Relationship between photospheric currents and coronal magnetic helicity for force-free bipolar fields

Aims. The origin and evolution of the magnetic helicity in the solar corona are not well understood. For instance, the magnetic helicity of an active region is often about 1042 Mx2 (1026 Wb2), but the observed processes whereby it is thought to be injected into the corona do not yet provide an accurate estimate of the resulting magnetic helicity budget or time evolution. The variation in magnetic helicity is important for understanding the physics of flares, coronal mass ejections, and their associated magnetic clouds. To shed light on this topic, we investigate here the changes in magnetic helicity due to electric currents in the corona for a single twisted flux tube that may model characteristic coronal structures such as active region filaments, sigmoids, or coronal loops. Methods. For a bipolar photospheric magnetic field and several distributions of current, we extrapolated the coronal field as a nonlinear force-free field. We then computed the relative magnetic helicity, as well as the self and mutual helicities. Results. Starting from a magnetic configuration with a moderate amount of current, the amount of magnetic helicity can increase by 2 orders of magnitude when the maximum current strength is increased by a factor of 2. The high sensitivity of magnetic helicity to the current density can partially explain discrepancies between measured values on the photosphere, in the corona, and in magnetic clouds. Our conclusion is that the magnetic helicity strongly depends on both the strength of the current density and also on its distribution. Conclusions. Only improved measurements of current density at the photospheric level will advance our knowledge of the magnetic helicity content in the solar atmosphere

Helical coronal ejections and their role in the solar cycle

The standard theory of the solar cycle in terms of an alpha-Omega dynamo hinges on a proper understanding of the nonlinear alpha effect. Boundary conditions play a surprisingly important role in determining the magnitude of alpha. For closed boundaries, the total magnetic helicity is conserved, and since the alpha effect produces magnetic helicity of one sign in the large scale field, it must simultaneously produce magnetic helicity of the opposite sign. It is this secondary magnetic helicity that suppresses the dynamo in a potentially catastrophic fashion. Open boundaries allow magnetic helicity to be lost. Simulations are presented that allow an estimate of alpha in the presence of open or closed boundaries, either with or without solar-like differential rotation. In all cases the sign of the magnetic helicity agrees with that observed at the solar surface (negative in the north, positive in the south), where significant amounts of magnetic helicity can be ejected via coronal mass ejections. It is shown that open boundaries tend to alleviate catastrophic alpha quenching. The importance of looking at current helicity instead of magnetic helicity is emphasized and the conceptual advantages are discussed.Comment: 8 pages, 7 figs, IAU Symp. 223, In: Multi-Wavelength Investigations of Solar Activity. Eds: A.V. Stepanov, E.E. Benevolenskaya & A.G. Kosoviche

Magnetic twist: a source and property of space weather

We present evidence for finite magnetic helicity density in the heliosphere and numerical models thereof, and relate it to the magnetic field properties of the dynamo in the solar convection zone. We use simulations and solar wind data to compute magnetic helicity either directly from the simulations, or indirectly using time series of the skew-symmetric components of the magnetic correlation tensor. We find that the solar dynamo produces negative magnetic helicity at small scales and positive at large scales. However, in the heliosphere these properties are reversed and the magnetic helicity is now positive at small scales and negative at large scales. We explain this by the fact that a negative diffusive magnetic helicity flux corresponds to a positive gradient of magnetic helicity, which leads to a change of sign from negative to positive values at some radius in the northern hemisphere.Comment: 7 pages, 12 Figures, accepted in Journal of Space Weather and Space Climat

Why coronal mass ejections are necessary for the dynamo

Large scale dynamo-generated fields are a combination of interlocked poloidal and toroidal fields. Such fields possess magnetic helicity that needs to be regenerated and destroyed during each cycle. A number of numerical experiments now suggests that stars may do this by shedding magnetic helicity. In addition to plain bulk motions, a favorite mechanism involves magnetic helicity flux along lines of constant rotation. We also know that the sun does shed the required amount of magnetic helicity mostly in the form of coronal mass ejections. Solar-like stars without cycles do not face such strong constraints imposed by magnetic helicity evolution and may not display coronal activity to that same extent. I discuss the evidence leading to this line of argument. In particular, I discuss simulations showing the generation of strong mean toroidal fields provided the outer boundary condition is left open so as to allow magnetic helicity to escape. Control experiments with closed boundaries do not produce strong mean fields.Comment: 2 pages, 2 figures, to appear in Highlights of Astronomy, ed. K. G. Strassmeier & A. Kosovichev, Astron. Soc. Pac. Conf. Se

Magnetic helicity and cosmological magnetic field

The magnetic helicity has paramount significance in nonlinear saturation of galactic dynamo. We argue that the magnetic helicity conservation is violated at the lepton stage in the evolution of early Universe. As a result, a cosmological magnetic field which can be a seed for the galactic dynamo obtains from the beginning a substantial magnetic helicity which has to be taken into account in the magnetic helicity balance at the later stage of galactic dynamo.Comment: 11 pages, no figures; v3: new references and new paragraphs added, discussion extended, some mistypings correcte

Small-scale magnetic helicity losses from a mean-field dynamo

Using mean-field models with a dynamical quenching formalism we show that in finite domains magnetic helicity fluxes associated with small-scale magnetic fields are able to alleviate catastrophic quenching. We consider fluxes that result either from advection by a mean flow, the turbulent mixing down the gradient of mean small-scale magnetic helicity concentration, or the explicit removal which may be associated with the effects of coronal mass ejections in the Sun. In the absence of shear, all the small-scale magnetic helicity fluxes are found to be equally strong both for large-scale and small-scale fields. In the presence of shear there is also an additional magnetic helicity flux associated with the mean field, but this flux does not alleviate catastrophic quenching. Outside the dynamo-active region there are neither sources nor sinks of magnetic helicity, so in a steady state this flux must be constant. It is shown that unphysical behavior emerges if the small-scale magnetic helicity flux is forced to vanish within the computational domain.Comment: 9 pages, 10 figures, submitted to MNRA

Scale-dependence of magnetic helicity in the solar wind

We determine the magnetic helicity, along with the magnetic energy, at high latitudes using data from the Ulysses mission. The data set spans the time period from 1993 to 1996. The basic assumption of the analysis is that the solar wind is homogeneous. Because the solar wind speed is high, we follow the approach first pioneered by Matthaeus et al. (1982, Phys. Rev. Lett. 48, 1256) by which, under the assumption of spatial homogeneity, one can use Fourier transforms of the magnetic field time series to construct one-dimensional spectra of the magnetic energy and magnetic helicity under the assumption that the Taylor frozen-in-flow hypothesis is valid. That is a well-satisfied assumption for the data used in this study. The magnetic helicity derives from the skew-symmetric terms of the three-dimensional magnetic correlation tensor, while the symmetric terms of the tensor are used to determine the magnetic energy spectrum. Our results show a sign change of magnetic helicity at wavenumber k~2 AU^{-1} (or frequency nu~2 uHz) at distances below 2.8 AU and at k~30 AU^{-1} (or nu~25 uHz) at larger distances. At small scales the magnetic helicity is positive at northern heliographic latitudes and negative at southern latitudes. The positive magnetic helicity at small scales is argued to be the result of turbulent diffusion reversing the sign relative to what is seen at small scales at the solar surface. Furthermore, the magnetic helicity declines toward solar minimum in 1996. The magnetic helicity flux integrated separately over one hemisphere amounts to about 10^{45} Mx^2/cycle at large scales and to a 3 times lower value at smaller scales.Comment: 8 pages, 6 figures, ApJ (in press