1. Johnny VanLandingham 7/13/2016
The Role of the Kozai-Lidov Mechanism in Black Hole Binary Mergers in Galactic Centers
Johnny VanLandingham
7/13/2016
ApJ Accepted -- arXiv:
Collaborators: M.C. Miller, D.P. Hamilton, D.C. Richardson

2. Gravitational Waves Detections: Detection rate: GW150914 & GW151226
~30 Msun BH’s; ~10 Msun BH’s
Detection rate:
9 – 240 Gpc-3 yr-1 (Abbott et al. 2016)
Motivation for me personally. As Cole quotes from John Wheeler: spacetime tells sources how to move and moving sources tell spacetime how to ripple
Timescale longer than a hubble time for a = 1, e = 0. Therefore want to change these.
“If you’ve really got your ear to the ground, you might have heard about…”
“What pathways might be responsible for this merger rate?”
Image Credit: Caltech/MIT/LIGO Lab
(Peters, 1964)

3. Yoshihide Kozai & Michael Lidov 1962
Antonini & Perets 2012
Explain Hierarchical. Expansion of Hamiltonian in ratio of sma. Initially massless satellite around sun w/ Jupiter perturbing
Explain superorbit
Explain subscripts
Conservation of z angular momentum
Critical angle
Binary inside of radius of influence of SMBH
In a chaotic environment, more opportunity to reach critical conditions.
Either need time to have several passages or such high eccentricity that merger in one pass

4. Method Simulations split into two steps. Step one: Step two:
Treat the BHB as a single 20 Msun particle.
Integrate all stars, SMBH, and BHB through several relaxation times.
Output complete state every ~10 yrs.
Step two:
Integrate just the 3-body problem.
Place the BHB at the correct center of mass position every ~10 yrs.
Works if updates are frequent compared to timescale of most effects
Works if star approaches within 1 AU rare.
If changes to superorbit properties doesn’t effect inner orbit properties

5. Systems much smaller than real galactic centers
Not strictly correct since it is not exactly keplerian, but close, SMBH dominant.
Mass segregation (possibly too dramatic)
Inclination wandering is important for Kozai

6. Emax =

7. Inspiral Rate (upper limit)
ƒmerge = 0.15
Nstars ≈ 2 x 106 for TK = Trlx around a 4 x 106 Msun SMBH.
Tmerger = Trlx at 1.2 pc from SMBH = 6 x 108 yrs
ƒBH = (Miralda-Escude & Gould 2000)
ƒbinary = 0.2 (Belczynski et al. 2004)
Observational constraint: 9 – 240 Gpc-3 yr-1 (Abbott et al. 2016)
“This is an upper limit because our 2-step simulation process allows large changes in the mutual inclination, while there is some evidence that slowly varying the superorbit inclination may not change the mutual inclination accordingly.”
f_bh with mass segregation
f_binary for population synthesis models of Bhs in the field.
Observational constraint using a marginal detection as well

8. Conclusions
First direct N-body calculations with a tight binary near a SMBH.
KL mechanism plays a large role in binary evolution.
Merger rate very uncertain, but consistent with observations so far.

9. Questions???

10. Effect of changing the inclination of the outer binary slowly…
Force applied on outer body.
Exponential increase in inclination over one KL cycle.
Mutual inclination change smaller than expected.
Larger for initially larger itot.
Hamers et al. 2015

11. Eccentric Inspirals Inspirals with e > 0.1 at 10 Hz.
Energy loss nearly impulsive.
Requires pericenter < 10-6 AU.
One example:
Eccentricity at 10 Hz = 0.58
Possible but not common.

12. 1k runs not enough kozai cycles before tidally separated.
Runs starting further out may fill in more of the space.
Outlier
Sensitive to details of loss cone, mass segregation

13. Scaled by relaxation time to better understand trends.
1k runs clearly slower rate.
Slower initially and possibly towards the end.

14. For a 10k run

15. Inspirals 81 0f 400 simulated BHBs merged.
10 of 100 in 1k simulations.
12 of 100 in 2.5k simulations.
32 of 100 in 5k simulations.
27 of 100 in 10k simulations.
All others end in tidal separation.
HNBody stalls at very small semi-major axis.

16. Complications
Effect of changing the inclination of the outer binary slowly…
(Hamers et al. 2015)

17. Merger Distance

18. Low-mass X-ray Binaries
All four within 1 parsec of Sgr A*
KL mechanism with SMBH as perturber could help explain this overabundance.
(Muno et al. 2005)