Proc. Neutrino Astrophysics - MPP Theory Group

104
exceeds a few 10 49 erg. Even worse, by far most of this energy is deposited in the surface-near
regions of the merged stars and will drive a mass loss (“neutrino wind”) which will pollute
the fireball with an unacceptably large baryon load.
The neutrino emission from the coalescence of two neutron stars is very different from the
case of head-on collisions in which neutrinos are emitted in two very short (about 1 millisecond)
and extremely luminous bursts reaching peak values of up to 4 × 10 54 erg/s [6]! This
gigantic neutrino luminosity leads to an energy deposition of about 10 50 erg by ν¯ν-annihilation
within only a few milliseconds. However, the surroundings of the collision site of the two neutron
stars are filled with more than 10 −2 M⊙ of ejected matter and the maximum values of
the Lorentz-factor Γ are only about 10 −3 , five orders of magnitude lower than required for
relativistic fireball expansion that could produce a GRB.
Snapshots of the density contours in the orbital plane for the considered 1.2M⊙-1.8M⊙
merger can be seen in Fig. 2. Initially (0ms < t < 3ms) the secondary is tidally elongated by
the primary and a mass transfer is initiated. The top left panel of Fig. 2 nicely shows how
matter is concentrated to flow through the L1-point onto the surface of the primary. As more
and more matter is taken away from the secondary it becomes ever more elongated (bottom
left panel). Most of the matter of the secondary finally ends up forming a rapidly rotating
surface layer of the primary, while a smaller part concentrates in an additional, extended thick
disk around the primary. This matter has enough angular momentum to stay in an accretion
torus even after the massive central body has most likely collapsed to a black hole.
Neutron Tori around Black Holes and GRBs
If the central, massive body did not collapse into a black hole, it would continue to radiate
neutrinos with high luminosities, like a massive, hot proto-neutron star in a supernova. But
instead of producing a relativistically expanding pair-plasma fireball, these neutrinos will
deposit their energy in the low-density matter of the surface and thus will cause a mass flow
known as neutrino-driven wind (e.g., [8]). Most of this energy is consumed lifting baryons in
the strong gravitational potential and the expansion is nonrelativistic.
This unfavorable situation is avoided if the central object collapses into a black hole on
a timescale of several milliseconds after the merging of the neutron stars. We simulated the
subsequent evolution by replacing the matter inside a certain radius by a vacuum sphere
(black hole) of the same mass. The region along the system axis was found to be evacuated
on the free fall timescale of a few milliseconds as the black hole sucks up the baryons. Thus an
essentially baryon-free funnel is produced where further baryon contamination is prevented by
centrifugal forces. This provides good conditions for the creation of a clean e ± γ fireball by ν¯νannihilation.
Also the thick disk closer to the equatorial plane loses matter into the black hole
until only gas with a specific angular momentum larger than j ∗ ∼ = 3Rsvk(3Rs) = √ 6GM/c
(Rs = 2GM/c 2 is the Schwarzschild radius of the black hole with mass M, vk(3Rs) the Kepler
velocity at the innermost stable circular orbit at 3Rs) is left on orbits around the black hole.
We find torus masses of up to Mt ≈ 0.2–0.3M⊙ at a time when a quasi-stationary state is
reached. The temperatures in the tori are 3–10MeV, maximum densities a few 10 12 g/cm 3 .
Typical neutrino luminosities during this phase are of the order of Lν ≈ 10 53 erg/s (60% ¯νe,
35% νe). With a maximum radiation efficiency of εr ≈ 0.057 for relativistic disk accretion
onto a nonrotating black hole we calculate an accretion rate of ˙ Mt = Lν/(c 2 εr) ∼ 1M⊙/s and
an accretion timescale of tacc = Mt/ ˙ Mt ∼ 0.2–0.3s. This is in very good agreement with the
analytical estimates of Ruffert et al. [5].