%% This is emulateapj.sty, version April, 3, 1999
%% if this date looks old please check for a newer version at the site below.
%%
%% `emulateapj' is a LaTeX (2.09 or 2e) style to approximate the Astrophysical
%% Journal (ApJ) page look. The length of the resulting document is close to
%% that in ApJ if postscript Times fonts are used instead of the standard CM
%% fonts (see below). `emulateapj' requires `multicol' package available
%% from CTAN archives (www.ctan.org).
%% 
%% The file emulateapj.sty is a modification of the AAS (American Astronomical
%% Society) preprint style aaspp4.sty, including pieces of the TeX
%% apjformat* by someone BLW. If a manuscript is prepared using the standard
%% AAS macros used for the electronic manuscript submission, the only thing
%% the user needs to do is to replace the style `aaspp4' with `emulateapj' in
%% the first line of the document. We tried not to touch any of the nonobvious
%% aaspp4 functionality to save trouble for users, so large parts of the code
%% are probably useless, about which we did not care.
%%
%% The latest version of emulateapj.sty is available from
%% http://hea-www.harvard.edu/~alexey/emulateapj/
%% To use Times postscript fonts, also use the accompanying file apjfonts.sty 
%% (at the site above, you can also pick up a package of font files).
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% Solutions for some common problems:
%% 
%% 1) Because `multicol' package cannot deal with floats of the width of the
%% single column, footnotes, figures, tables etc. can only be set across two
%% columns (that is, use `figure*' environment instead of `figure'.)
%% Alternatively, insert figures as non-floats in the exact place of the text
%% by hand.
%% 
%% 2) There is a command \submitted{your text} to replace the default text
%% in the upper left corner of the front page ("Draft version \today") with
%% `your text'. Use it before the title commands.
%% 
%% 3) There is a package option `onecolumn' (available only with LaTeX2e),
%% \usepackage[onecolumn]{emulateapj}, which sets the whole paper in one
%% column mode (as is done by the ApJ for papers with long equations). Even
%% if the document is `onecolumn', `thebibliography' or `references' are
%% typeset in two columns.
%% 
%% 4) For users of `deluxetable': in LaTeX2e, the table font size cannot be
%% reduced by simply putting a fontsize command inside the 'deluxetable'
%% environment. To change the font size, \tablefontsize command is defined.
%% To use, put e.g., \tablefontsize{\footnotesize} after \begin{deluxetable}.
%%
%% 5) The \title command makes the entire title text, even math, in upper
%% case. If you wish to preserve the lower case in some portion of the
%% title, use  the \lowercase macro, e.g. \title{Upper case text
%% \lowercase{$lower case$}} If you wish to suppress uppercasing in the
%% entire title, redefine the \uppercase macro locally: 
%% {\let\uppercase\relax \title{The Title} }
%% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Copyright 1996-1999 Alexey Vikhlinin and Maxim Markevitch.
%% For parts of the code, Copyright 1994 American Astronomical Society.
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License available from CTAN archives in
%% directory macros/latex/base/lppl.txt. This means you are free to use and
%% distribute this package; however, if you modify anything, please change the
%% file name and remove the authors' email addresses.
%%
%% Alexey Vikhlinin <alexey@head-cfa.harvard.edu>
%% Maxim Markevitch <maxim@head-cfa.harvard.edu>
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% History:
%%
%% circa 96 (MM) original version
%%  6.11.96 (AV) support for thebibliography added; also fix `tabular'
%% 12.12.96 (AV) add command \submitted
%% 10.01.97 (MM) raised title by 8mm, changed section spacing
%% 24.01.97 (AV) fixed Appendix
%% 24.02.97 (AV) fixed appendix interference with thebibliography
%%  7.03.97 (AV) fixed small bug in appendix
%% 16.03.97 (AV) changed definition of {references} and {thebibliography}
%%               to prohibit the page break between the reference section
%%               title and body and the split of a reference item across
%%               columns or pages.
%% 25.06.97 (AV) put \end{multicols} before \end{document} if they were not
%%               closed by bibliography or appendix.
%% 25.06.97 (AV) ``onecolumn'' option: \usepackage[onecolumn]{emulateapj}
%% 15.09.97 (AV) \tablefontsize for plano table to change the font size
%%               throughout the table
%% 15.09.97 (AV) (suggested by Joern Wilms wilms@astro.uni-tuebingen.de)
%%               redefine \figcapion to type the caption text in \footnotesize
%%               and change fnum@figure to type Fig.XXX in \sc
%% 15.09.97 (AV) define \tabcation which makes it possible to typeset
%%               non-floating tables.
%% 21.10.97 (AV) fix \keywords for long keyword lists.
%% 24.10.97 (AV) make title width = abstract
%% 10.12.97 (AV) prohibit hyphenation in the references
%% 10.12.97 (AV) make author list width = 0.9abstract
%% 28.02.98 (AV) define textheight equal to the whole number of lines.
%% 06.03.98 (AV) fix @firstsection in definition of \section
%% 11.05.98 (AV) A sectioning command definition was changed for Apr 4, 98
%%               version, which introduced a bug in labeling mechanism. It
%%               is fixed now.
%% 19.05.98 (AV) \frenchspacing inside references and thebibliography
%% 24.11.98 (AV) \caption{...} produces the right output for both tables and 
%%               and figures without the need of font changes and explicit
%%               alignments.
%% 22.12.98 (AV) Captions are put inside minipage so that in non-floating
%%               mode, they will not split across pages or columns.
%%  9.01.99 (AV) Fixed spurious spacing after \makecaption.
%%  4.03.99 (AV) Redefine eqnarray to remove additional spacing around tab
%%               characters.
%% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\emulapj@ver{04/03/99}

\@ifundefined{documentclass}{ % non-latex2e:
        \input{multicol.sty}\let\scshape=\sc%
        \@ifundefined{epsfbox}{\@input{epsf.sty}}{\relax}}
      {\RequirePackage{multicol,epsf,graphicx}\ProvidesPackage{emulateapj}}



%  ****************************************************
%  *             TWO AND SINGLE ONE COLUMN STYLES: AV *
%  ****************************************************
%
% I define `slocitlum' which is \relax if onecolumn option is chosen or
% plain multicols if twocolumn (default option); `slocitlum' is used
% everywhere except for `thebibliography' and `references' which should be
% always set in two columns.
%
\newenvironment{slocitlum}[1]{\relax}{\relax}
\@ifundefined{documentclass}{ % non-latex2e:
\renewenvironment{slocitlum}[1]{\begin{multicols}{#1}}{\end{multicols}}
}
{ % LaTeX2e; use package option mechanism
\DeclareOption{twocolumn}{
\renewenvironment{slocitlum}[1]{\begin{multicols}{#1}}{\end{multicols}}
}
\DeclareOption{onecolumn}{
\renewenvironment{slocitlum}[1]{\relax}{\relax}
}
\ExecuteOptions{twocolumn}
\ProcessOptions
}


%%%%% include atbeginend.sty by AV:

% Copy \begin and \end to \BeginEnvironment and \EndEnvironment
\let\BeginEnvironment=\begin
\let\EndEnvironment=\end
%% \ifundefined from TeXbook
\def\IfUnDef#1{\expandafter\ifx\csname#1\endcsname\relax}
% Null command needed to eat its argument
\def\NullCom#1{}
\def\begin#1{%
% if defined \BeforeBeg for this environment, execute it
\IfUnDef{BeforeBeg#1}\else\csname BeforeBeg#1\endcsname\fi%
\IfUnDef{AfterBeg#1}% This is done to skip the command for environments
                     % which can take arguments, like multicols; YOU MUST NOT
                     % USE \AfterBegin{...}{...} for such environments!
        \let\SaveBegEnd=\BeginEnvironment%
\else
        % Start this environment
                \BeginEnvironment{#1}%
        % and execute code after \begin{environment}
                \csname AfterBeg#1\endcsname
        \let\SaveBegEnd=\NullCom
\fi
\SaveBegEnd{#1}
}
\def\end#1{%
% execute code before \end{environment}
\IfUnDef{BeforeEnd#1}\else\csname BeforeEnd#1\endcsname\fi%
% close this environment
\EndEnvironment{#1}
% and execute code after \begin{environment}
\IfUnDef{AfterEnd#1}\else\csname AfterEnd#1\endcsname\fi%
}
\def\BeforeBegin#1#2{\expandafter\gdef\csname BeforeBeg#1\endcsname {#2}}
\def\BeforeEnd  #1#2{\expandafter\gdef\csname BeforeEnd#1\endcsname {#2}}
\def\AfterBegin #1#2{\expandafter\gdef\csname AfterBeg#1\endcsname {#2}}
\def\AfterEnd   #1#2{\expandafter\gdef\csname AfterEnd#1\endcsname{#2}}

%%%% end of atbeginend.sty


\def\revtex@ver{4.0}    % Version number of this file.
\def\revtex@date{25 Apr 95}     % Revision date.
\def\revtex@org{AAS}            % Sponsoring organization.
\def\revtex@jnl{AAS}            % Applicable journal, if specific.
\def\revtex@genre{emulateapj}   % Document "type".

%aas % Display identifying message on screen and in logfile.
%aas \typeout{\revtex@org\space \revtex@genre\space substyle,
%aas     v\revtex@ver\space <\revtex@date>.}

%  ****************************************
%  *            PAGE LAYOUT               *
%  ****************************************

% Page size, spacing parameters, etc.

%% (MM) for ApJ approx, using Times-Roman 10pt font:
\textwidth=18.55cm
\columnsep=8.5mm
\parindent=3.5mm
\voffset=-20mm
\hoffset=-9mm

\newlength{\abstrwidth}
\abstrwidth=15.9cm

\topmargin=0in
\headheight=.15in
\headsep=0.5in
\oddsidemargin=0in
\evensidemargin=0in
\parskip=0cm

\tolerance=600          % 3x "normal" value; cuts down on overfull complaints

\def\@tightleading{1.1}
\def\@doubleleading{1.6}

%% AV,MM, to have 63 lines per column, with textheight 25cm:
\def\baselinestretch{0.92}
\textheight=24.4cm
\textheight=63\baselineskip
\textheight=\baselinestretch\textheight
\ifdim\textheight>24.6cm\textheight=24.4cm\fi

\let\tighten=\relax
\let\tightenlines=\tighten
\let\singlespace=\relax
\let\doublespace=\relax

\def\eqsecnum{
    \@newctr{equation}[section]
    \def\theequation{\hbox{\normalsize\arabic{section}-\arabic{equation}}}}

\def\@journalname{The Astrophysical Journal}
\def\cpr@holder{American Astronomical Society}

\def\received#1{\gdef\@recvdate{#1}}    \received{}
\def\accepted#1{\gdef\@accptdate{#1}}   \accepted{}
\def\revised#1{\gdef\@revisedate{#1}}   \revised{}
\def\journalid#1#2{\gdef\@jourvol{#1}\gdef\@jourdate{#2}}
\def\articleid#1#2{\gdef\@startpage{#1}\gdef\@finishpage{#2}}
\def\paperid#1{\gdef\@paperid{#1}} \paperid{MS-0001-SAMP}
\def\ccc#1{\gdef\CCC@code{#1}} \ccc{000-00\$75.95-CDB}

\def\cpright#1#2{\@nameuse{cpr@#1} \gdef\cpr@year{#2}
    \typeout{`#1' copyright \cpr@year.}}

\newcount\@cprtype \@cprtype=\@ne       % Default copyright type.
\def\cpr@AAS{\@cprtype=1}
\def\cpr@PD{\@cprtype=2}
\def\cpr@Crown{\@cprtype=3}
\def\cpr@none{\@cprtype=4}
\def\cpr@ASP{\@cprtype=5}

\def\cpr@year{\number\year}             % Default copyright year.

\def\@slug{\par\noindent
    \ifcase\@cprtype
        \relax
    \or
        Copyright \cpr@year\space by the \cpr@holder.
    \or
        This article is in the public domain.
    \or
        Crown copyright \cpr@year\space by the \cpr@holder.
    \or
        No copyright is claimed for this article.
    \or
        Copyright \cpr@year\space by the ASP.
    \fi
    \par\noindent
    Manuscript number \@paperid.\par\noindent
    \CCC@code
}

%% running heads:
\def\lefthead#1{\gdef\@versohead{#1}} \lefthead{\relax}
\def\righthead#1{\gdef\@rectohead{#1}} \righthead{\relax}

%% MM Create "apjheads" page style:
\def\ps@apjheads{\let\@mkboth\markboth
    \def\@evenfoot{}
    \def\@evenhead{\lower9mm\hbox to\textwidth{
                     \rm\thepage\hfil \rm\@rectohead \hfil}}}
    \def\@oddfoot{}
    \def\@oddhead{\lower9mm\hbox to\textwidth{
                     \hfil\rm\@versohead\hfil \rm\thepage}}
\@twosidetrue
\ps@apjheads

% \@runheads determines formatting of running head information.

\def\@runheads{\@tempcnta\c@page
  \@whilenum \@tempcnta >0\do{
    \vskip 3ex
    \hbox to30pc{\small\expandafter\uppercase\expandafter{\@versohead}:
        \expandafter\uppercase\expandafter{\@rectohead}\hfil}
    \advance\@tempcnta by\m@ne}
}


\def\slugcomment#1{\gdef\slug@comment{#1}} \slugcomment{}

\newdimen\@slugcmmntwidth \@slugcmmntwidth .67\textwidth
\long\def\@makeslugcmmnt{\ifx\slug@comment\@empty\relax\else
    \setbox\@tempboxa\hbox{\slug@comment}
    \ifdim \wd\@tempboxa >\@slugcmmntwidth
        \hbox to\textwidth{\hss
            \parbox\@slugcmmntwidth\slug@comment}
    \else
        \hbox to\textwidth{\hfil\box\@tempboxa}  
    \fi
    \vskip 2ex
\fi}

\def\@rcvaccrule{\vrule\@width1.75in\@height0.5pt\@depth\z@}
\def\@dates{{\center\if@twocolumn\small\else\normalsize\fi%
    {\it Received}\space%
    \ifx\@empty\@recvdate\@rcvaccrule\else\@recvdate\fi;%
    \if@twocolumn\\[.5ex]\else\hspace{1.5em}\fi%
    {\it accepted}\space%
    \ifx\@empty\@accptdate\@rcvaccrule\else\@accptdate\fi%
    \endcenter}
}
\def\sluginfo{{\center
    \@dates
    %\@slug
    %\@runheads
    \endcenter}}
\let\dates=\sluginfo    % Backwards compatibility

%  ****************************************
%  *            FRONT MATTER              *
%  ****************************************

%% AV renewed
\@ifundefined{documentclass}{ % non-latex2e:
\let\abstract\relax
\let\endabstract\relax
\def\abstract{\bgroup\center\minipage{\abstrwidth}
\vspace{2pt}\centerline{ABSTRACT}   \vspace{3pt} \parindent=3.5mm}
\def\endabstract{\endminipage \endcenter \egroup}
}
{% LaTeX 2e definition
\renewenvironment{abstract}[0]{\center
    \begin{minipage}{\abstrwidth}
    \vspace{2pt}
    \centerline{ABSTRACT}
    \vspace{3pt}
    \parindent=3.5mm}
{\end{minipage}\endcenter}
}
\BeforeBegin{abstract}{\centerline{\small\it{\@submitted}}}

%% MM
%% "apjbot" for the title page:
\def\ps@apjbot{
    \def\@oddfoot{\raise7mm\hbox to\textwidth{\hfil\rm\thepage\hfil}}
    \def\@oddhead{}}

\def\title#1{{\thispagestyle{apjbot}
  \subtitle
  \vspace{12mm}
  \center
\begin{minipage}{\abstrwidth}
\center\uppercase{#1}\endcenter
\end{minipage}\endcenter}}

\def\author#1{
\vspace*{-1.5ex}%
{\topsep 3pt
\center
\begin{minipage}{0.9\abstrwidth}\center\small\scshape#1\endcenter\end{minipage}
\endcenter
}
\vspace*{-1pt}}
\let\authoraddr=\@gobble
\let\authoremail=\@gobble

\def\affil#1{\vspace*{-0.8ex}{\topsep 0pt\center
\begin{minipage}{0.9\abstrwidth}\center\footnotesize%
\def\baselinestretch{1.0}%
#1\endcenter\end{minipage}
\endcenter}}

\def\altaffilmark#1{$^{#1}$}
\def\altaffiltext#1#2{\footnotetext[#1]{#2}\stepcounter{footnote}}


% Redefine the LaTeX \and command for this style.
%% MM
\def\and{\vspace{0pt}{\topsep\z@\center {\sc and}\endcenter}\vspace{3pt}}

%  ****************************************
%  *             KEYWORDS                 *
%  ****************************************

\def\@keywordtext{Subject headings}
\def\@keyworddelim{---}

%% MM,AV
\newlength{\kwdtextwidth}
\settowidth{\kwdtextwidth}{{\it\@keywordtext:\/}}
\def\keywords#1{\begin{center}
  \begin{minipage}{\abstrwidth}
  \vspace*{-6pt}\raggedright
  \par\hangindent=\kwdtextwidth\hangafter=1 \noindent
  {\it\@keywordtext:\/}\space #1
  \end{minipage}  
\end{center}}

\let\subjectheadings=\keywords

\def\@kwds#1{#1\relax}


%  ****************************************
%  *             FOOTNOTES                *
%  ****************************************

%% MM
\skip\footins 2mm
\footnotesep 2ex
\let\footnoterule\relax

\def\notetoeditor#1{}%

%  ****************************************
%  *             SECTIONS                 *
%  ****************************************

\newif\if@firstsection \@firstsectiontrue

%% MM: section vertical indents by eye:
\def\section{%
    \if@firstsection\@firstsectionfalse\begin{slocitlum}{2}\fi%
    \@startsection{section}{1}{\z@}{10pt plus 2pt minus 1pt}{5pt}{\footnotesize \center}}

\def\subsection{\@startsection{subsection}{2}{\z@}{5pt plus 1pt minus 1pt}{5pt}%
{\normalsize\it \center}}

\def\subsubsection{\@startsection{subsubsection}{3}{\z@}%
    {2ex plus 1ex minus .2ex}{1ex plus .2ex}{\normalsize\it \center}}

\def\thesection{\@arabic{\c@section}}
\def\thesubsection{\thesection.\@arabic{\c@subsection}}
\def\thesubsubsection{\thesubsection.\@arabic{\c@subsubsection}}
\def\theparagraph{\thesubsubsection.\@arabic{\c@paragraph}}


\def\sec@upcase#1{\uppercase{#1}}
\def\subsec@upcase#1{\relax{#1}}

\def\secnum@size{\small}
\def\subsecnum@size{\normalsize}

%
% How the section number will appear in the section title - AV
\def\ApjSectionMarkInTitle#1{#1.\ }

\def\@sect#1#2#3#4#5#6[#7]#8%
{\@tempskipa #5\relax 
 \ifdim \@tempskipa >\z@ \begingroup
     #6\relax 
  \ifnum #2>\c@secnumdepth \def \@svsec {}\else 
    \refstepcounter{#1} \edef \@svsec {\ApjSectionMarkInTitle 
    {\csname the#1\endcsname}}\fi
  \@hangfrom {\hskip #3\relax 
    \ifnum #2=1\secnum@size {\rm\@svsec~}%
    \else \subsecnum@size {\rm\@svsec~}\fi }%
  {\interlinepenalty \@M 
   \ifnum #2=1\sec@upcase{#8}%
   \else \subsec@upcase{#8}\fi\par}\endgroup 
  \csname #1mark\endcsname {#7}\addcontentsline{toc}{#1}%
  {\ifnum #2>\c@secnumdepth \else \protect \numberline 
     {\csname the#1\endcsname }\fi #7}%
  \else 
  \ifnum #2>\c@secnumdepth \def \@svsec {}\else 
    \refstepcounter{#1} \edef \@svsec {\ApjSectionMarkInTitle 
    {\csname the#1\endcsname}}\fi
    \def \@svsechd {#6\hskip #3%
    \ifnum #2=1\secnum@size{\rm\@svsec~}\else\subsecnum@size{\rm\@svsec~}\fi%
    \ifnum #2=1\sec@upcase{#8}\else\subsec@upcase{#8}\fi%
     \csname #1mark\endcsname {#7}\addcontentsline{toc}{#1}%
      {\ifnum #2>\c@secnumdepth \else \protect \numberline {\csname
      the#1\endcsname }\fi #7}}\fi \@xsect {#5} \penalty 0
%-refstepcounter is now within a group. So \@currentlabel, which is normally
%-set by \refstepcounter is hidden within a group. Need to set it manually.
\protected@edef\@currentlabel{\csname p@#1\endcsname\csname the#1\endcsname}
}

% \def\@sect#1#2#3#4#5#6[#7]#8{%
%      \ifnum #2>\c@secnumdepth
%      \def\@svsec{}\else
% %     \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname.\ }\fi
%      \refstepcounter{#1}\edef\@svsec{\ApjSectionMarkInTitle{\csname the#1\endcsname}}\fi
%      \@tempskipa #5\relax
%       \ifdim \@tempskipa>\z@
%         \begingroup #6\relax
%           \@hangfrom{\hskip #3\relax%
%       \ifnum#2=1\secnum@size{\rm\@svsec}
%       \else\subsecnum@size{\rm\@svsec~}\fi%
%       }{\interlinepenalty \@M 
%       \ifnum#2=1\sec@upcase{#8}\else\subsec@upcase{#8}\fi\par}%
%         \endgroup
%        \csname #1mark\endcsname{#7}\addcontentsline
%          {toc}{#1}{\ifnum #2>\c@secnumdepth \else
%                       \protect\numberline{\csname the#1\endcsname}\fi
%                     #7}\else
%        \def\@svsechd{#6\hskip #3\@svsec \sec@upcase{#8}\csname #1mark\endcsname
%                       {#7}\addcontentsline
%                            {toc}{#1}{\ifnum #2>\c@secnumdepth \else
%                              \protect\numberline{\csname the#1\endcsname}\fi
%                        #7}}\fi
%      \@xsect{#5}
% % MM:
% \penalty 0}

\def\@ssect#1#2#3#4#5{\@tempskipa #3\relax
   \ifdim \@tempskipa>\z@
     \begingroup #4\@hangfrom{\hskip #1}{\interlinepenalty \@M
       \sec@upcase{#5}\par}\endgroup
   \else \def\@svsechd{#4\hskip #1\relax \sec@upcase{#5}}\fi
    \@xsect{#3}
% MM:
\penalty 0}


\def\acknowledgments{\vskip 3ex plus .8ex minus .4ex}
\let\acknowledgements=\acknowledgments                  % second spelling


%  ****************************************
%  *          APPENDIX                    *
%  ****************************************

\def\NoApjSectionMarkInTitle#1{\relax}
\renewenvironment{appendix}[0]{
        \if\inmulticols\inmulticolstest\end{slocitlum}\fi
        \vskip 10pt plus 2pt minus 1pt
        \centerline{\small APPENDIX}
        \@firstsectionfalse
          \setcounter{section}{0}
          \setcounter{subsection}{0}
          \setcounter{equation}{0}
%  \setcounter{figure}{0}
%  \setcounter{table}{0}
%  \def\fnum@figure{Figure \Alph{section}\thefigure:}
%  \def\fnum@table{Table \Alph{section}\thetable:}
          \def\thesection{\Alph{section}}
% \def\theequation{\hbox{\normalsize\Alph{section}\arabic{equation}}}
%
% The following command causes LaTeX 2e to overflow its parameter stack. If
% TeX is rebuilt with a larger parameter stack, this can be corrected: remove
% the three lines below and uncomment the line above.
%
  \@ifundefined{documentclass}
     {\def\theequation{\normalsize\hbox{\Alph{section}\arabic{equation}}}}
     {\def\theequation{\hbox{\Alph{section}\arabic{equation}}}}
  \def\thefigure{\thesection\@arabic\c@figure}
  \def\thetable{\thesection\@arabic\c@table}
%
% Do not use appendix numbers in the titles
  \def\ApjSectionMarkInTitle{\NoApjSectionMarkInTitle}
  \def\section{\setcounter{equation}{0}\@startsection {section}{1}{\z@} 
    {10pt}{5pt}{\centering\small}}
}{}
\BeforeBegin{appendix}{\if\inmulticols\inmulticolstest\end{slocitlum}}

% EQNARRAY with reduced spacing around tab characters - AV
\def\eqnarray{%
   \stepcounter{equation}%
   \def\@currentlabel{\p@equation\theequation}%
   \global\@eqnswtrue
   \setlength{\arraycolsep}{0.25\arraycolsep}
   \m@th
   \global\@eqcnt\z@
   \tabskip\@centering
   \let\\\@eqncr
   $$\everycr{}\halign to\displaywidth\bgroup
       \hskip\@centering$\displaystyle\tabskip\z@skip{##}$\@eqnsel
      &\global\@eqcnt\@ne\hskip \tw@\arraycolsep \hfil${##}$\hfil
      &\global\@eqcnt\tw@ \hskip \tw@\arraycolsep
         $\displaystyle{##}$\hfil\tabskip\@centering
      &\global\@eqcnt\thr@@ \hb@xt@\z@\bgroup\hss##\egroup
         \tabskip\z@skip
      \cr
}



%  ****************************************
%  *          EQUATION NUMBERING          *
%  ****************************************

\newcounter{cureqno}
\newenvironment{mathletters}{\refstepcounter{equation}%
    \setcounter{cureqno}{\value{equation}}%
    \let\@curtheeqn\theequation%
    \edef\cur@eqn{\theequation}%
    \def\theequation{\cur@eqn\alph{equation}}%
    \setcounter{equation}{0}}%
    {\let\theequation\@curtheeqn%
    \setcounter{equation}{\value{cureqno}}}

\def\eqnum#1{\def\theequation{#1}\let\@currentlabel\theequation
    \addtocounter{equation}{\m@ne}}


%  ****************************************
%  *          BIBLIOGRAPHY                *
%  ****************************************

\newenvironment{references}[0]{
    \vspace{3pt plus 3pt}
%     \hbox to \textwidth{\centerline{\footnotesize REFERENCES}}
%     \vspace{-5pt}
    \begin{multicols}{2}[\hbox to \textwidth{\centerline{\footnotesize
REFERENCES}} \vspace{-5pt}]
    \parindent=0cm \parskip=0cm
    \footnotesize \baselineskip=8pt \interlinepenalty \@M
    \hyphenpenalty=10000
    \frenchspacing    % AV - to get right spacing after ``et al.''
    \def\refpar{\par\hangindent=1.2em\hangafter=1}}
{\end{multicols}}

% redefine thebibliography
\renewenvironment{thebibliography}[1]{
            \vspace{3pt plus 3 pt}                                      % AV
            \begin{multicols}{2}[\hbox                                  % AV
                to \textwidth{\centerline{\footnotesize                 % AV
                REFERENCES}} \vspace{-5pt}]                             % AV
      \list{
           \@biblabel{\@arabic\c@enumiv}}%
           {
                \@openbib@code
                \parindent=0pt \parskip=0pt \parsep=0pt % AV
                \bibindent=0pt                          %
                \footnotesize \baselineskip=8pt  \interlinepenalty \@M  % AV
                \frenchspacing    % AV - to get right spacing after ``et al.''
                \hyphenpenalty=10000
                \itemindent=-1.0em                      %
                \itemsep=0pt                            %
                \listparindent=0pt                      %
                \settowidth\labelwidth{\@biblabel{#1}}  %
                \labelsep=0pt                           %
                \leftmargin=1.0em
                \advance\leftmargin\labelsep
                \usecounter{enumiv}%
                \let\p@enumiv\@empty
                \renewcommand\theenumiv{\@arabic\c@enumiv}}%
                \sloppy\clubpenalty4000\widowpenalty4000%
                \sfcode`\.\@m}
     {\def\@noitemerr
       {\@latex@warning{Empty `thebibliography' environment}}%
      \endlist\if\inmulticols\inmulticolstest\end{multicols}\fi}

% %% AV: 
\def\inmulticols{0}
\def\inmulticolstest{1}
\BeforeBegin{multicols}{\def\inmulticols{1}}
\AfterEnd{multicols}{\def\inmulticols{0}}
\BeforeBegin{slocitlum}{\def\inmulticols{1}}
\AfterEnd{slocitlum}{\def\inmulticols{0}}


\BeforeBegin{references}{\if\inmulticols\inmulticolstest\end{slocitlum}%
                        \else\vspace{10pt}\fi}
\BeforeBegin{thebibliography}{\if\inmulticols\inmulticolstest\end{slocitlum}%
                        \else\vspace{10pt}\fi}
\BeforeEnd{document}{\if\inmulticols\inmulticolstest\end{slocitlum}\fi}


%aas \subsection*{\small REFERENCES}
%aas \list{\null}{\leftmargin 1.2em\labelwidth\z@\labelsep\z@\itemindent -1.2em
%aas     \usecounter{enumi}}
%aas     \def\refpar{\relax}
%aas     \def\newblock{\hskip .11em plus .33em minus .07em}
%aas     \sloppy\clubpenalty4000\widowpenalty4000
%aas     \sfcode`\.=1000\relax}
%aas \def\endthebibliography{\endlist\revtex@pageid}

\def\@biblabel#1{\relax}
%\def\@cite#1#2{({#1\if@tempswa , #2\fi})}
\def\@cite#1#2{#1\if@tempswa , #2\fi}

\def\reference{\@ifnextchar\bgroup {\@reference}
        {\@latexerr{Missing key on reference command}
        {Each reference command should have a key corresponding to a markcite somewhere in the text}}}
\def\@reference#1{\relax\refpar}

\def\markcite{\@ifnextchar\bgroup{\@markcite}
        {\@latexerr{Missing key on markcite command}
        {Each markcite command should have a key corresponding to a reference somewhere in the references section}}}
\def\@markcite#1{\relax}

\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi
  \def\@citea{}\@cite{\@for\@citeb:=#2\do
    {\@citea\def\@citea{,\penalty\@m\ }\@ifundefined
       {b@\@citeb}{\@warning
       {Citation `\@citeb' on page \thepage \space undefined}}%
{\csname b@\@citeb\endcsname}}}{#1}}


%% subtitle header:
\def\submitted#1{\gdef\@submitted{#1}}
\def\subtitle{
  \vspace*{-12mm}
  \noindent
  {\scriptsize {\sc \@submitted} \\
        Preprint typeset using \LaTeX\ style emulateapj v.\ \emulapj@ver}
}
\let\slugcomment\submitted   % slugcomment == submitted
\submitted{Draft version \today}

%% AV: allow figures to take the whole page
\renewcommand{\topfraction}{1.0}
\renewcommand{\bottomfraction}{1.0}
\renewcommand{\textfraction}{0.0}


%  ****************************************
%  *         TABLES AND FIGURES           *
%  ****************************************

\setcounter{topnumber}{7}
\def\tablenotemark#1{\rlap{$^{\rm #1}$}}
\newtoks\@temptokenb
\def\tblnote@list{}

\def\tablenotetext#1#2{
    \@temptokena={\vspace{.5ex}{\noindent\llap{$^{#1}$}#2}\par}
    \@temptokenb=\expandafter{\tblnote@list}
    \xdef\tblnote@list{\the\@temptokenb\the\@temptokena}}

\def\spew@tblnotes{
  \ifx\tblnote@list\@empty\relax
  \else
    \vspace{3.2ex}
    \footnoterule
    \vspace{.4ex}
    {\footnotesize\tblnote@list}
    \gdef\tblnote@list{}
  \fi}

\def\endtable{\spew@tblnotes\end@float}
\@namedef{endtable*}{\spew@tblnotes\end@dblfloat}

\let\tableline=\hline

%\long\def\@makecaption#1#2{\vskip 2ex\noindent #1 #2\par}
\setlength{\belowcaptionskip}{0pt}
\setlength{\abovecaptionskip}{5pt}
\long\def\@makecaption#1#2{%
  \noindent\begin{minipage}{0.99\linewidth} %% \noindent is needed because
    %% otherwise minipage + parindent does not fit into the line and spurious
    %% vertical skip appear after caption
    \if\csname ftype@\@captype\endcsname 2  
      \vskip 2ex\noindent \centering\small\sc  #1 #2\par\medskip
    \else
      \vskip \abovecaptionskip\footnotesize\noindent #1 #2\par\vskip \belowcaptionskip
    \fi
  \end{minipage}
}

\def\tablenum#1{\def\thetable{#1}\let\@currentlabel\thetable
    \addtocounter{table}{\m@ne}}

\def\figurenum#1{\def\thefigure{#1}\let\@currentlabel\thefigure
    \addtocounter{figure}{\m@ne}}

\let\placetable=\@gobble
\let\placefigure=\@gobble
\let\placeplate=\@gobble

\def\figcaption{\@ifnextchar[{\@xfigcaption}{\@figcaption}}
% \def\@figcaption#1{{\def\@captype{figure}\caption{#1}}}
% \def\@xfigcaption[#1]#2{{\def\@captype{figure}\caption{#2}}}

%% suggested by Joern Wilms wilms@astro.uni-tuebingen.de 
%%                          wilms@rocinante.colorado.edu
\def\@figcaption#1{{\def\@captype{figure}\caption{\footnotesize #1}}}
\def\@xfigcaption[#1]#2{{\def\@captype{figure}\caption{\footnotesize #2}}}


\def\dummytable{\refstepcounter{table}}

%%%%
%%%% the code below is unchanged from aaspp4.sty:
%%%%

%  ****************************************
%  *           PLANO TABLES               *
%  ****************************************

\newbox\pt@box
\newdimen\pt@width
\newcount\pt@line
\newcount\pt@column
\newcount\pt@nlines
\newcount\pt@ncol
\newcount\pt@page

\def\colhead#1{\multicolumn{1}{c}{#1}\pt@addcol}
\def\tablecolumns#1{\pt@column=#1\pt@ncol=#1\gdef\pt@addcol{\relax}}
\def\tablecaption#1{\gdef\pt@caption{#1}} \def\pt@caption{\relax}
\def\tablehead#1{\gdef\pt@head{\hline\hline\relax\\[-1.7ex]
    #1\hskip\tabcolsep\\[.7ex]\hline\relax\\[-1.5ex]}} \def\pt@head{\relax}
\def\tabletail#1{\gdef\pt@tail{#1}} \def\pt@tail{\relax}
\def\tablewidth#1{\pt@width=#1} \pt@width\textwidth
\def\tableheadfrac#1{\gdef\pt@headfrac{#1}} \def\pt@headfrac{.1}
\def\tablefontsize#1{\gdef\pt@fontsize{#1}} \def\pt@fontsize{\relax}

\def\pt@calcnlines{\@tempdima\pt@headfrac\textheight
    \@tempdimb\textheight\advance\@tempdimb by-\@tempdima
    \@tempdima\arraystretch\baselineskip
    \divide\@tempdimb by\@tempdima
    \global\pt@nlines\@tempdimb}


\def\pt@tabular{\hbox \bgroup \pt@fontsize $\let\@acol\@ptabacol 
   \let\@classz\@tabclassz
   \let\@classiv\@tabclassiv \let\\\@tabularcr\@tabarray}

\def\@ptabacol{\edef\@preamble{\@preamble \hskip \tabcolsep\tabskip\fill}}

\def\fnum@ptable{Table \thetable}
\def\fnum@ptablecont{Table \thetable---{\it Continued}}

\newdimen\pt@tmpcapwidth
\def\set@mkcaption{\long\def\@makecaption##1##2{\ifdim\pt@width>\z@%
    \pt@tmpcapwidth\pt@width\else\pt@tmpcapwidth\textwidth\fi%
    \center\parbox{\pt@tmpcapwidth}{\center\sc##1\\[.5ex]##2\endcenter}%
    \endcenter}}
%\def\set@mkcaption{\long\def\@makecaption##1##2{
%    \center\sc##1\\[.5ex]##2\endcenter\vskip 1.5ex}}
\def\set@mkcaptioncont{\long\def\@makecaption##1##2{
    \center\sc##1\endcenter\vskip 1.5ex}}

\newenvironment{deluxetable}[1]{\def\pt@format{\string#1}%
    \set@tblnotetext\global\pt@ncol=0\global\pt@column=0\global\pt@page=1%
    \def\pt@addcol{\global\advance\pt@ncol by\@ne}}%
    {%\crcr\noalign{\vskip .7ex}\hline\endtabular%
    \pt@width\wd\pt@box\box\pt@box\spew@ptblnotes%
    \typeout{Page \the\pt@page\space of table \thetable\space has been set to 
           width \the\pt@width\space with \the\pt@nlines\space lines per page}%
    \endcenter\end@dblfloat}
\let\planotable=\deluxetable
\let\endplanotable=\enddeluxetable

\def\startdata{\pt@line=0\pt@calcnlines%
    \ifdim\pt@width>\z@\def\@halignto{to \pt@width}\else\def\@halignto{}\fi%
    \let\fnum@table=\fnum@ptable\set@mkcaption%
    \@dblfloat{table}\center\caption{\pt@caption}\leavevmode%
    \setbox\pt@box=\pt@tabular{\pt@format}\pt@head}
\def\enddata{\crcr\noalign{\vskip .7ex}\hline\endtabular}

\def\pt@nl{\global\advance\pt@line by\@ne%
  \ifnum\pt@line=\pt@nlines%
    \endtabular\pt@width\wd\pt@box\box\pt@box
    \typeout{Page \the\pt@page\space of table \thetable\space has been set to
             width \the\pt@width}%
    \global\advance\pt@page by\@ne%
    \endcenter\end@dblfloat\clearpage%
    \addtocounter{table}{\m@ne}%
    \let\fnum@table=\fnum@ptablecont\set@mkcaptioncont%
    \@dblfloat{table}\center\caption{\pt@caption}\leavevmode%
    \global\pt@ncol=\pt@column%  Either 0 or value of \tablecolumns 
    \global\pt@line=0%
    \setbox\pt@box=\pt@tabular{\pt@format}\pt@head%
  \else\\
  \fi}

\let\nl=\pt@nl
\let\nextline=\pt@nl

\def\tablevspace#1{\noalign{\vskip#1}}
\def\tablebreak{\pt@line\pt@nlines\advance\pt@line by\m@ne\pt@nl}

\def\cutinhead#1{\noalign{\vskip 1.5ex}
    \hline\pt@nl\noalign{\vskip -2.0ex}
    \multicolumn{\pt@ncol}{c}{#1}\pt@nl
    \noalign{\vskip .8ex}
    \hline\pt@nl\noalign{\vskip -2ex}}

\def\sidehead#1{\noalign{\vskip 1.5ex}
    \multicolumn{\pt@ncol}{@{\hskip\z@}l}{#1}\pt@nl
    \noalign{\vskip .5ex}}

\def\set@tblnotetext{\def\tablenotetext##1##2{{%
    \@temptokena={{\parbox{\pt@width}{\hskip1em$^{\rm ##1}$##2}}\par}%
    \@temptokenb=\expandafter{\tblnote@list}
    \xdef\tblnote@list{\the\@temptokenb\the\@temptokena}}}}

\def\spew@ptblnotes{
  \ifx\tblnote@list\@empty\relax
  \else
    \par
    \vspace{2ex}
    {\parskip=1.5ex%
    \tblnote@list}
    \gdef\tblnote@list{}
  \fi}

\def\tablerefs#1{\@temptokena={\vspace*{3ex}{%
    \parbox{\pt@width}{\hskip1em{\sc References.---}#1}\par}}%
    \@temptokenb=\expandafter{\tblnote@list}
    \xdef\tblnote@list{\the\@temptokenb\the\@temptokena}}

\def\tablecomments#1{\pt@fontsize\@temptokena={\vspace*{3ex}{%
    \parbox{\pt@width}{\hskip1em{\sc Note.---}#1}\par}}%
    \@temptokenb=\expandafter{\tblnote@list}
    \xdef\tblnote@list{\the\@temptokenb\the\@temptokena}}



%  ****************************************
%  *   FIGURE, TABLE, PLATE PARAMETERS    *
%  ****************************************

\newcounter{plate}
\def\theplate{\@arabic\c@plate}

\def\fps@plate{bp}
\def\ftype@plate{4}                     % Yes.  This must a power of 2.
\def\ext@plate{lof}                     % Put plates in LOF.
\def\fnum@plate{{\bf Plate \theplate.}}
\def\plate{\@float{plate}}
\let\endplate\end@float
\@namedef{plate*}{\@dblfloat{plate}}
\@namedef{endplate*}{\end@dblfloat}
\let\platewidth=\tablewidth
\def\platenum#1{\def\theplate{#1}\let\@currentlabel\theplate
    \addtocounter{plate}{\m@ne}}

\def\thefigure{\@arabic\c@figure}
\def\fnum@figure{{\footnotesize\sc ~~Fig.\space\thefigure.---}}

\def\thetable{\@arabic\c@table}
%%% Table captions without making a floating table
\def\tabcaption{\@ifnextchar[{\@xtabcaption}{\@tabcaption}}
\def\@tabcaption#1{{\def\@captype{table}\caption{#1}}}
\def\@xtabcaption[#1]#2{{\def\@captype{table}\caption{#2}}}
\def\fnum@table{{\centering{\sc Table~\thetable}\vskip0.7ex}}

\def\fps@figure{bp}
\def\fps@table{bp}

%  ****************************************
%  *           EPS INCLUSIONS             *
%  ****************************************


\def\eps@scaling{.95}
\def\epsscale#1{\gdef\eps@scaling{#1}}

\def\plotone#1{\centering \leavevmode
    \epsfxsize=\eps@scaling\columnwidth \epsfbox{#1}}

\def\plottwo#1#2{\centering \leavevmode
    \epsfxsize=.45\columnwidth \epsfbox{#1} \hfil
    \epsfxsize=.45\columnwidth \epsfbox{#2}}

\def\plotfiddle#1#2#3#4#5#6#7{\centering \leavevmode
    \vbox to#2{\rule{0pt}{#2}}
    \special{psfile=#1 voffset=#7 hoffset=#6 vscale=#5 hscale=#4 angle=#3}}

%  ****************************************
%  *            ABBREVIATIONS             *
%  ****************************************

\let\jnl@style=\rm
\def\ref@jnl#1{{\jnl@style#1}}

\def\aj{\ref@jnl{AJ}}                   % Astronomical Journal
\def\araa{\ref@jnl{ARA\&A}}             % Annual Review of Astron and Astrophys
\def\apj{\ref@jnl{ApJ}}                 % Astrophysical Journal
\def\apjl{\ref@jnl{ApJ}}                % Astrophysical Journal, Letters
\def\apjs{\ref@jnl{ApJS}}               % Astrophysical Journal, Supplement
\def\ao{\ref@jnl{Appl.~Opt.}}           % Applied Optics
\def\apss{\ref@jnl{Ap\&SS}}             % Astrophysics and Space Science
\def\aap{\ref@jnl{A\&A}}                % Astronomy and Astrophysics
\def\aapr{\ref@jnl{A\&A~Rev.}}          % Astronomy and Astrophysics Reviews
\def\aaps{\ref@jnl{A\&AS}}              % Astronomy and Astrophysics, Supplement
\def\azh{\ref@jnl{AZh}}                 % Astronomicheskii Zhurnal
\def\baas{\ref@jnl{BAAS}}               % Bulletin of the AAS
\def\jrasc{\ref@jnl{JRASC}}             % Journal of the RAS of Canada
\def\memras{\ref@jnl{MmRAS}}            % Memoirs of the RAS
\def\mnras{\ref@jnl{MNRAS}}             % Monthly Notices of the RAS
\def\pra{\ref@jnl{Phys.~Rev.~A}}        % Physical Review A: General Physics
\def\prb{\ref@jnl{Phys.~Rev.~B}}        % Physical Review B: Solid State
\def\prc{\ref@jnl{Phys.~Rev.~C}}        % Physical Review C
\def\prd{\ref@jnl{Phys.~Rev.~D}}        % Physical Review D
\def\pre{\ref@jnl{Phys.~Rev.~E}}        % Physical Review E
\def\prl{\ref@jnl{Phys.~Rev.~Lett.}}    % Physical Review Letters
\def\pasp{\ref@jnl{PASP}}               % Publications of the ASP
\def\pasj{\ref@jnl{PASJ}}               % Publications of the ASJ
\def\qjras{\ref@jnl{QJRAS}}             % Quarterly Journal of the RAS
\def\skytel{\ref@jnl{S\&T}}             % Sky and Telescope
\def\solphys{\ref@jnl{Sol.~Phys.}}      % Solar Physics
\def\sovast{\ref@jnl{Soviet~Ast.}}      % Soviet Astronomy
\def\ssr{\ref@jnl{Space~Sci.~Rev.}}     % Space Science Reviews
\def\zap{\ref@jnl{ZAp}}                 % Zeitschrift fuer Astrophysik
\def\nat{\ref@jnl{Nature}}              % Nature
\def\iaucirc{\ref@jnl{IAU~Circ.}}       % IAU Cirulars
\def\aplett{\ref@jnl{Astrophys.~Lett.}} % Astrophysics Letters
\def\apspr{\ref@jnl{Astrophys.~Space~Phys.~Res.}}
                % Astrophysics Space Physics Research
\def\bain{\ref@jnl{Bull.~Astron.~Inst.~Netherlands}} 
                % Bulletin Astronomical Institute of the Netherlands
\def\fcp{\ref@jnl{Fund.~Cosmic~Phys.}}  % Fundamental Cosmic Physics
\def\gca{\ref@jnl{Geochim.~Cosmochim.~Acta}}   % Geochimica Cosmochimica Acta
\def\grl{\ref@jnl{Geophys.~Res.~Lett.}} % Geophysics Research Letters
\def\jcp{\ref@jnl{J.~Chem.~Phys.}}      % Journal of Chemical Physics
\def\jgr{\ref@jnl{J.~Geophys.~Res.}}    % Journal of Geophysics Research
\def\jqsrt{\ref@jnl{J.~Quant.~Spec.~Radiat.~Transf.}}
                % Journal of Quantitiative Spectroscopy and Radiative Trasfer
\def\memsai{\ref@jnl{Mem.~Soc.~Astron.~Italiana}}
                % Mem. Societa Astronomica Italiana
\def\nphysa{\ref@jnl{Nucl.~Phys.~A}}   % Nuclear Physics A
\def\physrep{\ref@jnl{Phys.~Rep.}}   % Physics Reports
\def\physscr{\ref@jnl{Phys.~Scr}}   % Physica Scripta
\def\planss{\ref@jnl{Planet.~Space~Sci.}}   % Planetary Space Science
\def\procspie{\ref@jnl{Proc.~SPIE}}   % Proceedings of the SPIE

\let\astap=\aap
\let\apjlett=\apjl
\let\apjsupp=\apjs
\let\applopt=\ao

%  ****************************************
%  *            MISCELLANEOUS             *
%  ****************************************

\def\phn{\phantom{0}}       % Phantom numeral for aligning columns in tables
\def\phd{\phantom{.}}       % Phantom decimal for aligning columns in tables
\def\phs{\phantom{$-$}}     % Phantom minus sign for aligning columns in tables
\def\phm#1{\phantom{#1}}    % Generic \phantom command
\def\sun{\hbox{$\odot$}}
\def\earth{\hbox{$\oplus$}}
\def\lesssim{\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$}}}\hbox{$<$}}}}
\def\gtrsim{\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$}}}\hbox{$>$}}}}
\def\sq{\hbox{\rlap{$\sqcap$}$\sqcup$}}
\def\arcdeg{\hbox{$^\circ$}}
\def\arcmin{\hbox{$^\prime$}}
\def\arcsec{\hbox{$^{\prime\prime}$}}
\def\fd{\hbox{$.\!\!^{\rm d}$}}
\def\fh{\hbox{$.\!\!^{\rm h}$}}
\def\fm{\hbox{$.\!\!^{\rm m}$}}
\def\fs{\hbox{$.\!\!^{\rm s}$}}
\def\fdg{\hbox{$.\!\!^\circ$}}
\def\farcm{\hbox{$.\mkern-4mu^\prime$}}
\def\farcs{\hbox{$.\!\!^{\prime\prime}$}}
\def\fp{\hbox{$.\!\!^{\scriptscriptstyle\rm p}$}}
\def\micron{\hbox{$\mu$m}}

\let\la=\lesssim                        % For Springer A&A compliance...
\let\ga=\gtrsim

\def\case#1#2{\hbox{$\frac{#1}{#2}$}}
 
\def\slantfrac#1#2{\hbox{$\,^#1\!/_#2$}}
\def\onehalf{\slantfrac{1}{2}}
\def\onethird{\slantfrac{1}{3}}
\def\twothirds{\slantfrac{2}{3}}
\def\onequarter{\slantfrac{1}{4}}
\def\threequarters{\slantfrac{3}{4}}

\def\ubvr{\hbox{$U\!BV\!R$}}            % UBVR system
\def\ub{\hbox{$U\!-\!B$}}               % U-B
\def\bv{\hbox{$B\!-\!V$}}               % B-V
\def\vr{\hbox{$V\!-\!R$}}               % V-R
\def\ur{\hbox{$U\!-\!R$}}               % U-R

\def\ion#1#2{#1$\;${\small\rm\@Roman{#2}}\relax}

%\def\cellipsis{\hfill$\cdots$\hfill}
%\def\nodata{\multicolumn{1}{c}{$\cdots$}}
\def\nodata{ ~$\cdots$~ }

\newcount\lecurrentfam
\def\LaTeX{\lecurrentfam=\the\fam \leavevmode L\raise.42ex
        \hbox{$\fam\lecurrentfam\scriptstyle\kern-.3em A$}\kern-.15em\TeX}

%  ****************************************
%  *              DEBUGGING               *
%  ****************************************

\def\sizrpt{
    (\fontname\the\font): em=\the\fontdimen6\font, ex=\the\fontdimen5\font
    \typeout{
    (\fontname\the\font): em=\the\fontdimen6\font, ex=\the\fontdimen5\font
}}