--- /dev/null
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+\lyxformat 598
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass aastex62
+\begin_preamble
+\newcommand{\myemail}{skywalker@galaxy.far.far.away}
+%\slugcomment{Not to appear in Nonlearned J., 45.}
+\shorttitle{Djorgovski et al.}
+\shortauthors{Collapsed Cores in Globular Clusters}
+\end_preamble
+\use_default_options true
+\maintain_unincluded_children no
+\language english
+\language_package default
+\inputencoding utf8
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+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
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+\use_package mathdots 1
+\use_package mathtools 1
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+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
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+\shortcut idx
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+\end_index
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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"
+literal "false"
+
+\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
+
+\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 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
+
+https://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 and Ivan R.
+ King
+\end_layout
+
+\begin_layout Affiliation
+Astronomy Department, University of California, Berkeley, CA 94720
+\end_layout
+
+\begin_layout Altaffilation
+Visiting Astronomer
+\begin_inset Newline newline
+\end_inset
+
+ Cerro Tololo Inter-American Observatory.
+\begin_inset Newline newline
+\end_inset
+
+CTIO is operated by AURA Inc.
+\begin_inset space \space{}
+\end_inset
+
+under contract to the National Science Foundation.
+\end_layout
+
+\begin_layout Altaffilation
+Society of Fellows, Harvard University.
+\end_layout
+
+\begin_layout Altaffilation
+present address: Center for Astrophysics
+\begin_inset Newline newline
+\end_inset
+
+60 Garden Street, Cambridge, MA 02138
+\end_layout
+
+\begin_layout Author
+C.
+ D.
+ Biemesderfer
+\end_layout
+
+\begin_layout Affiliation
+National Optical Astronomy Observatories, Tucson, AZ 85719
+\end_layout
+
+\begin_layout Altaffilation
+Visiting Programmer, Space Telescope Science Institute
+\end_layout
+
+\begin_layout Altaffilation
+Patron, Alonso's Bar and Grill
+\end_layout
+
+\begin_layout Email
+aastex-help@aas.org
+\end_layout
+
+\begin_layout Author
+R.
+ J.
+ Hanisch
+\end_layout
+
+\begin_layout Affiliation
+Space Telescope Science Institute, Baltimore, MD 21218
+\end_layout
+
+\begin_layout Altaffilation
+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.
+
+\end_layout
+
+\begin_layout Keywords
+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 CommandInset citation
+LatexCommand citep
+key "hen61,lyn68,spi85"
+literal "false"
+
+\end_inset
+
+, but observation has been less alert to the phenomenon.
+ For many years the central brightness peak in M15
+\begin_inset CommandInset citation
+LatexCommand citep
+key "kin75,new78"
+literal "false"
+
+\end_inset
+
+ seemed a unique anomaly.
+ Then
+\begin_inset CommandInset citation
+LatexCommand citep
+key "aur82"
+literal "false"
+
+\end_inset
+
+ suggested a central peak in NGC 6397, and a limited photographic survey
+ of ours
+\begin_inset CommandInset citation
+LatexCommand citep
+after "Paper I"
+key "djo84"
+literal "false"
+
+\end_inset
+
+ found three more cases, including NGC 6624, whose sharp center had often
+ been remarked on
+\begin_inset CommandInset citation
+LatexCommand citep
+key "can78"
+literal "false"
+
+\end_inset
+
+.
+
+\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 $\times$
+\end_inset
+
+500 chip and a GEC 575
+\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
+
+385, with
+\begin_inset Formula $B,V,$
+\end_inset
+
+ and
+\begin_inset Formula $R$
+\end_inset
+
+ filters, and an RCA 512
+\begin_inset Formula $\times$
+\end_inset
+
+320, with
+\begin_inset Formula $U,B,V,R,$
+\end_inset
+
+ and
+\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
+
+ or even in
+\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.
+\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
+
+\begin_inset CommandInset citation
+LatexCommand citep
+key "kin68,pet76,har84,ort85"
+literal "false"
+
+\end_inset
+
+, as well as photoelectric profiles
+\begin_inset CommandInset citation
+LatexCommand citep
+key "kin66,kin75"
+literal "false"
+
+\end_inset
+
+ and electronographic profiles
+\begin_inset CommandInset citation
+LatexCommand citep
+key "kro84"
+literal "false"
+
+\end_inset
+
+.
+ In a few cases we judged normality by eye estimates on one of the Sky Surveys.
+\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 Plain Layout
+Footnotes can be inserted like this.
+\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 CommandInset citation
+LatexCommand cite
+key "hag86"
+literal "true"
+
+\end_inset
+
+; we briefly summarize below.
+\end_layout
+
+\begin_layout Subsection
+Formalism
+\end_layout
+
+\begin_layout Standard
+\begin_inset CommandInset label
+LatexCommand label
+name "bozomath"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+A tree-level amplitude in
+\begin_inset Formula $e^{+}e^{-}$
+\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}),
+\end{equation}
+
+\end_inset
+
+ where
+\begin_inset Formula $p$
+\end_inset
+
+ and
+\begin_inset Formula $\sigma$
+\end_inset
+
+ label the initial
+\begin_inset Formula $e^{\pm}$
+\end_inset
+
+ four-momenta and helicities
+\begin_inset Formula $(\sigma=\pm1)$
+\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
+
+ is a chirality projection operator
+\begin_inset Formula $(\tau=\pm1)$
+\end_inset
+
+.
+ The
+\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.
+\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 $\gamma$
+\end_inset
+
+ matrices are expressed in terms of
+\begin_inset Formula $2\times2$
+\end_inset
+
+ Pauli matrices
+\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}
+-1 & 0\\
+0 & 1
+\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}
+0 & (\hat{a})_{+}\\
+(\hat{a})_{-} & 0
+\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}
+(u)_{-}\\
+(u)_{+}
+\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 $\chi_{\lambda}(p)$
+\end_inset
+
+ with
+\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)
+\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}
+I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
+\end{equation}
+
+\end_inset
+
+ where
+\begin_inset Formula
+\[
+d_{1}=\sqrt{\left(\begin{array}{c}
+\frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
+\frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
+\]
+
+\end_inset
+
+
+\begin_inset Formula
+\[
+d_{2}=\sqrt{\left(\begin{array}{c}
+\frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
+\case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
+\]
+
+\end_inset
+
+
+\begin_inset Formula
+\[
+x_{1}=(x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta
+\]
+
+\end_inset
+
+
+\begin_inset Formula
+\[
+y_{1}=-(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In these expressions
+\begin_inset Formula $x_{0}$
+\end_inset
+
+,
+\begin_inset Formula $y_{0}$
+\end_inset
+
+ is the star center, and
+\begin_inset Formula $\Theta$
+\end_inset
+
+ is the angle with the
+\begin_inset Formula $x$
+\end_inset
+
+ axis.
+ Results of this task are shown in table
+\begin_inset space ~
+\end_inset
+
+
+\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 $M_{\text{\sun}}$
+\end_inset
+
+, 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 Preview
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+ion{Ca}{2}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ Roughly
+\begin_inset Formula $\nicefrac{4}{5}$
+\end_inset
+
+ of the electronically submitted abstracts for AAS meetings are error-free.
+
+\end_layout
+
+\begin_layout Acknowledgements
+We are grateful to V.
+ Barger, T.
+ Han, and R.
+ J.
+ N.
+ Phillips for doing the math in section
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "bozomath"
+
+\end_inset
+
+.
+ More information on the AAS\SpecialChar TeX
+ macros package are available at
+\begin_inset Flex URL
+status collapsed
+
+\begin_layout Plain Layout
+
+http://www.aas.org/publications/aastex
+\end_layout
+
+\end_inset
+
+ or the
+\begin_inset CommandInset href
+LatexCommand href
+name "AAS ftp site"
+target "ftp://www.aas.org/pubs/AAS ftp site"
+literal "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Software
+IRAF, AIPS, Astropy, ...
+\end_layout
+
+\begin_layout Appendix
+
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Auri\\`ere(1982)"
+key "aur82"
+literal "true"
+
+\end_inset
+
+Aurière, M.
+ 1982,
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+aap
+\end_layout
+
+\end_inset
+
+, 109, 301
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Canizares et al.(1978)"
+key "can78"
+literal "true"
+
+\end_inset
+
+Canizares, C.
+ R., Grindlay, J.
+ E., Hiltner, W.
+ A., Liller, W., and McClintock, J.
+ E.
+ 1978,
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+apj
+\end_layout
+
+\end_inset
+
+, 224, 39
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Djorgovski and King(1984)"
+key "djo84"
+literal "true"
+
+\end_inset
+
+Djorgovski, S., and King, I.
+ R.
+ 1984,
+\begin_inset Preview
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+apjl
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+, 277, L49
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Hagiwara and Zeppenfeld(1986)"
+key "hag86"
+literal "true"
+
+\end_inset
+
+Hagiwara, K., and Zeppenfeld, D.
+ 1986, Nucl.Phys., 274, 1
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Harris and van den Bergh(1984)"
+key "har84"
+literal "true"
+
+\end_inset
+
+Harris, W.
+ E., and van den Bergh, S.
+ 1984,
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+aj
+\end_layout
+
+\end_inset
+
+, 89, 1816
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "H\\`enon(1961)"
+key "hen61"
+literal "true"
+
+\end_inset
+
+Hénon, M.
+ 1961, Ann.d'Ap., 24, 369
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "King(1966)"
+key "kin66"
+literal "true"
+
+\end_inset
+
+King, I.
+ R.
+ 1966,
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+aj
+\end_layout
+
+\end_inset
+
+, 71, 276
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "King(1975)"
+key "kin75"
+literal "true"
+
+\end_inset
+
+King, I.
+ R.
+ 1975, Dynamics of Stellar Systems, A.
+ Hayli, Dordrecht: Reidel, 1975, 99
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "King et al.(1968)"
+key "kin68"
+literal "true"
+
+\end_inset
+
+King, I.
+ R., Hedemann, E., Hodge, S.
+ M., and White, R.
+ E.
+ 1968,
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+aj
+\end_layout
+
+\end_inset
+
+, 73, 456
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Kron et al.(1984)"
+key "kro84"
+literal "true"
+
+\end_inset
+
+Kron, G.
+ E., Hewitt, A.
+ V., and Wasserman, L.
+ H.
+ 1984,
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+pasp
+\end_layout
+
+\end_inset
+
+, 96, 198
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Lynden-Bell and Wood(1968)"
+key "lyn68"
+literal "true"
+
+\end_inset
+
+Lynden-Bell, D., and Wood, R.
+ 1968,
+\begin_inset Preview
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+mnras
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+, 138, 495
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Newell and O'Neil(1978)"
+key "new78"
+literal "true"
+
+\end_inset
+
+Newell, E.
+ B., and O'Neil, E.
+ J.
+ 1978,
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+apjs
+\end_layout
+
+\end_inset
+
+, 37, 27
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Ortolani et al.(1985)"
+key "ort85"
+literal "true"
+
+\end_inset
+
+Ortolani, S., Rosino, L., and Sandage, A.
+ 1985,
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+aj
+\end_layout
+
+\end_inset
+
+, 90, 473
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Peterson(1976)"
+key "pet76"
+literal "true"
+
+\end_inset
+
+Peterson, C.
+ J.
+ 1976,
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+aj
+\end_layout
+
+\end_inset
+
+, 81, 617
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "Spitzer(1985)"
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+
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+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
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+ 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
+ & Sneden (1988); (9) Gratton & Sneden 1991; (10) Kraft et al.
+ 1982; (11) LCL, or Laird, 1990; (12) Leep & Wallerstein 1981; (13) Luck
+ & Bond 1981; (14) Luck & Bond 1985; (15) Magain 1987; (16) Magain 1989;
+ (17) Peterson 1981; (18) Peterson, Kurucz, & Carney 1990; (19) RMB; (20)
+ Schuster & Nissen 1988; (21) Schuster & Nissen 1989b; (22) Spite et al.
+ 1984; (23) Spite & Spite 1986; (24) Hobbs & Thorburn 1991; (25) Hobbs et
+ al.
+ 1991; (26) Olsen 1983.
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+
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+
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+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
+
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+
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+
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+
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+\end_document
--- /dev/null
+<?xml version="1.0" encoding="UTF-8"?>
+<!-- This DocBook file was created by LyX 2.4.0dev
+ See http://www.lyx.org/ for more information -->
+<article xml:lang="en_US" xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:xi="http://www.w3.org/2001/XInclude" version="5.2">
+<info>
+</info>
+<section>
+<title>Introduction</title>
+<Standard>A focal problem today in the dynamics of globular clusters is core collapse. It has been predicted by theory for decades <biblioref endterm="hen61.lyn68.spi85-0" />, but observation has been less alert to the phenomenon. For many years the central brightness peak in M15 <biblioref endterm="kin75.new78-1" /> seemed a unique anomaly. Then <biblioref endterm="aur82" /> suggested a central peak in NGC 6397, and a limited photographic survey of ours <biblioref endterm="djo84" /> found three more cases, including NGC 6624, whose sharp center had often been remarked on <biblioref endterm="can78" />. </Standard>
+</section>
+<section>
+<title>Observations</title>
+<Standard>All our observations were short direct exposures with CCD's. At Lick Observatory we used a TI 500<inlineequation><alt role='tex'>\times</alt>
+ <m:math>
+
+ <m:mrow><m:mo>×</m:mo>
+ </m:mrow>
+ </m:math></inlineequation>500 chip and a GEC 575<inlineequation><alt role='tex'>\times</alt>
+ <m:math>
+
+ <m:mrow><m:mo>×</m:mo>
+ </m:mrow>
+ </m:math></inlineequation>385, on the 1-m Nickel reflector. The only filter available at Lick was red. At CTIO we used a GEC 575<inlineequation><alt role='tex'>\times</alt>
+ <m:math>
+
+ <m:mrow><m:mo>×</m:mo>
+ </m:mrow>
+ </m:math></inlineequation>385, with <inlineequation><alt role='tex'>B,V,</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow><m:mi>B</m:mi><m:mo>,</m:mo><m:mi>V</m:mi><m:mo>,</m:mo>
+ </m:mrow>
+ </m:mrow>
+ </m:math></inlineequation> and <inlineequation><alt role='tex'>R</alt>
+ <m:math>
+
+ <m:mrow><m:mi>R</m:mi>
+ </m:mrow>
+ </m:math></inlineequation> filters, and an RCA 512<inlineequation><alt role='tex'>\times</alt>
+ <m:math>
+
+ <m:mrow><m:mo>×</m:mo>
+ </m:mrow>
+ </m:math></inlineequation>320, with <inlineequation><alt role='tex'>U,B,V,R,</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow><m:mi>U</m:mi><m:mo>,</m:mo><m:mi>B</m:mi><m:mo>,</m:mo><m:mi>V</m:mi><m:mo>,</m:mo><m:mi>R</m:mi><m:mo>,</m:mo>
+ </m:mrow>
+ </m:mrow>
+ </m:math></inlineequation> and <inlineequation><alt role='tex'>I</alt>
+ <m:math>
+
+ <m:mrow><m:mi>I</m:mi>
+ </m:mrow>
+ </m:math></inlineequation> 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 <inlineequation><alt role='tex'>U</alt>
+ <m:math>
+
+ <m:mrow><m:mi>U</m:mi>
+ </m:mrow>
+ </m:math></inlineequation> or even in <inlineequation><alt role='tex'>B</alt>
+ <m:math>
+
+ <m:mrow><m:mi>B</m:mi>
+ </m:mrow>
+ </m:math></inlineequation>. All four cameras had scales of the order of 0.4 arcsec/pixel, and our field sizes were around 3 arcmin.</Standard>
+<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 <biblioref endterm="kin68.pet76.har84.ort85-2" />, as well as photoelectric profiles <biblioref endterm="kin66.kin75-3" /> and electronographic profiles <biblioref endterm="kro84" />. In a few cases we judged normality by eye estimates on one of the Sky Surveys.</Standard>
+</section>
+<section>
+<title>Helicity Amplitudes</title>
+<Standard>It has been realized that helicity amplitudes provide a convenient means for Feynman diagram<footnote><para>Footnotes can be inserted like this.</para>
+</footnote> 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 <biblioref endterm="hag86" />; we briefly summarize below.</Standard>
+<section>
+<title>Formalism</title>
+<Standard><anchor xml:id="bozomath" /></Standard>
+<Standard>A tree-level amplitude in <inlineequation><alt role='tex'>e^{+}e^{-}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow>
+ <m:msup>
+ <m:mrow><m:mi>e</m:mi>
+ </m:mrow>
+ <m:mrow><m:mo>+</m:mo>
+ </m:mrow>
+ </m:msup>
+ <m:msup>
+ <m:mrow><m:mi>e</m:mi>
+ </m:mrow>
+ <m:mrow><m:mo>-</m:mo>
+ </m:mrow>
+ </m:msup>
+ </m:mrow>
+ </m:mrow>
+ </m:math></inlineequation> collisions can be expressed in terms of fermion strings of the form <informalequation><alt role='tex'>\bar{v}(p_{2},\sigma_{2})P_{-\tau}\hat{a}_{1}\hat{a}_{2}\cdots\hat{a}_{n}u(p_{1},\sigma_{1}),</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow>
+ <m:mover>
+ <m:mrow><m:mi>v</m:mi>
+ </m:mrow><m:mo stretchy="true">¯</m:mo>
+ </m:mover><m:mo form='prefix' fence='true' stretchy='true' symmetric='true'><m:mrow>(</m:mrow></m:mo>
+
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>p</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>2</m:mn>
+ </m:mrow>
+ </m:msub><m:mo>,</m:mo>
+ <m:msub>
+ <m:mrow><m:mi>σ</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>2</m:mn>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+<m:mo form='postfix' fence='true' stretchy='true' symmetric='true'><m:mrow>)</m:mrow></m:mo>
+
+ <m:msub>
+ <m:mrow><m:mi>P</m:mi>
+ </m:mrow>
+ <m:mrow>
+ <m:mrow><m:mo>-</m:mo><m:mi>τ</m:mi>
+ </m:mrow>
+ </m:mrow>
+ </m:msub>
+ <m:msub>
+ <m:mrow>
+ <m:mover>
+ <m:mrow><m:mi>a</m:mi>
+ </m:mrow><m:mo stretchy="true">ˆ</m:mo>
+ </m:mover>
+ </m:mrow>
+ <m:mrow><m:mn>1</m:mn>
+ </m:mrow>
+ </m:msub>
+ <m:msub>
+ <m:mrow>
+ <m:mover>
+ <m:mrow><m:mi>a</m:mi>
+ </m:mrow><m:mo stretchy="true">ˆ</m:mo>
+ </m:mover>
+ </m:mrow>
+ <m:mrow><m:mn>2</m:mn>
+ </m:mrow>
+ </m:msub>
+ <m:mi>⋯
+ </m:mi>
+ <m:msub>
+ <m:mrow>
+ <m:mover>
+ <m:mrow><m:mi>a</m:mi>
+ </m:mrow><m:mo stretchy="true">ˆ</m:mo>
+ </m:mover>
+ </m:mrow>
+ <m:mrow><m:mi>n</m:mi>
+ </m:mrow>
+ </m:msub><m:mi>u</m:mi><m:mo form='prefix' fence='true' stretchy='true' symmetric='true'><m:mrow>(</m:mrow></m:mo>
+
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>p</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>1</m:mn>
+ </m:mrow>
+ </m:msub><m:mo>,</m:mo>
+ <m:msub>
+ <m:mrow><m:mi>σ</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>1</m:mn>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+<m:mo form='postfix' fence='true' stretchy='true' symmetric='true'><m:mrow>)</m:mrow></m:mo>
+<m:mo>,</m:mo>
+ </m:mrow>
+ </m:mrow>
+ </m:math></informalequation> where <inlineequation><alt role='tex'>p</alt>
+ <m:math>
+
+ <m:mrow><m:mi>p</m:mi>
+ </m:mrow>
+ </m:math></inlineequation> and <inlineequation><alt role='tex'>\sigma</alt>
+ <m:math>
+
+ <m:mrow><m:mi>σ</m:mi>
+ </m:mrow>
+ </m:math></inlineequation> label the initial <inlineequation><alt role='tex'>e^{\pm}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:msup>
+ <m:mrow><m:mi>e</m:mi>
+ </m:mrow>
+ <m:mrow><m:mo>±</m:mo>
+ </m:mrow>
+ </m:msup>
+ </m:mrow>
+ </m:math></inlineequation> four-momenta and helicities <inlineequation><alt role='tex'>(\sigma=\pm1)</alt>
+ <m:math>
+
+ <m:mrow><m:mo form='prefix' fence='true' stretchy='true' symmetric='true'><m:mrow>(</m:mrow></m:mo>
+
+ <m:mrow><m:mi>σ</m:mi><m:mo>=</m:mo><m:mo>±</m:mo><m:mn>1</m:mn>
+ </m:mrow>
+<m:mo form='postfix' fence='true' stretchy='true' symmetric='true'><m:mrow>)</m:mrow></m:mo>
+
+ </m:mrow>
+ </m:math></inlineequation>, <inlineequation><alt role='tex'>\hat{a}_{i}=a_{i}^{\mu}\gamma_{\nu}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow>
+ <m:msub>
+ <m:mrow>
+ <m:mover>
+ <m:mrow><m:mi>a</m:mi>
+ </m:mrow><m:mo stretchy="true">ˆ</m:mo>
+ </m:mover>
+ </m:mrow>
+ <m:mrow><m:mi>i</m:mi>
+ </m:mrow>
+ </m:msub><m:mo>=</m:mo>
+ <m:msubsup>
+ <m:mrow><m:mi>a</m:mi>
+ </m:mrow>
+ <m:mrow><m:mi>i</m:mi>
+ </m:mrow>
+ <m:mrow><m:mi>μ</m:mi>
+ </m:mrow>
+ </m:msubsup>
+ <m:msub>
+ <m:mrow><m:mi>γ</m:mi>
+ </m:mrow>
+ <m:mrow><m:mi>ν</m:mi>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:mrow>
+ </m:math></inlineequation> and <inlineequation><alt role='tex'>P_{\tau}=\frac{1}{2}(1+\tau\gamma_{5})</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>P</m:mi>
+ </m:mrow>
+ <m:mrow><m:mi>τ</m:mi>
+ </m:mrow>
+ </m:msub><m:mo>=</m:mo>
+ <m:mfrac>
+ <m:mrow><m:mn>1</m:mn>
+ </m:mrow>
+ <m:mrow><m:mn>2</m:mn>
+ </m:mrow>
+ </m:mfrac><m:mo form='prefix' fence='true' stretchy='true' symmetric='true'><m:mrow>(</m:mrow></m:mo>
+
+ <m:mrow><m:mn>1</m:mn><m:mo>+</m:mo><m:mi>τ</m:mi>
+ <m:msub>
+ <m:mrow><m:mi>γ</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>5</m:mn>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+<m:mo form='postfix' fence='true' stretchy='true' symmetric='true'><m:mrow>)</m:mrow></m:mo>
+
+ </m:mrow>
+ </m:mrow>
+ </m:math></inlineequation> is a chirality projection operator <inlineequation><alt role='tex'>(\tau=\pm1)</alt>
+ <m:math>
+
+ <m:mrow><m:mo form='prefix' fence='true' stretchy='true' symmetric='true'><m:mrow>(</m:mrow></m:mo>
+
+ <m:mrow><m:mi>τ</m:mi><m:mo>=</m:mo><m:mo>±</m:mo><m:mn>1</m:mn>
+ </m:mrow>
+<m:mo form='postfix' fence='true' stretchy='true' symmetric='true'><m:mrow>)</m:mrow></m:mo>
+
+ </m:mrow>
+ </m:math></inlineequation>. The <inlineequation><alt role='tex'>a_{i}^{\mu}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:msubsup>
+ <m:mrow><m:mi>a</m:mi>
+ </m:mrow>
+ <m:mrow><m:mi>i</m:mi>
+ </m:mrow>
+ <m:mrow><m:mi>μ</m:mi>
+ </m:mrow>
+ </m:msubsup>
+ </m:mrow>
+ </m:math></inlineequation> may be formed from particle four-momenta, gauge-boson polarization vectors or fermion strings with an uncontracted Lorentz index associated with final-state fermions.</Standard>
+<NoteToEditor>Figures 1 and 2 should appear side-by-side in print</NoteToEditor>
+<Standard>In the chiral representation the <inlineequation><alt role='tex'>\gamma</alt>
+ <m:math>
+
+ <m:mrow><m:mi>γ</m:mi>
+ </m:mrow>
+ </m:math></inlineequation> matrices are expressed in terms of <inlineequation><alt role='tex'>2\times2</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow><m:mn>2</m:mn><m:mo>×</m:mo><m:mn>2</m:mn>
+ </m:mrow>
+ </m:mrow>
+ </m:math></inlineequation> Pauli matrices <inlineequation><alt role='tex'>\sigma</alt>
+ <m:math>
+
+ <m:mrow><m:mi>σ</m:mi>
+ </m:mrow>
+ </m:math></inlineequation> and the unit matrix 1 as <informalequation><alt role='tex'>\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),\\
+\sigma_{\pm}^{\mu} & = & ({\textbf{1}},\pm\sigma),
+</alt>
+ <m:math>
+
+ <m:mtable>
+ <m:mtr>
+ <m:mtd>
+ <m:msup>
+ <m:mrow><m:mi>γ</m:mi>
+ </m:mrow>
+ <m:mrow><m:mi>μ</m:mi>
+ </m:mrow>
+ </m:msup>
+ </m:mtd>
+ <m:mtd><m:mo>=</m:mo>
+ </m:mtd>
+ <m:mtd>
+ <m:mrow><m:mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(</m:mo>
+ <m:mtable>
+ <m:mtr>
+ <m:mtd><m:mn>0</m:mn>
+ </m:mtd>
+ <m:mtd>
+ <m:msubsup>
+ <m:mrow><m:mi>σ</m:mi>
+ </m:mrow>
+ <m:mrow><m:mo>+</m:mo>
+ </m:mrow>
+ <m:mrow><m:mi>μ</m:mi>
+ </m:mrow>
+ </m:msubsup>
+ </m:mtd>
+ </m:mtr>
+ <m:mtr>
+ <m:mtd>
+ <m:msubsup>
+ <m:mrow><m:mi>σ</m:mi>
+ </m:mrow>
+ <m:mrow><m:mo>-</m:mo>
+ </m:mrow>
+ <m:mrow><m:mi>μ</m:mi>
+ </m:mrow>
+ </m:msubsup>
+ </m:mtd>
+ <m:mtd><m:mn>0</m:mn>
+ </m:mtd>
+ </m:mtr>
+ </m:mtable><m:mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)</m:mo><m:mo>,</m:mo>
+ <m:msup>
+ <m:mrow><m:mi>γ</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>5</m:mn>
+ </m:mrow>
+ </m:msup><m:mo>=</m:mo><m:mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(</m:mo>
+ <m:mtable>
+ <m:mtr>
+ <m:mtd>
+ <m:mrow><m:mo>-</m:mo><m:mn>1</m:mn>
+ </m:mrow>
+ </m:mtd>
+ <m:mtd><m:mn>0</m:mn>
+ </m:mtd>
+ </m:mtr>
+ <m:mtr>
+ <m:mtd><m:mn>0</m:mn>
+ </m:mtd>
+ <m:mtd><m:mn>1</m:mn>
+ </m:mtd>
+ </m:mtr>
+ </m:mtable><m:mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)</m:mo><m:mo>,</m:mo>
+ </m:mrow>
+ </m:mtd>
+ </m:mtr>
+ <m:mtr>
+ <m:mtd>
+ <m:msubsup>
+ <m:mrow><m:mi>σ</m:mi>
+ </m:mrow>
+ <m:mrow><m:mo>±</m:mo>
+ </m:mrow>
+ <m:mrow><m:mi>μ</m:mi>
+ </m:mrow>
+ </m:msubsup>
+ </m:mtd>
+ <m:mtd><m:mo>=</m:mo>
+ </m:mtd>
+ <m:mtd>
+ <m:mrow><m:mo form='prefix' fence='true' stretchy='true' symmetric='true'><m:mrow>(</m:mrow></m:mo>
+
+ <m:mrow>
+ <m:mrow>
+ <m:mstyle mathvariant='bold'><m:mn>1</m:mn>
+ </m:mstyle>
+ </m:mrow><m:mo>,</m:mo><m:mo>±</m:mo><m:mi>σ</m:mi>
+ </m:mrow>
+<m:mo form='postfix' fence='true' stretchy='true' symmetric='true'><m:mrow>)</m:mrow></m:mo>
+<m:mo>,</m:mo>
+ </m:mrow>
+ </m:mtd>
+ </m:mtr>
+ </m:mtable>
+ </m:math></informalequation> giving <informalequation><alt role='tex'>\hat{a}=\left(\begin{array}{cc}
+0 & (\hat{a})_{+}\\
+(\hat{a})_{-} & 0
+\end{array}\right),(\hat{a})_{\pm}=a_{\mu}\sigma_{\pm}^{\mu},</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow>
+ <m:mover>
+ <m:mrow><m:mi>a</m:mi>
+ </m:mrow><m:mo stretchy="true">ˆ</m:mo>
+ </m:mover><m:mo>=</m:mo><m:mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(</m:mo>
+ <m:mtable>
+ <m:mtr>
+ <m:mtd><m:mn>0</m:mn>
+ </m:mtd>
+ <m:mtd>
+ <m:mrow><m:mo>(</m:mo>
+ <m:mover>
+ <m:mrow><m:mi>a</m:mi>
+ </m:mrow><m:mo stretchy="true">ˆ</m:mo>
+ </m:mover>
+ <m:msub>
+ <m:mrow><m:mo>)</m:mo>
+ </m:mrow>
+ <m:mrow><m:mo>+</m:mo>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:mtd>
+ </m:mtr>
+ <m:mtr>
+ <m:mtd>
+ <m:mrow><m:mo>(</m:mo>
+ <m:mover>
+ <m:mrow><m:mi>a</m:mi>
+ </m:mrow><m:mo stretchy="true">ˆ</m:mo>
+ </m:mover>
+ <m:msub>
+ <m:mrow><m:mo>)</m:mo>
+ </m:mrow>
+ <m:mrow><m:mo>-</m:mo>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:mtd>
+ <m:mtd><m:mn>0</m:mn>
+ </m:mtd>
+ </m:mtr>
+ </m:mtable><m:mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)</m:mo><m:mo>,</m:mo><m:mo>(</m:mo>
+ <m:mover>
+ <m:mrow><m:mi>a</m:mi>
+ </m:mrow><m:mo stretchy="true">ˆ</m:mo>
+ </m:mover>
+ <m:msub>
+ <m:mrow><m:mo>)</m:mo>
+ </m:mrow>
+ <m:mrow><m:mo>±</m:mo>
+ </m:mrow>
+ </m:msub><m:mo>=</m:mo>
+ <m:msub>
+ <m:mrow><m:mi>a</m:mi>
+ </m:mrow>
+ <m:mrow><m:mi>μ</m:mi>
+ </m:mrow>
+ </m:msub>
+ <m:msubsup>
+ <m:mrow><m:mi>σ</m:mi>
+ </m:mrow>
+ <m:mrow><m:mo>±</m:mo>
+ </m:mrow>
+ <m:mrow><m:mi>μ</m:mi>
+ </m:mrow>
+ </m:msubsup><m:mo>,</m:mo>
+ </m:mrow>
+ </m:mrow>
+ </m:math></informalequation> The spinors are expressed in terms of two-component Weyl spinors as <informalequation><alt role='tex'>u=\left(\begin{array}{c}
+(u)_{-}\\
+(u)_{+}
+\end{array}\right),v={\textbf{(}}\vdag_{+}{\textbf{,}}\vdag_{-}{\textbf{)}}.</alt>MathML export failed. Please report this as a bug.</informalequation></Standard>
+<Standard>The Weyl spinors are given in terms of helicity eigenstates <inlineequation><alt role='tex'>\chi_{\lambda}(p)</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>χ</m:mi>
+ </m:mrow>
+ <m:mrow><m:mi>λ</m:mi>
+ </m:mrow>
+ </m:msub><m:mo form='prefix' fence='true' stretchy='true' symmetric='true'><m:mrow>(</m:mrow></m:mo>
+<m:mi>p</m:mi>
+<m:mo form='postfix' fence='true' stretchy='true' symmetric='true'><m:mrow>)</m:mrow></m:mo>
+
+ </m:mrow>
+ </m:mrow>
+ </m:math></inlineequation> with <inlineequation><alt role='tex'>\lambda=\pm1</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow><m:mi>λ</m:mi><m:mo>=</m:mo><m:mo>±</m:mo><m:mn>1</m:mn>
+ </m:mrow>
+ </m:mrow>
+ </m:math></inlineequation> by </Standard>
+<MathLetters>
+<informalequation><alt role='tex'>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)
+</alt>
+ <m:math>
+
+ <m:mtable>
+ <m:mtr>
+ <m:mtd>
+ <m:mrow><m:mi>u</m:mi><m:mo>(</m:mo><m:mi>p</m:mi><m:mo>,</m:mo><m:mi>λ</m:mi>
+ <m:msub>
+ <m:mrow><m:mo>)</m:mo>
+ </m:mrow>
+ <m:mrow><m:mo>±</m:mo>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:mtd>
+ <m:mtd><m:mo>=</m:mo>
+ </m:mtd>
+ <m:mtd>
+ <m:mrow><m:mo>(</m:mo><m:mi>E</m:mi><m:mo>±</m:mo><m:mi>λ</m:mi><m:mo>|</m:mo>
+ <m:mrow>
+ <m:mstyle mathvariant='bold'><m:mi>p</m:mi>
+ </m:mstyle>
+ </m:mrow><m:mo>|</m:mo>
+ <m:msup>
+ <m:mrow><m:mo>)</m:mo>
+ </m:mrow>
+ <m:mrow>
+ <m:mrow><m:mn>1</m:mn><m:mo>/</m:mo><m:mn>2</m:mn>
+ </m:mrow>
+ </m:mrow>
+ </m:msup>
+ <m:msub>
+ <m:mrow><m:mi>χ</m:mi>
+ </m:mrow>
+ <m:mrow><m:mi>λ</m:mi>
+ </m:mrow>
+ </m:msub><m:mo form='prefix' fence='true' stretchy='true' symmetric='true'><m:mrow>(</m:mrow></m:mo>
+<m:mi>p</m:mi>
+<m:mo form='postfix' fence='true' stretchy='true' symmetric='true'><m:mrow>)</m:mrow></m:mo>
+<m:mo>,</m:mo>
+ </m:mrow>
+ </m:mtd>
+ </m:mtr>
+ <m:mtr>
+ <m:mtd>
+ <m:mrow><m:mi>v</m:mi><m:mo>(</m:mo><m:mi>p</m:mi><m:mo>,</m:mo><m:mi>λ</m:mi>
+ <m:msub>
+ <m:mrow><m:mo>)</m:mo>
+ </m:mrow>
+ <m:mrow><m:mo>±</m:mo>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:mtd>
+ <m:mtd><m:mo>=</m:mo>
+ </m:mtd>
+ <m:mtd>
+ <m:mrow><m:mo>±</m:mo><m:mi>λ</m:mi><m:mo>(</m:mo><m:mi>E</m:mi><m:mo>∓</m:mo><m:mi>λ</m:mi><m:mo>|</m:mo>
+ <m:mrow>
+ <m:mstyle mathvariant='bold'><m:mi>p</m:mi>
+ </m:mstyle>
+ </m:mrow><m:mo>|</m:mo>
+ <m:msup>
+ <m:mrow><m:mo>)</m:mo>
+ </m:mrow>
+ <m:mrow>
+ <m:mrow><m:mn>1</m:mn><m:mo>/</m:mo><m:mn>2</m:mn>
+ </m:mrow>
+ </m:mrow>
+ </m:msup>
+ <m:msub>
+ <m:mrow><m:mi>χ</m:mi>
+ </m:mrow>
+ <m:mrow>
+ <m:mrow><m:mo>-</m:mo><m:mi>λ</m:mi>
+ </m:mrow>
+ </m:mrow>
+ </m:msub><m:mo form='prefix' fence='true' stretchy='true' symmetric='true'><m:mrow>(</m:mrow></m:mo>
+<m:mi>p</m:mi>
+<m:mo form='postfix' fence='true' stretchy='true' symmetric='true'><m:mrow>)</m:mrow></m:mo>
+
+ </m:mrow>
+ </m:mtd>
+ </m:mtr>
+ </m:mtable>
+ </m:math></informalequation>
+</MathLetters>
+</section>
+</section>
+<section>
+<title>Floating material and so forth</title>
+<Standard>Consider a task that computes profile parameters for a modified Lorentzian of the form <informalequation><alt role='tex'>I=\frac{1}{1+d_{1}^{P(1+d_{2})}}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow><m:mi>I</m:mi><m:mo>=</m:mo>
+ <m:mfrac>
+ <m:mrow><m:mn>1</m:mn>
+ </m:mrow>
+ <m:mrow>
+ <m:mrow><m:mn>1</m:mn><m:mo>+</m:mo>
+ <m:msubsup>
+ <m:mrow><m:mi>d</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>1</m:mn>
+ </m:mrow>
+ <m:mrow>
+ <m:mrow><m:mi>P</m:mi><m:mo form='prefix' fence='true' stretchy='true' symmetric='true'><m:mrow>(</m:mrow></m:mo>
+
+ <m:mrow><m:mn>1</m:mn><m:mo>+</m:mo>
+ <m:msub>
+ <m:mrow><m:mi>d</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>2</m:mn>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+<m:mo form='postfix' fence='true' stretchy='true' symmetric='true'><m:mrow>)</m:mrow></m:mo>
+
+ </m:mrow>
+ </m:mrow>
+ </m:msubsup>
+ </m:mrow>
+ </m:mrow>
+ </m:mfrac>
+ </m:mrow>
+ </m:mrow>
+ </m:math></informalequation> where <informalequation><alt role='tex'>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}}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>d</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>1</m:mn>
+ </m:mrow>
+ </m:msub><m:mo>=</m:mo>
+ <m:msqrt>
+ <m:mrow>
+ <m:msup>
+ <m:mrow><m:mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(</m:mo>
+ <m:mtable>
+ <m:mtr>
+ <m:mtd>
+ <m:mfrac>
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>x</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>1</m:mn>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>R</m:mi>
+ </m:mrow>
+ <m:mrow>
+ <m:mrow><m:mi>m</m:mi><m:mi>a</m:mi><m:mi>j</m:mi>
+ </m:mrow>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:mfrac>
+ </m:mtd>
+ </m:mtr>
+ </m:mtable><m:mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)</m:mo>
+ </m:mrow>
+ <m:mrow><m:mn>2</m:mn>
+ </m:mrow>
+ </m:msup><m:mo>+</m:mo>
+ <m:msup>
+ <m:mrow><m:mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(</m:mo>
+ <m:mtable>
+ <m:mtr>
+ <m:mtd>
+ <m:mfrac>
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>y</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>1</m:mn>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>R</m:mi>
+ </m:mrow>
+ <m:mrow>
+ <m:mrow><m:mi>m</m:mi><m:mi>i</m:mi><m:mi>n</m:mi>
+ </m:mrow>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:mfrac>
+ </m:mtd>
+ </m:mtr>
+ </m:mtable><m:mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)</m:mo>
+ </m:mrow>
+ <m:mrow><m:mn>2</m:mn>
+ </m:mrow>
+ </m:msup>
+ </m:mrow>
+ </m:msqrt>
+ </m:mrow>
+ </m:mrow>
+ </m:math></informalequation><informalequation><alt role='tex'>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}}</alt>MathML export failed. Please report this as a bug.</informalequation><informalequation><alt role='tex'>x_{1}=(x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>x</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>1</m:mn>
+ </m:mrow>
+ </m:msub><m:mo>=</m:mo><m:mo form='prefix' fence='true' stretchy='true' symmetric='true'><m:mrow>(</m:mrow></m:mo>
+
+ <m:mrow><m:mi>x</m:mi><m:mo>-</m:mo>
+ <m:msub>
+ <m:mrow><m:mi>x</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>0</m:mn>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+<m:mo form='postfix' fence='true' stretchy='true' symmetric='true'><m:mrow>)</m:mrow></m:mo>
+<m:mo>cos</m:mo><m:mo>Θ</m:mo><m:mo>+</m:mo><m:mo form='prefix' fence='true' stretchy='true' symmetric='true'><m:mrow>(</m:mrow></m:mo>
+
+ <m:mrow><m:mi>y</m:mi><m:mo>-</m:mo>
+ <m:msub>
+ <m:mrow><m:mi>y</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>0</m:mn>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+<m:mo form='postfix' fence='true' stretchy='true' symmetric='true'><m:mrow>)</m:mrow></m:mo>
+<m:mo>sin</m:mo><m:mo>Θ</m:mo>
+ </m:mrow>
+ </m:mrow>
+ </m:math></informalequation><informalequation><alt role='tex'>y_{1}=-(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>y</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>1</m:mn>
+ </m:mrow>
+ </m:msub><m:mo>=</m:mo><m:mo>-</m:mo><m:mo form='prefix' fence='true' stretchy='true' symmetric='true'><m:mrow>(</m:mrow></m:mo>
+
+ <m:mrow><m:mi>x</m:mi><m:mo>-</m:mo>
+ <m:msub>
+ <m:mrow><m:mi>x</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>0</m:mn>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+<m:mo form='postfix' fence='true' stretchy='true' symmetric='true'><m:mrow>)</m:mrow></m:mo>
+<m:mo>sin</m:mo><m:mo>Θ</m:mo><m:mo>+</m:mo><m:mo form='prefix' fence='true' stretchy='true' symmetric='true'><m:mrow>(</m:mrow></m:mo>
+
+ <m:mrow><m:mi>y</m:mi><m:mo>-</m:mo>
+ <m:msub>
+ <m:mrow><m:mi>y</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>0</m:mn>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+<m:mo form='postfix' fence='true' stretchy='true' symmetric='true'><m:mrow>)</m:mrow></m:mo>
+<m:mo>cos</m:mo><m:mo>Θ</m:mo>
+ </m:mrow>
+ </m:mrow>
+ </m:math></informalequation></Standard>
+<Standard>In these expressions <inlineequation><alt role='tex'>x_{0}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>x</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>0</m:mn>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:math></inlineequation>,<inlineequation><alt role='tex'>y_{0}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>y</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>0</m:mn>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:math></inlineequation> is the star center, and <inlineequation><alt role='tex'>\Theta</alt>
+ <m:math>
+
+ <m:mrow><m:mo>Θ</m:mo>
+ </m:mrow>
+ </m:math></inlineequation> is the angle with the <inlineequation><alt role='tex'>x</alt>
+ <m:math>
+
+ <m:mrow><m:mi>x</m:mi>
+ </m:mrow>
+ </m:math></inlineequation> axis. Results of this task are shown in table <xref linkend="tbl-2" />. It is not clear how these sorts of analyses may affect determination of <inlineequation><alt role='tex'>M_{\text{\sun}}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>M</m:mi>
+ </m:mrow>
+ <m:mrow>
+ <m:mstyle mathvariant='normal'><m:mo>☼</m:mo>
+ </m:mstyle>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:math></inlineequation>, but the assumption is that the alternate results should be less than 90° out of phase with previous values. We have no observations of <!-- \ion{Ca}{2} -->. Roughly <inlineequation><alt role='tex'>\nicefrac{4}{5}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mfrac bevelled='true'>
+ <m:mrow><m:mn>4</m:mn>
+ </m:mrow>
+ <m:mrow><m:mn>5</m:mn>
+ </m:mrow>
+ </m:mfrac>
+ </m:mrow>
+ </m:math></inlineequation> of the electronically submitted abstracts for AAS meetings are error-free. </Standard>
+<Acknowledgements>We are grateful to V. Barger, T. Han, and R. J. N. Phillips for doing the math in section <xref linkend="bozomath" />. More information on the AASTeX macros package are available at <link xlink:href="http://www.aas.org/publications/aastex">http://www.aas.org/publications/aastex</link> or the <link xlink:href="ftp://www.aas.org/pubs/AAS ftp site">AAS ftp site</link>.</Acknowledgements>
+<Software>IRAF, AIPS, Astropy, ...</Software>
+<Appendix></Appendix>
+<bibliography>
+<bibliomixed xml:id='aur82'>Aurière, M. 1982, <!-- \aap -->, 109, 301 </bibliomixed>
+<bibliomixed xml:id='can78'>Canizares, C. R., Grindlay, J. E., Hiltner, W. A., Liller, W., and McClintock, J. E. 1978, <!-- \apj -->, 224, 39 </bibliomixed>
+<bibliomixed xml:id='djo84'>Djorgovski, S., and King, I. R. 1984, <!-- \apjl -->, 277, L49 </bibliomixed>
+<bibliomixed xml:id='hag86'>Hagiwara, K., and Zeppenfeld, D. 1986, Nucl.Phys., 274, 1 </bibliomixed>
+<bibliomixed xml:id='har84'>Harris, W. E., and van den Bergh, S. 1984, <!-- \aj -->, 89, 1816 </bibliomixed>
+<bibliomixed xml:id='hen61'>Hénon, M. 1961, Ann.d'Ap., 24, 369 </bibliomixed>
+<bibliomixed xml:id='kin66'>King, I. R. 1966, <!-- \aj -->, 71, 276 </bibliomixed>
+<bibliomixed xml:id='kin75'>King, I. R. 1975, Dynamics of Stellar Systems, A. Hayli, Dordrecht: Reidel, 1975, 99 </bibliomixed>
+<bibliomixed xml:id='kin68'>King, I. R., Hedemann, E., Hodge, S. M., and White, R. E. 1968, <!-- \aj -->, 73, 456 </bibliomixed>
+<bibliomixed xml:id='kro84'>Kron, G. E., Hewitt, A. V., and Wasserman, L. H. 1984, <!-- \pasp -->, 96, 198 </bibliomixed>
+<bibliomixed xml:id='lyn68'>Lynden-Bell, D., and Wood, R. 1968, <!-- \mnras -->, 138, 495 </bibliomixed>
+<bibliomixed xml:id='new78'>Newell, E. B., and O'Neil, E. J. 1978, <!-- \apjs -->, 37, 27 </bibliomixed>
+<bibliomixed xml:id='ort85'>Ortolani, S., Rosino, L., and Sandage, A. 1985, <!-- \aj -->, 90, 473 </bibliomixed>
+<bibliomixed xml:id='pet76'>Peterson, C. J. 1976, <!-- \aj -->, 81, 617 </bibliomixed>
+<bibliomixed xml:id='spi85'>Spitzer, L. 1985, Dynamics of Star Clusters, J. Goodman and P. Hut, Dordrecht: Reidel, 109 </bibliomixed>
+<bibliomixed>
+</bibliomixed>
+<bibliomixed><table xml:id="tbl-2">
+<caption>Terribly relevant tabular information.</caption>
+
+<tbody>
+<tr>
+<td align='center' valign='top'>Star </td>
+<td align='right' valign='top'> Height </td>
+<td align='right' valign='top'> <inlineequation><alt role='tex'>d_{x}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>d</m:mi>
+ </m:mrow>
+ <m:mrow><m:mi>x</m:mi>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:math></inlineequation></td>
+<td align='right' valign='top'> <inlineequation><alt role='tex'>d_{y}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>d</m:mi>
+ </m:mrow>
+ <m:mrow><m:mi>y</m:mi>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:math></inlineequation></td>
+<td align='right' valign='top'> <inlineequation><alt role='tex'>n</alt>
+ <m:math>
+
+ <m:mrow><m:mi>n</m:mi>
+ </m:mrow>
+ </m:math></inlineequation></td>
+<td align='right' valign='top'> <inlineequation><alt role='tex'>\chi^{2}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:msup>
+ <m:mrow><m:mi>χ</m:mi>
+ </m:mrow>
+ <m:mrow><m:mn>2</m:mn>
+ </m:mrow>
+ </m:msup>
+ </m:mrow>
+ </m:math></inlineequation></td>
+<td align='right' valign='top'> <inlineequation><alt role='tex'>R_{maj}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>R</m:mi>
+ </m:mrow>
+ <m:mrow>
+ <m:mrow><m:mi>m</m:mi><m:mi>a</m:mi><m:mi>j</m:mi>
+ </m:mrow>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:math></inlineequation></td>
+<td align='right' valign='top'> <inlineequation><alt role='tex'>R_{min}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:msub>
+ <m:mrow><m:mi>R</m:mi>
+ </m:mrow>
+ <m:mrow>
+ <m:mrow><m:mi>m</m:mi><m:mi>i</m:mi><m:mi>n</m:mi>
+ </m:mrow>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:math></inlineequation></td>
+<td align='center' valign='top' colspan='1'><inlineequation><alt role='tex'>P</alt>
+ <m:math>
+
+ <m:mrow><m:mi>P</m:mi>
+ </m:mrow>
+ </m:math></inlineequation>a</td>
+<td align='right' valign='top'> <inlineequation><alt role='tex'>PR_{maj}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow><m:mi>P</m:mi>
+ <m:msub>
+ <m:mrow><m:mi>R</m:mi>
+ </m:mrow>
+ <m:mrow>
+ <m:mrow><m:mi>m</m:mi><m:mi>a</m:mi><m:mi>j</m:mi>
+ </m:mrow>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:mrow>
+ </m:math></inlineequation></td>
+<td align='right' valign='top'> <inlineequation><alt role='tex'>PR_{min}</alt>
+ <m:math>
+
+ <m:mrow>
+ <m:mrow><m:mi>P</m:mi>
+ <m:msub>
+ <m:mrow><m:mi>R</m:mi>
+ </m:mrow>
+ <m:mrow>
+ <m:mrow><m:mi>m</m:mi><m:mi>i</m:mi><m:mi>n</m:mi>
+ </m:mrow>
+ </m:mrow>
+ </m:msub>
+ </m:mrow>
+ </m:mrow>
+ </m:math></inlineequation></td>
+<td align='center' valign='top' colspan='1'><inlineequation><alt role='tex'>\Theta</alt>
+ <m:math>
+
+ <m:mrow><m:mo>Θ</m:mo>
+ </m:mrow>
+ </m:math></inlineequation>b</td>
+<td align='center' valign='top'>Ref.</td>
+</tr>
+<tr>
+<td align='center' valign='top'><!-- \tableline\tableline -->1 </td>
+<td align='right' valign='top'>33472.5 </td>
+<td align='right' valign='top'>-0.1 </td>
+<td align='right' valign='top'>0.4 </td>
+<td align='right' valign='top'>53 </td>
+<td align='right' valign='top'>27.4 </td>
+<td align='right' valign='top'>2.065 </td>
+<td align='right' valign='top'>1.940 </td>
+<td align='right' valign='top'>3.900 </td>
+<td align='right' valign='top'>68.3 </td>
+<td align='right' valign='top'>116.2 </td>
+<td align='right' valign='top'>-27.639</td>
+<td align='center' valign='top'>1,2</td>
+</tr>
+<tr>
+<td align='center' valign='top'> 2 </td>
+<td align='right' valign='top'>27802.4 </td>
+<td align='right' valign='top'>-0.3 </td>
+<td align='right' valign='top'>-0.2 </td>
+<td align='right' valign='top'>60 </td>
+<td align='right' valign='top'>3.7 </td>
+<td align='right' valign='top'>1.628 </td>
+<td align='right' valign='top'>1.510 </td>
+<td align='right' valign='top'>2.156 </td>
+<td align='right' valign='top'>6.8 </td>
+<td align='right' valign='top'>7.5 </td>
+<td align='right' valign='top'>-26.764</td>
+<td align='center' valign='top'>3</td>
+</tr>
+<tr>
+<td align='center' valign='top'> 3 </td>
+<td align='right' valign='top'>29210.6 </td>
+<td align='right' valign='top'>0.9 </td>
+<td align='right' valign='top'>0.3 </td>
+<td align='right' valign='top'>60 </td>
+<td align='right' valign='top'>3.4 </td>
+<td align='right' valign='top'>1.622 </td>
+<td align='right' valign='top'>1.551 </td>
+<td align='right' valign='top'>2.159 </td>
+<td align='right' valign='top'>6.7 </td>
+<td align='right' valign='top'>7.3 </td>
+<td align='right' valign='top'>-40.272</td>
+<td align='center' valign='top'>4</td>
+</tr>
+<tr>
+<td align='center' valign='top'> 4 </td>
+<td align='right' valign='top'>32733.8 </td>
+<td align='right' valign='top'>-1.2c</td>
+<td align='right' valign='top'>-0.5 </td>
+<td align='right' valign='top'>41 </td>
+<td align='right' valign='top'>54.8 </td>
+<td align='right' valign='top'>2.282 </td>
+<td align='right' valign='top'>2.156 </td>
+<td align='right' valign='top'>4.313 </td>
+<td align='right' valign='top'>117.4 </td>
+<td align='right' valign='top'>78.2 </td>
+<td align='right' valign='top'>-35.847</td>
+<td align='center' valign='top'>5,6</td>
+</tr>
+<tr>
+<td align='center' valign='top'> 5 </td>
+<td align='right' valign='top'> 9607.4 </td>
+<td align='right' valign='top'>-0.4 </td>
+<td align='right' valign='top'>-0.4 </td>
+<td align='right' valign='top'>60 </td>
+<td align='right' valign='top'>1.4 </td>
+<td align='right' valign='top'>1.669c</td>
+<td align='right' valign='top'>1.574 </td>
+<td align='right' valign='top'>2.343 </td>
+<td align='right' valign='top'>8.0 </td>
+<td align='right' valign='top'>8.9 </td>
+<td align='right' valign='top'>-33.417</td>
+<td align='center' valign='top'>7</td>
+</tr>
+<tr>
+<td align='center' valign='top'> 6 </td>
+<td align='right' valign='top'>31638.6 </td>
+<td align='right' valign='top'>1.6 </td>
+<td align='right' valign='top'>0.1 </td>
+<td align='right' valign='top'>39 </td>
+<td align='right' valign='top'>315.2 </td>
+<td align='right' valign='top'> 3.433 </td>
+<td align='right' valign='top'>3.075 </td>
+<td align='right' valign='top'>7.488 </td>
+<td align='right' valign='top'>92.1 </td>
+<td align='right' valign='top'>25.3 </td>
+<td align='right' valign='top'>-12.052 </td>
+<td align='center' valign='top'>8</td>
+</tr>
+</tbody>
+<Table note>a<!-- }{ -->Sample footnote for table <xref linkend="tbl-2" /> that was generated with the LaTeX table environment</Table note>
+<Table note>b<!-- }{ -->Yet another sample footnote for table <xref linkend="tbl-2" /></Table note>
+<Table note>c<!-- }{ -->Another sample footnote for table <xref linkend="tbl-2" /></Table note>
+<TableComments>We can also attach a long-ish paragraph of explanatory material to a table. Use \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 have not.</TableComments>
+<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 & Sneden (1988); (9) Gratton & Sneden 1991; (10) Kraft et al. 1982; (11) LCL, or Laird, 1990; (12) Leep & Wallerstein 1981; (13) Luck & Bond 1981; (14) Luck & Bond 1985; (15) Magain 1987; (16) Magain 1989; (17) Peterson 1981; (18) Peterson, Kurucz, & Carney 1990; (19) RMB; (20) Schuster & Nissen 1988; (21) Schuster & Nissen 1989b; (22) Spite et al. 1984; (23) Spite & Spite 1986; (24) Hobbs & Thorburn 1991; (25) Hobbs et al. 1991; (26) Olsen 1983.</TableRefs>
+</table>
+</bibliomixed>
+
+
+</bibliography>
+</section>
+
+</article>
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projects / features.git / commitdiff