Local simulations of the magnetized Kelvin-Helmholtz instability in neutron-star mergers

Abstract

Context. Global magnetohydrodynamic simulations show the growth of Kelvin-Helmholtz instabilities at the contact surface of two merging neutron stars. That region has been identified as the site of efficient amplification of magnetic fields. However, these global simulations, due to numerical limitations, were unable to determine the saturation level of the field strength, and thus the possible back-reaction of the magnetic field onto the flow. Aims. We investigate the amplification of initially weak magnetic fields in Kelvin-Helmholtz unstable shear flows, and the backreaction of the field onto the flow. Methods. We use a high-resolution finite-volume ideal MHD code to perform 2D and 3D local simulations of hydromagnetic shear flows, both for idealized systems and simplified models of merger flows. Results. In 2D, the magnetic field is amplified on time scales of less than 0.01 ms until it reaches locally equipartition with the kinetic energy. Subsequently, it saturates due to resistive instabilities that disrupt the Kelvin-Helmholtz unstable vortex and decelerate the shear flow on a secular time scale. We determine scaling laws of the field amplification with the initial field strength and the grid resolution. In 3D, the hydromagnetic mechanism seen in 2D may be dominated by purely hydrodynamic instabilities leading to less filed amplification. We find maximum magnetic fields ∼10 16 G locally, and rms maxima within the box ∼10 15 G. However, due to the fast decay of the shear flow such strong fields exist only for a short period (<0.1 ms). In the saturated state of most models, the magnetic field is mainly oriented parallel to the shear flow for rather strong initial fields, while weaker initial fields tend to lead to a more balanced distribution of the field energy among the components. In all models the flow shows small-scale features. The magnetic field is at most in energetic equipartition with the decaying shear flow. Conclusions. The magnetic field may be amplified efficiently to very high field strengths, the maximum field energy reaching values of the order of the kinetic energy associated with the velocity components transverse to the interface between the two neutron stars. However, the dynamic impact of the field onto the flow is limited to the shear layer, and it may not be adequate to produce outflows, because the time during which the magnetic field stays close to its maximum value is short compared to the time scale for launching an outflow (i.e., a few milliseconds).

Magnetized Moving Mesh Merger of a Carbon–oxygen White Dwarf Binary

“…This weaker growth is also inconsistent with the amplification to local kinetic equipartition seen in small-scale simulations (Obergaulinger et al 2010;Zrake & MacFadyen 2013), and is attributed to insufficient resolution in the NS merger simulations (Giacomazzo et al 2014;Kiuchi et al 2014, though see Dionysopoulou et al 2015). Giacomazzo et al (2014) incorporated a subgrid magnetic amplification model, calibrated using Zrake & MacFadyen (2013)s results, into their Eulerian NS merger simulation, and found E B amplification by a factor of 10 10 ∼ over a single dynamical time.…”

“…Magnetohydrodynamic (MHD) double NS binary merger simulations (e.g., Price & Rosswog 2006;Giacomazzo et al 2014;Kiuchi et al 2014) have found that Kelvin-Helmholtz vortices produced along the shear interface between the coalescing stars can amplify field strengths by orders of magnitude (Obergaulinger et al 2010;Zrake & MacFadyen 2013). The same should hold true for WD mergers.…”

Lattice Boltzmann study on Kelvin-Helmholtz instability: Roles of velocity and density gradients

“…the exponential growth manifests itself as a linear slope [52][53][54] (see Fig.6). Therefore, γ can be obtained from the slope of a linear function fitted to the initial growth stage.…”

Modeling the Early Afterglow in the Short and Hard GRB 090510

“…In the framework of sGRBs, the question of what field strengths could be reached in a merger remnant before it collapses to a BH has so far remained unanswered, neither evidence of magnetization in the jet has been found. Simulations have shown that during the merger the magnetic field strength can increase up to 10 16 G. The growth emerges from the transfer of hydrodynamical kinetic energy to electromagnetic energy via Kevin-Helmholtz instabilities and turbulent amplification (Price & Rosswog 2006;Zrake & MacFadyen 2013;Giacomazzo et al 2009;Obergaulinger et al 2010). The bright, short and hard GRB 090510 was detected by nifraija@astro.unam.mx, wlee@astro.unam.mx, pv0004@uah.edu and rbarniol@purdue.edu Fermi and Swift satellites (De Pasquale & et al 2010).…”