1. White Dwarf Binaries in Globular Clusters Fred Rasio (Northwestern)

2. Outline  WD - WD binaries only (CVs and WD - NS binaries in other talks)  Theoretical predictions from: N-body simulations with binaries and stellar evolution (Hurley & Shara) N-body simulations with binaries and stellar evolution (Hurley & Shara) Binary Population Synthesis with dynamics (Ivanova, Belczynski, Fregeau & FR) Binary Population Synthesis with dynamics (Ivanova, Belczynski, Fregeau & FR)  Merger rates, properties of binaries in LISA band

3. Why WD - WD binaries?  Most common type of compact binary in any environment  Close (merging) WD - WD binaries should be especially abundant in dense star clusters (Chen & Leonard 1993 ApJ 411,L75; Shara & Hurley 2002, ApJ 571, 830)  Most promising LISA sources in Galactic globular clusters (Benacquista, SPZ & FR 2001, CQG, 18, 4024)  Interesting merger products: Type Ia SN, NS or MSPs by “merger-induced collapse” (?)

4. Key Dynamical Processes  Destruction of wide binaries (not just soft binaries!)  Hardening of close binaries  Exchange interactions (tend to replace low-mass companion by more massive companion)  Most important: Interplay with stellar evolution (eg exchange interaction + CE)

5. Results from N-body Simulations  Hurley & Shara: NBODY4 + Hurley et al. Recipes for stellar evolution on GRAPE-6 NBODY4 + Hurley et al. Recipes for stellar evolution on GRAPE-6 N = 20,000 with 10% binaries, open cluster conditions, t f = 4 Gyr N = 20,000 with 10% binaries, open cluster conditions, t f = 4 Gyr  Even for these small, low-density clusters, dynamics plays a crucial role! (mainly through hardening and exchanges)  Merger rate for systems with M tot > M Ch is ~15 times higher than in a system with no dynamical interactions.  Implications for Type Ia SN rate, NS formation, Number of LISA sources in clusters, LISA Galactic background Cluster Field LISA merging ApJ 589, 179

6. Never explore parameter space !

7. Population Synthesis with Dynamics  Combine: StarTrack (Belczynski, Kalogera et al.) for binary evolution StarTrack (Belczynski, Kalogera et al.) for binary evolution FewBody (Fregeau) for dynamical 3-body and 4-body interactions FewBody (Fregeau) for dynamical 3-body and 4-body interactions Monte Carlo generation of interactions in core Monte Carlo generation of interactions in core Simplified model of cluster dynamics: Simplified model of cluster dynamics: Simplest: constant density “box” modelSimplest: constant density “box” model Current: two-zone model with core and haloCurrent: two-zone model with core and halo Ultimate: full dynamical Monte CarloUltimate: full dynamical Monte Carlo  Typical parameters: N ~ 10 5 with 50% - 100% binaries, globular cluster conditions, t f = 13 Gyr

8. Initial Primordial Binary Fractions…  Matching observed core binary fractions today of a few percent requires close to 100% binaries initially! (Ivanova, Belczynski, Fregeau, & FR 2003)

9. WD - WD Binary Mergers  Overall ~ 5 times more mergers with dynamics  For M tot > M Ch, ~ 100 times more mergers!

10. Binaries in the LISA band  Results from 10 independent cluster snapshots  May need ~ 100 - 500 to obtain meaningful distribution n c = 10 5 n c = 10 7