3,487 research outputs found

### Analytic properties of force-free jets in the Kerr spacetime -- III: uniform field solution

The structure of steady axisymmetric force-free magnetosphere of a Kerr black
hole (BH) is governed by a second-order partial differential equation of
$A_\phi$ depending on two "free" functions $\Omega(A_\phi)$ and $I(A_\phi)$,
where $A_\phi$ is the $\phi$ component of the vector potential of the
electromagnetic field, $\Omega$ is the angular velocity of the magnetic field
lines and $I$ is the poloidal electric current. In this paper, we investigate
the solution uniqueness. Taking asymptotically uniform field as an example,
analytic studies imply that there are infinitely many solutions approaching
uniform field at infinity, while only a unique one is found in general
relativistic magnetohydrodynamic simulations. To settle down the disagreement,
we reinvestigate the structure of the governing equation and numerically solve
it with given constraint condition and boundary condition. We find that the
constraint condition (field lines smoothly crossing the light surface (LS)) and
boundary conditions at horizon and at infinity are connected via radiation
conditions at horizon and at infinity, rather than being independent. With
appropriate constraint condition and boundary condition, we numerically solve
the governing equation and find a unique solution. Contrary to naive
expectation, our numerical solution yields a discontinuity in the angular
velocity of the field lines and a current sheet along the last field line
crossing the event horizon. We also briefly discuss the applicability of the
perturbation approach to solving the governing equation

### Neutrino and anti-neutrino transport in accretion disks

We numerically solve the one dimensional Boltzmann equation of the neutrino
and anti-neutrino transport in accretion disks and obtain the fully energy
dependent and direction dependent neutrino and anti-neutrino emitting spectra,
under condition that the distribution of the mass density,temperature and
chemical components are given. Then, we apply the resulting neutrino and
anti-neutrino emitting spectra to calculate the corresponding annihilation rate
of neutrino pairs above the neutrino dominated accretion disk and find that the
released energy resulting from the annihilation of neutrino pairs can not
provide sufficient energy for the most energetic short gamma ray bursts whose
isotropic luminosity can be as high as $10^{52}$ ergs/s unless the high
temperature zone where the temperature is beyond 10 MeV can stretch over 200 km
in the disk. We also compare the resulting luminosity of neutrinos and
anti-neutrinos with the results from the two commonly used approximate
treatment of the neutrino and anti-neutrino luminosity: the Fermi-Dirac black
body limit and a simplified model of neutrino transport, i.e., the gray body
model, and find that both of them overestimate the neutrino/anti-neutrino
luminosity and their annihilation rate greatly. Additionally, as did in Sawyer
(2003), we also check the validity of the two stream approximation, and find
that it is a good approximation to high accuracy.Comment: Phys. Rev. D in press, 15 preprint papers, 5 figure

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