Molecular Gas Properties in the Central Kiloparsec of Barred and Unbarred Spirals
Kartik Sheth
We study the molecular gas properties in the central kiloparsec of 29 barred and 15 unbarred spirals from the BIMA\footnote{Berkeley-Illinois-Maryland Association} Survey of Nearby Galaxies (SONG). We find that the mean nuclear molecular gas surface density of barred spirals ($\langle$$\Sigma_{nuc}$$\rangle$=309$\pm$71 \Msun\ pc$^{-2}$) is three times higher than that of unbarred spirals ($\langle$$\Sigma_{nuc}$$\rangle$=107$\pm$29 \Msun\ pc$^{-2}$). Nine out of the eleven bars with $\Sigma_{nuc} >$ 300 \Msun\ pc$^{-2}$ are early types. Comparison with estimates of the star formation threshold density ($\Sigma_{crit}$) indicates that enhanced star formation in bars may be due to a larger fraction having $\Sigma_{nuc} > typical\ \Sigma_{crit}$. We also find that barred spirals are more centrally concentrated than unbarred spirals. The median value of the concentration parameter for barred spirals (f$_{con}$=$\Sigma_{nuc}$/$\Sigma_{disk}$=27.7) is a factor of four higher than that for the unbarred spirals (f$_{con}$=6.2). Finally we investigate the dependence of the central concentration on bar properties and find it may be weakly correlated with the bulge size, but is not correlated with the bar length. This suggests that inner Lindblad resonances, bar ellipticity and circumnuclear star formation play important roles in determining the gas accretion in the central kiloparsec. \\ \noindent See http://www.astro.caltech.edu/$\sim$kartik/thesis.html for more detailed description of these thesis results. This research was made possible with funding from NSF grants AST-9981308, AST-9981289 and AST-9981546.
epsf.tex
%%% ====================================================================
%%%   This file is freely redistributable and placed into the
%%%   public domain by Tomas Rokicki.
%%%  @TeX-file{
%%%     author          = "Tom Rokicki",
%%%     version         = "2.7",
%%%     date            = "25 October 1996",
%%%     time            = "10:00:05 MDT",
%%%     filename        = "epsf.tex",
%%%     address         = "Tom Rokicki
%%%                        Box 2081
%%%                        Stanford, CA 94309
%%%                        USA",
%%%     telephone       = "+1 415 855 9989",
%%%     email           = "rokicki@cs.stanford.edu (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "PostScript, TeX",
%%%     supported       = "yes",
%%%     abstract        = "This file contains macros to support the inclusion
%%%                        of Encapsulated PostScript files in TeX documents.",
%%%     docstring       = "This file contains TeX macros to include an
%%%                        Encapsulated PostScript graphic.  It works
%%%                        by finding the bounding box comment,
%%%                        calculating the correct scale values, and
%%%                        inserting a vbox of the appropriate size at
%%%                        the current position in the TeX document.
%%%
%%%                        To use, simply say
%%%
%%%                        \input epsf % somewhere early on in your TeX file
%%%
%%%                        % then where you want to insert a vbox for a figure:
%%%                        \epsfbox{filename.ps}
%%%
%%%                        Alternatively, you can supply your own
%%%                        bounding box by
%%%
%%%                        \epsfbox[0 0 30 50]{filename.ps}
%%%
%%%                        This will not read in the file, and will
%%%                        instead use the bounding box you specify.
%%%
%%%                        The effect will be to typeset the figure as
%%%                        a TeX box, at the point of your \epsfbox
%%%                        command. By default, the graphic will have
%%%                        its `natural' width (namely the width of
%%%                        its bounding box, as described in
%%%                        filename.ps). The TeX box will have depth
%%%                        zero.
%%%
%%%                        You can enlarge or reduce the figure by
%%%                        saying
%%%
%%%                          \epsfxsize=<dimen> \epsfbox{filename.ps}
%%%                        or
%%%                          \epsfysize=<dimen> \epsfbox{filename.ps}
%%%
%%%                        instead. Then the width of the TeX box will
%%%                        be \epsfxsize and its height will be scaled
%%%                        proportionately (or the height will be
%%%                        \epsfysize and its width will be scaled
%%%                        proportionately).
%%%
%%%                        The width (and height) is restored to zero
%%%                        after each use, so \epsfxsize or \epsfysize
%%%                        must be specified before EACH use of
%%%                        \epsfbox.
%%%
%%%                        A more general facility for sizing is
%%%                        available by defining the \epsfsize macro.
%%%                        Normally you can redefine this macro to do
%%%                        almost anything.  The first parameter is
%%%                        the natural x size of the PostScript
%%%                        graphic, the second parameter is the
%%%                        natural y size of the PostScript graphic.
%%%                        It must return the xsize to use, or 0 if
%%%                        natural scaling is to be used.  Common uses
%%%                        include:
%%%
%%%                           \epsfxsize  % just leave the old value alone
%%%                           0pt         % use the natural sizes
%%%                           #1          % use the natural sizes
%%%                           \hsize      % scale to full width
%%%                           0.5#1       % scale to 50% of natural size
%%%                           \ifnum #1>\hsize\hsize\else#1\fi
%%%                                       % smaller of natural, hsize
%%%
%%%                        If you want TeX to report the size of the
%%%                        figure (as a message on your terminal when
%%%                        it processes each figure), say
%%%                        `\epsfverbosetrue'.
%%%
%%%                        If you only want to get the bounding box
%%%                        extents, without producing any output boxes
%%%                        or \special{}, then say
%%%                        \epsfgetbb{filename}.  The extents will be
%%%                        saved in the macros \epsfllx \epsflly
%%%                        \epsfurx \epsfury in PostScript units of
%%%                        big points.
%%%
%%%                        Revision history:
%%%
%%%                        ---------------------------------------------
%%%                        epsf.tex macro file:
%%%                        Originally written by Tomas Rokicki of
%%%                        Radical Eye Software, 29 Mar 1989.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Don Knuth, 3 Jan 1990.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Tomas Rokicki, 18 Jul 1990.
%%%                        Accept bounding boxes with no space after
%%%                        the colon.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 03 Dec 1991 [2.0].
%%%                        Add version number and date typeout.
%%%
%%%                        Use \immediate\write16 instead of \message
%%%                        to ensure output on new line.
%%%
%%%                        Handle nested EPS files.
%%%
%%%                        Handle %%BoundingBox: (atend) lines.
%%%
%%%                        Do not quit when blank lines are found.
%%%
%%%                        Add a few percents to remove generation of
%%%                        spurious blank space.
%%%
%%%                        Move \special output to
%%%                        \epsfspecial{filename} so that other macro
%%%                        packages can input this one, then change
%%%                        the definition of \epsfspecial to match
%%%                        another DVI driver.
%%%
%%%                        Move size computation to \epsfsetsize which
%%%                        can be called by the user; the verbose
%%%                        output of the bounding box and scaled width
%%%                        and height happens here.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 05 May 1992 [2.1].
%%%                        Wrap \leavevmode\hbox{} around \vbox{} with
%%%                        the \special so that \epsffile{} can be
%%%                        used inside \begin{center}...\end{center}
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 09 Dec 1992 [2.2].
%%%                        Introduce \epsfshow{true,false} and
%%%                        \epsfframe{true,false} macros; the latter
%%%                        suppresses the insertion of the PostScript,
%%%                        and instead just creates an empty box,
%%%                        which may be handy for rapid prototyping.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 14 Dec 1992 [2.3].
%%%                        Add \epsfshowfilename{true,false}.  When
%%%                        true, and \epsfshowfalse is specified, the
%%%                        PostScript file name will be displayed
%%%                        centered in the figure box.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 20 June 1993 [2.4].
%%%                        Remove non-zero debug setting of \epsfframemargin,
%%%                        and change margin handling to preserve EPS image
%%%                        size and aspect ratio, so that the actual
%%%                        box is \epsfxsize+\epsfframemargin wide by
%%%                        \epsfysize+\epsfframemargin high.
%%%                        Reduce output of \epsfshowfilenametrue to
%%%                        just the bare file name.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 13 July 1993 [2.5].
%%%                        Add \epsfframethickness for control of
%%%                        \epsfframe frame lines.
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 02 July 1996 [2.6]
%%%                        Add missing initialization \epsfatendfalse;
%%%                        the lack of this resulted in the wrong
%%%                        BoundingBox being picked up, mea culpa, sigh...
%%%                        ---------------------------------------------
%%%
%%%                        ---------------------------------------------
%%%                        Revised by Nelson H. F. Beebe
%%%                        <beebe@math.utah.edu>, 25 October 1996 [2.7]
%%%                        Update to match changes in from dvips 5-600
%%%                        distribution: new user-accessible macros:
%%%                        \epsfclipon, \epsfclipoff, \epsfdrafton,
%%%                        \epsfdraftoff, change \empty to \epsfempty.
%%%                        ---------------------------------------------
%%%  }
%%% ====================================================================

 \immediate\write16{This is `epsf.tex' v2.7 <25 October 1996>}%
%
\newread\epsffilein    % file to \read
\newif\ifepsfatend     % need to scan to LAST %%BoundingBox comment?
\newif\ifepsfbbfound   % success?
\newif\ifepsfdraft     % use draft mode?
\newif\ifepsffileok    % continue looking for the bounding box?
\newif\ifepsfframe     % frame the bounding box?
\newif\ifepsfshow      % show PostScript file, or just bounding box?
\epsfshowtrue          % default is to display PostScript file
\newif\ifepsfshowfilename % show the file name if \epsfshowfalse specified?
\newif\ifepsfverbose   % report what you're making?
\newdimen\epsfframemargin % margin between box and frame
\newdimen\epsfframethickness % thickness of frame rules
\newdimen\epsfrsize    % vertical size before scaling
\newdimen\epsftmp      % register for arithmetic manipulation
\newdimen\epsftsize    % horizontal size before scaling
\newdimen\epsfxsize    % horizontal size after scaling
\newdimen\epsfysize    % vertical size after scaling
\newdimen\pspoints     % conversion factor
%
\pspoints = 1bp        % Adobe points are `big'
\epsfxsize = 0pt       % default value, means `use natural size'
\epsfysize = 0pt       % ditto
\epsfframemargin = 0pt % default value: frame box flush around picture
\epsfframethickness = 0.4pt % TeX's default rule thickness
%
\def\epsfbox#1{\global\def\epsfllx{72}\global\def\epsflly{72}%
   \global\def\epsfurx{540}\global\def\epsfury{720}%
   \def\lbracket{[}\def\testit{#1}\ifx\testit\lbracket
   \let\next=\epsfgetlitbb\else\let\next=\epsfnormal\fi\next{#1}}%
%
% We use \epsfgetlitbb if the user specified an explicit bounding box,
% and \epsfnormal otherwise.  Because \epsfgetbb can be called
% separately to retrieve the bounding box, we move the verbose
% printing the bounding box extents and size on the terminal to
% \epsfstatus.  Therefore, when the user provided the bounding box,
% \epsfgetbb will not be called, so we must call \epsfsetsize and
% \epsfstatus ourselves.
%
\def\epsfgetlitbb#1#2 #3 #4 #5]#6{%
   \epsfgrab #2 #3 #4 #5 .\\%
   \epsfsetsize
   \epsfstatus{#6}%
   \epsfsetgraph{#6}%
}%
%
\def\epsfnormal#1{%
    \epsfgetbb{#1}%
    \epsfsetgraph{#1}%
}%
%
\def\epsfgetbb#1{%
%
%   The first thing we need to do is to open the
%   PostScript file, if possible.
%
    \openin\epsffilein=#1
    \ifeof\epsffilein
        \errmessage{Could not open file #1, ignoring it}%
    \else                       %process the file
        {%                      %start a group to contain catcode changes
            % Make all special characters, except space, to be of type
            % `other' so we process the file in almost verbatim mode
            % (TeXbook, p. 344).
            \chardef\other=12
            \def\do##1{\catcode`##1=\other}%
            \dospecials
            \catcode`\ =10
            \epsffileoktrue         %true while we are looping
            \epsfatendfalse     %[02-Jul-1996]: add forgotten initialization
            \loop               %reading lines from the EPS file
                \read\epsffilein to \epsffileline
                \ifeof\epsffilein %then no more input
                \epsffileokfalse %so set completion flag
            \else                %otherwise process one line
                \expandafter\epsfaux\epsffileline:. \\%
            \fi
            \ifepsffileok
            \repeat
            \ifepsfbbfound
            \else
                \ifepsfverbose
                    \immediate\write16{No BoundingBox comment found in %
                                    file #1; using defaults}%
                \fi
            \fi
        }%                      %end catcode changes
        \closein\epsffilein
    \fi                         %end of file processing
    \epsfsetsize                %compute size parameters
    \epsfstatus{#1}%
}%
%
% Clipping control:
\def\epsfclipon{\def\epsfclipstring{ clip}}%
\def\epsfclipoff{\def\epsfclipstring{\ifepsfdraft\space clip\fi}}%
\epsfclipoff % default for dvips is OFF
%
% The special that is emitted by \epsfsetgraph comes from this macro.
% It is defined separately to allow easy customization by other
% packages that first \input epsf.tex, then redefine \epsfspecial.
% This macro is invoked in the lower-left corner of a box of the
% width and height determined from the arguments to \epsffile, or
% from the %%BoundingBox in the EPS file itself.
%
% This version is for dvips:
\def\epsfspecial#1{%
     \epsftmp=10\epsfxsize
     \divide\epsftmp\pspoints
     \ifnum\epsfrsize=0\relax
       \special{PSfile=\ifepsfdraft psdraft.ps\else#1\fi\space
                llx=\epsfllx\space
                lly=\epsflly\space
                urx=\epsfurx\space
                ury=\epsfury\space
                rwi=\number\epsftmp
                \epsfclipstring
               }%
     \else
       \epsfrsize=10\epsfysize
       \divide\epsfrsize\pspoints
       \special{PSfile=\ifepsfdraft psdraft.ps\else#1\fi\space
                llx=\epsfllx\space
                lly=\epsflly\space
                urx=\epsfurx\space
                ury=\epsfury\space
                rwi=\number\epsftmp
                rhi=\number\epsfrsize
                \epsfclipstring
               }%
     \fi
}%
%
% \epsfframe macro adapted from the TeXbook, exercise 21.3, p. 223, 331.
% but modified to set the box width to the natural width, rather
% than the line width, and to include space for margins and rules
\def\epsfframe#1%
{%
  \leavevmode                   % so we can put this inside
                                % a centered environment
  \setbox0 = \hbox{#1}%
  \dimen0 = \wd0                                % natural width of argument
  \advance \dimen0 by 2\epsfframemargin         % plus width of 2 margins
  \advance \dimen0 by 2\epsfframethickness      % plus width of 2 rule lines
  \vbox
  {%
    \hrule height \epsfframethickness depth 0pt
    \hbox to \dimen0
    {%
      \hss
      \vrule width \epsfframethickness
      \kern \epsfframemargin
      \vbox {\kern \epsfframemargin \box0 \kern \epsfframemargin }%
      \kern \epsfframemargin
      \vrule width \epsfframethickness
      \hss
    }% end hbox
    \hrule height 0pt depth \epsfframethickness
  }% end vbox
}%
%
\def\epsfsetgraph#1%
{%
   %
   % Make the vbox and stick in a \special that the DVI driver can
   % parse.  \vfil and \hfil are used to place the \special origin at
   % the lower-left corner of the vbox.  \epsfspecial can be redefined
   % to produce alternate \special syntaxes.
   %
   \leavevmode
   \hbox{% so we can put this in \begin{center}...\end{center}
     \ifepsfframe\expandafter\epsfframe\fi
     {\vbox to\epsfysize
     {%
        \ifepsfshow
            % output \special{} at lower-left corner of figure box
            \vfil
            \hbox to \epsfxsize{\epsfspecial{#1}\hfil}%
        \else
            \vfil
            \hbox to\epsfxsize{%
               \hss
               \ifepsfshowfilename
               {%
                  \epsfframemargin=3pt % local change of margin
                  \epsfframe{{\tt #1}}%
               }%
               \fi
               \hss
            }%
            \vfil
        \fi
     }%
   }}%
   %
   % Reset \epsfxsize and \epsfysize, as documented above.
   %
   \global\epsfxsize=0pt
   \global\epsfysize=0pt
}%
%
%   Now we have to calculate the scale and offset values to use.
%   First we compute the natural sizes.
%
\def\epsfsetsize
{%
   \epsfrsize=\epsfury\pspoints
   \advance\epsfrsize by-\epsflly\pspoints
   \epsftsize=\epsfurx\pspoints
   \advance\epsftsize by-\epsfllx\pspoints
%
%   If `epsfxsize' is 0, we default to the natural size of the picture.
%   Otherwise we scale the graph to be \epsfxsize wide.
%
   \epsfxsize=\epsfsize{\epsftsize}{\epsfrsize}%
   \ifnum \epsfxsize=0
      \ifnum \epsfysize=0
        \epsfxsize=\epsftsize
        \epsfysize=\epsfrsize
        \epsfrsize=0pt
%
%   We have a sticky problem here:  TeX doesn't do floating point arithmetic!
%   Our goal is to compute y = rx/t. The following loop does this reasonably
%   fast, with an error of at most about 16 sp (about 1/4000 pt).
%
      \else
        \epsftmp=\epsftsize \divide\epsftmp\epsfrsize
        \epsfxsize=\epsfysize \multiply\epsfxsize\epsftmp
        \multiply\epsftmp\epsfrsize \advance\epsftsize-\epsftmp
        \epsftmp=\epsfysize
        \loop \advance\epsftsize\epsftsize \divide\epsftmp 2
        \ifnum \epsftmp>0
           \ifnum \epsftsize<\epsfrsize
           \else
              \advance\epsftsize-\epsfrsize \advance\epsfxsize\epsftmp
           \fi
        \repeat
        \epsfrsize=0pt
      \fi
   \else
     \ifnum \epsfysize=0
       \epsftmp=\epsfrsize \divide\epsftmp\epsftsize
       \epsfysize=\epsfxsize \multiply\epsfysize\epsftmp
       \multiply\epsftmp\epsftsize \advance\epsfrsize-\epsftmp
       \epsftmp=\epsfxsize
       \loop \advance\epsfrsize\epsfrsize \divide\epsftmp 2
       \ifnum \epsftmp>0
          \ifnum \epsfrsize<\epsftsize
          \else
             \advance\epsfrsize-\epsftsize \advance\epsfysize\epsftmp
          \fi
       \repeat
       \epsfrsize=0pt
     \else
       \epsfrsize=\epsfysize
     \fi
   \fi
}%
%
% Issue some status messages if the user requested them
%
\def\epsfstatus#1{% arg = filename
   \ifepsfverbose
     \immediate\write16{#1: BoundingBox:
                  llx = \epsfllx\space lly = \epsflly\space
                  urx = \epsfurx\space ury = \epsfury\space}%
     \immediate\write16{#1: scaled width = \the\epsfxsize\space
                  scaled height = \the\epsfysize}%
   \fi
}%
%
%   We still need to define the tricky \epsfaux macro. This requires
%   a couple of magic constants for comparison purposes.
%
{\catcode`\%=12 \global\let\epsfpercent=%\global\def\epsfbblit{%BoundingBox}}%
\global\def\epsfatend{(atend)}%
%
%   So we're ready to check for `%BoundingBox:' and to grab the
%   values if they are found.
%
%   If we find a line
%
%   %%BoundingBox: (atend)
%
%   then we ignore it, but set a flag to force parsing all of the
%   file, so the last %%BoundingBox parsed will be the one used.  This
%   is necessary, because EPS files can themselves contain other EPS
%   files with their own %%BoundingBox comments.
%
%   If we find a line
%
%   %%BoundingBox: llx lly urx ury
%
%   then we save the 4 values in \epsfllx, \epsflly, \epsfurx, \epsfury.
%   Then, if we have not previously parsed an (atend), we flag completion
%   and can stop reading the file.  Otherwise, we must keep on reading
%   to end of file so that we find the values on the LAST %%BoundingBox.
\long\def\epsfaux#1#2:#3\\%
{%
   \def\testit{#2}%             % save second character up to just before colon
   \ifx#1\epsfpercent           % then first char is percent (quick test)
       \ifx\testit\epsfbblit    % then (slow test) we have %%BoundingBox
            \epsfgrab #3 . . . \\%
            \ifx\epsfllx\epsfatend % then ignore %%BoundingBox: (atend)
                \global\epsfatendtrue
            \else               % else found %%BoundingBox: llx lly urx ury
                \ifepsfatend    % then keep parsing ALL %%BoundingBox lines
                \else           % else stop after first one parsed
                    \epsffileokfalse
                \fi
                \global\epsfbbfoundtrue
            \fi
       \fi
   \fi
}%
%
%   Here we grab the values and stuff them in the appropriate definitions.
%
\def\epsfempty{}%
\def\epsfgrab #1 #2 #3 #4 #5\\{%
   \global\def\epsfllx{#1}\ifx\epsfllx\epsfempty
      \epsfgrab #2 #3 #4 #5 .\\\else
   \global\def\epsflly{#2}%
   \global\def\epsfurx{#3}\global\def\epsfury{#4}\fi
}%
%
%   We default the epsfsize macro.
%
\def\epsfsize#1#2{\epsfxsize}%
%
%   Finally, another definition for compatibility with older macros.
%
\let\epsffile=\epsfbox
\endinput

sheth.tex
\documentstyle[11pt,newpasp,twoside,epsf]{article}
\markboth{Author \& Co-author}{APS Conf. Ser. Style}
\pagestyle{myheadings}
\nofiles
\def\vsys{v_{\rm sys}}
\def\vsun{v_{\sun}}
\def\Msun{$M_{\sun}$}
\def\ergs{ergs\ s$^{-1}$}
\def\Ha{H$\alpha$\ }
\def\Hb{H$\beta$\ }
\def\bm {beam$^{-1}$}
\def\yr {yr$^{-1}$}
\def\ecs {ergs\ cm$^{-2}$\ s$^{-1}$}
\def\kms{km s$^{-1}$}

% Some definitions I use in these instructions.

\def\emphasize#1{{\sl#1\/}}
\def\arg#1{{\it#1\/}}
\let\prog=\arg

\def\edcomment#1{\iffalse\marginpar{\raggedright\sl#1\/}\else\relax\fi}
\marginparwidth 1.25in
\marginparsep .125in
\marginparpush .25in
\reversemarginpar

\begin{document}
\title{Molecular Gas Properties in the Central Kiloparsec of Barred and Unbarred Spirals}
 \author{Kartik Sheth}
\affil{California Institute of Technology, MS 105-24, Pasadena, CA 91125 \\ \& University of Maryland, College Park, MD 20742-2421}

\begin{abstract}
We study the molecular gas properties in the central kiloparsec of 29
barred and 15 unbarred spirals from the
BIMA\footnote{Berkeley-Illinois-Maryland Association} Survey of Nearby
Galaxies (SONG).  We find that the mean nuclear molecular gas surface
density of barred spirals ($\langle$$\Sigma_{nuc}$$\rangle$=309$\pm$71
\Msun\ pc$^{-2}$) is three times higher than that of unbarred spirals
($\langle$$\Sigma_{nuc}$$\rangle$=107$\pm$29 \Msun\ pc$^{-2}$).  Nine
out of the eleven bars with $\Sigma_{nuc} >$ 300 \Msun\ pc$^{-2}$ are
early types. Comparison with estimates of the star formation threshold
density ($\Sigma_{crit}$) indicates that enhanced star formation in
bars may be due to a larger fraction having $\Sigma_{nuc} > typical\
\Sigma_{crit}$. We also find that barred spirals are more centrally
concentrated than unbarred spirals.  The median value of the
concentration parameter for barred spirals
(f$_{con}$=$\Sigma_{nuc}$/$\Sigma_{disk}$=27.7) is a factor of four
higher than that for the unbarred spirals (f$_{con}$=6.2).  Finally we
investigate the dependence of the central concentration on bar
properties and find it may be weakly correlated with the bulge size,
but is not correlated with the bar length.  This suggests that inner
Lindblad resonances, bar ellipticity and circumnuclear star formation
play important roles in determining the gas accretion in the central
kiloparsec. \\

\noindent See http://www.astro.caltech.edu/$\sim$kartik/thesis.html
for more detailed description of these thesis results.  This research
was made possible with funding from NSF grants AST-9981308,
AST-9981289 and AST-9981546.
\end{abstract}

\section{Introduction}
Bars play a key role in galaxy evolution by inducing dramatic changes
 on relatively short time scales ($\sim$10$^8$ years).  Bar-induced
 gas mixing is known to reduce the overall metallicity gradient (e.g.,
 Martin \& Roy 1994).  Three decades of observational studies show
 that circumnuclear starburst activity is associated with bars (e.g.,
 S\'ersic \& Pastoriza 1965; Hawarden et al. 1986; Ho, Fillipenko \&
 Sargent 1997).  Models suggest that bars may be effective mechanisms
 for feeding active galactic nuclei (Shlosman, Frank \& Begelman
 1988), forming new bulges, and for evolving late Hubble type galaxies
 into earlier types (e.g., Friedli \& Benz 1993; Norman, Sellwood \&
 Hasan 1996).  The most dramatic prediction of models is that a bar
 can destroy itself if sufficient mass accretes ($\sim$
 1-2\%M$_{disk}$) in the center.  Since these evolutionary changes
 depend not only on the gas inflow but on the gas {\em accretion}, we
 compare the gas properties of barred and unbarred spirals in the
 central kiloparsec (kpc); we focus on the molecular gas because it is
 the dominant component of the ISM in inner regions of spirals
 (Scoville 1990).

Though good evidence for inflowing gas has been presented (e.g.,
Regan, Sheth \& Vogel 1999), only one study has examined whether the
inflowing gas accumulates in the center (OVRO-NRO study, Sakamoto et
al. 1999).  This twenty galaxy sample, however, pre-selected centrally
concentrated galaxies because of a CO-brightness selection criterion.
Moreover, it contained only 4 late type spirals preventing comparative
studies across Hubble type.  Hence a study with a larger and more
uniform sample is warranted.  The BIMA SONG provides such a database
(Regan et al. 2001).  SONG consists of 29 barred spirals and 15
unbarred spirals selected as follows: $\delta >$ --20$^o$, $i <$
70$^o$, V$_{HEL} <$ 2000 \kms, and perhaps most importantly, m$_B <$
11.

\begin{figure}
\vspace{-0.2in}
\plottwo{signuc.ps}{signucbytype.talk.ps}
\caption{{\bf Left:} Histogram of $\Sigma_{nuc}$ in barred and
unbarred spirals from SONG.  Note the tail of high gas surface
densities in the barred spirals.  {\bf Right:} Same data now split
between early (Sa-Sbc) and late type (Sc-Sd) spirals.  Note that the 
highest gas surface densities are typically found in early type bars.}
\vspace{-0.2in}
\end{figure}

\section{Differences in Molecular Gas Surface Density}
In the left panel of Figure 1 we show the distribution of the nuclear
gas surface densities ($\Sigma_{nuc}$) in the central kpc diameter
region for all the SONG galaxies.  The mean $\Sigma_{nuc}$ for the
barred spirals ($\Sigma_{nuc}$=309.1$\pm$71.3 \Msun\ pc$^{-2}$) is
three times higher than that for the unbarred spirals
($\Sigma_{nuc}$=106.5$\pm$29.3 \Msun\ pc$^{-2}$).  A Kolmogrov-Smirnov
test shows that the distributions differ at a 96\% confidence level.
In the right panel, we show the same data split into early and late
type spirals. We find that the majority of the highest $\Sigma_{nuc}$
occur in early type galaxies. 9/11 bars with $\Sigma_{nuc} > $300 are
early types.

These differences in $\Sigma_{nuc}$ are important for understanding
circumnuclear star formation activity.  Using a simple gravitational
instability model (e.g., Kennicutt 1989), or a magneto-Jean's
instability model (e.g., Kim \& Ostriker 2001), we estimate that the
lower limit to the typical threshold or critical gas surface density
($\Sigma_{crit}$) is $\sim$100 \Msun\ pc$^{-2}$, assuming the
shallowest rotation curve from Sofue et al. (1999) and lowest velocity
dispersion from Galactic center measurements (Bally et al. 1988)
Though $\Sigma_{crit}$ undoubtedly varies from galaxy to galaxy
depending on the steepness of the rotation curve and the velocity
dispersion, 100 \Msun\ pc$^{-2}$ is a reasonable lower limit.

\begin{figure}
%\plotfiddle{sfschmidt.ps}{2.5in}{0}{40}{40}{-200}{0}
\vspace{0.9in}
\plotfiddle{sfschmidt.ps}{2.5in}{0}{37}{37}{-200}{0}
\plotfiddle{cenconc2.ps}{2.5in}{0}{37}{37}{-10}{200}
\vspace{-3.1in}
\caption{{\bf Left:} $\Sigma_{SFR}$ is plotted against $\Sigma_{nuc}$
for the SONG sample. The solid oval shows the high star formation
rates in galaxies above the threshold density (solid vertical line)
and the dashed oval shows the galaxies below the threshold.  The
diagonal line is the Schmidt law from Kennicutt (1998). {\bf Right:}
f$_{con}$ in barred and unbarred spirals is shown on a logarithmic
(left hand box) and a linear scale (right hand box); the two
distributions are distinctly different (P$_{K-S}$=0.07).  This is
strong statistical evidence for bar-induced gas inflow and accretion.}
\end{figure}

From Figure 1, we see that about half of the barred (16/29 or 55\%)
and unbarred (7/15 or 45\%) spirals have $\Sigma_{nuc} >$ 100 \Msun\
pc$^{-2}$.  But the highest gas surface densities in the unbarred
spirals are mostly between 100--200 \Msun\ pc$^{-2}$.  In fact, for
$\Sigma_{nuc} >$ 300 \Msun\ pc$^{-2}$, there is only 1/15 unbarred
spiral, compared to 11/29 barred spirals.  Considering that the
threshold density is likely to be higher than 100 \Msun pc${-2}$, and
in light of over three decades of studies indicating that bars, and
particularly {\em early type} bars, host circumnuclear starbursts, we
suggest that barred spirals are more prone to circumnuclear star
formation because a higher fraction have $\Sigma_{nuc} > typical\
\Sigma_{crit}$.  We investigate the star formation activity in the
SONG sample further in the next section.

\section{Star Formation Rates, Gas Surface Densities \& the Schmidt Law}

In the left panel of Figure 2, we plot the star formation rate surface
density ($\Sigma_{SFR}$) against the molecular gas surface densities.
Above the typical threshold value of 100 \Msun\ pc$^{-2}$ (shown by
the vertical solid line), we find higher star formation rates but
there is considerable scatter in the data.  These galaxies, mostly
early-type barred bars, are indicated with the solid oval; they tend
to lie along the Schmidt law (Kennicutt 1998).  Below the critical
density galaxies have significantly lower star formation activity
(dashed oval) but it is worthwhile noting that these galaxies have
higher $\Sigma_{SFR}$ than would be predicted from the Schmidt law;
this behavior needs further analysis.  These data confirm the
hypothesis in the previous section that galaxies above the thresold,
i.e. barred spirals, are, on average, prone to higher star formation
activity.

\section{Central Concentrations}

In this section, we examine the re-distribution of the gas by the bar
by calculating a concentration parameter,
f$_{con}$=$\Sigma_{nuc}$/$\Sigma_{disk}$, introduced by Sakamoto et
al. (1999).  The results are plotted in the right panel of Figure 2.
The barred spirals have a mean f$_{con}$ of 60.22$\pm$13.6 whereas the
unbarred spirals have a mean f$_{con}$ of 21.27$\pm$7.32.  A K-S test
shows that the probability of the two samples being drawn from the
same distribution is 7\%.  The SONG data confirm the basic result of
Sakamoto et al. that barred spirals are more centrally concentrated
than unbarred spirals.  The two studies together provide solid
statistical evidence for bar-induced gas transport to the central kpc.

We also find that $\sim$10$^8$ \Msun\ of gas must have been
transported in by the bar, consistent with the OVRO-NRO data.
However, the mean difference in the mass between barred and unbarred
spirals in our sample is 1.7 $\times$10$^8$ \Msun, smaller than the
value derived by Sakamoto et al. because our sample was less biased
towards centrally concentrated galaxies.  As discussed in Sakamoto et
al. (1999), if the mass inflow rate in bars is on the order of 1
\Msun\ \yr, the two studies indicate that the bar destruction time
scale is at least 10$^8$ years, consistent with modeling studies.

\section{Bar Properties and the Central Concentration}
Parameters such as the bar length (or equivalently its pattern speed),
bar ellipticity, and the strength of the bulge are responsible for
controlling the rate of the mass inflow.  One expects that the mass
inflow rate is increased whenever the bulge is small relative to the
bar, the bar is thin, and the bar is long.
\subsection{Bar Length}

The bar length is the most straightforward parameter to calculate.  In
the left panel of Figure 3, we compare the deprojected bar length,
normalized by the galaxy diameter, to the central concentrations.  We
find that there is {\em no} correlation between the bar length and
f$_{con}$.  

Since bar length is a function of the Hubble type (e.g., Elmegreen \&
Elmegreen 1985), we checked the relationship between f$_{con}$
and bar length within each Hubble type bin and found no correlation.
Thus we conclude that bar length alone is a poor indicator of the
central mass concentrations in barred spirals.  Other factors such as
the bar ellipticity or the nuclear star formation rate are equally, if
not more, important in determining the central gas concentration.

\subsection{Bulge type}
 
\begin{figure}
\vspace{0.8in}
\plotfiddle{cenconcvslength.ps}{2.7in}{0}{40}{40}{-210}{0}
\plotfiddle{cenconcvshub.ps}{2.7in}{0}{45}{45}{-46}{190}
\vspace{-3.7in}
\caption{{\bf Left:} f$_{con}$ is plotted against the normalized bar
lengths (a/D$_{25}$.  There is no correlation between the bar length
and the central concentration of gas, implying that bar ellipticity
and/or star formation are equally, if not more important.  {\bf
Right:} f$_{con}$ is plotted against the Hubble type for the barred
(left box) and unbarred spirals (right box).  There is a slight trend
of higher central concentrations in big bulges (i.e., earlier type
bars), but the trend is not statistically significant.}
\end{figure}

In the right hand panel of Figure 3 we compare f$_{con}$ to the bulge
size (using Hubble type as a proxy for bulge size).  For the barred
spirals (left box) we find that for each Hubble type
(ab:b:bc:c:cd:d) the mean value of the central concentration
(146:53:64:44:31:1) shows a trend of decreasing f$_{con}$ with later
Hubble types.  However there is large dispersion in the sample and a
least squares fit shows that the trend is not statistically
significant; a larger sample is necessary to confirm the trend.

If the central concentrations are higher in earlier type bars, then
the presence of inner Lindblad resonances may provide a satisfactory
explanation for the trend.  In models, the inflowing gas accumulates
in a circumnuclear ring located between the outer and inner ILR (Sheth
et al. 2000; Combes 1996).  Though the typical radius of such
circumnuclear rings is $\sim$ 1 kpc (e.g., Buta \& Combes 1996);
however, bigger bulges have deeper potentials and hence the ILR gas
ring is likely to be at smaller radii.

\section{Summary}

Using a 44 galaxy sample from SONG, we found that the central kpc of
bars have high molecular gas surface densities, and that a higher
fraction have $\Sigma_{nuc} > typical\ \Sigma_{crit}$; this may
explain the observed enhancement in circumnuclear star formation
activity in bars, particularly in early type bars.  We also find that
barred spirals are more centrally concentrated than unbarred spirals,
confirming the role of the bar in transporting gas inwards, consistent
with the OVRO-NRO study by Sakamoto et al. (1999).  The central
concentrations are weakly correlated with the bulge size, but not with
the bar length.  suggesting that ILRs, bar ellipticity and star
formation play equally important roles in determining the central kpc
gas properties.

\vspace{-0.1in}
\begin{references}
\reference Bally, J., Stark, A., Wilson, R. W., \& Henkel, C. 1988, \apj, 324, 223.
\reference Buta, R., \& Combes, F. 1996, Fundamentals of Cosmic Physics, 17, 95
\reference Combes, F. 1996, in {\em IAU Colloquium 157, Barred Galaxies}, eds. R. Buta, D.A. Crocker, \& B.G. Elmegreen, (San Francisco:ASP), 286
\reference Elmegreen, B.G., \& Elmegreen, D.M. 1985, \apj, 288, 438
\reference Friedli, D. \& Benz, W. 1993, \aap, 268, 65
\reference Hawarden, T. G., Mountain, C. M., Leggett, S. K., \& Puxley, P. J. 1986, \mnras, 221, 41
\reference Ho, L.C., Filippenko, A.V., \& Sargent, W.L.W. 1997, \apj, 487, 591
\reference Kennicutt, R.C. 1989, \apj, 344, 685
\reference Kennicutt, R.C. 1998, \apj, 498, 541
\reference Kim, W.T., \& Ostriker, E. 2001, \apj, submitted
\reference Martin, P., \& Roy, J. 1994, \apj, 424, 599
\reference Norman, C. A., Sellwood, J. A., \& Hasan, H. 1996, \apj, 462, 114
\reference Regan, M. W., Sheth, K., \& Vogel, S.N. 1999, \apj, 526, 97
\reference Regan, M.W., Helfer, T.T., Thornley, M.D., Sheth, K., Wong, T., Vogel, S.N., Blitz, L., \& Bock, D.C.-J. 2001, \apj, submitted
\reference Sakamoto, K., Okumura, S. K.,  Ishizuki, S., Scoville, N. Z. 1999, \apj, 525, 691
\reference Scoville, N.Z. 1990, in the {\em Proceedings of The Evolution of the Interstellar Medium}, ASP: San Francisco, CA (A91-55426 24-90), p. 49-61.
\reference S\'ersic, J.L. \& Pastoriza, M. 1965, PASP, 77, 287
\reference Shlosman, I., Frank, J., \& Begelman, M.C. 1989, Nature, 338, 45
\reference Sheth, K., Regan, M.W., Vogel, S.N., \& Teuben, P.J. 2000, \apj, 532, 221
\reference Sheth, K. 2001, Ph.D. Thesis, University of Maryland
\reference Sofue, Y., Tutui, Y., Honma, M., Tomita, A., Takamiya, T., Koda, J., \& Takeda, Y. 1999, \apj, 523, 136
\end{references}
\end{document}
