Active Region Formation through the Negative Effective Magnetic Pressure Instability

Abstract

The negative effective magnetic pressure instability operates on scales encompassing many turbulent eddies and is here discussed in connection with the formation of active regions near the surface layers of the Sun. This instability is related to the negative contribution of turbulence to the mean magnetic pressure that causes the formation of large-scale magnetic structures. For an isothermal layer, direct numerical simulations and mean-field simulations of this phenomenon are shown to agree in many details in that their onset occurs at the same depth. This depth increases with increasing field strength, such that the maximum growth rate of this instability is independent of the field strength, provided the magnetic structures are fully contained within the domain. A linear stability analysis is shown to support this finding. The instability also leads to a redistribution of turbulent intensity and gas pressure that could provide direct observational signatures.

Is the Small-Scale Magnetic Field Correlated With the Dynamo Cycle?

“…One may argue that the anti-Hale sunspot groups could be formed through the negative effective magnetic pressure instability Kemel et al 2013) because, for this to work, we only need a moderately weak magnetic field, which could be provided by the smallscale dynamo operating continuously in the Sun. The anti-Hale groups would then represent just the tail of a wide distribution of tilt angles (McClintock et al 2014).…”

Surface flux concentrations in a sphericalα2dynamo

“…2 and is also discussed below. We choose Q α = 1000 for the α quenching parameter so that the local value of B φ /B eq near the surface is between 10 and 20 percent, which is suitable for exciting NEMPI (Kemel et al 2012b). Meridional cross-sections of B φ /B eq0 together with magnetic field lines of B pol are shown in Fig.…”

“…Direct numerical simulations (DNS; see Brandenburg et al 2011;Kemel et al 2012a), mean-field simulations (MFS; see Brandenburg et al 2010Brandenburg et al , 2012Kemel et al 2012b;Käpylä et al 2012), and earlier analytic studies (Kleeorin et al 1989(Kleeorin et al , 1990(Kleeorin et al , 1996Kleeorin & Rogachevskii 1994;Rogachevskii & Kleeorin 2007) now provide conclusive evidence for the physical reality of NEMPI. However, open questions still need to be answered before it can be applied to detailed models of active regions and sunspot formation.…”

“…1 The analytic estimate of the growth rate of NEMPI, λ, based on an isothermal layer with H p = H ρ = const. is given by (Kemel et al 2012b)…”

“…We arrange the quenching of α such that the resulting mean magnetic field is in the appropriate interval to allow NEMPI to work. This means that the effective (mean-field) magnetic pressure locally has a negative derivative with respect to increasing normalized field strength (Kemel et al 2012b), so the mean toroidal magnetic field must be less than about 20% of the equipartition field strength.…”