Population of dynamically Population of dynamically formed triples in dense formed triples in dense

stellar systemsstellar 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

OutlineOutline

MethodMethod Binaries populationBinaries population Triples: formation rates & their Triples: formation rates & their

populationpopulation Effect on the cluster populationEffect on the cluster population

Static cluster background Static cluster background

core density ncore density ncc

dispersion velocity dispersion velocity escape velocity vescape velocity vescesc

Mass segregation (Fregeau et al. 2004)Mass segregation (Fregeau et al. 2004)

ttscsc(m) (m) <m>/m t <m>/m trhrh

RecoilRecoil ““+” : large populations, up to 10+” : large populations, up to 1066 stars stars““-” : cluster dynamics is not self-consistent-” : cluster dynamics is not self-consistent

Ivanova, Belczynski, Fregeau & Rasio 2005Ivanova, Belczynski, Fregeau & Rasio 2005

Population synthesis with Population synthesis with dynamicsdynamics

SS encounters SS encounters Mergers in physical collisionsMergers in physical collisions binary formation in physical collisions (new SPH binary formation in physical collisions (new SPH

code using “realistic” RG structure) code using “realistic” RG structure) (Lombardi et al. (Lombardi et al. 2005)2005)

TC-binary formations TC-binary formations ( Portegies Zwart & Meinen 1993)( Portegies Zwart & Meinen 1993)

BS & BB encountersBS & BB encounters using FewBody using FewBody (Fregeau et (Fregeau et al.2004)al.2004) exchangesexchanges ionizationsionizations (multiple) physical collisions(multiple) physical collisions triples formationtriples formation

EncountersEncountersQuickTime™ and a

Photo - JPEG decompressorare needed to see this picture.

Single stars: Single stars: analytic fits provided by analytic fits provided by Hurley et al. 2000 Hurley et al. 2000

Binary stars: Binary stars: (Belczysnki et al. 2002, 2005) (Belczysnki et al. 2002, 2005) Magnetic brakingMagnetic braking Mass transfer eventsMass transfer events Common envelope eventsCommon 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

TriplesTriples: no evolutionary treatment yet: no evolutionary treatment yet

Stellar evolutionStellar evolution

250,000 M250,000 M, modeled with 1,25, modeled with 1,25101066 stars, stars, 100% binaries initial100% binaries initial

IMF for primaries from 0.05MIMF for primaries from 0.05M to 100M to 100M (triple (triple power law by Kroupa 2002); Z=0.001power law by Kroupa 2002); Z=0.001

BinariesBinaries Flat mass ratio distributionFlat mass ratio distribution Periods from 0.1 d to 10Periods from 0.1 d to 1077 days days Thermal e distributionThermal e distribution

Core characteristicsCore characteristics: : nncc=10=1055 per pc per pc33

11 = 10 km/s = 10 km/s ttrhrh=10=1099 yr yr

““Typical” cluster modelTypical” cluster model

Basics of the binary dynamicsBasics of the binary dynamics

Collision time Collision time collcoll: : time between two time between two

successful collisions, successful collisions, collcoll = 1/n= 1/nccSS

Hardness Hardness : : ratio between binary binding ratio between binary binding energy and kinetic energy of an average objectenergy and kinetic energy of an average object

Soft binaries Soft binaries <1<1: : get softer; very likely to get softer; very likely to be destroyed through ionizationbe destroyed through ionization

Hard binaries Hard binaries >1>1: : get harder; the get harder; the encounter can result in the exchange of the encounter can result in the exchange of the companion (smaller mass component is replaced companion (smaller mass component is replaced by more massive intruder)by more massive intruder)

Binaries destruction: role of the Binaries destruction: role of the evolutionevolution

Destructions of only soft binaries (~60% of primordial binaries) & evolutionary destructions:

Upper limit

30% if <m> 0.5 M

24% if <m> 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%

Binaries periodsBinaries periods

7800 binaries in the core7800 binaries in the core

“Typical” GC, at 10 Gyr

6200 MS-MS 6200 MS-MS binaries in binaries in the core,the core,

1600 binaries 1600 binaries with a WDwith a WD

Triples: formation ratesTriples: formation rates

Stability criterion as in Mardling & Aarseth (2001)

Formation rates a typical cluster has about 5000 hier. stable triples formed throughout its evolution

Ntr/Nbin 0.05 fb <mb> <a> per Gyr

At 10 Gyr : <mb>1.0M, <a>10R, fb10%

Ntr/Nbin 5% per Gyr

NNtr tr 600/t 600/t991/3 1/3 per Gyr, at ages > 1 Gyrper Gyr, at ages > 1 Gyr

Triples: massesTriples: masses

Triples: periodsTriples: periods

Triples: eccentricitiesTriples: eccentricities

Triples: hardnessTriples: hardness

45% with > 1kt and only 7% with > 10kt

~half of hard triples have small mass outer companion

Triples and Kozai mechanismTriples and Kozai mechanism

Kozai mechanism causes large variations in the Kozai mechanism causes large variations in the eccentricity and inclination of the stars orbits eccentricity and inclination of the stars orbits and could drive the inner binary of the triple and could drive the inner binary of the triple system to merge before next interaction with system to merge before next interaction with other stars.other stars.

Kozai time-scale Kozai time-scale kozkoz as in Innanen et al. (1997) as in Innanen et al. (1997)

2 runs with completely the same initial 2 runs with completely the same initial population of 5population of 5101055 stars, in one run inner stars, in one run inner binaries in the formed triples are merged ifbinaries in the formed triples are merged if

tid < koz < coll

(tid as in Hut 1981 & 1982)

Triples: hardness and KozaiTriples: hardness and Kozai

1/3 of all triples - Kozai systems

Triples: Kozai & MS-MS inner Triples: Kozai & MS-MS inner binariesbinaries

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

Triples: Kozai & inner binaries Triples: Kozai & inner binaries with a compact companionwith 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.

Effect on binary periodsEffect on binary periods

Binaries vs triples (at 10 Gyr)Binaries vs triples (at 10 Gyr)

MSMS WDWD

MSMS 80%80% 13%13%

RGRG 0.7%0.7% 0.3%0.3%

WDWD 13%13% 7%7%

NSNS 0.3%0.3% 0.3%0.3%

Core binaries Inner binaries in triples

MSMS WDWD

MSMS 60% 60% 1/31/3

20% 20% 1/31/3

RGRG 2% 2% 1/31/3

1% 1% 1/31/3

WDWD 20% 20% 1/31/3

15% 15% 2/52/5

NSNS 1% 1% 1/41/4

0.7% 0.7% 00

MSMS 80% 80% 1/31/3

RGRG 0.7% 0.7% 1/21/2

WDWD 20% 20% 1/31/3

NSNS 0.%0.%

Outer star

ConclusionsConclusions Hierarchically stable triples are formed at the rate of about Hierarchically stable triples are formed at the rate of about

600/t600/t991/31/3. 5000 triples are formed throughout entire evolution in a . 5000 triples are formed throughout entire evolution in a

typical cluster typical cluster 1/2 are short lived soft triples, 1/4 are hard and stable with respect 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 to further encounters and 1/4 are hard and will possibly undergo an exchange interaction if one occuresan exchange interaction if one occures

75% of them have MS-MS inner binary and in 25% of them the 75% of them have MS-MS inner binary and in 25% of them the inner binary containing a compact objectinner binary containing a compact object

A “typical” triple: MA “typical” triple: M33/(M/(M11+M+M22))0.6, M0.6, M11+M+M221.2M1.2M, P, Pinin1 day, 1 day, PPoutout/P/Pinin 1000, a1000, ainin/a/aoutout 100, e 100, eoutout 0.8, 0.8, 1 kT1 kT

An inner binary of a triple is more likely to contain a compact An inner binary of a triple is more likely to contain a compact object than a core binary. Outer star follows the binaries object than a core binary. Outer star follows the binaries population.population.

1/3 of all triples are affected by Kozai mechanism1/3 of all triples are affected by Kozai mechanism A typical BS - product of Kozai-induced merger - is 1.1 MA typical BS - product of Kozai-induced merger - is 1.1 M, could , could

provide 10% of all BSsprovide 10% of all BSs A typical WD-MS binary merged due to Kozai-induced merger A typical WD-MS binary merged due to Kozai-induced merger

contains 0.8Mcontains 0.8M WD and 0.8M WD and 0.8M MS. Number of CVs is reduced by 1/3MS. Number of CVs is reduced by 1/3

Binaries destructionBinaries destruction

Field “core only”

Binaries destructionBinaries destruction