Relativistic Dynamical Calculations of Merging Black Hole-Neutron Star Binaries

1. Joshua Faber (NSF AAPF Fellow, UIUC) Stu Shapiro (UIUC) Keisuke Taniguchi (UIUC) Thomas Baumgarte (Bowdoin) Fred Rasio (Northwestern) Paper Submitted to PRD Relativistic Dynamical Calculations of Merging Black Hole-Neutron Star Binaries

2. Merging BH-NS binaries • Relativistic binaries projected to be a primary source of GW detections • GRB050509b may be located 35kpc from center of elliptical with low SFR -> binary compact object merger • More massive than NS-NS-> seen at greater distance (10-100/yr for LIGO II; Belczynski et al. 2002, Voss+Tauris2003) • May shed light on internal structure of NS, behavior of matter at high density • Violent disruption process exposes interior of NS for study • Links to GRB observations • Unclear whether they are a source of r-process elements

3. BHNS binaries: numerical issues • Only (Quasi-)Newtonian BH-NS dynamical calculations so far (Lee+Kluzniak, Janka et al., Rosswog et al.) • NSs are not Newtonian objects and require a hydrodynamic treatment • Self-gravity is important during tidal disruption • BHs do not exist in Newtonian or PN physics • Moving BHs require careful treatment of the singularity • More difficult than NSNS mergers; more difficult than BHBH, too?

4. Description of method • We assume an extreme mass ratio (Baumgarte et al.) • MBH>>MNS -> BH is fixed in place • Conformally Flat gravity (Isenberg; Wilson+Mathews): • GR minus 1 d.o.f. • Exact for spherically symmetric systems (Schwarzschild) • Einstein's Equations reduce to 5 linked non-linear elliptic eqs. • NS: Polytropic EOS, corotating • Low-compactness models from BSS -> disruption occurs outside the ISCO for larger mass ratios • Adiabatic evolution

5. Our hydrodynamical code • Smoothed Particle Hyrdodynamics (SPH) used to describe NS • ~100,000 particles • Field equations are solved using LORENE, a multi-domain, spheroidal, spectral methods solver • Solve for NS gravitational field in BH background • Similar to NSNS code of Faber, Grandclément and Rasio (2004)

6. Equilibrium configurations • Relaxed relativistic equilibrium BH-NS configurations • Initial conditions satisfy integrated Euler equation to <.001 • Derived from CF version of BSS • Future results from TBFS • Very nearly Keplerian

7. The stability of mass transfer • Stable vs. unstable mass transfer: • mass transfer should increase binary separation • Does NS shrink within its Roche Lobe? • Unstable: Immediate disruption • Stable: Periodic mass transfer?

8. Unstable mass transfer • Expected for soft EOS (e.g., Γ=1.5) • Rapid disruption • Much more dynamical than QE mass transfer description

9. “Stable” mass transfer • Not stable: GW losses drive mass loss instability • Periodic mass transfer can occur, since mass loss inward -> increase in binary separation

10. Evolution of mass loss and binary separation • Mass loss regulates the binary separation • Remnant develops orbital eccentricity • Orbital parameters evolve continuously • We overestimate mass loss outward

11. Conclusions • No stable mass transfer for BHNS binaries • Mass transfer plays important role in determining binary separation on dynamical timescale • Possibility of efficiently transferring angular momentum outward • GRB progenitor? • Future work: irrotational NS, physical compaction, AV • Drop extreme mass ratio limit • Eventually move BH into grid