-#LyX 1.5.0svn created this file. For more info see http://www.lyx.org/
-\lyxformat 276
+#LyX 2.2 created this file. For more info see http://www.lyx.org/
+\lyxformat 508
\begin_document
\begin_header
-\textclass aastex
+\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
+\use_default_options false
+\maintain_unincluded_children false
\language english
-\inputencoding default
-\font_roman default
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+\language_package default
+\inputencoding auto
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+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
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\font_sc false
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-\font_sf_scale 100
-\font_tt_scale 100
+\font_sf_scale 100 100
+\font_tt_scale 100 100
\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
\paperfontsize default
\spacing single
+\use_hyperref false
\papersize default
\use_geometry false
-\use_amsmath 0
-\use_esint 0
+\use_package amsmath 0
+\use_package amssymb 0
+\use_package cancel 0
+\use_package esint 0
+\use_package mathdots 1
+\use_package mathtools 0
+\use_package mhchem 1
+\use_package stackrel 0
+\use_package stmaryrd 0
+\use_package undertilde 0
\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
\use_bibtopic false
+\use_indices false
\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
-\defskip medskip
+\paragraph_indentation default
\quotes_language english
\papercolumns 1
\papersides 1
\paperpagestyle default
\tracking_changes false
\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
\end_header
\begin_body
-\begin_layout Title
+\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"
-Collapsed Cores in Globular Clusters, Gauge-Boson Couplings, and AASTeX
-Examples
+\end_inset
+
+ for details on how to use AASTeX.
+
\end_layout
-\begin_layout Author
+\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
-S.
- Djorgovski
-\begin_inset ERT
+\begin_layout Plain Layout
+
+http://journals.aas.org/authors/aastex/aastex.html#_download
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\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.
+
+\begin_inset Flex URL
status collapsed
-\begin_layout Standard
+\begin_layout Plain Layout
-\backslash
-altaffilmark{1,2,3}
+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
+\begin_inset Flex altaffilmark
+status open
+
+\begin_layout Plain Layout
+1,2,3
\end_layout
\end_inset
and Ivan R.
King
-\begin_inset ERT
+\begin_inset Flex altaffilmark
status collapsed
-\begin_layout Standard
-
-\backslash
-altaffilmark{1}
+\begin_layout Plain Layout
+1
\end_layout
\end_inset
\end_layout
\begin_layout Affiliation
-
Astronomy Department, University of California, Berkeley, CA 94720
\end_layout
\begin_layout Author
-
C.
D.
Biemesderfer
-\begin_inset ERT
+\begin_inset Flex altaffilmark
status collapsed
-\begin_layout Standard
-
-\backslash
-altaffilmark{4,5}
+\begin_layout Plain Layout
+4,5
\end_layout
\end_inset
\end_layout
\begin_layout Affiliation
-
National Optical Astronomy Observatories, Tucson, AZ 85719
\end_layout
\begin_layout Email
-
aastex-help@aas.org
\end_layout
\end_layout
\begin_layout Author
-
R.
J.
Hanisch
-\begin_inset ERT
+\begin_inset Flex altaffilmark
status collapsed
-\begin_layout Standard
-
-\backslash
-altaffilmark{5}
+\begin_layout Plain Layout
+5
\end_layout
\end_inset
\end_layout
\begin_layout Affiliation
-
Space Telescope Science Institute, Baltimore, MD 21218
\end_layout
-\begin_layout Standard
-
+\begin_layout Altaffilation
+\begin_inset Argument 1
+status open
-\begin_inset ERT
-status collapsed
+\begin_layout Plain Layout
+1
+\end_layout
-\begin_layout Standard
+\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.}
-\end_layout
-
-\begin_layout Standard
+\begin_inset space \space{}
+\end_inset
+under contract to the National Science Foundation.
\end_layout
-\begin_layout Standard
+\begin_layout Altaffilation
+\begin_inset Argument 1
+status open
-\backslash
-altaffiltext{2}{Society of Fellows, Harvard University.}
+\begin_layout Plain Layout
+2
\end_layout
-\begin_layout Standard
+\end_inset
+Society of Fellows, Harvard University.
\end_layout
-\begin_layout Standard
+\begin_layout Altaffilation
+\begin_inset Argument 1
+status open
-\backslash
-altaffiltext{3}{present address: Center for Astrophysics, 60 Garden Street,
- Cambridge, MA 02138}
+\begin_layout Plain Layout
+3
\end_layout
-\begin_layout Standard
+\end_inset
+present address: Center for Astrophysics, 60 Garden Street, Cambridge, MA
+ 02138
\end_layout
-\begin_layout Standard
+\begin_layout Altaffilation
+\begin_inset Argument 1
+status open
-\backslash
-altaffiltext{4}{Visiting Programmer, Space Telescope Science Institute}
-
+\begin_layout Plain Layout
+4
\end_layout
-\begin_layout Standard
+\end_inset
+Visiting Programmer, Space Telescope Science Institute
\end_layout
-\begin_layout Standard
+\begin_layout Altaffilation
+\begin_inset Argument 1
+status open
-\backslash
-altaffiltext{5}{Patron, Alonso's Bar and Grill}
+\begin_layout Plain Layout
+5
\end_layout
\end_inset
-
+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.
\end_layout
\begin_layout Keywords
-
-clusters: globular, peanut---bosons: bozos
+clusters: globular, peanut—bosons: bozos
\end_layout
\begin_layout Section
-
Introduction
\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
\begin_inset ERT
status collapsed
-\begin_layout Standard
+\begin_layout Plain Layout
+
\backslash
citep{hen61,lyn68,spi85}
\begin_inset ERT
status collapsed
-\begin_layout Standard
+\begin_layout Plain Layout
+
\backslash
citep{kin75,new78}
\begin_inset ERT
status collapsed
-\begin_layout Standard
+\begin_layout Plain Layout
+
\backslash
citet{aur82}
\begin_inset ERT
status collapsed
-\begin_layout Standard
+\begin_layout Plain Layout
+
\backslash
citep[Paper I]{djo84}
\begin_inset ERT
status collapsed
-\begin_layout Standard
+\begin_layout Plain Layout
+
\backslash
citep{can78}
\end_layout
\begin_layout Section
-
Observations
\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 \( \times \)
+\begin_inset Formula $\times$
\end_inset
500 chip and a GEC 575
-\begin_inset Formula \( \times \)
+\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 \( \times \)
+\begin_inset Formula $\times$
\end_inset
385, with
-\begin_inset Formula \( B,V, \)
+\begin_inset Formula $B,V,$
\end_inset
and
-\begin_inset Formula \( R \)
+\begin_inset Formula $R$
\end_inset
filters, and an RCA 512
-\begin_inset Formula \( \times \)
+\begin_inset Formula $\times$
\end_inset
320, with
-\begin_inset Formula \( U,B,V,R, \)
+\begin_inset Formula $U,B,V,R,$
\end_inset
and
-\begin_inset Formula \( I \)
+\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 \( U \)
+\begin_inset Formula $U$
\end_inset
or even in
-\begin_inset Formula \( B \)
+\begin_inset Formula $B$
\end_inset
.
\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
\begin_inset ERT
status collapsed
-\begin_layout Standard
+\begin_layout Plain Layout
+
\backslash
citep{kin68,pet76,har84,ort85}
\begin_inset ERT
status collapsed
-\begin_layout Standard
+\begin_layout Plain Layout
+
\backslash
citep{kin66,kin75}
\begin_inset ERT
status collapsed
-\begin_layout Standard
+\begin_layout Plain Layout
+
\backslash
citep{kro84}
\end_layout
\begin_layout Section
-
Helicity Amplitudes
\end_layout
\begin_layout Standard
-
It has been realized that helicity amplitudes provide a convenient means
for Feynman diagram
\begin_inset Foot
status collapsed
-\begin_layout Standard
-
+\begin_layout Plain Layout
Footnotes can be inserted like this.
\end_layout
amplitude squared becomes unwieldy.
Our calculations use the helicity techniques developed by other authors
-\begin_inset LatexCommand cite
+\begin_inset CommandInset citation
+LatexCommand cite
key "hag86"
+
\end_inset
; we briefly summarize below.
\end_layout
\begin_layout Subsection
-
Formalism
\end_layout
\begin_layout Standard
-
-
-\begin_inset LatexCommand label
+\begin_inset CommandInset label
+LatexCommand label
name "bozomath"
+
\end_inset
\end_layout
\begin_layout Standard
-
A tree-level amplitude in
-\begin_inset Formula \( e^{+}e^{-} \)
+\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}),
+\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}),
\end{equation}
\end_inset
where
-\begin_inset Formula \( p \)
+\begin_inset Formula $p$
\end_inset
and
-\begin_inset Formula \( \sigma \)
+\begin_inset Formula $\sigma$
\end_inset
label the initial
-\begin_inset Formula \( e^{\pm } \)
+\begin_inset Formula $e^{\pm}$
\end_inset
four-momenta and helicities
-\begin_inset Formula \( (\sigma =\pm 1) \)
+\begin_inset Formula $(\sigma=\pm1)$
\end_inset
,
-\begin_inset Formula \( \hat{a}_{i}=a^{\mu }_{i}\gamma _{\nu } \)
+\begin_inset Formula $\hat{a}_{i}=a_{i}^{\mu}\gamma_{\nu}$
\end_inset
and
-\begin_inset Formula \( P_{\tau }=\frac{1}{2}(1+\tau \gamma _{5}) \)
+\begin_inset Formula $P_{\tau}=\frac{1}{2}(1+\tau\gamma_{5})$
\end_inset
is a chirality projection operator
-\begin_inset Formula \( (\tau =\pm1 ) \)
+\begin_inset Formula $(\tau=\pm1)$
\end_inset
.
The
-\begin_inset Formula \( a^{\mu }_{i} \)
+\begin_inset Formula $a_{i}^{\mu}$
\end_inset
may be formed from particle four-momenta, gauge-boson polarization vectors
\end_layout
\begin_layout NoteToEditor
-
Figures 1 and 2 should appear side-by-side in print
\end_layout
\begin_layout Standard
-
In the chiral representation the
-\begin_inset Formula \( \gamma \)
+\begin_inset Formula $\gamma$
\end_inset
matrices are expressed in terms of
-\begin_inset Formula \( 2\times 2 \)
+\begin_inset Formula $2\times2$
\end_inset
Pauli matrices
-\begin_inset Formula \( \sigma \)
+\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_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}
-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
giving
-\begin_inset Formula \begin{equation}
-\hat{a}=\left( \begin{array}{cc}
+\begin_inset Formula
+\begin{equation}
+\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
The spinors are expressed in terms of two-component Weyl spinors as
-\begin_inset Formula \begin{equation}
-u=\left( \begin{array}{c}
+\begin_inset Formula
+\begin{equation}
+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_layout
\begin_layout Standard
-
The Weyl spinors are given in terms of helicity eigenstates
-\begin_inset Formula \( \chi _{\lambda }(p) \)
+\begin_inset Formula $\chi_{\lambda}(p)$
\end_inset
with
-\begin_inset Formula \( \lambda =\pm1 \)
+\begin_inset Formula $\lambda=\pm1$
\end_inset
by
\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)
+\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)
\end{eqnarray}
\end_inset
\end_layout
\begin_layout Section
-
Floating material and so forth
\end_layout
\begin_layout Standard
-
Consider a task that computes profile parameters for a modified Lorentzian
of the form
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
\end{equation}
\end_inset
where
-\begin_inset Formula \[
-d_{1}=\sqrt{\left( \begin{array}{c}
-\frac{x_{1}}{R_{maj}}
-\end{array}\right) ^{2}+\left( \begin{array}{c}
-\frac{y_{1}}{R_{min}}
-\end{array}\right) ^{2}}\]
+\begin_inset Formula
+\[
+d_{1}=\sqrt{\left(\begin{array}{c}
+\frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
+\frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
+\]
\end_inset
-\begin_inset Formula \[
-d_{2}=\sqrt{\left( \begin{array}{c}
-\frac{x_{1}}{PR_{maj}}
-\end{array}\right) ^{2}+\left( \begin{array}{c}
-\case {y_{1}}{PR_{min}}
-\end{array}\right) ^{2}}\]
+\begin_inset Formula
+\[
+d_{2}=\sqrt{\left(\begin{array}{c}
+\frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
+\case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
+\]
\end_inset
-\begin_inset Formula \[
-x_{1}=(x-x_{0})\cos \Theta +(y-y_{0})\sin \Theta \]
+\begin_inset Formula
+\[
+x_{1}=(x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta
+\]
\end_inset
-\begin_inset Formula \[
-y_{1}=-(x-x_{0})\sin \Theta +(y-y_{0})\cos \Theta \]
+\begin_inset Formula
+\[
+y_{1}=-(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
+\]
\end_inset
\end_layout
\begin_layout Standard
-
In these expressions
-\begin_inset Formula \( x_{0} \)
+\begin_inset Formula $x_{0}$
\end_inset
,
-\begin_inset Formula \( y_{0} \)
+\begin_inset Formula $y_{0}$
\end_inset
is the star center, and
-\begin_inset Formula \( \Theta \)
+\begin_inset Formula $\Theta$
\end_inset
is the angle with the
-\begin_inset Formula \( x \)
+\begin_inset Formula $x$
\end_inset
axis.
- Results of this task are shown in table\InsetSpace ~
+ Results of this task are shown in table
+\begin_inset space ~
+\end_inset
-\begin_inset LatexCommand ref
+
+\begin_inset CommandInset ref
+LatexCommand ref
reference "tbl-2"
+
\end_inset
.
It is not clear how these sorts of analyses may affect determination of
-\begin_inset Formula \( M_{\sun } \)
-\end_inset
-
-, but the assumption is that the alternate results should be less than 90
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-\backslash
-degr
-\backslash
-
-\end_layout
-
+\begin_inset Formula $M_{\sun}$
\end_inset
-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
\begin_inset ERT
status collapsed
-\begin_layout Standard
+\begin_layout Plain Layout
+
\backslash
ion{Ca}{2}
\begin_inset ERT
status collapsed
-\begin_layout Standard
+\begin_layout Plain Layout
+
\backslash
slantfrac{4}{5}
\end_layout
\begin_layout Standard
-
We are grateful to V.
Barger, T.
Han, and R.
J.
N.
- Phillips for doing the math in section\InsetSpace ~
+ Phillips for doing the math in section
+\begin_inset space ~
+\end_inset
-\begin_inset LatexCommand ref
+
+\begin_inset CommandInset ref
+LatexCommand ref
reference "bozomath"
+
\end_inset
.
- More information on the AASTeX macros package are available at
+ More information on the AAS\SpecialChar TeX
+ macros package are available at
+\begin_inset Flex URL
+status collapsed
-\begin_inset LatexCommand url
-target "http://www.aas.org/publications/aastex"
-\end_inset
+\begin_layout Plain Layout
+
+http://www.aas.org/publications/aastex
+\end_layout
+\end_inset
or the
\begin_inset ERT
status collapsed
-\begin_layout Standard
+\begin_layout Plain Layout
+
\backslash
-anchor{ftp://www.aas.org/pubs/}{AAS ftp site}
+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
.
+
+\end_layout
+
+\begin_layout Software
+IRAF, AIPS, Astropy, ...
+
\end_layout
\begin_layout Appendix
\end_layout
\begin_layout Section
-
Appendicial material
\end_layout
\begin_layout Standard
-
Consider once again a task that computes profile parameters for a modified
Lorentzian of the form
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
\end{equation}
\end_layout
\begin_layout MathLetters
-
-
-\begin_inset Formula \[
-d_{1}=\frac{3}{4}\sqrt{\left( \begin{array}{c}
-\frac{x_{1}}{R_{maj}}
-\end{array}\right) ^{2}+\left( \begin{array}{c}
-\frac{y_{1}}{R_{min}}
-\end{array}\right) ^{2}}\]
+\begin_inset Formula
+\[
+d_{1}=\frac{3}{4}\sqrt{\left(\begin{array}{c}
+\frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
+\frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
+\]
\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}}
+\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}}
\end{equation}
\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
+\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
\end{eqnarray}
\end_inset
\end_layout
\begin_layout Standard
-
For completeness, here is one last equation.
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
e=mc^{2}
\end{equation}
\end_layout
\begin_layout References
-\begin_inset LatexCommand bibitem
-label "Auri\`ere(1982)"
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Auri\\`ere(1982)"
key "aur82"
\end_inset
-Auriè
-re, M.
+Aurière, M.
1982,
\begin_inset ERT
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\end_layout
\end_inset
</cell>
-<cell alignment="right" valignment="top" bottomline="true" usebox="none">
+<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text
-\begin_layout Standard
-
+\begin_layout Plain Layout
92.1
\end_layout
\end_inset
</cell>
-<cell alignment="right" valignment="top" bottomline="true" usebox="none">
+<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text
-\begin_layout Standard
-
+\begin_layout Plain Layout
25.3
\end_layout
\end_inset
</cell>
-<cell alignment="right" valignment="top" bottomline="true" usebox="none">
+<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text
-\begin_layout Standard
-
+\begin_layout Plain Layout
-12.052
\end_layout
\end_inset
</cell>
-<cell alignment="right" valignment="top" bottomline="true" usebox="none">
+<cell alignment="right" valignment="top" usebox="none">
\begin_inset Text
-\begin_layout Standard
-
+\begin_layout Plain Layout
8
\end_layout
\end_layout
-\begin_layout Standard
-
-
+\begin_layout Table note
+a
\begin_inset ERT
status collapsed
-\begin_layout Standard
+\begin_layout Plain Layout
-\backslash
-tablenotetext{a}{Sample footnote for table~
-\backslash
-ref{tbl-2} that was generated with the
-\backslash
-LaTeX
-\backslash
- table environment}
+}{
\end_layout
-\begin_layout Standard
+\end_inset
+
+Sample footnote for table
+\begin_inset space ~
+\end_inset
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "tbl-2"
+
+\end_inset
+
+ that was generated with the \SpecialChar LaTeX
+ table environment
\end_layout
-\begin_layout Standard
+\begin_layout Table note
+b
+\begin_inset ERT
+status collapsed
-\backslash
-tablenotetext{b}{Yet another sample footnote for table~
-\backslash
-ref{tbl-2}}
+\begin_layout Plain Layout
+
+}{
\end_layout
-\begin_layout Standard
+\end_inset
+
+Yet another sample footnote for table
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "tbl-2"
+
+\end_inset
+
\end_layout
-\begin_layout Standard
+\begin_layout Table note
+c
+\begin_inset ERT
+status collapsed
-\backslash
-tablenotetext{c}{Another sample footnote for table~
-\backslash
-ref{tbl-2}}
+\begin_layout Plain Layout
+
+}{
\end_layout
\end_inset
+Another sample footnote for table
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "tbl-2"
+
+\end_inset
+
\end_layout
\begin_layout TableComments
-
We can also attach a long-ish paragraph of explanatory material to a table.
Use
\backslash
tablerefs to append a list of references.
The following references were from a different table: I've patched them
- in here to show how they look, but don't take them too seriously---I certainly
+ in here to show how they look, but don't take them too seriously—I certainly
have not.
\end_layout
\begin_layout TableRefs
-
(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
\end_inset
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-% LyX can load deluxetable files verbatim.
- To see this in action, uncomment the following
-\end_layout
-
-\end_inset
-
\end_layout
\begin_layout Standard
+\begin_inset Note Note
+status open
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-% line (delete the
-\end_layout
-
-\end_inset
-
-
-\begin_inset Quotes eld
-\end_inset
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-%
-\end_layout
-
-\end_inset
-
-
-\begin_inset Quotes erd
-\end_inset
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-) and copy the file table.tex from the AASTeX 5.0 distribution into
+\begin_layout Plain Layout
+LyX can load deluxetable files verbatim.
+ To see this in action, dissolve the following Note and copy the file table.tex
+ from the AASTeX 5.0 distribution into the same directory as this file.
\end_layout
\end_inset
\end_layout
\begin_layout Standard
+\begin_inset Note Note
+status open
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-% the same directory as this file.
-\end_layout
+\begin_layout Plain Layout
+\begin_inset CommandInset include
+LatexCommand input
+filename "table"
\end_inset
\end_layout
-\begin_layout Standard
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-%
-\end_layout
-
\end_inset
-\begin_inset Include \input{table}
-
-\end_inset
-
-
-
\end_layout
\end_body