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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82 Collapsed Cores in Globular Clusters, Gauge-Boson Couplings, and AAS\SpecialChar TeX
89 \begin_inset Flex altaffilmark
92 \begin_layout Plain Layout
100 \begin_inset Flex altaffilmark
103 \begin_layout Plain Layout
112 \begin_layout Affiliation
113 Astronomy Department, University of California, Berkeley, CA 94720
120 \begin_inset Flex altaffilmark
123 \begin_layout Plain Layout
132 \begin_layout Affiliation
133 National Optical Astronomy Observatories, Tucson, AZ 85719
148 \begin_inset Flex altaffilmark
151 \begin_layout Plain Layout
160 \begin_layout Affiliation
161 Space Telescope Science Institute, Baltimore, MD 21218
164 \begin_layout Altaffilation
165 \begin_inset Argument 1
168 \begin_layout Plain Layout
174 Visiting Astronomer, Cerro Tololo Inter-American Observatory.
175 CTIO is operated by AURA, Inc.
176 \begin_inset space \space{}
179 under contract to the National Science Foundation.
182 \begin_layout Altaffilation
183 \begin_inset Argument 1
186 \begin_layout Plain Layout
192 Society of Fellows, Harvard University.
195 \begin_layout Altaffilation
196 \begin_inset Argument 1
199 \begin_layout Plain Layout
205 present address: Center for Astrophysics, 60 Garden Street, Cambridge, MA
209 \begin_layout Altaffilation
210 \begin_inset Argument 1
213 \begin_layout Plain Layout
219 Visiting Programmer, Space Telescope Science Institute
222 \begin_layout Altaffilation
223 \begin_inset Argument 1
226 \begin_layout Plain Layout
232 Patron, Alonso's Bar and Grill
235 \begin_layout Abstract
236 This is a preliminary report on surface photometry of the major fraction
237 of known globular clusters, to see which of them show the signs of a collapsed
239 We also explore some diversionary mathematics and recreational tables.
243 \begin_layout Keywords
244 clusters: globular, peanut—bosons: bozos
247 \begin_layout Section
251 \begin_layout Standard
252 A focal problem today in the dynamics of globular clusters is core collapse.
253 It has been predicted by theory for decades
257 \begin_layout Plain Layout
261 citep{hen61,lyn68,spi85}
266 , but observation has been less alert to the phenomenon.
267 For many years the central brightness peak in M15
271 \begin_layout Plain Layout
280 seemed a unique anomaly.
285 \begin_layout Plain Layout
294 suggested a central peak in NGC 6397, and a limited photographic survey
299 \begin_layout Plain Layout
303 citep[Paper I]{djo84}
308 found three more cases, including NGC 6624, whose sharp center had often
313 \begin_layout Plain Layout
326 \begin_layout Section
330 \begin_layout Standard
331 All our observations were short direct exposures with CCD's.
332 At Lick Observatory we used a TI 500
333 \begin_inset Formula $\times$
336 500 chip and a GEC 575
337 \begin_inset Formula $\times$
340 385, on the 1-m Nickel reflector.
341 The only filter available at Lick was red.
342 At CTIO we used a GEC 575
343 \begin_inset Formula $\times$
347 \begin_inset Formula $B,V,$
351 \begin_inset Formula $R$
354 filters, and an RCA 512
355 \begin_inset Formula $\times$
359 \begin_inset Formula $U,B,V,R,$
363 \begin_inset Formula $I$
366 filters, on the 1.5-m reflector.
367 In the CTIO observations we tried to concentrate on the shortest practicable
368 wavelengths; but faintness, reddening, and poor short-wavelength sensitivity
369 often kept us from observing in
370 \begin_inset Formula $U$
374 \begin_inset Formula $B$
378 All four cameras had scales of the order of 0.4 arcsec/pixel, and our field
379 sizes were around 3 arcmin.
382 \begin_layout Standard
383 The CCD images are unfortunately not always suitable, for very poor clusters
384 or for clusters with large cores.
385 Since the latter are easily studied by other means, we augmented our own
386 CCD profiles by collecting from the literature a number of star-count profiles
391 \begin_layout Plain Layout
395 citep{kin68,pet76,har84,ort85}
400 , as well as photoelectric profiles
404 \begin_layout Plain Layout
413 and electronographic profiles
417 \begin_layout Plain Layout
427 In a few cases we judged normality by eye estimates on one of the Sky Surveys.
430 \begin_layout Section
434 \begin_layout Standard
435 It has been realized that helicity amplitudes provide a convenient means
440 \begin_layout Plain Layout
441 Footnotes can be inserted like this.
447 These amplitude-level techniques are particularly convenient for calculations
448 involving many Feynman diagrams, where the usual trace techniques for the
449 amplitude squared becomes unwieldy.
450 Our calculations use the helicity techniques developed by other authors
452 \begin_inset CommandInset citation
458 ; we briefly summarize below.
461 \begin_layout Subsection
465 \begin_layout Standard
466 \begin_inset CommandInset label
475 \begin_layout Standard
476 A tree-level amplitude in
477 \begin_inset Formula $e^{+}e^{-}$
480 collisions can be expressed in terms of fermion strings of the form
483 \bar{v}(p_{2},\sigma_{2})P_{-\tau}\hat{a}_{1}\hat{a}_{2}\cdots\hat{a}_{n}u(p_{1},\sigma_{1}),
489 \begin_inset Formula $p$
493 \begin_inset Formula $\sigma$
497 \begin_inset Formula $e^{\pm}$
500 four-momenta and helicities
501 \begin_inset Formula $(\sigma=\pm1)$
505 \begin_inset Formula $\hat{a}_{i}=a_{i}^{\mu}\gamma_{\nu}$
509 \begin_inset Formula $P_{\tau}=\frac{1}{2}(1+\tau\gamma_{5})$
512 is a chirality projection operator
513 \begin_inset Formula $(\tau=\pm1)$
518 \begin_inset Formula $a_{i}^{\mu}$
521 may be formed from particle four-momenta, gauge-boson polarization vectors
522 or fermion strings with an uncontracted Lorentz index associated with final-sta
526 \begin_layout NoteToEditor
527 Figures 1 and 2 should appear side-by-side in print
530 \begin_layout Standard
531 In the chiral representation the
532 \begin_inset Formula $\gamma$
535 matrices are expressed in terms of
536 \begin_inset Formula $2\times2$
540 \begin_inset Formula $\sigma$
543 and the unit matrix 1 as
546 \gamma^{\mu} & = & \left(\begin{array}{cc}
547 0 & \sigma_{+}^{\mu}\\
549 \end{array}\right),\gamma^{5}=\left(\begin{array}{cc}
552 \end{array}\right),\\
553 \sigma_{\pm}^{\mu} & = & ({\textbf{1}},\pm\sigma),
561 \hat{a}=\left(\begin{array}{cc}
564 \end{array}\right),(\hat{a})_{\pm}=a_{\mu}\sigma_{\pm}^{\mu},
569 The spinors are expressed in terms of two-component Weyl spinors as
572 u=\left(\begin{array}{c}
575 \end{array}\right),v={\textbf{(}}\vdag_{+}{\textbf{,}}\vdag_{-}{\textbf{)}}.
583 \begin_layout Standard
584 The Weyl spinors are given in terms of helicity eigenstates
585 \begin_inset Formula $\chi_{\lambda}(p)$
589 \begin_inset Formula $\lambda=\pm1$
595 \begin_layout MathLetters
598 u(p,\lambda)_{\pm} & = & (E\pm\lambda|{\textbf{p}}|)^{1/2}\chi_{\lambda}(p),\\
599 v(p,\lambda)_{\pm} & = & \pm\lambda(E\mp\lambda|{\textbf{p}}|)^{1/2}\chi_{-\lambda}(p)
607 \begin_layout Section
608 Floating material and so forth
611 \begin_layout Standard
612 Consider a task that computes profile parameters for a modified Lorentzian
616 I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
624 d_{1}=\sqrt{\left(\begin{array}{c}
625 \frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
626 \frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
634 d_{2}=\sqrt{\left(\begin{array}{c}
635 \frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
636 \case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
644 x_{1}=(x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta
652 y_{1}=-(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
660 \begin_layout Standard
662 \begin_inset Formula $x_{0}$
666 \begin_inset Formula $y_{0}$
669 is the star center, and
670 \begin_inset Formula $\Theta$
673 is the angle with the
674 \begin_inset Formula $x$
678 Results of this task are shown in table
683 \begin_inset CommandInset ref
690 It is not clear how these sorts of analyses may affect determination of
692 \begin_inset Formula $M_{\sun}$
695 , but the assumption is that the alternate results should be less than 90°
696 out of phase with previous values.
697 We have no observations of
701 \begin_layout Plain Layout
715 \begin_layout Plain Layout
724 of the electronically submitted abstracts for AAS meetings are error-free.
727 \begin_layout Acknowledgements
731 \begin_layout Standard
732 We are grateful to V.
737 Phillips for doing the math in section
742 \begin_inset CommandInset ref
749 More information on the AAS\SpecialChar TeX
750 macros package are available at
751 \begin_inset Flex URL
754 \begin_layout Plain Layout
756 http://www.aas.org/publications/aastex
765 \begin_layout Plain Layout
774 ftp://www.aas.org/pubs/
778 \begin_layout Plain Layout
789 \begin_layout Plain Layout
799 \begin_layout Appendix
803 \begin_layout Section
807 \begin_layout Standard
808 Consider once again a task that computes profile parameters for a modified
809 Lorentzian of the form
812 I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
820 \begin_layout MathLetters
823 d_{1}=\frac{3}{4}\sqrt{\left(\begin{array}{c}
824 \frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
825 \frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
833 d_{2}=\case{3}{4}\sqrt{\left(\begin{array}{c}
834 \frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
835 \case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
843 x_{1} & = & (x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta\\
844 y_{1} & = & -(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
852 \begin_layout Standard
853 For completeness, here is one last equation.
865 \begin_layout References
866 \begin_inset CommandInset bibitem
868 label "Auri\\`ere(1982)"
878 \begin_layout Plain Layout
890 \begin_layout References
891 \begin_inset CommandInset bibitem
893 label "Canizares et al.(1978)"
901 A., Liller, W., and McClintock, J.
907 \begin_layout Plain Layout
919 \begin_layout References
920 \begin_inset CommandInset bibitem
922 label "Djorgovski and King(1984)"
927 Djorgovski, S., and King, I.
933 \begin_layout Plain Layout
945 \begin_layout References
946 \begin_inset CommandInset bibitem
948 label "Hagiwara and Zeppenfeld(1986)"
953 Hagiwara, K., and Zeppenfeld, D.
954 1986, Nucl.Phys., 274, 1
957 \begin_layout References
958 \begin_inset CommandInset bibitem
960 label "Harris and van den Bergh(1984)"
966 E., and van den Bergh, S.
971 \begin_layout Plain Layout
983 \begin_layout References
984 \begin_inset CommandInset bibitem
986 label "H\\`enon(1961)"
992 1961, Ann.d'Ap., 24, 369
995 \begin_layout References
996 \begin_inset CommandInset bibitem
1009 \begin_layout Plain Layout
1021 \begin_layout References
1022 \begin_inset CommandInset bibitem
1023 LatexCommand bibitem
1031 1975, Dynamics of Stellar Systems, A.
1032 Hayli, Dordrecht: Reidel, 1975, 99
1035 \begin_layout References
1036 \begin_inset CommandInset bibitem
1037 LatexCommand bibitem
1038 label "King et al.(1968)"
1044 R., Hedemann, E., Hodge, S.
1051 \begin_layout Plain Layout
1063 \begin_layout References
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1065 LatexCommand bibitem
1066 label "Kron et al.(1984)"
1073 V., and Wasserman, L.
1079 \begin_layout Plain Layout
1091 \begin_layout References
1092 \begin_inset CommandInset bibitem
1093 LatexCommand bibitem
1094 label "Lynden-Bell and Wood(1968)"
1099 Lynden-Bell, D., and Wood, R.
1104 \begin_layout Plain Layout
1116 \begin_layout References
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1119 label "Newell and O'Neil(1978)"
1131 \begin_layout Plain Layout
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1144 \begin_inset CommandInset bibitem
1145 LatexCommand bibitem
1146 label "Ortolani et al.(1985)"
1151 Ortolani, S., Rosino, L., and Sandage, A.
1156 \begin_layout Plain Layout
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1170 LatexCommand bibitem
1171 label "Peterson(1976)"
1182 \begin_layout Plain Layout
1194 \begin_layout References
1195 \begin_inset CommandInset bibitem
1196 LatexCommand bibitem
1197 label "Spitzer(1985)"
1203 1985, Dynamics of Star Clusters, J.
1205 Hut, Dordrecht: Reidel, 109
1208 \begin_layout Standard
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1215 \begin_layout Standard
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1218 \begin_layout Plain Layout
1219 \begin_inset CommandInset label
1225 This is the first figure and it uses sgi9259.eps as its EPS figure file.
1233 \begin_layout Standard
1234 \begin_inset Caption FigCaption
1236 \begin_layout Plain Layout
1237 \begin_inset CommandInset label
1243 This is an example of a long figure caption that must be set as a paragraph.
1244 The processor has to buffer the text of the caption, so it is good not
1245 to be too wordy, but that would make for poor communication as well.
1254 \begin_layout Standard
1255 \begin_inset Caption FigCaption
1257 \begin_layout Plain Layout
1258 \begin_inset CommandInset label
1264 This figure has no associated EPS file, so the optional parameter is omitted.
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1274 \begin_inset Newpage clearpage
1280 \begin_layout Standard
1281 \begin_inset Float table
1286 \begin_layout Plain Layout
1287 \begin_inset Caption Standard
1289 \begin_layout Plain Layout
1290 Terribly relevant tabular information.
1291 \begin_inset CommandInset label
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1365 \begin_layout Plain Layout
1367 \begin_inset Formula $d_{y}$
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1378 \begin_layout Plain Layout
1380 \begin_inset Formula $n$
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1393 \begin_inset Formula $\chi^{2}$
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1419 \begin_inset Formula $R_{min}$
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1435 \begin_inset Flex tablenotemark
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1452 \begin_layout Plain Layout
1454 \begin_inset Formula $PR_{maj}$
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1465 \begin_layout Plain Layout
1467 \begin_inset Formula $PR_{min}$
1475 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
1478 \begin_layout Plain Layout
1479 \begin_inset Formula $\Theta$
1483 \begin_inset Flex tablenotemark
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2239 \begin_layout Plain Layout
2245 <cell alignment="right" valignment="top" usebox="none">
2248 \begin_layout Plain Layout
2262 \begin_layout Table note
2267 \begin_layout Plain Layout
2274 Sample footnote for table
2275 \begin_inset space ~
2279 \begin_inset CommandInset ref
2285 that was generated with the \SpecialChar LaTeX
2289 \begin_layout Table note
2294 \begin_layout Plain Layout
2301 Yet another sample footnote for table
2302 \begin_inset space ~
2306 \begin_inset CommandInset ref
2315 \begin_layout Table note
2320 \begin_layout Plain Layout
2327 Another sample footnote for table
2328 \begin_inset space ~
2332 \begin_inset CommandInset ref
2341 \begin_layout TableComments
2342 We can also attach a long-ish paragraph of explanatory material to a table.
2345 tablerefs to append a list of references.
2346 The following references were from a different table: I've patched them
2347 in here to show how they look, but don't take them too seriously—I certainly
2351 \begin_layout TableRefs
2352 (1) Barbuy, Spite, & Spite 1985; (2) Bond 1980; (3) Carbon et al.
2353 1987; (4) Hobbs & Duncan 1987; (5) Gilroy et al.
2354 1988: (6) Gratton & Ortolani 1986; (7) Gratton & Sneden 1987; (8) Gratton
2355 & Sneden (1988); (9) Gratton & Sneden 1991; (10) Kraft et al.
2356 1982; (11) LCL, or Laird, 1990; (12) Leep & Wallerstein 1981; (13) Luck
2357 & Bond 1981; (14) Luck & Bond 1985; (15) Magain 1987; (16) Magain 1989;
2358 (17) Peterson 1981; (18) Peterson, Kurucz, & Carney 1990; (19) RMB; (20)
2359 Schuster & Nissen 1988; (21) Schuster & Nissen 1989b; (22) Spite et al.
2360 1984; (23) Spite & Spite 1986; (24) Hobbs & Thorburn 1991; (25) Hobbs et
2362 1991; (26) Olsen 1983.
2370 \begin_layout Standard
2374 \begin_layout Plain Layout
2376 % LyX can load deluxetable files verbatim.
2377 To see this in action, uncomment the following
2385 \begin_layout Standard
2389 \begin_layout Plain Layout
2397 \begin_inset Quotes eld
2404 \begin_layout Plain Layout
2412 \begin_inset Quotes erd
2419 \begin_layout Plain Layout
2421 ) and copy the file table.tex from the AASTeX 5.0 distribution into
2429 \begin_layout Standard
2433 \begin_layout Plain Layout
2435 % the same directory as this file.
2443 \begin_layout Standard
2447 \begin_layout Plain Layout
2455 \begin_inset CommandInset include