Secular Evolution of Pre-Main Sequence
Triples
Erez Michaely
Advisor : Prof. Hagai Perets
Israel Institute of Technology, Haifa
Observations : Binaries
Introduction
• Close Low Mass binaries are likely to be a part of a triple system [Tokovinin 2006]
• O stars: Period distribution favors shorter periods than Opik law (log uniform) [Sana 2012]
Triples are very common
Introduction
•~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]
Previous Work : Eggleton & Kiseleva
Introduction
Kozai Cycles Tidal Friction• Harrington 1968• Mazeh & Shaham 1979• Kiseleva et al. 1998 used KCTF on the Algol system • Eggleton & Kiseleva 2001 and 2006 : KCTF might produce many close/contact binaries• Facrycky & Treaine 2007• Perets & Naoz 2013 – planetesimals• Many more. . .
•The calculation were made on MS systems
Previous Work : GR dissipation
Introduction
• Work have been done also for compact objects• Instead of tidal dissipation GR radiation• [Blaes et al. 2002]
Pre Main Sequence properties
Introduction
Pre-MS•Very big; size of giants•Convective•Contracts on a thermal timescale
•Good objects to undergo tidal friction
Secular Evolution scheme of Pre-MS triples
Introduction
3
21
Eccentric orbit induces tidal interactionDissipation of orbital energy
Tidal Friction•Simple model for equilibrium tides
Hut 1981 Model for equilibrium tides
8da R
dt a
Introduction
Stellar evolution parameters taken from MESA
Introduction
• MESA (Paxton 2010) stellar evolution code• Radius as a function of time• Radius of gyration
Secular dynamics up to an octupole expansion
Introduction
• Double averaged Hamiltonian, secular code [Michaely & Perets
2014] following [Ford 2000,Blaes2002]• Actually very similar to the code described by Silvia
• Two interacting rings • Equation of motion for the orbital elements
• Relevant timescales
3 12 2
312 2
3 22 2 0 1
2
2 1
2 1a e m mt
G m a
5 1 32 2 2
512 2
4 2 22 2 1 0 1
3
2 0 1 2 1
2 1 1a e e m mt
G m m m e a
ExampleKCTF on the Pre-MS for Low Mass Stars
Preliminary results
0 1 sunm M
1 0.5 sunm M
2 1 sunm M
1 2[AU]a
2 50[AU]a
1 0.01e
2 0.2e
70i
ExampleKCTF on the Pre-MS for High Mass Stars
Preliminary results
0 15 sunm M
1 20 sunm M
2 10 sunm M
1 8[AU]a
2 100[AU]a
1 0.01e
2 0.2e
70i
ExampleKCTF on the Pre-MS for High Mass Stars induce RLOF
Preliminary results
0 15 sunm M
1 20 sunm M
2 25 sunm M
1 8[AU]a
2 80[AU]a
1 0.01e
2 0.8e
80i
Coupling orbital energy with tidal interaction - helps
Energy Budget• Orbital energy is dissipated into the inner binary• The energy deposited into the star in for of heat• Heat inside the proto-star ‘help’ fight against the gravitational collapse• The pre-MS is longer, hence the mechanism is more efficient• Future work
Kozai-Lidov Oscillations
Summary•Triple dynamics and evolution is a reach field the implications on a variety of astrophysics aspects•Secular code with mass loss / transfer and tidal friction and stellar evolution was developed•Secular evolution in the Pre-MS phase is important• Period distributions• Mass function
•Systematic exploration of parameter space is available•A lot more can be done•Comments are welcomed•Stay tuned. . .