Hall effect and differential rotation in protoneutron stars

坍缩计算得出的结果是，新生的热质子中子星（PNS）的旋转是不同的。由于其极强的磁场，霍尔效应似乎对PNS很重要。如果剪切强度足够大，且霍尔参数Rb = wBr为有序单位，则微分旋转和霍尔效应共同产生剪切-霍尔失稳（SHI）。后者只有在非常热的年轻中子星上才能实现。如果中子星冷却下来，霍尔参数增大，系统稳定下来。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，磁旋不稳定性（MRI）起作用，但受到霍尔效应的修改。提出研究这种令人兴奋的情况，是为了解决在非线性情况下，SHI是否可以作为发电机，如果可以，以何种幅度。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励条件，它对天体物理对象（如中子星）的重要性必须加以检验。感应环形磁场只能达到相对于泰勒（或捏型）不稳定性稳定的振幅。另一方面，磁致角动量输运限制了微分旋转的寿命。因此，发电机对微分旋转的反向反应是一个基本的悬而未决的问题，它限制了发电机的寿命，也限制了激发磁场的振幅。

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.