1. Population of dynamically formed triples in dense stellar systems Natalia Ivanova Fred Rasio, Vicky Kalogera, John Fregeau, Laura Blecha, Ryan O'Leary (Northwestern) Chris Belczynski (New Mexico) Jamie Lombardi and Zach Proulx (Vassar College) ESO workshop on Multiple Stars across the H-R Diagram July 2005

2. Outline Method Method Binaries population Binaries population Triples: formation rates & their population Triples: formation rates & their population Effect on the cluster population Effect on the cluster population

3. Static cluster background Static cluster background core density n c core density n c dispersion velocity  dispersion velocity  escape velocity v esc escape velocity v esc Mass segregation (Fregeau et al. 2004) Mass segregation (Fregeau et al. 2004) t sc (m)  /m t rh t sc (m)  /m t rh Recoil Recoil “+” : large populations, up to 10 6 stars “-” : cluster dynamics is not self-consistent Ivanova, Belczynski, Fregeau & Rasio 2005 Ivanova, Belczynski, Fregeau & Rasio 2005 Population synthesis with dynamics

4. SS encounters SS encounters Mergers in physical collisions Mergers in physical collisions binary formation in physical collisions (new SPH code using “realistic” RG structure) (Lombardi et al. 2005) binary formation in physical collisions (new SPH code using “realistic” RG structure) (Lombardi et al. 2005) TC-binary formations ( Portegies Zwart & Meinen 1993) TC-binary formations ( Portegies Zwart & Meinen 1993) BS & BB encounters using FewBody (Fregeau et al.2004) BS & BB encounters using FewBody (Fregeau et al.2004) exchanges exchanges ionizations ionizations (multiple) physical collisions (multiple) physical collisions triples formation triples formation Encounters

5. Single stars: analytic fits provided by Hurley et al. 2000 Single stars: analytic fits provided by Hurley et al. 2000 Binary stars: (Belczysnki et al. 2002, 2005) Binary stars: (Belczysnki et al. 2002, 2005) Magnetic braking Magnetic braking Mass transfer events Mass transfer events Common envelope events Common envelope events Tidal circularization and synchronization Tidal circularization and synchronization Accretion on WDs, Ia SN and subCh Ia Accretion on WDs, Ia SN and subCh Ia Triples: no evolutionary treatment yet Triples: no evolutionary treatment yet Stellar evolution

6. 250,000 M , modeled with 1,25  10 6 stars, 100% binaries initial 250,000 M , modeled with 1,25  10 6 stars, 100% binaries initial IMF for primaries from 0.05M  to 100M  (triple power law by Kroupa 2002); Z=0.001 IMF for primaries from 0.05M  to 100M  (triple power law by Kroupa 2002); Z=0.001 Binaries Binaries Flat mass ratio distribution Flat mass ratio distribution Periods from 0.1 d to 10 7 days Periods from 0.1 d to 10 7 days Thermal e distribution Thermal e distribution Core characteristics: Core characteristics: n c =10 5 per pc 3 n c =10 5 per pc 3  1 = 10 km/s  1 = 10 km/s t rh =10 9 yr t rh =10 9 yr “Typical” cluster model

7. Basics of the binary dynamics Collision time  coll : time between two successful collisions,  coll = 1/n c  S Collision time  coll : time between two successful collisions,  coll = 1/n c  S Hardness  : ratio between binary binding energy and kinetic energy of an average object Hardness  : ratio between binary binding energy and kinetic energy of an average object Soft binaries  <1 : get softer; very likely to be destroyed through ionization Soft binaries  <1 : get softer; very likely to be destroyed through ionization Hard binaries  >1 : get harder; the encounter can result in the exchange of the companion (smaller mass component is replaced by more massive intruder) Hard binaries  >1 : get harder; the encounter can result in the exchange of the companion (smaller mass component is replaced by more massive intruder)

8. Binaries destruction: role of the evolution Destructions of only soft binaries (~60% of primordial binaries) & evolutionary destructions: Upper limit 30% if  0.5 M  24% if  1 M  50% of all hard binaries will undergo an encounter in 10Gyr, about half of them will be destroyed Only 22% of binaries will be left, and among binaries with a primary companion > 0.5 M  only 13%

9. Binaries periods 7800 binaries in the core “Typical” GC, at 10 Gyr 6200 MS-MS binaries in the core, 1600 binaries with a WD

10. Triples: formation rates Stability criterion as in Mardling & Aarseth (2001) Formation rates a typical cluster has about 5000 hier. stable triples formed throughout its evolution  N tr /N bin  0.05 f b per Gyr At 10 Gyr :  1.0M ,  10R , f b  10%  N tr /N bin  5% per Gyr  N tr  600/t 9 1/3 per Gyr, at ages > 1 Gyr

11. Triples: masses

12. Triples: periods

13. Triples: eccentricities

14. Triples: hardness 45% with  > 1kt and only 7% with  > 10kt ~half of hard triples have small mass outer companion

15. Triples and Kozai mechanism Kozai mechanism causes large variations in the eccentricity and inclination of the stars orbits and could drive the inner binary of the triple system to merge before next interaction with other stars. Kozai time-scale  koz as in Innanen et al. (1997) 2 runs with completely the same initial population of 5  10 5 stars, in one run inner binaries in the formed triples are merged if  tid <  koz <  coll (  tid as in Hut 1981 & 1982)

16. Triples: hardness and Kozai 1/3 of all triples - Kozai systems

17. Triples: Kozai & MS-MS inner binaries 73% of all triples have MS-MS inner binary, 30% of them are Kozai binary. Overall can provide ~10% of all BSs.

18. Triples: Kozai & inner binaries with a compact companion 23% of all triples have inner binary with a CO (8% -two CO), 40% of them are Kozai binary. If Kozai binaries merge, the number of CVs (observed at 10Gyr) is reduced by 1/3.

19. Effect on binary periods

20. Binaries vs triples (at 10 Gyr) MSWD MS80%13% RG0.7%0.3% WD13%7% NS0.3%0.3% Core binariesInner binaries in triplesMSWDMS 60% 1/3 20% 1/3 RG 2% 1/3 1% 1/3 WD 20% 1/3 15% 2/5 NS 1% 1/4 0.7% 0 MS 80% 1/3 RG 0.7% 1/2 WD 20% 1/3 NS0.% Outer star

21. Conclusions Hierarchically stable triples are formed at the rate of about 600/t 9 1/3. 5000 triples are formed throughout entire evolution in a typical cluster Hierarchically stable triples are formed at the rate of about 600/t 9 1/3. 5000 triples are formed throughout entire evolution in a typical cluster 1/2 are short lived soft triples, 1/4 are hard and stable with respect to further encounters and 1/4 are hard and will possibly undergo an exchange interaction if one occures 1/2 are short lived soft triples, 1/4 are hard and stable with respect to further encounters and 1/4 are hard and will possibly undergo an exchange interaction if one occures 75% of them have MS-MS inner binary and in 25% of them the inner binary containing a compact object 75% of them have MS-MS inner binary and in 25% of them the inner binary containing a compact object A “typical” triple: M 3 /(M 1 +M 2 )  0.6, M 1 +M 2  1.2M , P in  1 day, P out /P in  1000, a in /a out  100, e out  0.8,  1 kT A “typical” triple: M 3 /(M 1 +M 2 )  0.6, M 1 +M 2  1.2M , P in  1 day, P out /P in  1000, a in /a out  100, e out  0.8,  1 kT An inner binary of a triple is more likely to contain a compact object than a core binary. Outer star follows the binaries population. An inner binary of a triple is more likely to contain a compact object than a core binary. Outer star follows the binaries population. 1/3 of all triples are affected by Kozai mechanism 1/3 of all triples are affected by Kozai mechanism A typical BS - product of Kozai-induced merger - is 1.1 M , could provide 10% of all BSs A typical BS - product of Kozai-induced merger - is 1.1 M , could provide 10% of all BSs A typical WD-MS binary merged due to Kozai-induced merger contains 0.8M  WD and 0.8M  MS. Number of CVs is reduced by 1/3 A typical WD-MS binary merged due to Kozai-induced merger contains 0.8M  WD and 0.8M  MS. Number of CVs is reduced by 1/3

22. Binaries destruction Field “core only”

23. Binaries destruction