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Register a new userDynamics of a self-gravitating magnetized neutron source
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Added by
Aurora Perez Martinez
Publication date
2008
fields
Physics
and research's language is
English
Authors
D. Manreza Paret
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The dynamics of a self-gravitating neutron gas in presence of a magnetic field is being studied taking the equation of state of a magnetized neutron gas obtained in a previous study [2]. We work in a Bianchi I spacetime characterized by a Kasner metric, this metric allow us to take into account the anisotropy that introduces the magnetic field. The set of Einstein-Maxwell field equations for this gas becomes a dynamical system in a 4-dimensional phase space. We get numerical solutions of the system. In particular there is a unique point like solution for different initial conditions. Physically this singular solution may be associated with the collapse of a local volume of neutron material within a neutron star.
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We examine the dynamics of a self--gravitating magnetized neutron gas as a source of a Bianchi I spacetime described by the Kasner metric. The set of Einstein-Maxwell field equations can be expressed as a dynamical system in a 4-dimensional phase space. Numerical solutions of this system reveal the emergence of a point--like singularity as the final evolution state for a large class of physically motivated initial conditions. Besides the theoretical interest of studying this source in a fully general relativistic context, the resulting idealized model could be helpful in understanding the collapse of local volume elements of a neutron gas in the critical conditions that would prevail in the center of a compact object.
We use the Bianchi-I spacetime to study the local dynamics of a magnetized self-gravitating Fermi gas. The set of Einstein-Maxwell field equations for this gas becomes a dynamical system in a 4-dimensional phase space. We consider a qualitative study and examine numeric solutions for the degenerate zero temperature case. All dynamic quantities exhibit similar qualitative behavior in the 3-dimensional sections of the phase space, with all trajectories reaching a stable attractor whenever the initial expansion scalar H_{0} is negative. If H_{0} is positive, and depending on initial conditions, the trajectories end up in a curvature singularity that could be isotropic(singular point) or anisotropic (singular line). In particular, for a sufficiently large initial value of the magnetic field it is always possible to obtain an anisotropic type of singularity in which the line points in the same direction of the field.
A linear stability analysis has been performed onto a self-gravitating magnetized gas disk bounded by external pressure. The resulting dispersion relation is fully explained by three kinds of instability: a Parker-type instability driven by self-gravity, usual Jeans gravitational instability and convection. In the direction parallel to the magnetic fields, the magnetic tension completely suppresses the convection. If the adiabatic index $gamma$ is less than a certain critical value, the perturbations trigger the Parker as well as the Jeans instability in the disk. Consequently, the growth rate curve has two maxima: one at small wavenumber due to a combination of the Parker and Jeans instabilities, and the other at somewhat larger wavenumber mostly due to the Parker instability. In the horizontal direction perpendicular to the fields, the convection makes the growth rate increase monotonically upto a limiting value as the perturbation wavenumber gets large. However, at small wavenumbers, the Jeans instability becomes effective and develops a peak in the growth rate curve. Depending on the system parameters, the maximum growth rate of the convection may or may not be higher than the peak due to the Jeans-Parker instability. Therefore, a cooperative action of the Jeans and Parker instabilities can have chances to over-ride the convection and may develop large scale structures of cylindrical shape in non-linear stage. In thick disks the cylinder is expected to align its axis perpendicular to the field, while in thin ones parallel to it.
We use ZEUS-MP to perform high resolution, three-dimensional, super-Alfvenic turbulent simulations in order to investigate the role of magnetic fields in self-gravitating core formation within turbulent molecular clouds. Statistical properties of our super-Alfvenic model without gravity agree with previous similar studies. Including self-gravity, our models give the following results. They are consistent with the turbulent fragmentation prediction of the core mass distribution of Padoan & Nordlund. They also confirm that local gravitational collapse is not prevented by magnetohydrodynamic waves driven by turbulent flows, even when the turbulent Jeans mass exceeds the mass in the simulation volume. Comparison of results between 256^3 and 512^3 zone simulations reveals convergence in the collapse rate. Analysis of self-gravitating cores formed in the simulation shows that: (1) All cores formed are magnetically supercritical by at least an order of magnitude. (2) A power law relation between central magnetic field strength and density B_c propto rho_c^{1/2} is observed despite the cores being strongly supercritical. (3) Specific angular momentum j propto R^{3/2} for cores with radius R. (4) Most cores are prolate and triaxial in shape, in agreement with the results of Gammie et al.
In broad astrophysical contexts of large-scale gravitational collapses and outflows and as a basis for various further astrophysical applications, we formulate and investigate a theoretical problem of self-similar MHD for a non-rotating polytropic gas of quasi-spherical symmetry permeated by a completely random magnetic field. We derive two coupled nonlinear MHD ordinary differential equations (ODEs), examine properties of the magnetosonic critical curve, obtain various asymptotic and global semi-complete similarity MHD solutions, and qualify the applicability of our results. Unique to a magnetized gas cloud, a novel asymptotic MHD solution for a collapsing core is established. Physically, the similarity MHD inflow towards the central dense core proceeds in characteristic manners before the gas material eventually encounters a strong radiating MHD shock upon impact onto the central compact object. Sufficiently far away from the central core region enshrouded by such an MHD shock, we derive regular asymptotic behaviours. We study asymptotic solution behaviours in the vicinity of the magnetosonic critical curve. Numerically, we construct global semi-complete similarity MHD solutions that cross the magnetosonic critical curve zero, one, and two times. For comparison, counterpart solutions in the case of an isothermal unmagnetized and magnetized gas flows are demonstrated in the present MHD framework at nearly isothermal and weakly magnetized conditions. For a polytropic index $gamma=1.25$ or a strong magnetic field, different solution behaviours emerge. In these cases, there exist semi-complete similarity solutions crossing the magnetosonic critical curve only once, and the MHD counterpart of expansion-wave collapse solution disappears.
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