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: 1604.04948 Collaborators: M.C. Miller, D.P. Hamilton, D.C. Richardson

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)

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

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

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

Emax = 0.99985

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 = 0.016 (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

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.

Questions???

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

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.

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

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

For a 10k run

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.

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

Merger Distance

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)