#
APS April Meeting 2010

## Volume 55, Number 1

##
Saturday–Tuesday, February 13–16, 2010;
Washington, DC

### Session G4: Numerical Relativity and Astrophysics

8:30 AM–10:18 AM,
Sunday, February 14, 2010

Room: Thurgood Marshall North

Sponsoring
Units:
GGR DCOMP

Chair: Steven Detwiler, University of Florida

Abstract ID: BAPS.2010.APR.G4.1

### Abstract: G4.00001 : Statistical studies of Spinning Black-Hole Binaries*

8:30 AM–9:06 AM

Preview Abstract
Abstract

####
Author:

Carlos Lousto

(Rochester Institute of Technology-CCRG)

We study the statistical distribution of the spins of generic
black-hole binaries during the inspiral and merger, as well as
the distribution of the remnant mass, spin, and recoil velocity.
For the inspiral regime, we start with a random uniform
distribution of spin directions $\vec{S}_1$ and $\vec{S}_2$ over
the sphere and magnitudes $|\vec{S}_i/m_i^2|=0.97$ for different
mass ratios. Starting from a fiducial initial separation of
$r_i=50m$, we performs
3.5 post-Newtonian evolutions down to a separation of $r_f=5m$,
where $m=m_1+m_2$. At this final separation, we compute the
angular distribution of the spins with respect to the final
orbital angular momentum. We perform $16^4$ simulations for mass
ratios between $q=1$ and $q=1/16$ and compute the distribution of
the angles $\hat{\vec{L}}\cdot\hat{\vec{\Delta}}$ and
$\hat{\vec{L}}\cdot\hat{\vec{S}}$, directly related to recoil
velocities. We find a small but statistically significant bias of
the distribution towards counter-alignment of both scalar
products. To study the merger of black-hole binaries, we
introduce empirical formulae to describe the final remnant black
hole mass, spin, and recoil velocity for merging black-hole
binaries with arbitrary mass ratios and spins. Our formulae are
based on the post-Newtonian scaling with amplitude parameters
chosen to fit recently available fully nonlinear numerical
simulations. We then evaluate these formulae for randomly chosen
directions of the individual spins and magnitudes, and the
binary's mass ratio. We found that the magnitude of the recoil
velocity has a decaying e-folding distribution with a mean
value of $2500$ km/s, and a highly peaked angular distribution
along the final orbital axis. The distribution of the final
black-hole spin magnitude show an universal distribution highly
peaked at $S_f/m_f^2=0.73$ and with a nearly 25$^{\circ}$ degree
misalignment with respect to the final orbital angular momentum,
just prior to full merger of the holes.

*Research supported by NFS, NASA-HST grants.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2010.APR.G4.1