Hall effect and differential rotation in protoneutron stars

坍缩计算导致了新生的热质子中子星(PNS)的差动自转。由于它们的超强磁场，霍尔效应似乎对PNS很重要。如果剪切足够强，并且霍尔参数RB=WBR是有序的，则微分旋转和霍尔效应共同产生剪切霍尔不稳定性(SHI)。后者只有在非常热的年轻中子星上才能实现。如果中子星冷却，霍尔参数增大，系统稳定。SHI的一个重要特征是它明显依赖于磁场的符号。SHI只适用于平行于旋转轴的磁场。在相反的情况下，磁旋转不稳定性(MRI)是工作的，但受到霍尔效应的修正。我们建议研究这种激发情况，以解决在非线性情况下SHI是否可以充当发电机的问题，如果是的话，以什么幅度。我们已经找到了这种全新的非线性和非湍流发电机类型的激发条件，它对天体物理对象(如中子星)的重要性必须得到验证。感应环向磁场只能达到相对于Taylor(或Pinch-type)不稳定性稳定的幅度。另一方面，磁感应角动量输运限制了差分旋转的寿命。因此，发电机对差动旋转的这种反向反应是一个基本的悬而未决的问题，它限制了发电机制度的寿命，也限制了激励磁场的幅度。

Collapse calculations lead to the result that the hot newly born protoneutron stars (PNS) rotate differentially. Due to their extraordinary strong magnetic fields also the Hall effect appears to be important for PNS. Differential rotation and Hall effect together are known to produce the shear-Hall instability (SHI) if the shear is strong enough and the Hall parameter Rb = wBr is of order unity. The latter is realized only for very hot young neutron stars. If the neutron star cools down, the Hall parameter grows and the system is stabilized.An important characteristic of the SHI is its distinct dependence on the sign of the magnetic field. The SHI only works for magnetic fields parallel to the rotation axis. In the opposite case the magnetorotational instability (MRI) works but under modification by the Hall effect.It is proposed to study this exciting situation in order to attack the question whether in the nonlinear case the SHI can act as a dynamo and if YES with which amplitude. We have already found the excitation conditions for such a completely new nonlinear and nonturbulent dynamo type whose importance for astrophysical objects (such as neutron stars) must be checked.The induced toroidal magnetic fields can only reach amplitudes which are stable with respect to the Tayler (or pinch-type) instability. On the other hand the lifetime of differential rotation is restricted by the magnetic-induced angular momentum transport. This backreaction of the dynamo onto the differential rotation is thus a basic open question which limits the lifetime of the dynamo regime and also the amplitude of the excited magnetic fields.