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THE GALACTIC GLOBULAR CLUSTERNGC 3201: PRIMORDIAL BINARIES
AND TIDAL DYNAMICS
By
Patrick Cote B.Sc.. ~LSc.
A TheJi"
Submitted to the Faculty of Graduate Studies
in Partial Fulfillment of the Requiremenf.,
for the Degree
Doctor of PhilOJophy
McMaster University
June 1994
(c) Copyright by Patrick Cote, 1994.
DOCTOR OF PHILOSOPHY (1994)
{.\STROPHYSICS)~[d1.-\STER t-~lVERSITY
Hamilton, Ontario
TITLE: The Galactic Globular Clustt'r :\GC 3201: Prllllordial Binariesand Tidal Dynamics
.-\t-THOR: Patrick CoteB.Sc. (l-niwrsity of \\'estern Ontario)~LSc, (~Ic~laster Cnh'ersity)
SCPER\lSOR: Dr. D. L. \Yekh
Nl"~lBER OF PAGES: xv, 125
ii
ACKNOWLEDGElVIENTS
I am grateful to ),Idlaster Cniversity and the Department of Physics £.: .-\5-
tronomv for continued fundin!! I and XSERC for cominued in:miration I. \Yithout. - . ...
),Iarg, Wendy. CheryL Rosemary and Jackie to guide me through the paperwork. I
might never have escaped the confines of graduate schooL ending up. instead. like
a fossil entombed in GH-llO. The entire ensemble of students \\-ith whom I ha';e
shared an office over the last four years - Ste\'e Butterworth. Pat DurrelL Phil Fis-
cher, Dave Fleming, Steve Holland. Dean ),IeLaughlin. Kanan Patel. Jeff Secke:- and
Mark \Valker - are hereby acknowledged for not just their counsel and tolerance
but also for their unwavering eagerness to "talk shop"'. Especially profound thanks
are reserved for Phil Fischer. who expertly served as a sounding board throughout
the preparation of tbs thesis. The continuous encouragement of my family has
helped to ease the pain that ine"-itably accompanies the pursuit of a career in as-
tronomy. Thanks to the astronomy staff at MdIaster - Bill Harris. Ralph Pudritz.
Peter Suthcrland~Doug \Velch and Christine \Vilson - for almost never reminding
me of the fine line between professor and student. And to Doug \Yelch - ad,,;sor
extraordinaire and contagious enthusiast of everything astronomical - my sincere
gratitude. But. most of all. thank you Abby for your constancy and understanding
in all things great and small.
iii
iv
For Abby
\Ve can conclude that a project as grand as the
scientific-mythical construction of victory over human limitation is not something
that can be programmed by science. Even more, it comes from the \;tal energies
of masses of men sweating within the nightmare of creation - and it is not even in
man's hands to program. \Vho knows what form the forward momentum of life \\;ll
take in the time ahead or what it will make of our anguished searching. The most
that anyone of us can seem to do is to fashion something - an object or ourselves
- and drop it into the confusion, make an offering of it, so to speak, to :he life
force.
- Ernest Becker
\'
v
TABLE OF CONTENTS
..\.bstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. IX
List of Important Symbols.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Xl
List of ..\.cronyms xiii
List of Figures xiv
List of Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. x'·
Section 1 Overture .
1.1 Astronomical Context and Division of Labour , .
1.2 Observational Basics 8
Section 2 The Detection of an Extended Moving Group Near the Galactic
Disk 12
2.0 .-\bstract 12
2.1 Introduction............ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12
') .) Ob . . 1"_._ servatlons . ..... . . . . .... . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _
2.3 Monte Carlo Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13
2.-1 Ta.....onomy and ~Io,;ng Group Parameters.. . . . . . . . . . . . . . . . . . . . . . . . . . .. l-l
2.5 Conclusions and Future \Vork '" 15
Section 3 A Search for Binaries in Globular Cluster NGC 3201 16
vi
:to Abstract , 16
3.1 Introduction.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16
:3.~ Ohsen<l.tions and Reductions 1j'
3.3 The Radial Velocities.......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19
3.-1 The Binary Candidates 35
3.5 )'lodeling the Binary Population. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39
3.6 Discussion 40
3. j Summary 45
Section -l Dynamics of the Galactic Globular Cluster NGC 3201 4j
·4.0 .-\.bstract 48
4.1 Introduction 49
4.2 Observations and Reductions 51
·4.2.1 Surface Photometry and Star Counts 51
4.2.2 Radial Velocities 53
4.2.3 Structure in the Velocity Field....... . . . . . . . . . . . . . . . . . . . . . . . . . .. 54
4.3 Dynamical :\Iodels.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 59
4.3.1 Single- and )'(ulti-Mass Models 59
4.3.1.1 Luminosity-to-Mass Ratios 62
4.3.1.2 Fitting the ~Iodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 63
4.3.1.3 ~lonte Carlo Simulations 65
4.3.2 Xonparametric ).Iodels. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. 66
4.4 Results 68
4.4.1 Previous \Vork on NGC 3201 68
4.4.2 ~Iass-to-Light Ratios 69
4.4.3 )'lass Function Slope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 69
4.4.4 .~nisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ;1
4.5 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ;2
vii
Section 5 Future \Vork 103
Section 6 Appendix: Radial Velocity Simulations 106
Section 7 References 1:?4
viii
ABSTRACT
1859 radial velocities (median precision ~ 1 km S-I) have been measured for
1318 stars in the direction of the Galactic globular cluster XGC 3201. Since the
systemic radial velocity for NGC 3201 is 494.2 km 5- 1 , the field and cluster samples
separate unambiguously into two distinct samples. Analysis of the radial velocities
and APMjCCD photometry for the 879 field stars in our sample has revealed the
presence of a probable mm-;ng group of'" 13 stars '\vith radial velocity 75 km S-1
at a distance of 6 - 12 kpc. For the cluster members, we have multiple velocities
for 279 stars (known photometric variables excluded) spread over a ma."cimum of six
years. Comparison of the observed velocities to simulated datasets containing knovm.
numbers of binaries has yielded u.pper limi~ to the true binary fraction (for binaries
with 0.1 ~ P ~ 5 - 10 years and mass ratios in the range 0.1-1.0) of 0.06-0.10
(circular orbits) and 0.15-0.18 (eccentric orbits), consistent with the corresponding
incidence among nearby solar-type stars and among a sample of six other Galactic
globular clusters with measured binary fractions. NGC 3201 appears to be rotating
with an apparent projected rotation amplit11de of 1.22±0.25 km S-I. The observed
increase in ostensible rotation amplitude with distance from the cluster core may,
however, be due to either the projection of the cluster space velocity onto the
plane of the sky, or the preferential stripping of stars on prograde orbits near the
limiting radius due to the disk-shocking instability identified by Oh and Lin (1992).
BV CCD images have bef:n used to derive cluster surface brightness profiles which
extend out to ~ 18'. These profiles and the 399 mean radial velocities for non
variable cluster members have been analysed using both single- and multi-mass
King-Michie models and nonparametric techniq~es. Both methods suggest that
the cluster mass-to-light ratio is relatively fiat in the range 1.5 - 10 pc: M/Ls ~
ix
~I!L\.. = 2.0±0.2 in solar units. The best-fit mass function has a spectral index of
I :::: 0.75 ± 0.25, consistent \\;th recent findings that the fomi of the mass function
depends on the position relative to the potential of the Gala.'\."}o.
x
a
B j , B. 1,J.~ R, I
c
e
ErB- V)
E
1J
[Fe/HI
f(E,J)
I(e)
G
£3
MB
Mv
(m.M}o
(m.M)\!
M/L
[O/Fe]
p
II,E),Z
LIST OF IMPORTANT SYMBOLS
Amplitude of Projected Rotation Curve
Orbital Semi-:"lajor Axis
Right Ascension
Broadband Photometric ~Iagnitudes
Concentration Parameter
Surface Brightness uncertainty
Anisotropy ~'Ieasure
Declination
Eccentricity
Colour Excess in B- V
Ellipticity
Dimensionless Velocity Dispersion
Logarithmic Iron-to-Hydrogen Abundance
Distribution Function
Eccentricity Distribution
Gra\;tational Constant
Scale Luminosity
Absolute Blue Magnitude
Absolute Visual Magnitude
Reddening-Corrected True Distance Modulus
Apparent Visual Distance ~Iodulus
Mass-to-Light Ratio
Surface Brightness
Degrees of Freedom
Logarithmic Oxygen-to-Iron Abundance
Orbital Period
Velocity Components in Galactic Rest Frame
xi
r
Po
Ph
Pt
til
trO
trh
Td,O
< v~ >1/2
Vrot
'Wo
x
Position Angle
Nwnber of Stars per l7 nit ~lass
S~condary-to-Primary :Mass Ratio
Stellar Radius
Galactocentric Distance
Solar Radius
Projected Radius
Anisotropy Radius
Scale Radius
Tidal Radius
Central }.-Iass Density
Mean Density within Half-Mass Radius
Mean Density within Tidal Radius
Luminosity Density
Velocity Uncertainty; Core Velocity Dispersion
Cluster Disruption Timescale
Central Rela."<ation Time
Half-Mass Relaxation Time
Central Binary Disruption Time
Central rms Velocity
Mean Cluster Radial Velocity
Projected Rotation Velocity
Scale Velocity
Dimensionless Cluster Potential
Mass Function Spectral Index
Binary Fraction
Perpendicular Distance from Galactic Disk
xii
AAS
ADU
APM
AU
AGB
CCD
CMD
CTIO
HB
HST
lAS
IAU
IMF
lRAF
LMC
LSR
NLTT
QERGB
SBP
VDP
LIST OF ACRONYMS
American Astronomical Society
Analog-Digital Conversion ("nits
Automatic Plate )"Ieasuring
Astronomical Unit
Asymptotic Giant Branch
Charge Coupled De,,;ce
Color ~lagnitude Diagram
Cerro Tololo Inter-American Observatory
Horizontal Branch
Hubble Space Telescope
Institute for Advanced Study
International Astronomical 'Union
Initial Mass Function
Image Reduction and Analysis Facility
Large Magellanic Cloud
Local Standard of Rest
New Luyten Two Tenths
Quantum Efficiency
Red Giant Branch
Surface Brightness ProfilE'
Velocity Dispersion Profile
,j'
xiii
LIST OF FIGURES
Figure 1.1 BV Transmission Curves and Stellar Spectrum 11
Figure 2.1 Radial Velocity Histogram 13
Figure 2.2 Field Star Distribution 1-1
Figure 2.3 Field Star C~ID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. H
Figure 3.1 Radial Velocity Histogram 18
Figure 3.2 Photographic C~ID. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19
Figure 3.3 Binary Probabilities.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 38
Figure 3.4 NGC 3201 C~ID 38
Figure 3.5a Finder Chart for 20 Candidate Binaries. . . . . . . . . . . . . . . . . . . . . .. -11
Figure 3.5b Finder Chart for Outermost Binary Candidate.. . . . . . . . . . . . . .. 42
Figure 3.6 Dependence of Red Giant Radii on Luminosity 43
Figure 3.7 Model Velocity Distributions (Circular Orbits) 4-l
Figure 3.8 Model Velocity Distributions (Eccentric Orbits)... . . . . . . . . . . . .. 45
Figure 3.9 Radial Distribution of Candidate Binaries. . . . . . . . . . . . . . . . . . . . .. 45
Figure 4.1 Orientation of CCD Fields............ . . . . . . . . . . . . . . . . . . . . . . . .. 93
Figure 4.2 Radial Velocity versus Position Angle/Projected Radius 94
Figure 4.3 Cluster Rotation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 95
Figure 4.4 Vrot./u versus ellipticity for Galactic Globular Clusters 96
Figure 4.5 Location of Cluster Members on the Plane of the Sky. . . . . . . . .. 97
Figure 4.6 BV Surface Brightness Profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 98
Figure 4.7 Velocity Dispersion Profile 99
Figure 4.8 Mass Density and M/Lv Profile " 100
Figure 4.9 Mass Function Slope vs Position Relative to Galactic Potential 101
Figure 4.10 Mass Function Slope vs Disruption and Rela.'Ction Timescales 102
xiv
LIST OF TABLES
Table 2.1 Candidate Mo";ng Group Members 13
Table 3.1 Log of Observations IS
Table 3.2 Radial Velocities for NGC 3201 Photometric Variables. . . . . . . . .. 20
Table 3.3 Radial Velocities for NGC 3201 Member Stars 21
Table 3.4 Radial Velocities for NGC 3201 Field Stars 36
Table 3.5 Candidate Binaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39
Table 3.6 Velocity Differences ~ (8, 10) km s-1 Per Artificial Data Set. 43
Table 3.7 KoImolgorov-Smirnov Probabilities For Model Acceptance 44
Table 4.1 General Cluster Parameters 79
Table 4.2 BV Surface Brightness Profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 80
Table 4.3 Ellipticities for Galactic Globular Clusters. . . . . . . . . . . . . . . . . . . . .. 83
Table 4.4 Dependence of Apparent Rotation on Sample Size 84
Table 4.5 Adopted Mass Bins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 85
Table 4.6 V-Band Fitted Parameters 86
Table 4.7 B-Band Fitted Parameters ,. . . . . . . . . . . . . . . . . . .. . . . . . . . . . .. 87
Table 4.8 V-Band Derived Parameters 88
Table 4.9 B-Band Derived Parameters 89
xv