1 #LyX 2.4 created this file. For more info see https://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/examples/
9 \newcommand{\myemail}{skywalker@galaxy.far.far.away}
10 %\slugcomment{Not to appear in Nonlearned J., 45.}
11 \shorttitle{Djorgovski et al.}
12 \shortauthors{Collapsed Cores in Globular Clusters}
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55 \cite_engine_type authoryear
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88 \begin_layout Standard
89 \begin_inset Note Note
92 \begin_layout Plain Layout
95 Sample document for contributions to journals of the American Astronomical
98 \begin_inset CommandInset href
100 name "AASTeX user guide"
101 target "http://journals.aas.org/authors/aastex/aasguide.html"
106 for details on how to use AASTeX.
110 \begin_layout Plain Layout
113 An up-to-date sample LaTeX article using AASTeX is available under
114 \begin_inset Flex URL
117 \begin_layout Plain Layout
119 http://journals.aas.org/authors/aastex/aastex.html#_download
130 \begin_inset Note Note
133 \begin_layout Plain Layout
136 The AASTeX document class uses a different name since version 6.0 (2016/02/16).
137 Depending on the version installed on your system, set the document class
138 to American Astronomical Society (AASTeX v.
139 6) or American Astronomical Society (AASTeX v.
144 \begin_layout Plain Layout
149 \begin_inset Flex URL
152 \begin_layout Plain Layout
154 http://journals.aas.org/authors/aastex/revisionhistory.html
159 ) are only partially supported by LyX (see
160 \begin_inset Flex URL
163 \begin_layout Plain Layout
165 https://www.lyx.org/trac/ticket/10027
179 Collapsed Cores in Globular Clusters, Gauge-Boson Couplings, and AAS\SpecialChar TeX
185 Djorgovski and Ivan R.
189 \begin_layout Affiliation
190 Astronomy Department, University of California, Berkeley, CA 94720
193 \begin_layout Altaffilation
195 \begin_inset Newline newline
198 Cerro Tololo Inter-American Observatory.
199 \begin_inset Newline newline
202 CTIO is operated by AURA Inc.
203 \begin_inset space \space{}
206 under contract to the National Science Foundation.
209 \begin_layout Altaffilation
210 Society of Fellows, Harvard University.
213 \begin_layout Altaffilation
214 present address: Center for Astrophysics
215 \begin_inset Newline newline
218 60 Garden Street, Cambridge, MA 02138
227 \begin_layout Affiliation
228 National Optical Astronomy Observatories, Tucson, AZ 85719
231 \begin_layout Altaffilation
232 Visiting Programmer, Space Telescope Science Institute
235 \begin_layout Altaffilation
236 Patron, Alonso's Bar and Grill
249 \begin_layout Affiliation
250 Space Telescope Science Institute, Baltimore, MD 21218
253 \begin_layout Altaffilation
254 Patron, Alonso's Bar and Grill
257 \begin_layout Abstract
258 This is a preliminary report on surface photometry of the major fraction
259 of known globular clusters, to see which of them show the signs of a collapsed
261 We also explore some diversionary mathematics and recreational tables.
265 \begin_layout Keywords
266 clusters: globular, peanut—bosons: bozos
269 \begin_layout Section
273 \begin_layout Standard
274 A focal problem today in the dynamics of globular clusters is core collapse.
275 It has been predicted by theory for decades
276 \begin_inset CommandInset citation
278 key "hen61,lyn68,spi85"
283 , but observation has been less alert to the phenomenon.
284 For many years the central brightness peak in M15
285 \begin_inset CommandInset citation
292 seemed a unique anomaly.
294 \begin_inset CommandInset citation
301 suggested a central peak in NGC 6397, and a limited photographic survey
303 \begin_inset CommandInset citation
311 found three more cases, including NGC 6624, whose sharp center had often
313 \begin_inset CommandInset citation
324 \begin_layout Section
328 \begin_layout Standard
329 All our observations were short direct exposures with CCD's.
330 At Lick Observatory we used a TI 500
331 \begin_inset Formula $\times$
334 500 chip and a GEC 575
335 \begin_inset Formula $\times$
338 385, on the 1-m Nickel reflector.
339 The only filter available at Lick was red.
340 At CTIO we used a GEC 575
341 \begin_inset Formula $\times$
345 \begin_inset Formula $B,V,$
349 \begin_inset Formula $R$
352 filters, and an RCA 512
353 \begin_inset Formula $\times$
357 \begin_inset Formula $U,B,V,R,$
361 \begin_inset Formula $I$
364 filters, on the 1.5-m reflector.
365 In the CTIO observations we tried to concentrate on the shortest practicable
366 wavelengths; but faintness, reddening, and poor short-wavelength sensitivity
367 often kept us from observing in
368 \begin_inset Formula $U$
372 \begin_inset Formula $B$
376 All four cameras had scales of the order of 0.4 arcsec/pixel, and our field
377 sizes were around 3 arcmin.
380 \begin_layout Standard
381 The CCD images are unfortunately not always suitable, for very poor clusters
382 or for clusters with large cores.
383 Since the latter are easily studied by other means, we augmented our own
384 CCD profiles by collecting from the literature a number of star-count profiles
386 \begin_inset CommandInset citation
388 key "kin68,pet76,har84,ort85"
393 , as well as photoelectric profiles
394 \begin_inset CommandInset citation
401 and electronographic profiles
402 \begin_inset CommandInset citation
410 In a few cases we judged normality by eye estimates on one of the Sky Surveys.
413 \begin_layout Section
417 \begin_layout Standard
418 It has been realized that helicity amplitudes provide a convenient means
423 \begin_layout Plain Layout
424 Footnotes can be inserted like this.
430 These amplitude-level techniques are particularly convenient for calculations
431 involving many Feynman diagrams, where the usual trace techniques for the
432 amplitude squared becomes unwieldy.
433 Our calculations use the helicity techniques developed by other authors
435 \begin_inset CommandInset citation
442 ; we briefly summarize below.
445 \begin_layout Subsection
449 \begin_layout Standard
450 \begin_inset CommandInset label
459 \begin_layout Standard
460 A tree-level amplitude in
461 \begin_inset Formula $e^{+}e^{-}$
464 collisions can be expressed in terms of fermion strings of the form
467 \bar{v}(p_{2},\sigma_{2})P_{-\tau}\hat{a}_{1}\hat{a}_{2}\cdots\hat{a}_{n}u(p_{1},\sigma_{1}),
473 \begin_inset Formula $p$
477 \begin_inset Formula $\sigma$
481 \begin_inset Formula $e^{\pm}$
484 four-momenta and helicities
485 \begin_inset Formula $(\sigma=\pm1)$
489 \begin_inset Formula $\hat{a}_{i}=a_{i}^{\mu}\gamma_{\nu}$
493 \begin_inset Formula $P_{\tau}=\frac{1}{2}(1+\tau\gamma_{5})$
496 is a chirality projection operator
497 \begin_inset Formula $(\tau=\pm1)$
502 \begin_inset Formula $a_{i}^{\mu}$
505 may be formed from particle four-momenta, gauge-boson polarization vectors
506 or fermion strings with an uncontracted Lorentz index associated with final-sta
510 \begin_layout NoteToEditor
511 Figures 1 and 2 should appear side-by-side in print
514 \begin_layout Standard
515 In the chiral representation the
516 \begin_inset Formula $\gamma$
519 matrices are expressed in terms of
520 \begin_inset Formula $2\times2$
524 \begin_inset Formula $\sigma$
527 and the unit matrix 1 as
530 \gamma^{\mu} & = & \left(\begin{array}{cc}
531 0 & \sigma_{+}^{\mu}\\
533 \end{array}\right),\gamma^{5}=\left(\begin{array}{cc}
536 \end{array}\right),\\
537 \sigma_{\pm}^{\mu} & = & ({\textbf{1}},\pm\sigma),
545 \hat{a}=\left(\begin{array}{cc}
548 \end{array}\right),(\hat{a})_{\pm}=a_{\mu}\sigma_{\pm}^{\mu},
553 The spinors are expressed in terms of two-component Weyl spinors as
556 u=\left(\begin{array}{c}
559 \end{array}\right),v={\textbf{(}}\vdag_{+}{\textbf{,}}\vdag_{-}{\textbf{)}}.
567 \begin_layout Standard
568 The Weyl spinors are given in terms of helicity eigenstates
569 \begin_inset Formula $\chi_{\lambda}(p)$
573 \begin_inset Formula $\lambda=\pm1$
579 \begin_layout MathLetters
582 u(p,\lambda)_{\pm} & = & (E\pm\lambda|{\textbf{p}}|)^{1/2}\chi_{\lambda}(p),\\
583 v(p,\lambda)_{\pm} & = & \pm\lambda(E\mp\lambda|{\textbf{p}}|)^{1/2}\chi_{-\lambda}(p)
591 \begin_layout Section
592 Floating material and so forth
595 \begin_layout Standard
596 Consider a task that computes profile parameters for a modified Lorentzian
600 I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
608 d_{1}=\sqrt{\left(\begin{array}{c}
609 \frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
610 \frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
618 d_{2}=\sqrt{\left(\begin{array}{c}
619 \frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
620 \case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
628 x_{1}=(x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta
636 y_{1}=-(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
644 \begin_layout Standard
646 \begin_inset Formula $x_{0}$
650 \begin_inset Formula $y_{0}$
653 is the star center, and
654 \begin_inset Formula $\Theta$
657 is the angle with the
658 \begin_inset Formula $x$
662 Results of this task are shown in table
667 \begin_inset CommandInset ref
674 It is not clear how these sorts of analyses may affect determination of
676 \begin_inset Formula $M_{\text{\sun}}$
679 , but the assumption is that the alternate results should be less than 90°
680 out of phase with previous values.
681 We have no observations of
684 \begin_layout Standard
688 \begin_layout Plain Layout
704 \begin_inset Formula $\nicefrac{4}{5}$
707 of the electronically submitted abstracts for AAS meetings are error-free.
711 \begin_layout Acknowledgements
712 We are grateful to V.
717 Phillips for doing the math in section
722 \begin_inset CommandInset ref
729 More information on the AAS\SpecialChar TeX
730 macros package are available at
731 \begin_inset Flex URL
734 \begin_layout Plain Layout
736 http://www.aas.org/publications/aastex
742 \begin_inset CommandInset href
745 target "ftp://www.aas.org/pubs/AAS ftp site"
753 \begin_layout Software
754 IRAF, AIPS, Astropy, ...
757 \begin_layout Appendix
761 \begin_layout Section
765 \begin_layout Standard
766 Consider once again a task that computes profile parameters for a modified
767 Lorentzian of the form
770 I=\frac{1}{1+d_{1}^{P(1+d_{2})}}
778 \begin_layout MathLetters
781 d_{1}=\frac{3}{4}\sqrt{\left(\begin{array}{c}
782 \frac{x_{1}}{R_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
783 \frac{y_{1}}{R_{min}}\end{array}\right)^{2}}
791 d_{2}=\case{3}{4}\sqrt{\left(\begin{array}{c}
792 \frac{x_{1}}{PR_{maj}}\end{array}\right)^{2}+\left(\begin{array}{c}
793 \case{y_{1}}{PR_{min}}\end{array}\right)^{2}}
801 x_{1} & = & (x-x_{0})\cos\Theta+(y-y_{0})\sin\Theta\\
802 y_{1} & = & -(x-x_{0})\sin\Theta+(y-y_{0})\cos\Theta
810 \begin_layout Standard
811 For completeness, here is one last equation.
823 \begin_layout References
824 \begin_inset CommandInset bibitem
826 label "Auri\\`ere(1982)"
837 \begin_layout Plain Layout
849 \begin_layout References
850 \begin_inset CommandInset bibitem
852 label "Canizares et al.(1978)"
861 A., Liller, W., and McClintock, J.
867 \begin_layout Plain Layout
879 \begin_layout References
880 \begin_inset CommandInset bibitem
882 label "Djorgovski and King(1984)"
888 Djorgovski, S., and King, I.
893 \begin_layout Standard
897 \begin_layout Plain Layout
914 \begin_layout References
915 \begin_inset CommandInset bibitem
917 label "Hagiwara and Zeppenfeld(1986)"
923 Hagiwara, K., and Zeppenfeld, D.
924 1986, Nucl.Phys., 274, 1
927 \begin_layout References
928 \begin_inset CommandInset bibitem
930 label "Harris and van den Bergh(1984)"
937 E., and van den Bergh, S.
942 \begin_layout Plain Layout
954 \begin_layout References
955 \begin_inset CommandInset bibitem
957 label "H\\`enon(1961)"
964 1961, Ann.d'Ap., 24, 369
967 \begin_layout References
968 \begin_inset CommandInset bibitem
982 \begin_layout Plain Layout
994 \begin_layout References
995 \begin_inset CommandInset bibitem
1005 1975, Dynamics of Stellar Systems, A.
1006 Hayli, Dordrecht: Reidel, 1975, 99
1009 \begin_layout References
1010 \begin_inset CommandInset bibitem
1011 LatexCommand bibitem
1012 label "King et al.(1968)"
1019 R., Hedemann, E., Hodge, S.
1026 \begin_layout Plain Layout
1038 \begin_layout References
1039 \begin_inset CommandInset bibitem
1040 LatexCommand bibitem
1041 label "Kron et al.(1984)"
1049 V., and Wasserman, L.
1055 \begin_layout Plain Layout
1067 \begin_layout References
1068 \begin_inset CommandInset bibitem
1069 LatexCommand bibitem
1070 label "Lynden-Bell and Wood(1968)"
1076 Lynden-Bell, D., and Wood, R.
1078 \begin_inset Preview
1080 \begin_layout Standard
1084 \begin_layout Plain Layout
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1103 LatexCommand bibitem
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1117 \begin_layout Plain Layout
1129 \begin_layout References
1130 \begin_inset CommandInset bibitem
1131 LatexCommand bibitem
1132 label "Ortolani et al.(1985)"
1138 Ortolani, S., Rosino, L., and Sandage, A.
1143 \begin_layout Plain Layout
1155 \begin_layout References
1156 \begin_inset CommandInset bibitem
1157 LatexCommand bibitem
1158 label "Peterson(1976)"
1170 \begin_layout Plain Layout
1182 \begin_layout References
1183 \begin_inset CommandInset bibitem
1184 LatexCommand bibitem
1185 label "Spitzer(1985)"
1192 1985, Dynamics of Star Clusters, J.
1194 Hut, Dordrecht: Reidel, 109
1197 \begin_layout Standard
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1232 This is an example of a long figure caption that must be set as a paragraph.
1233 The processor has to buffer the text of the caption, so it is good not
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2212 \begin_layout Plain Layout
2218 <cell alignment="right" valignment="top" usebox="none">
2221 \begin_layout Plain Layout
2227 <cell alignment="right" valignment="top" usebox="none">
2230 \begin_layout Plain Layout
2236 <cell alignment="right" valignment="top" usebox="none">
2239 \begin_layout Plain Layout
2253 \begin_layout Table note
2258 \begin_layout Plain Layout
2265 Sample footnote for table
2266 \begin_inset space ~
2270 \begin_inset CommandInset ref
2276 that was generated with the \SpecialChar LaTeX
2280 \begin_layout Table note
2285 \begin_layout Plain Layout
2292 Yet another sample footnote for table
2293 \begin_inset space ~
2297 \begin_inset CommandInset ref
2306 \begin_layout Table note
2311 \begin_layout Plain Layout
2318 Another sample footnote for table
2319 \begin_inset space ~
2323 \begin_inset CommandInset ref
2332 \begin_layout TableComments
2333 We can also attach a long-ish paragraph of explanatory material to a table.
2336 tablerefs to append a list of references.
2337 The following references were from a different table: I've patched them
2338 in here to show how they look, but don't take them too seriously—I certainly
2342 \begin_layout TableRefs
2343 (1) Barbuy, Spite, & Spite 1985; (2) Bond 1980; (3) Carbon et al.
2344 1987; (4) Hobbs & Duncan 1987; (5) Gilroy et al.
2345 1988: (6) Gratton & Ortolani 1986; (7) Gratton & Sneden 1987; (8) Gratton
2346 & Sneden (1988); (9) Gratton & Sneden 1991; (10) Kraft et al.
2347 1982; (11) LCL, or Laird, 1990; (12) Leep & Wallerstein 1981; (13) Luck
2348 & Bond 1981; (14) Luck & Bond 1985; (15) Magain 1987; (16) Magain 1989;
2349 (17) Peterson 1981; (18) Peterson, Kurucz, & Carney 1990; (19) RMB; (20)
2350 Schuster & Nissen 1988; (21) Schuster & Nissen 1989b; (22) Spite et al.
2351 1984; (23) Spite & Spite 1986; (24) Hobbs & Thorburn 1991; (25) Hobbs et
2353 1991; (26) Olsen 1983.
2361 \begin_layout Standard
2362 \begin_inset Note Note
2365 \begin_layout Plain Layout
2366 LyX can load deluxetable files verbatim.
2367 To see this in action, dissolve the following Note and copy the file table.tex
2368 from the AASTeX 5.0 distribution into the same directory as this file.
2376 \begin_layout Standard
2377 \begin_inset Note Note
2380 \begin_layout Plain Layout
2381 \begin_inset CommandInset include