%                                                               l-aa.sty
% L-AA vers. 3.0, LaTeX style file for Astronomy & Astrophysics
% Style file
%                                                 (c) Springer-Verlag HD
%-----------------------------------------------------------------------
% Needs LATEX VERSION 2.09 <25 March 1992> without the NFSS
%
% Please report all errors via e-mail to SPRINGER@DHDSPRI6.bitnet
% or to the address mentioned on page 2 of the documentation
%
\typeout{Document Style `l-aa' version 3.0}

\frenchspacing
\def~{\penalty\@M\kern3pt}

\def\@ptsize{0} \@namedef{ds@11pt}{\def\@ptsize{1}}
\@namedef{ds@12pt}{\def\@ptsize{2}}
\def\ds@twoside{\@twosidetrue \@mparswitchtrue}
\def\ds@draft{\overfullrule 5\p@}
\def\ds@noframe{\let\picplace\vspace}
\newif\if@referee \@refereefalse
\def\ds@referee{\@refereetrue}

\def\picplace#1{\vbox{\hrule\@height 0.4pt\@width\hsize
\hbox to\hsize{\vrule\@width 0.4pt\@height#1\hfil
\vrule\@width 0.4pt\@height#1}\hrule\@height 0.4pt\@width\hsize}}

\@options
\ds@twoside

%\widowpenalty=9000
%\clubpenalty=9000
\widowpenalty=10000
\clubpenalty=10000
\def\thisbottomragged{\def\@textbottom{\vskip\z@ plus.0001fil
\global\let\@textbottom\relax}}

\lineskip 1pt \normallineskip 1pt
\def\baselinestretch{1}


\def\@normalsize{\@setsize\normalsize{12pt}\xpt\@xpt
\abovedisplayskip=3 mm plus6pt minus 4pt
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip=0mm plus6pt
\belowdisplayshortskip=2 mm plus4pt minus 4pt
\def\@listi{\topsep 4pt plus 2pt minus 2pt
\leftmargin \leftmargini
\parsep 0pt
\itemsep \parsep}}

\def\small{\@setsize\small{11pt}\ixpt\@ixpt
\abovedisplayskip 8.5pt plus 3pt minus 4pt
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus 2pt
\belowdisplayshortskip 4pt plus2pt minus 2pt
\def\@listi{\topsep 3pt plus 2pt minus 2pt
\leftmargin \leftmargini
\parsep 0pt
\itemsep \parsep}}

\let\footnotesize=\small

\def\large{\@setsize\large{17pt}\xvpt\@xvpt}
\def\Large{\@setsize\Large{17pt}\xvpt\@xvpt}
\def\LARGE{\@setsize\LARGE{20pt}\xviiipt\@xviiipt}
\def\huge{\@setsize\huge{25pt}\xviiipt\@xviiipt}
\def\Huge{\@setsize\Huge{30pt}\xviiipt\@xviiipt}

\def\scriptsize{\@setsize\scriptsize{8pt}\viipt\@viipt}
\def\tiny{\@setsize\tiny{6pt}\vpt\@vpt}
%\def\large{\@setsize\large{17pt}\xivpt\@xivpt}
%\def\Large{\@setsize\Large{17pt}\xivpt\@xivpt}
%\def\LARGE{\@setsize\LARGE{20pt}\xviipt\@xviipt}
%\def\huge{\@setsize\huge{25pt}\xviipt\@xviipt}
%\def\Huge{\@setsize\Huge{30pt}\xviipt\@xviipt}
\@normalsize\rm

\parskip 0pt plus 1pt
\topsep 10pt plus2pt minus5pt
\partopsep 0pt
\itemsep 0pt plus 1pt
\parindent 1.5em
\leftmargin    \parindent
\leftmargini   \leftmargin
\leftmarginii  \leftmargin
\leftmarginiii \leftmargin
\leftmarginiv  \leftmargin
\leftmarginv   \leftmargin
\leftmarginvi  \leftmargin
\labelwidth\leftmargini
\labelsep 4pt
\advance\labelwidth-\labelsep
\def\@listii{\leftmargin\leftmarginii
 \labelwidth\leftmarginii\advance\labelwidth-\labelsep
 \topsep \z@}
\def\@listiii{\leftmargin\leftmarginiii
 \labelwidth\leftmarginiii\advance\labelwidth-\labelsep
 \topsep \z@}
\def\@listiv{\leftmargin\leftmarginiv
 \labelwidth\leftmarginiv\advance\labelwidth-\labelsep}
\def\@listv{\leftmargin\leftmarginv
 \labelwidth\leftmarginv\advance\labelwidth-\labelsep}
\def\@listvi{\leftmargin\leftmarginvi
 \labelwidth\leftmarginvi\advance\labelwidth-\labelsep}

% Margins, textwidth and textheight are set to A&A formatting
% conventions:

\oddsidemargin 63pt \evensidemargin 63pt \marginparwidth 90pt
\marginparsep 11pt
% The next offsets are set to get well centered output from our
% laserprinter. Users may set the required offsets for local equipment
% by adjusting equivalent values in their DVI to printer program.
 \voffset -3cm
 \hoffset -3.2cm
\topmargin 27pt \headheight 12pt \headsep 14pt \footheight 12pt
\footskip 30pt
\textheight=56pc
\textwidth=180mm
\columnsep=4mm
\columnseprule=0pt
\hfuzz=2pt
\vfuzz=2pt
\tolerance=1000

\footnotesep 8pt
\skip\footins 9pt plus 4pt minus 2pt
\floatsep 12pt plus 2pt minus 2pt
\textfloatsep 20pt plus 2pt minus 4pt
\intextsep 20pt plus 2pt minus 2pt
\@maxsep 20pt
\dblfloatsep 12pt plus 2pt minus 2pt
\dbltextfloatsep 20pt plus 2pt minus 4pt
\@dblmaxsep 20pt
\@fptop 0pt plus 1fil
\@fpsep 8pt plus 2fil
\@fpbot 0pt plus 1fil
\@dblfptop 0pt plus 1fil
\@dblfpsep 8pt plus 2fil
\@dblfpbot 0pt plus 1fil
\marginparpush 5pt

\@lowpenalty 51 \@medpenalty 151 \@highpenalty 301 \@beginparpenalty
-\@lowpenalty \@endparpenalty -\@lowpenalty \@itempenalty -\@lowpenalty

\def\vec#1{\ifmmode\mathchoice{\mbox{\boldmath$\displaystyle#1$}}
{\mbox{\boldmath$\textstyle#1$}}
{\mbox{\boldmath$\scriptstyle#1$}}
{\mbox{\boldmath$\scriptscriptstyle#1$}}\else
\hbox{\boldmath$\textstyle#1$}\fi}

\def\tens#1{\ifmmode\mathchoice{\mbox{$\sf\displaystyle#1$}}
{\mbox{$\sf\textstyle#1$}}
{\mbox{$\sf\scriptstyle#1$}}
{\mbox{$\sf\scriptscriptstyle#1$}}\else
\hbox{$\sf\textstyle#1$}\fi}

\def\part{\par \addvspace{4ex} \@afterindentfalse \secdef\@part\@spart}
\def\@part[#1]#2{\ifnum \c@secnumdepth >\m@ne \refstepcounter{part}
\addcontentsline{toc}{part}{\thepart \hspace{1em}#1}\else
\addcontentsline{toc}{part}{#1}\fi { \parindent 0pt \raggedright \ifnum
\c@secnumdepth >\m@ne \Large \bf Part \thepart \par \nobreak \fi \huge
\bf #2\par } \nobreak \vskip 3ex \@afterheading }
\def\@spart#1{{\parindent 0pt \raggedright \huge \bf #1\par} \nobreak
\vskip 3ex \@afterheading }

% Section definitions have been adapted to produce (sub)section headings
% in A&A typefaces.
\def\section{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex minus
 -.2ex}{1.5ex plus .2ex}{\normalsize\bf\boldmath}}
\def\subsection{\@startsection{subsection}{2}{\z@}{-3.25ex plus -1ex
minus -.2ex}{1.5ex plus .2ex}{\normalsize\it}}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-3.25ex plus
-1ex minus -.2ex}{1.5ex plus .2ex}{\normalsize}}
\def\paragraph{\@startsection {paragraph}{4}{\z@}{3.25ex plus 1ex minus
.2ex}{-.6em}{\normalsize\it}}
\def\subparagraph#1{\typeout{AandA Warning: You should not use
\protect\subparagraph \space in this style.}\vskip0.5cm
You should not use $\backslash${\tt subparagraph} in this
style.\vskip0.5cm}

\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
     \@tempskipa #5\relax
      \ifdim \@tempskipa>\z@
 \begingroup #6\relax
   \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\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 #8\csname #1mark\endcsname
        {#7}\addcontentsline
      {toc}{#1}{\ifnum #2>\c@secnumdepth \else
        \protect\numberline{\csname the#1\endcsname.}\fi
         #7}}\fi
     \@xsect{#5}}

\def\@xsect#1{\@tempskipa #1\relax
      \ifdim \@tempskipa>\z@
       \par \nobreak
       \addvspace{\@tempskipa}
       \@afterheading
    \else \global\@nobreakfalse \global\@noskipsectrue
       \everypar{\if@noskipsec \global\@noskipsecfalse
     \clubpenalty\@M \hskip -\parindent
     \begingroup \@svsechd \endgroup \unskip
     \hskip -#1
    \else       \clubpenalty \@clubpenalty
      \everypar{}\fi}\fi\ignorespaces}

\setcounter{secnumdepth}{3}

\def\appendix{\par
 \setcounter{section}{0}
 \setcounter{subsection}{0}
 \def\thesection{\Alph{section}}
 \renewcommand{\theequation}{\thesection\arabic{equation}}
 \setcounter{equation}{0}
 \@addtoreset{equation}{section}}

% End of art10.sty

\def\labelenumi{\arabic{enumi}.}
\def\theenumi{\arabic{enumi}}
\def\labelenumii{(\alph{enumii})}
\def\theenumii{\alph{enumii}}
\def\p@enumii{\theenumi}
\def\labelenumiii{\roman{enumiii}.}
\def\theenumiii{\roman{enumiii}}
\def\p@enumiii{\theenumi(\theenumii)}
\def\labelenumiv{\Alph{enumiv}.}
\def\theenumiv{\Alph{enumiv}}
\def\p@enumiv{\p@enumiii\theenumiii}

\def\labelitemi{\bf --}
\def\labelitemii{\bf --}
\def\labelitemiii{$\bullet$}
\def\labelitemiv{$\cdot$}

\def\verse{\let\\=\@centercr
 \list{}{\itemsep\z@ \itemindent -1.5em\listparindent \itemindent
 \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]}
\let\endverse\endlist
\def\quotation{\list{}{\listparindent 1.5em
 \itemindent\listparindent
 \rightmargin\leftmargin \parsep 0pt plus 1pt}\item[]}
\let\endquotation=\endlist
\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
\let\endquote=\endlist

\def\descriptionlabel#1{\hspace\labelsep \bf #1}
\def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin
 \let\makelabel\descriptionlabel}}
\let\enddescription\endlist


\def\theequation{\arabic{equation}}


\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
 \else \newpage \fi \thispagestyle{empty}\c@page\z@}
\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}

\arraycolsep 2.5pt \tabcolsep 6pt
\arrayrulewidth .4pt \doublerulesep 2pt
\tabbingsep \labelsep

\skip\@mpfootins = \skip\footins
\fboxsep = 3pt \fboxrule = .4pt

\newcounter{part}
\newcounter {section}
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
\newcounter {paragraph}[subsubsection]
\newcounter {subparagraph}[paragraph]

% Following commands have been adapted to produce (sub)section headings
% according to A&A layout (a period after each number).

\def\thepart{\Roman{part}} \def\thesection {\arabic{section}}
\def\thesubsection {\thesection.\arabic{subsection}}
\def\thesubsubsection {\thesubsection.\arabic{subsubsection}}
\def\theparagraph {\thesubsubsection.\arabic{paragraph}}
\def\thesubparagraph {\theparagraph.\arabic{subparagraph}}

\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{3}

\def\tableofcontents{\section*{Contents}
 \@starttoc{toc}}
\def\l@part#1#2{\addpenalty{\@secpenalty}
 \addvspace{2.25em plus 1pt} \begingroup
 \@tempdima 3em \parindent \z@ \rightskip \@pnumwidth \parfillskip
-\@pnumwidth
 {\large \bf \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}}\par
 \nobreak \endgroup}
\def\l@section#1#2{\addpenalty{\@secpenalty} \addvspace{0.5em plus 1pt}
\@tempdima 1.5em \begingroup
 \parindent \z@ \rightskip \@pnumwidth
 \parfillskip -\@pnumwidth
 \bf \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}\par
 \endgroup}
\def\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}
\def\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
\def\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}
\def\l@subparagraph{\@dottedtocline{5}{10em}{5em}}
\def\listoffigures{\section*{List of Figures}\@starttoc{lof}}
\def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
\def\listoftables{\section*{List of Tables}\@starttoc{lot}}
\let\l@table\l@figure


% \list parameters have been adjusted in the `thebibliography'
% environment to the match A&A layout of References.
\def\thebibliography#1{\small\section*{References}\list
% The \arabic{enumi} command has been removed because we don't use
% numbered citations in astronomical journals.
 {}{\setlength\labelwidth{1.4em}\leftmargin\labelwidth
 \setlength\parsep{0pt}\setlength\itemsep{0pt}
 \setlength{\itemindent}{-\leftmargin}
 \usecounter{enumi}}
 \def\newblock{\hskip .11em plus .33em minus -.07em}
 \sloppy
 \sfcode`\.=1000\relax}
\let\endthebibliography=\endlist

\newif\if@restonecol
\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi
\columnseprule \z@
\columnsep 35pt\twocolumn[\section*{Index}]
 \thispagestyle{plain}\parindent\z@
 \parskip\z@ plus .3pt\relax\let\item\@idxitem}
\def\@idxitem{\par\hangindent 40pt}
\def\subitem{\par\hangindent 40pt \hspace*{20pt}}
\def\subsubitem{\par\hangindent 40pt \hspace*{30pt}}
\def\endtheindex{\if@restonecol\onecolumn\else\clearpage\fi}
\def\indexspace{\par \vskip 10pt plus 5pt minus 3pt\relax}

\def\footnoterule{\kern-3\p@
 \hrule width 2cm
 \kern 2.6\p@}

\long\def\@makefntext#1{\parindent 1em\noindent
 \hbox to 1.5em{\hss$^{\@thefnmark}$}#1}

\setcounter{topnumber}{4}
\def\topfraction{.9}
\setcounter{bottomnumber}{1}
\def\bottomfraction{.3}
\setcounter{totalnumber}{6}
\def\textfraction{.15}
\def\floatpagefraction{.85}
\setcounter{dbltopnumber}{3}
\def\dbltopfraction{.85}
\def\dblfloatpagefraction{.85}

% Captions of figures and tables are spaced differently in A&A.
% There is only one \caption command in LaTeX, so we have to let
% the \caption command know whether it is used within the `figure'
% environment or within the `table' environment to decide what to do.

\def\aafigurecaption{figure}

\long\def\@makecaption#1#2{%
\makeatletter
\ifx\@captype\aafigurecaption\vskip5mm\else\vskip10pt\fi
\makeatother
\small
% Make sure that `Table <N>.' or `Fig. <N>.' is typeset in boldface:
 \setbox\@tempboxa\hbox{{\bf #1} #2}
 \ifdim \wd\@tempboxa >\hsize \unhbox\@tempboxa\par \else \hbox
to\hsize{\box\@tempboxa\hfil}
 \fi
\makeatletter
\ifx\@captype\aafigurecaption\else\vskip6pt\fi
\makeatother}

\newcounter{figure}
\def\thefigure{\@arabic\c@figure}
\def\fps@figure{htbp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{Fig.\ \thefigure.}
\def\figure{\small\rm\@float{figure}}
\let\endfigure\end@float
\@namedef{figure*}{\small\rm\@dblfloat{figure}}
\@namedef{endfigure*}{\end@dblfloat}

\newcounter{table}
\def\thetable{\@arabic\c@table}
\def\fps@table{htbp}
\def\ftype@table{2}
\def\ext@table{lot}
\def\fnum@table{Table \thetable.}
\def\table{\small\rm\@float{table}}
\let\endtable\end@float
\@namedef{table*}{\small\rm\@dblfloat{table}}
\@namedef{endtable*}{\end@dblfloat}

% LaTeX does not provide a command to enter the authors institute
% addresses. The \institute command is defined here.

\newcounter{@inst}
\newcounter{@auth}
\newdimen\instindent

\def\institute#1{\gdef\@institute{#1}}

\def\institutename{\par
 \begingroup
 \parindent=0pt
 \parskip=0pt
 \setcounter{@inst}{1}%
 \def\and{\par\stepcounter{@inst}%
 \noindent
 \hbox to\instindent{\hss$^{\the@inst}$\enspace}\ignorespaces}%
 \setbox0=\vbox{\def\thanks##1{}\@institute}
 \ifnum\c@@inst>9\relax\setbox0=\hbox{$^{88}$\enspace}%
                 \else\setbox0=\hbox{$^{8}$\enspace}\fi
 \instindent=\wd0\relax
 \ifnum\c@@inst=1\relax
 \else
   \setcounter{@inst}{1}%
   \noindent
   \hbox to\instindent{\hss$^{\the@inst}$\enspace}\ignorespaces
 \fi
 \ignorespaces
 \@institute\par
 \endgroup}

\def\offprints#1{\begingroup
\def\protect{\noexpand\protect\noexpand}\xdef\@thanks{\@thanks
\protect\footnotetext[0]{\unskip\hskip-1.5em{\it Send offprint requests
to\/}: \ignorespaces#1}}\endgroup\ignorespaces}

\def\@thanks{}

\long\def\@makefntext#1{\parindent 1em\noindent
            \hbox to1.5em{$\m@th^{\@thefnmark}$\hss}#1}

\def\@fnsymbol#1{\ifcase#1\or\star\or{\star\star}\or{\star\star\star}%
   \or \dagger\or \ddagger\or
   \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger
   \or \ddagger\ddagger \else\@ctrerr\fi\relax}

\def\inst#1{\unskip$^{#1}$}
\def\fnmsep{\unskip$^,$}

\def\subtitle#1{\gdef\@subtitle{#1}}
\def\@subtitle{}

\def\headnote#1{\gdef\@headnote{#1}}
\def\@headnote{}

\def\thesaurus#1{\gdef\@thesaurus{#1}}
\def\@thesaurus{missing; you have not inserted them}%

\def\maketitle{\par
 \begingroup
 \def\thefootnote{\fnsymbol{footnote}}
 \if@twocolumn
   \twocolumn[\@maketitle]
 \else
   \newpage \@maketitle
 \fi
 \global\@topnum\z@
 \thispagestyle{empty}\@thanks
 \def\protect{\noexpand\protect\noexpand}
 \let\inst=\@gobble
 \let\fnmsep=\@gobble
 \let\thanks=\@gobble
 \xdef\@title{\@title\unskip}
 \def\stripauthor##1\and##2\endauthor{%
    \xdef\@author{##1\unskip\unskip\if!##2!\else\ et al.\fi}}
 \expandafter\stripauthor\@author\and\endauthor
 \endgroup
 \setcounter{footnote}{0}
 \setbox0=\hbox{\small\rm\@author\unskip: \@title\unskip}
 \dimen@=\wd0\relax
 \advance\dimen@ by 2cm
 \ifdim\dimen@>\textwidth
    \typeout{^^JAandA Warning: The running head built automatically from
             \string\author\space and \string\title
             ^^Jexceeds the pagewidth, please supply a shorter form
             ^^Jusing \string\markboth\string{...\string}\string{...\string}
             after the \string\maketitle-command.}%
    \setbox0=\hbox{\small\rm Please give a shorter version with:
             {\tt\string\markboth\string{...\string}\string{...\string}}}%
 \fi
 \setbox\runheadbox=\hbox{\unhbox0}
 \def\@oddhead{\small\rm\hfil\copy\runheadbox\hfil\llap{\thepage}}
 \def\@evenhead{\small\rm\rlap{\thepage}\hfil\copy\runheadbox\hfil}
 \let\maketitle\relax
 \let\@maketitle\relax
 \gdef\@thanks{}\gdef\@author{}\gdef\@title{}\gdef\@subtitle{}%
 \let\thanks\relax}

\def\AALogo{\setbox254=\hbox{ ASTROPHYSICS }%
\vbox{\baselineskip=10pt\hrule\hbox{\vrule\vbox{\kern3pt
\hbox to\wd254{\hfil ASTRONOMY\hfil}
\hbox to\wd254{\hfil AND\hfil}\copy254
\hbox to\wd254{\hfil\number\day.\number\month.\number\year\hfil}
\kern3pt}\vrule}\hrule}}
\def\makeheadbox{{\hbox to\textwidth{%
\hbox to0pt{\vbox{\hsize=30cc\baselineskip=12pt\hrule\hbox
to\hsize{\vrule\kern3pt\vbox{\kern3pt
\hbox{\bf A\&A manuscript no.}
\hbox{(will be inserted by hand later)}
\kern3pt\hrule\kern3pt\bf
\hbox{Your thesaurus codes are:}
\hbox{\rightskip=0pt plus3em\advance\hsize by-7pt
\vbox{\noindent\ignorespaces\@thesaurus}}
\kern3pt}\hfil\kern3pt\vrule}\hrule}\hss}
\hfil\llap{\quad\AALogo}}}}

\def\@maketitle{\newpage
 \rm\vbox to0pt{}\vskip-8mm
 \makeheadbox
\if!\@headnote!\else {\LARGE \it
  \vskip 8.89mm
  \pretolerance=10000
  \rightskip=0pt plus 3cm
  \noindent\@headnote \par}\vskip -3.7mm\fi
 \vskip11.712mm
 {\LARGE \bf\boldmath
  \pretolerance=10000
  \rightskip=0pt plus 4cm
  \noindent\ignorespaces
  \@title \par}\vskip .3cm
\if!\@subtitle!\else {\Large \bf\boldmath
  \vskip .05cm
  \pretolerance=10000
  \rightskip=0pt plus 3cm
  \noindent\@subtitle \par}\vskip10pt\fi
 {\bf \lineskip .5em
\setbox0=\vbox{\setcounter{@auth}{1}\def\and{\stepcounter{@auth}}%
\def\thanks##1{}\@author\global\c@@inst=\c@@auth}%
\def\lastand{\ifnum\c@@inst=2\relax\unskip{} and \else
\unskip, and \fi}%
\setcounter{@auth}{1}%
\def\and{\stepcounter{@auth}\ifnum\c@@auth=\c@@inst\lastand\else
\unskip, \fi}%
 \noindent\ignorespaces\@author\vskip.125cm}
 \small\rm
 \institutename
 \vskip .35cm
 \noindent\@date
 \par
 \vskip 21pt}

\mark{{}{}}

\def\markboth#1#2{%
\setbox0=\hbox{\small\rm\ignorespaces#1\unskip}
\dimen@=\wd0
\advance\dimen@ by 2cm\relax
\ifdim\dimen@>\textwidth
   \typeout{^^JAandA Warning: The running head you supplied in
            ^^Jusing \string\markboth\string{...\string}\string{...\string}
            ^^Jexceeds the pagewidth, please give a shorter form
            ^^Jafter the \string\maketitle-command.}%
   \setbox0=\hbox{\small\rm Please give a shorter version with:
            {\tt\string\markboth\string{...\string}\string{...\string}}}%
\fi
 \setbox\runheadbox=\hbox{\unhbox0}}

\def\ps@myheadings{\let\@mkboth=\@gobbletwo
\def\@oddhead{\small\rm\hfil\thepage\hfil
}\def\@oddfoot{}\def\@evenhead{\small\rm\hfil\thepage\hfil
}\def\@evenfoot{}\def\sectionmark##1{}\def\subsectionmark##1{}}
\newbox\runheadbox

\def\today{\ifcase\month\or
 January\or February\or March\or April\or May\or June\or
 July\or August\or September\or October\or November\or December\fi
 \space\number\day, \number\year}

\ps@myheadings \pagenumbering{arabic}

\if@referee
  \onecolumn
\else
  \twocolumn
\fi
\sloppy
\flushbottom
\marginparwidth 48pt

\def\@array[#1]#2{\setbox\@arstrutbox=\hbox{\vrule
     height\arraystretch \ht\strutbox
     depth\arraystretch \dp\strutbox
     width\z@}\@mkpream{@{}#2}\edef\@preamble{\halign \noexpand\@halignto
\bgroup \tabskip\z@ \@arstrut \@preamble \tabskip\z@ \cr}%
\let\@startpbox\@@startpbox \let\@endpbox\@@endpbox
  \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi
  \bgroup \let\par\relax
  \let\@sharp##\let\protect\relax \lineskip\z@\baselineskip\z@\@preamble}

% include fleqn.sty
\def\[{\relax\ifmmode\@badmath\else
 \begin{trivlist}%
 \@beginparpenalty\predisplaypenalty
 \@endparpenalty\postdisplaypenalty
 \item[]\leavevmode
 \hbox to\linewidth\bgroup $\m@th\displaystyle
 \hskip\mathindent\bgroup\fi}

\def\]{\relax\ifmmode \egroup $\hfil
       \egroup \end{trivlist}\else \@badmath \fi}

\def\equation{\@beginparpenalty\predisplaypenalty
  \@endparpenalty\postdisplaypenalty
\refstepcounter{equation}\trivlist \item[]\leavevmode
  \hbox to\linewidth\bgroup $\m@th% $ TO MAKE DOLLAR NESTING OK
  \displaystyle
\hskip\mathindent}

\def\endequation{$\hfil
           \displaywidth\linewidth\@eqnnum\egroup \endtrivlist}

\def\eqnarray{\stepcounter{equation}\let\@currentlabel=\theequation
\global\@eqnswtrue
\global\@eqcnt\z@\tabskip\mathindent\let\\=\@eqncr
\abovedisplayskip\topsep\ifvmode\advance\abovedisplayskip\partopsep\fi
\belowdisplayskip\abovedisplayskip
\belowdisplayshortskip\abovedisplayskip
\abovedisplayshortskip\abovedisplayskip
$$\m@th\halign
to\linewidth\bgroup\@eqnsel\hskip\@centering$\displaystyle\tabskip\z@
  {##}$&\global\@eqcnt\@ne \hskip 2\arraycolsep \hfil${##}$\hfil
  &\global\@eqcnt\tw@ \hskip 2\arraycolsep $\displaystyle{##}$\hfil
   \tabskip\@centering&\llap{##}\tabskip\z@\cr}

\def\endeqnarray{\@@eqncr\egroup
      \global\advance\c@equation\m@ne$$\global\@ignoretrue
      }

\newdimen\mathindent
% A&A does not indent equations:
\mathindent = 0pt
% End of `fleqn.sty

\def\abstract{\trivlist\item[\hskip\labelsep
{\bf Abstract.}]}
\def\endabstract{\endtrivlist\vskip0.5cm\hrule
\vskip3ptplus12pt\null}

% Define \keywords

\def\keywords{\par\vspace{12pt}\noindent{\bf Key words: }}

% Define \acknowledgements

\def\acknowledgements{\par\addvspace{6pt}\small\rm
\trivlist\item[\hskip\labelsep{\em Acknowledgements.\/}]}
\def\endacknowledgements{\endtrivlist\addvspace{6pt}}

% Redefine \@cite so no square brackets are output.
% Redefine \@biblabel so the label is not output in the bibliography.

\def\@cite#1#2{{#1\if@tempswa , #2\fi}}
\def\@biblabel#1{}

\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}}
\def\sq{\ifmmode\squareforqed\else{\unskip\nobreak\hfil
\penalty50\hskip1em\null\nobreak\hfil\squareforqed
\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi}

\def\sun{\hbox{$\odot$}}
\def\la{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
<\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
<\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr\sim\cr}}}}}
\def\ga{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\sim\cr}}}}}
\def\degr{\hbox{$^\circ$}}
\def\arcmin{\hbox{$^\prime$}}
\def\arcsec{\hbox{$^{\prime\prime}$}}
\def\utw{\smash{\rlap{\lower5pt\hbox{$\sim$}}}}
\def\udtw{\smash{\rlap{\lower6pt\hbox{$\approx$}}}}
\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\cor{\mathrel{\mathchoice {\hbox{$\widehat=$}}{\hbox{$\widehat=$}}
{\hbox{$\scriptstyle\hat=$}}
{\hbox{$\scriptscriptstyle\hat=$}}}}
\def\sol{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr\sim\cr<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\sim\cr
<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\sim\cr
<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
\sim\cr<\cr}}}}}
\def\sog{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr\sim\cr>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\sim\cr
>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
\sim\cr>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
\sim\cr>\cr}}}}}
\def\lse{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
<\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
<\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr\simeq\cr}}}}}
\def\gse{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\simeq\cr}}}}}
\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1.5pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\noalign{\vskip-1.5pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\noalign{\vskip-1pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\noalign{\vskip-0.5pt}<\cr}}}}}
\def\leogr{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\noalign{\vskip-1.5pt}>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
<\cr\noalign{\vskip-1.5pt}>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
<\cr\noalign{\vskip-1pt}>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr\noalign{\vskip-0.5pt}>\cr}}}}}
\def\loa{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
<\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
<\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr\approx\cr}}}}}
\def\goa{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\approx\cr}}}}}
\def\diameter{{\ifmmode\mathchoice
{\ooalign{\hfil\hbox{$\displaystyle/$}\hfil\crcr
{\hbox{$\displaystyle\mathchar"20D$}}}}
{\ooalign{\hfil\hbox{$\textstyle/$}\hfil\crcr
{\hbox{$\textstyle\mathchar"20D$}}}}
{\ooalign{\hfil\hbox{$\scriptstyle/$}\hfil\crcr
{\hbox{$\scriptstyle\mathchar"20D$}}}}
{\ooalign{\hfil\hbox{$\scriptscriptstyle/$}\hfil\crcr
{\hbox{$\scriptscriptstyle\mathchar"20D$}}}}
\else{\ooalign{\hfil/\hfil\crcr\mathhexbox20D}}%
\fi}}


\def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip
\halign{\hfil
$\displaystyle##$\hfil\cr\gets\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\gets
\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\gets
\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
\gets\cr\to\cr}}}}}
\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr
\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr
\noalign{\vskip1pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr
\noalign{\vskip0.9pt}=\cr}}}}}
\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr
\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr
\noalign{\vskip1pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr
\noalign{\vskip0.9pt}=\cr}}}}}
\def\bbbr{{\rm I\!R}} %reelle Zahlen
\def\bbbm{{\rm I\!M}}
\def\bbbn{{\rm I\!N}} %natuerliche Zahlen
\def\bbbf{{\rm I\!F}}
\def\bbbh{{\rm I\!H}}
\def\bbbk{{\rm I\!K}}
\def\bbbp{{\rm I\!P}}
\def\bbbone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-4mu l}
{\rm 1\mskip-4.5mu l} {\rm 1\mskip-5mu l}}}
\def\bbbc{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}}}
\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm
Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}}}
\def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm
T$}\hbox{\hbox to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hbox
to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hbox
to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox
to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}}}
\def\bbbs{{\mathchoice
{\setbox0=\hbox{$\displaystyle     \rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox
to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle        \rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox
to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle      \rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox
to0pt{\kern0.5\wd0\vrule height0.45\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.4\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox
to0pt{\kern0.55\wd0\vrule height0.45\ht0\hss}\box0}}}}
\def\bbbz{{\mathchoice {\hbox{$\sf\textstyle Z\kern-0.4em Z$}}
{\hbox{$\sf\textstyle Z\kern-0.4em Z$}}
{\hbox{$\sf\scriptstyle Z\kern-0.3em Z$}}
{\hbox{$\sf\scriptscriptstyle Z\kern-0.2em Z$}}}}
\def\ts{\thinspace}

\def\typeset{\vfill{\small\rm\noindent This article was processed by the
                    author using Springer-Verlag \LaTeX\ A\&A style file
                    {\it L-AA\/} version 3.\par}}

\def\enddocument{\par\typeset
                 \@checkend{document}\clearpage\begingroup
\if@filesw \immediate\closeout\@mainaux
\def\global\@namedef##1##2{}\def\newlabel{\@testdef r}%
%\def\bibcite{\@testdef b}
\def\@testbibciteaa ##1##2##3{\def\@tempa{##3}%
\if!##2!\else
 \expandafter\ifx \csname##1@##2\endcsname \@tempa \else \@tempswatrue\fi
\fi}\def\bibcite{\@testbibciteaa b}%
\@tempswafalse\makeatletter\input \jobname.aux
\if@tempswa \@warning{Label(s) may have changed. Rerun to get
cross-references right}\fi\fi\endgroup\deadcycles\z@\@@end}
\endinput
