Topological Currents in Neutron Stars: Kicks, Precession, Toroidal Fields, and Magnetic Helicity

More recently the role of anomalies in QCD has been studied at finite baryon density [3,4] and similar phenomena have been studied in condensed matter systems [5,6,7]. Since these first steps many other applications of anomalies in dense QCD have been considered: an analysis of the axion physics and microscopic derivation of anomalies [8,9]; studying the vortex structure due to the anomalies currents in neutron stars (type-I versus type-II superconductivity) [10]; the charge separation effect at the relativistic heavy ion collider (RHIC) [11,12]; magnetism of nuclear and quark matter [13]; anomaly mediated neutrinophoton interactions at finite baryon density [14]; the chiral magnetic effect at RHIC [15] and many others.

For this paper we are interested in the result where a topological vector current (along with an axial current) is induced in the background of an external magnetic field when the chemical potentials of the right and left-handed fermions are not equal, µ r = µ l . As argued in [8] this phenomenon depends only on the presence of chiral symmetry and not on whether the chiral symmetry is spontaneously broken. Applications of this induced vector current have been discussed in neutron star physics [10] and RHIC related physics [15]. In [10] it was shown that a non-dissipating vector current running along the magnetic flux tubes may change the behaviour of superconductivity from type-II to type-I, even though the Landau-Ginzburg parameter κ > 1/ √ 2 suggests type-II behaviour. It was also argued that the triangular lattice of flux tubes-the Abrikosov lattice-may be completely destroyed due to the helical instability in the presence of the induced vector current. This would resolve the apparent contradiction with the precession of the neutron stars [16,17]. For another mechanisms that may resolve this contradiction see [18,19,20,21].

Our goal is to present a quantitative analysis of the conditions when parity violation (µ r = µ l ) occurs in dense stars and a persistent, topological current is induced. We claim that topological vector currents do exist in dense stars and we consider applications that may help explain many phenomena in dense stars, such as kicks and toroidal fields.

It is well known that the weak interactions (where parity is strongly violated) play a dominant role in neutron star physics. Producing the asymmetry µ r = µ l for a given process is common in the bulk of neutron stars, but we are interested in coherent parity violating effects when the asymmetry appears in macroscopically large regions. Sections 3-7 are devoted to estimating the induced current in different environments that may exist in neutron stars, while Section 8 is devoted to possible applications of the topological currents. Readers interested in applications may go directly to Section 8, skipping the technical aspects of Sections 3-7.

If non-dissipating vector currents are induced they can transfer momentum either by escaping the star or radiating photons. Our kick engine continues to work even when temperature drops well below T MeV. This is because it is the chemical potential (µ lµ r ) = 0 that drives the kick, not the temperature. This leads to long sustained kicks, rather than short natal kicks. In Section 8 we use a rough calculation to demonstrate that our kick mechanism can explain the proper motion of hyperfast pulsars with v > 800 km/s, particularly B1508+55 moving at v = 1083 +103 -90 km/s [22]. A detailed calculation can be found in [23]. See [24] for a review of kick velocities.

The kick naturally produces a magnetic field-momentum correlation P • B . Though it is believed that the spin and magnetic field are correlated somehow, the sustained nature of the kicks allows a rotation-kick correlation P • Ω to form regardless of the angle between the star’s rotation and magnetic field. A neutron star spins on the order of milliseconds and the kick occurs over hundreds of years. This gives rise to a cylindrical symmetry which causes the the force of the kick to average along the axis of rotation. The nature of the spinmagnetic field correlation can produce kicks that are either aligned or anti-aligned with the spin axis. Regardless of its direction, this correlation is a P-odd effect, which indicates it must be generated by a P-odd mechanism such as the parity violating processes that power our current. In fact, long, sustained kicks are observa

…(Full text truncated)…