Competition of rotation and stratification in flux concentrations

Abstract

Context. In a strongly stratified turbulent layer, a uniform horizontal magnetic field can become unstable and spontaneously form local flux concentrations due to a negative contribution of turbulence to the large-scale (mean-field) magnetic pressure. This mechanism, which is called negative effective magnetic pressure instability (NEMPI), is of interest in connection with dynamo scenarios in which most of the magnetic field resides in the bulk of the convection zone and not at the bottom, as is often assumed. Recent work using mean-field hydromagnetic equations has shown that NEMPI becomes suppressed at rather low rotation rates with Coriolis numbers as low as 0.1. Aims. Here we extend these earlier investigations by studying the effects of rotation both on the development of NEMPI and on the effective magnetic pressure. We also quantify the kinetic helicity resulting from direct numerical simulations (DNS) with Coriolis numbers and strengths of stratification comparable to values near the solar surface and compare it with earlier work at smaller scale separation ratios. Further, we estimate the expected observable signals of magnetic helicity at the solar surface. Methods. To calculate the rotational effect on the effective magnetic pressure we consider both DNS and analytical studies using the τ approach. To study the effects of rotation on the development of NEMPI we use both DNS and mean-field calculations of the three-dimensional hydromagnetic equations in a Cartesian domain. Results. We find that the growth rates of NEMPI from earlier mean-field calculations are well reproduced with DNS, provided the Coriolis number is below 0.06. In that case, kinetic and magnetic helicities are found to be weak and the rotational effect on the effective magnetic pressure is negligible as long as the production of flux concentrations is not inhibited by rotation. For faster rotation, dynamo action becomes possible. However, there is an intermediate range of rotation rates where dynamo action on its own is not yet possible, but the rotational suppression of NEMPI is being alleviated. Conclusions. Production of magnetic flux concentrations through the suppression of turbulent pressure appears to be possible only in the uppermost layers of the Sun, where the convective turnover time is less than two hours.

Magnetic flux concentrations from dynamo-generated fields

“…We begin by reproducing some of the DNS results of Losada et al (2013), who found the suppression of the growth rate of NEMPI with increasing values of Co and a subsequent enhancement at larger values, which they interpreted as being the result of dynamo action in the presence of an externally applied magnetic field. We also use DNS to determine independently the expected efficiency of the dynamo by estimating the α effect from kinetic helicity measurements and by computing both α effect and turbulent diffusivity directly using the test-field method (TFM).…”

“…In studying this process in detail, we have a chance of detecting new joint effects resulting from the two instabilities, which is one of the goals of the present paper. However, these two instabilities may also compete against each other, as was already noted by Losada et al (2013). The large-scale dynamo effect relies on the combined presence of rotation and stratification, while NEMPI requires stratification and large enough scale separation.…”

“…In the cases considered by Losada et al (2012Losada et al ( , 2013, the stratification parameter was Gr = 0.03, which is rather small compared with the estimated solar value of Gr = 0.16 (see the conclusions of Losada et al 2013). One can expect that larger values of Gr would result in correspondingly larger values of the maximum permissible value of Co, for which NEMPI is still excited, but this has not yet been investigated in detail.…”

Magnetic flux concentrations in a polytropic atmosphere

“…Our present study therefore supports ideas about a shallow origin for active regions and sunspots (Brandenburg 2005;Brandenburg et al 2010;Kitiashvili et al 2010;Stein & Nordlund 2012), contrary to common thinking that sunspots form near the bottom of the convective zone (Parker 1975;Spiegel & Weiss 1980;D'Silva & Choudhuri 1993). More specifically, the studies of Losada et al (2013) point toward the possibility that magnetic flux concentrations form in the top 6 Mm, i.e., in the upper part of the supergranulation layer.…”

Surface flux concentrations in a sphericalα2dynamo

“…A more physical alternative is to use only nonhelical forcing, but to include rotation to produce helicity in conjunction with the stratification. Such models have recently been considered by Losada et al (2013), who found that NEMPI begins to be suppressed by rotation at Coriolis numbers somewhat below those where α 2 -type dynamo action sets in. Furthermore, there is now evidence that the combined action of NEMPI and the dynamo instability has a lower threshold than the dynamo alone.…”