Global simulations of Tayler instability in stellar interiors: The stabilizing effect of gravity. (arXiv:1909.02897v1 [astro-ph.SR])

Global simulations of Tayler instability in stellar interiors: The stabilizing effect of gravity. (arXiv:1909.02897v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Guerrero_G/0/1/0/all/0/1">G. Guerrero</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Sordo_F/0/1/0/all/0/1">F. Del Sordo</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Bonanno_A/0/1/0/all/0/1">A. Bonanno</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Smolarkiewicz_P/0/1/0/all/0/1">P. K. Smolarkiewicz</a>

Unveiling the evolution of toroidal field instability, known as Tayler
instability, is essential to understand the strength and topology of the
magnetic fields observed in early-type stars, in the isothermal core of the red
giants, or in any stellar radiative zone. We want to study the non-linear
evolution of the instability of a toroidal field stored in a stably stratified
stellar interior in spherical symmetry in the absence of rotation. In
particular, we intend to quantify the suppression of the instability as a
function of the Brunt-V”ais”ala ($omega_{rm BV}$) and the Alfv’en
($omega_{rm A}$) frequencies. We use the MHD equations as implemented in the
anelastic approximation in the EULAG-MHD code and perform a large series of
high-resolution numerical simulations of the instability exploring the
parameter space for the $omega_{rm BV}$ and $omega_{rm A}$. We show that
beyond a critical value gravity strongly suppress the instability, in agreement
with the linear analysis. The intensity of the initial field also plays an
important role, as weaker fields show much slower growth rates. Moreover, in
the case of very low gravity, the fastest growing modes have a large
characteristic radial scale, at variance with the case of strong gravity, where
modes with small radial scale are excited too. In particular, the number of
growing radial modes ranges from $k_rapprox 1$ to $k_rapprox 18$ depending on
the gravity and the magnetic field strength. Our results illustrate that the
anelastic approximation can efficiently describe the evolution of toroidal
field instability in realistic stellar interiors. Moreover, the suppression of
the instability as a consequence of increasing values of $omega_{rm BV}$
might play a role to explain the magnetic desert in Ap/Bp stars, since weak
fields are only marginally unstable in the case of strong gravity.

Unveiling the evolution of toroidal field instability, known as Tayler
instability, is essential to understand the strength and topology of the
magnetic fields observed in early-type stars, in the isothermal core of the red
giants, or in any stellar radiative zone. We want to study the non-linear
evolution of the instability of a toroidal field stored in a stably stratified
stellar interior in spherical symmetry in the absence of rotation. In
particular, we intend to quantify the suppression of the instability as a
function of the Brunt-V”ais”ala ($omega_{rm BV}$) and the Alfv’en
($omega_{rm A}$) frequencies. We use the MHD equations as implemented in the
anelastic approximation in the EULAG-MHD code and perform a large series of
high-resolution numerical simulations of the instability exploring the
parameter space for the $omega_{rm BV}$ and $omega_{rm A}$. We show that
beyond a critical value gravity strongly suppress the instability, in agreement
with the linear analysis. The intensity of the initial field also plays an
important role, as weaker fields show much slower growth rates. Moreover, in
the case of very low gravity, the fastest growing modes have a large
characteristic radial scale, at variance with the case of strong gravity, where
modes with small radial scale are excited too. In particular, the number of
growing radial modes ranges from $k_rapprox 1$ to $k_rapprox 18$ depending on
the gravity and the magnetic field strength. Our results illustrate that the
anelastic approximation can efficiently describe the evolution of toroidal
field instability in realistic stellar interiors. Moreover, the suppression of
the instability as a consequence of increasing values of $omega_{rm BV}$
might play a role to explain the magnetic desert in Ap/Bp stars, since weak
fields are only marginally unstable in the case of strong gravity.

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