Advisor : Prof. Hagai Perets. Israel Institute of Technology, Haifa

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1 Secular Dynamics in Hierarchical Three-Body Systems with Mass Loss and MassErez Michaely Advisor : Prof. Hagai Perets Israel Institute of Technology, Haifa

2 Context Systematically exploring triple systems Systems: Triple Stellar Star and 2 planets Planet in a binary Exploring: Dynamics Evolution

3 Observations ~15% of all stars reside in triple [Raghavan 2010] Possibly >50% of stars with M>5Msun are in triples [Remage Evans 2011 ] Vast majority of multiple systems are hierarchical [Tokovinin 1997]

4 Hierarchical triple systems R? r

5 Dynamics Hamiltonian: Expanded Hamiltonian:

6 Dynamics Hamiltonian in Delaunay s elements (l,g,h;l,g,h) Up to the octupole term

7 Secular Dynamics For long time behavior double averaging can be done Averaging over mean anomalies Hamilton equation of motion

8 Time Scales Qaudrupole Term: 2π a2 ( 1 e2 3 t2 : 1 2 ) (m m1 ) G m2 a1 2 2 Octupole Term: 2π a2 ( 1 e2 4 t3 : tgr 2 ) 5 2 (1 e 2 1 ) 1 2 ( m0 + m1 ) G m2 m0 m1 e2 a [Naoz et. al. 2013] 3 2

9 Kozai Oscillations Kozai (1962) and Lidov (1962) showed an oscillatory behavior of the inner eccentricity and the mutual inclination Conservative process semi major axis are constants Mutual torque exchanges angular momentum

10 Kozai Oscillations

11 Kozai Oscillations quadrupole m2 = 40 M Jupiter a2 = 100[AU] e2 = 0.6 m1 = 1M Jupiter a1 = 6[AU] e1 = i = 65 o m0 = 1M e

12 Kozai Oscillations quadrupole

13 Kozai Oscillations - octupole

14 Kozai Oscillations Kozai period 2 PKozai P outer Pinner ( m0 + m1 ) m2 a2 ( m0 + m1 ) = Pinner m2 a1 3 Importance of octupole term a1 m0 m1 e2 ε 3 = 2 a m + m 1 e

15 Secular Mass Loss Slow mass loss is assumed Isotropic mass loss is assumed No conservation of energy d m0 d α dt a= = dt m1 + m0 m1 + m0 d α m1 G1 = G1 dt m0 ( m0 + m1 ) α m2 d G2 = G1 dt m0 ( m0 + m1 ) d d d H = G1 cos i1 + G2 cos i2 dt dt dt

16 Mass Allow mass transfer inside the inner binary Allow mass transfer to the inner binary ψ Mass transfer efficiency parameter Mass transfer to the inner binary is assumed to be proportional to the object m0 d mass. m0 = α + ψ 1,0 γ +ψ 2,01 β dt m0 + m1 m1 d m1 = γ +ψ 0,1 α +ψ 2,01 β dt m0 + m1 d m2 = β dt

17 MIEK (Mass loss Induced Eccentric Kozai) [Shappee & Thompson 2013] Importance of the octupole terms increases/decreases with mass loss in the inner binary. a1 m0 m1 e2 ε 3 = 2 a2 m0 + m1 1 e2

18 MIEK (Mass loss Induced Eccentric Kozai) a2 = 250[AU] e2 = 0.7 m2 = 6 M e m1 = 6.5M e a1 = 10[AU] e1 = 0.1 i = 60 o m0 = 7 M e Mass loss: t = 3[ Myr ] t = 1[ Myr ] m0 ( t = 4Myr ) = 1.15M e

19 MIEK (Mass loss Induced Eccentric Kozai)

20 MIEK (Mass loss Induced Eccentric Kozai)

21 SEFO (Secular Evolution Freeze Out) m2 Kozai period changes with a2 ( m0 + m1 ) Pinner m2 a1 3 PKozai Octupole term becomes less important a1 m0 m1 e2 ε 3 = 2 a2 m0 + m1 1 e2

22 SEFO (Secular Evolution Freeze Out) a2 = 250[AU] e2 = 0.7 m2 = 6.5M e m1 = 6M e a1 = 10[AU] e1 = 0.1 Mass loss : t = 1[ Myr ] t = 1[ Myr ] t = 3[ Myr ] t = 1[ Myr ] i = 60 o m0 = 7 M e m0 ( t = 2Myr ) = 1.15M e m2 ( t = 4Myr ) = 1.15M e

23 SEFO (Secular Evolution Freeze Out)

24 SEFO (Secular Evolution Freeze Out)

25 Creating Very Close Binaries Mass transfer to the inner binary will shrink its semi-major axis d α a= dt m1 + m0 Shorter period time Pinner a13 = 2π G ( m0 + m1 )

26 Creating Very Close Binaries a2 = 20[AU] e2 = 0.6 m2 = 7 M e m1 = 0.6 M e i = 60 a1 = 0.1[AU] e1 = 0.01 o m0 = 0.5M e Mass loss and Mass transfer : t = 0.1[ Myr ] t = 0.1[ Myr ] m2 ( t = 0.2Myr ) = 1.15M e ψ 2,01 = 0.2

27 Creating Very Close Binaries

28 Creating Very Close Binaries

29 Secular code with mass loss and mass transfer was developed Systematic exploration of parameter space is available Different evolutionary channels : MIEK SEFO Very close binary can be formed (Blue stragglers?) Exciting GR effects (not discussed here) And more

30 Future Work Realistic mass loss Realistic mass transfer Tidal friction models Many more...

31 Thank you