1 #LyX 2.2 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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56 \paperorientation portrait
66 \paragraph_separation indent
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68 \quotes_language english
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81 \begin_layout Standard
82 \begin_inset Note Note
85 \begin_layout Plain Layout
88 Sample document for contributions to journals of the American Astronomical
91 \begin_inset CommandInset href
93 name "AASTeX user guide"
94 target "http://journals.aas.org/authors/aastex/aasguide.html"
98 for details on how to use AASTeX.
102 \begin_layout Plain Layout
105 An up-to-date sample LaTeX article using AASTeX is available under
106 \begin_inset Flex URL
109 \begin_layout Plain Layout
111 http://journals.aas.org/authors/aastex/aastex.html#_download
122 \begin_inset Note Note
125 \begin_layout Plain Layout
128 The AASTeX document class uses a different name since version 6.0 (2016/02/16).
129 Depending on the version installed on your system, set the document class
130 to American Astronomical Society (AASTeX v.
131 6) or American Astronomical Society (AASTeX v.
136 \begin_layout Plain Layout
141 \begin_inset Flex URL
144 \begin_layout Plain Layout
146 http://journals.aas.org/authors/aastex/revisionhistory.html
151 ) are only partially supported by LyX (see
152 \begin_inset Flex URL
155 \begin_layout Plain Layout
157 http://www.lyx.org/trac/ticket/10027
171 Collapsed Cores in Globular Clusters, Gauge-Boson Couplings, and AAS\SpecialChar TeX
178 \begin_inset Flex altaffilmark
181 \begin_layout Plain Layout
189 \begin_inset Flex altaffilmark
192 \begin_layout Plain Layout
201 \begin_layout Affiliation
202 Astronomy Department, University of California, Berkeley, CA 94720
209 \begin_inset Flex altaffilmark
212 \begin_layout Plain Layout
221 \begin_layout Affiliation
222 National Optical Astronomy Observatories, Tucson, AZ 85719
237 \begin_inset Flex altaffilmark
240 \begin_layout Plain Layout
249 \begin_layout Affiliation
250 Space Telescope Science Institute, Baltimore, MD 21218
253 \begin_layout Altaffilation
254 \begin_inset Argument 1
257 \begin_layout Plain Layout
263 Visiting Astronomer, Cerro Tololo Inter-American Observatory.
264 CTIO is operated by AURA, Inc.
265 \begin_inset space \space{}
268 under contract to the National Science Foundation.
271 \begin_layout Altaffilation
272 \begin_inset Argument 1
275 \begin_layout Plain Layout
281 Society of Fellows, Harvard University.
284 \begin_layout Altaffilation
285 \begin_inset Argument 1
288 \begin_layout Plain Layout
294 present address: Center for Astrophysics, 60 Garden Street, Cambridge, MA
298 \begin_layout Altaffilation
299 \begin_inset Argument 1
302 \begin_layout Plain Layout
308 Visiting Programmer, Space Telescope Science Institute
311 \begin_layout Altaffilation
312 \begin_inset Argument 1
315 \begin_layout Plain Layout
321 Patron, Alonso's Bar and Grill
324 \begin_layout Abstract
325 This is a preliminary report on surface photometry of the major fraction
326 of known globular clusters, to see which of them show the signs of a collapsed
328 We also explore some diversionary mathematics and recreational tables.
332 \begin_layout Keywords
333 clusters: globular, peanut—bosons: bozos
336 \begin_layout Section
340 \begin_layout Standard
341 A focal problem today in the dynamics of globular clusters is core collapse.
342 It has been predicted by theory for decades
346 \begin_layout Plain Layout
350 citep{hen61,lyn68,spi85}
355 , but observation has been less alert to the phenomenon.
356 For many years the central brightness peak in M15
360 \begin_layout Plain Layout
369 seemed a unique anomaly.
374 \begin_layout Plain Layout
383 suggested a central peak in NGC 6397, and a limited photographic survey
388 \begin_layout Plain Layout
392 citep[Paper I]{djo84}
397 found three more cases, including NGC 6624, whose sharp center had often
402 \begin_layout Plain Layout
415 \begin_layout Section
419 \begin_layout Standard
420 All our observations were short direct exposures with CCD's.
421 At Lick Observatory we used a TI 500
422 \begin_inset Formula $\times$
425 500 chip and a GEC 575
426 \begin_inset Formula $\times$
429 385, on the 1-m Nickel reflector.
430 The only filter available at Lick was red.
431 At CTIO we used a GEC 575
432 \begin_inset Formula $\times$
436 \begin_inset Formula $B,V,$
440 \begin_inset Formula $R$
443 filters, and an RCA 512
444 \begin_inset Formula $\times$
448 \begin_inset Formula $U,B,V,R,$
452 \begin_inset Formula $I$
455 filters, on the 1.5-m reflector.
456 In the CTIO observations we tried to concentrate on the shortest practicable
457 wavelengths; but faintness, reddening, and poor short-wavelength sensitivity
458 often kept us from observing in
459 \begin_inset Formula $U$
463 \begin_inset Formula $B$
467 All four cameras had scales of the order of 0.4 arcsec/pixel, and our field
468 sizes were around 3 arcmin.
471 \begin_layout Standard
472 The CCD images are unfortunately not always suitable, for very poor clusters
473 or for clusters with large cores.
474 Since the latter are easily studied by other means, we augmented our own
475 CCD profiles by collecting from the literature a number of star-count profiles
480 \begin_layout Plain Layout
484 citep{kin68,pet76,har84,ort85}
489 , as well as photoelectric profiles
493 \begin_layout Plain Layout
502 and electronographic profiles
506 \begin_layout Plain Layout
516 In a few cases we judged normality by eye estimates on one of the Sky Surveys.
519 \begin_layout Section
523 \begin_layout Standard
524 It has been realized that helicity amplitudes provide a convenient means
529 \begin_layout Plain Layout
530 Footnotes can be inserted like this.
536 These amplitude-level techniques are particularly convenient for calculations
537 involving many Feynman diagrams, where the usual trace techniques for the
538 amplitude squared becomes unwieldy.
539 Our calculations use the helicity techniques developed by other authors
541 \begin_inset CommandInset citation
547 ; we briefly summarize below.
550 \begin_layout Subsection
554 \begin_layout Standard
555 \begin_inset CommandInset label
564 \begin_layout Standard
565 A tree-level amplitude in
566 \begin_inset Formula $e^{+}e^{-}$
569 collisions can be expressed in terms of fermion strings of the form
572 \bar{v}(p_{2},\sigma_{2})P_{-\tau}\hat{a}_{1}\hat{a}_{2}\cdots\hat{a}_{n}u(p_{1},\sigma_{1}),
578 \begin_inset Formula $p$
582 \begin_inset Formula $\sigma$
586 \begin_inset Formula $e^{\pm}$
589 four-momenta and helicities
590 \begin_inset Formula $(\sigma=\pm1)$
594 \begin_inset Formula $\hat{a}_{i}=a_{i}^{\mu}\gamma_{\nu}$
598 \begin_inset Formula $P_{\tau}=\frac{1}{2}(1+\tau\gamma_{5})$
601 is a chirality projection operator
602 \begin_inset Formula $(\tau=\pm1)$
607 \begin_inset Formula $a_{i}^{\mu}$
610 may be formed from particle four-momenta, gauge-boson polarization vectors
611 or fermion strings with an uncontracted Lorentz index associated with final-sta
615 \begin_layout NoteToEditor
616 Figures 1 and 2 should appear side-by-side in print
619 \begin_layout Standard
620 In the chiral representation the
621 \begin_inset Formula $\gamma$
624 matrices are expressed in terms of
625 \begin_inset Formula $2\times2$
629 \begin_inset Formula $\sigma$
632 and the unit matrix 1 as
635 \gamma^{\mu} & = & \left(\begin{array}{cc}
636 0 & \sigma_{+}^{\mu}\\
638 \end{array}\right),\gamma^{5}=\left(\begin{array}{cc}
641 \end{array}\right),\\
642 \sigma_{\pm}^{\mu} & = & ({\textbf{1}},\pm\sigma),
650 \hat{a}=\left(\begin{array}{cc}
653 \end{array}\right),(\hat{a})_{\pm}=a_{\mu}\sigma_{\pm}^{\mu},
658 The spinors are expressed in terms of two-component Weyl spinors as
661 u=\left(\begin{array}{c}
664 \end{array}\right),v={\textbf{(}}\vdag_{+}{\textbf{,}}\vdag_{-}{\textbf{)}}.
672 \begin_layout Standard
673 The Weyl spinors are given in terms of helicity eigenstates
674 \begin_inset Formula $\chi_{\lambda}(p)$
678 \begin_inset Formula $\lambda=\pm1$
684 \begin_layout MathLetters
687 u(p,\lambda)_{\pm} & = & (E\pm\lambda|{\textbf{p}}|)^{1/2}\chi_{\lambda}(p),\\
688 v(p,\lambda)_{\pm} & = & \pm\lambda(E\mp\lambda|{\textbf{p}}|)^{1/2}\chi_{-\lambda}(p)
696 \begin_layout Section
697 Floating material and so forth
700 \begin_layout Standard
701 Consider a task that computes profile parameters for a modified Lorentzian
705 I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
713 d_{1}=\sqrt{\left(\begin{array}{c}
714 \frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
715 \frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
723 d_{2}=\sqrt{\left(\begin{array}{c}
724 \frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
725 \case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
733 x_{1}=(x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta
741 y_{1}=-(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
749 \begin_layout Standard
751 \begin_inset Formula $x_{0}$
755 \begin_inset Formula $y_{0}$
758 is the star center, and
759 \begin_inset Formula $\Theta$
762 is the angle with the
763 \begin_inset Formula $x$
767 Results of this task are shown in table
772 \begin_inset CommandInset ref
779 It is not clear how these sorts of analyses may affect determination of
781 \begin_inset Formula $M_{\text{\sun}}$
784 , but the assumption is that the alternate results should be less than 90°
785 out of phase with previous values.
786 We have no observations of
790 \begin_layout Plain Layout
801 \begin_inset Formula $\nicefrac{4}{5}$
804 of the electronically submitted abstracts for AAS meetings are error-free.
808 \begin_layout Acknowledgements
812 \begin_layout Standard
813 We are grateful to V.
818 Phillips for doing the math in section
823 \begin_inset CommandInset ref
830 More information on the AAS\SpecialChar TeX
831 macros package are available at
832 \begin_inset Flex URL
835 \begin_layout Plain Layout
837 http://www.aas.org/publications/aastex
846 \begin_layout Plain Layout
855 ftp://www.aas.org/pubs/
859 \begin_layout Plain Layout
870 \begin_layout Plain Layout
881 \begin_layout Software
882 IRAF, AIPS, Astropy, ...
886 \begin_layout Appendix
890 \begin_layout Section
894 \begin_layout Standard
895 Consider once again a task that computes profile parameters for a modified
896 Lorentzian of the form
899 I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
907 \begin_layout MathLetters
910 d_{1}=\frac{3}{4}\sqrt{\left(\begin{array}{c}
911 \frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
912 \frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
920 d_{2}=\case{3}{4}\sqrt{\left(\begin{array}{c}
921 \frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
922 \case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
930 x_{1} & = & (x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta\\
931 y_{1} & = & -(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
939 \begin_layout Standard
940 For completeness, here is one last equation.
952 \begin_layout References
953 \begin_inset CommandInset bibitem
955 label "Auri\\`ere(1982)"
965 \begin_layout Plain Layout
977 \begin_layout References
978 \begin_inset CommandInset bibitem
980 label "Canizares et al.(1978)"
988 A., Liller, W., and McClintock, J.
994 \begin_layout Plain Layout
1006 \begin_layout References
1007 \begin_inset CommandInset bibitem
1008 LatexCommand bibitem
1009 label "Djorgovski and King(1984)"
1014 Djorgovski, S., and King, I.
1020 \begin_layout Plain Layout
1032 \begin_layout References
1033 \begin_inset CommandInset bibitem
1034 LatexCommand bibitem
1035 label "Hagiwara and Zeppenfeld(1986)"
1040 Hagiwara, K., and Zeppenfeld, D.
1041 1986, Nucl.Phys., 274, 1
1044 \begin_layout References
1045 \begin_inset CommandInset bibitem
1046 LatexCommand bibitem
1047 label "Harris and van den Bergh(1984)"
1053 E., and van den Bergh, S.
1058 \begin_layout Plain Layout
1070 \begin_layout References
1071 \begin_inset CommandInset bibitem
1072 LatexCommand bibitem
1073 label "H\\`enon(1961)"
1079 1961, Ann.d'Ap., 24, 369
1082 \begin_layout References
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1084 LatexCommand bibitem
1096 \begin_layout Plain Layout
1108 \begin_layout References
1109 \begin_inset CommandInset bibitem
1110 LatexCommand bibitem
1118 1975, Dynamics of Stellar Systems, A.
1119 Hayli, Dordrecht: Reidel, 1975, 99
1122 \begin_layout References
1123 \begin_inset CommandInset bibitem
1124 LatexCommand bibitem
1125 label "King et al.(1968)"
1131 R., Hedemann, E., Hodge, S.
1138 \begin_layout Plain Layout
1150 \begin_layout References
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1152 LatexCommand bibitem
1153 label "Kron et al.(1984)"
1160 V., and Wasserman, L.
1166 \begin_layout Plain Layout
1178 \begin_layout References
1179 \begin_inset CommandInset bibitem
1180 LatexCommand bibitem
1181 label "Lynden-Bell and Wood(1968)"
1186 Lynden-Bell, D., and Wood, R.
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1205 LatexCommand bibitem
1206 label "Newell and O'Neil(1978)"
1218 \begin_layout Plain Layout
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1232 LatexCommand bibitem
1233 label "Ortolani et al.(1985)"
1238 Ortolani, S., Rosino, L., and Sandage, A.
1243 \begin_layout Plain Layout
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1257 LatexCommand bibitem
1258 label "Peterson(1976)"
1269 \begin_layout Plain Layout
1281 \begin_layout References
1282 \begin_inset CommandInset bibitem
1283 LatexCommand bibitem
1284 label "Spitzer(1985)"
1290 1985, Dynamics of Star Clusters, J.
1292 Hut, Dordrecht: Reidel, 109
1295 \begin_layout Standard
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1330 This is an example of a long figure caption that must be set as a paragraph.
1331 The processor has to buffer the text of the caption, so it is good not
1332 to be too wordy, but that would make for poor communication as well.
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2260 <cell alignment="right" valignment="top" usebox="none">
2263 \begin_layout Plain Layout
2269 <cell alignment="right" valignment="top" usebox="none">
2272 \begin_layout Plain Layout
2278 <cell alignment="right" valignment="top" usebox="none">
2281 \begin_layout Plain Layout
2287 <cell alignment="right" valignment="top" usebox="none">
2290 \begin_layout Plain Layout
2296 <cell alignment="right" valignment="top" usebox="none">
2299 \begin_layout Plain Layout
2305 <cell alignment="right" valignment="top" usebox="none">
2308 \begin_layout Plain Layout
2314 <cell alignment="right" valignment="top" usebox="none">
2317 \begin_layout Plain Layout
2323 <cell alignment="right" valignment="top" usebox="none">
2326 \begin_layout Plain Layout
2332 <cell alignment="right" valignment="top" usebox="none">
2335 \begin_layout Plain Layout
2349 \begin_layout Table note
2354 \begin_layout Plain Layout
2361 Sample footnote for table
2362 \begin_inset space ~
2366 \begin_inset CommandInset ref
2372 that was generated with the \SpecialChar LaTeX
2376 \begin_layout Table note
2381 \begin_layout Plain Layout
2388 Yet another sample footnote for table
2389 \begin_inset space ~
2393 \begin_inset CommandInset ref
2402 \begin_layout Table note
2407 \begin_layout Plain Layout
2414 Another sample footnote for table
2415 \begin_inset space ~
2419 \begin_inset CommandInset ref
2428 \begin_layout TableComments
2429 We can also attach a long-ish paragraph of explanatory material to a table.
2432 tablerefs to append a list of references.
2433 The following references were from a different table: I've patched them
2434 in here to show how they look, but don't take them too seriously—I certainly
2438 \begin_layout TableRefs
2439 (1) Barbuy, Spite, & Spite 1985; (2) Bond 1980; (3) Carbon et al.
2440 1987; (4) Hobbs & Duncan 1987; (5) Gilroy et al.
2441 1988: (6) Gratton & Ortolani 1986; (7) Gratton & Sneden 1987; (8) Gratton
2442 & Sneden (1988); (9) Gratton & Sneden 1991; (10) Kraft et al.
2443 1982; (11) LCL, or Laird, 1990; (12) Leep & Wallerstein 1981; (13) Luck
2444 & Bond 1981; (14) Luck & Bond 1985; (15) Magain 1987; (16) Magain 1989;
2445 (17) Peterson 1981; (18) Peterson, Kurucz, & Carney 1990; (19) RMB; (20)
2446 Schuster & Nissen 1988; (21) Schuster & Nissen 1989b; (22) Spite et al.
2447 1984; (23) Spite & Spite 1986; (24) Hobbs & Thorburn 1991; (25) Hobbs et
2449 1991; (26) Olsen 1983.
2457 \begin_layout Standard
2458 \begin_inset Note Note
2461 \begin_layout Plain Layout
2462 LyX can load deluxetable files verbatim.
2463 To see this in action, dissolve the following Note and copy the file table.tex
2464 from the AASTeX 5.0 distribution into the same directory as this file.
2472 \begin_layout Standard
2473 \begin_inset Note Note
2476 \begin_layout Plain Layout
2477 \begin_inset CommandInset include