Reconnection of magnetic field in neutron stars driven by electron mass term in triangle anomaly

1. Reconnection of magnetic field in neutron stars driven by electron mass term in triangle anomaly Maxim Dvornikov (in collaboration with V.B.Semikoz) IZMIRAN, Moscow, Russia Tomsk State University, Russia

2. Outline • Adler-Bell-Jackiw anomaly • Mean spin of plasma (chiral separation effect) • Pseudoscalar contribution in quasiclassical limit • Chemical potential of plasma in magnetic field • Evolution of magnetic helicity in finite volume • Reconnection of magnetic field in neutron star • Conclusion

3. References • M. Dvornikov & V.B. Semikoz, Magnetic helicity evolution in a neutron star accounting for the Adler-Bell-Jackiw anomaly, JCAP 08 (2018) 021 [arXiv:1805.04910]

4. Conservation of axial current for classical massless fermions • For chiral fermions with m = 0,γ5 = iγ0γ1γ2γ3 is conserved operator: [γ5,H]=0, where H = (αp) is Hamiltonian • Noether theorem implies that the classical chiral current should be conserved

5. Adler anomaly for chiral charged fermions γαγ5 • If chiral particle has nonzero electric charge e, in presence of electromagnetic field Fμν = (E,B) the axial current is no longer conserved due to quantum effects (Adler, 1969; Bell & Jackiw, 1969) γμ γν

6. Mass correction to Adler anomaly • Non-conservation of axial current also holds true for massive fermions (Ioffe, 2006) If we represent ψT= (ψR,ψL), then Chiral imbalance Mean spin of plasma New pseudoscalar

7. Mean spin • External magnetic field B = Bez • Mean spin reads (Semikoz & Valle, 1997) If fermions are ultrarelativistic This result is known as the chiral separation effect (Metlitski & Zhitnitsky, 2005) since S = JA

8. Computation of pseudoscalar in external magnetic field • If magnetic field is weak, eB << Ep2, we can use plane waves approximation (Wentzel-Kramers-Brillouin approximation) for the calculation of the pseudoscalar 2im<ψ+γ0γ5ψ> = -div(S5) • Dvornikov & Semikoz (2018) obtained that Equilibrium spin distribution function (Silin, 1968) -γ= E/m is the Lorentz factor - Pseudoscalar computation in E||B was made by Fukushima et al. (2018)

9. Magnetic helicity |L| = 5 In classical MHD, magnetic helicity in finite volume evolves as Magnetic helicity was first introduced by Gauss (1833) Magnetic helicity is conserved in the perfectly conducting fluid Magnetic helicity is gauge invariant In the system of two linked magnetic fluxes, magnetic helicity takes the form (Berger, 1999)

10. Quantum contributions to helicity evolution Dvornikov & Semikoz (2018): Seff = 0 in nonrelativistic plasma, Ep = m Seff = S = - eμeB/2π2 in ultrarelativistic plasma, Ep >> m

11. Chemical potential of degenerate plasma in external magnetic field Nunokawa, et al. (1997): We assume the axially symmetric magnetic field B = B(r,θ)

12. Helicity evolution in neutron star • Dvornikov (2016) found that chiral imbalance in NS vanishes for 10-11 s. Thus we take thatnR = nL. • We assume the quadrupole configuration of the magnetic field B(r,θ)=Bp(r)[cos(2θ) er+sin(2θ)eθ]+Bϕ(r)cos(θ)eϕ The explicit form of function A was obtained by Dvornikov & Semikoz (2018)

13. Comparison of classical and quantum contributions • Evolution of total helicity consists of two terms: dH/dt = (dH/dt)class + (dH/dt)quant • Classical contribution arises from the surface term known in MHD (see above): (dH/dt)class ~ BpR3 <v> • We consider core of NS (μe = 100 MeV and R = 105 cm) and assume rigid rotation • In this case, (dH/dt)quant >> (dH/dt)class

14. Magnetar bursts Magnetars are supposed to be highly magnetized compact stars with B > 1015 G (Turolla et al., 2016) Origin of such strong magnetic fields is an open question of modern astrophysics Magnetars are observed by electromagnetic emission in X-ray and gamma-ray regions ranging from short bursts to giant flares Mechanism of electromagnetic emission of magnetars is unclear

15. Reconnection is change of magnetic field topology resulting in dissipation of magnetic energy (Priest & Forbes, 2000) Reconnection is pulsar magnetosphere can result in magnetar bursts (Thompson, et al, 2002) Implication for reconnection of magnetic field lines - Calculated quantum correction to helicity change can be interpreted as intertwining of two thin magnetic tubes: (dH/dt)quant = dθ/dtFpFt, where dθ/dt is angular velocity with which magnetic loop bases are twisting one around other causing interlacing of flux tubes - Released energy can cause magnetar bursts

16. Conclusion • We studied Adler-Bell-Jackiw anomaly for massive particles • Both mean spin and pseudoscalar contributions were accounted for in external magnetic field • Pseudoscalar was computed in WKB approximation in relatively weak magnetic field • These terms are quantum correction to magnetic helicity evolution • We estimated this quantum correction in core of NS and found that it can be greater than classical contribution known in MHD • Results can be relevant for reconnection of magnetic field lines and magnetar bursts

17. Acknowledgements I am thankful to Organizers of ICPPA-2018 for invitation RFBR (Russia)