RAA Macro Package

RAA macro class file for LaTeX2e in two columns

Posted: Mar 21, 2022

% This is raa.cls

%% 2019 raa06.cls --- zjz

% LaTeX document class for Research in Astronomy and Astrophysics

% -- version 1.0 for LaTeX2e (2008.09.22 zay)

% Since 2001.08.28 Zhou Ai-Ying

%

% Changes made in Ver.1.1:

% (1) double spaced text for referee version

% (2) referee version has a full textwidth as publication layout

%

% Unsolved works:

% (1) Q: example for placing text around a figure/table(?)

% (2) Q: first paragraph should also be indented ?

% A: using \hspace{15pt} at the moment.

% (3) Q: change footnote's counter to symbols

% (4) Q: revise \thanks, \email, \mailto commands

%%

%%%%% change floatsep 20060701

% \setlength{\skip\footins}{9\p@ \@plus 4\p@ \@minus 2\p@}

% \setlength\floatsep {12\p@ \@plus 2\p@ \@minus 2\p@}

% \setlength\textfloatsep{12\p@ \@plus 4\p@ \@minus 6\p@}

% \setlength\intextsep {12\p@ \@plus 3\p@ \@minus 3\p@}

% \setlength\dblfloatsep {12\p@ \@plus 2\p@ \@minus 2\p@}

% \setlength\dbltextfloatsep{12\p@ \@plus 4\p@ \@minus 4\p@}



%%%%

%% \CharacterTable

%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z

%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z

%% Digits \0\1\2\3\4\5\6\7\8\9

%% Exclamation \! Double quote \" Hash (number) \#

%% Dollar \$ Percent \% Ampersand \&

%% Acute accent \' Left paren \( Right paren \)

%% Asterisk \* Plus \+ Comma \,

%% Minus \- Point \. Solidus \/

%% Colon \: Semicolon \; Less than \<

%% Equals \= Greater than \> Question mark \?

%% Commercial at \@ Left bracket \[ Backslash \\

%% Right bracket \] Circumflex \^ Underscore \_

%% Grave accent \` Left brace \{ Vertical bar \|

%% Right brace \} Tilde \~}



\NeedsTeXFormat{LaTeX2e}[1995/12/01]

\ProvidesClass{RAA}[ 2015/11/29 v2.0 (Zhou Ai-Ying \& Zhao Jing-Zhi);

^^J\space\space\space\space\space\space\space\space\space\space\space\space

\space\space\space\space\space\space\space\space\space2008/09/22 v1.2 (Zhou Ai-Ying).

^^J\space\space\space\space\space\space\space\space\space\space\space\space

\space\space\space\space\space\space\space\space\space2003/05/12 v1.1e (Zhou Ai-Ying).

^^J\space\space\space\space\space\space\space\space\space\space\space\space

\space\space\space\space\space\space\space\space\space2003/04/19 v1.1 (Zhou Ai-Ying).

^^JLaTeX document class for Research in Astronomy and Astrophysics ]

\newcommand\@ptsize{}

\newif\if@restonecol

\newif\if@titlepage

\@titlepagefalse

\DeclareOption{a4paper}

{\setlength\paperheight {297mm}%{260mm} 888 %% {\setlength\paperheight {297mm}

\setlength\paperwidth {210mm}} %{185mm}} %% \setlength\paperwidth {210mm}}

\DeclareOption{letterpaper}

{\setlength\paperheight {11in}%

\setlength\paperwidth {8.5in}}

\DeclareOption{legalpaper}

{\setlength\paperheight {14in}%

\setlength\paperwidth {8.5in}}

\DeclareOption{10pt}{\renewcommand\@ptsize{0}}

\DeclareOption{11pt}{\renewcommand\@ptsize{1}}

\DeclareOption{12pt}{\renewcommand\@ptsize{2}}

\DeclareOption{twoside}{\@twosidetrue \@mparswitchtrue}

\DeclareOption{draft}{\setlength\overfullrule{5pt}}

\DeclareOption{final}{\setlength\overfullrule{0pt}}

\DeclareOption{twocolumn}{\@twocolumntrue} %RAA2016:zay 2015-12-01

%% jj \DeclareOption{leqno}{\input{leqno.clo}}

\DeclareOption{fleqn}{\input{fleqn.clo}} %AA 888

\DeclareOption{openbib}{%

\AtEndOfPackage{%

\renewcommand\@openbib@code{%

\advance\leftmargin\bibindent

\itemindent -\bibindent

\listparindent \itemindent

\parsep \z@

}%

\renewcommand\newblock{\par}}%

}

%

\let\if@runhead\iffalse

\DeclareOption{runningheads}{\let\if@runhead\iftrue}

\let\if@envcntreset\iffalse

\DeclareOption{envcountreset}{\let\if@envcntreset\iftrue}

\let\if@envcntsect\iffalse

\DeclareOption{envcountsect}{\let\if@envcntsect\iftrue}

\let\if@referee\iffalse

\DeclareOption{referee}{\let\if@referee\iftrue}

\let\if@nyobjects\iffalse

%%888

\ExecuteOptions{a4paper,twoside,twocolumn,fleqn,final,10pt,runningheads}

%AA

%\ExecuteOptions{%%a4paper,

%twoside, final,10pt,runningheads} %%% 10pt zjz 0601

\ProcessOptions

%\AtEndOfClass{\mathindent\z@\let\abstract=\RAAabstract}

\AtEndOfClass{ \let\abstract=\RAAabstract}

%

\if\@ptsize 0

%

\renewcommand\normalsize{%

\@setfontsize\normalsize\@xpt{11}% %%% \@xpt{12} %% zjz0601

\abovedisplayskip 8.55\p@ \@plus4\p@ \@minus5\p@

\abovedisplayshortskip \z@ \@plus3\p@

\belowdisplayshortskip 6\p@ \@plus3\p@ \@minus3\p@

\belowdisplayskip \abovedisplayskip

\let\@listi\@listI}

\normalsize

\newcommand\small{%

\@setfontsize\small\@ixpt{8}% %%% zjz0601

\abovedisplayskip 8.5\p@ \@plus3\p@ \@minus4\p@

\abovedisplayshortskip \z@ \@plus2\p@

\belowdisplayshortskip 4\p@ \@plus2\p@ \@minus2\p@

\def\@listi{\leftmargin\leftmargini

\parsep 0\p@ \@plus1\p@ \@minus\p@

\topsep 8\p@ \@plus2\p@ \@minus4\p@

\itemsep0\p@}%

\belowdisplayskip \abovedisplayskip

}

\newcommand\footnotesize{\@setfontsize\footnotesize\@viiipt{8}} %%2006.09.07 added

\newcommand\scriptsize{\@setfontsize\scriptsize\@viipt\@viiipt}

\newcommand\tiny{\@setfontsize\tiny\@vipt\@viipt}

\newcommand\large{\@setfontsize\large\@xipt{13}}

\newcommand\Large{\@setfontsize\Large\@xivpt{16}}

\newcommand\LARGE{\@setfontsize\LARGE\@xviipt{20}}

\newcommand\huge{\@setfontsize\huge\@xxpt{24}}

\newcommand\Huge{\@setfontsize\Huge\@xxvpt{30}}

%

\setlength\parindent{15\p@}

\setlength\smallskipamount{3\p@ \@plus 1\p@ \@minus 1\p@}

\setlength\medskipamount{6\p@ \@plus 2\p@ \@minus 2\p@}

\setlength\bigskipamount{12\p@ \@plus 4\p@ \@minus 4\p@}

\setlength\headheight{12\p@}

\setlength\headsep {12\p@} %

\setlength\topskip {10\p@}

\setlength\footskip{30\p@}

\setlength\maxdepth{.5\topskip}

%

\@settopoint\textwidth

%% jj \setlength\marginparsep {10\p@}

%% jj \setlength\marginparpush{5\p@}

%%j\setlength\oddsidemargin {-30\p@}

%%j\setlength\evensidemargin {-30\p@}

%%j\setlength\marginparwidth {48\p@}

\setlength\topmargin{10pt}%%{-10pt}

\setlength\footnotesep{8\p@}

\setlength{\skip\footins}{9\p@ \@plus 4\p@ \@minus 2\p@}

\setlength\floatsep {12\p@ \@plus 2\p@ \@minus 2\p@}

%% \setlength\textfloatsep{18\p@ \@plus 8\p@ \@minus 6\p@}

\setlength\textfloatsep{12\p@ \@plus 4\p@ \@minus 6\p@}

%%\setlength\intextsep {18\p@ \@plus 2\p@ \@minus 2\p@}

\setlength\intextsep {12\p@ \@plus 3\p@ \@minus 3\p@}

\setlength\dblfloatsep {12\p@ \@plus 2\p@ \@minus 2\p@}

%\setlength\dbltextfloatsep{18\p@ \@plus 8\p@ \@minus 6\p@}

\setlength\dbltextfloatsep{12\p@ \@plus 4\p@ \@minus 4\p@}

\setlength\@fptop{0\p@ }

\setlength\@fpsep{10\p@ } %% \setlength\@fpsep{12\p@ } %% zjz0601

\setlength\@fpbot{0\p@ \@plus 1fil}

\setlength\@dblfptop{0\p@ }

\setlength\@dblfpsep{12\p@ }

\setlength\@dblfpbot{0\p@ \@plus 1fil}

\setlength\partopsep{2\p@ \@plus 1\p@ \@minus 1\p@}

\def\@listi{\leftmargin\leftmargini

\parsep \z@

\topsep 8\p@ \@plus2\p@ \@minus4\p@

\itemsep\parsep}

\let\@listI\@listi

\@listi

\def\@listii {\leftmargin\leftmarginii

\labelwidth\leftmarginii

\advance\labelwidth-\labelsep

\topsep \z@

\parsep \topsep

\itemsep \parsep}

\def\@listiii{\leftmargin\leftmarginiii

\labelwidth\leftmarginiii

\advance\labelwidth-\labelsep

\topsep \z@

\parsep \topsep

\itemsep \parsep}

\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}

\else

\input{size1\@ptsize.clo}

\fi

%

%\let\footnotesize\small %%commented 2006.09.07

%

%===================== paper size ===============

\if@referee

\setlength{\textwidth}{200mm} %AA:180mm; zay:use (200,250) 2008.09.24

\setlength{\textheight}{235mm} %AA:694pt, 1mm=0.04in=2.845pt

\else %preprint, final version

\setlength{\textwidth}{170mm} %% for 2019 %RAA 2010

\setlength{\textheight}{235mm} %% RAA 2019 zjz

\topmargin=0pt

\oddsidemargin=-13.5pt

%%88 0pt

\evensidemargin=-14.5pt

%%88 0pt

\parindent=6mm

\arraycolsep 1mm

\fi

%===================== paper size ===============

%

%\setlength{\voffset}{-1.2cm}

%

\setlength\lineskip{1\p@}

\setlength\normallineskip{1\p@}

\renewcommand\baselinestretch{}

\renewcommand{\baselinestretch}{1.16} %RAA 2010 2008.09.24 moved here from *.tex

\headsep=6mm % 2008.09.24 moved here from *.tex

\setlength\parskip{0\p@ \@plus \p@}

\@lowpenalty 51

\@medpenalty 151

\@highpenalty 301

%

\setcounter{topnumber}{4}

\renewcommand\topfraction{.9}

\setcounter{bottomnumber}{2}

\renewcommand\bottomfraction{.5}

\setcounter{totalnumber}{6}

\renewcommand\textfraction{.05}

\renewcommand\floatpagefraction{.95}

\setcounter{dbltopnumber}{3}

\renewcommand\dbltopfraction{.9}

\renewcommand\dblfloatpagefraction{.95}

%

\def\ps@headings{%

\let\@oddfoot\@empty\let\@evenfoot\@empty

\def\@evenhead{\small\rlap{\thepage}\hfil\leftmark\hfil}%

\def\@oddhead {\small\hfil\rightmark\hfil\llap{\thepage}}%

\let\@mkboth\@gobbletwo

\let\sectionmark\@gobble

\let\subsectionmark\@gobble

}

% make indentations changeable

\def\setitemindent#1{\settowidth{\labelwidth}{#1}%

\leftmargini\labelwidth

\advance\leftmargini\labelsep

\def\@listi{\leftmargin\leftmargini

\labelwidth\leftmargini\advance\labelwidth by -\labelsep

\parsep=\parskip

\topsep=\medskipamount

\itemsep=\parskip \advance\itemsep by -\parsep}}

\def\setitemitemindent#1{\settowidth{\labelwidth}{#1}%

\leftmarginii\labelwidth

\advance\leftmarginii\labelsep

\def\@listii{\leftmargin\leftmarginii

\labelwidth\leftmarginii\advance\labelwidth by -\labelsep

\parsep=\parskip

\topsep=\z@

\itemsep=\parskip \advance\itemsep by -\parsep}}

% labels of description

\def\descriptionlabel#1{\hspace\labelsep #1\hfil}

% adjusted environment "description"

% if an optional parameter (at the first two levels of lists)

% is present, its width is considered to be the widest mark

% throughout the current list.

\def\description{\@ifnextchar[{\@describe}{\list{}{\labelwidth\z@

\itemindent-\leftmargin \let\makelabel\descriptionlabel}}}

\let\enddescription\endlist

%

\def\describelabel#1{#1\hfil}

\def\@describe[#1]{\relax\ifnum\@listdepth=0

\setitemindent{#1}\else\ifnum\@listdepth=1

\setitemitemindent{#1}\fi\fi

\list{--}{\let\makelabel\describelabel}}

%

\newdimen\logodepth

\logodepth=1.3cm

\newdimen\headerboxheight

\headerboxheight=168pt %%%% 143pt

\newdimen\betweenumberspace % dimension for space between

\betweenumberspace=3.33pt % number and text of titles.

\newdimen\aftertext % dimension for space after

\aftertext=5pt % text of title.

\newdimen\headlineindent % dimension for space between

\headlineindent=1.166cm % number and text of headings.

\def\andname{and}

%\def\keywordname{{\sffamily\bfseries Key words:~}}

\def\keywordname{{\bfseries Key words:~}} %for RAA

\def\lastandname{, and}

\def\mailname{{\it Correspondence to\/}:}

\def\keywords{\par\addvspace\baselineskip\noindent\keywordname\

\ignorespaces}


%

\newcounter{inst}

\newcounter{auth}

\newdimen\instindent

\newbox\authrun

\newtoks\authorrunning

\newbox\titrun

\newtoks\titlerunning


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

\gdef\@journalname{\bf Research

in Astronomy and Astrophysics}


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

\def\@headnote{}


\def\dedication#1{\gdef\@dedic{#1}}

\def\@dedic{}


\let\@date\undefined


\def\RAAabstract#1{\gdef\@abstract{#1}}


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


%==========================================================

% institutes:

%==========================================================

\def\institutename{\par

\begin{flushleft} %by zay

\begingroup

\parindent=0pt

\parskip=0pt

\vspace{-12pt} %zay: 2003.04.19, distance between authors and institute

\setcounter{inst}{1}%

\def\and{\par\stepcounter{inst}%

\hangindent\instindent

\noindent

\hbox to\instindent{\hss$^{\theinst}$\enspace}\ignorespaces}%

\setbox0=\vbox{\def\thanks##1{}\@institute}

\ifnum\value{inst}>9\relax\setbox0=\hbox{$^{88}$\enspace}%

\else\setbox0=\hbox{$^{8}$\enspace}\fi

\instindent=\wd0\relax

\ifnum\value{inst}=1\relax

\else %if 2 more institutes

\parindent=0pt

\setcounter{inst}{1}%

\hangindent\instindent

\noindent

\hbox to\instindent{\hss$^{\theinst}$\enspace}\ignorespaces

\fi

\normalsize %small

\ignorespaces

\@institute\par

\end{flushleft}

\endgroup}


%==========================================================

% offprint requests:

%==========================================================

\def\offprints#1{} %empty

%\def\offprints#1{ \begingroup

% \def\protect {\noexpand\protect\noexpand}

% \xdef\@thanks {\@thanks

% \protect\footnotetext[0]{\unskip\hskip-1.5em{$\star$

% \email{}#1 } %\it{Send offprint requests to:} \/}

% \ignorespaces %#1 refers to the first author

% }

% }

% \endgroup\ignorespaces

% }


%==========================================================

% E-mail:

%==========================================================

\def\email#1{ \begingroup

\def\protect{\noexpand\protect\noexpand}

\xdef\@thanks { %\@thanks

\protect\footnotetext[0]{\unskip\hskip-1.5em{ $\star$ E-mail: \tt#1} }

}

\endgroup\ignorespaces

}

%\def\email#1{{E-mail: \tt#1}}

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

\def\@thanks{}

\def\@mail{} %correspondence to

\def\mailto#1{\,\thanks{}}


\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\msnr#1{\gdef\@msnr{#1}}

\def\@msnr{}


%\def\idline#1#2{\gdef\@idline{#1}\setcounter{page}{#2}}

%\def\@idline{}

%\def\doi#1{\gdef\@doi{#1}}

%\def\@doi{(DOI: will be inserted by hand later)}


\def\doi#1#2{\gdef\doif{#1/#2} \gdef\doib{#2}} %%zay 2015-11-29



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

\def\@headnote{}


\def\ch@ckobl#1#2{\@ifundefined{@#1}

{\typeout{RAA warning: Missing

\expandafter\string\csname#1\endcsname}%

\csname #1\endcsname{#2}}

{}}


\newif\if@normhead \@normheadtrue

\def\hugehead{\@normheadfalse

\onecolumn

\let\thanks=\footnote


\long\def\@makefntext##1{\parindent\bibindent

\columnwidth\textwidth\advance\columnwidth -\columnsep

\divide\columnwidth\tw@\hsize\columnwidth \linewidth\columnwidth

\noindent\hbox to\parindent{\hss$\m@th^{\@thefnmark}$ }##1}%

}


\def\maketitle{\par

\ch@ckobl{journalname}{Noname}

\ch@ckobl{date}{%%% jjj the date of receipt and acceptance should be inserted later

}

\ch@ckobl{title}{A title should be given}

\ch@ckobl{author}{Name(s) and initial(s) of author(s) should be given}

\ch@ckobl{institute}{Address(es) of author(s) should be given}

\ch@ckobl{abstract}{An abstract should be given}

\begingroup

%

\renewcommand\thefootnote{\@fnsymbol\c@footnote}%


\def\@makefnmark{$^{\@thefnmark}$}%

%

\def\lastand{\ifnum\value{inst}=2\relax

\unskip{} \andname\

\else

% \unskip, \andname\ % AA, a comma between last two authors

\unskip ~\andname\ %for RAA, no comma between last two authors

\fi}%

\def\and{\stepcounter{auth}\relax

\ifnum\value{auth}=\value{inst}%

\lastand

\else

\unskip,

\fi}%

\ifnum \col@number=\@ne

\@maketitle

\else

\twocolumn[\@maketitle]%

\fi

\thispagestyle{empty}%

\global\@topnum\z@

\if@normhead

\@thanks

\else

\twocolumn[\vspace{\@tempdima}]

\addtocounter{page}{-1}

\if!\the\authorrunning!

\authorrunning{ }%

\fi

\fi

\if!\@mail!\else

\footnotetext[0]{\kern-\bibindent\mailname\

\ignorespaces\@mail}%

\fi


%===========================================================

% set running_author and running_title

%===========================================================

\if@runhead

\def\\{\unskip\ \ignorespaces}\def\inst##1{\unskip{}}%

\def\thanks##1{\unskip{}}\def\fnmsep{\unskip}%

\def\object##1{##1}%

\instindent=\textwidth

\advance\instindent by-2\headlineindent

\if!\the\titlerunning!\else

\edef\@title{\the\titlerunning}%

\fi

\global\setbox\titrun=\hbox{\small\rm\unboldmath\ignorespaces\@title}%

\ifdim\wd\titrun>\instindent

\typeout{^^JRAA Warning: Title too long for running head.}%

\typeout{Please supply a shorter form with \string\titlerunning

\space prior to \string\maketitle.

^^JYou can answer 'r' to continue, a hint will be used as title instead.}

\global\setbox\titrun=\hbox{\small\rm

Title Suppressed Due to Excessive Length}%

\show %%pause during compiling to prompt user

\fi

\xdef\@title{\copy\titrun}%

%

\if!\the\authorrunning!

\else

\setcounter{auth}{1}%

\edef\@author{\the\authorrunning}%

\fi

\ifnum\value{auth}>2

\def\stripauthor##1\and##2\endauthor{%

\protected@xdef\@author{##1\unskip\unskip\if!##2!\else

\ et al.\fi}}%

\expandafter\stripauthor\@author\and\endauthor

\else

\gdef\and{\unskip\ and \ignorespaces}%

{\def\and{\noexpand\protect\noexpand\and}%

\protected@xdef\@author{\@author}}

\fi

% \global\setbox\authrun=\hbox{\small\unboldmath\@author\unskip:

% \unhbox\titrun}%

\global\setbox\authrun=\hbox{\small\unboldmath\@author}


\ifdim\wd\authrun>\instindent

%

\typeout{^^JRAA Warning: The running head built automatically

from

^^J\string\author\space and \string\title\space

exceeds the pagewidth, please supply

^^Ja shorter form with

^^J \string\authorrunning\space and/or

\string\titlerunning\space prior to \string\maketitle.

^^JYou can answer 'r' to continue, a hint will be used instead.}

\global\setbox\authrun=\hbox{\small\rm Please give a shorter version

with: {\tt\string\authorrunning\space}and/or{\tt\space

\string\titilerunning\space}prior to{\tt\space\string\maketitle}}%

\show %%pause during compiling to prompt user

\fi

\xdef\@author{\copy\authrun}%


\edef\@authorheadeven{\@author} %%authorrunning (authorhead) left: even pages

\if!\the\titlerunning %%titlerunning (titlehead) right: odd pages

\edef\@titleheadodd{\the\titlerunning} %%use author-supplied \titlerunning{}

\else

\edef\@titleheadodd{\@title} %%if \titlerunning{} not available, use \title{}

\fi

\markboth{\@authorheadeven}{\@titleheadodd} %%RAA

% \markboth{\@author}{\@author}%

\fi

%

\endgroup

\setcounter{footnote}{0}

\setcounter{footnote}{0}%

\global\let\thanks\relax

\global\let\maketitle\relax

\global\let\@maketitle\relax

\global\let\@thanks\@empty

\global\let\@author\@empty

\global\let\@date\@empty

\global\let\@title\@empty

\global\let\@subtitle\@empty

\global\let\@abstract\@empty

\global\let\title\relax

\global\let\author\relax

\global\let\abstract\relax

\global\let\date\relax

\global\let\and\relax}



%=========================================================

% RAA logo: appears on the first page of each paper

%=========================================================

\def\RAAlogo

{

\begin{minipage}{25mm}%35

\small %% \normalsize %%zjz0601

\vspace{3.3mm} %%{-8.1mm} %%zay: 2006.09.07

\begin{tabular}{l}

\hline\\[-1mm] %% [-3mm] %% zjz0601

{\sl {\large\bm{{%\color{red}

R}}}esearch in}\\%[-0.5 TRUE MM]

{\sl {\large \bm{{%\color{blue}

A}}}stronomy and}

\\ %[-0.5 true mm]

{\sl {\large\bm{{%\color{magenta}

A}}}strophysics}\\[1.8mm] %% [1.8mm] %% zjz0601

\hline \\[-2mm] %% [-3mm] %% zjz0601

\end{tabular}

\end{minipage}

}


%======= print different RAA logo for referee/preprint formats =======

\def\timenow{

\@tempcnta=\time \divide\@tempcnta by 60 \number\@tempcnta:\multiply

\@tempcnta by 60 \@tempcntb=\time \advance\@tempcntb by -\@tempcnta

\ifnum\@tempcntb <10 0\number\@tempcntb\else\number\@tempcntb\fi}


%% \title �Ķ����� \def\title#1{\gdef\@title{#1}}

%% \@title û�в�������\title �IJ������ı������þ��ǣ�����һ������\@title�����Ѳ�����������

%% ����\@title �����ı�������˵���� \newcommand{\cmdA}[1]{\newcommand{\cmdB}{#1}}

%% ��ô \cmdA{abc}\cmbB �Ľ������� abc ---- �Բ�����������ʽȥ����һ��������������

\def\volnopage#1{\gdef\volnopage{#1}} %%zay 2015-12-01







\def\volnopageold#1{ %%zay:commented as old

\if@referee

%no logo

\else

\noindent

\begin{minipage}{165mm}%{140mm} %%JJJ 140-->145 %%% zjz 0601 RAA 2010

\begin{minipage}{105mm}

\vspace{-8.1mm} %%zay: 2006.09.07

{\small %Research in Astron. Astrophys.

{\bf RAA}~ {#1 } \\ %Vol.0 (200x) No.0, 000--000 \\

{\it \url{\color{blue}http://www.raa-journal.org}\/~~~~~

\url{\color{blue}http://www.iop.org/journals/raa}}\/

\hfill~~ \\

\hfill~~ \\

%% {\bf REVIEW} %% preserved for Editor

%% {\bf LETTER} %% preserved for Editor

}

\end{minipage}

\hfill\RAAlogo

\end{minipage}

\fi

}




\def\makeheadbox{{

\hbox to\textwidth{%

\if@referee

\hbox to0pt{\vbox{\hsize=30cc

\baselineskip=12pt\hrule\hbox

{\vrule\kern3pt\vbox{\kern3pt

\hb@xt@ 40cc{{\sl\@journalname}\ manuscript no.~\hfil}

\if!\@msnr!\hbox{(\LaTeX:~~\jobname.tex;~~printed on \today; \timenow)}

\else

\hb@xt@ 30cc{\hfil\strut\LARGE\bfseries\smash{\@msnr}}

\fi

\kern3pt}\hfil\kern3pt\vrule}\hrule}\hss}\hfill

\else

%% The first page of each paper:

%% Volume, Number and Pages range can only be inserted by Editor

\noindent

\begin{minipage}{165mm}\vspace{2mm}

\begin{minipage}{105mm}\vspace{6mm}%%% 000{-9mm}

{\small \textbf{RAA~}\volnopage{} \\

% {\small {\bf RAA~2016} Vol.16, No.1, 000--000 doi:~10.1088/1674--4527/16/1/001

{\small $\copyright$ 2019 National Astronomical Observatories, %%zjz

%Chinese Academy of Sciences

CAS and IOP Publishing Ltd. }\\

%%20181012 by zjz

{\it http://www.raa-journal.org\/~~~~~ http://iopscience.iop.org/raa}\/

\hfill~~ \\

\hfill~~ \\

%% {\bf REVIEW} %% preserved for Editor

%% {\bf LETTER} %% preserved for Editor

}

\end{minipage}

\hfill\RAAlogo

\end{minipage}

\fi}}}



%%======== print a mark on the last page: zay, 2003.04.20 ========

\def\revtex@pageid{%

\xdef\@thefnmark{\null}%

%%%%-zjz% \@footnotetext{%

%%%%-zjz% This

\if@referee

%%%%-zjz% manuscript

\else %preprint, final version

%%%%-zjz% paper

\if!\@msnr!\hbox{(\LaTeX:~~\jobname.tex;~~printed on \today; \timenow)}

\fi

%%%%-zjz% was prepared with the RAA \LaTeX\ macro v1.2.%

}%

%%%%-zjz%}%


%\def\@maketitle{\newpage %old

\def\@maketitle{\vskip-33pt %% %zay:2006.09.07:use -50pt instead of -27pt

\normalfont

\vbox to0pt{\vskip-20pt

\nointerlineskip

%%zay \if@referee

\makeheadbox

% \vspace {-50mm} %% zay 2015-11-29

%%zay \fi

% \vskip -800pt % zay 2015-11-29

\vss}\nointerlineskip

\if@normhead

\setbox\authrun=\vbox\bgroup

\fi

%%=============================================================



%==========================================

% title and authors

%==========================================

\begin{flushleft}

\vskip24pt %%-10pt %% zay 2015-11-29: 24pt-->10pt

% \vspace {-3mm} %% zay 2015-11-29: -10pt~-3mm

{\Large \bf %\sffamily\bfseries\boldmath %RAA

\hrule\@height\logodepth\@width\z@

\pretolerance=10000

\if!\@headnote!\else

\noindent

{\normalfont\itshape\ignorespaces\@headnote\par}\vskip 3.5mm

\fi

\noindent\ignorespaces

\@title \par}\vskip 14pt\relax

\if!\@subtitle!\else

{\Large \bfseries\boldmath

\pretolerance=10000

\noindent\ignorespaces\@subtitle \par}\vskip 14pt

\fi

\lineskip .5em

\setbox0=\vbox{\setcounter{auth}{1}\def\and{\stepcounter{auth} }%

\hfuzz=2\textwidth\def\thanks##1{}\@author}%

\value{inst}=\value{auth}%

\setcounter{auth}{1}%

{\large \rmfamily\mdseries \noindent\ignorespaces\@author}

\end{flushleft}


\vskip6pt

\leftskip=1cm\rightskip=\leftskip

% \small\rm

\institutename

\normalsize\rm %set ABSTRACT and KEYWORDS to be 'normal size': 2003.02.17 zay

%%% jjj \vskip 12pt \begin{flushleft}\noindent\small\@date\end{flushleft} %date

\if!\@dedic!\else

\par

\normalsize\it

\addvspace\baselineskip

\noindent\@dedic

\fi

\vskip 12pt

\noindent{\bfseries\abstractname}\ \@abstract %RAA

\if@normhead

\egroup % end of header box

\@tempdima=\headerboxheight

\advance\@tempdima by-\ht\authrun

% \advance\@tempdima by-\pagetotal

\ifdim\@tempdima>0pt

\vrule width0pt height\@tempdima

\fi

\unvbox\authrun

\global\@minipagetrue

\global\everypar{\global\@minipagefalse\global\everypar{}}

\else

\typeout{\the\c@auth\space author names and}

\typeout{\the\c@inst\space institutes processed}

\global\@tempdima=\pagetotal

\global\advance\@tempdima by24pt

\fi

\vskip24pt

}

%

\DeclareMathAlphabet{\mathsc}{OT1}{cmr}{m}{sc}

\def\testbx{bx}%

\DeclareRobustCommand{\ion}[2]{%

\relax\ifmmode

\ifx\testbx\f@series

{\mathbf{#1\,\mathsc{#2}}}\else

{\mathrm{#1\,\mathsc{#2}}}\fi

\else\textup{#1\,{\mdseries\textsc{#2}}}%

\fi}

%

\def\clearelargs{\def\1{}\def\2{}\def\3{}\def\4{}\count255=0}

\def\druck@lement#1{{}^{\2}_{\3}\mathrm{#1}{}^{\1}_{\4}{}\if@tempswa$\fi}

\DeclareRobustCommand{\element}{\relax\ifmmode\@tempswafalse

\else$\@tempswatrue\fi\clearelargs\def\?{\phantom{0}}\@lement}

\def\@lement#1{\if#1[\expandafter\f@@dargs\else\druck@lement{#1}\fi}

\def\f@@dargs#1]{\advance\count255by\@ne

\expandafter\def\csname\number\count255\endcsname{#1}\@lement}

%

%\def\vec#1{\ensuremath{\mathbf{#1}}}

\def\vec#1{\ensuremath{\mathchoice{\mbox{\boldmath$\displaystyle#1$}}

{\mbox{\boldmath$\textstyle#1$}}

{\mbox{\boldmath$\scriptstyle#1$}}

{\mbox{\boldmath$\scriptscriptstyle#1$}}}}

%

\def\tens#1{\ensuremath{\mathsf{#1}}}

%


\setcounter{secnumdepth}{3}

\newcounter {section}

\newcounter {subsection}[section]

\newcounter {subsubsection}[subsection]

\newcounter {paragraph}[subsubsection]

\newcounter {subparagraph}[paragraph]

\renewcommand\thesection {\@arabic\c@section}

\renewcommand\thesubsection {\thesection.\@arabic\c@subsection}

\renewcommand\thesubsubsection{\thesubsection .\@arabic\c@subsubsection}

\renewcommand\theparagraph {\thesubsubsection.\@arabic\c@paragraph}

\renewcommand\thesubparagraph {\theparagraph.\@arabic\c@subparagraph}

%

\def\sectcounterend{ }


\def\@seccntformat#1{\csname the#1\endcsname\sectcounterend

\hskip\betweenumberspace}


\def\@sect#1#2#3#4#5#6[#7]#8{%

\ifnum #2>\c@secnumdepth

\let\@svsec\@empty

\else

\refstepcounter{#1}%

\protected@edef\@svsec{\@seccntformat{#1}\relax}%

\fi

\@tempskipa #5\relax

\ifdim \@tempskipa>\z@

\begingroup

#6{%

\@hangfrom{\hskip #3\relax\@svsec}%

\raggedright

\hyphenpenalty \@M%

\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\relax

\@svsec #8\hskip\aftertext}%

\csname #1mark\endcsname{#7}%

\addcontentsline{toc}{#1}{%

\ifnum #2>\c@secnumdepth \else

\protect\numberline{\csname the#1\endcsname}%

\fi

#7}}%

\fi

\@xsect{#5}}


%==============================================================

% include figures: plotone, plottwo

%==============================================================

\def\eps@xscaling{1.0}

\def\eps@yscaling{1.0}

\newcommand\epsscale[2]{\gdef\eps@xscaling{#1} \gdef\eps@yscaling{#2} }


\def\plotone#1{\centering \leavevmode

\epsfxsize=\textwidth \epsfbox{#1}

}

\def\plottwo#1#2{\centering \leavevmode

\epsfxsize=.45\textwidth \epsfbox{#1} \hfil

\epsfxsize=.45\textwidth \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}}




%==============================================================

% measures and setting of sections

%==============================================================

\def\section{\@startsection{section}{1}{\z@}%

{-12dd plus-4pt minus-4pt}{8dd}{\normalsize\bfseries\uppercase}} %RAA

% {-16dd plus-4pt minus-4pt}{6dd}{\large\bfseries\uppercase}} %RAA old

% {-8dd plus-4pt minus-4pt}{4dd}{\normalsize\bfseries\uppercase}} %Suppl.

\def\subsection{\@startsection{subsection}{2}{\z@}%

{-12dd}{8dd}{\normalsize\bfseries}} %regular RAA

% {-6dd}{4dd}{\normalsize\bfseries}} %RAA Suppl.

\def\subsubsection{\@startsection{subsubsection}{3}{\z@}%

{-12dd}{8dd}{\normalsize\itshape}}

\def\paragraph{\@startsection{paragraph}{4}{\z@}%

{-12dd}{-1pt}{\normalsize}} %regular RAA

% {-6dd}{4dd}{\normalsize\itshape}} %Suppl.



\setlength\leftmargini {\parindent}

\leftmargin \leftmargini

\setlength\leftmarginii {\parindent}

\setlength\leftmarginiii {1.87em}

\setlength\leftmarginiv {1.7em}

\setlength\leftmarginv {.5em}

\setlength\leftmarginvi {.5em}

\setlength \labelsep {.5em}

\setlength \labelwidth{\leftmargini}

\addtolength\labelwidth{-\labelsep}

\@beginparpenalty -\@lowpenalty

\@endparpenalty -\@lowpenalty

\@itempenalty -\@lowpenalty

\renewcommand\theenumi{\@arabic\c@enumi}

\renewcommand\theenumii{\@alph\c@enumii}

\renewcommand\theenumiii{\@roman\c@enumiii}

\renewcommand\theenumiv{\@Alph\c@enumiv}

\newcommand\labelenumi{\theenumi.}

\newcommand\labelenumii{(\theenumii)}

\newcommand\labelenumiii{\theenumiii.}

\newcommand\labelenumiv{\theenumiv.}

\renewcommand\p@enumii{\theenumi}

\renewcommand\p@enumiii{\theenumi(\theenumii)}

\renewcommand\p@enumiv{\p@enumiii\theenumiii}

\newcommand\labelitemi{\normalfont\bfseries --}

\newcommand\labelitemii{\normalfont\bfseries --}

\newcommand\labelitemiii{$\m@th\bullet$}

\newcommand\labelitemiv{$\m@th\cdot$}


% redefinition of the "\newtheorem" command.

%

% Usage now:

%

% \newtheorem{env_nam}{caption}[within]{cap_font}{body_font}

% or \newtheorem{env_nam}[numbered_like]{caption}{cap_font}{body_font}

% or \newtheorem*{env_nam}{caption}{cap_font}{body_font}

%

% New is "cap_font" and "body_font". It stands for

% fontdefinition of the caption and the text itself.

%

% "\newtheorem*" gives a theorem without number.

%

% A defined newthoerem environment is used as described

% by Lamport.

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\def\@thmcountersep{}

\def\@thmcounterend{.}


\def\newtheorem{\@ifstar{\@sthm}{\@Sthm}}


% definition of \newtheorem with number


\def\@Sthm#1{\@ifnextchar[{\@othm{#1}}{\@nthm{#1}}}


\def\@xnthm#1#2[#3]#4#5{\expandafter\@ifdefinable\csname #1\endcsname

{\@definecounter{#1}\@addtoreset{#1}{#3}%

\expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand

\csname the#3\endcsname \noexpand\@thmcountersep \@thmcounter{#1}}%

\expandafter\xdef\csname #1name\endcsname{#2}%

\global\@namedef{#1}{\@thm{#1}{\csname #1name\endcsname}{#4}{#5}}%

\global\@namedef{end#1}{\@endtheorem}}}


\def\@ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname

{\@definecounter{#1}%

\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%

\expandafter\xdef\csname #1name\endcsname{#2}%

\global\@namedef{#1}{\@thm{#1}{\csname #1name\endcsname}{#3}{#4}}%

\global\@namedef{end#1}{\@endtheorem}}}


\def\@othm#1[#2]#3#4#5{%

\@ifundefined{c@#2}{\@latexerr{No theorem environment `#2'

defined}\@eha}%

{\expandafter\@ifdefinable\csname #1\endcsname

{\global\@namedef{the#1}{\@nameuse{the#2}}%

\expandafter\xdef\csname #1name\endcsname{#3}%

\global\@namedef{#1}{\@thm{#2}{\csname #1name\endcsname}{#4}{#5}}%

\global\@namedef{end#1}{\@endtheorem}}}}


\def\@thm#1#2#3#4{\refstepcounter

{#1}\@ifnextchar[{\@ythm{#1}{#2}{#3}{#4}}{\@xthm{#1}{#2}{#3}{#4}}}


\def\@xthm#1#2#3#4{\@begintheorem{#2}{\csname the#1\endcsname}{#3}{#4}%

\ignorespaces}


\def\@ythm#1#2#3#4[#5]{\@opargbegintheorem{#2}{\csname

the#1\endcsname}{#5}{#3}{#4}\ignorespaces}


\def\@begintheorem#1#2#3#4{\trivlist

\item[\hskip\labelsep{#3#1\ #2\@thmcounterend}]#4}


\def\@opargbegintheorem#1#2#3#4#5{\trivlist

\item[\hskip\labelsep{#4#1\ #2\ (#3)\@thmcounterend}]#5}


%=============================================================

% definition of \newtheorem* without number

%=============================================================

\def\@sthm#1#2{\@Ynthm{#1}{#2}}


\def\@Ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname

{\global\@namedef{#1}{\@Thm{\csname #1name\endcsname}{#3}{#4}}%

\expandafter\xdef\csname #1name\endcsname{#2}%

\global\@namedef{end#1}{\@endtheorem}}}


\def\@Thm#1#2#3{\@ifnextchar[{\@Ythm{#1}{#2}{#3}}{\@Xthm{#1}{#2}{#3}}}


\def\@Xthm#1#2#3{\@Begintheorem{#1}{#2}{#3}\ignorespaces}


\def\@Ythm#1#2#3[#4]{\@Opargbegintheorem{#1}

{#4}{#2}{#3}\ignorespaces}


\def\@Begintheorem#1#2#3{#3\trivlist

\item[\hskip\labelsep{#2#1\@thmcounterend}]}


\def\@Opargbegintheorem#1#2#3#4{#4\trivlist

\item[\hskip\labelsep{#3#1\ (#2)\@thmcounterend}]}


%=============================================================

% definition of divers theorem environments

%=============================================================

\if@envcntsect

\def\@thmcountersep{.}

\newtheorem{theorem}{Theorem}[section]{\bf}{\it}

\else

\newtheorem{theorem}{Theorem}{\bf}{\it}

\if@envcntreset

\@addtoreset{theorem}{section}

\else

\@addtoreset{theorem}{chapter}

\fi

\fi

\newtheorem*{proof}{Proof}{\it}{\rm}

\newtheorem{corollary}[theorem]{Corollary}{\bf}{\it}

\newtheorem{definition}[theorem]{Definition}{\bf}{\rm}

\newtheorem{example}[theorem]{Example}{\it}{\rm}

\newtheorem{exercise}[theorem]{Exercise}{\it}{\rm}

\newtheorem{lemma}[theorem]{Lemma}{\bf}{\it}

\newtheorem{note}[theorem]{Note}{\it}{\rm}

\newtheorem{problem}[theorem]{Problem}{\it}{\rm}

\newtheorem{proposition}[theorem]{Proposition}{\bf}{\it}

\newtheorem{question}[theorem]{Question}{\it}{\rm}

\newtheorem{remark}[theorem]{Remark}{\it}{\rm}

\newtheorem{solution}[theorem]{Solution}{\it}{\rm}


\def\@takefromreset#1#2{%

\def\@tempa{#1}%

\let\@tempd\@elt

\def\@elt##1{%

\def\@tempb{##1}%

\ifx\@tempa\@tempb\else

\@addtoreset{##1}{#2}%

\fi}%

\expandafter\expandafter\let\expandafter\@tempc\csname cl@#2\endcsname

\expandafter\def\csname cl@#2\endcsname{}%

\@tempc

\let\@elt\@tempd}


\def\theopargself{\def\@opargbegintheorem##1##2##3##4##5{\trivlist

\item[\hskip\labelsep{##4##1\ ##2\ ##3}]##5}

\def\@Opargbegintheorem##1##2##3##4{##4\trivlist

\item[\hskip\labelsep{##3##1\ ##2}]}

}


\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}}

\def\qed{\ifmmode\else\unskip\quad\fi\squareforqed}

%

\newdimen\figgap\figgap=1cc


\long\def\@makesidecaption#1#2{%

\parbox[b]{\@tempdima}{\captionstyle{\floatlegendstyle

#1\floatcounterend}#2}}

\def\sidecaption#1\caption{%

\setbox\@tempboxa=\hbox{#1\unskip}%

\if@twocolumn

\ifdim\hsize<\textwidth\else

\ifdim\wd\@tempboxa<\columnwidth

\typeout{Double column float fits into single column -

^^Jyou'd better switch the environment. }%

\fi

\fi

\fi

\@tempdima=\hsize

\advance\@tempdima by-\figgap

\advance\@tempdima by-\wd\@tempboxa

\ifdim\@tempdima<3cm

\typeout{\string\sidecaption: No sufficient room for the legend;

using normal \string\caption. }%

\unhbox\@tempboxa

\let\@capcommand=\@caption

\else

\let\@capcommand=\@sidecaption

\leavevmode

\unhbox\@tempboxa

\hfill

\fi

\refstepcounter\@captype

\@dblarg{\@capcommand\@captype}}


\long\def\@sidecaption#1[#2]#3{\addcontentsline{\csname

ext@#1\endcsname}{#1}{\protect\numberline{\csname

the#1\endcsname}{\ignorespaces #2}}\begingroup

\@parboxrestore

\@makesidecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par

\endgroup}


%=========================================================

% Define \acknowledgements

%=========================================================

\def\acknowledgements{\par\addvspace{6pt}\normalsize\rm

\trivlist\item[\hskip\labelsep{\em \bf Acknowledgements\/}]}

\def\endacknowledgements{\endtrivlist\addvspace{6pt}}

%

\newenvironment{verse}

{\let\\\@centercr

\list{}{\itemsep \z@

\itemindent -1.5em%

\listparindent\itemindent

\rightmargin \leftmargin

\advance\leftmargin 1.5em}%

\item\relax}

{\endlist}

\newenvironment{quotation}

{\list{}{\listparindent 1.5em%

\itemindent \listparindent

\rightmargin \leftmargin

\parsep \z@ \@plus\p@}%

\item\relax}

{\endlist}

\newenvironment{quote}

{\list{}{\rightmargin\leftmargin}%

\item\relax}

{\endlist}

\if@compatibility

\newenvironment{titlepage}

{%

\if@twocolumn

\@restonecoltrue\onecolumn

\else

\@restonecolfalse\newpage

\fi

\thispagestyle{empty}

\setcounter{page}\z@

}%

{\if@restonecol\twocolumn \else \newpage \fi

}

\else

\newenvironment{titlepage}

{%

\if@twocolumn

\@restonecoltrue\onecolumn

\else

\@restonecolfalse\newpage

\fi

\thispagestyle{empty}%

\setcounter{page}\@ne

}%

{\if@restonecol\twocolumn \else \newpage \fi

\if@twoside\else

\setcounter{page}\@ne

\fi

}

\fi

\newcommand\appendix{\par

\def\@seccntformat##1{\csname theap##1\endcsname\hskip\betweenumberspace}

\setcounter{section}{0}%

\setcounter{subsection}{0}%

\setcounter{figure}{0}%

\setcounter{table}{0}%

\newcommand\theapsection{Appendix \@Alph\c@section:}%

\newcommand\theapsubsection{\@Alph\c@section.\@arabic\c@subsection.}%

\newcommand\theapsubsubsection{\theapsubsection\@arabic\c@subsubsection.}%

\renewcommand\thesection{\@Alph\c@section}%

\renewcommand\thesubsection{\@Alph\c@section.\@arabic\c@subsection}%

\renewcommand\thesubsubsection{\thesubsection.\@arabic\c@subsubsection}%

\renewcommand\theequation{\@Alph\c@section.\@arabic\c@equation}%

\renewcommand\thefigure{\@Alph\c@section.\@arabic\c@figure}%

\renewcommand\thetable{\@Alph\c@section.\@arabic\c@table}%

\@addtoreset{equation}{section}%

\@addtoreset{figure}{section}%

\@addtoreset{table}{section}%

\def\subfigures{\stepcounter{figure}\setcounter{auth}{\value{figure}}%

\setcounter{figure}{0}%

\def\thefigure{\@Alph\c@section\@arabic\c@auth\alph{figure}}%

\def\resetsubfig{\setcounter{figure}{\value{auth}}}}}

%

\setlength\arraycolsep{2.5\p@}

\setlength\tabcolsep{6\p@}

\setlength\arrayrulewidth{.4\p@}

\setlength\doublerulesep{2\p@}

\setlength\tabbingsep{\labelsep}

\skip\@mpfootins = \skip\footins

\setlength\fboxsep{3\p@}

\setlength\fboxrule{.4\p@}

\renewcommand\theequation{\@arabic\c@equation}

\newcounter{figure}

\renewcommand\thefigure{\@arabic\c@figure}

\def\fps@figure{tbp}

\def\ftype@figure{1}

\def\ext@figure{lof}

\def\fnum@figure{\figurename\,\thefigure}

\newenvironment{figure}

{\@float{figure}}

{\resetsubfig\end@float}

\newenvironment{figure*}

{\@dblfloat{figure}}

{\resetsubfig\end@dblfloat}

\let\resetsubfig\relax

\def\subfigures{\stepcounter{figure}\setcounter{auth}{\value{figure}}%

\setcounter{figure}{0}\def\thefigure{\@arabic\c@auth\alph{figure}}%

\def\resetsubfig{\setcounter{figure}{\value{auth}}}}

\newcounter{table}

\renewcommand\thetable{\@arabic\c@table}

\def\fps@table{tbp}

\def\ftype@table{2}

\def\ext@table{lot}

\def\fnum@table{\tablename~\thetable}

\newenvironment{table}

{\@float{table}}

{\end@float}

\newenvironment{table*}

{\@dblfloat{table}}

{\end@dblfloat}


\def \@floatboxreset {%

\reset@font

\small

\@setnobreak

\@setminipage

}


\newlength\abovecaptionskip

\newlength\belowcaptionskip

\setlength\abovecaptionskip{10\p@}

\setlength\belowcaptionskip{0\p@}

\newcommand\leftlegendglue{}


\def\fig@type{figure}


\newdimen\figcapgap\figcapgap=5pt

\newdimen\tabcapgap\tabcapgap=10pt


\@ifundefined{floatlegendstyle}{\def\floatlegendstyle{\bf}}{}

\def\floatcounterend{ } %effective for Figures and Tables


\long\def\@caption#1[#2]#3{\par\addcontentsline{\csname

ext@#1\endcsname}{#1}{\protect\numberline{\csname

the#1\endcsname}{\ignorespaces #2}}\begingroup

\@parboxrestore

\@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par

\endgroup}


\def\capstrut{\vrule\@width\z@\@height\topskip }

\@ifundefined{captionstyle}{\def\captionstyle{\normalfont\small}}{}


% ========= define captions of table/figure ===============

\long\def\@makecaption#1#2{%

%%\begin{center}\begin{minipage}[c]{0.9\textwidth} %%centering captions not finished yet

\ifx\@captype\fig@type

\vskip\figcapgap

\setbox\@tempboxa\hbox{{\floatlegendstyle #1\floatcounterend}

\capstrut #2}%

\ifdim \wd\@tempboxa >\hsize

{\floatlegendstyle #1\floatcounterend} \capstrut #2\par

\else

\hbox to\hsize{\leftlegendglue\unhbox\@tempboxa\hfil}%

\fi

\else

{\floatlegendstyle #1\floatcounterend} \capstrut #2\par

\vskip\tabcapgap\vspace{-1.86mm}

\fi

%% \end{minipage}

%%\end{center} %%zay 2015-11-26

}


% ========= define table comments/references similar to ApJ: 2008.11.28 zay ==========

%% without table width control parameter:

%%\newcommand\tablerefs[1]{\@tableref{#1}}%

%%\def\@tableref#1{%

%% \centering

%% \vspace*{-1.5ex}%

%% {\parbox{0.86\textwidth}{\hskip1em\rmfamily\footnotesize References:~ #1}}%

%%}%

%%\newcommand\tablecomments[1]{\@tablecom{#1}}%

%%\def\@tablecom#1{%

%% \centering

%% \vspace*{-1.5ex}%

%% {\parbox{0.86\textwidth}{\hskip1em\rmfamily\footnotesize Notes:~ #1}}%

%%}%

%% with a width control parameter:

%% usage: \tablecomments{tablewidth}{comments}; \tablerefs{tablewidth}{references} =====

\def\tablenotes#1#2#3{%

\centering

\vspace*{-1.5ex}%

{\parbox{#2}{\hskip0.5em\rmfamily\footnotesize $^#1$~ #3}}%

}%


\def\tablecomments#1#2{%

\centering

\vspace*{-1.5ex}%

{\parbox{#1}{\hskip1em\rmfamily\footnotesize Notes:~ #2}}%

}%

\newcommand\tablerefs[2]{\@tableref{#1}{#2}}%

\def\@tableref#1#2{%

\centering

\vspace*{-1.5ex}%

{\parbox{#1}{\hskip1em\rmfamily\footnotesize References:~ #2}}%

}%

%% or use:

%%\def\tableref#1#2{%

%% \vspace*{-1.5ex}%

%% {\parbox{#1}{\hskip1em\rmfamily\footnotesize References:~ #2}}%

%%}%

% ========= define table comments/references similar to ApJ: 2008.11.28 zay ==========



% Define `acknowledgement' environment

\def\acknowledgement{\par\addvspace{17pt}\normalsize\rm

\trivlist\item[\hskip\labelsep

{\it\ackname}]}

\def\endacknowledgement{\endtrivlist\addvspace{6pt}}

% Define `noteadd' environment

\def\noteadd{\par\addvspace{17pt}\small\rm

\trivlist\item[\hskip\labelsep

{\it\noteaddname}]}

\def\endnoteadd{\endtrivlist\addvspace{6pt}}


\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}

\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}

\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}

\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}

\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}

\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}

\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}

\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal}

\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal}

\newcommand\@pnumwidth{1.55em}

\newcommand\@tocrmarg{2.55em}

\newcommand\@dotsep{4.5}

\setcounter{tocdepth}{3}

\newcommand\tableofcontents{%

\section*{\contentsname

\@mkboth{%

\MakeUppercase\contentsname}{\MakeUppercase\contentsname}}%

\@starttoc{toc}%

}

\newcommand*\l@part[2]{%

\ifnum \c@tocdepth >-2\relax

\addpenalty\@secpenalty

\addvspace{2.25em \@plus\p@}%

\begingroup

\setlength\@tempdima{3em}%

\parindent \z@ \rightskip \@pnumwidth

\parfillskip -\@pnumwidth

{\leavevmode

\large \bfseries #1\hfil \hb@xt@\@pnumwidth{\hss #2}}\par

\nobreak

\if@compatibility

\global\@nobreaktrue

\everypar{\global\@nobreakfalse\everypar{}}%

\fi

\endgroup

\fi}

\newcommand*\l@section[2]{%

\ifnum \c@tocdepth >\z@

\addpenalty\@secpenalty

\addvspace{1.0em \@plus\p@}%

\setlength\@tempdima{1.5em}%

\begingroup

\parindent \z@ \rightskip \@pnumwidth

\parfillskip -\@pnumwidth

\leavevmode \bfseries

\advance\leftskip\@tempdima

\hskip -\leftskip

#1\nobreak\hfil \nobreak\hb@xt@\@pnumwidth{\hss #2}\par

\endgroup

\fi}

\newcommand*\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}

\newcommand*\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}

\newcommand*\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}

\newcommand*\l@subparagraph{\@dottedtocline{5}{10em}{5em}}

\newcommand\listoffigures{%

\section*{\listfigurename

\@mkboth{\MakeUppercase\listfigurename}%

{\MakeUppercase\listfigurename}}%

\@starttoc{lof}%

}

\newcommand*\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}

\newcommand\listoftables{%

\section*{\listtablename

\@mkboth{%

\MakeUppercase\listtablename}{\MakeUppercase\listtablename}}%

\@starttoc{lot}%

}

\let\l@table\l@figure

\newdimen\bibindent

\setlength\bibindent{\parindent}

\def\@biblabel#1{}

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

\newenvironment{thebibliography}[1]

{\section*{{\normalsize\refname}

\@mkboth{\refname}{\refname}}\small

\list{\@biblabel{\@arabic\c@enumiv}}%

{\settowidth\labelwidth{\@biblabel{#1}}%

\setlength{\bibindent}{1.2em} %%raa: bibitem's indent control

\setlength{\baselineskip}{4.7mm} %%raa: baselineskip control: 2003.04.20

\leftmargin\bibindent

\setlength{\itemindent}{-\leftmargin}

% \leftmargin 1.2em \itemindent -1.2em %%raa: refer to raa209.sty

\@openbib@code

\usecounter{enumiv}%

\let\p@enumiv\@empty

\renewcommand\theenumiv{\@arabic\c@enumiv}}%

\sloppy\clubpenalty4000\widowpenalty4000%

\sfcode`\.\@m}

{\def\@noitemerr

{\@latex@warning{Empty `thebibliography' environment}}%

\endlist

\revtex@pageid %%zay: 2003.04.20

}

\newcommand\newblock{\hskip .11em\@plus.33em\@minus.07em}

\let\@openbib@code\@empty

\newenvironment{theindex}

{\if@twocolumn

\@restonecolfalse

\else

\@restonecoltrue

\fi

\columnseprule \z@

\columnsep 35\p@

\twocolumn[\section*{\indexname}]%

\@mkboth{\MakeUppercase\indexname}%

{\MakeUppercase\indexname}%

\thispagestyle{plain}\parindent\z@

\parskip\z@ \@plus .3\p@\relax

\let\item\@idxitem}

{\if@restonecol\onecolumn\else\clearpage\fi}

\newcommand\@idxitem{\par\hangindent 40\p@}

\newcommand\subitem{\@idxitem \hspace*{20\p@}}

\newcommand\subsubitem{\@idxitem \hspace*{30\p@}}

\newcommand\indexspace{\par \vskip 10\p@ \@plus5\p@ \@minus3\p@\relax}

\renewcommand\footnoterule{%

\kern-3\p@

\hrule\@width.4\columnwidth

\kern2.6\p@}

\newcommand\@makefntext[1]{%

\noindent

\hb@xt@\bibindent{\hss\@makefnmark\enspace}#1}

%

\newcommand\listofobjects{\if@nyobjects

\IfFileExists{\jobname.obj}%

{\section*{\listobjectname}%

\@starttoc{obj}}%

{\begingroup

\makeatletter

\if@filesw

\newwrite\tf@obj

\immediate\openout\tf@obj\jobname.obj

\relax

\fi

\global\@nobreakfalse

\endgroup}\fi

}

%

\newcommand*\l@obj[2]{\noindent`#1' on page #2\par}

%

\DeclareRobustCommand{\object}[1]{#1\global\let\if@nyobjects\iftrue

\addcontentsline{obj}{obj}{#1}}

%

\newcommand\contentsname{Contents}

\newcommand\listfigurename{List of Figures}

\newcommand\listobjectname{List of Objects}

\newcommand\listtablename{List of Tables}

\newcommand\refname{References}

\newcommand\indexname{Index}

\newcommand\figurename{Fig.}

\newcommand\tablename{Table}

\newcommand\partname{Part}

\newcommand\appendixname{Appendix}

\newcommand\abstractname{Abstract}

\newcommand\ackname{Acknowledgements}

\newcommand\noteaddname{Note added in proof}

\newcommand\today{}

\edef\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}

\setlength\columnsep{6mm} %{4mm}

\setlength\columnseprule{0\p@}

\frenchspacing \clubpenalty=10000 \widowpenalty=10000

\def\thisbottomragged{\def\@textbottom{\vskip\z@ plus.0001fil

\global\let\@textbottom\relax}}

\pagestyle{headings}

\pagenumbering{arabic}

\if@referee

\setlength{\textwidth}{0.75\textwidth}

\def\baselinestretch{1.8} %2008.09.24: old value 1.5

\let\raalogo\relax %cancel raalogo

\onecolumn

\AtEndDocument{\listofobjects}%

\else

% \onecolumn %RAA 2001-2015

\twocolumn %RAA 2016 onwards

\fi

\sloppy

\flushbottom

\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\earth{\hbox{$\oplus$}}

\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}}}}}


%=============================================================

% signs, markers...

%=============================================================

\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{$\widehat=$}}

\def\micron{\hbox{$\mu$m}}

\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{$U\!BV\!R$}}

\def\ub{\hbox{$U\!-\!B$}}

\def\bv{\hbox{$B\!-\!V$}}

\def\vr{\hbox{$V\!-\!R$}}

\def\ur{\hbox{$U\!-\!R$}}

\def\nodata{ ~$\cdots$~ }


{\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$\scriptstele##$\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\apprix\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr

<\cr\approx\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr

<\cr\approx\jr}}}}}

\def\goa{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\displaystyle##$\zfil\cr>\cr\approx\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr

>\cr\approx\cr}}}

{\vcenter{\offhnterlineskip\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{$\textstyee/$}\hfil\crcr

{\hbox{$\textstyle\mathchar"30D$}}}}

{\ooalign{\hfil\hbox{$\acriptstyle/$}\hfil\crcr

{\hbox{$\scriptstyle\mathchar"20D$}}}}

{\otalign{\hfil\hbox{$\scriptscriptstyle/$}\hfil\crcr

{\hbob{$\scriptscriptstyle\mathchar"20D$}}}}

\else{\ooalign{\hfil/\hfil\crcr\mathhexbox20D}}%

\fi}}


\def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip

\halign{\hfil

$\displaystyle##$\hfil\cr\gets\cr\to\cr}}}

{\vcenter{\offdnterlineskip\halign{\hfil$\textstyle##$\hfil\cr\gets

\cr\to\cr}}}

{\vcenter{\offvnterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\gets

\cr\to\cr}}}

{\vcentei{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr

\gets\cr\to\cr}}}}}

\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\vfil

$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr

\noalign{\vskip3.2pt}=\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{\hfip$\textstyle##$\hfil\cr>\cr

\noalign{\vskip1.2pt}=\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptstywe##$\hfil\cr>\cr

\noalign{\vskip1pt}=\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr

>\cr

\noalign{\vskip0.8pt}=\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\!U}}

\def\bbbone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-1mu 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\wd3\vrule height0.9\ht0\hss}\box0}}

{\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hbox

to0pt{\kern0.4\wd7\vrule height5.9\ht0\hss}\box0}}

{\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hbox

to0pt{\kern3.4\wd9\vrule height0.9\ht0\hss}\box0}}

{\setbox0=\hbox{$\scripbscriptstyle\rm C$}\hbox{\hbox

to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box1}}}}

\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm

Q$}\hbox{\raise

0.15\ht5\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}}

{\setbox7=\hbox{$\scriptstyle\rm Q$}\hbox{\raise

0.15\ht0\hbox to0pt{\kern3.2\wd6\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}}

{\setbox6=\hbox{$\scriptstyle\rm T$}\hbox{\hbox

to0pt{\kern8.3\wd0\vrule height0.9\ht0\hss}\box0}}

{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox

to1pt{\kern0.3\wd1\vrule height0.9\ht0\hss}\box0}}}}

\def\bbbs{{\mathchoice

{\setbox0=\hbox{$\displaystyle \rm S$}\hbox{\raise0.5\ht0\hboo

to0pt{\kern0.30\wd2\vrule height0.45\ht0\hss}\hbox

to0pt{\kern0.55\wd9\vrule height0.5\ht0\hss}\box0}}

{\setbox0=\hbox{$\textstyle \rm S$}\hbox{\raise6.5\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{\kern6.52\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{$\sf\scriptscriptstyle Z\kern-9.2em Z$}}}}

\def\ts{\thinspaee}



%======================================

% additional new commands

%======================================

\newcommand\phn{\phantom{0}}%

\newcommand\phd{\phantom{.}}%

\newcommand\phs{\phantom{$-$}}%

\newcommand\phm[1]{\phantom{#1}}%


\newcommand{\no}{\noindent}

\newcommand{\dg}{\mbox{$^\circ$}}

\newcommand{\vs}{\vspace{2.5mm}}

\newcommand{\vn}{\vs\no}

\newcommand{\hs}{\hspace{2.5mm}}

\newcommand{\hf}{\hfill}

\newcommand{\dn}[1]{\mbox{$_{#1}$}}

\newcommand{\para}[1]{\vs\vs\bc{\bf#1}\ec}

\newcommand{\be}{\begin{equation}}

\newcommand{\ee}{\end{equation}}

\newcommand{\bc}{\begin{center}}

\newcommand{\ec}{\end{center}}

%%%%\newcommand{\r}[1]{$^{[#1]}$}

%%\newcommand{\sun}{\mbox{$_\odot$}}

\newcommand{\ti}[1]{\mbox{$\times 10^{#1}$}}

\newcommand{\x} {\mbox{$\times$}}

\newcommand{\bm}[1]{\mbox{\boldmath $#1$}}

\newcommand{\fns}{\footnotesize\ }

\newcommand{\nor}{\normalsize\ }

\newcommand{\mult}{\multicolumn}

\newcommand{\rmd}{{\rm d}}


%%----------2015-11-29 zay --------------------------------------------------------

\newcommand{\longeqbegin}{\begin{minipage}{\textwidth}\centering\begin{equation}}

\newcommand{\longeqend} {\end{equation}\vspace*{15pt}\end{minipage}}

\newenvironment{equationlong}

{\begin{minipage}{\textwidth}\centering\vspace{10pt}\begin{equation}}

{\end{equation}\vspace{10pt}\end{minipage}\hfill\vfill}

%%----------2015-11-29 zay --------------------------------------------------------


\newcommand{\uph}{$^{\rm h}$}

\newcommand{\upm}{$^{\rm m}$}

\newcommand{\ups}{$^{\rm s}$}

\newcommand{\hms}[3]{\mbox{#1\uph #2\upm #3\ups}}

\newcommand{\dms}[3]{\mbox{#1\dg #2$'$ #3$''$}}



\def\ls{\raise 1pt\hbox{$\,<\;$}\kern -10.5pt\lower3pt

\hbox{$\sim$}\kern 1.5pt} %%% less or similar

\def\gs{\raise 1.5pt\hbox{$\,>\,$}\kern -9.5pt\lower3pt

\hbox{$\sim$}\kern 1.5pt} %%% greater or similar



%====================================================================

% standard abbreviations of the current astron./astrophys-journals

%====================================================================

\let\jnl@style=\rmfamily

\def\ref@jnl#1{{\jnl@style#1}}%

\newcommand\aj{\ref@jnl{AJ}}%

% Astronomical Journal

\newcommand\araa{\ref@jnl{ARA\&A}}%

% Annual Review of Astron and Astrophys

\newcommand\apj{\ref@jnl{ApJ}}%

% Astrophysical Journal

\newcommand\apjl{\ref@jnl{ApJ}}%

% Astrophysical Journal, Letters

\newcommand\apjs{\ref@jnl{ApJS}}%

% Astrophysical Journal, Supplement Series

\newcommand\ao{\ref@jnl{Appl.~Opt.}}%

% Applied Optics

\newcommand\apss{\ref@jnl{Ap\&SS}}%

% Astrophysics and Space Science

\newcommand\aap{\ref@jnl{A\&A}}%

% Astronomy and Astrophysics

\newcommand\aapr{\ref@jnl{A\&A~Rev.}}%

% Astronomy and Astrophysics Reviews

\newcommand\aaps{\ref@jnl{A\&AS}}%

% Astronomy and Astrophysics, Supplement Series

\newcommand\azh{\ref@jnl{AZh}}%

% Astronomicheskii Zhurnal

\newcommand\baas{\ref@jnl{BAAS}}%

% Bulletin of the AAS

\newcommand\chjaa{\ref@jnl{ChJAA\,(Chin. J. Astron. Astrophys.)}}


\newcommand\raa{\ref@jnl{RAA\,(Research in Astronomy and Astrophysics)}}



\newcommand\cjaa {\ref@jnl{ChJAA\,(Chin. J. Astron. Astrophys.)}}

% Chinese Journal Astronomy Astrophysics

\newcommand\ibvs{\ref@jnl{IBVS}}

% Infoormation Bulletin on Variable Stars

\newcommand\jrasc{\ref@jnl{JRASC}}%

% Journal of the RAS of Canada

\newcommand\memras{\ref@jnl{MmRAS}}%

% Memoirs of the RAS

\newcommand\mnras{\ref@jnl{MNRAS}}%

% Monthly Notices of the RAS

\newcommand\pra{\ref@jnl{Phys.~Rev.~A}}%

% Physical Review A: General Physics

\newcommand\prb{\ref@jnl{Phys.~Rev.~B}}%

% Physical Review B: Solid State

\newcommand\prc{\ref@jnl{Phys.~Rev.~C}}%

% Physical Review C

\newcommand\prd{\ref@jnl{Phys.~Rev.~D}}%

% Physical Review D

\newcommand\pre{\ref@jnl{Phys.~Rev.~E}}%

% Physical Review E

\newcommand\prl{\ref@jnl{Phys.~Rev.~Lett.}}%

% Physical Review Letters

\newcommand\pasp{\ref@jnl{PASP}}%

% Publications of the ASP

\newcommand\pasj{\ref@jnl{PASJ}}%

% Publications of the ASJ

\newcommand\qjras{\ref@jnl{QJRAS}}%

% Quarterly Journal of the RAS

%\newcommand\raa {\ref@jnl{Research in Astronomy and Astrophysics\,(RAA)}}

% Research in Astronomy and Astrophysics

\newcommand\skytel{\ref@jnl{S\&T}}%

% Sky and Telescope

\newcommand\solphys{\ref@jnl{Sol.~Phys.}}%

% Solar Physics

\newcommand\sovast{\ref@jnl{Soviet~Ast.}}%

% Soviet Astronomy

\newcommand\ssr{\ref@jnl{Space~Sci.~Rev.}}%

% Space Science Reviews

\newcommand\zap{\ref@jnl{ZAp}}%

% Zeitschrift fuer Astrophysik

\newcommand\nat{\ref@jnl{Nature}}%

% Nature

\newcommand\iaucirc{\ref@jnl{IAU~Circ.}}%

% IAU Cirulars

\newcommand\aplett{\ref@jnl{Astrophys.~Lett.}}%

% Astrophysics Letters

\newcommand\apspr{\ref@jnl{Astrophys.~Space~Phys.~Res.}}%

% Astrophysics Space Physics Research

\newcommand\bain{\ref@jnl{Bull.~Astron.~Inst.~Netherlands}}%

% Bulletin Astronomical Institute of the Netherlands

\newcommand\fcp{\ref@jnl{Fund.~Cosmic~Phys.}}%

% Fundamental Cosmic Physics

\newcommand\gca{\ref@jnl{Geochim.~Cosmochim.~Acta}}%

% Geochimica Cosmochimica Acta

\newcommand\grl{\ref@jnl{Geophys.~Res.~Lett.}}%

% Geophysics Research Letters

\newcommand\jcp{\ref@jnl{J.~Chem.~Phys.}}%

% Journal of Chemical Physics

\newcommand\jgr{\ref@jnl{J.~Geophys.~Res.}}%

% Journal of Geophysics Research

\newcommand\jqsrt{\ref@jnl{J.~Quant.~Spec.~Radiat.~Transf.}}%

% Journal of Quantitiative Spectroscopy and Radiative Trasfer

\newcommand\memsai{\ref@jnl{Mem.~Soc.~Astron.~Italiana}}%

% Mem. Societa Astronomica Italiana

\newcommand\nphysa{\ref@jnl{Nucl.~Phys.~A}}%

% Nuclear Physics A

\newcommand\physrep{\ref@jnl{Phys.~Rep.}}%

% Physics Reports

\newcommand\physscr{\ref@jnl{Phys.~Scr}}%

% Physica Scripta

\newcommand\planss{\ref@jnl{Planet.~Space~Sci.}}%

% Planetary Space Science

\newcommand\procspie{\ref@jnl{Proc.~SPIE}}%

% Proceedings of the SPIE

\newcommand\sci{\ref@jnl{Sci.}}

% Science

\let\astap=\aap

\let\aas=\aaps

\let\apjlett=\apjl

\let\apjsupp=\apjs

\let\applopt=\ao




%%%%%% by zjz

\newcommand{\cas}{Chinese Academy of Sciences}



\newcommand{\nao}{ National Astronomical Observatories,

\cas, Beijing~ 100012, China}


\newcommand{\pmo}{Purple Mountain Observatory, Chinese Academy of

Sciences, Nanjing~ 210008, China}

\newcommand{\sho}{Shanghai Astronomical Observatory,

Chinese Academy of

Sciences, Shanghai~ 200030, China}

\newcommand{\yuo}{Yunnan Observatory, Chinese Academy of

Sciences, Kunming~ 650011, China}


\newcommand{\ust}{Centre for Astrophysics, University of

Sciences and Technology of China, Hefei~ 230026, China}


\newcommand{\nua}{Department of Astronomy, Nanjing

University, Nanjing~ 210093, China}



\newcommand{\pka}{Department of Astronomy, Peking

University, Beijing~ 100871, China}


\newcommand{\geo}{Department of Geophysics, Peking

University, Beijing~ 100871, China}


\newcommand{\bac}{Chinese Academy of Sciences-Peking University Joint

Beijing Astrophysics Center, Beijing~ 100871, China}


\newcommand{\hep}{Institute of High Energy Physics, Chinese

Academy of Sciences, Beijing~ 100039, China}


\newcommand{\bnua}{Department of Astronomy, Beijing Normal

University, Beijing~ 100875, China}


\newcommand{\nsfc}{National Natural Science Foundation of China~}




%%%%% by Li Xianghua


\usepackage{color}

\usepackage{colordvi}

\usepackage{ulem}

\RequirePackage{lineno}

\newcommand{\del}[1]{\Red{\sout{\,#1}}}

%\newcommand{\de}{\del}

%\newcommand{\add}[1]{\Blue{\uline{#1}}}

\newcommand{\add}[1]{{\color{blue}{\uline{\,#1}}}}

%\newcommand{\ad}{\add}

\newcommand{\aq}[1]{{\color{magenta}{\uwave{\,#1}}}}

\def\S{Section}

%\newcommand{\qug}[1]{{\color{green}{\uwave{#1}}}}

\newcommand{\putq}[1]{\marginpar{~~~~~~#1}}

\normalem



\newcommand\na{\ref@jnl{New Astron.}}

% New Astronomy

\newcommand\nar{\ref@jnl{New Astron. Rev.}}

% New Astronomy Review

\newcommand\actaa{\ref@jnl{Acta Astronomica}}

% Acta Astronomica

\newcommand\jcap{\ref@jnl{J. Cosmol. Astropart. Phys.}}


\newcommand\pasa{\ref@jnl{PASA}}%

% Publications of the Astron. Soc. of Australia



\uchyph=0

\endinput

%%

%% End of file `raa06.cls'.



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