Title
Collapsed Cores in Globular Clusters, Gauge-Boson Couplings, and AASTeX atex
efault Examples Author
S. Djorgovski atex
altaffilmark<#8#>1,2,3<#8#> efault and Ivan R. King atex
altaffilmark<#9#>1<#9#> Affiliation
Astronomy Department, University of California, Berkeley, CA 94720 Author
C. D. Biemesderfer atex
altaffilmark<#10#>4,5<#10#> Affiliation
National Optical Astronomy Observatories, Tucson, AZ 85719 Email
aastex-help@aas.org And
Author
R. J. Hanisch atex
altaffilmark<#11#>5<#11#> Affiliation
Space Telescope Science Institute, Baltimore, MD 21218 Standard
atex
altaffiltext<#12#>1<#12#><#13#>Visiting Astronomer, Cerro Tololo Inter-American Observatory. CTIO is operated by AURA, Inc. under contract to the National Science Foundation.<#13#> Standard
atex
altaffiltext<#14#>2<#14#><#15#>Society of Fellows, Harvard University.<#15#> Standard
atex
altaffiltext<#16#>3<#16#><#17#>present address: Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138<#17#> Standard
atex
altaffiltext<#18#>4<#18#><#19#>Visiting Programmer, Space Telescope Science Institute<#19#>
Standard
atex
altaffiltext<#20#>5<#20#><#21#>Patron, Alonso's Bar and Grill<#21#> Abstract
This is a preliminary report on surface photometry of the major fraction of known globular clusters, to see which of them show the signs of a collapsed core. We also explore some diversionary mathematics and recreational tables.
Keywords
clusters: globular, peanut---bosons: bozos Section
Introduction Standard
A focal problem today in the dynamics of globular clusters is core collapse. It has been predicted by theory for decades atex
citep<#22#>hen61,lyn68,spi85<#22#> efault , but observation has been less alert to the phenomenon. For many years the central brightness peak in M15 atex
citep<#23#>kin75,new78<#23#> efault seemed a unique anomaly. Then atex
citet<#24#>aur82<#24#> efault suggested a central peak in NGC 6397, and a limited photographic survey of ours atex
citep[Paper I]<#25#>djo84<#25#> efault found three more cases, including NGC 6624, whose sharp center had often been remarked on atex
citep<#26#>can78<#26#> efault .
Section
Observations Standard
All our observations were short direct exposures with CCD's. At Lick Observatory we used a TI 500 _inset Formula × inset
500 chip and a GEC 575 _inset Formula × inset
385, on the 1-m Nickel reflector. The only filter available at Lick was red. At CTIO we used a GEC 575 _inset Formula × inset
385, with _inset Formula B, V, inset
and _inset Formula R inset
filters, and an RCA 512 _inset Formula × inset
320, with _inset Formula U, B, V, R, inset
and _inset Formula I inset
filters, on the 1.5-m reflector. In the CTIO observations we tried to concentrate on the shortest practicable wavelengths; but faintness, reddening, and poor short-wavelength sensitivity often kept us from observing in _inset Formula U inset
or even in _inset Formula B inset
. All four cameras had scales of the order of 0.4 arcsec/pixel, and our field sizes were around 3 arcmin. Standard
The CCD images are unfortunately not always suitable, for very poor clusters or for clusters with large cores. Since the latter are easily studied by other means, we augmented our own CCD profiles by collecting from the literature a number of star-count profiles
atex
citep<#27#>kin68,pet76,har84,ort85<#27#> efault , as well as photoelectric profiles atex
citep<#28#>kin66,kin75<#28#> efault and electronographic profiles atex
citep<#29#>kro84<#29#> efault . In a few cases we judged normality by eye estimates on one of the Sky Surveys. Section
Helicity Amplitudes Standard
It has been realized that helicity amplitudes provide a convenient means for Feynman diagram _float footnote Standard
Footnotes can be inserted like this. float evaluations. These amplitude-level techniques are particularly convenient for calculations involving many Feynman diagrams, where the usual trace techniques for the amplitude squared becomes unwieldy. Our calculations use the helicity techniques developed by other authors
_inset LatexCommand [#hag86#
inset
; we briefly summarize below. Subsection
Formalism Standard
inset
Standard
A tree-level amplitude in
_inset Formula
collisions can be expressed in terms of fermion strings of the form _inset Formula
|
(1) |
inset
where _inset Formula p inset
and _inset Formula σ inset
label the initial _inset Formula e± inset
four-momenta and helicities
_inset Formula
,
_inset Formula
and
_inset Formula
is a chirality projection operator
_inset Formula
.
The
_inset Formula
may be formed from particle four-momenta, gauge-boson polarization vectors or fermion strings with an uncontracted Lorentz index associated with final-sta te fermions. NoteToEditor
Figures 1 and 2 should appear side-by-side in print Standard
In the chiral representation the _inset Formula γ inset
matrices are expressed in terms of _inset Formula 2×2 inset
Pauli matrices _inset Formula σ inset
and the unit matrix 1 as
_inset Formula
γμ | = | ||
σμ± | = | (1,±σ), |
inset
giving _inset Formula
|
(2) |
inset
The spinors are expressed in terms of two-component Weyl spinors as _inset Formula
u = |
(3) |
inset
Standard
The Weyl spinors are given in terms of helicity eigenstates
_inset Formula
with
_inset Formula
by MathLetters
_inset Formula
u(p, λ)± | = | (E±λ|p|)1/2χλ(p), | (4) |
v(p, λ)± | = | ±λ(E |
(5) |
inset
Section
Floating material and so forth Standard
Consider a task that computes profile parameters for a modified Lorentzian of the form _inset Formula
I = |
(6) |
inset
where _inset Formula
inset
_inset Formula
inset
_inset Formula
inset
_inset Formula
inset
Standard
In these expressions _inset Formula x0 inset
, _inset Formula y0 inset
is the star center, and _inset Formula Θ inset
is the angle with the _inset Formula x inset
axis. Results of this task are shown in table _separator
_inset LatexCommand #tbl-2#154>
inset
. It is not clear how these sorts of analyses may affect determination of
_inset Formula M
, but the assumption is that the alternate results should be less than 90 atex
degr
efault out of phase with previous values. We have no observations of atex
ion<#156#>Ca<#156#><#157#>2<#157#> efault . Roughly atex
slantfrac<#158#>4<#158#><#159#>5<#159#> efault of the electronically submitted abstracts for AAS meetings are error-free. Acknowledgements
Standard
We are grateful to V. Barger, T. Han, and R. J. N. Phillips for doing the math in section _separator
_inset LatexCommand #bozomath#160>
inset
. More information on the AASTeX macros package are available at atex
_inset LatexCommand http://www.aas.org/publications/aastex
inset
efault or the atex
anchor<#162#>ftp://www.aas.org/pubs/<#162#><#163#>AAS ftp site<#163#> efault . Appendix
Section
Appendicial material Standard
Consider once again a task that computes profile parameters for a modified Lorentzian of the form _inset Formula
I = |
(7) |
inset
where MathLetters
_inset Formula
inset
_inset Formula
d2 = |
(8) |
inset
_inset Formula
x1 | = | (x - x0)cosΘ + (y - y0)sinΘ | (9) |
y1 | = | - (x - x0)sinΘ + (y - y0)cosΘ | (10) |
inset
Standard
For completeness, here is one last equation.
_inset Formula
e = mc2 | (11) |
inset
References
Auriıè re, M. 1982, atex
aap efault , 109, 301 References
Canizares, C. R., Grindlay, J. E., Hiltner, W. A., Liller, W., and McClintock, J. E. 1978, atex
apj efault , 224, 39 References
Djorgovski, S., and King, I. R. 1984, atex
apjl efault , 277, L49 References
Hagiwara, K., and Zeppenfeld, D. 1986, Nucl.Phys., 274, 1 References
Harris, W. E., and van den Bergh, S. 1984, atex
aj efault , 89, 1816 References
Hıé non, M. 1961, Ann.d'Ap., 24, 369 References
King, I. R. 1966, atex
aj efault , 71, 276 References
King, I. R. 1975, Dynamics of Stellar Systems, A. Hayli, Dordrecht: Reidel, 1975, 99 References
King, I. R., Hedemann, E., Hodge, S. M., and White, R. E. 1968, atex
aj efault , 73, 456 References
Kron, G. E., Hewitt, A. V., and Wasserman, L. H. 1984, atex
pasp efault , 96, 198 References
Lynden-Bell, D., and Wood, R. 1968, atex
mnras efault , 138, 495 References
Newell, E. B., and O'Neil, E. J. 1978, atex
apjs efault , 37, 27 References
Ortolani, S., Rosino, L., and Sandage, A. 1985, atex
aj efault , 90, 473 References
Peterson, C. J. 1976, atex
aj efault , 81, 617 References
Spitzer, L. 1985, Dynamics of Star Clusters, J. Goodman and P. Hut, Dordrecht: Reidel, 109 Standard
atex
clearpage FigCaption
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This is the first figure and it uses sgi9259.eps as its EPS figure file. FigCaption
inset
This is an example of a long figure caption that must be set as a paragraph. The processor has to buffer the text of the caption, so it is good not to be too wordy, but that would make for poor communication as well.
FigCaption
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This figure has no associated EPS file, so the optional parameter is omitted.
Standard
atex
clearpage Standard
_float tab
Caption
_space_bottom medskip
Terribly relevant tabular information.
_inset LatexCommand
inset
Standard multicol5 7 13 0 0 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 4 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 4 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 4 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 4 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 4 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 4 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 4 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 4 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 4 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 4 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 4 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 8 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 8 1 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 1 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 1 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 1 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 1 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 1 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 1 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 1 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 1 8 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 1 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 1 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 1 8 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 8 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 8 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 8 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 8 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 8 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 8 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 0 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 8 0 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot; 0 4 0 1 0 0 0 ;SPMquot;;SPMquot; ;SPMquot;;SPMquot;
Star
Height
_inset Formula dx inset
_inset Formula dy inset
_inset Formula n inset
_inset Formula χ2 inset
_inset Formula Rmaj inset
_inset Formula Rmin inset
_inset Formula P inset
atex
tablenotemark<#238#>a<#238#> efault
_inset Formula PRmaj inset
_inset Formula PRmin inset
_inset Formula Θ inset
atex
tablenotemark<#241#>b<#241#> efault
Ref.
atex
tableline
tableline
efault
1
33472.5
-0.1
0.4
53
27.4
2.065
1.940
3.900
68.3
116.2
-27.639
1,2
2
27802.4
-0.3
-0.2
60
3.7
1.628
1.510
2.156
6.8
7.5
-26.764
3
3
29210.6
0.9
0.3
60
3.4
1.622
1.551
2.159
6.7
7.3
-40.272
4
4
32733.8
-1.2
atex
tablenotemark<#242#>c<#242#> efault
-0.5
41
54.8
2.282
2.156
4.313
117.4
78.2
-35.847
5,6
5
9607.4
-0.4
-0.4
60
1.4
1.669
atex
tablenotemark<#243#>c<#243#> efault
1.574
2.343
8.0
8.9
-33.417
7
6
31638.6
1.6
0.1
39
315.2
3.433
3.075
7.488
92.1
25.3
-12.052
8
Standard
atex
tablenotetext<#244#>a<#244#><#275#>Sample footnote for table~ ref<#245#>tbl-2<#245#> that was generated with the LaTeX table environment<#275#> Standard
atex
tablenotetext<#246#>b<#246#><#276#>Yet another sample footnote for table~ ref<#247#>tbl-2<#247#><#276#> Standard
atex
tablenotetext<#248#>c<#248#><#277#>Another sample footnote for table~ ref<#249#>tbl-2<#249#><#277#> TableComments
We can also attach a long-ish paragraph of explanatory material to a table. Use tablerefs to append a list of references. The following references were from a different table: I've patched them in here to show how they look, but don't take them too seriously---I certainly have not. TableRefs
(1) Barbuy, Spite, ;SPMamp; Spite 1985; (2) Bond 1980; (3) Carbon et al. 1987; (4) Hobbs ;SPMamp; Duncan 1987; (5) Gilroy et al. 1988: (6) Gratton ;SPMamp; Ortolani 1986; (7) Gratton ;SPMamp; Sneden 1987; (8) Gratton ;SPMamp; Sneden (1988); (9) Gratton ;SPMamp; Sneden 1991; (10) Kraft et al. 1982; (11) LCL, or Laird, 1990; (12) Leep ;SPMamp; Wallerstein 1981; (13) Luck ;SPMamp; Bond 1981; (14) Luck ;SPMamp; Bond 1985; (15) Magain 1987; (16) Magain 1989; (17) Peterson 1981; (18) Peterson, Kurucz, ;SPMamp; Carney 1990; (19) RMB; (20) Schuster ;SPMamp; Nissen 1988; (21) Schuster ;SPMamp; Nissen 1989b; (22) Spite et al. 1984; (23) Spite ;SPMamp; Spite 1986; (24) Hobbs ;SPMamp; Thorburn 1991; (25) Hobbs et al. 1991; (26) Olsen 1983. float Standard
atex To see this in action, uncomment the following Standard
atex efault
_inset Quotes eld inset
atex efault
_inset Quotes erd inset
atex ) and copy the file table.tex from the AASTeX 5.0 distribution into Standard
atex Standard
atex
_inset Include
inset
_end