Blue stragglers

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Blue Stragglers

by

J o h n A nd ers O u ellette B.Sc. Victoria 1991

A D issertation S ubm itted in P artial Fulfillment of the Requirem ents for the Degree of

Do c t o r o f P h i l o s o p h y

in th e D epartm ent of Physics and A stronom y

We accept this thesis as conforming to the required standard.

Dr. C. J. Pritchet, Supervisor (D epartm ent o f Physics Sc Astronom y)

r. J. B. Tatum ,

Dr. J. B. Tatum , D epartm ental M em ber (D epartm ent o f Physics Sc A stronom y)

________________________

Dr. D. A. VandenBerg, D epartm ental M em ber (D epartm ent o f Physics Sc Astronom y)

O utefde M embetj (D epartm ent o f C hem istry)

Dr. M Mateo, E x te rn a lE x a m in e r (U niversity o f Michigan, A n n Arbor)

A ll rights reserved. T hesis m a y n o t be reproduced in whole o r in part, by photocopy o r o th er m eans, w ithout the p erm issio n o f the author.

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Supervisor: D r. C . J . P r itc h e t

A b stract

B lue stragglers a re e n ig m a tic stars which a p p e a r to h av e u n d e rg o n e som e form of reju v en atio n, b rin g in g th e m near th e zero-age m a in seq u en ce o f th e cluster in w hich th e y resid e. T h e m ost likely e x p la n a tio n for th e ex isten ce o f these stars is th a t th e y h av e form ed recently, th ro u g h th e m e rg e r o f tw o sta rs, either th ro u g h a d ire c t ste lla r collision, or th ro u g h b in a ry m a ss-tran sfe r a n d coalescence. T h is th e sis p resen ts models o f th e re m n a n ts o f th e se p ro cesses, and a com parison o f th e predictions o f th ese m odels w ith o bserved blue stragglers in several clu sters.

T h e predictions o f sm o o th e d p article h y d ro d y nam ic sim u latio n s o f collid ing stars have b een used to c re a te m odels a p p ro p ria te for in p u t in to a stellar evolution code. Since th e se m odels develop only th in , sh o rt-liv ed , convective envelopes, an g u lar m o m e n tu m loss via a m agnetically d riv e n s te lla r w ind is unlikely to be a viable m ech an ism for slowing th e rap id ly ro ta tin g b lu e stra g glers p redicted by th e coUisional scenario. A ngular m o m e n tu m tra n s fe r to e ith e r a circum stellar disk (possibly coUisional ejec ta ) o r a n e a rb y co m p an ion rem ain plausible m ech an ism s for explaining th e low ro ta tio n velocities observed for m ost blue strag g lers.

In addition to th ese m od els o f coUisional m ergers, sim pU stic m odels o f th e rem n an ts o f b in ary coalescence a n d m ass-transfer w ere also dev elo ped . T h e predictions of b o th sets o f m odels were com pared w ith th e o b serv ed blue straggler pop u latio n s o f six globular clusters (N G C 104, N G C 2419, N G C 5024, NGC 6809, N G C 7099). W hile m ost o f th e c lu s te rs ’ b lu e strag g lers a p p e a r to be weU m a tc h e d by th e predictions o f th e coUisional m erg ers, th e blue stragglers in th e c lu ste r w ith th e highest c e n tra l d en sity , N G C 7099, a p p e a r to be a h y b rid p o p u la tio n o f b o th coUisional a n d b in a ry m erg ers. T h e blue stragglers o f N G C 2419 — th e least dense o f th e c lu sters stu d ie d h ere —

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m

are well m atch ed solely by th e predictions of th e coUisional m erg ers o f eq ual m ass stars. H ow ever, d u e to th e low density o f th is c lu ste r, it is likely th a t som e fraction o f th e se blue stragglers are being form ed v ia b in a ry m ergers a n d th a t th e sim ple m odels o f b in a ry mergers used h ere a re in a d e q u a te . Exarniners:a i d e r s :

Dr. C. J. Pritchet, Supervisor (D epartm ent o f Physics & A stro n om y)

r. J. b J Tatum , L

Dr. J. By Tatum, D epartm ental M em ber (Department o f Physics & A stronom y)

Dr. D. A. VandenBerg, D epartm ental Member (D epartm ent o f Physics &

Astronomy)

pmber (Department o f C hem istry)

our,/C?utstde

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C o n te n ts

T it le i A b s tr a c t U C o n te n ts iv L ist o f T a b le s v i L ist o f F ig u r e s v ii A c k n o w le d g e m e n ts x D e d ic a t io n x ii 1 I n t r o d u c t io n 1 1.1 W h a t a re B lu e S tr a g g l e r s ? ... 1 1.2 Scope o f th is W o r k ... 8 2 B lu e S t r a g g le r s 9 2.1 O b se rv e d P ro p e rtie s o f B lue S t r a g g l e r s ... 10 2.1.1 O b se rv e d M a s s e s ... 10 2.1.2 B in a ry Blue S t r a g g l e r s ... 15 2.1.3 P u ls a tin g Blue S tr a g g le rs ... 20 2.1.4 R o ta tio n R a t e s ...21 2.1.5 C h em ical A b u n d a n c e s ... 22 2.2 F o rm a tio n M e c h a n is m s ...24 2.2.1 F oreg ro u n d C o n ta m i n a t io n ... 24

2.2.2 D elay ed S tar F o rm atio n ... 28 2.2.3 C h em ical M ixing an d N on-fcherm al P ressure S u p p o rt . 29

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C O N T E N T S V 2.2.4 B inary M ass T r a n s f e r ...30 2.2.5 B inary C o a le s c e n c e ... 34 2.2.6 Stellar Collisions ... 36 3 D e v e lo p m e n t o f M o d e ls 4 0 3.1 R em n an ts o f S te lla r C o llis io n s ...40

3.1.1 P red ictio n s from H y d ro d y n a m ic S t r a t i f i c a t i o n ...42

3.1.2 Physical S tru c tu re o f M erg er R e m n a n ts ... 50

3.2 C o n stru ctio n o f In itia l M odels... 50

3.3 E vo lu tio n ary T racks ...57

3.3.1 Surface C o n v e c t i o n ... 58

3.3.2 Core C o n v ectio n ... 65

3.3.3 C onsequences o f C alcu la te d M ixing Scales...66

3.4 Fully-m ixed M o d e l s ...67

4 C o m p a r is o n w it h O b s e r v a t io n s 7 2 4.1 N G C 104 (47 T uc) ... 87

4.1.1 Are B lue Stragglers N o rm a l S ta rs? ... 87

4.1.2 O th er P ossibilities ... 107 4.1.3 D is c u s s io n ... 116 4.2 N G C 2 4 1 9 ... 120 4.3 N G C 5024 ... 125 4.4 N G C 6397 ... 132 4.5 N G C 6809 ... 138 4.6 N G C 7099 ... 139 4.7 S u m m ary a n d D is c u s s io n ... 149

4.7.1 U n c ertain ty in derived p o p u la tio n r a t i o s ... 149

4.7.2 R o ta tio n o f CoUisional M e r g e r s ...155

4.7.3 Blue S trag g lers as D y n a m ica l P r o b e s ... 158

5 C o n c lu s io n s 1 6 5 5.1 D irections for F u tu re S t u d y ... 168

G lo s s a r y 1 7 9

A p p e n d i x A 1 8 4

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L ist o f T ab les

2.1 B lu e S trag g ler V ariability ... 17 3.1 L ist o f A ssu m ed C luster P a r a m e te r s ... 58 4.1 S elected C l u s t e r s ... 74 4.2 D ista n c e M od uli, R eddenings an d Shifts for S elected C lusters. 74 4.3 C lu ste r S tru c tu ra l an d D ynam ical P ro p e rtie s - I ...75 4.4 C lu ste r S tru c tu ra l an d D ynam ical P ro p e rtie s - II ... 75 4.5 47 T uc — S ta tis tic a l com parison w ith m odels ... 104 4.6 47 T uc — S ta tistic a l com parison w ith m odels using d a ta subset 110 4.7 47 T u c — S ta tistic a l com parison w ith m odels using re stric ted

p olygon ... 113 121 132 136 148 148 4.8 N G C 2419 — S tatistics for m ost likely p o p u la tio n ra tio s . . . 4.9 N G C 5024 — S tatistics for th e m ost likely p o p u la tio n ratios 4.10 N G C 6397 — S tatistics for th e m ost likely p o p u la tio n ratios 4.11 S u m m a ry o f blue straggler form ation r a t e s ... 4.12 S u m m a ry o f blue straggler p o p u l a t i o n s ...

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L ist o f F ig u r e s

1.1 CMD o f N G C 6397 ... 1.2 CM D o f N G C 7099 ... 1.3 CMD o f N G C 6397, w ith tracks

2.1 log g — log T e // d iag ram for N G C 6397 ... 2.2 log g — log T e // d iag ram for 47 T u c ... 2.3 P red ictio n s o f th e B ahcall S oneira m odel for N G C 5024 2.4 P red ictio n s o f th e B ah call & S oneira m odel for N G C 6397 2.5 P red ictio n s o f th e B ahcall & S oneira m odel for N G C 7099

3 4 5 12 13 25 26 27 3.1 D ensity {p) a n d h y d ro d y n am ic en tro p y (A) profiles for p o ly 

tropes 43

3.2 H ydrogen m a ss frac tio n profiles for poly tro p ic m ergers . . . . 44

3.3 D ensity (p) a n d h y d ro d y n am ic e n tro p y (>l) profiles for re a l s ta rs 48 3.4 H ydrogen m a ss frac tio n profiles for stellar m e r g e r s ...49

3.5 E v o lu tio n ary tra c k s for varying am o u n ts a n d d istrib u tio n s o f in jected e n e r g y ... 56

3.6 E v o lu tio n ary tra c k s for m etal-p o o r m erger r e m n a n t s ... 59

3.7 E v o lu tio n ary tra c k s for m etal-rich m erger r e m n a n t s ... 60

3.8 E v o lu tio n ary tra c k s for fully-m ixed m erger r e m n a n t s ... 70

3.9 E v o lu tio n ary tra c k s for fully-m ixed m erger r e m n a n t s ... 71

4.1 C o lo u r-m ag n itu d e d iag ram o f 47 Tuc (N G C 1 0 4 ) ...76

4.2 C o lo u r-m ag n itu d e diagram o f N G C 2 4 1 9 ...77 4.3 C o lo u r-m ag n itu d e diagram o f N G C 5024 ... 78 4.4 C o lo u r-m ag n itu d e diagram o f N G C 6397 ... 79 4.5 C o lo u r-m ag n itu d e diagram o f N G C 6809 ( B V ) ... 80 4.6 C o lo u r-m ag n itu d e diagram o f N G C 6809 ( V I ) ... 81 4.7 C o lo u r-m ag n itu d e diagram o f N G C 7099 ... 82 vu

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L I S T OF F IG U R E S vüi

4.8 Fiduciéds o f m e ta l-p o o r clu sters ( B V ) ... 84

4.9 F id u cials o f m etéJ-p o o r clu sters ( V I ) ... 85

4.10 C M D o f 47 T uc, w ith evolu tio n ary tra c k s... 88

4.11 D e m o n stra tio n o f C u m u lativ e A g e ... 90

4.12 P h o to m e tric m ass d e term in a tio n s of blue stra g g le rs...92

4.13 P h o to m e tric m ass d e term in a tio n s of blue strag g lers, w ith er- ro rb a rs ...95

4.14 M ass d is trib u tio n o f b lu e stragglers in 47 T u c ...96

4.15 C M D o f fak e b lu e strag g lers draw n &om s ta n d a rd tra c k s . . . 97

4.16 D e m o n stra tio n o f ...99

4.17 D e m o n stra tio n o f A z w ith fake blue s t r a g g l e r s ...100

4.18 A z d is trib u tio n o f blue stragglers in 47 T u c ... 101

4.19 A z d is trib u tio n o f tu rn o ff m ergers in 47 T u c ...109

4.20 In d iv id u a l likelihoods for th e blue stragglers in 47 T u c ...112

4.21 Likelihoods for different pop u lation ra tio s in 47 T u c ... 114

4.22 R eal a n d fake b lu e strag g lers in 47 T u c ... 117

4.23 D is trib u tio n o f b lu e strag g ler masses in N G C 47 T u c ...118

4.24 Likelihoods for different pop u lation ra tio s in N G C 2419 . . . . 122

4.25 R eal a n d fake b lu e strag g lers in NGC 2 4 1 9 ...123

4.26 D is trib u tio n o f b lu e stra g g ler masses in N G C 2 4 1 9 ...126

4.27 R eal a n d fake b lu e strag g lers in NGC 5024 ... 127

4.28 In d iv id u a l likelihoods for blue stragglers in N G C 5024 ... 128

4.29 Likelihoods for different pop u latio n ra tio s in N G C 5024 . . . . 130

4.30 D is trib u tio n o f b lu e stra g g ler masses in N G C 5024 ... 131

4.31 R eal a n d fake b lu e strag g lers in NGC 6397 ... 133

4.32 In d iv id u a l likelihoods for blue stragglers in N G C 6397 ... 134

4.33 Likelihoods for different p o p u latio n ra tio s in N G C 6397 . . . . 135

4.35 R eal a n d fake b lu e strag g lers in NGC 6809 ( B V ) ... 140

4.36 R eal a n d fake b lu e strag g lers in NGC 6809 ( V I ) ... 141

4.37 Likelihoods for different p o p u latio n ra tio s in N G C 6809 . . . . 142

4.38 D is trib u tio n o f blue stra g g ler masses in N G C 6809 ... 143

4.39 R eal a n d fake b lu e strag g lers in N GC 7099 ... 145

4.40 Likelihoods for different pop u latio n ra tio s in N G C 7099 . . . . 146

4.42 U n c e rta in tie s in th e p o p u la tio n ratios for N G C 2 4 1 9 ...153

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L IS T OF F IG U R E S ix

5.1 E v o lu tio n ary t r a c k s ...172 5.2 P e te rse n D iag ram s ...173 5.3 F irst set o f fak e blue stragglers ...185 5.4 Likelihoods fo r various population ratio s m a tc h in g first fake

d a t a s e t ... 186 5.5 Second set o f fake blue s t r a g g l e r s ... 188 5.6 Likelihoods fo r various population ratio s m atch in g second fake

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A ck n o w led g em e n ts

W h a t e x a c tly does one put in th e A cknow ledgem ents section? Ideally, as far as I u n d e rs ta n d , it is the a p p ro p riate place to recognise those who have assisted, en co u rag ed , a n d sup p o rted me d u rin g th e w ritin g of this d issertatio n (and during all o f th e tim e leading up to th e c o n ta c t of the proverbial pen w ith th e eq u ally proverbial p ap er). This d is se rta tio n is already a b o u t 200 pages long, acknow ledging all those who hav e a ssisted me in some way in reaching this p o in t would bring th a t up to a b o u t 400 pages. A quick read th ro u g h th e A cknow ledgem ents in th e d isse rta tio n s o f p a st A stro-grads gave me a clearer p ic tu re - an d some tim e to reflect on th e people th a t actu ally w rote th o se pages. H ere goes.

It seems co m m o n practice to acknow ledge o n e ’s spouse last, allowing th e last w ords to give em phasis to th e en co u rag em en t a n d em otional su p p o rt given by th is sin g u larly im p o rtan t person. I c a n ’t do th a t. A ndrea is th e first th o u g h t in m y m in d a t the beginning of th e day, h er love and w arm th are m ore essential to m e th a n the rising of th e S u n . H er place is a t th e beginning. Her sparkling b lu e eyes have encouraged m e (a n d c a p tu re d m e), h er m usical voice has consoled m e (an d charm ed m e), h er presen ce has sup p o rted me (and sustained m e). She has given m e th e s tre n g th to co n tin u e, and to finish, this dissertatio n .

It has ta k e n m e far too long to get to th is p o in t, b u t Chris P ritc h e t, m y supervisor, has d e m o n strated an alm ost god like p a tie n ce while th is disser ta tio n was being w ritte n . I always left our ta lk s reg ard in g my w ork w ith a renew ed sense o f o ptim ism . His support (b o th financial and scientific) has

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A C K N O W L E D G E M E N T S xi

been g re a tly a p p re c ia te d .

I have to th a n k D on V andenB erg for allow ing m e to u se his excellent stellar evolution co d e, w ith o u t which th e w ork in this d is se rta tio n w ould not have b een possible.

O f course, th e o th e r sta ff a n d faculty h ere in th e D e p a rtm e n t have also helped w ith th e ir w ords o f encouragem ent a n d advice: A nn G ow er, D avid H artw ick, R uss R o b b , Je re m y T atu m (who was actu a lly m y in te rim su p erv i sor w hen I first s ta r te d as a g ra d u a te s tu d e n t), a n d S tep h en so n Y ang. D avid B alam has alw ays h a d tim e a n d u n d e rstan d in g for th e g ra d u a te s tu d e n ts in th e d e p a rtm e n t; h e is to m an y a kind, w ell-respected uncle w ith a tw isted sense o f h u m o u r. C o lin Scarfe deserves acknow ledgem ent for h is p ro p h e tic al rem ark w hich he m a d e a little over th re e years ago: “...ta k e y o u r b e st guess a t how long you th in k it will ta k e you to finish a n d m u ltip ly t h a t by tt: th a t wiU be how long it will a c tu a lly tak e you to fin ish ....” 1 w ould h a v e preferred it if he h a d chosen a sm aller m a th e m atica l c o n sta n t.

M y tim e h e re o n th e fo u rth floor o f th e E llio tt building h a s overlap p ed w ith m an y g ra d u a te s tu d e n ts who have left m e w ith lastin g m em o ries: lu n ch tim e discussions a n d th e slow dow nw ards sp iral th e y in ev itab ly to o k ; sh o u ts of fru stra tio n echoing dow n th e halls durin g co m m u n al gam es o f m a ze , x tre k , xconq, x b la st, a n d q u ak e; cigars; Friday b e e r-tim e (a n d th e c o m m e n ts I re ceived w hen I e ith e r left early or d id n ’t go so t h a t I could be w ith m y sweetie a t hom e); video n ig h ts (it was an innocent m istake!).

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To m y wife, A n d re a, a n d to o u r first child, whose arriv al we awcdt eagerly.

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C h a p ter 1

I n tr o d u c tio n

1.1 What are Blue Stragglers?

A sim ple definition o f blue stragglers is th a t th e y are h o t, bright, m assive, m ain sequence s ta rs ex isting am o n g a p o p u latio n o f evolved stars.^ F igures 1.1 and 1.2 show c o lo u r-m ag n itu d e diagram s for th e globular clusters N G C 6397 (Kcduzny, 1997) a n d N G C 7099 (M30; G u h a th a k u r ta et a i, 1998). Ac cording to can o n ical th eo ry , th e m ost m assive, core hydrogen burn in g , m ain sequence stars in clu sters such as these are lo c a te d a t th e m ain sequence turnoff, while th e o th e r sequences (th e sub-giant b ra n c h , th e red giant b ran ch , a n d th e h o rizo n tal b ra n c h ) a re defined by th e ev o lu tio n o f stars a fte r th e y have left th e m ain sequence. T h e blue strag g ler sequence extends b eyond th e tu rn o ff to w here, in m uch younger clu sters, m ain-sequence s ta rs m ore m assive th a n th e c u rre n t tu rn o ff s ta rs would lie. F ig u re 1.3 shows th e sam e colour-m agnitude d ia g ra m as show n in F igure 1.1 w ith theo retical

evolution-^This definition is so m ew h at biased tow ard describing blue stragglers in clusters. Blue stragglers have been show n to exist in th e field o f th e G a lax y (H obbs & M athieu 1991; Glaspey, P ritch et Sc S te tso n 1994) w here it is not u nusual to find ‘norm al’ stars m atch in g th e sam e description.

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C H A P T E R L I N T R O D U C T I O N 2

a ry track s for sta rs o f various m asses o verplotted. T h e fa c t t h a t b lu e s tra g glers ap p ear to be m o re m assive th a n th e tu rn o ff sta rs (a n a p p e a ra n c e w hich is su p p o rte d by sp ectro sco p ic o b serv atio n s), is th e essence o f th e e n ig m a t h a t blue stragglers re p re se n t: if th e y a re m assive sta rs, th e n th e y sh ould have evolved away from th e m a in sequence long ago.

B u t does th e p resen ce o f blu e stragglers really in d ic a te a p ro b le m w ith s ta n d a rd stellcir th e o ry ? A fte r all, th e agreem ent o f c u rre n t ste lla r calcu la tions w ith observations o f sta rs in o u r own G alaxy (e.g. R en zin i & Fusi P ecci, 1988) d em o n strates th a t th e m odels a re qu ite a d e q u a te . O n th e o th e r h a n d , th e re are known om issions a n d sim plifications in th e s ta n d a rd th e o rie s, b u t none seem a d eq u a te to e x p lain how blue stragglers can a p p a re n tly re m a in on th e m ain sequence w hile th e th e bulk of th e stars in th e ir p a re n t c lu ste r h ap p ily evolve in a cc o rd a n ce w ith th e theo retical p red ictio n s.

If blue stragglers w ere fo rm ed a t th e sam e tim e as th e re s t o f th e sta rs in th e cluster, w ith th e sam e - a p p a re n tly high - m asses as th e y now possess, th e n th e y m ust in d ic a te a p ro b lem w ith ou r s ta n d a rd tr e a tm e n t o f s te lla r for m a tio n and evolution. C an o n ical stellar th eo ry a tte m p ts to m o d el s ta rs as gciseous spheres w hich a re in h y d ro sta tic a n d th e rm a l e q u ilib riu m ; th e ‘evo lu tio n ’ of a s ta r is a re s u lt o f th e continuous a d ju stm e n t o f th e (q u a si-sta tic ) equilibrium s tru c tu re o f th e s ta r in response to th e ch an g in g co n d itio n s in th e interior. D eviations fro m th is idealised s tru c tu re , d u e to , for e x am p le, ro ta tio n or th e p resen ce o f a close com panion s ta r, will re s u lt in th e s t a r ’s evolution d ep artin g fro m th e p re d ic te d course. In g en eral, how ever, d e p a r tu res significcint eno u g h to m odify th e lifetim e o f a s ta r sig n ifican tly will also resu lt in the s ta r h av in g o th e r, observable, peculiarities: for ex am p le,

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ex-C H A P T E R 1. I N T R O D U ex-C T I O N — 2 — 0 -6 — 8 - 0 . 5 BS -MS TO F ie ld S t a r s

I #

. ; :

0.5 CB-V)„ 1.5

Figure 1.1: C o lo u r-m a g n itu d e diagram for th e g lo b u la r cluster N G C 6397 (K aluzny et al., 1997). T h e various e v o lu tio n a ry sequences are labelled as follows: BS - b lu e stra g g le rs, SOB - su b -g ia n t b ra n c h , R G B - red g ia n t branch, H B - h o riz o n ta l b ra n c h , MS T O - m a in seq u en ce turnoff.

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C H A P T E R 1. I N T R O D U C T IO N - 4 r

r

Jr..' ' HB : . BS . SGB MS TO Field S t a r s

®

‘S : ' ■< ;■

0.5 1.5 ( B - V ) ,

Figure 1.2: C o lo u r-m ag n itu d e d iag ram for th e globular c lu ster N G C 7099 (M30; G u h a th a k u r ta et oZ., 1997). Sequences a re labelled as in F ig u re 1.1.

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C H A P T E R L I N T R O D U C T I O N ± X - 2 r 4 -8 - 0 . 5 0.5 ( B - V ) , 1.5

F igure 1.3: C M D o f N G C 6397 w ith evolutionary tra c k s overlaid. T h e m asses in d icated are in so lar m asses.

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C H A P T E R 1. I N T R O D U C T I O N 6

tre m e ro ta tio n , which could e x te n d th e lifetim e o f a sta r by a fa c to r o f tw o or m ore (C lem ent, 1994) by p ro v id in g a n o n -th e rm a l form o f p ressu re s u p p o r t, re d u c in g th e req u irem en ts for n u c lea r e n erg y generation, w ould also re s u lt in th e s ta r having a m u ch low er lu m in o sity a n d te m p e ra tu re th a n a sim ila r, n o n -ro ta tin g star.

N a tu re , perhaps bein g lo a th to follow th eo ry , provides sta rs for w h ich d ev iatio n s a t some level fro m th e a ssu m p tio n s im plicit in th e s ta n d a rd th e ories a re th e norm ra th e r th a n th e e x ce p tio n . For instance: all sta rs r o ta te , m a n y s ta rs are m em bers o f b in a ry sy ste m s, a n d com position v a ria tio n s a re seen am o n g stars even w ith in c lu sters (w h ere we usually assu m e a ll s ta rs fo rm w ith th e sam e co m p o sitio n ). A n d y e t th e sta n d a rd m odels have p ro v e n to be q u ite successful in th e ir p re d ic tio n o f ste lla r evolution: d e p a rtu re s fro m th eo ry , d u e to th e afo rem en tio n ed processes a n d others, a re o b serv ed (e.g. V an d en B erg , Larson, & D e P ro p ris 1998), b u t a re genereilly sm all. T h e ob vious in te rp re ta tio n o f th is is th a t, for th e m a jo rity of sta rs, can o nical s te lla r th e o ry is a n ad eq u ate a p p ro x im a tio n to reality.

Since th e sta n d a rd th e o rie s seem sufficient, it may be th a t th e e v o lu tio n o f blue stragglers, assu m in g th e y h av e m a in ta in e d th e sam e m ass o v e r th e course o f th eir lives, differs d ra m a tic a lly fro m th a t of n o rm a l sta rs. O n th e o th e r h a n d , if a process co u ld b e fo u n d to e x te n d th e life o f a s ta r by a larg e fa c to r (such as in te rn a l m ixing o r som e n o n -th erm al p ressu re s u p p o rt; W h eeler 1979, Saio &: W h eeler 1981), it is unlikely th a t a s ta r, being a ffe c te d by th is process, would follow th e n o rm a l co u rse o f evolution (th a t p re d ic te d b y th e sta n d a rd m odels): since blue stra g g lers a p p e a r to h ave m asses consis te n t w ith th eir location in th e co lo u r-m a g n itu d e diagram a n d a p p e a r to h av e

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n o rm a l in tern al s tru c tu re s (S ch o e n b e rn er & N ap iw o tzk i, 1994) th eir evolu tio n cannot d e v iate g re a tly fro m th a t o f a norm al s ta r. R ecalling th e ex am p le o f a rapidly ro ta tin g s ta r : d u e to its lowered te m p e ra tu re a n d lum inosity, it wül a p p e a r to b e a low er m ass s ta r th a n it actu ally is, po ssib ly p rev en tin g it from being identified as a b lu e strag g ler.

If blue stragglers do n o t differ fro m normed sta rs solely in th e ir evolution, th e n th eir fo rm atio n m u s t differ also. T his provides a seco n d answ er to th e q u estio n posed earlier: if b lu e strag g lers do no t form in th e sam e fashion as n o rm a l stars, th e n th e y do n o t necessarily in d icate a flaw in o u r theories o f steUcir evolution. If, fo r e x a m p le , blu e stragglers do evolve cis norm al s ta rs, a n d p erh ap s fo rm in th e sa m e m a im e r as norm al s ta rs, b u t fo rm ed la te r th a n th e o th e r stars in th e c lu ste r, th e n th e y would n a tu ra lly a p p e a r as m ain sequence stars e x te n d in g ab o v e th e tu rn o ff (those s ta r s form ing w ith a m ass less th a n th a t o f a tu rn o ff s ta r w ould likely blend in w ith th e less evolved, b u t n o rm al, cluster m ain seq u e n c e). In o th e r words, if o n e could, th ro u g h som e h y p o th e tic al m ech an ism , fo rm a n otherw ise n o rm al s ta r long after s ta rs o f th e sam e m ass h a d ev olv ed aw ay, th e s ta r could th e n evolve in th e ‘c o rre c t’ m a n n e r and still a p p e a r as a blue strag g ler.

Since canonical th e o ry is a p p a re n tly on sound fo o tin g , a n d processes by w hich the evolution o f b lu e strag g lers can be a lte re d do n o t present th e m selves, it is likely th a t it is in th e ir fo rm atio n th a t b lu e strag g lers differ from n o rm a l stars. T h is is n o t to say t h a t th e processes w hich can a lte r th e evolu tio n o f a s ta r (such as r o ta tio n o r bincirity) are n o t a c tin g on blue stragglers — in fact, th e re is n o th in g to say t h a t these processes a re n o t m ore effective a m o n g blue strag g lers th a n n o rm a l s ta rs. T h ro u g h o u t th is work, I will be

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assum ing th e sta tu s quo: can o n ical th e o ry holds for b lu e stragglers as it ap  p aren tly does for n o rm al s ta rs, a n d th a t deviations from th e theory have no m ore an effect on blue stragglers th a n th e y a p p e a r to have on norm al stars.

1.2 Scope of this Work

T he m ain goal o f th is work is to develop and evolve m odels o f th e re m n a n ts of stellar collisions. Stellar collisions have been p ro p o sed as a possible for m ation m echan ism for blue strag g lers (Hills &: Day, 1976) a n d are very likely to occur in g lo b u lar clusters, especially if in te ra ctio n ra te s a re enhanced by the presence o f a p o p u latio n o f binaries (L eonard & F a h lm a n , 1991). T hese models, once d ev eloped, will b e co m p ared to th e o bserved populations o f blue stragglers in several globular c lu sters w ith pro m in en t b lu e straggler p o p u la tions.

C h a p te r 2 co n tain s a review o f blue stragglers, th e theories proposed for th e ir fo rm atio n a n d th e o b serv atio n s which have b e e n m ad e of th em . In C h ap ter 3 I will describe th e m odels o f stellar re m n a n ts, w hich will be used in C h a p te r 4 in a com parison w ith observed blue strag g lers.

E xecutive su m m a ry : B lue strag g lers are blue a n d tw in k ly an d , m uch like the little s ta r im m o rtalised in song, we w onder w h at th e y are.

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C h a p ter 2

B lu e S tr a g g le r s

T h ere have been m an y m ech an ism s proposed for th e fo rm a tio n o f blue stra g glers and, like an y o th e r th eo ry , th e ir success is g au g ed by th e ir a g re em e n t w ith observations. H ow ever, th e situ a tio n seem s so m ew h at to o co m p licated to allow for a single th e o ry to ex p lain all blue stragglers: no single m ech an ism is able to explain all o f th e o bserv ed properties o f blue strag g lers. E n v iro n m en tal factors (e.g. s te lla r density, b inary fractio n a n d p erio d d is trib u tio n , th e presence of gas a n d d u s t) play a role in th e efficiency o f m o st o f th e proposed fo rm atio n m ech an ism s, so it is reasonable to re q u ire th a t a m ech anism be able to ex p lain th e observations o f blue strag g lers in its p re fe rre d environm ent.

In this C h a p te r, I will review th e observed p ro p e rtie s o f blue strag g lers outside th e co n tex t o f a n y o f th e proposed m echanism s; only a fte r th e o bser vations have been review ed will I describe th ese m ech an ism s in a n y d etail.

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C H A P T E R 2. B L U E S T R A G G L E R S 10

2.1 Observed Properties of Blue Stragglers

2 .1 .1

O b serv ed M a s s e s

B ecause of th e ir lo c atio n o n th e co lo u r-m ag n itu d e d ia g ra m (C M D ^ ) - gen erally b rig h ter th a n th e p a re n t c lu ster’s m ain -seq u en ce tu rn o ff (M S T O ) (see Figures 1.1 a n d 1.2) - b lu e stragglers a re u su ally assu m e d to b e m assive s ta rs. However, th e m ass o f a s ta r is one o f th e m o st difficult p ro p e rtie s to determ ine: th e o n ly w ay to m easure th e m ass o f a s ta r w ith o u t re s o rt ing to assu m p tio n s a b o u t its lum inosity, or e v o lu tio n a ry s ta te , is th ro u g h its g rav ita tio n a l effect on n e a rb y o b je cts. For stcirs o th e r th a n th e S u n , th is is possible only in b in a ry sy ste m s. A lthough th e re a re blue strag g lers w hich a re com ponents o f b in a ry sy stem s (e.g. K alu zn y 1997, K alu zn y et al. 1996, Y an &: R eid 1996) none h av e b een stu d ied w ith th e in te n tio n o f o b ta in in g m ass estim ates. D e sp ite th is , th e re are o th e r, less d ire c t m e th o d s, w hich can b e used to e stim a te th e m ass of a blue strag gler.

Shara et al. (1997) a n d R odgers & R o b e rts (1995) a tte m p te d to d e te r m ine th e m ass o f blue stra g g lers in 47 T uc a n d N G C 6397, respectiv ely , by spectroscopically m e asu rin g th e ir surface g rav ities a n d te m p e ra tu re s . T h e m easu rem en ts o f S h a ra et al., w hich were m ore precise th a n th o se o f R odgers & R o b erts, showed th a t B SS-19 in 47 Tuc ( G u h a th a k u r ta et al. 1992) has a mass of 1.70 ± 0.40Ai®, ro u g h ly twice th e m ain -seq u en ce tu rn o ff m ass of th e cluster as inferred fro m isochrone fits to th e c lu ste r C M D . T h e re su lts of R odgers &: R o b erts sim ilarly showed th a t th e b lu e strag g lers in N G C 6397 a re , on average, m o re m assiv e th a n the c lu ster tu rn o ff s ta rs. U n fo rtu n ate ly ,

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th e m e th o d u sed in b o th studies req u ired t h a t th e absolute lu m in o sity o f th e stars b e know n, o r assu m ed .

It is possible to use th e surface g rav ities a n d te m p e ra tu re s m e a su re d by R odgers &: R o b e rts a n d S h ara et al. to e s tim a te th e masses o f blue s tra g  glers in a d ifferen t, d ista n ce in d ep en d en t, m e th o d . Figures 2.1 a n d 2.2 show log ÿ —log Tef f d ia g ra m s for N G C 6397 a n d 47 T uc, w ith th e m e asu re m e n ts o f R odgers & R o b e rts a n d S h ara et al. also p lo tte d . Since the surface g ra v itie s and te m p e ra tu re s a re deriv ed &om sp ectro sco p ic observations by co m p ariso n w ith m odel a tm o sp h e re s, th e re is no d ista n c e dep en d en ce (alth o u g h th e re is a reddening d e p en d e n c e on th e results o f S h a ra et al., b u t it is a sm all effect). R odgers & R o b e rts found masses for th e b lu e stragglers in N G C 6397 ra n g ing from 0.62M© to 1.15A/©, which a re q u ite different th a n th e fairly n a rro w range o f m asses in fe rred from th e log g — log T * // diagram — this difference is pro b ab ly d u e in p a rt to th e poor p h o to m e try th e y used for th e lu m in o sity inform ation n ecessary for th e ir einalysis. T h e m ass Shara et al. fo u n d for BSS-19 agrees q u ite well w ith th e m ass fro m th e log g — log T e// d ia g ra m (~ 1.55M©) — it is also ra th e r en co u rag in g to n o te th a t th is m ass ag rees w ith th e p h o to m e tric m ass derived from th e C M D in Figure 2.2, a lth o u g h the appéirent e v o lu tio n a ry s ta te of th e b lu e stra g g ler is different in th e tw o diagram s.

S tro m g ren 4-colour p h o to m e try has also b e e n used (S trom & S tro m 1970, Bond & M cC o nn ell 1971, B ond & P e rry 1971) to show th a t blue stra g g lers have n o rm al su rfa ce gravities for th e ir lo c atio n s on th e C M D , su g g estin g th a t th e y m u st b e m ore m assive th a n th e s ta rs w hich are lower on th e m ain - sequence — in clu d in g th e clu ster tu rn o ff s ta rs .

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C H A P T E R 2. B L U E S T R A G G L E R S 12 0 2 4 6 - 0.2 0 0.2 0.4 0.6 0.8 (B-V)o 3.5 4.5 l\o 1 4 0 1 -3 0 1 2 0 1 10 l - 0 0 o g o \ \ 0.70 3.7 3.9 3. 8 4.1 4 log T^ff

F ig u re 2.1; Top - C M D for th e blue stragglers in N G C 6397 from A lcaino

et a/.(1987) (filled circles) w hich were studied by R odgers & R oberts (1995).

T h e p h o to m etry for th e blue stragglers from A lcaino et al. is som ew hat noisy, so th e p h o to m etry show n from Lauzeral et a/.(1992), w hich is of m uch b e tte r quality, is shown for reference. T h e evolutionary tra c k s a re of a m etallicity a p p ro p riate for N G C 6397 ([F e/H ]= -2.14, [a /F e ]= 0 .3 ) a n d have th e sam e m asses as those show n in th e b o tto m diagram . B o tto m - logy — log T e// diagram for th e blue strag g lers stu d ied by R odgers & R o b erts. A ty p ical l-<r e rro r bar is shown in th e d iag ram for reference. T h e evolutionary tra c k s are labelled in u n its of solar m asses.

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C H A P T E R 2. B L U E S T R A G G L E R S 13 0 2 oo 4 6 0 0.2 0 .4 0.6 0.8 1 3 .5 r-C£ O 4 .5 I 10 1 00_{0 so} 0 80 _{0 70} 3 .6 3 .9 3 .8 3 .7 4 log T,

F igure 2.2: T op - C M D fo r the blue strag g lers in 47 T uc from G u h a th a k u r ta

et al. (1992). B SS-19 (filled circle) was th e blue s tra g g le r ta rg e te d by S h a ra

et al. (1997). T h e ev o lu tio n ary tra c k s a re o f a m e ta llic ity a p p ro p ria te fo r 47 Tuc ([F e /H ]= -0 .8 3 , [a /F 'e ]= 0 .3 ) a n d have th e sam e m asses as those show n in th e b o tto m d ia g ra m . B o tto m - log g — log T *// d ia g ra m for th e blue s tra g g le r stu d ied by S h a ra et al.. A typical \-<r e rro r b a r is show n in th e d iag ram for reference. T h e e v o lu tio n a ry tracks a re labelled in u n its o f solar m asses.

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C H A P T E R 2. BLU E S T R A G G L E R S 14

A n in d icatio n of w h eth er or n o t b lu e stra g g lers are m ore massive th a n o th e r s ta rs in th e parent clu ster can b e fo u n d by com paring th e ir radial dis tr i b u tio n to th a t of o th e r c lu ster s ta rs. D u e to m ass segregation, the m o re m assiv e s ta rs, w hether th e y are single s ta r s o r tig h tly b o un d binaries, will te n d to se ttle to th e core o f a clu ster on a tim escale equal to th e relax atio n tim e o f th e clu ster. B lue stragglers a re fo u n d to be m ore centrally con c e n tr a te d th a n th e cluster giants a n d m ain -seq u en ce stars (e.g. Sarajedini & F o rre s te r 1995, G u h a th a k u rta et al. 1994, S arajed in i 1994, Ferraro et al. 1992, C ô té et al. 1991, N em ec & H arris 1987) a n d as centrally co n cen trated as c lu s te r binairies (M athieu & L a th a m 1986, E d m o n d s et al. 1996).

W ith several 10 m eter class telescopes available, or becom ing available so o n , it should be possible to m ake d ire c t m easu rem en ts o f th e masses of th o se blue stragglers th a t éire in b in a ry sy ste m s. Since o b tain in g sp ectro scopic m easu rem en ts o f a b in ary blue s tra g g le r over its en tire o rb it - neces sa ry to d e te rm in e orbital p a ra m ete rs a n d , h en ce, its mass - w ould be tim e co n su m in g (on telescopes w hich a re in e x tre m e ly high d em an d ), mciss es tim a te s for single blue stragglers, such as th o se obtain ed by Shara et al. (1997), w ould m ake m ore efficient use o f telesco p e tim e. Also, d e term in a tio n o f th e surface gravity a n d effective te m p e ra tu re of a large num ber o f b lu e stra g g lers in a cluster w ould be in v a lu a b le for studies of th e ir evolution since th e se m easurem ents could be c o m p a re d d irectly with stellar evolution calc u la tio n s, w ithout having to re so rt to u n c e rta in co lo ur-tem p eratu re a n d b o lo m e tric corrections (e.g. F igures 2.1 a n d 2.2).

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2.1.2 B in a ry B lu e S tragglers

B etw een ~ 15% (D u q u e n n o y & M ayor 1990, P a d g e t et al. 1997) a n d 50% (A bt 1979) o f th e s ta rs we see in th e sky a re actu a lly binaries. W h e th e r a sim ilar frequency o f b in a rity exists am ong th e sta rs in clu sters, p a rtic u la rly globular clusters ( G C ) , is still a m a tte r of som e d e b a te (e.g. C ôté et al. 1994, Yan & M ateo 1994, Y an &: R eid 1996, C ôté et al. 1996). A lth o u g h th e exact n a tu re o f th e c o n n ectio n betw een blue stragglers a n d binaries is u n clear, th e m ore successful m ech an ism s for th e p ro d u ctio n o f blue stragglers are d ep en d en t in a t le ast som e way on binaries, a n d should m ake predictions ab o u t th e bin ary p ro p e rtie s o f th e blue stragglers them selves.

Surveys for b in aries in clu sters have been done e ith e r p h o to m etrically or spectroscopically. P h o to m e tric surveys for binaries rely on th e chance alignm ent of th e p la n e o f th e o rb it o f a clu ster b in ary a n d th e line o f sight (i.e. inclin atio n i ~ 90°) for d e tec tio n . If such a n alignm ent occurs, th e n one com ponent of th e b in a ry will periodically eclipse th e o th e r, causing a change in th e com bined a p p a re n t b rig htn ess o f th e o b je ct. This m e th o d relies largely on serendipity: th e in c lin a tio n o f th e binary to th e line o f sight m u st b e such th a t eclipses will o c cu r, a n d observations of th e s ta r m u st b e done b o th in a n d out o f eclipse in o rd e r to d e te c t its bin ary n a tu re . Spectroscopic surveys rely on rad ial velocity v a ria tio n s. As th e two com ponents of th e b in a ry o rb it th e ir com m on cen tre o f g rav ity , th e sta rs will undergo velocity shifts which will be visible to a n ob serv er as shifts o f th e co m p on ents’ sp ec tra l lines. A lth o u g h this m e th o d also req u ires th a t th e inchnation be large, eclipses do n ot have to occur.

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stragglers. T h is ta b le co n stitu tes a ra th e r m ixed bag o f ob serv atio n s: all b u t tw o (L a th a m & M ilone 1996, S try k er & H riv n ak 1984) a r e p h o to m e tric surveys, m ost a re o f ra th e r short (3-5 n ig h ts o f observations) d u ra tio n , a n d all have different p h o to m e tric accuracy a t th e m a g n itu d e of th e blue strag g lers a n d , hence, differing degrees of sen sitiv ity to p h o to m etric v ariatio n s. T h e colum ns in th e tab le show the n u m b er o f blue stragglers m o n ito red Nb s

(according to th e a u th o rs, or the n u m b e r a p p ea rin g in th e su rv e y ’s C M D ), th e n u m b e r o f b in a ry blue stragglers* N^bt d e te c te d by th e survey, a n d th e n u m b er o f p u lsa tin g blue stragglers Npbt observed. T h e n u m b e r of m o n ito red blue stragglers is som ew hat a rb itra ry for som e clusters (th o s e m ark ed w ith a “ ’) due to c o n ta m in a tio n from foreground sta rs. T h e n u m b e rs p re sen te d in this ta b le a re by no m eans com plete: only a couple o f th e c lu sters have b e e n surveyed over close to th e ir entire a re a (e.g. w C en, M 67) a n d none o f th e surveys are necessarily com plete in th e ir d etectio n s o f variable blue strag g lers, due to th e d u ra tio n o f th e observations a n d /o r p h o to m e tric accuracy.

A ccording to th e num bers in T able 2.1, th e observed fractio n o f b lu e stragglers in g lo b u lar clusters which are b in a ry system s is fbin ~ 0.03. T h is, how ever, is n o t th e true fraction of b in a ry blue strag g lers: as m e n tio n e d above, a p h o to m e tric search for binaries is com pletely d e p e n d e n t u p o n th e chance alig n m en t o f th e binary o rb ital p lan e near to th e lin e of sight; th is m eans th a t th e se surveys are sensitive only to a sm all fra c tio n o f all b in a rie s. Also, because th e chance o f observing a n eclipse decreases as th e p e rio d o f th e b in ary in creases, th ese same surveys a re sensitive only to short p e rio d b inaries. B ecau se o f th ese biases, th e co rrectio n needed to e stim a te th e tr u e

*By ‘bin ary blue stragglers’ 1 mean ‘blue stragglers which are o n e com ponent o f a

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T ab le 2.1: B lu e S trag g ler V ariability

C lu ster •Nb5 R eference

G lo b u lar C lu sters

N G C 104(47 Tuc) 25 3 3 E dm onds et al. 1996

N G C 288 43 0 6 K alu zn y 1996

K alu zn y et al. 1998 N G C 5053 27 0 5 N em ec et al. 1995

N G C 5139(w Cen) 2 0 0 1 1 24 K alu zn y et al. 1996

K alu zn y et al. 1997 N G C 5272(M3) 30 1 3 N em ec & P a rk 1996 30 0 2 G u h a th a k u rta et al. 1994 N G C 5466 47 3 6 M ateo et al. 1990 N G C 5904(M5) 24 0 1 D rissen S h a ra 1998 N G C 6121(M4) 50 2 0 K aluzny et al. 1997c N G C 6366 27 0 0 Hcirris 1993 N G C 6397 49 0 2 K aluzny 1997

18 0 5 R u b en ste in & B ailyn 1996

NGC6838(M 71)* 1 0 0 0 Y an & M ateo 1994 R u p re c h t 106 35 0 3 K aluzn y et al. 1995 O p e n C lu sters N G C 188 14 0 K aluzn y Sc S h ara 1987 N G C 2420* 3 0 K aluzny Sc S h ara 1988 N G C 2682 1 0 6 0 L a th a m Sc M ilone 1996 6 1 2 G illiland et al. 1991 N G C 6802' 6 0 K aluzny Sc S h a ra 1988 N G C 6819' 2 0 1 K aluzny Sc S h a ra 1988

1 1 R o b b , C ard in al Sc O u e lle tte 1997

M e lo tte 6 6 6 0 K aluzny Sc S h ara 1988

B erkeley 39' 25 4 0 K aluzny et al. 1993

CoUinder 261' 40 1 0 0 M azu r et al. 1995

N G C 6791' 25 3 0 R ucinski et al. 1996

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fractio n o f b in a ry b lu e stragglers &om th e re s u lts o f p h o to m etric surveys is large. P e rh a p s a b e tte r indication o f th e tr u e b in a ry fractio n comes from spectroscopic su rv ey s, such as th a t o f L a th a m & M ilone (1996): o f th e 10 blue strag g lers th e y h av e m onitored, 6 h av e tu rn e d o u t to be binaries w ith

periods in th e ra n g e o f a few days to sev e ra l y ears. Since spectroscopic surveys do n o t re q u ire as close a n a lig n m e n t o f th e o rb ita l plane w ith th e line of sig h t, a n d since velocity veiriations o c c u r over th e e n tire orbit, n o t ju s t du rin g eclipses, th e size o f th e correction n e e d e d to e stim a te th e tru e fractio n o f b in ary b lue stra g g lers is sm aller.

T h e frac tio n o f b lu e stragglers in o p e n clu sters (O C s ) which are a p p a r e n tly in b in ary sy ste m s is /wn ~ 0.16 fro m all o f th e o p en cluster surveys n o ted in T able 2.1, o r fbin ~ 0.13 from o n ly th e p h o to m e tric surveys. C om  parison o f th e re su lts from globular c lu ste r su rv ey s a n d op en cluster surveys is m ore c o rrectly d o n e using only th e re s u lts o f th e p h o to m etric surveys in open clu sters, since no spectroscopic su rv e y s for b in a ry blue stragglers in globular clu sters h av e b een done, a n d th e biases in th e resu ltin g p h o to m etric vcilues for fbin sh o u ld b e roughly th e sam e . F ro m th e resu lts of th e p h o to  m etric surveys, fbin in o p en clusters is ro u g h ly four tim es th a t in globuleir clusters. A lth o u g h p a r t o f this difference co u ld b e d u e to incom pleteness in th e surveys th em selv es, th e change in fbin fro m low d e n sity open clusters to high d en sity g lo b u lar clu sters implies t h a t th e fo rm atio n m echanism (s) for blue strag g lers differs w ith th e local ste lla r e n v iro n m e n t a n d /o r cluster age.

For co m p ariso n , th e fraction o f s ta rs th a t a re eclipsing binaries in th e solar n eig h b o u rh o o d is ~ 0.003 (H u t et al. 1992). T h e fact th a t th e b in ary fractio n in g lo b u lar c lu sters is roughly te n tim e s th a t observed locally po ints

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to binaries a n d blue strag g lers having some close co n n ectio n .

O f those blue strag g lers w hich are observed to b e eclipsing binaries, roughly 50% are a ctu a lly W U rsae M ajoris ( W U M a ) s ta rs w hich are contact b inaries - bin ary stars in w hich th e two com ponents a re o rb itin g w ithin a com m on envelope m ad e o f m a te ria l c o n trib u ted from each s ta r.

Spectroscopic surveys for blue stragglers in clu sters are necessary to ob- tciin a b e tte r u n d e rsta n d in g o f th e b in ary n a tu re o f b lu e stragglers. Milone & L ath am (1994) have u n d e rta k e n such a survey in several open clusters. To d a te , results for only one c lu ster, M 67, have been p re sen te d , b u t th e y find th a t o f the te n blue strag g lers th e y have been m o n ito rin g , six are in binary system s - none o f w hich a re eclipsing binaries. O f th e se six binary system s th a t Milone & L a th a m have found, four are in eccen tric orb its.

S tryker &: H riv n ak (1984) o b ta in e d sp ectra for 7 b lu e stragglers in N G C 7789 a n d d e te c te d no ra d ia l velocity variations, on th e basis o f a com pari son betw een observed a n d ex p ec te d sc a tte r in th e d eriv ed velocities. T heir observations were sp re ad o u t over ~ 300 days, b u t only roughly a dozen s p e c tra were o b ta in e d p e r s ta r. W hile th eir resu lts a re not as sensitive to long period binaries as th o se o f M ilone & L atham (1994), S try k er & H rivnak should have easily d e te c te d sh o rte r period binaries d u e to th e ir much larger velocity am plitudes.

As will be discussed la te r, b in a rity am ong blue strag g lers, a n d th e prop erties of such binaries (e.g. p erio d , eccentricity), a re o b serv atio n s which can possibly be used to discern betw een different blue stra g g ler form ation m ech anism s. A dditionally, since it is possible th a t th e b in a ry properties of blue stragglers will change w ith en v iro n m en t, knowledge o f th e binary charac

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teristics in, say, g lo b u lar c lu ster cores would also b e useful (e.g. E dm o n d s

et a /.,1999).

2 .1 .3

P u ls a tin g B lu e S tra g g lers

A n add itio n al p h en o m en o n w hich a p p e a rs to have som e co n n ectio n to blue stragglers is p u lsatio n . W ith in a fairly narrow , n e arly v e rtic a l b a n d in th e C M D , called th e in sta b ility strip, s ta rs a re p o ten tially u n s ta b le to pulsatio ns. .\m o n g th e lum inous gian ts, th e classical C epheids a n d W V Irginis stars p u lsate w ith p erio d s ranging from ~ 1 0 — 1 0 0 days; on th e h o riz o n ta l b ran ch

(th e location of th e low m ass, core h eliu m burning s ta r s ) , th e R R Lyrae stars p u lsate w ith p erio d s of ~ 0.5 days; n e a r th e m ain -seq u en ce, S S cuti an d SX Phœ nicis s ta rs p u ls a te w ith p erio d s of ~ 0.03 — 0.3 d ay s. T h e p u lsatin g blue stragglers belong to e ith e r th e S S cu ti or SX P h œ n ic is class o f p u lsatin g stars (collectively, th e se will be re fe rre d to as D w arf C ep h eid s or D C s ) .

From T able 2.1, th e fractio n o f b lu e stragglers th a t a re observed to be p u lsatin g is fpb, ~ 0 . 1 0 in globular clusters a n d fpb, ~ 0 . 0 2 in o p en clus

te rs. O f those blue stragglers w hich a re actu ally lo c a te d in th e in sta b ility strip , ^ 30% are a c tu a lly o bserved to pulsate. A m ong s ta rs in th e solar neighbourhood w ith th e sam e s p e c tra l ty p e as th e D C s, ~ 30 — 50% a re ob served to p u lsate (B reg er 1979), w hile v irtu ally all o f th e g ia n t s ta rs lo cated in th e in stab ility s trip p u lsate. T h e fa c t th a t all o f th e m ain -seq u en ce stars located in th e in sta b ility strip do n o t pu lsate could be re la te d to som e phys ical process w hich stabilises th o se s ta rs against p u lsa tio n . A lte rn a tiv e ly , th e pulsational a m p litu d e o f th ese s ta rs m ig h t be to o low to have b e en d e te c te d in th e variability surveys.

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Solano & F e rn le y (1997) have show n th a t th e p u ls a tio n a m p litu d e a n d ro ta tio n velo city o f D C s a re re la te d in th a t those w ith low ro ta tio n velocities show a m u ch b ro a d e r d is trib u tio n o f pulsation a m p litu d e s th a n th o se w ith high ro ta tio n velocities: fast ro ta to rs show very sm all p u lsatio n a m p litu d e s ( < O.lOmag). I t is possible th a t th o se stars in th e in sta b ility s trip w hich do not a p p e a r to p u lsa te a re , in fa c t, fast ro ta to rs , a n d so have a sm all pulsation a m p litu d e . H ow ever, B reger (1979) p o in ts o u t th a t m a n y o f th e non -pu lsato rs in th e in sta b ility strip are sp ectro sco pically an o m alo u s A m stars, w hich a re u su ally slow ro ta to rs . K aluzny et al. (1997a) n o te th a t roughly 2 /3 o f th e p u lsatin g blue stragglers in th e ir sam p le for w C en have p u lsatio n al a m p litu d e s below 0 . 1 0 m ag.

2 .1 .4

R o ta t io n R a te s

T h e ro ta tio n ra te s o f n o rm a l m ain-sequence sta rs, like o u r Sun, a re o b serv ed to be ro u gh ly c o rre la te d w ith sp e c tra l type: th e av erag e ro ta tio n velo city o f early ty p e s ta rs (O a n d B) in th e solar neighbourhood is Vrot ~ 2 0 0 k m /s ; for

m id -sp ectral ty p e s (A to early F ) th e average ro ta tio n velocity d ro p s stea d ily w ith spectreil ty p e dow n to Vrot ~ 70 k m /s a t sp e c tra l ty p e F2; below s p e c tra l ty p e F , th e a v erag e ro ta tio n velocity drops rap id ly below Vrot ~ 10 k m /s . Since b lue stra g g lers have s p e c tra l ty p e s in th e ran g e o f A to early F , we w ould expect th e m to b e fairly ra p id ly ro ta tin g , w ith th e av erag e ro ta tio n velocity in the ran g e o f ~ 1 0 0 — 180 k m /s . H owever, m e asu re d ro ta tio n velocities for blue stragglers ty p ic a lly fall below th is.

P e te rso n et al. (1984) find th a t th e ro ta tio n velocities o f blue strag g lers in M67 (N G C 2682) v a ry from 10 k m /s to 120 k m /s , w ith s p e c tra l ty p e s

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from B8 to A8. Also, for a sam ple of field blue strag g lers, G lasp ey et al.

(1994) found ro ta tio n velocities consistently below 100 k m /s . O f course, w hen a ro ta tio n velocity is d eterm in ed for a s ta r, w h a t is a ctu a lly m easured is VVotsini - th e p ro je c tio n o f th e tru e ro ta tio n velocity. For th e field stars, ro ta tio n velocities have b een ob tain ed for a large en o u g h sam p le for each sp ec tra l ty p e th a t a s ta tis tic a l correction can be a p p lie d to e stim a te th e tru e ro ta tio n velocity (t = 90°). A pplying a similcir so rt o f correction to th e average ro ta tio n velocity o f blue stragglers shows th a t th e y a re slightly slower th a n n o rm al ro ta to rs (M ath y s 1991). O f course, a com p lete survey — m easuring ro ta tio n velocities o f a large sam ple o f blue stragglers in different environm ents — w ould b e useful in this in sta n ce , especially since ro tatio n m ay be one way to d iscrim in a te betw een possible fo rm atio n m echanism s for blue stragglers.

The only re p o rte d o b serv atio n of the ro ta tio n velocity of a blue straggler in a globular clu ster (S h a ra et al. 1997) is V s in i = 155 ± 55 k m /s for BSS- 19 in 47 Tuc (G u h a th a k u rta et al. 1992). T h is is hig h , b u t n o t necessarily unusual for its sp e c tra l ty p e (A 7V ), nor is it ro ta tin g n e ar to its e stim ate d break-up velocity o f ~ 410 k m /s .

2 .1 .5

C h em ica l A b u n d a n ces

M athys (1991) an aly sed tw o o f th e M67 blue strag g lers, F153 a n d F185, in d etail. O ne of th e tw o s ta rs stu d ied , F153, was classified as a n A m star^ while th e o th e r s ta r, F 185, was not stric tly classified as a n A m s ta r, b u t

^The Am phenom enon is a chem ical peculiarity am ong som e A sta rs causing them to be u n d erab u n d an t in som e elem ents (e.g. Ca, Sc, Si), relative to iron, while norm al (or ‘so lar') in others. T h e driving m echanism is th o u g h t to be diffusion.

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had som e o f th e sam e peculiarities as F153. M ath y s fo u n d th a t th e tw o stars had nearly id e n tic al, roughly solar, abundances in m o st e lem en ts, ex cep t th a t F 153 was e x tre m ely u n d e ra b u n d a n t in calcium a n d sca n d iu m while F185 was u n d e ra b u n d an t in calcium , b u t no t in scandium . A n a d d itio n a l peculiarity of these stars is t h a t , while th e ab u n d an ce o f n itro g en is ro u g hly solar, the to ta l a b u n d an c e o f carb o n , nitrogen an d oxygen is low er th a n solar. A dding to th e growing list o f chem ical peculiarities o f th e se s ta rs , th e y have 0 / N and C /N ratio s sim ilar to M67 giants which have b ro u g h t n u clear processed m aterial to th e ir surface (th e ‘first dredge-up’).

In a d d itio n to those peculiarities observed by M a th y s (1991), P ritc h e t &: G laspey (1991) a n d H obbs & M athieu (1991) fo u n d th a t blu e stragglers are u n d e ra b u n d a n t in lith iu m , suggesting th a t som e form o f m ixing o f th e surface layers o f th e se sta rs has occurred. T h e d ep letio n o f lith iu m can be used as a n in d ic a to r o f m ixing for these stars b ecause, for n o rm a l, quiescently evolving stars in th e sam e te m p e ra tu re ran g e éis th e blue stragg lers stu d ied, th e lith iu m a b u n d a n c e is ex p ected to be en h an ced , o r d e p le te d only slightly, by th e effects o f diffusion (B oesgaard, 1987) — th e sam e holds for A m stars. However, lith iu m is destroyed a t te m p e ratu res g re a te r th a n ~ 2.5 x 10®K, so an observed d e p letio n o f lith iu m can be explained b y th e m ixing o f m aterial from th e in te rio r to th e surface o f th e sta r. Since th e d red g e-u p o f nuclear processed m a te ria l du rin g th e ascent of th e gian t b ra n c h re su lts in 0 / N and C /N ratio s w hich are lower th a n those o f m ain-sequence s ta rs , th e g ia n t like com position ra tio s observed by M athys a n d th e o b serv ed lith iu m depletion are strong in d ic a to rs o f som e very deep m ixing o ccu rrin g d u rin g th e blue straggler fo rm atio n process. As concluded by P r itc h e t & G laspey, all for

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m a tio n m echanism s w hich do n o t involve som e sort o f m ixing o f m a te ria l to th e su rface o f th e blue stra g g le rs can be ru le d o u t by th ese o b serv atio n s — a t least for th e M67 blue stra g g lers.

V ery little is know n a b o u t th e surface ab u n d an ces of a n y o f blue s tra g glers o th e r th a n th o se in M 67 a n d a few field blue stra g g lers (e.g. H obbs &: M a th ie u 1991, G lasp ey et al. 1994 ). S im ilar studies of b lu e strag g lers in g lo b u lar clusters have y et to b e done, a lth o u g h a low reso lu tio n sp ectro sco p ic s tu d y o f six blue strag g lers in u> C en by D a C osta, N orris & V illu m sen (1986) fo u n d no evidence for ch em ical p ecu liarities.

2.2 Formation Mechanisms

S everal possible fo rm atio n m ech an ism s for b lue stragglers h av e b e e n p ro p o sed since th e y were n o te d by S an d ag e (1953) in th e globular c lu s te r M3 a n d b y Jo h n so n & Sandage (1955) in th e op en c lu ste r M67. T h is sec tio n will o u tlin e th e pro p o sed m echanism s a n d th e evidence for and a g ain st e a c h o f th e m .

2 .2 .1

F oreground C o n ta m in a tio n

P e rh a p s th e sim plest e x p la n a tio n for blue stragglers, a t le a st th o se in clus te rs , is th a t they a re n o t physically asso ciated w ith th e c lu s te r a t all, b u t a re m erely objects in th e foreground; such o bjects could easily fall in to th e region on th e CM D w h ere b lu e strag g lers a re observed if th e y hav e th e co r re c t colour. A lthough su ch c o n ta m in a tio n o f th e blue stra g g ler region does o c cu r, especially for th o se c lu sters w hich lie near th e g a lac tic p la n e, m a n y blue stragglers can b e show n to be likely clu ster m em b ers on th e basis o f p ro p e r m otion or ra d ia l v elo city studies (e.g. G irard et al. 1989, M ilone &

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1=333 b = 7 9 .8

2 2 ^

B - V

F ig u re 2.3: E x a m p le o f foreground c o n ta m in a tio n for N G C 5024 (1=333, b = 7 9 .8 ) using th e B a h call &: Soneira (1984) m o d el. T h e d is trib u tio n of m odel ‘foreground s t a r s ’ {open squares) were fo u n d by finding th e p re d ic ted num ber of s ta rs, u sin g B ah c a ll &: Soneira m odel, w ith in sm all (0.1 x 0.5) colour- m ag n itu d e b in s a n d th e n random ly d is trib u tin g th e a p p ro p ria te num ber of p o in ts w ith in e ach b in . T h e field size w hich was o b serv ed is 12' x 13'; th e o bserved C M D for N G C 5024 is p lo tted w ith filled circles (R ey et al., 1998).

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1=338.2 b = - 1 2

/

B - V

F ig u re 2.4: Sam e as F ig u re 2.3, e x c e p t for N G C 6397 (1=338.2,b = -1 2 ). T h e field size is 13' x 13' (K aluzny, 1997).

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C H A P T E R 2. B L U E S T R A G G L E R S 27 1 = 2 7 .2 b = - 4 6 . 8 14 16 10 20 22 B - V Figure 2.5: S am e as F ig u re 2.3, e x ce p t for N G C 7099 (1=27.2, b = -4 6 .8 ). Field size is 5.1 sq u are arc-m in u tes (G u h a th k u rta et al., 1998).

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L ath am 1994). F or clu sters a t h igh galactic la titu d e s , th e prob ab ility o f con tam in a tio n by b rig h t, blue, fo reg ro u n d o b je cts c a n a c c o u n t for only a sm all fractio n o f o b serv ed blue strag g lers.

T he R ah call Ss S oneira m o d el o f th e G alax y c a n b e used to p red ict th e nu m b er o f s ta rs p e r sq u are a rc -m in u te as a fu n c tio n o f G alactic la titu d e a n d longitude. In essence, th e m o d el assum es scale le n g th s a n d stellar densities for the G alactic d isk , bulge, a n d halo , a n d assigns a p p ro p ria te lum inosity a n d colour functions to each co m p o n en t: in te g ra tin g a lo n g th e line o f sight gives th e num bers a n d a p p a re n t m a g n itu d e s o f s ta rs. F ig u re s 2.3,2 4, a n d 2.5 show th e CMDs for N G C 5024 (R ey et a/., 1998), N G C 6397 (K aluzny, 1997), a n d N G C 7099 ( G u h a th k u rta et al., 1998), respectively, w ith th e p red icted d istri b u tio n of fo reg ro u n d sta rs also p lo tte d . W hile th e B a h c a ll & Soneira m odel over-predicts th e n u m b e r o f s ta rs a t sm all ( |6| < 20°) G alactic la titu d e s, th e

predictions a re rea so n a b le for h ig h er la titu d e s. F o r th e th re e clusters show n here, th e n u m b e r o f fo reg ro u n d s ta rs p re d ic ted in th e blue straggler region is obviously sm aller th a n th e o bserved n u m b e r o f s ta r s , suggesting th a t th e blue stragglers o b serv ed in th e se clusters a re n o t fo reg ro u n d stars.

2 .2 .2

D e la y e d S ta r F orm ation

Since blue strag g lers a re a p p a re n tly younger th a n th e re s t of th e stars in th e ir p a re n t clu sters, o n e obvious e x p lan a tio n is th a t th e y form ed m ore re c en tly th a n th e re st of th e s ta rs in th e clu ster. If th is m echzm ism is actin g in a cluster, th e n th e b lu e strag g lers should be, e x c e p t for th e ir anom alous age, presu m ab ly n o rm a l s ta rs: th e y should possess n o rm a l ab u n d an ces, b in a ry p ro p erties, ro ta tio n ra te s , etc..