LISA double BHs

Dynamics in gaseous nuclear disk

Outlines

• Dynamical evolution of MBHBs

• Code introduction

• Initial conditions of the simulations

• Results

• Future work

MBHs coalescence (1)

● Dynamical friction (tidal stripping, efficient only for “major mergers”)

● Three body interactions (loss cone depletion… ask to Sesana)

● Gravitational wave emission

Collisionless background (Begelman, Blanford & Rees 1980)

MBHs coalescence (2)

Gaseous background

● Dynamical friction (2) (Escala, Larson, Coppi & Maradones 2004)

● Gravitational torque by ellipsoidal deformation (Escala, Larson, Coppi & Maradones 2004)

● Gravitational wave emission

● Gravitational torque in circumnuclear gap (Armitage & Natarajan 2005)

● Dynamical friction (1) (Kazantzidis et al. 2005)

Stellar bulge (Plummer):

Gaseous disk (Mestel):

Initial condition

Equation of state

P=K ργ γ = 5/3 (pure adiabatic evolution)

Code: Gadget Springel, Yoshida & White 2001

SPH: Smoothed Particle Hydrodynamics

Stellar and gaseous environment are sampled statistically (Monte Carlo)

Any “particle” has a spherical distribution of mass:

Code: Gadget Springel, Yoshida & White 2001

Gravitational potential is computed with a tree algorithm

Computational cost ~ N log N

Cell opening criterion: Ml2/r4 < α2 M/r2

α > r / l (geometrical criterium)

Euler equation(for gas particles)

Escala et al. 2005 Dotti et al. in preparation

MDISK = 5 10 9 M

RDISK = 400 pcMBULGE = 6.98 MDISK

a = 200 pc

MDISK = 10 8 M

RDISK = 109 pcMBULGE = 6.98 MDISK

a = 55 pc

Parameters varying:

Clumpiness

Orbital inclination angle

BH to gas mass ratio

Parameters varying:

BH1 to BH2 mass ratio

Eccentricity

2.6 × 10 5 K < T < 4.2 × 10 5 K

i = 0 º i = 22.5 ºi = 45 º i = 67.5 º

0.010.030.050.10.30.5

Dotti et al. in preparation

MDISK = 10 8 M

RDISK = 109 pcMBULGE = 6.98 MDISK

a = 55 pc

Parameters varying:

BH1 to BH2 mass ratio

Eccentricity

T ~ 10 4 K

Run A: (equal mass / circular)

Run A: (equal mass / circular)

Run B: (equal mass / elliptical)

Run E: (equal mass / elliptical / no gas)

Predicted by: Colpi et al. 1999 van den Bosch et al. 1999

Run A / B: (equal mass)

Escala et al. 2004

Run C: (unequal mass / circular)

Run D: (unequal mass / elliptical)

Run F (unequal mass / elliptical /retrograde )

Accretion implications

Variation of the mass of one of BHs in binary has some dynamical effects… If angular momentum is conserved:

Sesana et al. in preparation

Scale considerations (1)

In my simulation we have a spatial resolution of ~ 1 pc

For this separation, the two MBHs can not coalesce in an Hubble time for GW emission.

We are preparing higher resolution simulations, but ...

“using finer and finer resolution may be a waste of time unless the physics is consistent with the scale”

Take home message I, Joe Monaghan.

Scale considerations (2)

High resolution simulations (HRSs) could investigate long-scales of the order of accretion radius of ours MBHs, of the local instability of a realistic self gravitating disk, etc.

So, HRSs allow (and force) us to implement new featuresof the code, corresponding to different physical phenomena:

• Star formation

• Black holes treated as sink particles

• Realistic cooling-heating

Scale considerations (3)

HRSs imply an increase of computational time

With the collaboration of Simone Callegari, a student ofMilano Bicocca, we are modifying the code to include anarbitrary static component of the gravitational potential in order to reduce the number of “live” particles without losing resolution

As a test, we run a simulation of a Hernquist stellar Bulge in a NFW halo of DM, with an “live” halo and a “dead” halo