakspace  {}5.3\hbox {} for details. }}{54}}
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\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces  $B/D$ is plotted against Hubble type for our sample. Barred and unbarred populations are separated, but the mean values for barred and unbarred together in each bin are shown.This plot can be compared against the corresponding plot in Graham (2001), based on a smaller sample of galaxies. Our mean $H$-band $B/D$ ratios are comparable to the the means $K$-band $B/D$ in Graham (2001). Both studies also find that $B/D$ shows a large range for each Hubble type, while the mean $B/D$ declines from Sa to Sc galaxies. }}{55}}
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\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces This figure shows $B/T$ plotted against the redshift of the last major merger for the models described in \S  5.5\hbox {} and shown in Figure 19\hbox {}. Galaxies with more recent major mergers are bound to have higher $B/T$ because less time is available for disks to be built.}}{56}}
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\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces  For galaxies with total stellar mass $M_* \geq 1.0 \times 10^{10} M_\odot $, this figure shows the observed cumulative fraction (solid line with symbols) of spiral galaxies with $B/T\leq 0.75$ (the limit on $B/T$ is imposed to exclude any ellipticals produced in the models). The three panels are identical but sorted by bar class, Hubble type, and bulge S\'ersic index. The dashed line is the cumulative fraction of $B/T$ in spirals predicted by cosmological semi-analytical models from Burkert \& Khochfar (2008, in prep.) for the same stellar mass range. The dotted line denotes those systems having only minor mergers, while the thick dots denote systems having both major and minor mergers. About 20\% of spirals experience a major merger. These models assume every major merger of mass ratio $M_1/M_2 \geq 1/4$ produces a spheroid with $B/T\sim 1$.}}{57}}
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\@writefile{lof}{\contentsline {figure}{\numberline {20}{\ignorespaces This panel is calculated identically to Figure 19\hbox {}, except that the condition for disk destruction in major mergers has been relaxed to mass ratio $M_1/M_2 \geq 1/6$. In this case, about 30\% of spirals undergo major mergers. The model underpredicts the data by about 10\% near $B/T=0.4$. Since the ``Minor Only'' curve lies so near the $Sb\leq T \leq Sc$ and $n<2$ curves, such systems are likely built from a combination of major and minor mergers, but predominantly by mergers with $M_1/M_2 <1/6$. }}{58}}
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\@writefile{lof}{\contentsline {figure}{\numberline {21}{\ignorespaces  We show the distribution of S\'ersic indexes derived by fitting a single S\'ersic index to a representative set of 1:1 merger remnants in the simulations of Hopkins {et al.\nobreakspace  {}}2008 (in prep). Note that while $\sim $\nobreakspace  {}22\% of the remnants have classical $n>4$, as much as 20\% have low $n< 2.5$, while 50\% have $n < 3$. This suggests that intermediate $2<n<4$ bulges can result from major mergers that have residual gas left-over after violent relaxation. [Figure: courtesy of Phil Hopkins] }}{59}}
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\@writefile{lof}{\contentsline {figure}{\numberline {22}{\ignorespaces  Upper left: Mean and individual Bar/$T$ plotted against Hubble type. Upper right: Mean and individual bar s\'ersic indexes plotted against Hubble type. Lower left: Bar/$T$ plotted against total galaxy stellar mass. The mean Bar/$T$ in bins of stellar mass is indicated. Lower right: Bar S\'ersic index plotted against total galaxy stellar mass. All plots: The error bars where shown indicate error on the mean.}}{60}}
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\@writefile{lof}{\contentsline {figure}{\numberline {23}{\ignorespaces Systems with Bar/$T$ near or above $\sim 0.3$. }}{61}}
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\@writefile{lof}{\contentsline {figure}{\numberline {24}{\ignorespaces  Upper left: Bar/$T$ is plotted against peak bar ellipticity from MJ07. Upper right: Bar/$T$ is plotted against bar S\'ersic index. Lower left: Bar/$T$ is plotted against bulge S\'ersic index. Lower right: Bar/$T$ is plotted against mean bar/bulge luminosity ratio. All plots: Mean Bar/$T$ is calculated for bins along the ordinate axis. The error bars indicate error on the mean.}}{62}}
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