1 #LyX 2.3 created this file. For more info see http://www.lyx.org/
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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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86 \begin_layout Standard
87 \begin_inset Note Note
90 \begin_layout Plain Layout
93 Sample document for contributions to journals of the American Astronomical
96 \begin_inset CommandInset href
98 name "AASTeX user guide"
99 target "http://journals.aas.org/authors/aastex/aasguide.html"
104 for details on how to use AASTeX.
108 \begin_layout Plain Layout
111 An up-to-date sample LaTeX article using AASTeX is available under
112 \begin_inset Flex URL
115 \begin_layout Plain Layout
117 http://journals.aas.org/authors/aastex/aastex.html#_download
128 \begin_inset Note Note
131 \begin_layout Plain Layout
134 The AASTeX document class uses a different name since version 6.0 (2016/02/16).
135 Depending on the version installed on your system, set the document class
136 to American Astronomical Society (AASTeX v.
137 6) or American Astronomical Society (AASTeX v.
142 \begin_layout Plain Layout
147 \begin_inset Flex URL
150 \begin_layout Plain Layout
152 http://journals.aas.org/authors/aastex/revisionhistory.html
157 ) are only partially supported by LyX (see
158 \begin_inset Flex URL
161 \begin_layout Plain Layout
163 http://www.lyx.org/trac/ticket/10027
177 Collapsed Cores in Globular Clusters, Gauge-Boson Couplings, and AAS\SpecialChar TeX
184 \begin_inset Flex altaffilmark
187 \begin_layout Plain Layout
195 \begin_inset Flex altaffilmark
198 \begin_layout Plain Layout
207 \begin_layout Affiliation
208 Astronomy Department, University of California, Berkeley, CA 94720
215 \begin_inset Flex altaffilmark
218 \begin_layout Plain Layout
227 \begin_layout Affiliation
228 National Optical Astronomy Observatories, Tucson, AZ 85719
243 \begin_inset Flex altaffilmark
246 \begin_layout Plain Layout
255 \begin_layout Affiliation
256 Space Telescope Science Institute, Baltimore, MD 21218
259 \begin_layout Altaffilation
260 \begin_inset Argument 1
263 \begin_layout Plain Layout
269 Visiting Astronomer, Cerro Tololo Inter-American Observatory.
270 CTIO is operated by AURA, Inc.
271 \begin_inset space \space{}
274 under contract to the National Science Foundation.
277 \begin_layout Altaffilation
278 \begin_inset Argument 1
281 \begin_layout Plain Layout
287 Society of Fellows, Harvard University.
290 \begin_layout Altaffilation
291 \begin_inset Argument 1
294 \begin_layout Plain Layout
300 present address: Center for Astrophysics, 60 Garden Street, Cambridge, MA
304 \begin_layout Altaffilation
305 \begin_inset Argument 1
308 \begin_layout Plain Layout
314 Visiting Programmer, Space Telescope Science Institute
317 \begin_layout Altaffilation
318 \begin_inset Argument 1
321 \begin_layout Plain Layout
327 Patron, Alonso's Bar and Grill
330 \begin_layout Abstract
331 This is a preliminary report on surface photometry of the major fraction
332 of known globular clusters, to see which of them show the signs of a collapsed
334 We also explore some diversionary mathematics and recreational tables.
338 \begin_layout Keywords
339 clusters: globular, peanut—bosons: bozos
342 \begin_layout Section
346 \begin_layout Standard
347 A focal problem today in the dynamics of globular clusters is core collapse.
348 It has been predicted by theory for decades
352 \begin_layout Plain Layout
356 citep{hen61,lyn68,spi85}
361 , but observation has been less alert to the phenomenon.
362 For many years the central brightness peak in M15
366 \begin_layout Plain Layout
375 seemed a unique anomaly.
380 \begin_layout Plain Layout
389 suggested a central peak in NGC 6397, and a limited photographic survey
394 \begin_layout Plain Layout
398 citep[Paper I]{djo84}
403 found three more cases, including NGC 6624, whose sharp center had often
408 \begin_layout Plain Layout
421 \begin_layout Section
425 \begin_layout Standard
426 All our observations were short direct exposures with CCD's.
427 At Lick Observatory we used a TI 500
428 \begin_inset Formula $\times$
431 500 chip and a GEC 575
432 \begin_inset Formula $\times$
435 385, on the 1-m Nickel reflector.
436 The only filter available at Lick was red.
437 At CTIO we used a GEC 575
438 \begin_inset Formula $\times$
442 \begin_inset Formula $B,V,$
446 \begin_inset Formula $R$
449 filters, and an RCA 512
450 \begin_inset Formula $\times$
454 \begin_inset Formula $U,B,V,R,$
458 \begin_inset Formula $I$
461 filters, on the 1.5-m reflector.
462 In the CTIO observations we tried to concentrate on the shortest practicable
463 wavelengths; but faintness, reddening, and poor short-wavelength sensitivity
464 often kept us from observing in
465 \begin_inset Formula $U$
469 \begin_inset Formula $B$
473 All four cameras had scales of the order of 0.4 arcsec/pixel, and our field
474 sizes were around 3 arcmin.
477 \begin_layout Standard
478 The CCD images are unfortunately not always suitable, for very poor clusters
479 or for clusters with large cores.
480 Since the latter are easily studied by other means, we augmented our own
481 CCD profiles by collecting from the literature a number of star-count profiles
486 \begin_layout Plain Layout
490 citep{kin68,pet76,har84,ort85}
495 , as well as photoelectric profiles
499 \begin_layout Plain Layout
508 and electronographic profiles
512 \begin_layout Plain Layout
522 In a few cases we judged normality by eye estimates on one of the Sky Surveys.
525 \begin_layout Section
529 \begin_layout Standard
530 It has been realized that helicity amplitudes provide a convenient means
535 \begin_layout Plain Layout
536 Footnotes can be inserted like this.
542 These amplitude-level techniques are particularly convenient for calculations
543 involving many Feynman diagrams, where the usual trace techniques for the
544 amplitude squared becomes unwieldy.
545 Our calculations use the helicity techniques developed by other authors
547 \begin_inset CommandInset citation
554 ; we briefly summarize below.
557 \begin_layout Subsection
561 \begin_layout Standard
562 \begin_inset CommandInset label
571 \begin_layout Standard
572 A tree-level amplitude in
573 \begin_inset Formula $e^{+}e^{-}$
576 collisions can be expressed in terms of fermion strings of the form
579 \bar{v}(p_{2},\sigma_{2})P_{-\tau}\hat{a}_{1}\hat{a}_{2}\cdots\hat{a}_{n}u(p_{1},\sigma_{1}),
585 \begin_inset Formula $p$
589 \begin_inset Formula $\sigma$
593 \begin_inset Formula $e^{\pm}$
596 four-momenta and helicities
597 \begin_inset Formula $(\sigma=\pm1)$
601 \begin_inset Formula $\hat{a}_{i}=a_{i}^{\mu}\gamma_{\nu}$
605 \begin_inset Formula $P_{\tau}=\frac{1}{2}(1+\tau\gamma_{5})$
608 is a chirality projection operator
609 \begin_inset Formula $(\tau=\pm1)$
614 \begin_inset Formula $a_{i}^{\mu}$
617 may be formed from particle four-momenta, gauge-boson polarization vectors
618 or fermion strings with an uncontracted Lorentz index associated with final-sta
622 \begin_layout NoteToEditor
623 Figures 1 and 2 should appear side-by-side in print
626 \begin_layout Standard
627 In the chiral representation the
628 \begin_inset Formula $\gamma$
631 matrices are expressed in terms of
632 \begin_inset Formula $2\times2$
636 \begin_inset Formula $\sigma$
639 and the unit matrix 1 as
642 \gamma^{\mu} & = & \left(\begin{array}{cc}
643 0 & \sigma_{+}^{\mu}\\
645 \end{array}\right),\gamma^{5}=\left(\begin{array}{cc}
648 \end{array}\right),\\
649 \sigma_{\pm}^{\mu} & = & ({\textbf{1}},\pm\sigma),
657 \hat{a}=\left(\begin{array}{cc}
660 \end{array}\right),(\hat{a})_{\pm}=a_{\mu}\sigma_{\pm}^{\mu},
665 The spinors are expressed in terms of two-component Weyl spinors as
668 u=\left(\begin{array}{c}
671 \end{array}\right),v={\textbf{(}}\vdag_{+}{\textbf{,}}\vdag_{-}{\textbf{)}}.
679 \begin_layout Standard
680 The Weyl spinors are given in terms of helicity eigenstates
681 \begin_inset Formula $\chi_{\lambda}(p)$
685 \begin_inset Formula $\lambda=\pm1$
691 \begin_layout MathLetters
694 u(p,\lambda)_{\pm} & = & (E\pm\lambda|{\textbf{p}}|)^{1/2}\chi_{\lambda}(p),\\
695 v(p,\lambda)_{\pm} & = & \pm\lambda(E\mp\lambda|{\textbf{p}}|)^{1/2}\chi_{-\lambda}(p)
703 \begin_layout Section
704 Floating material and so forth
707 \begin_layout Standard
708 Consider a task that computes profile parameters for a modified Lorentzian
712 I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
720 d_{1}=\sqrt{\left(\begin{array}{c}
721 \frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
722 \frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
730 d_{2}=\sqrt{\left(\begin{array}{c}
731 \frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
732 \case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
740 x_{1}=(x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta
748 y_{1}=-(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
756 \begin_layout Standard
758 \begin_inset Formula $x_{0}$
762 \begin_inset Formula $y_{0}$
765 is the star center, and
766 \begin_inset Formula $\Theta$
769 is the angle with the
770 \begin_inset Formula $x$
774 Results of this task are shown in table
779 \begin_inset CommandInset ref
786 It is not clear how these sorts of analyses may affect determination of
788 \begin_inset Formula $M_{\text{\sun}}$
791 , but the assumption is that the alternate results should be less than 90°
792 out of phase with previous values.
793 We have no observations of
797 \begin_layout Plain Layout
808 \begin_inset Formula $\nicefrac{4}{5}$
811 of the electronically submitted abstracts for AAS meetings are error-free.
815 \begin_layout Acknowledgements
819 \begin_layout Standard
820 We are grateful to V.
825 Phillips for doing the math in section
830 \begin_inset CommandInset ref
837 More information on the AAS\SpecialChar TeX
838 macros package are available at
839 \begin_inset Flex URL
842 \begin_layout Plain Layout
844 http://www.aas.org/publications/aastex
853 \begin_layout Plain Layout
862 ftp://www.aas.org/pubs/
866 \begin_layout Plain Layout
877 \begin_layout Plain Layout
888 \begin_layout Software
889 IRAF, AIPS, Astropy, ...
893 \begin_layout Appendix
897 \begin_layout Section
901 \begin_layout Standard
902 Consider once again a task that computes profile parameters for a modified
903 Lorentzian of the form
906 I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
914 \begin_layout MathLetters
917 d_{1}=\frac{3}{4}\sqrt{\left(\begin{array}{c}
918 \frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
919 \frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
927 d_{2}=\case{3}{4}\sqrt{\left(\begin{array}{c}
928 \frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
929 \case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
937 x_{1} & = & (x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta\\
938 y_{1} & = & -(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
946 \begin_layout Standard
947 For completeness, here is one last equation.
959 \begin_layout References
960 \begin_inset CommandInset bibitem
962 label "Auri\\`ere(1982)"
973 \begin_layout Plain Layout
985 \begin_layout References
986 \begin_inset CommandInset bibitem
988 label "Canizares et al.(1978)"
997 A., Liller, W., and McClintock, J.
1003 \begin_layout Plain Layout
1015 \begin_layout References
1016 \begin_inset CommandInset bibitem
1017 LatexCommand bibitem
1018 label "Djorgovski and King(1984)"
1024 Djorgovski, S., and King, I.
1030 \begin_layout Plain Layout
1042 \begin_layout References
1043 \begin_inset CommandInset bibitem
1044 LatexCommand bibitem
1045 label "Hagiwara and Zeppenfeld(1986)"
1051 Hagiwara, K., and Zeppenfeld, D.
1052 1986, Nucl.Phys., 274, 1
1055 \begin_layout References
1056 \begin_inset CommandInset bibitem
1057 LatexCommand bibitem
1058 label "Harris and van den Bergh(1984)"
1065 E., and van den Bergh, S.
1070 \begin_layout Plain Layout
1082 \begin_layout References
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1084 LatexCommand bibitem
1085 label "H\\`enon(1961)"
1092 1961, Ann.d'Ap., 24, 369
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1097 LatexCommand bibitem
1110 \begin_layout Plain Layout
1122 \begin_layout References
1123 \begin_inset CommandInset bibitem
1124 LatexCommand bibitem
1133 1975, Dynamics of Stellar Systems, A.
1134 Hayli, Dordrecht: Reidel, 1975, 99
1137 \begin_layout References
1138 \begin_inset CommandInset bibitem
1139 LatexCommand bibitem
1140 label "King et al.(1968)"
1147 R., Hedemann, E., Hodge, S.
1154 \begin_layout Plain Layout
1166 \begin_layout References
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1168 LatexCommand bibitem
1169 label "Kron et al.(1984)"
1177 V., and Wasserman, L.
1183 \begin_layout Plain Layout
1195 \begin_layout References
1196 \begin_inset CommandInset bibitem
1197 LatexCommand bibitem
1198 label "Lynden-Bell and Wood(1968)"
1204 Lynden-Bell, D., and Wood, R.
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1224 label "Newell and O'Neil(1978)"
1237 \begin_layout Plain Layout
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1251 LatexCommand bibitem
1252 label "Ortolani et al.(1985)"
1258 Ortolani, S., Rosino, L., and Sandage, A.
1263 \begin_layout Plain Layout
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1277 LatexCommand bibitem
1278 label "Peterson(1976)"
1290 \begin_layout Plain Layout
1302 \begin_layout References
1303 \begin_inset CommandInset bibitem
1304 LatexCommand bibitem
1305 label "Spitzer(1985)"
1312 1985, Dynamics of Star Clusters, J.
1314 Hut, Dordrecht: Reidel, 109
1317 \begin_layout Standard
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1353 The processor has to buffer the text of the caption, so it is good not
1354 to be too wordy, but that would make for poor communication as well.
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2282 <cell alignment="right" valignment="top" usebox="none">
2285 \begin_layout Plain Layout
2291 <cell alignment="right" valignment="top" usebox="none">
2294 \begin_layout Plain Layout
2300 <cell alignment="right" valignment="top" usebox="none">
2303 \begin_layout Plain Layout
2309 <cell alignment="right" valignment="top" usebox="none">
2312 \begin_layout Plain Layout
2318 <cell alignment="right" valignment="top" usebox="none">
2321 \begin_layout Plain Layout
2327 <cell alignment="right" valignment="top" usebox="none">
2330 \begin_layout Plain Layout
2336 <cell alignment="right" valignment="top" usebox="none">
2339 \begin_layout Plain Layout
2345 <cell alignment="right" valignment="top" usebox="none">
2348 \begin_layout Plain Layout
2354 <cell alignment="right" valignment="top" usebox="none">
2357 \begin_layout Plain Layout
2371 \begin_layout Table note
2376 \begin_layout Plain Layout
2383 Sample footnote for table
2384 \begin_inset space ~
2388 \begin_inset CommandInset ref
2394 that was generated with the \SpecialChar LaTeX
2398 \begin_layout Table note
2403 \begin_layout Plain Layout
2410 Yet another sample footnote for table
2411 \begin_inset space ~
2415 \begin_inset CommandInset ref
2424 \begin_layout Table note
2429 \begin_layout Plain Layout
2436 Another sample footnote for table
2437 \begin_inset space ~
2441 \begin_inset CommandInset ref
2450 \begin_layout TableComments
2451 We can also attach a long-ish paragraph of explanatory material to a table.
2454 tablerefs to append a list of references.
2455 The following references were from a different table: I've patched them
2456 in here to show how they look, but don't take them too seriously—I certainly
2460 \begin_layout TableRefs
2461 (1) Barbuy, Spite, & Spite 1985; (2) Bond 1980; (3) Carbon et al.
2462 1987; (4) Hobbs & Duncan 1987; (5) Gilroy et al.
2463 1988: (6) Gratton & Ortolani 1986; (7) Gratton & Sneden 1987; (8) Gratton
2464 & Sneden (1988); (9) Gratton & Sneden 1991; (10) Kraft et al.
2465 1982; (11) LCL, or Laird, 1990; (12) Leep & Wallerstein 1981; (13) Luck
2466 & Bond 1981; (14) Luck & Bond 1985; (15) Magain 1987; (16) Magain 1989;
2467 (17) Peterson 1981; (18) Peterson, Kurucz, & Carney 1990; (19) RMB; (20)
2468 Schuster & Nissen 1988; (21) Schuster & Nissen 1989b; (22) Spite et al.
2469 1984; (23) Spite & Spite 1986; (24) Hobbs & Thorburn 1991; (25) Hobbs et
2471 1991; (26) Olsen 1983.
2479 \begin_layout Standard
2480 \begin_inset Note Note
2483 \begin_layout Plain Layout
2484 LyX can load deluxetable files verbatim.
2485 To see this in action, dissolve the following Note and copy the file table.tex
2486 from the AASTeX 5.0 distribution into the same directory as this file.
2494 \begin_layout Standard
2495 \begin_inset Note Note
2498 \begin_layout Plain Layout
2499 \begin_inset CommandInset include