<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">% SAMPLE2.TEX -- AASTeX macro package tutorial paper.

% The first item in a LaTeX file must be a \documentstyle command to
% declare the overall style of the paper.  The two \documentstyle lines
% that are relevant for the AASTeX macros are shown; one is commented out
% so that the file can be processed.

\documentstyle[12pt,aasms]{article}
%\documentstyle[11pt,aaspp]{article}
%\documentstyle[aaspptwo]{article}

% There are two optional preamble declarations that enable to user to
% control certain formatting options.  \tighten is used with the
% aasms substyle to turn off double-spacing; don't do this for
% actual manuscripts intended for editorial review, only for your friends.
%
% \eqsecnum changes the way equations are numbered.  Normally,
% equations are just numbered sequentially through the entire paper.
% If \eqsecnum appears in the preamble, equation numbers will
% be sequential through each section, and will be formatted "(sec-eqn)",
% where sec is the current section number and eqn is the number of the
% equation within that section.  \eqsecnum can be used with
% either substyle.

%\tighten
%\eqsecnum

% Here's some slug-line data.  They're never printed out by these
% substyles because they're only relevant to the actual publication
% process, and these styles aren't used in publication (yet).
% The receipt and acceptance dates would be filled in by the editorial
% staff on the appropriate dates; they are commented out in this sample
% so that the abstract environment prints out rules so that the dates
% can be typed onto the manuscript according to current practice.

\received{4 August 1988}
%\accepted{23 September 1988}
\journalid{337}{15 January 1989}
\articleid{11}{14}

% This is the end of the "preamble".  Now we wish to start with the
% real material for the paper, which we indicate with \begin{document}.
% Following the \begin{document} command is the front matter for the
% paper, viz., the title, author and address data, the abstract, and
% any keywords or subject headings that are relevant.

\slugcomment{Not to appear in Nonlearned J., 45.}

\begin{document}

\title{Collapsed Cores in Globular Clusters,\\
    Gauge-Boson Couplings,\\
    and AAS\TeX\ Macro Sample}

\author{S. Djorgovski\altaffilmark{1,2,3} and Ivan R. King\altaffilmark{1}}
\affil{Astronomy Department, University of California,
    Berkeley, CA 94720}

\author{C. D. Biemesderfer\altaffilmark{4,5}}
\affil{National Optical Astronomy Observatories, Tucson, AZ 85719}

\and

\author{R. J. Hanisch\altaffilmark{5}}
\affil{Space Telescope Science Institute, Baltimore, MD 21218}

% Notice that each of these authors has alternate affiliations, which
% are identified by the \altaffilmark after each name.  The actual alternate
% affiliation information is typeset in footnotes at the bottom of the
% first page, and the text itself is specified in \altaffiltext commands.
% There is a separate \altaffiltext for each alternate affiliation
% indicated above.

\altaffiltext{1}{Visiting Astronomer, Cerro Tololo Inter-American Observatory. 
CTIO is operated by AURA, Inc.\ under contract to the National Science
Foundation.} 
\altaffiltext{2}{Society of Fellows, Harvard University.} 
\altaffiltext{3}{present address: Center for Astrophysics,
    60 Garden Street, Cambridge, MA 02138}
\altaffiltext{4}{Visiting Programmer, Space Telescope Science Institute}
\altaffiltext{5}{Patron, Alonso's Bar and Grill}

% The abstract environment prints out the receipt and acceptance dates
% if they are relevant for the journal style.  For the aasms style, they
% will print out as horizontal rules for the editorial staff to type
% on, so long as the author does not include \received and \accepted
% commands.  This should not be done, since \received and \accepted dates
% are not known to the author.

\begin{abstract}
This is a preliminary report on surface photometry of the major 
fraction of known globular clusters, to see which of them show the signs 
of a collapsed core.
We also show off the results of some recreational mathematics,
and give pause to consider the dangers of the too fertile mind.
\end{abstract}

\keywords{clusters: globular, peanut --- bosons: bozos}
%\keywords{globular clusters,peanut clusters,bosons,bozos}

% That's it for the front matter.  On to the main body of the paper.
% We'll only put in tutorial remarks at the beginning of each section
% so you can see entire sections together.
%
% In the first two sections, you should notice the use of the LaTeX \cite
% command to identify citations.  The citations are tied to the
% reference list via symbolic tags.  We have chosen the first three
% characters of the first author's name plus the last two numeral of the
% year of publication.  The corresponding reference has a \bibitem
% command in the reference list below.
%
% Please go to the LaTeX manual for a complete description of the
% \cite-\bibitem mechanism.

\section{Introduction}

A focal problem today in the dynamics of globular clusters is 
core collapse.  It has been predicted by theory
for decades (\cite{hen61,lyn68,spi85}), but
observation has been less alert to the phenomenon. For many years the 
central brightness peak in M15 (\cite{kin75,new78})
seemed a unique anomaly.  Then Auri\`ere (1982) suggested a central peak 
in NGC 6397, and a limited photographic survey of ours (\cite[Paper I]{djo84})
found three more cases, including NGC 6624, whose
sharp center had often been remarked on (e.g., \cite{can78}).

\section{Observations}

All our observations were short direct exposures with CCD's.  At
Lick Observatory we used a TI 500$\times$500 chip 
and a GEC 575$\times$385, on the 1-m Nickel reflector.  The only
filter available at Lick was red.  At CTIO we used a GEC 575$\times$385, with
$B, V,$ and $R$ filters, and an RCA 512$\times$320, with $U, B, V, R,$ and $I$
filters, on the 1.5-m reflector. In the CTIO observations we tried to
concentrate on the shortest practicable wavelengths; but faintness, reddening,
and poor short-wavelength sensitivity often kept us from observing in $U$ or
even in $B$. All four cameras had scales of the order of 0.4 arcsec/pixel, and
our field sizes were around 3 arcmin. 

The CCD images are unfortunately not always suitable, for very poor 
clusters or for clusters with large cores.  Since the latter are easily 
studied by other means, we augmented our own CCD profiles by collecting
from the literature a number of star-count
profiles (\cite{kin68,pet76,har84,ort85}),
as well as photoelectric profiles (\cite{kin66}) and 
electronographic profiles (\cite{kro84}).
In a few cases we judged normality by eye estimates on one of the Sky
Surveys. 

% In this section, we see the use of the \subsection command to set off
% an independent subsection.  We only have one here; usually there would
% be several.
%
% We show the use of several of the displayed math environments described
% in the User Guide, and you get a healthy dose of mathematical typesetting
% examples.  Also, observe the use of the LaTeX \label command after the
% \subsection to give a symbolic tag to the subsection for cross-referencing
% in a \ref command.  LaTeX automatically numbers the sections, equations,
% tables, etc. as it goes, so in general you don't know what number something
% is going to have.  We'll refer to the "hairymath" section a little later.

\section{Helicity Amplitudes}

It has been realized that helicity amplitudes provide a convenient means
for Feynman diagram\footnote{Footnotes can be inserted like this.}
evaluations.  These amplitude-level techniques
are particularly convenient for calculations involving many Feynman
diagrams, where the usual trace techniques for the amplitude
squared becomes unwieldy.  Our calculations use the helicity techniques
developed by other authors (\cite{hag86}); we briefly summarize below.

\subsection{Formalism} \label{hairymath}

A tree-level amplitude in $e^+e^-$ collisions can be expressed in
terms of fermion strings of the form
\begin{equation}
\bar v(p_2,\sigma_2)P_{-\tau}\not\!a_1\not\!a_2\cdots
\not\!a_nu(p_1,\sigma_1)\;,
\end{equation}
where $p$ and $\sigma$ label the initial $e^{\pm}$ four-momenta
and helicities $(\sigma = \pm 1)$, $\not\!a_i=a^\mu_i\gamma_\nu$
and $P_\tau=\frac{1}{2}(1+\tau\gamma_5)$ is a chirality projection
operator $(\tau = \pm1)$.  The $a^\mu_i$ may be formed from particle
four-momenta, gauge-boson polarization vectors or fermion strings with
an uncontracted Lorentz index associated with final-state fermions.

In the chiral representation the $\gamma$ matrices are expressed
in terms of $2\times 2$ Pauli matrices $\sigma$ and the unit matrix 1 as
\begin{mathletters}
\begin{eqnarray}
\gamma^\mu \: &amp; = &amp;
\: \left(
\begin{array}{cc}
0 &amp; \sigma^\mu_+ \\
\sigma^\mu_- &amp; 0
\end{array} \; \; \right)\;,
\;\gamma^5= \left(
\begin{array}{cc}
-1 &amp; \; 0\\
0 &amp; \; 1
\end{array} \; \; \right) \;, \nonumber \\ &amp; &amp; \\
\sigma^\mu_{\pm} \:&amp; = &amp; \: ({\bf 1} ,\pm \sigma)\;, \nonumber
\end{eqnarray}
\end{mathletters}
giving
\begin{equation}
\not\!a= \left(
\begin{array}{cc}
0 &amp; (\not\!a)_+\\
(\not\!a)_- &amp; 0
\end{array}\right),\;(\not\!a)_\pm=a_\mu\sigma^\mu_\pm\;,
\end{equation}
The spinors are expressed in terms of two-component Weyl spinors as
\begin{equation}
u=\left(
\begin{array}{c}
(u)_-\\
(u)_+
\end{array}\right),\;v={\bf (}(v)^\dagger_+{\bf ,} \; (v)^\dagger_-{\bf )}\;.
\eqnum{3A}
\end{equation}
The Weyl spinors are given in terms of helicity eigenstates
$\chi_\lambda(p)$ with $\lambda=\pm1$ by
\begin{eqnarray}
u(p,\lambda)_\pm &amp; = &amp; (E\pm\lambda|{\bf p}|)^{1/2}\chi_\lambda(p)\;,
\nonumber \\ &amp; &amp; \\
v(p,\lambda)_\pm &amp; = &amp; \pm\lambda(E\mp\lambda|{\bf p}|)^{1/2}\chi
_{-\lambda}(p) \nonumber
\end{eqnarray}

% In these sections, we see some additional math-related markup, and we
% have references to one of the tables (occurs later in the document)
% and the "hairymath" section immediately preceding this one.
%
% In the second paragraph, note the use of in-text math ($stuff$) including
% a couple of the miscellaneous symbol commands defined in the AASTeX macro
% package.
%
% This is the last section of the paper, so there is an \acknowledgments
% section at the end of the main body.

\section{Floating material and so forth}

Consider a task that computes profile parameters for a modified
Lorentzian of the form
\begin{equation}
I = \frac{1}{1 + d_{1}^{P (1 + d_{2} )}}
\end{equation}
where
\begin{displaymath}
d_{1} = \sqrt{ \left( \begin{array}{c} \frac{x_{1}}{R_{maj}} 
\end{array} \right) ^{2} + 
\left( \begin{array}{c} \frac{y_{1}}{R_{min}} \end{array} \right) ^{2} }
\end{displaymath}
\begin{displaymath}
d_{2} = \sqrt{ \left( \begin{array}{c} \frac{x_{1}}{P R_{maj}}
\end{array} \right) ^{2} + 
\left( \begin{array}{c} \case{y_{1}}{P R_{min}} \end{array} \right) ^{2} }
\end{displaymath}
\[x_{1} = (x - x_{0}) \cos \Theta + (y - y_{0}) \sin \Theta \]
\[y_{1} = -(x - x_{0}) \sin \Theta + (y - y_{0}) \cos \Theta \]

In these expressions $x_{0}$,$y_{0}$ is the star center, and $\Theta$ is the
angle with the $x$ axis.  Results of this task are shown in table~\ref{tbl-1}.
It is not clear how these sorts of analyses may affect determination of
$M_{\sun}$ and $M_{\earth}$, but the assumption is that the alternate results
should be less than 90\deg\ out of phase with previous values.
We have no observations of \ion{Ca}{2}.
Roughly \slantfrac{4}{5} of the electronically submitted abstracts
for AAS meetings are error-free.

\acknowledgments

We are grateful to V. Barger, T. Han, and R. J. N. Phillips for
doing the math in section~\ref{hairymath}.

\appendix
\section{Floating material and so forth}

Consider a task that computes profile parameters for a modified
Lorentzian of the form
\begin{equation}
I = \frac{1}{1 + d_{1}^{P (1 + d_{2} )}}
\end{equation}
where
\begin{mathletters}
\begin{displaymath}
d_{1} = \frac{3}{4} \sqrt{ \left( \begin{array}{c} \frac{x_{1}}{R_{maj}} 
\end{array} \right) ^{2} + 
\left( \begin{array}{c} \frac{y_{1}}{R_{min}} \end{array} \right) ^{2} }
\end{displaymath}
\begin{equation}
d_{2} = \case{3}{4} \sqrt{ \left( \begin{array}{c} \frac{x_{1}}{P R_{maj}}
\end{array} \right) ^{2} + 
\left( \begin{array}{c} \case{y_{1}}{P R_{min}} \end{array} \right) ^{2} }
\end{equation}
\begin{eqnarray}
x_{1} &amp; = &amp; (x - x_{0}) \cos \Theta + (y - y_{0}) \sin \Theta\\
y_{1} &amp; = &amp; -(x - x_{0}) \sin \Theta + (y - y_{0}) \cos \Theta
\end{eqnarray}
\end{mathletters}

For completeness, here is one last equation.
\begin{equation}
e = mc^2
\end{equation}

% That's the end of the main body of the paper.  Now we will have some
% back matter.
%
% Tables are usually supposed to be submitted one per page, following
% the main body of the text, so before each table we would have a
% \clearpage to force a page break at that point.  There should also
% be a \clearpage after the last table so that it gets forced onto
% its own page, too.
%
% The tabular data is aligned within the "tabular" environment.  Observe
% that our tabular environment is embedded within a "center" environment,
% which is in turn inside a "table" environment.  Exercise for the reader:
% Why do you think we used the "table*" environment?
%
% We need the table environment for autonumbering and caption generation,
% which is why it is not enough to have a centered tabular.
%
% Within the tabular environment, please note that we use no vertical
% rules, and the only horizontal rule is the \tableline (*not* an \hline)
% which delimits the column headings from the tabular data.  Also note
% that a couple of the column headings require special annotation, i.e.,
% footnotes for tables.  They are marked and tagged with \tablenotemark.
% \tablenotemarks could be placed on individual data entries as well,
% but be careful not to go berserk doing this.

\clearpage

\begin{table*}
\begin{center}
\begin{tabular}{crrrrrrrrrrr}
Star &amp; Height &amp; $d_{x}$ &amp; $d_{y}$ &amp; $n$ &amp; $\chi^2$ &amp; $R_{maj}$ &amp; $R_{min}$ &amp;
\multicolumn{1}{c}{$P$\tablenotemark{a}} &amp; $P R_{maj}$ &amp; $P R_{min}$ &amp; 
\multicolumn{1}{c}{$\Theta$\tablenotemark{b}} \\
\tableline
1 &amp;33472.5 &amp;-0.1 &amp;0.4  &amp;53 &amp;27.4 &amp;2.065  &amp;1.940 &amp;3.900 &amp;68.3 &amp;116.2 &amp;-27.639\\
2 &amp;27802.4 &amp;-0.3 &amp;-0.2 &amp;60 &amp;3.7  &amp;1.628  &amp;1.510 &amp;2.156 &amp;6.8  &amp;7.5 &amp;-26.764\\
3 &amp;29210.6 &amp;0.9  &amp;0.3  &amp;60 &amp;3.4  &amp;1.622  &amp;1.551 &amp;2.159 &amp;6.7  &amp;7.3 &amp;-40.272\\
4 &amp;32733.8 &amp;-1.2 &amp;-0.5 &amp;41 &amp;54.8 &amp;2.282  &amp;2.156 &amp;4.313 &amp;117.4 &amp;78.2 &amp;-35.847\\
5 &amp; 9607.4 &amp;-0.4 &amp;-0.4 &amp;60 &amp;1.4  &amp;1.669  &amp;1.574 &amp;2.343 &amp;8.0  &amp;8.9 &amp;-33.417\\
6 &amp;31638.6 &amp;1.6  &amp;0.1  &amp;39 &amp;315.2 &amp; 3.433 &amp;3.075 &amp;7.488 &amp;92.1 &amp;25.3 &amp;-12.052\\
\end{tabular}
\end{center}

% Text for table footnotes must follow the tabular environment but must
% be inside the table environment.  Note that it is OK to put \ref's
% in \tablenotetext's.

\tablenotetext{a}{Sample footnote for table~\ref{tbl-1}}
\tablenotetext{b}{Another sample footnote for table~\ref{tbl-1}}
\tablenotetext{c}{Footnote with no call out}
\tablenotetext{d}{Another footnote with no call out}
\tablenotetext{e}{A further additional footnote with no call out}

% The caption contains only the caption text.  The "Table N." identification
% is generated by the \caption command on its own.
%
% It is necessary to \label tables and figures *after* the \caption has been
% specified because the table/figure number is generated by \caption, not
% by \begin{whatever}.

\caption{Terribly relevant tabular information.} \label{tbl-1}

\end{table*}

\begin{table*}
\begin{center}
\begin{tabular}{crrrrrrrrrrr}
Star &amp; Height &amp; $d_{x}$ &amp; $d_{y}$ &amp; $n$ &amp; $\chi^2$ &amp; $R_{maj}$ &amp; $R_{min}$ &amp;
\multicolumn{1}{c}{$P$\tablenotemark{t}} &amp; $P R_{maj}$ &amp; $P R_{min}$ &amp; 
\multicolumn{1}{c}{$\Theta$\tablenotemark{u}} \\
\tableline
1 &amp;33472.5 &amp;-0.1 &amp;0.4  &amp;53 &amp;27.4 &amp;2.065  &amp;1.940 &amp;3.900 &amp;68.3 &amp;116.2 &amp;-27.639\\
2 &amp;27802.4 &amp;-0.3 &amp;-0.2 &amp;60 &amp;3.7  &amp;1.628  &amp;1.510 &amp;2.156 &amp;6.8  &amp;7.5 &amp;-26.764\\
3 &amp;29210.6 &amp;0.9  &amp;0.3  &amp;60 &amp;3.4  &amp;1.622  &amp;1.551 &amp;2.159 &amp;6.7  &amp;7.3 &amp;-40.272\\
4 &amp;32733.8 &amp;-1.2\tablenotemark{v} &amp;-0.5 &amp;41 &amp;54.8 &amp;2.282  &amp;2.156 &amp;4.313 &amp;117.4 &amp;78.2 &amp;-35.847\\
5 &amp; 9607.4 &amp;-0.4 &amp;-0.4 &amp;60 &amp;1.4  &amp;1.669\tablenotemark{v}  &amp;1.574 &amp;2.343 &amp;8.0  &amp;8.9 &amp;-33.417\\
6 &amp;31638.6 &amp;1.6  &amp;0.1  &amp;39 &amp;315.2 &amp; 3.433 &amp;3.075 &amp;7.488 &amp;92.1 &amp;25.3 &amp;-12.052\\
\end{tabular}
\end{center}

% Text for table footnotes must follow the tabular environment but must
% be inside the table environment.  Note that it is OK to put \ref's
% in \tablenotetext's.

\tablenotetext{t}{Sample footnote for table~\ref{tbl-2}}
\tablenotetext{v}{Yet another sample footnote for table~\ref{tbl-2}}
\tablenotetext{u}{Another sample footnote for table~\ref{tbl-2}}

% The caption contains only the caption text.  The "Table N." identification
% is generated by the \caption command on its own.
%
% It is necessary to \label tables and figures *after* the \caption has been
% specified because the table/figure number is generated by \caption, not
% by \begin{whatever}.

\tablenum{1A}
\caption{
More terribly relevant tabular information.  Notice that it is possible
to have more than one table on a page where each can have associated
independent notes.  We extend the caption with
further pointless drivel to see the effects of lengthy text on
caption formatting.} \label{tbl-2}

\tablecomments{We can also attach a long-ish paragraph of explanatory
material to a table.  This would be done for journals where long
captions are not permitted (usually because the caption is regarded
as the table's title).  A different command would be used if the
paragraph contained a list of references for the table.}

\end{table*}

\include{samp2tbl}

% This is the last table for this paper (as well as the first), so we
% should follow it with a \clearpage.  In order to force all the floating
% tables out of their buffers and onto vertical page lists, we must use
% \clearpage rather than \newpage.

\clearpage

% Now comes the reference list.  In this document, we used \cite to call
% out citations, so we must use \bibitem in the reference list, which
% means we use the LaTeX thebibliography environment.  Please note that
% \begin{thebibliography} is followed by a null argument.  If you forget
% this, mayhem ensues, and LaTeX will say "Perhaps a missing item?" when
% you run it.  Do not call us, do not send mail when this happens.  Put
% the silly {} after the \begin{thebibliography}.
%
% Each reference has a \bibitem command to define the citation format
% and the symbolic tag, as well as a \reference command which sets up
% formatting parameters for the reference list itself.
%
% If we had not bothered with the \cite-\bibitem business, calling out
% the references outselves, the reference list could be enclosed in
% a references environment (\begin{references} has no null argument),
% and there would be no need for the leading \bibitem's.

\begin{thebibliography}{}
\bibitem[Auri\`ere 1982]{aur82} \reference Auri\`ere, M.  1982, \astap,
    109, 301
\bibitem[Canizares et al.\ 1978]{can78} \reference Canizares, C. R.,
    Grindlay, J. E., Hiltner, W. A., Liller, W., and 
    McClintock, J. E.  1978, \apj, 224, 39
\bibitem[Djorgovski and King 1984]{djo84} \reference Djorgovski, S.,
    and King, I. R.  1984, \apjlett, 277, L49
\bibitem[Hagiwara and Zeppenfeld 1986]{hag86} \reference Hagiwara, K., and
    Zeppenfeld, D.  1986, Nucl.Phys., 274, 1
\bibitem[Harris and van den Bergh 1984]{har84} \reference Harris, W. E.,
    and van den Bergh, S.  1984, \aj, 89, 1816
\bibitem[H\`enon 1961]{hen61} \reference H\'enon, M.  1961, Ann.d'Ap., 24, 369
\bibitem[King 1966]{kin66} \reference King, I. R.  1966, \aj, 71, 276
\bibitem[King 1975]{kin75} \reference King, I. R.  1975, Dynamics of
    Stellar Systems, A. Hayli, Dordrecht: Reidel, 1975, 99
\bibitem[King et al.,\ 1968]{kin68} \reference King, I. R., Hedemann, E.,
    Hodge, S. M., and White, R. E.  1968, \aj, 73, 456
\bibitem[Kron et al.,\ 1984]{kro84} \reference Kron, G. E., Hewitt, A. V.,
    and Wasserman, L. H.  1984, \pasp, 96, 198
\bibitem[Lynden-Bell and Wood 1968]{lyn68} \reference Lynden-Bell, D.,
    and Wood, R.  1968, \mnras, 138, 495
\bibitem[Newell and O'Neil 1978]{new78} \reference Newell, E. B.,
    and O'Neil, E. J.  1978, \apjsupp, 37, 27
\bibitem[Ortolani et al.,\ 1985]{ort85} \reference Ortolani, S., Rosino, L.,
    and Sandage, A.  1985, \aj, 90, 473
\bibitem[Peterson 1976]{pet76} \reference Peterson, C. J.  1976, \aj, 81, 617
\bibitem[Spitzer 1985]{spi85} \reference Spitzer, L.  1985, Dynamics of
    Star Clusters, J. Goodman and P. Hut, Dordrecht: Reidel, 109
\end{thebibliography}

% Finally, we have figure captions.  Usually these must be on a separate
% page, although unlike table, it is often permissible to have several
% figure captions on the same page.  We force the page break between
% the reference list and the figure captions.
%
% The \caption command in the figure environment works like the one in the
% table environment (it's the same one, actually), except that this one
% produces identification text that reads "Figure N."

\clearpage

\begin{figure}
\plotone{sgi9259.eps}
\caption{We use the \LaTeX\ {\tt figure} environment syntax to set this
figure caption.}
\end{figure}

% That's all, folks.
%
% The technique of segregating major semantic components of the document
% within "environments" is a very good one, but you as an author have to
% come up with a way of making sure each \begin{whatzit} has a corresponding
% \end{whatzit}.  If you miss one, LaTeX will probably complain a great
% deal during the composition of the document.  Occasionally, you get away
% with it right up to the \end{document}, in which case, you will see
% "\begin{whatzit} ended by \end{document}".

\end{document}
</pre></body></html>