1 #LyX 2.2 created this file. For more info see http://www.lyx.org/
5 \save_transient_properties true
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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 $M_{\sun}$
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
804 \begin_layout Plain Layout
813 of the electronically submitted abstracts for AAS meetings are error-free.
816 \begin_layout Acknowledgements
820 \begin_layout Standard
821 We are grateful to V.
826 Phillips for doing the math in section
831 \begin_inset CommandInset ref
838 More information on the AAS\SpecialChar TeX
839 macros package are available at
840 \begin_inset Flex URL
843 \begin_layout Plain Layout
845 http://www.aas.org/publications/aastex
854 \begin_layout Plain Layout
863 ftp://www.aas.org/pubs/
867 \begin_layout Plain Layout
878 \begin_layout Plain Layout
889 \begin_layout Software
890 IRAF, AIPS, Astropy, ...
894 \begin_layout Appendix
898 \begin_layout Section
902 \begin_layout Standard
903 Consider once again a task that computes profile parameters for a modified
904 Lorentzian of the form
907 I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
915 \begin_layout MathLetters
918 d_{1}=\frac{3}{4}\sqrt{\left(\begin{array}{c}
919 \frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
920 \frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
928 d_{2}=\case{3}{4}\sqrt{\left(\begin{array}{c}
929 \frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
930 \case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
938 x_{1} & = & (x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta\\
939 y_{1} & = & -(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
947 \begin_layout Standard
948 For completeness, here is one last equation.
960 \begin_layout References
961 \begin_inset CommandInset bibitem
963 label "Auri\\`ere(1982)"
973 \begin_layout Plain Layout
985 \begin_layout References
986 \begin_inset CommandInset bibitem
988 label "Canizares et al.(1978)"
996 A., Liller, W., and McClintock, J.
1002 \begin_layout Plain Layout
1014 \begin_layout References
1015 \begin_inset CommandInset bibitem
1016 LatexCommand bibitem
1017 label "Djorgovski and King(1984)"
1022 Djorgovski, S., and King, I.
1028 \begin_layout Plain Layout
1040 \begin_layout References
1041 \begin_inset CommandInset bibitem
1042 LatexCommand bibitem
1043 label "Hagiwara and Zeppenfeld(1986)"
1048 Hagiwara, K., and Zeppenfeld, D.
1049 1986, Nucl.Phys., 274, 1
1052 \begin_layout References
1053 \begin_inset CommandInset bibitem
1054 LatexCommand bibitem
1055 label "Harris and van den Bergh(1984)"
1061 E., and van den Bergh, S.
1066 \begin_layout Plain Layout
1078 \begin_layout References
1079 \begin_inset CommandInset bibitem
1080 LatexCommand bibitem
1081 label "H\\`enon(1961)"
1087 1961, Ann.d'Ap., 24, 369
1090 \begin_layout References
1091 \begin_inset CommandInset bibitem
1092 LatexCommand bibitem
1104 \begin_layout Plain Layout
1116 \begin_layout References
1117 \begin_inset CommandInset bibitem
1118 LatexCommand bibitem
1126 1975, Dynamics of Stellar Systems, A.
1127 Hayli, Dordrecht: Reidel, 1975, 99
1130 \begin_layout References
1131 \begin_inset CommandInset bibitem
1132 LatexCommand bibitem
1133 label "King et al.(1968)"
1139 R., Hedemann, E., Hodge, S.
1146 \begin_layout Plain Layout
1158 \begin_layout References
1159 \begin_inset CommandInset bibitem
1160 LatexCommand bibitem
1161 label "Kron et al.(1984)"
1168 V., and Wasserman, L.
1174 \begin_layout Plain Layout
1186 \begin_layout References
1187 \begin_inset CommandInset bibitem
1188 LatexCommand bibitem
1189 label "Lynden-Bell and Wood(1968)"
1194 Lynden-Bell, D., and Wood, R.
1199 \begin_layout Plain Layout
1211 \begin_layout References
1212 \begin_inset CommandInset bibitem
1213 LatexCommand bibitem
1214 label "Newell and O'Neil(1978)"
1226 \begin_layout Plain Layout
1238 \begin_layout References
1239 \begin_inset CommandInset bibitem
1240 LatexCommand bibitem
1241 label "Ortolani et al.(1985)"
1246 Ortolani, S., Rosino, L., and Sandage, A.
1251 \begin_layout Plain Layout
1263 \begin_layout References
1264 \begin_inset CommandInset bibitem
1265 LatexCommand bibitem
1266 label "Peterson(1976)"
1277 \begin_layout Plain Layout
1289 \begin_layout References
1290 \begin_inset CommandInset bibitem
1291 LatexCommand bibitem
1292 label "Spitzer(1985)"
1298 1985, Dynamics of Star Clusters, J.
1300 Hut, Dordrecht: Reidel, 109
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1338 This is an example of a long figure caption that must be set as a paragraph.
1339 The processor has to buffer the text of the caption, so it is good not
1340 to be too wordy, but that would make for poor communication as well.
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2268 <cell alignment="right" valignment="top" usebox="none">
2271 \begin_layout Plain Layout
2277 <cell alignment="right" valignment="top" usebox="none">
2280 \begin_layout Plain Layout
2286 <cell alignment="right" valignment="top" usebox="none">
2289 \begin_layout Plain Layout
2295 <cell alignment="right" valignment="top" usebox="none">
2298 \begin_layout Plain Layout
2304 <cell alignment="right" valignment="top" usebox="none">
2307 \begin_layout Plain Layout
2313 <cell alignment="right" valignment="top" usebox="none">
2316 \begin_layout Plain Layout
2322 <cell alignment="right" valignment="top" usebox="none">
2325 \begin_layout Plain Layout
2331 <cell alignment="right" valignment="top" usebox="none">
2334 \begin_layout Plain Layout
2340 <cell alignment="right" valignment="top" usebox="none">
2343 \begin_layout Plain Layout
2357 \begin_layout Table note
2362 \begin_layout Plain Layout
2369 Sample footnote for table
2370 \begin_inset space ~
2374 \begin_inset CommandInset ref
2380 that was generated with the \SpecialChar LaTeX
2384 \begin_layout Table note
2389 \begin_layout Plain Layout
2396 Yet another sample footnote for table
2397 \begin_inset space ~
2401 \begin_inset CommandInset ref
2410 \begin_layout Table note
2415 \begin_layout Plain Layout
2422 Another sample footnote for table
2423 \begin_inset space ~
2427 \begin_inset CommandInset ref
2436 \begin_layout TableComments
2437 We can also attach a long-ish paragraph of explanatory material to a table.
2440 tablerefs to append a list of references.
2441 The following references were from a different table: I've patched them
2442 in here to show how they look, but don't take them too seriously—I certainly
2446 \begin_layout TableRefs
2447 (1) Barbuy, Spite, & Spite 1985; (2) Bond 1980; (3) Carbon et al.
2448 1987; (4) Hobbs & Duncan 1987; (5) Gilroy et al.
2449 1988: (6) Gratton & Ortolani 1986; (7) Gratton & Sneden 1987; (8) Gratton
2450 & Sneden (1988); (9) Gratton & Sneden 1991; (10) Kraft et al.
2451 1982; (11) LCL, or Laird, 1990; (12) Leep & Wallerstein 1981; (13) Luck
2452 & Bond 1981; (14) Luck & Bond 1985; (15) Magain 1987; (16) Magain 1989;
2453 (17) Peterson 1981; (18) Peterson, Kurucz, & Carney 1990; (19) RMB; (20)
2454 Schuster & Nissen 1988; (21) Schuster & Nissen 1989b; (22) Spite et al.
2455 1984; (23) Spite & Spite 1986; (24) Hobbs & Thorburn 1991; (25) Hobbs et
2457 1991; (26) Olsen 1983.
2465 \begin_layout Standard
2466 \begin_inset Note Note
2469 \begin_layout Plain Layout
2470 LyX can load deluxetable files verbatim.
2471 To see this in action, dissolve the following Note and copy the file table.tex
2472 from the AASTeX 5.0 distribution into the same directory as this file.
2480 \begin_layout Standard
2481 \begin_inset Note Note
2484 \begin_layout Plain Layout
2485 \begin_inset CommandInset include