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Register a new userMeasuring stellar magnetic helicity density
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Helicity is a fundamental property of a magnetic field but to date it has only been possible to observe its evolution in one star - the Sun. In this paper we provide a simple technique for mapping the large-scale helicity density across the surface of any star using only observable quantities: the poloidal and toroidal magnetic field components (which can be determined from Zeeman-Doppler imaging) and the stellar radius. We use a sample of 51 stars across a mass range of 0.1-1.34 M$_odot$ to show how the helicity density relates to stellar mass, Rossby number, magnetic energy and age. We find that the large-scale helicity density increases with decreasing Rossby number $R_o$, peaking at $R_o simeq 0.1$, with a saturation or decrease below that. For both fully- and partially-convective stars we find that the mean absolute helicity density scales with the mean squared toroidal magnetic flux density according to the power law: $|langle{h,}rangle|$ $propto$ $langle{rm{B_{tor}}^2_{},rangle}^{0.86,pm,0.04}$. The scatter in this relation is consistent with the variation across a solar cycle, which we compute using simulations and observations across solar cycles 23 and 24 respectively. We find a significant decrease in helicity density with age.
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The helicity of a magnetic field is a fundamental property that is conserved in ideal MHD. It can be explored in the stellar context by mapping large-scale magnetic fields across stellar surfaces using Zeeman-Doppler imaging. A recent study of 51 stars in the mass range 0.1-1.34 M$_odot$ showed that the photospheric magnetic helicity density follows a single power law when plotted against the toroidal field energy, but splits into two branches when plotted against the poloidal field energy. These two branches divide stars above and below $sim$ 0.5 M$_odot$. We present here a novel method of visualising the helicity density in terms of the linkage of the toroidal and poloidal fields that are mapped across the stellar surface. This approach allows us to classify the field linkages that provide the helicity density for stars of different masses and rotation rates. We find that stars on the lower-mass branch tend to have toroidal fields that are non-axisymmetric and so link through regions of positive and negative poloidal field. A lower-mass star may have the same helicity density as a higher-mass star, despite having a stronger poloidal field. Lower-mass stars are therefore less efficient at generating large-scale helicity.
It is generally believed that the evolution of magnetic helicity has a close relationship with solar activity. Before the launch of SDO, earlier studies have mostly used MDI/SOHO line of sight magnetograms and assumed that magnetic fields are radial when calculating magnetic helicity injection rate from photospheric magnetograms. However, this assumption is not necessarily true. Here we use the vector magnetograms and line of sight magnetograms, both taken by HMI/SDO, to estimate the effects of non-radial magnetic field on measuring magnetic helicity injection rate. We find that: 1) The effect of non-radial magnetic field on estimating tangential velocity is relatively small; 2) On estimating magnetic helicity injection rate, the effect of non-radial magnetic field is strong when active regions are observed near the limb and is relatively small when active regions are close to disk center; 3) The effect of non-radial magnetic field becomes minor if the amount of accumulated magnetic helicity is the only concern.
Magnetic helicity fluxes in turbulently driven alpha^2 dynamos are studied to demonstrate their ability to alleviate catastrophic quenching. A one-dimensional mean-field formalism is used to achieve magnetic Reynolds numbers of the order of 10^5. We study both diffusive magnetic helicity fluxes through the mid-plane as well as those resulting from the recently proposed alternate dynamic quenching formalism. By adding shear we make a parameter scan for the critical values of the shear and forcing parameters for which dynamo action occurs. For this $alphaOmega$ dynamo we find that the preferred mode is antisymmetric about the mid-plane. This is also verified in 3-D direct numerical simulations.
In the paper we study the helicity density patterns which can result from the emerging bipolar regions. Using the relevant dynamo model and the magnetic helicity conservation law we find that the helicity density pattern around the bipolar regions depends on the configuration of the ambient large-scale magnetic field, and in general they show the quadrupole distribution. The position of this pattern relative to the equator can depend on the tilt of the bipolar region. We compute the time-latitude diagrams of the helicity density evolution. The longitudinally averaged effect of the bipolar regions show two bands of sign for the density distribution in each hemisphere. Similar helicity density patterns are provided by the helicity density flux from the emerging bipolar regions subjected to the surface differential rotation. Examining effect of helicity fluxes from the bipolar regions on the large-scale dynamo we find that its effect to the dynamo saturation is negligible.
In the solar corona, magnetic helicity slowly and continuously accumulates in response to plasma flows tangential to the photosphere and magnetic flux emergence through it. Analyzing this transfer of magnetic helicity is key for identifying its role in the dynamics of active regions (ARs). The connectivity-based helicity flux density method was recently developed for studying the 2D and 3D transfer of magnetic helicity in ARs. The method takes into account the 3D nature of magnetic helicity by explicitly using knowledge of the magnetic field connectivity, which allows it to faithfully track the photospheric flux of magnetic helicity. Because the magnetic field is not measured in the solar corona, modeled 3D solutions obtained from force-free magnetic field extrapolations must be used to derive the magnetic connectivity. Different extrapolation methods can lead to markedly different 3D magnetic field connectivities, thus questioning the reliability of the connectivity-based approach in observational applications. We address these concerns by applying this method to the isolated and internally complex AR 11158 with different magnetic field extrapolation models. We show that the connectivity-based calculations are robust to different extrapolation methods, in particular with regards to identifying regions of opposite magnetic helicity flux. We conclude that the connectivity-based approach can be reliably used in observational analyses and is a promising tool for studying the transfer of magnetic helicity in ARs and relate it to their flaring activity.
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