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 ρ γ 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: Ml 2 /r 4 < α 2 M/r 2 α > r / l (geometrical criterium) Euler equation (for gas particles)

Escala et al Dotti et al. in preparation M DISK = 5  10 9 M  R DISK = 400 pc M BULGE = 6.98  M DISK a = 200 pc M DISK = 10 8 M  R DISK = 109 pc M BULGE = 6.98  M DISK a = 55 pc Parameters varying: Clumpiness Orbital inclination angle BH to gas mass ratio Parameters varying: BH 1 to BH 2 mass ratio Eccentricity 2.6 × 10 5 K < T < 4.2 × 10 5 K i = 0 º i = 22.5 º i = 45 º i = 67.5 º Dotti et al. in preparation M DISK = 10 8 M  R DISK = 109 pc M BULGE = 6.98  M DISK a = 55 pc Parameters varying: BH 1 to BH 2 mass ratio Eccentricity T ~ 10 4 K

Run A: (equal mass / circular)

Run B: (equal mass / elliptical)

Run E: (equal mass / elliptical / no gas) Predicted by: Colpi et al 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 features of 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 of Milano Bicocca, we are modifying the code to include an arbitrary 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