# LOCAL SIMULATIONS OF THE MAGNETOROTATIONAL INSTABILITY IN CORE-COLLAPSE SUPERNOVAE

## Abstract

Bearing in mind the application of core-collapse supernovae, we study the nonlinear properties of the magnetorotational instability (MRI) by means of three-dimensional simulations in the framework of a local shearing box approximation. By systematically changing the shear rates that symbolize the degree of differential rotation in nascent proto-neutron stars (PNSs), we derive a scaling relation between the turbulent stress sustained by the MRI and the shear-vorticity ratio. Our parametric survey shows a power-law scaling between the turbulent stress (((w {sub tot}))) and the shear-vorticity ratio (g{sub q} ) as ((w {sub tot})){proportional_to}g {sup {delta}} {sub q} with an index of {delta} {approx} 0.5. The MRI-amplified magnetic energy has a similar scaling relative to the turbulent stress, while the Maxwell stress has a slightly smaller power-law index ({approx}0.36). By modeling the effect of viscous heating rates from MRI turbulence, we show that the stronger magnetic fields, or the larger shear rates initially imposed, lead to higher dissipation rates. For a rapidly rotating PNS with a spin period in milliseconds and with strong magnetic fields of 10{sup 15} G, the energy dissipation rate is estimated to exceed 10{sup 51} erg s{sup -1}. Our results suggest that the conventional magnetohydrodynamic (MHD) mechanism ofmore »

- Authors:

- Department of Computational Science, Graduate School of System Informatics, Kobe University, Nada, Kobe 657-8501 (Japan)
- Center for Computational Astrophysics, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588 (Japan)
- Institute of Laser Engineering, Osaka University, 1-1, Yamadaoka, Suita (Japan)

- Publication Date:

- OSTI Identifier:
- 22086391

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal

- Additional Journal Information:
- Journal Volume: 759; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0004-637X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; ASTRONOMY; ASTROPHYSICS; COMPUTERIZED SIMULATION; COSMIC NEUTRINOS; ENERGY LOSSES; GRAVITATIONAL COLLAPSE; HEATING RATE; INDEXES; INSTABILITY; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; NEUTRON STARS; NONLINEAR PROBLEMS; ROTATION; SHEAR; SPIN; STRESSES; SUPERNOVAE; TURBULENCE

### Citation Formats

```
Masada, Youhei, Takiwaki, Tomoya, Kotake, Kei, and Sano, Takayoshi, E-mail: ymasada@harbor.kobe-u.ac.jp, E-mail: kkotake@th.nao.ac.jp, E-mail: sano@ile.ac.jp.
```*LOCAL SIMULATIONS OF THE MAGNETOROTATIONAL INSTABILITY IN CORE-COLLAPSE SUPERNOVAE*. United States: N. p., 2012.
Web. doi:10.1088/0004-637X/759/2/110.

```
Masada, Youhei, Takiwaki, Tomoya, Kotake, Kei, & Sano, Takayoshi, E-mail: ymasada@harbor.kobe-u.ac.jp, E-mail: kkotake@th.nao.ac.jp, E-mail: sano@ile.ac.jp.
```*LOCAL SIMULATIONS OF THE MAGNETOROTATIONAL INSTABILITY IN CORE-COLLAPSE SUPERNOVAE*. United States. doi:10.1088/0004-637X/759/2/110.

```
Masada, Youhei, Takiwaki, Tomoya, Kotake, Kei, and Sano, Takayoshi, E-mail: ymasada@harbor.kobe-u.ac.jp, E-mail: kkotake@th.nao.ac.jp, E-mail: sano@ile.ac.jp. Sat .
"LOCAL SIMULATIONS OF THE MAGNETOROTATIONAL INSTABILITY IN CORE-COLLAPSE SUPERNOVAE". United States. doi:10.1088/0004-637X/759/2/110.
```

```
@article{osti_22086391,
```

title = {LOCAL SIMULATIONS OF THE MAGNETOROTATIONAL INSTABILITY IN CORE-COLLAPSE SUPERNOVAE},

author = {Masada, Youhei and Takiwaki, Tomoya and Kotake, Kei and Sano, Takayoshi, E-mail: ymasada@harbor.kobe-u.ac.jp, E-mail: kkotake@th.nao.ac.jp, E-mail: sano@ile.ac.jp},

abstractNote = {Bearing in mind the application of core-collapse supernovae, we study the nonlinear properties of the magnetorotational instability (MRI) by means of three-dimensional simulations in the framework of a local shearing box approximation. By systematically changing the shear rates that symbolize the degree of differential rotation in nascent proto-neutron stars (PNSs), we derive a scaling relation between the turbulent stress sustained by the MRI and the shear-vorticity ratio. Our parametric survey shows a power-law scaling between the turbulent stress (((w {sub tot}))) and the shear-vorticity ratio (g{sub q} ) as ((w {sub tot})){proportional_to}g {sup {delta}} {sub q} with an index of {delta} {approx} 0.5. The MRI-amplified magnetic energy has a similar scaling relative to the turbulent stress, while the Maxwell stress has a slightly smaller power-law index ({approx}0.36). By modeling the effect of viscous heating rates from MRI turbulence, we show that the stronger magnetic fields, or the larger shear rates initially imposed, lead to higher dissipation rates. For a rapidly rotating PNS with a spin period in milliseconds and with strong magnetic fields of 10{sup 15} G, the energy dissipation rate is estimated to exceed 10{sup 51} erg s{sup -1}. Our results suggest that the conventional magnetohydrodynamic (MHD) mechanism of core-collapse supernovae is likely to be affected by MRI-driven turbulence, which we speculate, on the one hand, could harm the MHD-driven explosions due to the dissipation of the shear rotational energy at the PNS surface; or, on the other hand, its energy deposition might be potentially favorable for the working of the neutrino-heating mechanism.},

doi = {10.1088/0004-637X/759/2/110},

journal = {Astrophysical Journal},

issn = {0004-637X},

number = 2,

volume = 759,

place = {United States},

year = {2012},

month = {11}

}