-#This file was created by <mike> Sun Jul 25 23:59:27 1999
-#LyX 1.0 (C) 1995-1999 Matthias Ettrich and the LyX Team
-\lyxformat 2.15
-\textclass aastex
+#LyX 2.2 created this file. For more info see http://www.lyx.org/
+\lyxformat 508
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin /systemlyxdir/examples/
+\textclass aastex6
\begin_preamble
\newcommand{\vdag}{(v)^\dagger}
\newcommand{\myemail}{skywalker@galaxy.far.far.away}
\shorttitle{Djorgovski et al.}
\shortauthors{Collapsed Cores in Globular Clusters}
\end_preamble
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+\use_package amssymb 0
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+\use_indices false
\paperorientation portrait
+\suppress_date false
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+\index Index
+\shortcut idx
+\color #008000
+\end_index
\secnumdepth 3
\tocdepth 3
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\quotes_language english
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+\end_header
+
+\begin_body
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+\noindent
+\align left
+Sample document for contributions to journals of the American Astronomical
+ Society (AAS).
+ Please consult the
+\begin_inset CommandInset href
+LatexCommand href
+name "AASTeX user guide"
+target "http://journals.aas.org/authors/aastex/aasguide.html"
+
+\end_inset
+
+ for details on how to use AASTeX.
+
+\end_layout
+
+\begin_layout Plain Layout
+\noindent
+\align left
+An up-to-date sample LaTeX article using AASTeX is available under
+\begin_inset Flex URL
+status open
+
+\begin_layout Plain Layout
+
+http://journals.aas.org/authors/aastex/aastex.html#_download
+\end_layout
+
+\end_inset
+
+.
+\end_layout
-\layout Title
+\end_inset
-Collapsed Cores in Globular Clusters, Gauge-Boson Couplings, and AASTeX
-\latex latex
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+\noindent
+\align left
+The AASTeX document class uses a different name since version 6.0 (2016/02/16).
+ Depending on the version installed on your system, set the document class
+ to American Astronomical Society (AASTeX v.
+ 6) or American Astronomical Society (AASTeX v.
+ 5).
+
+\end_layout
+
+\begin_layout Plain Layout
+\noindent
+\align left
+New features (cf.
-\latex default
-Examples
-\layout Author
+\begin_inset Flex URL
+status collapsed
+
+\begin_layout Plain Layout
+
+http://journals.aas.org/authors/aastex/revisionhistory.html
+\end_layout
+
+\end_inset
+) are only partially supported by LyX (see
+\begin_inset Flex URL
+status collapsed
+
+\begin_layout Plain Layout
+
+http://www.lyx.org/trac/ticket/10027
+\end_layout
+
+\end_inset
+
+).
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Title
+Collapsed Cores in Globular Clusters, Gauge-Boson Couplings, and AAS\SpecialChar TeX
+ Examples
+\end_layout
+
+\begin_layout Author
S.
Djorgovski
-\latex latex
+\begin_inset Flex altaffilmark
+status open
+
+\begin_layout Plain Layout
+1,2,3
+\end_layout
+
+\end_inset
-\backslash
-altaffilmark{1,2,3}
-\latex default
and Ivan R.
King
-\latex latex
+\begin_inset Flex altaffilmark
+status collapsed
+
+\begin_layout Plain Layout
+1
+\end_layout
+
+\end_inset
-\backslash
-altaffilmark{1}
-\layout Affiliation
+\end_layout
+
+\begin_layout Affiliation
Astronomy Department, University of California, Berkeley, CA 94720
-\layout Author
+\end_layout
+\begin_layout Author
C.
D.
Biemesderfer
-\latex latex
+\begin_inset Flex altaffilmark
+status collapsed
+
+\begin_layout Plain Layout
+4,5
+\end_layout
+
+\end_inset
+
-\backslash
-altaffilmark{4,5}
-\layout Affiliation
+\end_layout
+\begin_layout Affiliation
National Optical Astronomy Observatories, Tucson, AZ 85719
-\layout Email
+\end_layout
+\begin_layout Email
aastex-help@aas.org
-\layout And
+\end_layout
-\layout Author
+\begin_layout And
+\end_layout
+
+\begin_layout Author
R.
J.
Hanisch
-\latex latex
+\begin_inset Flex altaffilmark
+status collapsed
+
+\begin_layout Plain Layout
+5
+\end_layout
+
+\end_inset
-\backslash
-altaffilmark{5}
-\layout Affiliation
+\end_layout
+
+\begin_layout Affiliation
Space Telescope Science Institute, Baltimore, MD 21218
-\layout Standard
+\end_layout
+
+\begin_layout Altaffilation
+\begin_inset Argument 1
+status open
+\begin_layout Plain Layout
+1
+\end_layout
-\latex latex
+\end_inset
-\backslash
-altaffiltext{1}{Visiting Astronomer, Cerro Tololo Inter-American Observatory.
+Visiting Astronomer, Cerro Tololo Inter-American Observatory.
CTIO is operated by AURA, Inc.
-\backslash
- under contract to the National Science Foundation.}
-\layout Standard
+\begin_inset space \space{}
+\end_inset
+
+under contract to the National Science Foundation.
+\end_layout
+\begin_layout Altaffilation
+\begin_inset Argument 1
+status open
-\latex latex
+\begin_layout Plain Layout
+2
+\end_layout
-\backslash
-altaffiltext{2}{Society of Fellows, Harvard University.}
-\layout Standard
+\end_inset
+Society of Fellows, Harvard University.
+\end_layout
-\latex latex
+\begin_layout Altaffilation
+\begin_inset Argument 1
+status open
-\backslash
-altaffiltext{3}{present address: Center for Astrophysics, 60 Garden Street,
- Cambridge, MA 02138}
-\layout Standard
+\begin_layout Plain Layout
+3
+\end_layout
+\end_inset
-\latex latex
+present address: Center for Astrophysics, 60 Garden Street, Cambridge, MA
+ 02138
+\end_layout
-\backslash
-altaffiltext{4}{Visiting Programmer, Space Telescope Science Institute}
-
-\layout Standard
+\begin_layout Altaffilation
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+4
+\end_layout
+
+\end_inset
+
+Visiting Programmer, Space Telescope Science Institute
+\end_layout
+
+\begin_layout Altaffilation
+\begin_inset Argument 1
+status open
+\begin_layout Plain Layout
+5
+\end_layout
-\latex latex
+\end_inset
-\backslash
-altaffiltext{5}{Patron, Alonso's Bar and Grill}
-\layout Abstract
+Patron, Alonso's Bar and Grill
+\end_layout
+\begin_layout 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 explore some diversionary mathematics and recreational tables.
-\layout Keywords
+\end_layout
-clusters: globular, peanut---bosons: bozos
-\layout Section
+\begin_layout Keywords
+clusters: globular, peanut—bosons: bozos
+\end_layout
+\begin_layout Section
Introduction
-\layout Standard
+\end_layout
+\begin_layout Standard
A focal problem today in the dynamics of globular clusters is core collapse.
It has been predicted by theory for decades
-\latex latex
+\begin_inset ERT
+status collapsed
-\backslash
+\begin_layout Plain Layout
+
+
+\backslash
citep{hen61,lyn68,spi85}
-\latex default
+\end_layout
+
+\end_inset
+
, but observation has been less alert to the phenomenon.
For many years the central brightness peak in M15
-\latex latex
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
-\backslash
+\backslash
citep{kin75,new78}
-\latex default
+\end_layout
+
+\end_inset
+
seemed a unique anomaly.
Then
-\latex latex
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
-\backslash
+
+\backslash
citet{aur82}
-\latex default
+\end_layout
+
+\end_inset
+
suggested a central peak in NGC 6397, and a limited photographic survey
of ours
-\latex latex
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
-\backslash
+
+\backslash
citep[Paper I]{djo84}
-\latex default
+\end_layout
+
+\end_inset
+
found three more cases, including NGC 6624, whose sharp center had often
been remarked on
-\latex latex
+\begin_inset ERT
+status collapsed
-\backslash
+\begin_layout Plain Layout
+
+
+\backslash
citep{can78}
-\latex default
+\end_layout
+
+\end_inset
+
.
-\layout Section
+\end_layout
+\begin_layout Section
Observations
-\layout Standard
+\end_layout
+\begin_layout Standard
All our observations were short direct exposures with CCD's.
At Lick Observatory we used a TI 500
-\begin_inset Formula \( \times \)
-\end_inset
+\begin_inset Formula $\times$
+\end_inset
500 chip and a GEC 575
-\begin_inset Formula \( \times \)
-\end_inset
+\begin_inset Formula $\times$
+\end_inset
385, on the 1-m Nickel reflector.
The only filter available at Lick was red.
At CTIO we used a GEC 575
-\begin_inset Formula \( \times \)
-\end_inset
+\begin_inset Formula $\times$
+\end_inset
385, with
-\begin_inset Formula \( B,V, \)
-\end_inset
+\begin_inset Formula $B,V,$
+\end_inset
and
-\begin_inset Formula \( R \)
-\end_inset
+\begin_inset Formula $R$
+\end_inset
filters, and an RCA 512
-\begin_inset Formula \( \times \)
-\end_inset
+\begin_inset Formula $\times$
+\end_inset
320, with
-\begin_inset Formula \( U,B,V,R, \)
-\end_inset
+\begin_inset Formula $U,B,V,R,$
+\end_inset
and
-\begin_inset Formula \( I \)
-\end_inset
+\begin_inset Formula $I$
+\end_inset
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
-\begin_inset Formula \( U \)
-\end_inset
+\begin_inset Formula $U$
+\end_inset
or even in
-\begin_inset Formula \( B \)
-\end_inset
+\begin_inset Formula $B$
+\end_inset
.
All four cameras had scales of the order of 0.4 arcsec/pixel, and our field
sizes were around 3 arcmin.
-\layout Standard
+\end_layout
+\begin_layout Standard
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
-\latex latex
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
-\backslash
+\backslash
citep{kin68,pet76,har84,ort85}
-\latex default
+\end_layout
+
+\end_inset
+
, as well as photoelectric profiles
-\latex latex
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
-\backslash
+\backslash
citep{kin66,kin75}
-\latex default
+\end_layout
+
+\end_inset
+
and electronographic profiles
-\latex latex
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
-\backslash
+
+\backslash
citep{kro84}
-\latex default
+\end_layout
+
+\end_inset
+
.
In a few cases we judged normality by eye estimates on one of the Sky Surveys.
-\layout Section
+\end_layout
+\begin_layout Section
Helicity Amplitudes
-\layout Standard
+\end_layout
+\begin_layout Standard
It has been realized that helicity amplitudes provide a convenient means
for Feynman diagram
-\begin_float footnote
-\layout Standard
+\begin_inset Foot
+status collapsed
+\begin_layout Plain Layout
Footnotes can be inserted like this.
-\end_float
+\end_layout
+
+\end_inset
+
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
-\begin_inset LatexCommand \cite{hag86}
+\begin_inset CommandInset citation
+LatexCommand cite
+key "hag86"
-\end_inset
+\end_inset
; we briefly summarize below.
-\layout Subsection
+\end_layout
+\begin_layout Subsection
Formalism
-\layout Standard
-
+\end_layout
-\begin_inset LatexCommand \label{bozomath}
+\begin_layout Standard
+\begin_inset CommandInset label
+LatexCommand label
+name "bozomath"
-\end_inset
+\end_inset
-\layout Standard
+\end_layout
+\begin_layout Standard
A tree-level amplitude in
-\begin_inset Formula \( e^{+}e^{-} \)
-\end_inset
+\begin_inset Formula $e^{+}e^{-}$
+\end_inset
collisions can be expressed in terms of fermion strings of the form
\begin_inset Formula
\begin{equation}
-\bar{v}(p_{2},\sigma _{2})P_{-\tau }\hat{a}_{1}\hat{a}_{2}\cdots \hat{a}_{n}u(p_{1},\sigma _{1}),
+\bar{v}(p_{2},\sigma_{2})P_{-\tau}\hat{a}_{1}\hat{a}_{2}\cdots\hat{a}_{n}u(p_{1},\sigma_{1}),
\end{equation}
-\end_inset
+\end_inset
where
-\begin_inset Formula \( p \)
-\end_inset
+\begin_inset Formula $p$
+\end_inset
and
-\begin_inset Formula \( \sigma \)
-\end_inset
+\begin_inset Formula $\sigma$
+\end_inset
label the initial
-\begin_inset Formula \( e^{\pm } \)
-\end_inset
+\begin_inset Formula $e^{\pm}$
+\end_inset
four-momenta and helicities
-\begin_inset Formula \( (\sigma =\pm 1) \)
-\end_inset
+\begin_inset Formula $(\sigma=\pm1)$
+\end_inset
,
-\begin_inset Formula \( \hat{a}_{i}=a^{\mu }_{i}\gamma _{\nu } \)
-\end_inset
+\begin_inset Formula $\hat{a}_{i}=a_{i}^{\mu}\gamma_{\nu}$
+\end_inset
and
-\begin_inset Formula \( P_{\tau }=\frac{1}{2}(1+\tau \gamma _{5}) \)
-\end_inset
+\begin_inset Formula $P_{\tau}=\frac{1}{2}(1+\tau\gamma_{5})$
+\end_inset
is a chirality projection operator
-\begin_inset Formula \( (\tau =\pm1 ) \)
-\end_inset
+\begin_inset Formula $(\tau=\pm1)$
+\end_inset
.
The
-\begin_inset Formula \( a^{\mu }_{i} \)
-\end_inset
+\begin_inset Formula $a_{i}^{\mu}$
+\end_inset
may be formed from particle four-momenta, gauge-boson polarization vectors
or fermion strings with an uncontracted Lorentz index associated with final-sta
te fermions.
-\layout NoteToEditor
+\end_layout
+\begin_layout NoteToEditor
Figures 1 and 2 should appear side-by-side in print
-\layout Standard
+\end_layout
+\begin_layout Standard
In the chiral representation the
-\begin_inset Formula \( \gamma \)
-\end_inset
+\begin_inset Formula $\gamma$
+\end_inset
matrices are expressed in terms of
-\begin_inset Formula \( 2\times 2 \)
-\end_inset
+\begin_inset Formula $2\times2$
+\end_inset
Pauli matrices
-\begin_inset Formula \( \sigma \)
-\end_inset
+\begin_inset Formula $\sigma$
+\end_inset
and the unit matrix 1 as
\begin_inset Formula
-\begin{eqnarray}
-\gamma ^{\mu } & = & \left( \begin{array}{cc}
-0 & \sigma ^{\mu }_{+}\\
-\sigma ^{\mu }_{-} & 0
-\end{array}\right) ,\gamma ^{5}=\left( \begin{array}{cc}
+\begin{eqnarray*}
+\gamma^{\mu} & = & \left(\begin{array}{cc}
+0 & \sigma_{+}^{\mu}\\
+\sigma_{-}^{\mu} & 0
+\end{array}\right),\gamma^{5}=\left(\begin{array}{cc}
-1 & 0\\
0 & 1
-\end{array}\right) ,\nonumber \\
-\sigma ^{\mu }_{\pm } & = & ({\textbf {1}},\pm \sigma ),\nonumber
-\end{eqnarray}
+\end{array}\right),\\
+\sigma_{\pm}^{\mu} & = & ({\textbf{1}},\pm\sigma),
+\end{eqnarray*}
-\end_inset
+\end_inset
giving
\begin_inset Formula
\begin{equation}
-\hat{a}=\left( \begin{array}{cc}
+\hat{a}=\left(\begin{array}{cc}
0 & (\hat{a})_{+}\\
(\hat{a})_{-} & 0
-\end{array}\right) ,(\hat{a})_{\pm }=a_{\mu }\sigma ^{\mu }_{\pm },
+\end{array}\right),(\hat{a})_{\pm}=a_{\mu}\sigma_{\pm}^{\mu},
\end{equation}
-\end_inset
+\end_inset
The spinors are expressed in terms of two-component Weyl spinors as
\begin_inset Formula
\begin{equation}
-u=\left( \begin{array}{c}
+u=\left(\begin{array}{c}
(u)_{-}\\
(u)_{+}
-\end{array}\right) ,v={\textbf {(}}\vdag _{+}{\textbf {,}}\vdag _{-}{\textbf {)}}.
+\end{array}\right),v={\textbf{(}}\vdag_{+}{\textbf{,}}\vdag_{-}{\textbf{)}}.
\end{equation}
-\end_inset
+\end_inset
-\layout Standard
+\end_layout
+\begin_layout Standard
The Weyl spinors are given in terms of helicity eigenstates
-\begin_inset Formula \( \chi _{\lambda }(p) \)
-\end_inset
+\begin_inset Formula $\chi_{\lambda}(p)$
+\end_inset
with
-\begin_inset Formula \( \lambda =\pm1 \)
-\end_inset
+\begin_inset Formula $\lambda=\pm1$
+\end_inset
by
-\layout MathLetters
-
+\end_layout
+\begin_layout MathLetters
\begin_inset Formula
\begin{eqnarray}
-u(p,\lambda )_{\pm } & = & (E\pm \lambda |{\textbf {p}}|)^{1/2}\chi _{\lambda }(p),\\
-v(p,\lambda )_{\pm } & = & \pm \lambda (E\mp \lambda |{\textbf {p}}|)^{1/2}\chi _{-\lambda }(p)
+u(p,\lambda)_{\pm} & = & (E\pm\lambda|{\textbf{p}}|)^{1/2}\chi_{\lambda}(p),\\
+v(p,\lambda)_{\pm} & = & \pm\lambda(E\mp\lambda|{\textbf{p}}|)^{1/2}\chi_{-\lambda}(p)
\end{eqnarray}
-\end_inset
+\end_inset
-\layout Section
+\end_layout
+\begin_layout Section
Floating material and so forth
-\layout Standard
+\end_layout
+\begin_layout Standard
Consider a task that computes profile parameters for a modified Lorentzian
of the form
\begin_inset Formula
I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
\end{equation}
-\end_inset
+\end_inset
where
\begin_inset Formula
\[
-d_{1}=\sqrt{\left( \begin{array}{c}
-\frac{x_{1}}{R_{maj}}
-\end{array}\right) ^{2}+\left( \begin{array}{c}
-\frac{y_{1}}{R_{min}}
-\end{array}\right) ^{2}}\]
+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_inset
+\end_inset
\begin_inset Formula
\[
-d_{2}=\sqrt{\left( \begin{array}{c}
-\frac{x_{1}}{PR_{maj}}
-\end{array}\right) ^{2}+\left( \begin{array}{c}
-\case {y_{1}}{PR_{min}}
-\end{array}\right) ^{2}}\]
+d_{2}=\sqrt{\left(\begin{array}{c}
+\frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
+\case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
+\]
-\end_inset
+\end_inset
\begin_inset Formula
\[
-x_{1}=(x-x_{0})\cos \Theta +(y-y_{0})\sin \Theta \]
+x_{1}=(x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta
+\]
-\end_inset
+\end_inset
\begin_inset Formula
\[
-y_{1}=-(x-x_{0})\sin \Theta +(y-y_{0})\cos \Theta \]
+y_{1}=-(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
+\]
-\end_inset
+\end_inset
-\layout Standard
+\end_layout
+\begin_layout Standard
In these expressions
-\begin_inset Formula \( x_{0} \)
-\end_inset
+\begin_inset Formula $x_{0}$
+\end_inset
,
-\begin_inset Formula \( y_{0} \)
-\end_inset
+\begin_inset Formula $y_{0}$
+\end_inset
is the star center, and
-\begin_inset Formula \( \Theta \)
-\end_inset
+\begin_inset Formula $\Theta$
+\end_inset
is the angle with the
-\begin_inset Formula \( x \)
-\end_inset
+\begin_inset Formula $x$
+\end_inset
axis.
Results of this task are shown in table
-\protected_separator
+\begin_inset space ~
+\end_inset
+
-\begin_inset LatexCommand \ref{tbl-2}
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "tbl-2"
-\end_inset
+\end_inset
.
It is not clear how these sorts of analyses may affect determination of
-\begin_inset Formula \( M_{\sun } \)
-\end_inset
+\begin_inset Formula $M_{\sun}$
+\end_inset
-, but the assumption is that the alternate results should be less than 90
-\latex latex
-
-\backslash
-degr
-\backslash
-
-\latex default
-out of phase with previous values.
+, but the assumption is that the alternate results should be less than 90°
+ out of phase with previous values.
We have no observations of
-\latex latex
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
-\backslash
+
+\backslash
ion{Ca}{2}
-\latex default
+\end_layout
+
+\end_inset
+
.
Roughly
-\latex latex
+\begin_inset ERT
+status collapsed
-\backslash
+\begin_layout Plain Layout
+
+
+\backslash
slantfrac{4}{5}
-\latex default
+\end_layout
+
+\end_inset
+
of the electronically submitted abstracts for AAS meetings are error-free.
-\layout Acknowledgements
+\end_layout
+
+\begin_layout Acknowledgements
-\layout Standard
+\end_layout
+\begin_layout Standard
We are grateful to V.
Barger, T.
Han, and R.
J.
N.
Phillips for doing the math in section
-\protected_separator
+\begin_inset space ~
+\end_inset
-\begin_inset LatexCommand \ref{bozomath}
-\end_inset
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "bozomath"
+
+\end_inset
.
- More information on the AASTeX macros package are available at
-\latex latex
+ More information on the AAS\SpecialChar TeX
+ macros package are available at
+\begin_inset Flex URL
+status collapsed
-\begin_inset LatexCommand \url{http://www.aas.org/publications/aastex}
+\begin_layout Plain Layout
-\end_inset
+http://www.aas.org/publications/aastex
+\end_layout
+\end_inset
-\latex default
or the
-\latex latex
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+anchor{
+\end_layout
+
+\end_inset
+
+ftp://www.aas.org/pubs/
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}{
+\end_layout
+
+\end_inset
+
+AAS ftp site
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
-\backslash
-anchor{ftp://www.aas.org/pubs/}{AAS ftp site}
-\latex default
.
-\layout Appendix
+
+\end_layout
-\layout Section
+\begin_layout Software
+IRAF, AIPS, Astropy, ...
+
+\end_layout
+\begin_layout Appendix
+
+\end_layout
+
+\begin_layout Section
Appendicial material
-\layout Standard
+\end_layout
+\begin_layout Standard
Consider once again a task that computes profile parameters for a modified
Lorentzian of the form
\begin_inset Formula
I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
\end{equation}
-\end_inset
+\end_inset
where
-\layout MathLetters
-
+\end_layout
+\begin_layout MathLetters
\begin_inset Formula
\[
-d_{1}=\frac{3}{4}\sqrt{\left( \begin{array}{c}
-\frac{x_{1}}{R_{maj}}
-\end{array}\right) ^{2}+\left( \begin{array}{c}
-\frac{y_{1}}{R_{min}}
-\end{array}\right) ^{2}}\]
+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_inset
+\end_inset
\begin_inset Formula
\begin{equation}
-d_{2}=\case {3}{4}\sqrt{\left( \begin{array}{c}
-\frac{x_{1}}{PR_{maj}}
-\end{array}\right) ^{2}+\left( \begin{array}{c}
-\case {y_{1}}{PR_{min}}
-\end{array}\right) ^{2}}
+d_{2}=\case{3}{4}\sqrt{\left(\begin{array}{c}
+\frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
+\case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
\end{equation}
-\end_inset
+\end_inset
\begin_inset Formula
\begin{eqnarray}
-x_{1} & = & (x-x_{0})\cos \Theta +(y-y_{0})\sin \Theta \\
-y_{1} & = & -(x-x_{0})\sin \Theta +(y-y_{0})\cos \Theta
+x_{1} & = & (x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta\\
+y_{1} & = & -(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
\end{eqnarray}
-\end_inset
+\end_inset
-\layout Standard
+\end_layout
+\begin_layout Standard
For completeness, here is one last equation.
\begin_inset Formula
e=mc^{2}
\end{equation}
-\end_inset
+\end_inset
-\layout References
-\bibitem [Auri\`ere(1982)]{aur82}
+\end_layout
-Auri\i \`{e}
-re, M.
+\begin_layout References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Auri\\`ere(1982)"
+key "aur82"
+
+\end_inset
+
+Aurière, M.
1982,
-\latex latex
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
-\backslash
+\backslash
aap
-\latex default
+\end_layout
+
+\end_inset
+
, 109, 301
-\layout References
-\bibitem [Canizares et al.(1978)]{can78}
+\end_layout
+
+\begin_layout References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Canizares et al.(1978)"
+key "can78"
+
+\end_inset
Canizares, C.
R., Grindlay, J.
A., Liller, W., and McClintock, J.
E.
1978,
-\latex latex
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
-\backslash
+
+\backslash
apj
-\latex default
+\end_layout
+
+\end_inset
+
, 224, 39
-\layout References
-\bibitem [Djorgovski and King(1984)]{djo84}
+\end_layout
+
+\begin_layout References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Djorgovski and King(1984)"
+key "djo84"
+
+\end_inset
Djorgovski, S., and King, I.
R.
1984,
-\latex latex
+\begin_inset ERT
+status collapsed
-\backslash
+\begin_layout Plain Layout
+
+
+\backslash
apjl
-\latex default
+\end_layout
+
+\end_inset
+
, 277, L49
-\layout References
-\bibitem [Hagiwara and Zeppenfeld(1986)]{hag86}
+\end_layout
+
+\begin_layout References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Hagiwara and Zeppenfeld(1986)"
+key "hag86"
+
+\end_inset
Hagiwara, K., and Zeppenfeld, D.
1986, Nucl.Phys., 274, 1
-\layout References
-\bibitem [Harris and van den Bergh(1984)]{har84}
+\end_layout
+
+\begin_layout References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Harris and van den Bergh(1984)"
+key "har84"
+
+\end_inset
Harris, W.
E., and van den Bergh, S.
1984,
-\latex latex
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
-\backslash
+\backslash
aj
-\latex default
+\end_layout
+
+\end_inset
+
, 89, 1816
-\layout References
-\bibitem [H\`enon(1961)]{hen61}
+\end_layout
+
+\begin_layout References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "H\\`enon(1961)"
+key "hen61"
-H\i \'{e}
-non, M.
+\end_inset
+
+Hénon, M.
1961, Ann.d'Ap., 24, 369
-\layout References
-\bibitem [King(1966)]{kin66}
+\end_layout
+
+\begin_layout References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "King(1966)"
+key "kin66"
+
+\end_inset
King, I.
R.
1966,
-\latex latex
+\begin_inset ERT
+status collapsed
-\backslash
+\begin_layout Plain Layout
+
+
+\backslash
aj
-\latex default
+\end_layout
+
+\end_inset
+
, 71, 276
-\layout References
-\bibitem [King(1975)]{kin75}
+\end_layout
+
+\begin_layout References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "King(1975)"
+key "kin75"
+
+\end_inset
King, I.
R.
1975, Dynamics of Stellar Systems, A.
Hayli, Dordrecht: Reidel, 1975, 99
-\layout References
-\bibitem [King et al.(1968)]{kin68}
+\end_layout
+
+\begin_layout References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "King et al.(1968)"
+key "kin68"
+
+\end_inset
King, I.
R., Hedemann, E., Hodge, S.
M., and White, R.
E.
1968,
-\latex latex
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
-\backslash
+\backslash
aj
-\latex default
+\end_layout
+
+\end_inset
+
, 73, 456
-\layout References
-\bibitem [Kron et al.(1984)]{kro84}
+\end_layout
+
+\begin_layout References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Kron et al.(1984)"
+key "kro84"
+
+\end_inset
Kron, G.
E., Hewitt, A.
V., and Wasserman, L.
H.
1984,
-\latex latex
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
-\backslash
+\backslash
pasp
-\latex default
+\end_layout
+
+\end_inset
+
, 96, 198
-\layout References
-\bibitem [Lynden-Bell and Wood(1968)]{lyn68}
+\end_layout
+
+\begin_layout References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Lynden-Bell and Wood(1968)"
+key "lyn68"
+
+\end_inset
Lynden-Bell, D., and Wood, R.
1968,
-\latex latex
+\begin_inset ERT
+status collapsed
-\backslash
+\begin_layout Plain Layout
+
+
+\backslash
mnras
-\latex default
+\end_layout
+
+\end_inset
+
, 138, 495
-\layout References
-\bibitem [Newell and O'Neil(1978)]{new78}
+\end_layout
+
+\begin_layout References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Newell and O'Neil(1978)"
+key "new78"
+
+\end_inset
Newell, E.
B., and O'Neil, E.
J.
1978,
-\latex latex
+\begin_inset ERT
+status collapsed
-\backslash
+\begin_layout Plain Layout
+
+
+\backslash
apjs
-\latex default
+\end_layout
+
+\end_inset
+
, 37, 27
-\layout References
-\bibitem [Ortolani et al.(1985)]{ort85}
+\end_layout
+
+\begin_layout References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Ortolani et al.(1985)"
+key "ort85"
+
+\end_inset
Ortolani, S., Rosino, L., and Sandage, A.
1985,
-\latex latex
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
-\backslash
+
+\backslash
aj
-\latex default
+\end_layout
+
+\end_inset
+
, 90, 473
-\layout References
-\bibitem [Peterson(1976)]{pet76}
+\end_layout
+
+\begin_layout References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Peterson(1976)"
+key "pet76"
+
+\end_inset
Peterson, C.
J.
1976,
-\latex latex
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
-\backslash
+
+\backslash
aj
-\latex default
+\end_layout
+
+\end_inset
+
, 81, 617
-\layout References
-\bibitem [Spitzer(1985)]{spi85}
+\end_layout
+
+\begin_layout References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Spitzer(1985)"
+key "spi85"
+
+\end_inset
Spitzer, L.
1985, Dynamics of Star Clusters, J.
Goodman and P.
Hut, Dordrecht: Reidel, 109
-\layout Standard
+\end_layout
+\begin_layout Standard
+\begin_inset Newpage clearpage
+\end_inset
-\latex latex
-\backslash
-clearpage
-\layout FigCaption
+\end_layout
+\begin_layout Standard
+\begin_inset Caption FigCaption
-\begin_inset LatexCommand \label{fig1}
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "fig1"
-\end_inset
+\end_inset
This is the first figure and it uses sgi9259.eps as its EPS figure file.
-\layout FigCaption
+\end_layout
+
+\end_inset
+
+\end_layout
-\begin_inset LatexCommand \label{fig2}
+\begin_layout Standard
+\begin_inset Caption FigCaption
-\end_inset
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "fig2"
+
+\end_inset
This is an example of a long figure caption that must be set as a paragraph.
The processor has to buffer the text of the caption, so it is good not
to be too wordy, but that would make for poor communication as well.
-\layout FigCaption
+\end_layout
+
+\end_inset
+
+\end_layout
-\begin_inset LatexCommand \label{fig3}
+\begin_layout Standard
+\begin_inset Caption FigCaption
-\end_inset
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "fig3"
+
+\end_inset
This figure has no associated EPS file, so the optional parameter is omitted.
-\layout Standard
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage clearpage
+\end_inset
+
+\end_layout
-\latex latex
+\begin_layout Standard
+\begin_inset Float table
+wide false
+sideways false
+status open
-\backslash
-clearpage
-\layout Standard
+\begin_layout Plain Layout
+\begin_inset Caption Standard
-\begin_float tab
-\layout Caption
-\added_space_bottom medskip
+\begin_layout Plain Layout
Terribly relevant tabular information.
-\begin_inset LatexCommand \label{tbl-2}
-
-\end_inset
-
-
-\layout Standard
-\LyXTable
-multicol5
-7 13 0 0 -1 -1 -1 -1
-0 0 0 0
-0 0 0 0
-0 0 0 0
-0 0 0 0
-0 0 0 0
-0 0 0 0
-0 0 0 0
-8 0 0 "" ""
-4 0 0 "" ""
-4 0 0 "" ""
-4 0 0 "" ""
-4 0 0 "" ""
-4 0 0 "" ""
-4 0 0 "" ""
-4 0 0 "" ""
-4 0 0 "" ""
-4 0 0 "" ""
-4 0 0 "" ""
-4 0 0 "" ""
-8 0 0 "" ""
-0 8 1 1 0 0 0 "" ""
-0 4 1 1 0 0 0 "" ""
-0 4 1 1 0 0 0 "" ""
-0 4 1 1 0 0 0 "" ""
-0 4 1 1 0 0 0 "" ""
-0 4 1 1 0 0 0 "" ""
-0 4 1 1 0 0 0 "" ""
-0 4 1 1 0 0 0 "" ""
-1 8 0 0 0 0 0 "" ""
-0 4 1 1 0 0 0 "" ""
-0 4 1 1 0 0 0 "" ""
-1 8 0 0 0 0 0 "" ""
-0 8 0 0 0 0 0 "" ""
-0 8 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
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-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 8 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 8 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 8 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
-0 4 0 0 0 0 0 "" ""
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-0 4 0 1 0 0 0 "" ""
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-0 4 0 1 0 0 0 "" ""
-0 4 0 1 0 0 0 "" ""
-0 4 0 1 0 0 0 "" ""
+\begin_inset CommandInset label
+LatexCommand label
+name "tbl-2"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="13">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="right" valignment="top" width="0pt">
+<column alignment="right" valignment="top" width="0pt">
+<column alignment="right" valignment="top" width="0pt">
+<column alignment="right" valignment="top" width="0pt">
+<column alignment="right" valignment="top" width="0pt">
+<column alignment="right" valignment="top" width="0pt">
+<column alignment="right" valignment="top" width="0pt">
+<column alignment="right" valignment="top" width="0pt">
+<column alignment="right" valignment="top" width="0pt">
+<column alignment="right" valignment="top" width="0pt">
+<column alignment="right" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
Star
-\newline
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
Height
-\newline
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
-\begin_inset Formula \( d_{x} \)
-\end_inset
+\begin_inset Formula $d_{x}$
+\end_inset
+
+\end_layout
-\newline
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
-\begin_inset Formula \( d_{y} \)
-\end_inset
+\begin_inset Formula $d_{y}$
+\end_inset
+
+\end_layout
-\newline
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
-\begin_inset Formula \( n \)
-\end_inset
+\begin_inset Formula $n$
+\end_inset
+
+
+\end_layout
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
-\newline
+\begin_layout Plain Layout
-\begin_inset Formula \( \chi ^{2} \)
-\end_inset
+\begin_inset Formula $\chi^{2}$
+\end_inset
-\newline
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
-\begin_inset Formula \( R_{maj} \)
-\end_inset
+\begin_inset Formula $R_{maj}$
+\end_inset
+
+
+\end_layout
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
-\newline
+\begin_layout Plain Layout
-\begin_inset Formula \( R_{min} \)
-\end_inset
+\begin_inset Formula $R_{min}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+\begin_layout Plain Layout
+\begin_inset Formula $P$
+\end_inset
-\newline
-\begin_inset Formula \( P \)
-\end_inset
+\begin_inset Flex tablenotemark
+status collapsed
+\begin_layout Plain Layout
+a
+\end_layout
-\latex latex
+\end_inset
-\backslash
-tablenotemark{a}
-\latex default
-\newline
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
-\begin_inset Formula \( PR_{maj} \)
-\end_inset
+\begin_inset Formula $PR_{maj}$
+\end_inset
+
+
+\end_layout
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
-\newline
+\begin_layout Plain Layout
-\begin_inset Formula \( PR_{min} \)
-\end_inset
+\begin_inset Formula $PR_{min}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+\begin_layout Plain Layout
+\begin_inset Formula $\Theta$
+\end_inset
-\newline
-\begin_inset Formula \( \Theta \)
-\end_inset
+\begin_inset Flex tablenotemark
+status collapsed
+\begin_layout Plain Layout
+b
+\end_layout
-\latex latex
+\end_inset
-\backslash
-tablenotemark{b}
-\latex default
-\newline
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
Ref.
-\newline
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
-\latex latex
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
-\backslash
+\begin_layout Plain Layout
+
+
+\backslash
tableline
-\backslash
+\backslash
tableline
-\latex default
+\end_layout
+
+\end_inset
+
1
-\newline
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
33472.5
-\newline
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
-0.1
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+\end_layout
+
+\end_inset
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+<cell alignment="right" valignment="top" usebox="none">
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+
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0.4
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+\end_layout
+
+\end_inset
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+
+\begin_layout Plain Layout
53
-\newline
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
27.4
-\newline
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
2.065
-\newline
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
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+
+\begin_layout Plain Layout
1.940
-\newline
+\end_layout
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+<cell alignment="right" valignment="top" usebox="none">
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+
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3.900
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+
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68.3
-\newline
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+<cell alignment="right" valignment="top" usebox="none">
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116.2
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+<cell alignment="right" valignment="top" usebox="none">
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-27.639
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1,2
-\newline
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+
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+
+\begin_layout Plain Layout
2
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+<cell alignment="right" valignment="top" usebox="none">
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+
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27802.4
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+
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-0.3
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+
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We can also attach a long-ish paragraph of explanatory material to a table.
Use
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tablerefs to append a list of references.
The following references were from a different table: I've patched them
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(1) Barbuy, Spite, & Spite 1985; (2) Bond 1980; (3) Carbon et al.
1987; (4) Hobbs & Duncan 1987; (5) Gilroy et al.
1988: (6) Gratton & Ortolani 1986; (7) Gratton & Sneden 1987; (8) Gratton
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al.
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