A global model of the magnetorotational instability in protoneutron stars

Abstract

Context. Magnetars are isolated neutron stars characterized by their variable high-energy emission which is powered by the dissipation of enormous internal magnetic fields. The measured spin-down of magnetars constrains the magnetic dipole to be in the range of 10 14 to 10 15 G. The magnetorotational instability (MRI) is considered to be a promising mechanism to amplify the magnetic field in fastrotating protoneutron stars and form magnetars. This scenario is supported by many local studies which have shown that magnetic fields could be amplified by the MRI on small scales. However, the efficiency of the MRI at generating a dipole field is still unknown.Aims. To answer this question, we study the MRI dynamo in an idealized global model of a fast rotating protoneutron star with differential rotation. Methods. Using the pseudo-spectral code MagIC, we perform three-dimensional incompressible MHD simulations in spherical geometry with explicit diffusivities where the differential rotation is forced at the outer boundary. We performed a parameter study in which we varied the initial magnetic field and investigated different magnetic boundary conditions. These simulations were compared to local shearing box simulations performed with the code Snoopy. Results. We obtain a self-sustained turbulent MRI-driven dynamo, whose saturated state is independent of the initial magnetic field. The MRI generates a strong turbulent magnetic field of B ≥ 2 × 10 15 G and a non-dominant magnetic dipole, which represents systematically about 5% of the averaged magnetic field strength. Interestingly, this dipole is tilted towards the equatorial plane. By comparing these results with shearing box simulations, we find that local models can reproduce fairly well several characteristics of global MRI turbulence such as the kinetic and magnetic spectra. The turbulence is nonetheless more vigorous in the local models than in the global ones. Moreover, too large boxes allow for elongated structures to develop without any realistic curvature constraint, which may explain why these models tend to overestimate the field amplification. Conclusions. Overall, our results support the ability of the MRI to form magnetar-like large-scale magnetic fields. They furthermore predict the presence of a stronger small-scale magnetic field. The resulting magnetic field could be important to power outstanding stellar explosions, such as superluminous supernovae (SLSNe) and gamma-ray bursts (GRBs).

Two-dimensional numerical study for magnetic field dependence of neutrino-driven core-collapse supernova models

“…The exponential growth of the magnetic field is beneficial to amplify the weak seed field of the stellar core to the dynamically relevant level. The magnetic field amplification due to the magnetorotational instability (MRI; Balbus & Hawley 1991) is a candidate for the efficient field amplification mechanism in the rotating stellar cores (Akiyama et al 2003;Masada et al 2006Masada et al , 2007Masada et al , 2012Masada et al , 2015Obergaulinger et al 2009;Sawai et al 2013b;Sawai & Yamada 2014, 2016Mösta et al 2015;Rembiasz et al 2016;Reboul-Salze et al 2020).…”

Insights into non-axisymmetric instabilities in three-dimensional rotating supernova models with neutrino and gravitational-wave signatures

“…Strong magnetic fields may suppress the low-𝑇/|𝑊 | instability (Fu & Lai 2011;Muhlberger et al 2014). The impact of the magnetorotational instability (MRI) on the explosion mechanism is also a long-standing issue (Akiyama et al 2003;Masada et al 2015;Sawai & Yamada 2016;Guilet & Müller 2015;Mösta et al 2015;Rembiasz et al 2016;Reboul-Salze et al 2020). The MRI should certainly affect the angular momentum profile and affect the low-𝑇/|𝑊 | instability (Bugli et al 2018).…”

General Relativistic Mean-field Dynamo Model for Proto-neutron Stars

“…The choice of this high central rotation rate is due to the desire to maximize the Ω effect. Note that the equation of state (EoS) and the rotation profile we use are more appropriate for an NS than for a PNS (e.g., [21]). However, the aim of this preliminary work is to verify whether the dynamo model could be a realistic scheme for generating proto-magnetar, taking into account, for the first time, non-ideal effects in general relativity.…”

“…In the original magnetar model [16] the strength of the magnetic field is the result of the growth a) Electronic mail: luca.delzanna@unifi.it of the seed field amplified by the dynamo mechanism -a process through which a rotating, convecting, and electrically conducting fluid can generate a magnetic field by self-inductive action converting kinetic energy into magnetic energy -in the proto-neutron star (PNS), the remnant of the supernova explosion which represents the first phase of life of a NS. The amplification of the magnetic field by a turbulent dynamo can occur either by a convective dynamo (e.g., [17; 18]) or the magnetorotational instability (MRI, e.g., [19][20][21]).…”