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6 \origin /systemlyxdir/examples/
9 \newcommand{\myemail}{skywalker@galaxy.far.far.away}
10 %\slugcomment{Not to appear in Nonlearned J., 45.}
11 \shorttitle{Djorgovski et al.}
12 \shortauthors{Collapsed Cores in Globular Clusters}
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48 \use_package mathdots 1
49 \use_package mathtools 1
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55 \cite_engine_type authoryear
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70 \paragraph_separation indent
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88 \begin_layout Standard
89 \begin_inset Note Note
92 \begin_layout Plain Layout
95 Sample document for contributions to journals of the American Astronomical
98 \begin_inset CommandInset href
100 name "AASTeX user guide"
101 target "http://journals.aas.org/authors/aastex/aasguide.html"
106 for details on how to use AASTeX.
110 \begin_layout Plain Layout
113 An up-to-date sample LaTeX article using AASTeX is available under
114 \begin_inset Flex URL
117 \begin_layout Plain Layout
119 http://journals.aas.org/authors/aastex/aastex.html#_download
130 \begin_inset Note Note
133 \begin_layout Plain Layout
136 The AASTeX document class uses a different name since version 6.0 (2016/02/16).
137 Depending on the version installed on your system, set the document class
138 to American Astronomical Society (AASTeX v.
139 6) or American Astronomical Society (AASTeX v.
144 \begin_layout Plain Layout
149 \begin_inset Flex URL
152 \begin_layout Plain Layout
154 http://journals.aas.org/authors/aastex/revisionhistory.html
159 ) are only partially supported by LyX (see
160 \begin_inset Flex URL
163 \begin_layout Plain Layout
165 https://www.lyx.org/trac/ticket/10027
179 Collapsed Cores in Globular Clusters, Gauge-Boson Couplings, and AAS\SpecialChar TeX
185 Djorgovski and Ivan R.
189 \begin_layout Affiliation
190 Astronomy Department, University of California, Berkeley, CA 94720
193 \begin_layout Altaffilation
195 \begin_inset Newline newline
198 Cerro Tololo Inter-American Observatory.
199 \begin_inset Newline newline
202 CTIO is operated by AURA Inc.
203 \begin_inset space \space{}
206 under contract to the National Science Foundation.
209 \begin_layout Altaffilation
210 Society of Fellows, Harvard University.
213 \begin_layout Altaffilation
214 present address: Center for Astrophysics
215 \begin_inset Newline newline
218 60 Garden Street, Cambridge, MA 02138
227 \begin_layout Affiliation
228 National Optical Astronomy Observatories, Tucson, AZ 85719
231 \begin_layout Altaffilation
232 Visiting Programmer, Space Telescope Science Institute
235 \begin_layout Altaffilation
236 Patron, Alonso's Bar and Grill
249 \begin_layout Affiliation
250 Space Telescope Science Institute, Baltimore, MD 21218
253 \begin_layout Altaffilation
254 Patron, Alonso's Bar and Grill
257 \begin_layout Abstract
258 This is a preliminary report on surface photometry of the major fraction
259 of known globular clusters, to see which of them show the signs of a collapsed
261 We also explore some diversionary mathematics and recreational tables.
265 \begin_layout Keywords
266 clusters: globular, peanut—bosons: bozos
269 \begin_layout Section
273 \begin_layout Standard
274 A focal problem today in the dynamics of globular clusters is core collapse.
275 It has been predicted by theory for decades
276 \begin_inset CommandInset citation
278 key "hen61,lyn68,spi85"
283 , but observation has been less alert to the phenomenon.
284 For many years the central brightness peak in M15
285 \begin_inset CommandInset citation
292 seemed a unique anomaly.
294 \begin_inset CommandInset citation
301 suggested a central peak in NGC 6397, and a limited photographic survey
306 \begin_layout Plain Layout
310 citep[Paper I]{djo84}
315 found three more cases, including NGC 6624, whose sharp center had often
317 \begin_inset CommandInset citation
328 \begin_layout Section
332 \begin_layout Standard
333 All our observations were short direct exposures with CCD's.
334 At Lick Observatory we used a TI 500
335 \begin_inset Formula $\times$
338 500 chip and a GEC 575
339 \begin_inset Formula $\times$
342 385, on the 1-m Nickel reflector.
343 The only filter available at Lick was red.
344 At CTIO we used a GEC 575
345 \begin_inset Formula $\times$
349 \begin_inset Formula $B,V,$
353 \begin_inset Formula $R$
356 filters, and an RCA 512
357 \begin_inset Formula $\times$
361 \begin_inset Formula $U,B,V,R,$
365 \begin_inset Formula $I$
368 filters, on the 1.5-m reflector.
369 In the CTIO observations we tried to concentrate on the shortest practicable
370 wavelengths; but faintness, reddening, and poor short-wavelength sensitivity
371 often kept us from observing in
372 \begin_inset Formula $U$
376 \begin_inset Formula $B$
380 All four cameras had scales of the order of 0.4 arcsec/pixel, and our field
381 sizes were around 3 arcmin.
384 \begin_layout Standard
385 The CCD images are unfortunately not always suitable, for very poor clusters
386 or for clusters with large cores.
387 Since the latter are easily studied by other means, we augmented our own
388 CCD profiles by collecting from the literature a number of star-count profiles
390 \begin_inset CommandInset citation
392 key "kin68,pet76,har84,ort85"
397 , as well as photoelectric profiles
398 \begin_inset CommandInset citation
405 and electronographic profiles
406 \begin_inset CommandInset citation
414 In a few cases we judged normality by eye estimates on one of the Sky Surveys.
417 \begin_layout Section
421 \begin_layout Standard
422 It has been realized that helicity amplitudes provide a convenient means
427 \begin_layout Plain Layout
428 Footnotes can be inserted like this.
434 These amplitude-level techniques are particularly convenient for calculations
435 involving many Feynman diagrams, where the usual trace techniques for the
436 amplitude squared becomes unwieldy.
437 Our calculations use the helicity techniques developed by other authors
439 \begin_inset CommandInset citation
446 ; we briefly summarize below.
449 \begin_layout Subsection
453 \begin_layout Standard
454 \begin_inset CommandInset label
463 \begin_layout Standard
464 A tree-level amplitude in
465 \begin_inset Formula $e^{+}e^{-}$
468 collisions can be expressed in terms of fermion strings of the form
471 \bar{v}(p_{2},\sigma_{2})P_{-\tau}\hat{a}_{1}\hat{a}_{2}\cdots\hat{a}_{n}u(p_{1},\sigma_{1}),
477 \begin_inset Formula $p$
481 \begin_inset Formula $\sigma$
485 \begin_inset Formula $e^{\pm}$
488 four-momenta and helicities
489 \begin_inset Formula $(\sigma=\pm1)$
493 \begin_inset Formula $\hat{a}_{i}=a_{i}^{\mu}\gamma_{\nu}$
497 \begin_inset Formula $P_{\tau}=\frac{1}{2}(1+\tau\gamma_{5})$
500 is a chirality projection operator
501 \begin_inset Formula $(\tau=\pm1)$
506 \begin_inset Formula $a_{i}^{\mu}$
509 may be formed from particle four-momenta, gauge-boson polarization vectors
510 or fermion strings with an uncontracted Lorentz index associated with final-sta
514 \begin_layout NoteToEditor
515 Figures 1 and 2 should appear side-by-side in print
518 \begin_layout Standard
519 In the chiral representation the
520 \begin_inset Formula $\gamma$
523 matrices are expressed in terms of
524 \begin_inset Formula $2\times2$
528 \begin_inset Formula $\sigma$
531 and the unit matrix 1 as
534 \gamma^{\mu} & = & \left(\begin{array}{cc}
535 0 & \sigma_{+}^{\mu}\\
537 \end{array}\right),\gamma^{5}=\left(\begin{array}{cc}
540 \end{array}\right),\\
541 \sigma_{\pm}^{\mu} & = & ({\textbf{1}},\pm\sigma),
549 \hat{a}=\left(\begin{array}{cc}
552 \end{array}\right),(\hat{a})_{\pm}=a_{\mu}\sigma_{\pm}^{\mu},
557 The spinors are expressed in terms of two-component Weyl spinors as
560 u=\left(\begin{array}{c}
563 \end{array}\right),v={\textbf{(}}\vdag_{+}{\textbf{,}}\vdag_{-}{\textbf{)}}.
571 \begin_layout Standard
572 The Weyl spinors are given in terms of helicity eigenstates
573 \begin_inset Formula $\chi_{\lambda}(p)$
577 \begin_inset Formula $\lambda=\pm1$
583 \begin_layout MathLetters
586 u(p,\lambda)_{\pm} & = & (E\pm\lambda|{\textbf{p}}|)^{1/2}\chi_{\lambda}(p),\\
587 v(p,\lambda)_{\pm} & = & \pm\lambda(E\mp\lambda|{\textbf{p}}|)^{1/2}\chi_{-\lambda}(p)
595 \begin_layout Section
596 Floating material and so forth
599 \begin_layout Standard
600 Consider a task that computes profile parameters for a modified Lorentzian
604 I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
612 d_{1}=\sqrt{\left(\begin{array}{c}
613 \frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
614 \frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
622 d_{2}=\sqrt{\left(\begin{array}{c}
623 \frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
624 \case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
632 x_{1}=(x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta
640 y_{1}=-(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
648 \begin_layout Standard
650 \begin_inset Formula $x_{0}$
654 \begin_inset Formula $y_{0}$
657 is the star center, and
658 \begin_inset Formula $\Theta$
661 is the angle with the
662 \begin_inset Formula $x$
666 Results of this task are shown in table
671 \begin_inset CommandInset ref
678 It is not clear how these sorts of analyses may affect determination of
680 \begin_inset Formula $M_{\text{\sun}}$
683 , but the assumption is that the alternate results should be less than 90°
684 out of phase with previous values.
685 We have no observations of
689 \begin_layout Plain Layout
700 \begin_inset Formula $\nicefrac{4}{5}$
703 of the electronically submitted abstracts for AAS meetings are error-free.
707 \begin_layout Acknowledgements
708 We are grateful to V.
713 Phillips for doing the math in section
718 \begin_inset CommandInset ref
725 More information on the AAS\SpecialChar TeX
726 macros package are available at
727 \begin_inset Flex URL
730 \begin_layout Plain Layout
732 http://www.aas.org/publications/aastex
741 \begin_layout Plain Layout
750 ftp://www.aas.org/pubs/
754 \begin_layout Plain Layout
765 \begin_layout Plain Layout
776 \begin_layout Software
777 IRAF, AIPS, Astropy, ...
781 \begin_layout Appendix
785 \begin_layout Section
789 \begin_layout Standard
790 Consider once again a task that computes profile parameters for a modified
791 Lorentzian of the form
794 I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
802 \begin_layout MathLetters
805 d_{1}=\frac{3}{4}\sqrt{\left(\begin{array}{c}
806 \frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
807 \frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
815 d_{2}=\case{3}{4}\sqrt{\left(\begin{array}{c}
816 \frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
817 \case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
825 x_{1} & = & (x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta\\
826 y_{1} & = & -(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
834 \begin_layout Standard
835 For completeness, here is one last equation.
847 \begin_layout References
848 \begin_inset CommandInset bibitem
850 label "Auri\\`ere(1982)"
861 \begin_layout Plain Layout
873 \begin_layout References
874 \begin_inset CommandInset bibitem
876 label "Canizares et al.(1978)"
885 A., Liller, W., and McClintock, J.
891 \begin_layout Plain Layout
903 \begin_layout References
904 \begin_inset CommandInset bibitem
906 label "Djorgovski and King(1984)"
912 Djorgovski, S., and King, I.
918 \begin_layout Plain Layout
930 \begin_layout References
931 \begin_inset CommandInset bibitem
933 label "Hagiwara and Zeppenfeld(1986)"
939 Hagiwara, K., and Zeppenfeld, D.
940 1986, Nucl.Phys., 274, 1
943 \begin_layout References
944 \begin_inset CommandInset bibitem
946 label "Harris and van den Bergh(1984)"
953 E., and van den Bergh, S.
958 \begin_layout Plain Layout
970 \begin_layout References
971 \begin_inset CommandInset bibitem
973 label "H\\`enon(1961)"
980 1961, Ann.d'Ap., 24, 369
983 \begin_layout References
984 \begin_inset CommandInset bibitem
998 \begin_layout Plain Layout
1010 \begin_layout References
1011 \begin_inset CommandInset bibitem
1012 LatexCommand bibitem
1021 1975, Dynamics of Stellar Systems, A.
1022 Hayli, Dordrecht: Reidel, 1975, 99
1025 \begin_layout References
1026 \begin_inset CommandInset bibitem
1027 LatexCommand bibitem
1028 label "King et al.(1968)"
1035 R., Hedemann, E., Hodge, S.
1042 \begin_layout Plain Layout
1054 \begin_layout References
1055 \begin_inset CommandInset bibitem
1056 LatexCommand bibitem
1057 label "Kron et al.(1984)"
1065 V., and Wasserman, L.
1071 \begin_layout Plain Layout
1083 \begin_layout References
1084 \begin_inset CommandInset bibitem
1085 LatexCommand bibitem
1086 label "Lynden-Bell and Wood(1968)"
1092 Lynden-Bell, D., and Wood, R.
1097 \begin_layout Plain Layout
1109 \begin_layout References
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1111 LatexCommand bibitem
1112 label "Newell and O'Neil(1978)"
1125 \begin_layout Plain Layout
1137 \begin_layout References
1138 \begin_inset CommandInset bibitem
1139 LatexCommand bibitem
1140 label "Ortolani et al.(1985)"
1146 Ortolani, S., Rosino, L., and Sandage, A.
1151 \begin_layout Plain Layout
1163 \begin_layout References
1164 \begin_inset CommandInset bibitem
1165 LatexCommand bibitem
1166 label "Peterson(1976)"
1178 \begin_layout Plain Layout
1190 \begin_layout References
1191 \begin_inset CommandInset bibitem
1192 LatexCommand bibitem
1193 label "Spitzer(1985)"
1200 1985, Dynamics of Star Clusters, J.
1202 Hut, Dordrecht: Reidel, 109
1205 \begin_layout Standard
1206 \begin_inset Newpage clearpage
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1240 This is an example of a long figure caption that must be set as a paragraph.
1241 The processor has to buffer the text of the caption, so it is good not
1242 to be too wordy, but that would make for poor communication as well.
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1288 \begin_layout Plain Layout
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2226 <cell alignment="right" valignment="top" usebox="none">
2229 \begin_layout Plain Layout
2235 <cell alignment="right" valignment="top" usebox="none">
2238 \begin_layout Plain Layout
2244 <cell alignment="right" valignment="top" usebox="none">
2247 \begin_layout Plain Layout
2261 \begin_layout Table note
2266 \begin_layout Plain Layout
2273 Sample footnote for table
2274 \begin_inset space ~
2278 \begin_inset CommandInset ref
2284 that was generated with the \SpecialChar LaTeX
2288 \begin_layout Table note
2293 \begin_layout Plain Layout
2300 Yet another sample footnote for table
2301 \begin_inset space ~
2305 \begin_inset CommandInset ref
2314 \begin_layout Table note
2319 \begin_layout Plain Layout
2326 Another sample footnote for table
2327 \begin_inset space ~
2331 \begin_inset CommandInset ref
2340 \begin_layout TableComments
2341 We can also attach a long-ish paragraph of explanatory material to a table.
2344 tablerefs to append a list of references.
2345 The following references were from a different table: I've patched them
2346 in here to show how they look, but don't take them too seriously—I certainly
2350 \begin_layout TableRefs
2351 (1) Barbuy, Spite, & Spite 1985; (2) Bond 1980; (3) Carbon et al.
2352 1987; (4) Hobbs & Duncan 1987; (5) Gilroy et al.
2353 1988: (6) Gratton & Ortolani 1986; (7) Gratton & Sneden 1987; (8) Gratton
2354 & Sneden (1988); (9) Gratton & Sneden 1991; (10) Kraft et al.
2355 1982; (11) LCL, or Laird, 1990; (12) Leep & Wallerstein 1981; (13) Luck
2356 & Bond 1981; (14) Luck & Bond 1985; (15) Magain 1987; (16) Magain 1989;
2357 (17) Peterson 1981; (18) Peterson, Kurucz, & Carney 1990; (19) RMB; (20)
2358 Schuster & Nissen 1988; (21) Schuster & Nissen 1989b; (22) Spite et al.
2359 1984; (23) Spite & Spite 1986; (24) Hobbs & Thorburn 1991; (25) Hobbs et
2361 1991; (26) Olsen 1983.
2369 \begin_layout Standard
2370 \begin_inset Note Note
2373 \begin_layout Plain Layout
2374 LyX can load deluxetable files verbatim.
2375 To see this in action, dissolve the following Note and copy the file table.tex
2376 from the AASTeX 5.0 distribution into the same directory as this file.
2384 \begin_layout Standard
2385 \begin_inset Note Note
2388 \begin_layout Plain Layout
2389 \begin_inset CommandInset include