Large $\mathrm{Pm}$ small-scale kinematic dynamo in protoneutron stars

Abstract

Magnetars are young, isolated neutron stars that possess an exceptionally strong magnetic field, with surface dipolar strengths on the order of $10^{15}$ G. One of the plausible scenarios for generating such a strong field is an exponential amplification by a turbulent convective dynamo during the protoneutron star phase. However, the short expected duration of the convection ($\sim 10$ s) imposes a stringent constraint on the dynamo growth rate. We perform an extensive set of 82 three-dimensional convective dynamo simulations in the anelastic approximation and investigate the kinematic phase to quantify the dynamo growth rate $\gamma$. We find that $\gamma$ increases with both the magnetic Prandtl number $\mathrm{Pm}$ and the Rayleigh number $\mathrm{Ra}$, with the most unstable mode becoming highly non-axisymmetric and multipolar. We further observe a gradual transition from large-scale to small-scale dynamo as the magnetic Reynolds number $\mathrm{Rm}$ increases, resulting in a magnetic field that is predominantly concentrated at small scales. The trend remains unchanged when the outer magnetic boundary condition is varied. Since resolving the increasingly small scales becomes numerically impractical, we employ the theoretical small-scale Kazantsev dynamo model to explore the large $\mathrm{Pm}$ regime characteristic of protoneutron stars. The model qualitatively captures the growth rate behaviour observed in simulations and, upon extrapolation to the large $\mathrm{Pm}$ limit, indicates that $\gamma$ is only weakly dependent on the resistivity in a PNS. Under conditions relevant to the PNS, this model predicts a magnetic energy growth rate of the order of $\sim 1$ ms${}^{-1}$.

14 pages, 11 figures, 1 table. Published in Phys. Rev. E

References in corpus (12)

• Producing ultra-strong magnetic fields in neutron star mergers
• How mergers magnetise massive stars
• Semi-global simulations of the magneto-rotational instability in core collapse supernovae
• Magnetic field amplification in turbulent astrophysical plasmas
• Formation Rates and Evolution Histories of Magnetars
• A systematic study of proto-neutron star convection in three-dimensional core-collapse supernova simulations
• Turbulent dynamo in a conducting fluid and partially ionized gas
• Origin of neutron star magnetic fields
• Numerical simulations of the magnetorotational instability in protoneutron stars: I. Influence of buoyancy
• Fluctuation dynamo at finite correlation times and the Kazantsev spectrum
• Magnetic dynamo action in random flows with zero and finite correlation times
• Stellar population modelling of neutron stars and black holes: spatially-resolved graveyards in MaNGA/SDSS-IV galaxies