1. Models of Blue Stragglers part I A talk for Hans Zinnecker (sort of). Alison Sills, McMaster University

2. Collision Models  Sills (1997-2009), Glebbeek (2008-2010)  head-on (S97, G08) and off-axis collisions (S01)  With rotation (S05)  Post-main sequence (S09)  Different compositions of parents (GS10)  Take result of collision simulations or MMAS/MMAMS  Evolve in time using detailed stellar evolution code

3. Glebbeek & Pols 2008 Collision products look like normal stars (almost) Red: collision product Blue: normal star of same mass Lifetimes of collision products shortened by a factor that depends on evolutionary history of parents

4. Effect of Impact Parameter Sills et al 2005 Same parents, three different impact parameters (0.25, 0.5, 1.0 (R 1 +R 2 ) Little structural difference, some difference in internal angular velocity

5. Binary Mass Transfer Models  Deng, Chen, Han (2004-2011)  Binary evolution with a stellar evolution code simultaneously evolving both components  Stability of mass transfer depends on structure of donor (see Natasha’s talk tomorrow)  Stable mass transfer calculated directly (mass moved from star 1 to star 2, then both stars evolved over each timestep)  Dynamical mass transfer assumed to produce a fully mixed merger product  Case A, case B, case C calculated  Solar metallicity – most compared to M67

6. Case A mass transfer (primary on MS) Tian et al. 2006 Evolution is complicated, but stars spend significant time in BS region Outcome depends on masses and initial period Mass transferring binaries lie between dashed line and ~giant branch

7. Different locations in CMD Lu et al 2011 + = case A mass transfer = case B mass transfer = merged models (case A with smaller mass ratios)

8. Parameterized models  BSE (Hurley et al 2002)  Binary evolution followed using (semi-)analytic prescriptions for stellar evolution and interaction events  Collisions – product is fully mixed, current age set by average of parents’ time along MS  Mass transfer – if R star > R Roche, with timescale determined by structure of two stars  Wind accretion – Bondi-Hoyle accretion of primary’s stellar wind  All evolutionary states of stars included  Also common envelope evolution, mass loss, collisions between non-MS stars, tidal evolution, angular momentum loss mechanisms….  Similar codes: SeBa (Portegies Zwart & Verbunt 1996), StarTrack (Belczynski et al. 2008)  Easily implemented into dynamics codes to study dynamical impacts on binary evolution

9. Models of Individual Blue Stragglers (part II – with some repetition, some clarifications, and a side topic or two) Alison Sills

10. (for Melvyn) Luminosity functions Ferraro et al 2003 Observed luminosity functions (in F255W) for 6 clusters, normalized to turnoff luminosity

11. Collision Models  Sills (1997-2009), Glebbeek (2008-2010)  head-on (S97, G08) and off-axis collisions (S01)  With rotation (S05)  Post-main sequence (S09)  Different compositions of parents (GS10)  Take result of collision simulations or MMAS/MMAMS  Evolve in time using detailed stellar evolution code

12. Luminosity and temperature functions Ferraro et al 2003 Collision tracks for variety of parent mass combinations, single-binary interactions + likelihood of collision, drawn from IMF, assumed binary fraction….. We predicted that the binary fraction in NGC 288 was much higher than in M80

13. Rotation is a problem Sills et al. 2001 Same collision product, but with initial angular velocity divided by factor of 5, 10, 100, and 1000. If velocity not reduced, star spins up past break- up during descent to main sequence Rotational mixing: helium to surface, hydrogen to core. Long, blue life.

14. A possible spin-down mechanism? Start with off-axis collision, and evolve in YREC. Spins up as it contracts. Outer layers hit break-up and are lost. If star has a magnetic field, then we can lock it to a disk after first 0.1 M  is lost (invoked for young low M stars in open clusters) Still spins faster than a normal star of the same mass – but not so much mixing Sills, Adams & Davies 2005

15. Post-MS evolution gives E-BSS Sills et al. 2009 HB E-BSS AGB Collision tracks for different combinations of parent stars Points are 10 7 years apart HB and AGB determined by M=0.8 M  track E-BSS box determined from observations in 3 clusters (M3, M80, 47 Tuc)

16. Binary Mass Transfer Models  Deng, Chen, Han (2004-2011)  Binary evolution with a stellar evolution code simultaneously evolving both components  Stable mass transfer calculated directly (mass moved from star 1 to star 2, then both stars evolved over each timestep)  Dynamical mass transfer assumed to produce a fully mixed merger product  Case A, case B, case C calculated  Solar metallicity – most compared to M67

17. Different locations in CMD Lu et al 2011 + = case A mass transfer = case B mass transfer = merged models (case A with smaller mass ratios) Are mergers the explanation for the blue sequence in M30?

18. Mergers from case A Chen & Han 2008 Monte-Carlo model for M67 (dashed line is not ZAMS?) Monte-Carlo model for NGC 2660 (1.2 Gyr) If mergers really are fully mixed, then they’ll lie ~on the ZAMS – inconsistent with NGC 188, M30, and other GCs. Environmental effect?

19. Parameterized models  BSE (Hurley et al 2002)  Binary evolution followed using (semi-)analytic prescriptions for stellar evolution and interaction events  Collisions – product is fully mixed, current age set by average of parents’ time along MS  Mass transfer – if R star > R Roche, with timescale determined by structure of two stars  Wind accretion – Bondi-Hoyle accretion of primary’s stellar wind  All evolutionary states of stars included  Also common envelope evolution, mass loss, collisions between non-MS stars, tidal evolution, angular momentum loss mechanisms….  Similar codes: SeBa (Portegies Zwart & Verbunt 1996), StarTrack (Belczynski et al. 2008)  Easily implemented into dynamics codes to study dynamical impacts on binary evolution

20. Do the models get things right?  Position in CMD: yes (by definition)…..in a broad sense  Mass: Well…..  Rotation rate: Basically no What else could we look at?

21. Surface Abundances  Different formation mechanisms should produce different surface abundances  Collisions: probably remove lithium, but otherwise little/no surface abundance differences  Binary mass transfer: depends on the time of mass transfer and masses of primary/secondary  Need to be careful about effects of subsequent evolution on abundances

22. Pulsation  Blue stragglers can be SX Phe stars (low metallicity δ Scuti stars (dwarf Cepheid stars)) – radial pulsators  Pulsations can give us fundamental stellar parameters such as mass, composition, etc.  Few models (Santolamazza et al. 2001, Templeton et al. 2002)  concerned with location of instability strip, not individual properties  First large compilation of data for SX Phe’s in GCs (263 SX Phe stars in 46 GCs)

23. SX Phe in Local Group Cohen & Sarajedini 2012 Sub-luminous GC SX Phe stars could have higher helium abundances – from BS formation process or from 2 nd generation? They are blue stragglers. Most SX Phe stars fit the period-luminosity relation well.

24. Side topic: Link to Multiple Populations?  Two generations of stars in globular clusters?  Second generation is enriched with the products of hot hydrogen burning (enhanced He but not C+N+O)  Any connection to blue stragglers?

25. Population mixing changes CMD position, lifetime Glebbeek, Sills & Leigh 2010 M=0.6 M  + 0. 4 M 

26. Luminosity function and colour distribution of blue stragglers in NGC 2808 best fit by mixed population of Y=0.24 and Y=0.32 parent stars (solid blue lines) Results for other clusters consistent with their inferred second generation populations Glebbeek, Sills & Leigh 2010 Population mixing fits colour distributions better

27. Same radial distributions? Lardo et al 2011 Plus NGC 2419 and  Cen  flat in both blue stragglers and second generation Red arrows mark measured blue straggler minima SG giants/FG giants

28. Individual models: what is needed?  Binary models: (much) more parameter space coverage  Mergers (Coalescence): are they really fully mixed?  Collisional models: do we need multiple He parent populations? Do we need them at all?  Pulsation properties look like a useful way of getting information out of blue stragglers – need specific models  Magnetic fields, anyone? (Bob?)  But we do need to deal with angular momentum redistribution/loss for both collisions and mergers