1 #LyX 2.3 created this file. For more info see http://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/examples/
9 \newcommand{\vdag}{(v)^\dagger}
10 \newcommand{\myemail}{skywalker@galaxy.far.far.away}
11 \slugcomment{Not to appear in Nonlearned J., 45.}
12 \shorttitle{Djorgovski et al.}
13 \shortauthors{Collapsed Cores in Globular Clusters}
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69 \paragraph_separation indent
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87 \begin_layout Standard
88 \begin_inset Note Note
91 \begin_layout Plain Layout
94 Sample document for contributions to journals of the American Astronomical
97 \begin_inset CommandInset href
99 name "AASTeX user guide"
100 target "http://journals.aas.org/authors/aastex/aasguide.html"
105 for details on how to use AASTeX.
109 \begin_layout Plain Layout
112 An up-to-date sample LaTeX article using AASTeX is available under
113 \begin_inset Flex URL
116 \begin_layout Plain Layout
118 http://journals.aas.org/authors/aastex/aastex.html#_download
129 \begin_inset Note Note
132 \begin_layout Plain Layout
135 The AASTeX document class uses a different name since version 6.0 (2016/02/16).
136 Depending on the version installed on your system, set the document class
137 to American Astronomical Society (AASTeX v.
138 6) or American Astronomical Society (AASTeX v.
143 \begin_layout Plain Layout
148 \begin_inset Flex URL
151 \begin_layout Plain Layout
153 http://journals.aas.org/authors/aastex/revisionhistory.html
158 ) are only partially supported by LyX (see
159 \begin_inset Flex URL
162 \begin_layout Plain Layout
164 https://www.lyx.org/trac/ticket/10027
178 Collapsed Cores in Globular Clusters, Gauge-Boson Couplings, and AAS\SpecialChar TeX
185 \begin_inset Flex altaffilmark
188 \begin_layout Plain Layout
196 \begin_inset Flex altaffilmark
199 \begin_layout Plain Layout
208 \begin_layout Affiliation
209 Astronomy Department, University of California, Berkeley, CA 94720
216 \begin_inset Flex altaffilmark
219 \begin_layout Plain Layout
228 \begin_layout Affiliation
229 National Optical Astronomy Observatories, Tucson, AZ 85719
244 \begin_inset Flex altaffilmark
247 \begin_layout Plain Layout
256 \begin_layout Affiliation
257 Space Telescope Science Institute, Baltimore, MD 21218
260 \begin_layout Altaffilation
261 \begin_inset Argument 1
264 \begin_layout Plain Layout
271 Visiting Astronomer, Cerro Tololo Inter-American Observatory.
272 CTIO is operated by AURA, Inc.
273 \begin_inset space \space{}
276 under contract to the National Science Foundation.
279 \begin_layout Altaffilation
280 \begin_inset Argument 1
283 \begin_layout Plain Layout
290 Society of Fellows, Harvard University.
293 \begin_layout Altaffilation
294 \begin_inset Argument 1
297 \begin_layout Plain Layout
304 present address: Center for Astrophysics, 60 Garden Street, Cambridge, MA
308 \begin_layout Altaffilation
309 \begin_inset Argument 1
312 \begin_layout Plain Layout
319 Visiting Programmer, Space Telescope Science Institute
322 \begin_layout Altaffilation
323 \begin_inset Argument 1
326 \begin_layout Plain Layout
333 Patron, Alonso's Bar and Grill
336 \begin_layout Abstract
337 This is a preliminary report on surface photometry of the major fraction
338 of known globular clusters, to see which of them show the signs of a collapsed
340 We also explore some diversionary mathematics and recreational tables.
344 \begin_layout Keywords
345 clusters: globular, peanut—bosons: bozos
348 \begin_layout Section
352 \begin_layout Standard
353 A focal problem today in the dynamics of globular clusters is core collapse.
354 It has been predicted by theory for decades
358 \begin_layout Plain Layout
362 citep{hen61,lyn68,spi85}
367 , but observation has been less alert to the phenomenon.
368 For many years the central brightness peak in M15
372 \begin_layout Plain Layout
381 seemed a unique anomaly.
386 \begin_layout Plain Layout
395 suggested a central peak in NGC 6397, and a limited photographic survey
400 \begin_layout Plain Layout
404 citep[Paper I]{djo84}
409 found three more cases, including NGC 6624, whose sharp center had often
414 \begin_layout Plain Layout
427 \begin_layout Section
431 \begin_layout Standard
432 All our observations were short direct exposures with CCD's.
433 At Lick Observatory we used a TI 500
434 \begin_inset Formula $\times$
437 500 chip and a GEC 575
438 \begin_inset Formula $\times$
441 385, on the 1-m Nickel reflector.
442 The only filter available at Lick was red.
443 At CTIO we used a GEC 575
444 \begin_inset Formula $\times$
448 \begin_inset Formula $B,V,$
452 \begin_inset Formula $R$
455 filters, and an RCA 512
456 \begin_inset Formula $\times$
460 \begin_inset Formula $U,B,V,R,$
464 \begin_inset Formula $I$
467 filters, on the 1.5-m reflector.
468 In the CTIO observations we tried to concentrate on the shortest practicable
469 wavelengths; but faintness, reddening, and poor short-wavelength sensitivity
470 often kept us from observing in
471 \begin_inset Formula $U$
475 \begin_inset Formula $B$
479 All four cameras had scales of the order of 0.4 arcsec/pixel, and our field
480 sizes were around 3 arcmin.
483 \begin_layout Standard
484 The CCD images are unfortunately not always suitable, for very poor clusters
485 or for clusters with large cores.
486 Since the latter are easily studied by other means, we augmented our own
487 CCD profiles by collecting from the literature a number of star-count profiles
492 \begin_layout Plain Layout
496 citep{kin68,pet76,har84,ort85}
501 , as well as photoelectric profiles
505 \begin_layout Plain Layout
514 and electronographic profiles
518 \begin_layout Plain Layout
528 In a few cases we judged normality by eye estimates on one of the Sky Surveys.
531 \begin_layout Section
535 \begin_layout Standard
536 It has been realized that helicity amplitudes provide a convenient means
541 \begin_layout Plain Layout
542 Footnotes can be inserted like this.
548 These amplitude-level techniques are particularly convenient for calculations
549 involving many Feynman diagrams, where the usual trace techniques for the
550 amplitude squared becomes unwieldy.
551 Our calculations use the helicity techniques developed by other authors
553 \begin_inset CommandInset citation
560 ; we briefly summarize below.
563 \begin_layout Subsection
567 \begin_layout Standard
568 \begin_inset CommandInset label
577 \begin_layout Standard
578 A tree-level amplitude in
579 \begin_inset Formula $e^{+}e^{-}$
582 collisions can be expressed in terms of fermion strings of the form
585 \bar{v}(p_{2},\sigma_{2})P_{-\tau}\hat{a}_{1}\hat{a}_{2}\cdots\hat{a}_{n}u(p_{1},\sigma_{1}),
591 \begin_inset Formula $p$
595 \begin_inset Formula $\sigma$
599 \begin_inset Formula $e^{\pm}$
602 four-momenta and helicities
603 \begin_inset Formula $(\sigma=\pm1)$
607 \begin_inset Formula $\hat{a}_{i}=a_{i}^{\mu}\gamma_{\nu}$
611 \begin_inset Formula $P_{\tau}=\frac{1}{2}(1+\tau\gamma_{5})$
614 is a chirality projection operator
615 \begin_inset Formula $(\tau=\pm1)$
620 \begin_inset Formula $a_{i}^{\mu}$
623 may be formed from particle four-momenta, gauge-boson polarization vectors
624 or fermion strings with an uncontracted Lorentz index associated with final-sta
628 \begin_layout NoteToEditor
629 Figures 1 and 2 should appear side-by-side in print
632 \begin_layout Standard
633 In the chiral representation the
634 \begin_inset Formula $\gamma$
637 matrices are expressed in terms of
638 \begin_inset Formula $2\times2$
642 \begin_inset Formula $\sigma$
645 and the unit matrix 1 as
648 \gamma^{\mu} & = & \left(\begin{array}{cc}
649 0 & \sigma_{+}^{\mu}\\
651 \end{array}\right),\gamma^{5}=\left(\begin{array}{cc}
654 \end{array}\right),\\
655 \sigma_{\pm}^{\mu} & = & ({\textbf{1}},\pm\sigma),
663 \hat{a}=\left(\begin{array}{cc}
666 \end{array}\right),(\hat{a})_{\pm}=a_{\mu}\sigma_{\pm}^{\mu},
671 The spinors are expressed in terms of two-component Weyl spinors as
674 u=\left(\begin{array}{c}
677 \end{array}\right),v={\textbf{(}}\vdag_{+}{\textbf{,}}\vdag_{-}{\textbf{)}}.
685 \begin_layout Standard
686 The Weyl spinors are given in terms of helicity eigenstates
687 \begin_inset Formula $\chi_{\lambda}(p)$
691 \begin_inset Formula $\lambda=\pm1$
697 \begin_layout MathLetters
700 u(p,\lambda)_{\pm} & = & (E\pm\lambda|{\textbf{p}}|)^{1/2}\chi_{\lambda}(p),\\
701 v(p,\lambda)_{\pm} & = & \pm\lambda(E\mp\lambda|{\textbf{p}}|)^{1/2}\chi_{-\lambda}(p)
709 \begin_layout Section
710 Floating material and so forth
713 \begin_layout Standard
714 Consider a task that computes profile parameters for a modified Lorentzian
718 I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
726 d_{1}=\sqrt{\left(\begin{array}{c}
727 \frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
728 \frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
736 d_{2}=\sqrt{\left(\begin{array}{c}
737 \frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
738 \case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
746 x_{1}=(x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta
754 y_{1}=-(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
762 \begin_layout Standard
764 \begin_inset Formula $x_{0}$
768 \begin_inset Formula $y_{0}$
771 is the star center, and
772 \begin_inset Formula $\Theta$
775 is the angle with the
776 \begin_inset Formula $x$
780 Results of this task are shown in table
785 \begin_inset CommandInset ref
792 It is not clear how these sorts of analyses may affect determination of
794 \begin_inset Formula $M_{\text{\sun}}$
797 , but the assumption is that the alternate results should be less than 90°
798 out of phase with previous values.
799 We have no observations of
803 \begin_layout Plain Layout
814 \begin_inset Formula $\nicefrac{4}{5}$
817 of the electronically submitted abstracts for AAS meetings are error-free.
821 \begin_layout Acknowledgements
825 \begin_layout Standard
826 We are grateful to V.
831 Phillips for doing the math in section
836 \begin_inset CommandInset ref
843 More information on the AAS\SpecialChar TeX
844 macros package are available at
845 \begin_inset Flex URL
848 \begin_layout Plain Layout
850 http://www.aas.org/publications/aastex
859 \begin_layout Plain Layout
868 ftp://www.aas.org/pubs/
872 \begin_layout Plain Layout
883 \begin_layout Plain Layout
894 \begin_layout Software
895 IRAF, AIPS, Astropy, ...
899 \begin_layout Appendix
903 \begin_layout Section
907 \begin_layout Standard
908 Consider once again a task that computes profile parameters for a modified
909 Lorentzian of the form
912 I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
920 \begin_layout MathLetters
923 d_{1}=\frac{3}{4}\sqrt{\left(\begin{array}{c}
924 \frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
925 \frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
933 d_{2}=\case{3}{4}\sqrt{\left(\begin{array}{c}
934 \frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
935 \case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
943 x_{1} & = & (x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta\\
944 y_{1} & = & -(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
952 \begin_layout Standard
953 For completeness, here is one last equation.
965 \begin_layout References
966 \begin_inset CommandInset bibitem
968 label "Auri\\`ere(1982)"
979 \begin_layout Plain Layout
991 \begin_layout References
992 \begin_inset CommandInset bibitem
994 label "Canizares et al.(1978)"
1003 A., Liller, W., and McClintock, J.
1009 \begin_layout Plain Layout
1021 \begin_layout References
1022 \begin_inset CommandInset bibitem
1023 LatexCommand bibitem
1024 label "Djorgovski and King(1984)"
1030 Djorgovski, S., and King, I.
1036 \begin_layout Plain Layout
1048 \begin_layout References
1049 \begin_inset CommandInset bibitem
1050 LatexCommand bibitem
1051 label "Hagiwara and Zeppenfeld(1986)"
1057 Hagiwara, K., and Zeppenfeld, D.
1058 1986, Nucl.Phys., 274, 1
1061 \begin_layout References
1062 \begin_inset CommandInset bibitem
1063 LatexCommand bibitem
1064 label "Harris and van den Bergh(1984)"
1071 E., and van den Bergh, S.
1076 \begin_layout Plain Layout
1088 \begin_layout References
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1090 LatexCommand bibitem
1091 label "H\\`enon(1961)"
1098 1961, Ann.d'Ap., 24, 369
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1103 LatexCommand bibitem
1116 \begin_layout Plain Layout
1128 \begin_layout References
1129 \begin_inset CommandInset bibitem
1130 LatexCommand bibitem
1139 1975, Dynamics of Stellar Systems, A.
1140 Hayli, Dordrecht: Reidel, 1975, 99
1143 \begin_layout References
1144 \begin_inset CommandInset bibitem
1145 LatexCommand bibitem
1146 label "King et al.(1968)"
1153 R., Hedemann, E., Hodge, S.
1160 \begin_layout Plain Layout
1172 \begin_layout References
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1174 LatexCommand bibitem
1175 label "Kron et al.(1984)"
1183 V., and Wasserman, L.
1189 \begin_layout Plain Layout
1201 \begin_layout References
1202 \begin_inset CommandInset bibitem
1203 LatexCommand bibitem
1204 label "Lynden-Bell and Wood(1968)"
1210 Lynden-Bell, D., and Wood, R.
1215 \begin_layout Plain Layout
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1229 LatexCommand bibitem
1230 label "Newell and O'Neil(1978)"
1243 \begin_layout Plain Layout
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1257 LatexCommand bibitem
1258 label "Ortolani et al.(1985)"
1264 Ortolani, S., Rosino, L., and Sandage, A.
1269 \begin_layout Plain Layout
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1284 label "Peterson(1976)"
1296 \begin_layout Plain Layout
1308 \begin_layout References
1309 \begin_inset CommandInset bibitem
1310 LatexCommand bibitem
1311 label "Spitzer(1985)"
1318 1985, Dynamics of Star Clusters, J.
1320 Hut, Dordrecht: Reidel, 109
1323 \begin_layout Standard
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1359 The processor has to buffer the text of the caption, so it is good not
1360 to be too wordy, but that would make for poor communication as well.
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2288 <cell alignment="right" valignment="top" usebox="none">
2291 \begin_layout Plain Layout
2297 <cell alignment="right" valignment="top" usebox="none">
2300 \begin_layout Plain Layout
2306 <cell alignment="right" valignment="top" usebox="none">
2309 \begin_layout Plain Layout
2315 <cell alignment="right" valignment="top" usebox="none">
2318 \begin_layout Plain Layout
2324 <cell alignment="right" valignment="top" usebox="none">
2327 \begin_layout Plain Layout
2333 <cell alignment="right" valignment="top" usebox="none">
2336 \begin_layout Plain Layout
2342 <cell alignment="right" valignment="top" usebox="none">
2345 \begin_layout Plain Layout
2351 <cell alignment="right" valignment="top" usebox="none">
2354 \begin_layout Plain Layout
2360 <cell alignment="right" valignment="top" usebox="none">
2363 \begin_layout Plain Layout
2377 \begin_layout Table note
2382 \begin_layout Plain Layout
2389 Sample footnote for table
2390 \begin_inset space ~
2394 \begin_inset CommandInset ref
2400 that was generated with the \SpecialChar LaTeX
2404 \begin_layout Table note
2409 \begin_layout Plain Layout
2416 Yet another sample footnote for table
2417 \begin_inset space ~
2421 \begin_inset CommandInset ref
2430 \begin_layout Table note
2435 \begin_layout Plain Layout
2442 Another sample footnote for table
2443 \begin_inset space ~
2447 \begin_inset CommandInset ref
2456 \begin_layout TableComments
2457 We can also attach a long-ish paragraph of explanatory material to a table.
2460 tablerefs to append a list of references.
2461 The following references were from a different table: I've patched them
2462 in here to show how they look, but don't take them too seriously—I certainly
2466 \begin_layout TableRefs
2467 (1) Barbuy, Spite, & Spite 1985; (2) Bond 1980; (3) Carbon et al.
2468 1987; (4) Hobbs & Duncan 1987; (5) Gilroy et al.
2469 1988: (6) Gratton & Ortolani 1986; (7) Gratton & Sneden 1987; (8) Gratton
2470 & Sneden (1988); (9) Gratton & Sneden 1991; (10) Kraft et al.
2471 1982; (11) LCL, or Laird, 1990; (12) Leep & Wallerstein 1981; (13) Luck
2472 & Bond 1981; (14) Luck & Bond 1985; (15) Magain 1987; (16) Magain 1989;
2473 (17) Peterson 1981; (18) Peterson, Kurucz, & Carney 1990; (19) RMB; (20)
2474 Schuster & Nissen 1988; (21) Schuster & Nissen 1989b; (22) Spite et al.
2475 1984; (23) Spite & Spite 1986; (24) Hobbs & Thorburn 1991; (25) Hobbs et
2477 1991; (26) Olsen 1983.
2485 \begin_layout Standard
2486 \begin_inset Note Note
2489 \begin_layout Plain Layout
2490 LyX can load deluxetable files verbatim.
2491 To see this in action, dissolve the following Note and copy the file table.tex
2492 from the AASTeX 5.0 distribution into the same directory as this file.
2500 \begin_layout Standard
2501 \begin_inset Note Note
2504 \begin_layout Plain Layout
2505 \begin_inset CommandInset include