On the periodicity of linear and nonlinear oscillatory reconnection. (arXiv:1811.08831v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Thurgood_J/0/1/0/all/0/1">J.O. Thurgood</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Pontin_D/0/1/0/all/0/1">D.I. Pontin</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+McLaughlin_J/0/1/0/all/0/1">J.A. McLaughlin</a>
(Abridged for ArXiv) An injection of energy towards a magnetic null point can
drive reversals of current sheet polarity leading to time-dependent Oscillatory
Reconnection, which is a possible explanation of how periodic phenomena can be
generated when reconnection occurs in the solar atmosphere. However, the
details of what controls the period of these oscillations is poorly understood,
despite being crucial in assessing whether OR can account for observed periodic
behaviour. This paper aims to highlight that different types of reconnection
reversal are supported about null points, and that these are distinct from the
oscillation on the closed-boundary, linear systems considered in the 1990s. In
particular, we explore the features of a nonlinear oscillation local to the
null point, and examine the effect of resistivity and perturbation energy on
the period, contrasting it to the linear case. It is found that in the linear
systems, the inverse Lundquist number dictates the period, provided the
perturbation energy is small relative to the inverse Lundquist number defined
on the boundary, regardless of the broadband structure of the initial
perturbation. However, when the perturbation energy exceeds the threshold
required for ‘nonlinear’ null collapse to occur, a complex oscillation of the
magnetic field is produced which is, at best, only weakly-dependent on the
resistivity. The resultant periodicity is strongly influenced by the amount of
free energy, with more energetic perturbations producing higher-frequency
oscillations. Crucially, with regards to typical solar-based and
astrophysical-based input energies, we demonstrate that the majority far exceed
the threshold for nonlinearity to develop. This substantially alters the
properties and periodicity of both null collapse and subsequent OR. Therefore,
nonlinear regimes of OR should be considered in solar and astrophysical
contexts.
(Abridged for ArXiv) An injection of energy towards a magnetic null point can
drive reversals of current sheet polarity leading to time-dependent Oscillatory
Reconnection, which is a possible explanation of how periodic phenomena can be
generated when reconnection occurs in the solar atmosphere. However, the
details of what controls the period of these oscillations is poorly understood,
despite being crucial in assessing whether OR can account for observed periodic
behaviour. This paper aims to highlight that different types of reconnection
reversal are supported about null points, and that these are distinct from the
oscillation on the closed-boundary, linear systems considered in the 1990s. In
particular, we explore the features of a nonlinear oscillation local to the
null point, and examine the effect of resistivity and perturbation energy on
the period, contrasting it to the linear case. It is found that in the linear
systems, the inverse Lundquist number dictates the period, provided the
perturbation energy is small relative to the inverse Lundquist number defined
on the boundary, regardless of the broadband structure of the initial
perturbation. However, when the perturbation energy exceeds the threshold
required for ‘nonlinear’ null collapse to occur, a complex oscillation of the
magnetic field is produced which is, at best, only weakly-dependent on the
resistivity. The resultant periodicity is strongly influenced by the amount of
free energy, with more energetic perturbations producing higher-frequency
oscillations. Crucially, with regards to typical solar-based and
astrophysical-based input energies, we demonstrate that the majority far exceed
the threshold for nonlinearity to develop. This substantially alters the
properties and periodicity of both null collapse and subsequent OR. Therefore,
nonlinear regimes of OR should be considered in solar and astrophysical
contexts.
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