Dynamical formation ! of black-hole X -ray binaries Ross Church ! - PowerPoint PPT Presentation

Dynamical formation ! of black-hole X -ray binaries Ross Church ! Department of Astronomy and Theoretical Physics ! Lund University ! ! ! With thanks to: ! Melvyn B. Davies (Lund), Seppo Mikkola (Turku) !

Black-hole X -ray binaries in GCs Miller-Jones et al. (2015)

Is the tidal capture of black holes enhanced by binaries?

Tidal capture of BHs by binaries Two aspects: 1. Black hole - star tidal interactions SPH 2. Three-body (BH + binary) simulations ARCHAIN

Setup 5 M � black hole 0 . 6 M � or 0 . 8 M � main-sequence star Range of pericentre separations Measure: �✏ = � E/µ δ M ? α J = J final /J initial

Results q = 1 R � q = 2 R � Very strong function of pericentre separation

Results Change in specific energy 1 1 1.25 1.5 1.75 0 . 1 2 2.125 Lines are fits using 2.25 2.375 functional form of − δ� (Solar units) 2.5 0 . 01 2.625 Fabian, Pringle & 2.75 Rees (1975) 10 − 3 M 1 = 0 . 8 M � 10 − 4 M 1 = 0 . 6 M � exp (f1c [log ( x ) ]) exp (f106 [log ( x ) ]) 10 − 5 1 2 3 4 q = r min / R �

Tidal capture of BHs by binaries Two aspects: 1. Black hole - star tidal interactions SPH 2. Three-body (BH + binary) simulations ARCHAIN

Simulation setup 3-body scattering experiment (binary + black hole) M 1 = 0 . 8 M � M 2 = 0 . 6 M � M • = 5 M � Binary initially 100 au, thermal eccentricity distribution Impact parameter distribution d N d b ∝ b v ∞ = 10 km / s

Outcomes: flyby Flyby Flyby 500 3000 250 1000 300 x i,j / R � y/ R � 0 100 30 − 250 10 − 500 − 500 − 250 0 250 500 − 75000 − 50000 − 25000 0 − 10 5 x/ R � ( t − t 0 ) / τ � Star 1 Star 2 BH x 1 , 2 x 1 , 3 x 2 , 3

Outcomes: exchange Clean exchange Clean exchange 2000 3000 1000 1000 x i,j / R � y/ R � 300 0 100 − 1000 30 − 2000 10 − 2000 − 1000 0 1000 2000 − 80000 − 40000 0 40000 80000 x/ R � ( t − t 0 ) / τ � x 1 , 2 x 1 , 3 x 2 , 3 Star 1 Star 2 BH

Outcomes: collision Direct collision Direct collision 2000 5000 1000 2000 1000 x i,j / R � y/ R � 0 500 − 1000 200 100 − 2000 − 2000 − 1000 0 1000 2000 − 10 5 − 75000 − 50000 − 25000 0 x/ R � ( t − t 0 ) / τ � Star 1 Star 2 BH x 1 , 2 x 1 , 3 x 2 , 3

Outcomes: "dirty" capture Type A capture (star survives) Type A capture (star survives) 2000 10000 1000 1000 x i,j / R � y/ R � 0 100 − 1000 10 − 2000 1 − 2000 − 1000 0 1000 2000 0 5 × 10 6 10 7 1 . 5 × 10 7 2 × 10 7 x/ R � ( t − t 0 ) / τ � Star 1 Star 2 BH x 1 , 2 x 1 , 3 x 2 , 3

Outcomes: "dirty" capture Type A capture (star survives) Type A capture (star survives) 10000 10000 1000 1000 x i,j / R � x i,j / R � 100 100 10 10 1 1 0 5 × 10 6 10 7 1 . 5 × 10 7 2 × 10 7 1 . 675 × 10 7 1 . 7 × 10 7 1 . 725 × 10 7 1 . 75 × 10 7 1 . 775 × 10 7 ( t − t 0 ) / τ � ( t − t 0 ) / τ � x 1 , 2 x 1 , 3 x 2 , 3 x 1 , 2 x 1 , 3 x 2 , 3

Outcomes: "messy" capture Type B capture (star shredded) Type B capture (star shredded) 2000 10000 1000 1000 x i,j / R � y/ R � 0 100 − 1000 10 − 2000 1 − 2000 − 1000 0 1000 2000 0 5 × 10 6 10 7 1 . 5 × 10 7 x/ R � ( t − t 0 ) / τ � Star 1 Star 2 BH x 1 , 2 x 1 , 3 x 2 , 3

Outcomes: "messy" capture Type B capture (star shredded) Type B capture (star shredded) 10000 1000 1000 x i,j / R � x i,j / R � 100 100 10 10 1 1 0 5 × 10 6 10 7 1 . 5 × 10 7 9 . 75 × 10 6 10 7 1 . 025 × 10 7 1 . 05 × 10 7 1 . 075 × 10 7 ( t − t 0 ) / τ � ( t − t 0 ) / τ � x 1 , 2 x 1 , 3 x 2 , 3 x 1 , 2 x 1 , 3 x 2 , 3

Three routes to a close MS-BH binary 1. Undergo a dirty exchange and circularise 1 Inner ⋆ 1, type A Blue circles: ! Inner ⋆ 2, type A Inner ⋆ 1, type B dirty exchanges ! Inner ⋆ 2, type B 0 . 8 q = 2 . 75 R � (star survives) q = 3 R � q = 4 R � 0 . 6 e 0 . 4 Final binary ! Red circles: ! too wide to ! messy exchanges ! 0 . 2 circularise (star destroyed) 0 10 30 100 300 1000 a/ R �

Three routes to a close MS-BH binary 2. Form a dirty triple and circularise Dirty triples, inner orbit properties, a i = 100 R � 0 . 5 Inner ⋆ 1, type A Inner ⋆ 2, type A Inner ⋆ 1, type B Artificial effect: ! Inner ⋆ 2, type B 0 . 4 q = 2 . 75 R � tidal cut-off at q = 3 R � q = 4 R � 4 R � 0 . 3 e 0 . 2 0 . 1 Red: messy Blue: dirty 0 4 5 6 a/ R �

Three routes to a close MS-BH binary 3. A messy triple leads to common-envelope evolution Dirty triples, inner orbit properties, a i = 100 R � 0 . 5 Inner ⋆ 1, type A Inner ⋆ 2, type A Inner ⋆ 1, type B Inner ⋆ 2, type B 0 . 4 q = 2 . 75 R � q = 3 R � q = 4 R � 0 . 3 e 0 . 2 0 . 1 Red: messy 0 4 5 6 a/ R �

Three routes to a close MS-BH binary 3. A messy triple leads to common-envelope evolution Dirty triples, outer orbit properties, a i = 100 R � 1 Inner ⋆ 1, type A Inner ⋆ 2, type A Inner ⋆ 1, type B Inner ⋆ 2, type B 0 . 8 q = 10 R � q = 30 R � q = 100 R � q = 300 R � 0 . 6 e 0 . 4 0 . 2 0 1000 10000 10 5 a/ R �

Coming soon 1. Numbers and rates 2. Other stellar masses 3. MS-BH + MS rather than MS-MS + BH